Precision medicine for optimal dosage of combined therapies systems and methods of use thereof

Abstract

The present invention provides in vitro, in silico, and in vivo methods, and combinations thereof, for optimizing dosages of combination therapies for treating cancer. The present invention additionally provides therapeutic methods and compositions for treating cancer using optimized dosages of the combination therapies.

Description

[0001] PRECISION MEDICINE FOR OPTIMAL DOSAGE OF COMBINED THERAPIES SYSTEMS AND METHODS OF USE THEREOF

[0002] FIELD OF THE INVENTION

[0003] The present invention is directed to methods for optimizing dosage of a combination treatment (e.g., comprising two therapeutic agents) for the treatment of proliferative cell disorders (e.g., cancers). Also provided are related treatment methods, kits, and compositions.

[0004] BACKGROUND

[0005] Cancer remains one of the most deadly threats to human health. Certain cancers can metastasize and grow rapidly in an uncontrolled manner, making timely detection and treatment extremely difficult. In the U.S., cancer affects nearly 1 .3 million new patients each year and is the second leading cause of death after heart disease, accounting for approximately one in four deaths.

[0006] Combining drugs is crucial for enhancing anti-cancer responses. However, the potential of pre- clinical data in identifying suitable combinations and dosage is often underutilized. Methods for optimizing suitable dosage of combination treatments are needed.

[0007] SUMMARY OF THE INVENTION

[0008] The present invention provides in vitro, in silica, and in vivo methods, and combinations thereof, for optimizing dosages of combination treatments for treating cancer, as well as therapeutic methods, kits, and compositions based on the optimized dosages of the combination treatments (e.g., two therapeutic agents) for treating the cancer.

[0009] In one aspect, the invention features a method of determining one or more in vitro combination dosages each comprising a first in vitro dosage of a first therapeutic agent and a second in vitro dosage of a second therapeutic agent for inhibiting growth or inducing cell death of a cancer cell line comprising a cancer: (a) administering a dilution matrix comprising a first dilution series of the first therapeutic agent and a second dilution series of the second therapeutic agent to the cancer cell line; and (b) determining an excess over bliss score (bliss excess) for each element of the dilution matrix based on a growth inhibition assay or cytotoxicity assay, wherein the one or more in vitro combination dosages are the elements of the dilution matrix having a positive bliss excess.

[0010] In some embodiments, the positive bliss excess is from 0.2 to 1 (e.g., from 0.3 to 1 , from 0.4 to 1 , from 0.5 to 1 , from 0.6 to 1 , from 0.7 to 1 , from 0.8 to 1 , from 0.9 to 1 , from 0.2 to 0.9, from 0.3 to 0.9, from 0.4 to 0.9, from 0.5 to 0.9, from 0.6 to 0.9, from 0.7 to 0.9, from 0.8 to 0.9, from 0.2 to 0.8, from 0.3 to 0.8, from 0.4 to 0.8, from 0.5 to 0.8, from 0.6 to 0.8, from 0.7 to 0.8, from 0.2 to 0.7, from 0.3 to 0.7, from 0.4 to 0.7, from 0.5 to 0.7, from 0.6 to 0.7, from 0.2 to 0.6, from 0.3 to 0.6, from 0.4 to 0.6, from 0.5 to 0.6, from 0.2 to 0.5, from 0.3 to 0.5, from 0.4 to 0.5, from 0.2 to 0.4, from 0.3 to 0.4, from 0.2 to 0.3; e.g., 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, or 1 ). In some embodiments, the positive bliss excess is from 0.5 to 1 . In some embodiments, the positive bliss excess is from 0.7 to 1 .

[0011] In some embodiments, the bliss excess is determined from steady state dose-responses determined for each element of the dilution matrix. In some embodiments, the steady state dose-responses are determined using a set of ordinary differential equations (ODEs). In some embodiments, the set of ODEs are generated using BioNetGen 2.2. In some embodiments, the set of ODEs are generated using a model of a biological pathway comprising the cancer, the first therapeutic agent, and the second therapeutic agent. In some embodiments, the biological pathway is an EGFR / MAPK signaling pathway. In some embodiments, the model is a second-generation MAPK Adaptive Resistance Model (MARM2.0). In some embodiments, the steady state dose-responses are when the relative change of all species in the set of ODEs is less than 0.1% (e.g., less than 0.09%, less than 0.08%, less than 0.07%, less than 0.06%, less than 0.05%, less than 0.04%, less than 0.03%, less than 0.02%, less than 0.01%, less than 0.005%, less than 0.001%; e.g., 0.09%, 0.08%, 0.07%, 0.06%, 0.05%, 0.04%, 0.03%, 0.02%, 0.01%, 0.005%, or 0.001%) over a period of at least 4 hours (e.g., at least 8 hours, at least 12 hours, at least 16 hours, at least 20 hours, at least 24 hours; e.g., over a course of about 4 hours, 8 hours, 12 hours, 16 hours, 20 hours, or 24 hours).

[0012] In some embodiments, the first dilution series comprises 4 to 20 doses (e.g., 8 to 20, 10 to 20, 12 to 20, 16 to 20, 4 to 16, 8 to 16, 10 to 16, 12 to 16, 4 to 12, 8 to 12, 10 to 12, 4 to 10, 8 to 10, 4 to 8 doses; e.g., 4, 5, 6, 7, 8, 9, 10, 11 , 12, 13, 14, 15, 16, 17, 18, 19, or 20 doses). In some embodiments, the first dilution series comprises 10 doses.

[0013] In some embodiments, the second dilution series comprises 4 to 20 doses (e.g., 8 to 20, 10 to 20, 12 to 20, 16 to 20, 4 to 16, 8 to 16, 10 to 16, 12 to 16, 4 to 12, 8 to 12, 10 to 12, 4 to 10, 8 to 10, 4 to 8 doses; e.g., 4, 5, 6, 7, 8, 9, 10, 11 , 12, 13, 14, 15, 16, 17, 18, 19, or 20 doses). In some embodiments, the second dilution series comprises 10 doses.

[0014] In some embodiments, the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer. In some embodiments, the skin cancer is melanoma.

[0015] In some embodiments, the cancer cell line comprises UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC-62, RVH-421 , SK-MEL- 24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, CGLG800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA- MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0016] In some embodiments, the melanoma comprises a mutation of a biomarker gene. In some embodiments, the melanoma comprises a BRAF mutation or an NRAS mutation.

[0017] In some embodiments, the BRAF mutation is a V600E mutation. In some embodiments, the cancer cell line comprises WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, CGLG800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242I, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0018] In some embodiments, the NRAS mutation is a Q61 hotspot mutation. In some embodiments, the cancer cell line comprises SK-MEL-30, SK-MEL-2, MEL-JUSO, or Hs852.T. In some embodiments, the one or more in vitro combination dosages are determined using a growth inhibition assay. In some embodiments, the one or more in vitro combination dosages are determined using a cytotoxicity assay.

[0019] In some embodiments, the first therapeutic agent comprises a small molecule inhibitor, a protein, a nucleic acid, or a CAR-T cell.

[0020] In some embodiments, the first therapeutic agent comprises a MEK inhibitor. In some embodiments, the first therapeutic agent comprises cobimetinib.

[0021] In some embodiments, the second therapeutic agent comprises a small molecule inhibitor, a protein, a nucleic acid, or a CAR-T cell. In some embodiments, the second therapeutic agent comprises a pan-RAF inhibitor. In some embodiments, the second therapeutic agent comprises belvarafenib.

[0022] In another aspect, the invention features a method of determining one or more combination in vivo dosages each comprising a first in vivo dosage of a first therapeutic agent and a second in vivo dosage of a second therapeutic agent for treating a cancer comprising converting the one or more in vitro combination dosages determined in the preceding aspect to the one or more combination in vivo dosages based on the plasma free drug concentrations of the first therapeutic agent administered according to a dilution series to a subject and the plasma free drug concentrations of the second therapeutic agent administered according to a dilution series to a subject. In some embodiments, the subject is a mouse or a human.

[0023] In another aspect, the invention features a method of treating a cancer in an individual by administering a first therapeutic agent and a second therapeutic agent according to any one of the one or more combination in vivo dosages determined in the preceding aspect. In some embodiments, the individual is a human.

[0024] In some embodiments, the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

[0025] In some embodiments, the skin cancer is melanoma.

[0026] In some embodiments, the melanoma comprises a mutation of a biomarker gene. In some embodiments, the melanoma comprises a BRAF mutation or an NRAS mutation. In some embodiments, the BRAF mutation is a V600E mutation. In some embodiments, the NRAS mutation is a Q61 hotspot mutation.

[0027] In some embodiments, the first therapeutic agent and the second therapeutic agent exhibit a synergistic effect when administered to the individual according to the one of the one or more combination in vivo dosages.

[0028] BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG. 1 A is a heatmap showing the result of a single-agent drug screen on 43 melanoma cell lines, including ones with BRAF or NRAS mutations. Drug effectiveness was quantified using IC50 values. NRAS_mut = NRAS mutant; BRAF_mut = BRAF mutant; MEKi = MEK inhibitor; panRAFi = pan-RAF inhibitor; BRAFi = BRAF inhibitor.

[0030] FIG. 1B is a heatmap showing the result of a combination drug screen on the same 43 melanoma cell lines as in FIG. 1 A. Drug combination synergies were quantified using Bliss scores. BRAFi = BRAF inhibitor; MEKi = MEK inhibitor; panRAFi = pan-RAF inhibitor.

[0031] FIG. 1C is a series of heatmaps showing the measured in vitro effects of Cobimetinib and Belvarafenib combinations on the relative viability of select melanoma cell lines with drug synergies quantified by Bliss excess. MEKi = MEK inhibitor; panRAFi = pan-RAF inhibitor.

[0032] FIG. 2A is a schematic of the MAPK pathway in melanomas with NRAS Q61 mutations. RBD = Ras-binding domain.

[0033] FIG. 2B is a schematic of the MAPK pathway in melanomas with BRAF V600 mutations. RBD = Ras-binding domain.

[0034] FIG. 2C is a series of western blot gel images showing the quantification of phosphorylated MEK (pMEK), total MEK, phosphorylated ERK (pERK), and total ERK in MEL-JUSO cells treated with varying concentrations of Cobimetinib with or without Belvarafenib. %pMEK and %pERK were calculated from pMEK and pERK DMSO control-normalized band intensities divided by DMSO-normalized total MEK and ERK, respectively. Belva = Belvarafenib; Cobi = Cobimetinib.

[0035] FIG. 2D is a series of western blot gel images showing the quantification of pMEK, total MEK, pERK, and total ERK in A375 cells treated with varying concentrations of Cobimetinib with or without Belvarafenib. %pMEK and %pERK were calculated from pMEK and pERK DMSO control-normalized band intensities divided by DMSO-normalized total MEK and ERK, respectively. Belva = Belvarafenib; Cobi = Cobimetinib.

[0036] FIG. 2E is a series of line graphs showing model predictions for steady-state percentages of active RAF, pMEK, and pERK under varying concentrations of Belvarafenib and Cobimetinib. Results are shown for both BRAF V600E and NRAS Q61 models. Belva = Belvarafenib; Cobi = Cobimetinib.

[0037] FIG. 3A is a series of heatmaps showing mechanistic modeling predictions for pMEK and pERK steady-state levels under indicated concentrations of Belvarafenib and Cobimetinib in a BRAF V600E model. Reported values are shown relative to drugless conditions. Drug synergy analysis was quantified via Bliss excess.

[0038] FIG. 3B is a series of heatmaps showing mechanistic modeling predictions for pMEK and pERK steady-state levels under indicated concentrations of Belvarafenib and Cobimetinib in a NRAS Q61 model. Reported values are shown relative to drugless conditions. Drug synergy analysis was quantified via Bliss excess.

[0039] FIG. 3C is a series of graphs comparing model predictions (top) and immunofluorescence data (bottom) for pERK levels in response to Cobimetinib and Belvarafenib combinations. Results for BRAF V600E model and cell line, A-375 (left), and NRAS Q61 model and cell line, IPC-298 (right), are shown.

[0040] FIG. 4A is a schematic showing the conversion of relative viability to growth rate inhibition (GR) metric for IPC-298 in vitro drug responses and projection of mouse pharmacokinetic (PK) data onto in vitro responses to obtain predicted tumor growth rates.

[0041] FIG. 4B is a pair of line graphs showing the comparison between predicted tumor growth rates using in vitro IPC-298 drug response and mouse PK data (left) and experimentally measured in vivo tumor growth rates in mice (right) as affected by varying concentrations of Cobimetinib and Belvarafenib. PK = pharmacokinetics; Belva = Belvarafenib; Cobi = Cobimetinib.

[0042] FIG. 5A is a schematic showing the workflow for mapping in vivo free drug concentrations onto in vitro drug responses to predict cell responses and drug synergies of Cobimetinib and Belvarafenib at clinically equivalent concentrations. GR = normalized growth rate inhibition; panRAFi = pan-RAF inhibitor; MEKi = MEK inhibitor; QOD = once every other day; QD = once daily; BID = twice daily.

[0043] FIG. 5B is a series of heatmaps showing predicted viability of cell panels and drug synergies at clinically equivalent drug concentrations of Cobimetinib and Belvarafenib in A-375 and IPC-298 cells. GR = normalized growth rate inhibition; QOD = once every other day; QD = once daily; BID = twice daily.

[0044] FIG. 6A is a series of heatmaps and trajectory plots showing individual virtual patient PK trajectories resulting from the indicated regimen of Cobimetinib and Belvarafenib projected onto in vitro responses in A-375 or IPC-298 cell lines. BID = twice daily; QD = once daily; QOD = once every other day; GR = normalized growth rate inhibition; RAFi = RAF inhibitor; MEKi = MEK inhibitor.

[0045] FIG. 6B is a series of violin plots showing the distribution of GR metric values (left) and Bliss excess values (right) measured from 75 single patient trajectories based on A-375 or IPC-298 model. Multiple drug regimens are compared; rows and columns indicate the Cobimetinib and Belvarafenib doses used in the specific drug regimen. GR = normalized growth rate inhibition; QOD = once every other day; QD = once daily; BID = twice daily; MEKi = MEK inhibitor; RAFi = RAF inhibitor.

[0046] FIG. 7A is a pair of line graphs showing simulated tumor growth under indicated Belvarafenib and Cobimetinib regimens for BRAF and NRAS mutant melanoma patients. Belva monotherapy (mono) is 400 or 450 mg twice daily. BRAF+ = BRAF mutant; NRAS+ = NRAS mutant; Belva = Belvarafenib; Cobi = Cobimetinib; QOD = once every other day; TIW = three times a week; QD = once daily.

[0047] FIG. 7B is a pair of box plots showing distribution of tumor growth rates for indicated Belvarafenib and Cobimetinib regimen within simulated populations of patients with BRAF V600E (top) or NRAS Q61 (bottom) tumors. Belva mono is 400 or 450 mg twice daily. BRAF+ = BRAF mutant; NRAS+ = NRAS mutant; Belva = Belvarafenib; Cobi = Cobimetinib; QOD = once every other day; TIW = three times a week; QD = once daily.

[0048] FIG. 8A is a line graph showing body weight change of mice with IPC-298 xenograft treated with indicated Belvarafenib and Cobimetinib regimen over time. Belva = Belvarafenib; Cobi = Cobimetinib.

[0049] FIG. 8B is a series of volcano plots showing gene expression response in IPC-298 xenografts in mice at indicated times and doses of Belvarafenib and Cobimetinib. Upregulated or downregulated genes are marked in shading and named on the sides. PO = orally; QDx21 = once daily for 21 days; Cobi = Cobimetinib; Belva = Belvarafenib.

[0050] FIG. 9 is a series of uncropped western blot gel images with quantifications corresponding to the gel images in FIGS. 2C and 2D. The percentage of phosphorylated ERK (%pERK) was calculated as the ratio of the DMSO control-normalized pERK and total ERK band intensities. The percentage of phosphorylated MEK (%pMEK) was calculated as the ratio of the DMSO control-normalized pMEK and total MEK band intensities. Belva = Belvarafenib; Cobi = Cobimetinib.

[0051] FIG. 10A is a series of line graphs showing model predictions for percentages of active RAF, pMEK, and pERK over time. Models were initially in steady state without drug addition before being dosed with indicated Cobimetinib and Belvarafenib concentrations at t = 0. pRAF = phosphorylated RAF; Cobi = Cobimetinib; Belva = Belvarafenib.

[0052] FIG. 10B is a series of line graphs showing model predictions for steady state percentages of active RAF, pMEK, and pERK under indicated levels of Belvarafenib and Cobimetinib. Results are shown for NRAS Q61 model without pRAF feedback mechanism. Cobi = Cobimetinib; Belva = Belvarafenib.

[0053] FIG. 11 is a series of line graphs showing the pharmacokinetic trajectories corresponding to the drug regimen and virtual patient combinations in FIG. 6A. Data are shown for 96 hours (corresponding to at least two complete cycles of drug concentrations). Data for the first 48 hours were used for the analysis shown in FIG. 6A. Cobi = Cobimetinib; QD = once daily; QOD = once every other day; BID = twice daily.

[0054] FIG. 12 is a pair of box plots showing the simulation of shrinking rate of BRAF or NRAS mutant tumors in human patients treated with various combinations of Belvarafenib and Cobimetinib. Belva mono is 400 or 450 mg twice daily. BRAF+ = BRAF mutant; NRAS+ = NRAS mutant; Belva = Belvarafenib; Cobi = Cobimetinib; QOD = once every other day; TIW = three times a week; QD = once daily.

[0055] DETAILED DESCRIPTION OF THE INVENTION

[0056] I. Introduction

[0057] The present invention provides in vitro, in silica, and in vivo methods, and combinations thereof, for optimizing dosages of combination treatments for treating cancer, as well as therapeutic methods, kits, and compositions based on the optimized dosages of the combination treatments (e.g., two therapeutic agents) for treating the cancer (e.g., colorectal cancer, ovarian cancer, lung cancer, pancreatic cancer, and skin cancer (e.g., melanoma)). The invention is based, at least in part, on the discovery that the combination of in vitro, in silica, and / or in vivo methods can be used to determine optimized dosages of a combination treatment comprising two therapeutic agents, and in particular, wherein administration of the two therapeutic agents. In particular instances, the two therapeutic agents include a pan-RAF inhibitor (e.g., belvarafenib) and a MEK inhibitor (e.g., cobimetinib).

[0058] II. Definitions

[0059] It is to be understood that aspects and embodiments of the invention described herein include “comprising,” “consisting,” and “consisting essentially of” aspects and embodiments. As used herein, the singular form “a,” “an,” and “the” includes plural references unless indicated otherwise.

[0060] The term “about” as used herein refers to the usual error range for the respective value readily known to the skilled person in this technical field. Reference to “about” a value or parameter herein includes (and describes) embodiments that are directed to that value or parameter per se. For example, description referring to “about X” includes description of “X.” For numerical values, the term “about” a numerical value includes the value ± 10%.

[0061] The term “MAPK signaling pathway” refers to the mitogen-activated protein kinase signaling pathway (e.g., the RAS / RAF / MEK / ERK signaling pathway) and encompasses a family of conserved serine / threonine protein kinases (e.g., the mitogen-activated protein kinases (MAPKs)). Abnormal regulation of the MAPK pathway contributes to uncontrolled proliferation, invasion, metastases, angiogenesis, and diminished apoptosis. The RAS family of GTPases includes KRAS, HRAS, and NRAS. The RAF family of serine / threonine protein kinases includes ARAF, BRAF, and CRAF (RAF1 ). Exemplary MAPKs include the extracellular signal-regulated kinase 1 and 2 (i.e. , ERK1 and ERK2), the c- Jun N-terminal kinases 1 -3 (i.e., JNK1 , JNK2, and JNK3), the p38 isoforms (i.e., p38a, p38p, p38y, and p386), and Erk5. Additional MAPKs include Nemo-like kinase (NLK), Erk3 / 4 (i.e., ERK3 and ERK4), and Erk7 / 8 (i.e., ERK7 and ERK8). In some instances, the MAPK signaling pathway additionally includes epidermal growth factor receptor (EGFR), and is referred to as an EGFR / MAPK signaling pathway.”

[0062] The term “MAPK signaling inhibitor” or “MAPK pathway signaling inhibitor” refers to a molecule that decreases, blocks, inhibits, abrogates, or interferes with signal transduction through the MAPK pathway (e.g., the RAS / RAF / MEK / ERK pathway). In some embodiments, a MAPK signaling inhibitor may inhibit the activity of one or more proteins involved in the activation of MAPK signaling. In some embodiments, a MAPK signaling inhibitor may increase the activity of one or more proteins involved in the inhibition of MAPK signaling. MAPK signaling inhibitors include, but are not limited to, MEK inhibitors (e.g., MEK1 inhibitors, MEK2 inhibitors, and inhibitors of both MEK1 and MEK2), RAF inhibitors (e.g., ARAF inhibitors, BRAF inhibitors, CRAF inhibitors, and pan-RAF inhibitors (i.e., RAF inhibitors that are inhibiting more than one member of the RAF family (i.e., two or all three of ARAF, BRAF, and CRAF), e.g., pan-RAF dimer inhibitors (i.e., pan-RAF inhibitors that can bind and inhibit RAF dimers (e.g., RAF heterodimers))), and ERK inhibitors (e.g., ERK1 inhibitors and ERK2 inhibitors).

[0063] The term “MEK inhibitor” or “MEK antagonist” refers to molecule that decreases, blocks, inhibits, abrogates, or interferes with MEK (e.g., MEK1 and / or MEK2) activation or function. In a particular embodiment, a MEK inhibitor has a binding affinity (dissociation constant) to MEK of about 1 ,000 nM or less. In another embodiment, a MEK inhibitor has a binding affinity to MEK of about 100 nM or less. In another embodiment, a MEK inhibitor has a binding affinity to MEK of about 50 nM or less. In another embodiment, a MEK inhibitor has a binding affinity to MEK of about 10 nM or less. In another embodiment, a MEK inhibitor has a binding affinity to MEK of about 1 nM or less. In a particular embodiment, a MEK inhibitor inhibits MEK signaling with an IC50 of 1 ,000 nM or less. In another embodiment, a MEK inhibitor inhibits MEK signaling with an IC50 of 500 nM or less. In another embodiment, a MEK inhibitor inhibits MEK signaling with an IC50 of 50 nM or less. In another embodiment, a MEK inhibitor inhibits MEK signaling with an IC50 of 10 nM or less. In another embodiment, a MEK inhibitor inhibits MEK signaling with an IC50 of 1 nM or less. Examples of MEK inhibitors that may be used in accordance with the invention include, without limitation, cobimetinib (e.g., cobimetinib hemifumarate; COTELLIC®), trametinib, binimetinib, selumetinib, pimasertinib, refametinib, GDC-0623, PD-0325901 , and BI-847325, or a pharmaceutically acceptable salt thereof. MEK inhibitors may inhibit only MEK or may inhibit MEK and one or more additional targets. A particular MEK inhibitor described herein is cobimetinib.

[0064] The term “pan-RAF inhibitor” or “pan-RAF antagonist” refers to a molecule that decreases, blocks, inhibits, abrogates, or interferes with the activation or function of two or more RAF family members (e.g., two or more of ARAF, BRAF, and CRAF). In one embodiment, the pan-RAF inhibitor inhibits all three RAF family members (i.e., ARAF, BRAF, and CRAF) to some extent. In a particular embodiment, a pan-RAF inhibitor has a binding affinity (dissociation constant) to one, two, or three of ARAF, BRAF, and / or CRAF of about 1 ,000 nM or less. In another embodiment, a pan-RAF inhibitor has a binding affinity to one, two, or three of ARAF, BRAF, and / or CRAF of about 100 nM or less. In another embodiment, a pan-RAF inhibitor has a binding affinity to one, two, or three of ARAF, BRAF, and / or CRAF of about 50 nM or less. In another embodiment, a pan-RAF inhibitor has a binding affinity to one, two, or three of ARAF, BRAF, and / or CRAF of about 10 nM or less. In another embodiment, a pan-RAF inhibitor has a binding affinity to one, two, or three of ARAF, BRAF, and / or CRAF of about 1 nM or less. In a particular embodiment, a pan-RAF inhibitor inhibits ARAF, BRAF, and / or CRAF signaling with an IC50 of 1 ,000 nM or less. In another embodiment, a pan-RAF inhibitor inhibits ARAF, BRAF, and / or CRAF signaling with an IC50 of 500 nM or less. In another embodiment, a pan-RAF inhibitor inhibits ARAF, BRAF, and / or CRAF signaling with an IC50 of 50 nM or less. In another embodiment, a pan-RAF inhibitor inhibits ARAF, BRAF, and / or CRAF signaling with an IC50 of 10 nM or less. In another embodiment, a pan-RAF inhibitor inhibits ARAF, BRAF, and / or CRAF signaling with an IC50 of 1 nM or less. Examples of pan-RAF inhibitors that may be used in accordance with the invention include, without limitation, LY-3009120, HM95573 (GDC-5573), LXH-254, MLN2480, BeiGene-283, RXDX-105, BAL3833, regorafenib, and sorafenib, or a pharmaceutically acceptable salt thereof. A particular pan-RAF inhibitor described herein is belvarafenib.

[0065] In some embodiments, the pan-RAF inhibitor is a “pan-RAF dimer inhibitor” that can bind and inhibit RAF dimers (e.g., RAF heterodimers, e.g., BRAF-CRAF heterodimers). Pan-RAF dimer inhibitors may also bind and inhibit RAF monomers, in addition to RAF dimers (e.g., RAF heterodimers, e.g., BRAF- CRAF heterodimers). Pan-RAF dimer inhibitors include, for example, Type II RAF inhibitors that are capable of decreasing, blocking, inhibiting, abrogating, or interfering with the activation or function of two or more RAF family members. A particular pan-RAF dimer inhibitor described herein is belvarafenib.

[0066] An “NRAS activating mutation” is any mutation of the NRAS gene (i.e., a nucleic acid mutation) or NRAS protein (i.e., an amino acid mutation) that results in aberrant NRAS protein function associated with increased and / or constitutive activity by favoring the active GTP-bound state of the NRAS protein. The mutation may be at conserved sites that favor GTP binding and constitutively active NRAS protein. In some instances, the mutation is at one or more of codons 12, 13, and 16 of the NRAS gene. Exemplary NRAS activating mutations include, for example, NRAS-Q61 R, NRAS-Q61 K, NRAS-G12D, NRAS-G13D, NRAS-G12S, NRAS-G12C, NRAS-G12V, NRAS-G12A, NRAS-G12R, NRAS-G13C, NRAS-G13A, NRAS-G13R, NRAS-G13S, NRAS-G13V, NRAS-Q61 H, NRAS-Q61 E, NRAS-Q61 L, and NRAS-Q61 P, as well as corresponding nucleic acid mutations in the NRAS gene that encode for the denoted amino acid alteration of the NRAS protein. In particular, an NRAS mutation described herein is an NRAS Q61 hotspot mutation, which includes NRAS-Q61 R, NRAS-Q61 K, NRAS-Q61 H, NRAS-Q61 E, NRAS-Q61 L, and NRAS-Q61 P.

[0067] A “BRAF activating mutation” is any mutation of the BRAF gene (i.e., a nucleic acid mutation) or B-Raf protein (i.e., an amino acid mutation) that results in aberrant B-Raf protein function associated with increased and / or constitutive activity by favoring the active state of the B-Raf protein. The mutation may be at conserved sites that favor RAS-GTP binding and constitutively active B-Raf protein. In some instances, the mutation is at codon 600 of the BRAF gene. Exemplary BRAF activating mutations include, for example, BRAF-V600E, BRAF-V600K, BRAF-V600R, and BRAF-V600D, as well as corresponding nucleic acid mutations in the BRAF gene that encode for the denoted amino acid alteration of the B-Raf protein. A particular BRAF mutation described herein is a BRAF V600E mutation.

[0068] An “individual,” “patient,” or “subject” herein refers to an animal (including, e.g., a mammal, such as a dog, a cat, a horse, a rabbit, a zoo animal, a cow, a pig, a sheep, a non-human primate, and a human), eligible for treatment who is experiencing, has experienced, has risk of developing, or has a family history of one or more signs, symptoms, or other indicators of a cell proliferative disease or disorder, such as a cancer. Intended to be included as a patient is any patient involved in clinical research trials not showing any clinical sign of disease, involved in epidemiological studies, or once used as controls.

[0069] The term “antibody” herein is used in the broadest sense and encompasses various antibody structures, including but not limited to monoclonal antibodies, polyclonal antibodies, multispecific antibodies (e.g., bispecific antibodies), and antibody fragments so long as they exhibit the desired antigen-binding activity.

[0070] A “mutation” is a deletion, insertion, or substitution of one or more nucleotides or one or more amino acids relative to a reference nucleotide sequence or reference amino acid sequence, respectively, such as a wild-type sequence.

[0071] The term “small molecule” refers to any molecule with a molecular weight of about 2,000 daltons or less, preferably of about 500 daltons or less.

[0072] The term “detection” includes any means of detecting, including direct and indirect detection.

[0073] The term “biomarker” as used herein refers to an indicator molecule or set of molecules (e.g., predictive, diagnostic, and / or prognostic indicator), which can be detected in a sample.

[0074] The “presence” of a biomarker, as used herein, is a detectable amount in a biological sample. These can be measured by methods known to one skilled in the art and also disclosed herein.

[0075] The term “sample,” as used herein, refers to a composition that is obtained or derived from a subject (e.g., individual of interest) that contains a cellular and / or other molecular entity that is to be characterized and / or identified, for example, based on physical, biochemical, chemical, and / or physiological characteristics. For example, the phrase “disease sample” and variations thereof refers to any sample obtained from a subject of interest that would be expected or is known to contain the cellular and / or molecular entity that is to be characterized. Samples include, but are not limited to, tissue samples (e.g., tumor tissue samples), primary or cultured cells or cell lines, cell supernatants, cell lysates, platelets, serum, plasma, vitreous fluid, lymph fluid, synovial fluid, follicular fluid, seminal fluid, amniotic fluid, milk, whole blood, blood-derived cells, urine, cerebro-spinal fluid, saliva, sputum, tears, perspiration, mucus, tumor lysates, and tissue culture medium, tissue extracts such as homogenized tissue, tumor tissue, cellular extracts, and combinations thereof.

[0076] By “tissue sample” is meant a collection of similar cells obtained from a tissue of a subject or individual. The source of the tissue sample may be solid tissue as from a fresh, frozen and / or preserved organ, tissue sample, biopsy, and / or aspirate; blood or any blood constituents such as plasma; bodily fluids such as cerebral spinal fluid, amniotic fluid, peritoneal fluid, or interstitial fluid; and cells from any time in gestation or development of the subject. The tissue sample may also be primary or cultured cells or cell lines. Optionally, the tissue sample is obtained from a disease tissue / organ. For instance, a “tumor tissue sample” is a tissue sample obtained from a tumor or other cancerous tissue. The tissue sample may contain a mixed population of cell types (e.g., tumor cells and non-tumor cells, cancerous cells and non-cancerous cells). The tissue sample may contain compounds that are not naturally intermixed with the tissue in nature, such as preservatives, anticoagulants, buffers, fixatives, nutrients, antibiotics, or the like.

[0077] A “reference sample,” “reference cell,” “reference tissue,” “control sample,” “control cell,” or “control tissue,” as used herein, refers to a sample, cell, tissue, standard, or level that is used for comparison purposes. In one embodiment, a reference level, reference sample, reference cell, reference tissue, control sample, control cell, or control tissue is obtained from a healthy and / or non-diseased part of the body (e.g., tissue or cells) of the same subject or individual. For example, the reference level, reference sample, reference cell, reference tissue, control sample, control cell, or control tissue may be healthy and / or non-diseased cells or tissue adjacent to the diseased cells or tissue (e.g., cells or tissue adjacent to a tumor). In another embodiment, a reference sample is obtained from an untreated tissue and / or cell of the body of the same subject or individual. In yet another embodiment, a reference level, reference sample, reference cell, reference tissue, control sample, control cell, or control tissue is obtained from a healthy and / or non-diseased part of the body (e.g., tissues or cells) of an individual who is not the subject or individual. In even another embodiment, a reference level, reference sample, reference cell, reference tissue, control sample, control cell, or control tissue is obtained from an untreated tissue and / or cell of the body of an individual who is not the subject or individual.

[0078] For the purposes herein a “section” of a tissue sample means a single part or piece of a tissue sample, for example, a thin slice of tissue or cells cut from a tissue sample (e.g., a tumor sample). It is to be understood that multiple sections of tissue samples may be taken and subjected to analysis, provided that it is understood that the same section of tissue sample may be analyzed at both morphological and molecular levels, or analyzed with respect to polypeptides (e.g., by immunohistochemistry) and / or polynucleotides (e.g., by in situ hybridization).

[0079] A “therapeutically effective amount” refers to an amount of a therapeutic agent to treat or prevent a disease or disorder in a mammal. In the case of cancers, the therapeutically effective amount of the therapeutic agent may reduce the number of cancer cells; reduce the primary tumor size; inhibit (i.e. , slow to some extent and preferably stop) cancer cell infiltration into peripheral organs; inhibit (i.e., slow to some extent and preferably stop) tumor metastasis; inhibit, to some extent, tumor growth; and / or relieve to some extent one or more of the symptoms associated with the disorder. To the extent the drug may prevent growth and / or kill existing cancer cells, it may be cytostatic and / or cytotoxic. For cancer therapy, efficacy in vivo can, for example, be measured by assessing the duration of survival, time to disease progression (TTP), response rates (e.g., CR and PR), duration of response, and / or quality of life.

[0080] The terms “cancer” and “cancerous” refer to or describe the physiological condition in mammals that is typically characterized by unregulated cell growth. Included in this definition are benign and malignant cancers. Examples of cancer include, but are not limited to, carcinoma; lymphoma; blastoma (including medulloblastoma and retinoblastoma); sarcoma (including liposarcoma and synovial cell sarcoma); neuroendocrine tumors (including carcinoid tumors, gastrinoma, and islet cell cancer); mesothelioma; schwannoma (including acoustic neuroma); meningioma; adenocarcinoma; melanoma; and leukemia or lymphoid malignancies. More particular examples of such cancers include bladder cancer (e.g., urothelial bladder cancer (e.g., transitional cell or urothelial carcinoma, non-muscle invasive bladder cancer, muscle-invasive bladder cancer, and metastatic bladder cancer) and non-urothelial bladder cancer); squamous cell cancer (e.g., epithelial squamous cell cancer); lung cancer, including small-cell lung cancer (SCLC), non-small cell lung cancer (NSCLC), adenocarcinoma of the lung, and squamous carcinoma of the lung; cancer of the peritoneum; hepatocellular cancer; gastric or stomach cancer, including gastrointestinal cancer; pancreatic cancer; glioblastoma; cervical cancer; ovarian cancer; liver cancer; hepatoma; breast cancer (including metastatic breast cancer); colon cancer; rectal cancer; colorectal cancer; uterine cancer; brain cancer; bone cancer; salivary gland carcinoma; kidney or renal cancer; prostate cancer; vulval cancer; thyroid cancer; hepatic carcinoma; anal carcinoma; penile carcinoma; a gastric cancer; endometrial cancer; Merkel cell cancer; mycosis fungoides; testicular cancer; esophageal cancer; tumors of the biliary tract; head and neck cancer; and hematological malignancies. In some embodiments, the cancer is triple-negative metastatic breast cancer, including any histologically confirmed triple-negative (ER-, PR-, HER2-) adenocarcinoma of the breast with locally recurrent or metastatic disease (where the locally recurrent disease is not amenable to resection with curative intent). In some embodiments, the cancer is skin cancer, including a melanoma, e.g., a melanoma with locally recurrent or metastatic disease (where the locally recurrent disease is not amenable to resection with curative intent). Any cancer can be at early stage or at late stage. By “early stage cancer” or “early stage tumor” is meant a cancer that is not invasive or metastatic or is classified as a Stage 0, 1 , or 2 cancer. In contrast, “late stage cancer” or “late stage tumor” is meant a cancer that is classified as a Stage 3 or 4 cancer.

[0081] The term “tumor,” as used herein, refers to all neoplastic cell growth and proliferation, whether malignant or benign, and all pre-cancerous and cancerous cells and tissues. The terms “cancer,” “cancerous,” and “tumor” are not mutually exclusive as referred to herein.

[0082] The term “pharmaceutical formulation” refers to a preparation which is in such form as to permit the biological activity of an active ingredient contained therein to be effective, and which contains no additional components which are unacceptably toxic to a subject to which the formulation would be administered.

[0083] A “pharmaceutically acceptable excipient” refers to an ingredient in a pharmaceutical formulation, other than an active ingredient, which is nontoxic to a subject. A pharmaceutically acceptable excipient includes, but is not limited to, a buffer, carrier, stabilizer, or preservative.

[0084] The term “pharmaceutically acceptable salt” denotes salts which are not biologically or otherwise undesirable. Pharmaceutically acceptable salts include both acid and base addition salts. The phrase “pharmaceutically acceptable” indicates that the substance or composition must be compatible chemically and / or toxicologically, with the other ingredients comprising a formulation, and / or the mammal being treated therewith.

[0085] The term “pharmaceutically acceptable acid addition salt” denotes those pharmaceutically acceptable salts formed with inorganic acids, such as hydrochloric acid, hydrobromic acid, sulfuric acid, nitric acid, carbonic acid, phosphoric acid, and organic acids selected from aliphatic, cycloaliphatic, aromatic, araliphatic, heterocyclic, carboxylic, and sulfonic classes of organic acids, such as formic acid, acetic acid, propionic acid, glycolic acid, gluconic acid, lactic acid, pyruvic acid, oxalic acid, malic acid, maleic acid, malonic acid, succinic acid, fumaric acid, tartaric acid, citric acid, aspartic acid, ascorbic acid, glutamic acid, anthranilic acid, benzoic acid, cinnamic acid, mandelic acid, embonic acid, phenylacetic acid, methanesulfonic acid “mesylate”, ethanesulfonic acid, p-toluenesulfonic acid, and salicyclic acid.

[0086] The term “pharmaceutically acceptable base addition salt” denotes those pharmaceutically acceptable salts formed with an organic or inorganic base. Examples of acceptable inorganic bases include sodium, potassium, ammonium, calcium, magnesium, iron, zinc, copper, manganese, and aluminum salts. Salts derived from pharmaceutically acceptable organic nontoxic bases includes salts of primary, secondary, and tertiary amines, substituted amines, including naturally occurring substituted amines, cyclic amines, and basic ion exchange resins, such as isopropylamine, trimethylamine, diethylamine, triethylamine, tripropylamine, ethanolamine, 2-diethylaminoethanol, trimethamine, dicyclohexylamine, lysine, arginine, histidine, caffeine, procaine, hydrabamine, choline, betaine, ethylenediamine, glucosamine, methylglucamine, theobromine, purines, piperazine, piperidine, N- ethylpiperidine, and polyamine resins.

[0087] As used herein, “treatment” (and grammatical variations thereof such as “treat” or “treating”) refers to clinical intervention in an attempt to alter the natural course of the individual being treated, and can be performed either for prophylaxis or during the course of clinical pathology. Desirable effects of treatment include, but are not limited to, preventing occurrence or recurrence of disease, alleviation of symptoms, diminishment of any direct or indirect pathological consequences of the disease, preventing metastasis, decreasing the rate of disease progression, amelioration or palliation of the disease state, and remission or improved prognosis. In some embodiments, a pan-RAF dimer inhibitor is used in combination with a MEK inhibitor to delay development of a disease or to slow the progression of a cancer.

[0088] The term “anti-cancer therapy” refers to a therapy useful in treating cancer. Examples of anticancer therapeutic agents include, but are limited to, cytotoxic agents, chemotherapeutic agents, growth inhibitory agents, agents used in radiation therapy, anti-angiogenesis agents, apoptotic agents, antitubulin agents, and other agents to treat cancer, for example, anti-CD20 antibodies, platelet derived growth factor inhibitors (e.g., GLEEVEC® (imatinib mesylate)), a COX-2 inhibitor (e.g., celecoxib), interferons, cytokines, antagonists (e.g., neutralizing antibodies) that bind to one or more of the following targets PDGFR-p, BlyS, APRIL, BCMA receptor(s), TRAIL / Apo2, other bioactive and organic chemical agents, and the like. Combinations thereof are also included in the invention.

[0089] The term “cytotoxic agent” as used herein refers to a substance that inhibits or prevents the function of cells and / or causes destruction of cells. The term is intended to include radioactive isotopes (e.g., At211, I131, I125, Y90, Re186, Re188, Sm153, Bi212, P32, and radioactive isotopes of Lu), chemotherapeutic agents, e.g., methotrexate, adriamicin, vinca alkaloids (vincristine, vinblastine, etoposide), doxorubicin, melphalan, mitomycin C, chlorambucil, daunorubicin or other intercalating agents, enzymes and fragments thereof such as nucleolytic enzymes, antibiotics, and toxins such as small molecule toxins or enzymatically active toxins of bacterial, fungal, plant or animal origin, including fragments and / or variants thereof, and the various antitumor or anticancer agents disclosed below. Other cytotoxic agents are described below. A tumoricidal agent causes destruction of tumor cells. A “chemotherapeutic agent” is a chemical compound useful in the treatment of cancer. Examples of chemotherapeutic agents include alkylating agents such as thiotepa and CYTOXAN® (cyclosphosphamide); alkyl sulfonates such as busulfan, improsulfan and piposulfan; aziridines such as benzodopa, carboquone, meturedopa, and uredopa; ethylenimines and methylmelamines including altretamine, triethylenemelamine, triethylenephosphoramide, triethylenethiophosphoramide and trimethylol melamine; acetogenins (especially bullatacin and bullatacinone); delta-9-tetrahydrocannabinol (dronabinol, MARINOL®); beta-lapachone; lapachol; colchicines; betulinic acid; a camptothecin (including the synthetic analogue topotecan (HYCAMTIN®), CPT-11 (irinotecan, CAMPTOSAR®), acetylcamptothecin, scopolectin, and 9-aminocamptothecin); bryostatin; callystatin; CC-1065 (including its adozelesin, carzelesin and bizelesin synthetic analogues); podophyllotoxin; podophyllinic acid; teniposide; cryptophycins (particularly cryptophycin 1 and cryptophycin 8); dolastatin; duocarmycin (including the synthetic analogues, KW-2189 and CB1 -TM1 ); eleutherobin; pancratistatin; a sarcodictyin; spongistatin; nitrogen mustards such as chlorambucil, chlornaphazine, cyclophosphamide, estramustine, ifosfamide, mechlorethamine, mechlorethamine oxide hydrochloride, melphalan, novembichin, phenesterine, prednimustine, trofosfamide, and uracil mustard; nitrosoureas such as carmustine, chlorozotocin, fotemustine, lomustine, nimustine, and ranimnustine; antibiotics such as the enediyne antibiotics (e.g., calicheamicin, especially calicheamicin y11 and calicheamicin w11 (see, e.g., Nicolaou et al., Angew. Chem Inti. Ed. Engl., 33: 183-186 (1994)), dynemicin, including dynemicin A, an esperamicin, as well as neocarzinostatin chromophore and related chromoprotein enediyne antibiotic chromophores), aclacinomycins, actinomycin, authramycin, azaserine, bleomycins, cactinomycin, carubicin, carminomycin, carzinophilin, chromomycin, dactinomycin, daunorubicin, detorubicin, 6-diazo-5-oxo-L- norleucine, ADRIAMYCIN® (doxorubicin) (including morpholino-doxorubicin, cyanomorpholinodoxorubicin, 2-pyrrolino-doxorubicin and deoxydoxorubicin), epirubicin, esorubicin, idarubicin, marcellomycin, mitomycins such as mitomycin C, mycophenolic acid, nogalamycin, olivomycins, peplomycin, potfiromycin, puromycin, quelamycin, rodorubicin, streptonigrin, streptozocin, tubercidin, ubenimex, zinostatin, and zorubicin; anti-metabolites such as methotrexate and 5-fluorouracil (5-FU); folic acid analogues such as denopterin, methotrexate, pteropterin, trimetrexate; purine analogs such as fludarabine, 6-mercaptopurine, thiamiprine, thioguanine; pyrimidine analogs such as ancitabine, azacitidine, 6-azauridine, carmofur, cytarabine, dideoxyuridine, doxifluridine, enocitabine, floxuridine; androgens such as calusterone, dromostanolone propionate, epitiostanol, mepitiostane, testolactone; anti-adrenals such as aminoglutethimide, mitotane, trilostane; folic acid replenishers such as frolinic acid; aceglatone; aldophosphamide glycoside; aminolevulinic acid; eniluracil; amsacrine; bestrabucil; bisantrene; edatraxate; defofamine; demecolcine; diaziquone; eflornithine; elliptinium acetate; an epothilone; etoglucid; gallium nitrate; hydroxyurea; lentinan; lonidamine; maytansinoids such as maytansine and ansamitocins; mitoguazone; mitoxantrone; mopidanmol; nitracrine; pentostatin; phenamet; pirarubicin; losoxantrone; 2-ethylhydrazide; procarbazine; PSK® polysaccharide complex (JHS Natural Products, Eugene, OR); razoxane; rhizoxin; sizofiran; spirogermanium; tenuazonic acid; triaziquone; 2,2’,2”-trichlorotriethylamine; trichothecenes (especially T-2 toxin, verracurin A, roridin A and anguidine); urethan; vindesine (ELDISINE®, FILDESIN®); dacarbazine; mannomustine; mitobronitol; mitolactol; pipobroman; gacytosine; arabinoside (“Ara-C”); thiotepa; taxoids, for example taxanes including TAXOL® (paclitaxel) (Bristol-Myers Squibb Oncology, Princeton, N.J.), ABRAXANE™ (Cremophor-free, albumin-engineered nanoparticle formulation of paclitaxel) (American Pharmaceutical Partners, Schaumberg, Illinois), and TAXOTERE® (docetaxel) (Rhone-Poulenc Rorer, Antony, France); chlorambucil; gemcitabine (GEMZAR®); 6-thioguanine; mercaptopurine; methotrexate; platinum or platinum-based chemotherapy agents and platinum analogs, such as cisplatin, carboplatin, oxaliplatin (ELOXATIN™), satraplatin, picoplatin, nedaplatin, triplatin, and lipoplatin; vinblastine (VELBAN®); platinum; etoposide (VP-16); ifosfamide; mitoxantrone; vincristine (ONCOVIN®); oxaliplatin; leucovovin; vinorelbine (NAVELBINE®); novantrone; edatrexate; daunomycin; aminopterin; ibandronate; topoisomerase inhibitor RFS 2000; difluoromethylornithine (DMFO); retinoids such as retinoic acid; capecitabine (XELODA®); pharmaceutically acceptable salts or acids of any of the above; as well as combinations of two or more of the above such as CHOP, an abbreviation for a combined therapy of cyclophosphamide, doxorubicin, vincristine, and prednisolone, and FOLFOX, an abbreviation for a treatment regimen with oxaliplatin (ELOXATIN™) combined with 5-FU and leucovorin. Additional chemotherapeutic agents include the cytotoxic agents useful as antibody drug conjugates, such as maytansinoids (DM1 , for example) and the auristatins MMAE and MMAF, for example.

[0090] “Chemotherapeutic agents” also include “anti-hormonal agents” or “endocrine therapeutics” that act to regulate, reduce, block, or inhibit the effects of hormones that can promote the growth of cancer, and are often in the form of systemic, or whole-body treatment. They may be hormones themselves. Examples include anti-estrogens and selective estrogen receptor modulators (SERMs), including, for example, tamoxifen (including NOLVADEX® tamoxifen), EVISTA® raloxifene, droloxifene, 4- hydroxytamoxifen, trioxifene, keoxifene, LY117018, onapristone, and FARESTON® toremifene; antiprogesterones; estrogen receptor down-regulators (ERDs); agents that function to suppress or shut down the ovaries, for example, leutinizing hormone-releasing hormone (LHRH) agonists such as LUPRON® and ELIGARD® leuprolide acetate, goserelin acetate, buserelin acetate and tripterelin; other antiandrogens such as flutamide, nilutamide and bicalutamide; and aromatase inhibitors that inhibit the enzyme aromatase, which regulates estrogen production in the adrenal glands, such as, for example, 4(5)-imidazoles, aminoglutethimide, MEGASE® megestrol acetate, AROMASIN® exemestane, formestanie, fadrozole, RIVISOR® vorozole, FEMARA® letrozole, and ARIMIDEX® anastrozole. In addition, such definition of chemotherapeutic agents includes bisphosphonates such as clodronate (for example, BONEFOS® or OSTAC®), DIDROCAL® etidronate, NE-58095, ZOMETA® zoledronic acid / zoledronate, FOSAMAX® alendronate, AREDIA® pamidronate, SKELID® tiludronate, or ACTONEL® risedronate; as well as troxacitabine (a 1 ,3-dioxolane nucleoside cytosine analog); antisense oligonucleotides, particularly those that inhibit expression of genes in signaling pathways implicated in aberrant cell proliferation, such as, for example, PKC-alpha, Raf, H-Ras, and epidermal growth factor receptor (EGFR); vaccines such as THERATOPE® vaccine and gene therapy vaccines, for example, ALLOVECTIN® vaccine, LEUVECTIN® vaccine, and VAXID® vaccine; LURTOTECAN® topoisomerase 1 inhibitor; ABARELIX® rmRH; lapatinib ditosylate (an ErbB-2 and EGFR dual tyrosine kinase smallmolecule inhibitor also known as GW572016); and pharmaceutically acceptable salts or acids of any of the above. Chemotherapeutic agents also include antibodies such as alemtuzumab (Campath®), bevacizumab (AVASTIN®, Genentech); cetuximab (ERBITUX®, Imclone); panitumumab (VECTIBIX®, Amgen), rituximab (RITUXAN®, Genentech / Biogen Idee), pertuzumab (OMNITARG®, 2C4, Genentech), trastuzumab (HERCEPTIN®, Genentech), tositumomab (Bexxar®, Corixa), and the antibody drug conjugate, gemtuzumab ozogamicin (MYLOTARG®, Wyeth). Additional humanized monoclonal antibodies with therapeutic potential as agents in combination with the compounds of the invention include: apolizumab, aselizumab, atlizumab, bapineuzumab, bivatuzumab mertansine, cantuzumab mertansine, cedelizumab, certolizumab pegol, cidfusituzumab, cidtuzumab, daclizumab, eculizumab, efalizumab, epratuzumab, erlizumab, felvizumab, fontolizumab, gemtuzumab ozogamicin, inotuzumab ozogamicin, ipilimumab, labetuzumab, lintuzumab, matuzumab, mepolizumab, motavizumab, motovizumab, natalizumab, nimotuzumab, nolovizumab, numavizumab, ocrelizumab, omalizumab, palivizumab, pascolizumab, peefusituzumab, pectuzumab, pexelizumab, ralivizumab, ranibizumab, reslivizumab, reslizumab, resyvizumab, rovelizumab, ruplizumab, sibrotuzumab, siplizumab, sontuzumab, tacatuzumab tetraxetan, tadocizumab, talizumab, tefibazumab, tocilizumab, toralizumab, tucotuzumab celmoleukin, tucusituzumab, umavizumab, urtoxazumab, ustekinumab, visilizumab, and the antiinterleukin-12 (ABT-874 / J695, Wyeth Research and Abbott Laboratories), which is a recombinant exclusively human-sequence, full-length lgG1 A antibody genetically modified to recognize interleukin-12 p40 protein.

[0091] Chemotherapeutic agents also include “EGFR inhibitors,” which refers to compounds that bind to or otherwise interact directly with EGFR and prevent or reduce its signaling activity, and is alternatively referred to as an “EGFR antagonist.” Examples of such agents include antibodies and small molecules that bind to EGFR. Examples of antibodies which bind to EGFR include MAb 579 (ATCC CRL HB 8506), MAb 455 (ATCC CRL HB8507), MAb 225 (ATCC CRL 8508), MAb 528 (ATCC CRL 8509) (see, US Patent No. 4,943, 533, Mendelsohn et al.) and variants thereof, such as chimerized 225 (C225 or Cetuximab; ERBUTIX®) and reshaped human 225 (H225) (see, WO 96 / 40210, Imclone Systems Inc.); IMC-11 F8, a fully human, EGFR-targeted antibody (Imclone); antibodies that bind type II mutant EGFR (US Patent No. 5,212,290); humanized and chimeric antibodies that bind EGFR as described in US Patent No. 5,891 ,996; and human antibodies that bind EGFR, such as ABX-EGF or Panitumumab (see WO98 / 50433, Abgenix / Amgen); EMD 55900 (Stragliotto et al. Eur. J. Cancer 32 A :636-640 (1996)); EMD7200 (matuzumab) a humanized EGFR antibody directed against EGFR that competes with both EGF and TGF-alpha for EGFR binding (EMD / Merck); human EGFR antibody, HuMax-EGFR (GenMab); fully human antibodies known as E1 .1 , E2.4, E2.5, E6.2, E6.4, E2.11 , E6.3, and E7.6.3 and described in US 6,235,883; MDX-447 (Medarex Inc); and mAb 806 or humanized mAb 806 (Johns et al., J. Biol. Chem. 279(29) :30375-30384 (2004)). The anti-EGFR antibody may be conjugated with a cytotoxic agent, thus generating an immunoconjugate (see, e.g., EP 659,439A2, Merck Patent GmbH). EGFR antagonists include small molecules such as compounds described in US Patent Nos.: 5,616,582, 5,457,105, 5,475,001 , 5,654,307, 5,679,683, 6,084,095, 6,265,410, 6,455,534, 6,521 ,620, 6,596,726, 6,713,484, 5,770,599, 6,140,332, 5,866,572, 6,399,602, 6,344,459, 6,602,863, 6,391 ,874, 6,344,455, 5,760,041 , 6,002,008, and 5,747,498, as well as the following PCT publications: WO 98 / 14451 , WO 98 / 50038, WO 99 / 09016, and WO 99 / 24037. Particular small molecule EGFR antagonists include OSI- 774 (CP-358774, erlotinib, TARCEVA® Genentech / OSI Pharmaceuticals); PD 183805 (Cl 1033, 2- propenamide, N-[4-[(3-chloro-4-fluorophenyl)amino]-7-[3-(4-morpholinyl)propoxy]-6-quinazolinyl]-, dihydrochloride, Pfizer Inc.); ZD1839, gefitinib (IRESSA®) 4-(3’-Chloro-4’-fluoroanilino)-7-methoxy-6-(3- morpholinopropoxy)quinazoline, AstraZeneca); ZM 105180 ((6-amino-4-(3-methylphenyl-amino)- quinazoline, Zeneca); BIBX-1382 (N8-(3-chloro-4-fluoro-phenyl)-N2-(1 -methyl-piperidin-4-yl)-pyrimido[5,4- d]pyrimidine-2,8-diamine, Boehringer Ingelheim); PKI-166 ((R)-4-[4-[(1 -phenylethyl)amino]-1 H-pyrrolo[2,3- d]pyrimidin-6-yl]-phenol); (R)-6-(4-hydroxyphenyl)-4-[(1 -phenylethyl)amino]-7H-pyrrolo[2,3-d]pyrimidine); CL-387785 (N-[4-[(3-bromophenyl)amino]-6-quinazolinyl]-2-butynamide); EKB-569 (N-[4-[(3-chloro-4- fluorophenyl)amino]-3-cyano-7-ethoxy-6-quinolinyl]-4-(dimethylamino)-2-butenamide) (Wyeth); AG1478 (Pfizer); AG1571 (SU 5271 ; Pfizer); and dual EGFR / HER2 tyrosine kinase inhibitors such as lapatinib (TYKERB®, GSK572016 or N-[3-chloro-4-[(3 fluorophenyl)methoxy]phenyl]- 6[5[[[2methylsulfonyl)ethyl]amino]methyl]-2-furanyl]-4-quinazolinamine).

[0092] Chemotherapeutic agents also include “tyrosine kinase inhibitors” including the EGFR-targeted drugs noted in the preceding paragraph; small molecule HER2 tyrosine kinase inhibitors such as TAK165 available from Takeda; CP-724,714, an oral selective inhibitor of the ErbB2 receptor tyrosine kinase (Pfizer and OSI); dual-HER inhibitors such as EKB-569 (available from Wyeth) which preferentially binds EGFR but inhibits both HER2 and EGFR-overexpressing cells; lapatinib (GSK572016; available from Glaxo-SmithKline), an oral HER2 and EGFR tyrosine kinase inhibitor; PKI-166 (available from Novartis); pan-HER inhibitors such as canertinib (CI-1033; Pharmacia); Raf-1 inhibitors such as antisense agent ISIS-5132 available from ISIS Pharmaceuticals which inhibit Raf-1 signaling; non-HER targeted TK inhibitors such as imatinib mesylate (GLEEVEC®, available from Glaxo SmithKline); multi-targeted tyrosine kinase inhibitors such as sunitinib (SUTENT®, available from Pfizer); VEGF receptor tyrosine kinase inhibitors such as vatalanib (PTK787 / ZK222584, available from Novartis / Schering AG); MAPK extracellular regulated kinase I inhibitor CI-1040 (available from Pharmacia); quinazolines, such as PD 153035 and 4-(3-chloroanilino)quinazoline; pyridopyrimidines; pyrimidopyrimidines; pyrrolopyrimidines, such as CGP 59326, CGP 60261 and CGP 62706; pyrazolopyrimidines; 4-(phenylamino)-7H-pyrrolo[2,3- d]pyrimidines; curcumin (diferuloylmethane); 4,5-bis(4-fluoroanilino)phthalimide; tyrphostins containing nitrothiophene moieties; PD-0183805 (Warner-Lamber); antisense molecules (e.g., those that bind to HER-encoding nucleic acid); quinoxalines (US Patent No. 5,804,396); tyrphostins (US Patent No. 5,804,396); ZD6474 (Astra Zeneca); PTK-787 (Novartis / Schering AG); pan-HER inhibitors such as CI- 1033 (Pfizer); Affinitac™ (ISIS 3521 ; Isis / Lilly); imatinib mesylate (GLEEVEC®); PKI 166 (Novartis); GW2016 (Glaxo SmithKline); CI-1033 (Pfizer); EKB-569 (Wyeth); semaxinib (Pfizer); ZD6474 (AstraZeneca); PTK-787 (Novartis / Schering AG); INC-1 C11 (Imclone), rapamycin (sirolimus, RAPAMUNE®); or as described in any of the following patent publications: US Patent No. 5,804,396; WO 1999 / 09016 (American Cyanamid); WO 1998 / 43960 (American Cyanamid); WO 1997 / 38983 (Warner Lambert); WO 1999 / 06378 (Warner Lambert); WO 1999 / 06396 (Warner Lambert); WO 1996 / 30347 (Pfizer, Inc); WO 1996 / 33978 (Zeneca); WO 1996 / 3397 (Zeneca) and WO 1996 / 33980 (Zeneca).

[0093] Chemotherapeutic agents also include dexamethasone, interferons, colchicine, metoprine, cyclosporine, amphotericin, metronidazole, alemtuzumab, alitretinoin, allopurinol, amifostine, arsenic trioxide, asparaginase, BCG live, bevacizumab, bexarotene, cladribine, clofarabine, darbepoetin alfa, denileukin, dexrazoxane, epoetin alfa, elotinib, filgrastim, histrelin acetate, ibritumomab, interferon alfa- 2a, interferon alfa-2b, lenalidomide, levamisole, mesna, methoxsalen, nandrolone, nelarabine, nofetumomab, oprelvekin, palifermin, pamidronate, pegademase, pegaspargase, pegfilgrastim, pemetrexed disodium, plicamycin, porfimer sodium, quinacrine, rasburicase, sargramostim, temozolomide, VM-26, 6-TG, toremifene, tretinoin, ATRA, valrubicin, zoledronate, and zoledronic acid, and pharmaceutically acceptable salts thereof.

[0094] Chemotherapeutic agents also include hydrocortisone, hydrocortisone acetate, cortisone acetate, tixocortol pivalate, triamcinolone acetonide, triamcinolone alcohol, mometasone, amcinonide, budesonide, desonide, fluocinonide, fluocinolone acetonide, betamethasone, betamethasone sodium phosphate, dexamethasone, dexamethasone sodium phosphate, fluocortolone, hydrocortisone-17- butyrate, hydrocortisone-17-valerate, aclometasone dipropionate, betamethasone valerate, betamethasone dipropionate, prednicarbate, clobetasone-17-butyrate, clobetasol-17-propionate, fluocortolone caproate, fluocortolone pivalate and fluprednidene acetate; immune selective antiinflammatory peptides (ImSAIDs) such as phenylalanine-glutamine-glycine (FEG) and its D-isomeric form (feG) (IMULAN BioTherapeutics, LLC); anti-rheumatic drugs such as azathioprine, ciclosporin (cyclosporine A), D-penicillamine, gold salts, hydroxychloroquine, leflunomideminocycline, sulfasalazine, tumor necrosis factor alpha (TNFa) blockers such as etanercept (ENBREL®), infliximab (REMICADE®), adalimumab (HUMIRA®), certolizumab pegol (CIMZIA®), golimumab (SIMPONI®), Interleukin 1 (IL-1 ) blockers such as anakinra (KINERET®), T-cell co-stimulation blockers such as abatacept (ORENCIA®), Interleukin 6 (IL-6) blockers such as tocilizumab (ACTEMERA®); Interleukin 13 (IL-13) blockers such as lebrikizumab; Interferon alpha (IFN) blockers such as rontalizumab; beta 7 integrin blockers such as rhuMAb Beta7; IgE pathway blockers such as Anti-M1 prime; secreted homotrimeric LTa3 and membrane bound heterotrimer LTa1 / p2 blockers such as anti-lymphotoxin alpha (LTa); miscellaneous investigational agents such as thioplatin, PS-341 , phenylbutyrate, ET-18-OCH3, and farnesyl transferase inhibitors (L- 739749, L-744832); polyphenols such as quercetin, resveratrol, piceatannol, epigallocatechine gallate, theaflavins, flavanols, procyanidins, betulinic acid; autophagy inhibitors such as chloroquine; delta-9- tetrahydrocannabinol (dronabinol, MARINOL®); beta-lapachone; lapachol; colchicines; betulinic acid; acetylcamptothecin, scopolectin, and 9-aminocamptothecin); podophyllotoxin; tegafur (UFTORAL®); bexarotene (TARGRETIN®); bisphosphonates such as clodronate (for example, BONEFOS® or OSTAC®), etidronate (DIDROCAL®), NE-58095, zoledronic acid / zoledronate (ZOMETA®), alendronate (FOSAMAX®), pamidronate (AREDIA®), tiludronate (SKELID®), or risedronate (ACTONEL®); epidermal growth factor receptor (EGF-R); vaccines such as THERATOPE® vaccine; perifosine; COX-2 inhibitors (e.g., celecoxib or etoricoxib); proteosome inhibitors (e.g., PS341 ); CCI-779; tipifarnib (R11577); sorafenib; ABT510; Bcl-2 inhibitors such as oblimersen sodium (GENASENSE®); pixantrone; farnesyltransferase inhibitors such as lonafarnib (SCH 6636, SARASAR™); and pharmaceutically acceptable salts or acids of any of the above; as well as combinations of two or more of the above.

[0095] The term “prodrug” as used herein refers to a precursor form of a pharmaceutically active substance that is less cytotoxic to tumor cells compared to the parent drug and is capable of being enzymatically activated or converted into the more active parent form. See, for example, Wilman, “Prodrugs in Cancer Chemotherapy” Biochemical Society Transactions, 14, pp. 375-382, 615th Meeting Belfast (1986) and Stella et al., “Prodrugs: A Chemical Approach to Targeted Drug Delivery,” Directed Drug Delivery, Borchardt et al., (ed.), pp. 247-267, Humana Press (1985). The prodrugs of this invention include, but are not limited to, phosphate-containing prodrugs, thiophosphate-containing prodrugs, sulfate-containing prodrugs, peptide-containing prodrugs, D-amino acid-modified prodrugs, glycosylated prodrugs, p-lactam-containing prodrugs, optionally substituted phenoxyacetamide-containing prodrugs or optionally substituted phenylacetamide-containing prodrugs, 5-fluorocytosine and other 5-fluorouridine prodrugs which can be converted into the more active cytotoxic free drug. Examples of cytotoxic drugs that can be derivatized into a prodrug form for use in this invention include, but are not limited to, those chemotherapeutic agents described above.

[0096] A “growth inhibitory agent” when used herein refers to a compound or composition which inhibits growth and / or proliferation of a cell (e.g., a cell whose growth is dependent on MAPK pathway signaling) either in vitro or in vivo. Thus, the growth inhibitory agent may be one which significantly reduces the percentage of cells in S phase. Examples of growth inhibitory agents include agents that block cell cycle progression (at a place other than S phase), such as agents that induce G1 arrest and M-phase arrest. Classical M-phase blockers include the vincas (vincristine and vinblastine), taxanes, and topoisomerase II inhibitors such as the anthracycline antibiotic doxorubicin ((8S-cis)-10-[(3-amino-2,3,6-trideoxy-a-L-lyxo- hexapyranosyl)oxy]-7,8,9,10-tetrahydro-6,8,11 -trihydroxy-8-(hydroxyacetyl)-1 -methoxy-5,12- naphthacenedione), epirubicin, daunorubicin, etoposide, and bleomycin. Those agents that arrest G1 also spill over into S-phase arrest, for example, DNA alkylating agents such as tamoxifen, prednisone, dacarbazine, mechlorethamine, cisplatin, methotrexate, 5-fluorouracil, and ara-C. Further information can be found in “The Molecular Basis of Cancer," Mendelsohn and Israel, eds., Chapter 1 , entitled “Cell cycle regulation, oncogenes, and antineoplastic drugs” by Murakami et al. (WB Saunders: Philadelphia, 1995), especially p. 13. The taxanes (paclitaxel and docetaxel) are anticancer drugs both derived from the yew tree. Docetaxel (TAXOTERE®, Rhone-Poulenc Rorer), derived from the European yew, is a semisynthetic analogue of paclitaxel (TAXOL®, Bristol-Myers Squibb). Paclitaxel and docetaxel promote the assembly of microtubules from tubulin dimers and stabilize microtubules by preventing depolymerization, which results in the inhibition of mitosis in cells.

[0097] By “radiation therapy” is meant the use of directed gamma rays or beta rays to induce sufficient damage to a cell so as to limit its ability to function normally or to destroy the cell altogether. It will be appreciated that there will be many ways known in the art to determine the dosage and duration of treatment. Typical treatments are given as a one-time administration and typical dosages range from 10 to 200 units (Grays) per day.

[0098] As used herein, “administering” means a method of giving a dosage of a compound (e.g., an inhibitor or antagonist) or a pharmaceutical composition (e.g., a pharmaceutical composition including an inhibitor or antagonist) to a subject (e.g., a patient). Administering can be by any suitable means, including parenteral, intrapulmonary, and intranasal, and, if desired for local treatment, intralesional administration. Parenteral infusions include, for example, intramuscular, intravenous, intraarterial, intraperitoneal, or subcutaneous administration. Dosing can be by any suitable route, e.g., by injections, such as intravenous or subcutaneous injections, depending in part on whether the administration is brief or chronic. Various dosing schedules including but not limited to single or multiple administrations over various time-points, bolus administration, and pulse infusion are contemplated herein.

[0099] The term “co-administered” is used herein to refer to administration of two or more therapeutic agents, where at least part of the administration overlaps in time. Accordingly, concurrent administration includes a dosing regimen when the administration of one or more agent(s) continues after discontinuing the administration of one or more other agent(s).

[0100] By “reduce or inhibit” is meant the ability to cause an overall decrease of 20%, 30%, 40%, 50%, 60%, 70%, 75%, 80%, 85%, 90%, 95%, or greater. Reduce or inhibit can refer, for example, to the level of activity and / or function of a protein in the EGFR / MAPK or MAPK signaling pathway (e.g., RAF and / or MEK). Additionally, reduce or inhibit can refer, for example, to the symptoms of the disorder (e.g., cancer) being treated, the presence or size of metastases, or the size of the primary tumor.

[0101] The term “package insert” is used to refer to instructions customarily included in commercial packages of therapeutic products, that contain information about the indications, usage, dosage, administration, combination therapy, contraindications, and / or warnings concerning the use of such therapeutic products.

[0102] An “article of manufacture” is any manufacture (e.g., a package or container) or kit comprising at least one reagent, e.g., a medicament for treatment of a disease or disorder (e.g., cancer), or a probe for specifically detecting a biomarker (e.g., a BRAF V600E mutation or an NRAS Q61 hotspot mutation) described herein. In certain embodiments, the manufacture or kit is promoted, distributed, or sold as a unit for performing the methods described herein.

[0103] The term “second generation MAPK Adaptive Resistance Model” or “MARM 2.0” refers to a model of the EGFR / MAPK signaling pathway. MARM2.0 has 17 distinct molecular species: 11 proteins, three mRNA species and three small molecule inhibitor classes. Proteins include EGFR, BRAF, CRAF, MEK and ERK, the dual specificity phosphatase DUSP, guanine nucleotide exchange factor SOS1 , GTPase RAS, E3 ubiquitin ligase CBL, adaptor protein GRB2, and RTK negative regulator SPRY. EGF, RAFi, panRAFi and MEKi. Additionally, optional kinetic and energetic parameters include inhibitors that correspond to any of 10 different small molecules that are used as human therapeutics or pre-clinical tools. These include the RAFi compounds vemurafenib, dabrafenib, PLX8394, the panRAFi (Box 2) compounds LY3009120 and AZ628, and MEKi compounds cobimetinib, trametinib, selumetinib, binimetinib and PD0325901 . MARM 2.0 is additionally described in Frohlich et al., Molecular Systems Biology. e10988, 2023.

[0104] The term “BioNetGen 2.2” refers to an open-source software package for rule-based modeling of complex biochemical systems. See Harris et al., Bioinformatics. 32(21 ):3366-3368, 2016.

[0105] The term “Bliss score” refers to scoring of the synergistic effects, e.g., of two therapeutic agents administered in combination, as determined using a Bliss independence dose-response surface model. The term “excess over Bliss” or “Bliss excess” refers to the percent excess of the Bliss score prediction using the average response measures at each combination dose. In some instances, the percent excess is expressed as a decimal (e.g., between 0 and ±1 ). III. Methods

[0106] A. Methods for Determining Dosage i. In vitro methods

[0107] In one aspect, a method is provided for determining one or more in vitro combination dosages each comprising a first in vitro dosage of a first therapeutic agent and a second in vitro dosage of a second therapeutic agent for inhibiting growth or inducing cell death of a cancer cell line comprising a cancer, wherein the method includes (a) administering a dilution matrix comprising a first dilution series of the first therapeutic agent and a second dilution series of the second therapeutic agent to the cancer cell line; and (b) determining an excess over bliss score (bliss excess) for each element of the dilution matrix based on a growth inhibition assay or cytotoxicity assay, wherein the one or more in vitro combination dosages are the elements of the dilution matrix having a positive bliss excess.

[0108] In some instances, the positive bliss excess is from 0.2 to 1 (e.g., from 0.3 to 1 , from 0.4 to 1 , from 0.5 to 1 , from 0.6 to 1 , from 0.7 to 1 , from 0.8 to 1 , from 0.9 to 1 , from 0.3 to 0.5, from 0.3 to 0.7, from 0.5 to 7, from 0.4 to 0.8, from 0.6 to 0.8, from 0.7 to 0.9, or from 0.6 to 0.; e.g., about 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, or 1 ). In some instances, the positive bliss excess is from 0.5 to 1 . In some instances, the positive bliss excess is from 0.7 to 1 .

[0109] In some instances, the bliss excess is determined from steady state dose-responses determined for each element of the dilution matrix. In some instances, the steady state dose-responses are determined using a set of ordinary differential equations (ODEs). In some instances, the set of ODEs are generated using BioNetGen 2.2. In some instances, the set of ODEs are generated using a model of a biological pathway comprising the cancer, the first therapeutic agent, and the second therapeutic agent. In some instances, the biological pathway is an epidermal growth factor receptor (EGFR) / mitogen- activated protein kinase (MAPK) signaling pathway. In some instances, the biological pathway is a MAPK signaling pathway. In some instances, model is a second-generation MAPK Adaptive Resistance Model (MARM2.0). In some instances, the steady state dose-responses are when the relative change of all species in the set of ODEs is less than 0.1% (e.g., less than 0.05%, less than 0.01%, less than 0.005%, or less than 0.001%) over a period of at least 4 hours (e.g., 5, 6, 7, 8, 9, 10, 11 , 12 hours, or more).

[0110] In some instances, the first dilution series comprises 4 to 20 (e.g., 4, 5, 6, 7, 8, 9, 10, 11 , 12, 13, 14, 15, 16, 17, 18, 19, or 20) doses. In some instances, the first dilution series comprises 10 doses.

[0111] In some instances, the second dilution series comprises 4 to 20 (e.g., 4, 5, 6, 7, 8, 9, 10, 11 , 12, 13, 14, 15, 16, 17, 18, 19, or 20) doses. In some instances, the second dilution series comprises 10 doses.

[0112] In some instances, the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

[0113] In some instances, the skin cancer is melanoma.

[0114] In some instances, the cancer cell line comprises UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC-62, RVH-421 , SK-MEL- 24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA- MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39. In some instances, the cancer cell line is UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23- mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, CGLG800, COLO853, MEL- HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR- 1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0115] In some instances, the melanoma comprises a mutation of a biomarker gene. In some instances, the melanoma comprises a BRAF mutation or an NRAS mutation.

[0116] In some instances, the BRAF mutation is a V600E mutation. In some instances, the cancer cell line having a BRAF V600E mutation comprises WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242I, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39. In some instances, the cancer cell line having a BRAF V600E mutation is WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242I, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB- 435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0117] In some instances, the NRAS mutation is a Q61 hotspot mutation. In some instances, the cancer cell line having an NRAS Q61 hotspot mutation comprises SK-MEL-30, SK-MEL-2, MEL-JUSO, or Hs852.T. In some instances, the cancer cell line having an NRAS Q61 hotspot mutation is SK-MEL-30, SK-MEL-2, MEL-JUSO, or Hs852.T.

[0118] In some instances, the one or more in vitro combination dosages are determined using a growth inhibition assay.

[0119] In some instances, the one or more in vitro combination dosages are determined using a cytotoxicity assay.

[0120] In some instances, the first therapeutic agent comprises a small molecule inhibitor, a protein (e.g., a polypeptide, e.g., an antibody or an enzyme; e.g., a monospecific or bispecific antibody), a nucleic acid (e.g., a DNA or an RNA; e.g., an antisense oligonucleotide), or a chimeric antigen receptor (CAR)-T cell.

[0121] In some instances, the first therapeutic agent comprises a MEK inhibitor. In some instances, the first therapeutic agent comprises cobimetinib (CAS #: 934660-93-2) or a pharmaceutically acceptable salt thereof.

[0122] In some instances, the second therapeutic agent comprises a small molecule inhibitor, a protein (e.g., a polypeptide, e.g., an antibody or an enzyme), a nucleic acid (e.g., a DNA or an RNA), or a CAR-T cell.

[0123] In some instances, the second therapeutic agent comprises a panRAF inhibitor. In some instances, the second therapeutic agent comprises belvarafenib (CAS #: 14461 13-23-0) or a pharmaceutically acceptable salt thereof. ii. In vivo methods

[0124] In one aspect, a method is provided for determining one or more combination in vivo dosages each comprising a first in vivo dosage of a first therapeutic agent and a second in vivo dosage of a second therapeutic agent for treating a cancer comprising converting the one or more in vitro combination dosages determined in according to any of the methods described herein to the one or more combination in vivo dosages based on the plasma free drug concentrations of the first therapeutic agent administered according to a dilution series to a subject and the plasma free drug concentrations of the second therapeutic agent administered according to a dilution series to a subject.

[0125] In some instances, the subject is a mouse or a human.

[0126] In some instances, the method includes administering the first or second therapeutic agent according to a dilution series to the subject or a population of the subjects and determining the plasma free drug concentration in the subject or the population of subjects at each dilution in the series to determine the plasma free drug concentration that corresponds to each administered in vivo dosage (i.e., each dilution of the dilution series). Determination of the in vivo dosage corresponding to each in vitro dosage comprises matching the plasma free drug concentration (e.g., corresponding to each in vivo dosage) to the closest in vitro dosage. iii. Drug combination screen

[0127] In one aspect, a method is provided for determining one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib. In an exemplary method, the drugs are obtained via in-house synthesis or purchased from commercial vendors. A fully automated transfer system by Nova Technology (Innovate Engineering, 9 Merry Ln, East Hanover, NJ 07936, USA) is used to transfer the material from a dry library, solubilize them with DMSO, and then log the solutions into a compound management system. A high-throughput liquid chromatography mass spectrometry / ultraviolet absorbance / charged aerosol detector / chemiluminescent nitrogen detector (LCMS / UV / CAD / CLND) system is used to verify the identity, purity, and concentration of drugs used in the Genentech Cell Line Screening Initiative (gCSI) screens. The LCMS / UV / CAD / CLND system consists of an LCMS / UV system (Shimadzu, 7102 Riverwood Drive Columbia, MD 21046, USA) with an LC-30AD solvent pump, 2020 MS, a SH-30AC autosampler, an SP-M30A UV detector, and a CTO-20A column oven; a CORONA™ VEO™ RS CAD (Thermo Scientific, 168 Third Avenue. Waltham, MA 02451 , USA); and a model 8060 CLND. Drugs with lower than 80% purity and 20% below expected concentration are excluded. An ECHO® 555 acoustic drop ejection (ADE) liquid handler (Labcyte, 170 Rose Orchard Way San Jose, CA 95134, USA) is fully integrated in the ultra-high-throughput screening (uHTS) system to dispense DMSO solubilized compounds. Nine-point dose-response curves at 1 :3 dilution are generated using ADE as a means of transferring library compounds at ultra-low volume (in nanoliter scale) to achieve direct dilution of the compounds. The starting doses for Vemurafenib, Belvarafenib, and Cobimetinib are 10, 10, and 5 pM, respectively. The uHTS system delivers assay-ready daughter plates at a concentration of 31 ,000. A DMSO backfill step is performed to achieve an equal volume of DMSO in each well. Assay-ready drug plates are stored at -80 °C until the day of compound addition and subjected to a single freeze-thaw cycle. The use of ADE technology limits the final DMSO concentration in assay plates to 0.1%, which has a negligible effect on cell growth. Seeding densities are optimized for each cell line to obtain 70-80% confluence after 6 days. The cells are plated into 384-well plates (Greiner, Bad Haller Str. 32, 4550 Kremsmunster, Austria, 781091 ) and then treated with the compound the following day in a final DMSO concentration of 0.1%. The relative numbers of viable cells are measured by luminescence using CELLTITER-GLO® (Promega, 2800 Woods Hollow Road Madison, Wl 53711 , USA, G7573). iv. Higher drug dose resolution combination responses

[0128] In one aspect, a method is provided for assessing the response to one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib, with high drug-dose resolution. In an exemplary method, higher drug dose-resolved 10 x 10 drug combination responses are generated, which center around clinically relevant doses for 5 cell lines: A375, IPC-298, MEL-JUSO, SK- MEL-2, and SK-MEL-30. The seeding densities of the cells are optimized to obtain 70-80% confluence after 6 days. The cells are seeded into 384-well plates 24 hours prior to compound addition and treated with the compound the following day (final DMSO concentration of 0.1%). The compound stocks, 10 mM in DMSO, are supplied by Genentech Compound Management. Belvarafenib and Cobimetinib are dosed using an HP 300 automatic dose dispenser as a 10 x 10 combinatorial drug matrix with serial dose dilutions starting from 1 to 0.002 pM for Belvarafenib and 0.5 to 0.002 pM for Cobimetinib. After 120 hours, relative numbers of viable cells are measured using CELLTITER-GLO® (Promega, G7573). v. l / l / iesfern blots

[0129] In one aspect, a method is provided for assessing the response to one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib, by western blot analysis. In an exemplary method, anti-MEK1 (12671 , western blot (WB) 1 :1000), anti-pMEK (S217 / S221 ) rabbit monoclonal antibody (mAb) (41 G9) (9154, WB 1 :1000), anti-ERK (9107, WB 1 :1000), and anti-pERK (T202 / Y204) (9101 , WB 1 :1000) are purchased from Cell Signaling Technology (3 Trask Ln, Beverly, MA 01915, USA). Infrared (IR)-conjugated secondary antibodies, Goat anti-Mouse 680LT (926-68020, WB: 1 :10,000), and Goat anti-Rabbit 800CW (926-32211 , WB: 1 :10,000) are purchased from Li-Cor (4647 Superior St, Lincoln, NE 68504, USA). All Western blots are scanned on Li-Cor ODYSSEY® CLX using duplexed IR-conjugated secondary antibodies.

[0130] SK-MEL-28, A-375, and SK-MEL-2 cells are obtained from American Type Culture Collection (ATCC). IPC-298 and MEL-JUSO cells are obtained from Deutsche Sammlung von Mikroorganismen und Zellkulturen (DSMZ). The cell lines are maintained in the recommended media and supplemented with 10% heat-inactivated fetal bovine serum (FBS) (HyClone, 925 W 1800 S, Logan, UT 84321 , USA, SH3007003HI), 1 x GLUTAMAX™ (Gibco, 168 Third Avenue. Waltham, MA 02451 , USA, 35050-061 ), and 1 x Penicillin-Streptomycin (Gibco, 15140-122).

[0131] Immunoblotting is performed using standard methods. In an exemplary method, the cells are briefly washed in ice-cold phosphate buffered saline (PBS) and lysed in the following lysis buffer (1 % NP- 40, 50 mM Tris, pH 7.8, 150 mM NaCI, and 5 mM EDTA) plus a protease inhibitor mixture (COMPLETE™ mini tablets; Roche Applied Science, Grenzacherstrasse 124, 4058 Basel, Switzerland, 11836170001 ) and phosphatase inhibitor mix (ThermoFisher Scientific, 168 Third Avenue. Waltham, MA 02451 , USA, 78420). The lysates are centrifuged at 15,000 rpm for 10 min at 4 °C, and the protein concentration is determined by BCA (ThermoFisher Scientific, 23227). Equal amounts of protein are resolved by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) on NUPAGE™, 4-12% Bis-Tris Gels (ThermoFisher Scientific, WG-1403) and transferred to a nitrocellulose membrane (Bio-Rad, 1000 Alfred Nobel Dr, Hercules, CA 94547, USA, 170-4159). After blocking in a blocking buffer (Li-Cor, 927-40000), the membranes are incubated with the indicated primary antibodies and analyzed by the addition of secondary antibodies IRDYE® 680LT Goat anti-Mouse IgG (Li-Cor, 926-68050) or IRDYE® 800CW Goat anti-Rabbit IgG (Li-Cor, 926-3221 1 ). The membranes are visualized on a Li-Cor ODYSSEY® CLx Scanner. vi. Immunofluorescence and high-content imaging

[0132] In one aspect, a method is provided for assessing the response to one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib, by immunofluorescence followed by high-content imaging analysis. In an exemplary method, cells are washed twice with 1 x PBS and fixed with 4% paraformaldehyde (PFA) for 15 min at 25 °C. To remove PFA, the cells are washed with 1 x PBS three times, and PFA is quenched by incubating the cells with 50 mM NH4CI for 10 min at 25 °C. The cells are then rinsed twice with PBS and permeabilized with ice-cold methanol for 10 min at -20 °C. Following permeabilization, the cells are first incubated with a blocking buffer for 1 hour at room temperature (1 x PBS / 5% normal serum / 0.3% TRITON™ X-100), followed by overnight incubation with the primary antibody against phospho-ERK (Cell Signaling Technology, catalog no. 4370S) at 1 :800 dilution at 4 °C. The next day, the cells are washed three times with 1 x PBS and incubated for one hour at room temperature with the secondary antibody (Jackson ImmunoResearch Laboratories, 872 W Baltimore Pike, West Grove, PA 19390, USA, catalog no. 71 1 -606-152). To stain the nucleus and cell body, the cells are incubated with NUCBLUE™ Fixed Cell READYPROBES™ Reagent (catalog number: R37606) and HCS CELLMASK™ Blue Stain (catalog number: H32720) for 20 min at room temperature. Finally, the cells are washed three times with 1 x PBS and imaged on the Opera PHENIX™ high-content screening (HCS) machine (PerkinElmer, 710 Bridgeport Ave, Shelton, CT 06484, USA) using the 40x water immersion objective using confocal modality. Analysis and quantification are conducted on HARMONY™ (PerkinElmer) software. vii. Tumor volume experiments in xenografts

[0133] In one aspect, a method is provided for assessing the response to one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib, by measuring tumor volumes in mice treated with the therapeutic agents. In an exemplary method, G03083045.23-6 (free base of GDC-5573, Lot 23-6; hereafter referred to as Belvarafenib) is obtained as a solution at concentrations of 3.3 mg / mL and 6.6 mg / mL (expressed as free-base equivalents) in 5% dimethyl sulfide / 5% CREMOPHOR® EL. Cobimetinib (GDC-0973, Lot 150-10) is obtained as a solution at concentrations of 1 .1 mg / mL (expressed as free-base equivalents) in 0.5% (w / v) methylcellulose / 0.2% TWEEN® 80. All concentrations are calculated based on a mean body weight of 22 g for the NCr.nude mouse strain used in this method. The vehicle controls are 5% dimethyl sulfide / 5% CREMOPHOR®EL and 0.5% (w / v) methylcellulose / 0.2% TWEEN® 80. Test articles are stored in a refrigerator set to maintain a temperature range of 4-7 °C. All treatments and vehicle control dosing solutions are prepared once a week for three weeks.

[0134] Female NCr.nude mice that are 6-7 weeks old are obtained from Taconic Biosciences (New York, NY, USA), weighing an average of 22 g. The mice are housed at Genentech in standard rodent micro-isolator cages and are acclimated to the study conditions at least 3 days before tumor cell implantation. Only animals that appear to be healthy and that are free of obvious abnormalities are used for the method.

[0135] Human melanoma IPC-298 cells are obtained from the ATCC (Rockville, MD, USA), harboring NRAS Q61 L mutation. The cells are cultured in vitro, harvested in log-phase growth, and resuspended in Hank’s Balanced Salt Solution (HBSS) containing MATRIGEL® (BD Biosciences; San Jose, CA, USA) at a 1 :1 ratio. The cells are then implanted subcutaneously in the right lateral thorax of 140 NCr.nude mice. Each mouse is injected with 20 x 106cells in a volume of 100 mL. Tumors are monitored until they reached a mean tumor volume of 250-300 mm3. Mice are distributed into six groups based on tumor volume, with n = 10 mice per group. The mean tumor volume across all six groups is expected to be 240 mm3at the initiation of dosing.

[0136] Mice are given vehicles (100 pL 5% DMSO / 5% CREMOPHOR® EL (CremEL) and 100 pL 0.5% methylcellulose (MCT)), 15 mg / kg or 30 mg / kg Belvarafenib (expressed as free-base equivalents) and 5 mg / kg Cobimetinib (expressed as free-base equivalents). All treatments are administered on a daily basis (QD) orally (PO) by gavage for 21 days in a volume of 100 mL for Belvarafenib or Cobimetinib. Tumor sizes and mouse body weights are recorded twice weekly over the course of the study. Mice are promptly euthanized when tumor volume exceeded 2000 mm3or if body weight loss is >20% of their starting weight.

[0137] All drug concentrations are calculated based on a mean body weight of 22 g for the NCr.nude mouse strain used in this method. Tumor volumes are measured in two dimensions (length and width) using Ultra Cal-IV calipers (model 54-10-111 ; Fred V. Fowler Co.; Newton, MA, USA) and analyzed using Excel, version 14.2.5 (Microsoft Corporation; Redmond, WA, USA). The tumor volume is calculated with the following formula: tumor size (mm3) = (longer measurement x shorter measurement2) x 0.5. Animal body weights are measured using an ADVENTURER™ Pro AV812 scale (Ohaus Corporation; Pine Brook, NJ, USA). Percent weight change is calculated using the following formula: body weight change (%) = [(current body weight / initial body weight) - 1 ) x 100].

[0138] Percent animal weight is tracked for each individual animal while on study, and the percent change in body weight for each group is calculated and plotted. A generalized additive mixed model (GAMM) is employed to analyze the transformed tumor volumes over time. As tumors generally exhibit exponential growth, tumor volumes are subjected to natural log transformation before analysis. Changes in tumor volumes over time in each group are described by fits (i.e. , regression splines with autogenerated spline bases) generated using customized functions in R version 3.4.2 (28 September 2017) (R Development Core Team 2008; R Foundation for Statistical Computing; Vienna, Austria). For assessment of gene expression in harvested tumors, total RNA is extracted from xenograft tumor tissue using RNEASY® Plus Mini kits (Qiagen, Qiagen Str. 1 , 40724 Hilden, Germany) following the manufacturer’s instructions. RNA quantity is determined using a NANODROP™ spectrophotometer (Thermo Fisher Scientific). Transcriptional readouts are assessed using a Fluidigm BIOMARK™ HD System (Standard BioTools, 2 Tower PI Suite 2000, South San Francisco, CA 94080, USA) according to the manufacturer’s recommendations. RNA (100 ng) is subjected to cDNA synthesis and pre-amplification using the High-Capacity cDNA RT Kit and TAQMAN™ PreAmp Master Mix (Thermo Fisher Scientific) per the manufacturer’s protocol. Following amplification, the samples are diluted 1 :4 with Tris EDTA pH 8.0 and qPCR is conducted using a Fluidigm 96.96 DYNAMIC ARRAY™ and the Fluidigm BIOMARK™ HD System (Standard BioTools) according to the manufacturer’s recommendations. Cycle threshold (Ct) values are converted to fold changes or percentages in relative expression values (2~<AACt>) by subtracting the mean of the housekeeping reference genes from the mean of each target gene followed by subtraction of the mean vehicle ACt from the mean sample ACt.

[0139] Blood is harvested from mice treated for 4 days and 3 hours after the last dosing to quantify the free concentrations of drugs in plasma. For example, the concentration of Belvarafenib and Cobimetinib in each sample is determined using a non-validated LC-MS / MS method using labeled internal standards (Cobimetinib: 13C6, Belvarafenib: d5) with qualified curve ranges (Cobimetinib: 1 .00 to 100 ng / mL with 2000 ng / mL dilution quality control (QC), Belvarafenib: 5.00 to 5000 ng / mL with 75,000 ng / mL dilution QC) using specific columns (Cobimetinib: WATERS™ Xbridge C18, 50 x 2.1 mm, 3.5 urn, Belvarafenib: Phenomenex ONYX™ Monolithic C18, 50 x 2.0 mm) and MS / MS transition ranges (Cobimetinib: 532.2- 249.1 , Belvarafenib: 479.1-328.0, 13C6 Cobimetinib: 538.2-255.1 , Belvarafenib-d5: 484.1-333.1 ). The lower limit of quantitation (LLOQ) is expected to be 1 .00 ng / mL for Cobimetinib and 5.00 ng / mL for Belvarafenib. Free plasma concentrations are calculated by multiplying the plasma concentration in each sample with the fraction unbound in plasma. viii. Computational dynamic modeling of MAPK signaling

[0140] In one aspect, a method is provided for dynamically modeling MAPK signaling in response to one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib. In an exemplary method, the MARM2 model is written in the PySB framework and describes interactions of the EGFR / MAPK signaling pathway. The model, along with relevant parameters, trained on a range of conditions with MEK and RAF inhibitors, is obtained from Frohlich, F. and Gerosa, L. et al. A curation step is performed wherein unnecessary species and their associated model components are removed. The pan-RAF inhibitor Belvarafenib is implemented by setting ep_RAF_RAF_mod_RAFi_double_ddG = 0, removing the reduction in binding affinity of a type 1 .5 RAF inhibitor (Vemurafenib) to a partially inhibited RAF dimer. For NRAS Q61 mutants, the hydrolysis rate of NRAS GTP, catalyze_NF1_RAS_gdp_kcatr, is reduced by a factor of 10, and the stability of CRAF dimers, ep_RAF_RAF_mod_RASgtp_double_ddG, is reduced by a factor of 5. Furthermore, since CRAF is the dominant RAF species in NRAS Q61 , BRAF is removed in order to greatly reduce the model size and computation times. The reduced tendency for phosphorylated CRAF to bind to RAS and form dimers is an important negative feedback mechanism, which is referred to as pRAF feedback. To better understand the impacts of this feedback, an extra NRAS Q61 model is generated with the feedback removed. Through this process, three models are obtained: BRAF V600E, NRAS Q61 with pRAF feedback, and NRAS Q61 without pRAF feedback.

[0141] Each model is converted to a set of ordinary differential equations (ODEs) using BioNetGen (BNG) and then simulated until a steady state is reached. The steady state is achieved when the relative change in all species is less than 0.1% over a period of at least 4 hours. For the steady-state doseresponses, 100 inhibitor dose conditions are generated from 10 Cobimetinib doses (0 pM and 9 doses from 10-2.75 pM to 100 pM) and 10 Belvarafenib doses (0 pM and 9 doses from 10-2.25 pM to 100.5 pM). The initial steady-state system is subjected to one of these dose conditions and then simulated until the steady state is reached. The full simulation times for all conditions are expected to be as follows: BRAF V600E — 475 s, NRAS Q61 without pRAF feedback — 474 s, and NRAS Q61 with pRAF feedback — 330 s. Bliss values are then generated from the steady-state values using the synergy Python library. For the time course responses, the initial steady-state system is simulated for 24 hours and then dosed with Cobimetinib (0.5 pM) and either 0 or 133 nM of Belvarafenib. The system is then simulated for 8 additional hours. The full simulation times are expected to be as follows: NRAS Q61 without pRAF feedback — 32 s, NRAS Q61 with pRAF feedback — 32 s, and BRAF V600E — 27 s. ix. Analysis of drug dose-responses

[0142] In one aspect, a method is provided for analyzing the dose-response of one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib. In an exemplary method, cell viability data are processed to relative viability to obtain single-agent fits and metrics (e.g., IC50, maximum effect (Emax), and area under curve (AUC)), as well as drug combination fits and metrics such as highest single agent (HSA) and Bliss scores. For example, single-agent fits for each drug and cell line are obtained using the drm fitting function from the drc R package using a three-parameter (LL.3u) or a four-parameter (LL.4) log-logistic function that relates drug dose to relative viability. For drug combination data, HSA and Bliss scores are calculated as the average of the 10% highest HSA and Bliss excess values observed across the full dose ranges tested, respectively. HSA and Bliss excess values for each dose combination tested are calculated by subtracting the observed response against the expected response under the HSA and Bliss models. As an observed response, a smoothened version of the experimental drug combination matrix of relative viability obtained by fitting dose-response curves along every fixed dose of each drug and averaging the fitted values is used. The HSA expectation matrix is calculated by selecting for each dose combination the maximum response of each individual agent in the observed response. The Bliss expectation is calculated using the Bliss independence formula given as the sum of the responses of the individual drugs minus their product. Data import, processing, and calculations are performed using the R package gDR. x. Projection of in vivo free drug concentrations on in vitro growth responses

[0143] In one aspect, a method is provided for projecting the in vivo free drug concentrations of one or more therapeutic agents, such as cobimetinib and belvarafenib, on in vitro growth responses of tumors to the therapeutic agents. In an exemplary method, nominal drug concentrations associated with growth viability responses are converted to free drug concentrations in order to project the free drug concentrations measured in vivo in mice or patients. For example, nominal drug concentrations are multiplied by the fraction unbound (fu) of Belvarafenib and Cobimetinib, which is expected to be 0.034 in 10% FBS media and estimated to be 0.068 in 5% FBS media for Belvarafenib and expected to be 0.196 in 10% FBS media and 0.3 in 5% FBS media for Cobimetinib. To estimate the viability of responses or Bliss excess values at corresponding in vivo free drug doses, the matrix with corresponding dose-matrix responses with units converted to free drug concentrations is interpolated using the function interp2 from the pracma R package. xi. Prediction of tumor growth inhibition in xenografts

[0144] In one aspect, a method is provided for predicting the tumor growth rate inhibition (GR) metric in mice with xenografts treated with one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib. In an exemplary method, the GR metric is calculated from the relative viability of IPC-298 cells treated with a combination of Belvarafenib and Cobimetinib by setting an experimentally measured untreated doubling time of 60 hours using the gDR package. The resulting GR metric is converted to control-normalized growth rates, i.e. , the growth rate of treated cells divided by the growth rate of the control cells. The growth rate of the control-treated IPC-298 xenograft tumors is calculated using the doubling time of 18 days estimated from measured tumor volumes to be 0.0385 day-1. Using free drug concentrations measured in mice for Belvarafenib and Cobimetinib, corresponding control-normalized growth rates are estimated from the in vitro matrix dose-response. The control- normalized growth rates are multiplied by the baseline tumor growth to predict the growth rate achieved by tumors at any given dosing regimen. The obtained growth rates are used in an exponential growth model to simulate tumor volumes in time and compared to experimental data. xi i. Pharmacokinetic (PK) modeling of drug concentrations in patients

[0145] In one aspect, a method is provided for modeling the concentrations of one or more therapeutic agents, such as cobimetinib and belvarafenib, in patients treated with one or more combination dosages for the one or more therapeutic agents. In an exemplary method, synthetic PK profiles are generated for Belvarafenib and Cobimetinib, which recapitulate the population level PK variability expected for each respective compound. For each compound, 500 synthetic PK profiles are generated at each of the following dosing regimens (Belva: 50 mg QD, 100 mg twice daily (BID), 200 mg BID, and 400 mg BID; Cobi: 20 mg once every other day (QOD), 20 mg QD, 40 mg QD, and 60 mg QD). These simulations are performed in R 4.1 .1 using mrgsolve based on the published population PK (popPK) model for Cobimetinib and a popPK model developed on the available individual time-concentration profiles from n = 243 patients treated with Belvarafenib in clinical trial reference Nos. NCT03118817, NCT02405065, and NCT03284502. Both models are developed using the non-linear mixed effects approach as implemented in NONMEM. Simulations are conducted until steady state, after which the drug levels are recorded for use. In particular, of the 30 days of simulation, days 22-26 are saved for analysis, providing at least two complete cycles of drug concentrations for each condition. Simulated plasma total drug concentrations in ng / mL are divided by the corresponding molecular weight (Belvarafenib = 478.93 g / mol, Cobimetinib = 531 .3 g / mol) to obtain total drug concentrations in gM. These are multiplied by the fraction unbound in plasma measured at 0.00258 for Belvarafenib and 0.052 for Cobimetinib. xiii. Clinical tumor growth simulations

[0146] In one aspect, a method is provided for simulating clinical tumor growth in response to one or more combination dosages for one or more therapeutic agents, such as cobimetinib and belvarafenib. In an exemplary method, a clinical tumor growth inhibition (TGI) model is used to describe the tumor dynamics of patients treated in clinical trial reference Nos. NCT031 18817 and NCT03284502. This model is developed using the population approach as implemented in NONMEM version 7.5.0. The model that best described the observed tumor dynamics is a biexponential growth model. In this model, tumor dynamics evolve from an estimated initial tumor size TSo, with key treatment-related parameters describing the tumor growth rate constant (KG) (1 / week) and tumor shrinkage rate constants (KS) (1 / week). Individual empirical Bayesian estimates (EBEs) for KG and KS are summarized in melanoma patients and stratified by mutational status. Model-based tumor dynamics are simulated for 1 year for each of these groups based on the mean KG and KS for the group given the same TSo = 50.

[0147] B. Treatment Methods

[0148] The present invention provides methods for an individual, e.g., having a cancer, by administering to the individual a first therapeutic agent and a second therapeutic agent according to any one of the one or more combination in vivo dosages determined in any of the methods described herein.

[0149] In some instances, the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

[0150] In some instances, the skin cancer is melanoma.

[0151] In some instances, the cancer cell line comprises UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC-62, RVH-421 , SK-MEL- 24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, CGLG800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA- MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39. In some instances, the cancer cell line is UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23- mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL- HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR- 1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0152] In some instances, the melanoma comprises a mutation of a biomarker gene. In some instances, the melanoma comprises a BRAF mutation or an NRAS mutation. In some instances, the BRAF mutation is a V600E mutation. In some instances, the NRAS mutation is a Q61 hotspot mutation. Administration

[0153] Treatment according to any of the methods described herein (e.g., administering a first therapeutic agent and a second therapeutic agent according to any one of the one or more combination in vivo dosages determined in any of the methods described herein) may result in, for example, a reduction in tumor size or an increase in progression-free survival (PFS) and / or overall survival (OS) in an individual administered the treatment. In some instances, administration of the first and second therapeutic agents (e.g., a pan-RAF inhibitor (e.g., a pan-RAF dimer inhibitor) and a MEK inhibitor; e.g., cobimetinib and belvarafenib) according to the optimized in vivo dosages results in a synergistic (or greater than additive) therapeutic benefit to the individual.

[0154] A composition comprising a first and second therapeutic agent (e.g., a pan-RAF inhibitor and a MEK inhibitor) will be formulated and administered in a fashion consistent with good medical practice. Factors for consideration in this context include the particular type of cancer being treated (e.g., a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer), the particular mammal being treated (e.g., human), the clinical condition of the individual patient, the cause of the cancer, the site of delivery of the agent, possible side-effects, the type of inhibitor, the method of administration, the scheduling of administration, and other factors known to medical practitioners. The effective amount of the first and second therapeutic agents (e.g., pan-RAF inhibitor and MEK inhibitor) to be administered will be governed by such considerations.

[0155] Treatment with a first and second therapeutic agent (e.g., a pan-RAF inhibitor and a MEK inhibitor), or pharmaceutically acceptable salts thereof, can be carried out according to standard methods. For example, exemplary methods for administration of the MEK inhibitor, cobimetinib (e.g., cobimetinib fumarate (COTELLIC®)), are described in Prescribing Information for cobimetinib fumarate (COTELLIC®) in the United States, Genentech, Inc. (November 10, 2015), which is incorporated herein by reference in its entirety.

[0156] If multiple exposures of a first and second therapeutic agent (e.g., a pan-RAF inhibitor and a MEK inhibitor) are provided, each exposure may be provided using the same or a different administration means. In one embodiment, each exposure is given by oral administration. In one embodiment, each exposure is by intravenous administration. In another embodiment, each exposure is given by subcutaneous administration. In yet another embodiment, the exposures are given by both intravenous and subcutaneous administration.

[0157] The duration of therapy can be continued for as long as medically indicated or until a desired therapeutic effect (e.g., those described herein) is achieved. In certain embodiments, the therapy is continued for 1 month, 2 months, 4 months, 6 months, 8 months, 10 months, 1 year, 2 years, 3 years, 4 years, 5 years, or for a period of years up to the lifetime of the subject. Routes of Administration

[0158] A first and second therapeutic agent (e.g., a pan-RAF inhibitor and a MEK inhibitor) may be formulated, dosed, and administered in a fashion consistent with good medical practice. Factors for consideration in this context include the cancer, the particular mammal being treated, the clinical condition of the individual patient, the cause of the disorder, the site of delivery of the agent, the method of administration, the scheduling of administration, and other factors known to medical practitioners. For example, a pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) need not be, but is optionally formulated with and / or administered concurrently with, a MEK inhibitor, optionally in further combination with one or more agents currently used to prevent or treat the disorder (e.g., cancer).

[0159] For the prevention or treatment of a cancer, the appropriate dosages of a pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor described herein (when used alone or in combination with one or more other additional therapeutic agents) will depend on the type of disease (e.g., cancer) to be treated, the severity and course of the disease, whether the inhibitors are administered for preventive or therapeutic purposes, previous therapy, the patient’s clinical history and response to the inhibitors, and the discretion of the attending physician. The pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor are suitably administered to the patient at one time or over a series of treatments. For repeated administrations over several days or longer, depending on the condition, the treatment would generally be sustained until a desired suppression of disease symptoms occurs. Such doses may be administered intermittently, e.g., every week or every three weeks (e.g., such that the patient receives, for example, from about two to about twenty, or e.g., about six doses of the pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor). An initial higher loading dose, followed by one or more lower doses may be administered. However, other dosage regimens may be useful. The progress of this therapy is easily monitored by conventional techniques and assays.

[0160] The pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor can be administered by any suitable means, including orally, parenteral, topical, subcutaneous, intraperitoneal, intrapulmonary, intranasal, and / or intralesional administration. Parenteral infusions include intramuscular, intravenous, intraarterial, intraperitoneal, or subcutaneous administration. Intrathecal administration is also contemplated. In addition, the pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor may suitably be administered by pulse infusion, e.g., with declining doses of one or both inhibitors. Optionally, the dosing is given by oral administration.

[0161] If multiple exposures of a pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) in combination with a MEK inhibitor are provided, each exposure may be provided using the same or a different administration means. In another embodiment, each exposure is given intravenously (i.v.). In another embodiment, each exposure is given by subcutaneous (s.c.) administration. In yet another embodiment, the exposures are given by both i.v. and s.c. administration.

[0162] Combination Therapy

[0163] The therapeutic methods described herein generally include administration of more than one therapeutic agent (e.g., a pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) in combination with a MEK inhibitor, e.g., belvarafenib and cobimetinib). In general, for the prevention or treatment of disease, the pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor are suitably administered to the patient at one time or over a series of treatments. The pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor) and MEK inhibitor are administered according to the optimized in vivo dosages described herein. The progress of this therapy is easily monitored by conventional techniques and assays.

[0164] In one embodiment, the subject has never been previously administered any drug(s) to treat cancer. In another embodiment, the subject or patient have been previously administered one or more medicaments(s) to treat cancer. In a further embodiment, the subject or patient is not responsive to one or more of the medicaments that had been previously administered. Such drugs to which the subject may be non-responsive include, for example, anti-neoplastic agents, chemotherapeutic agents, cytotoxic agents, and / or growth inhibitory agents.

[0165] IV. Compositions and Uses Thereof

[0166] The invention is based, in part, on the discovery that in vivo, in vitro, and in silica methods can be used, e.g., in combination, to determine optimized dosages for administration of a combination of two therapeutic agents, e.g., a pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor, e.g., belvarafenib) and a MEK inhibitor (e.g., cobimetinib), for treating individuals suffering from cancer, whereby administration of the combination of therapeutic agents according to the optimized in vivo dosages results in a synergistic effect in treatment.

[0167] In some instances, the invention therefore provides a composition including a pan-RAF inhibitor (e.g., pan-RAF dimer inhibitor, e.g., belvarafenib) and a MEK inhibitor (e.g., cobimetinib) for use in a method of treating an individual having a cancer (e.g., colorectal cancer, ovarian cancer, lung cancer, pancreatic cancer, and skin cancer (e.g., melanoma)), according to the optimized in vivo dosages determined according to the methods described herein. In particular, the compositions may include one or both of the therapeutic agents, e.g., the pan-RAF inhibitor, the MEK inhibitor, or both the pan-RAF inhibitor and the MEK inhibitor, formulated at a dosage suitable for administration according to the optimized in vivo dosages determined according to the methods described herein.

[0168] In some instances, the invention provides pharmaceutical composition comprising a composition described hereinabove.

[0169] In some instances, the invention provides a composition, such as a composition described herein hereinabove, for use in the therapeutic treatment of a cancer (e.g., a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer).

[0170] In some instances, the invention provides the use of a composition described herein hereinabove for the preparation of a medicament for the therapeutic treatment of a cancer (e.g., a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer).

[0171] In any of the above instances, the cancer may be selected from the group consisting of a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric carcinoma, an esophageal cancer, a mesothelioma, a melanoma, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a glioblastoma, a cervical cancer, a thymic carcinoma, a leukemia, a lymphoma, a myeloma, a mycosis fungoides, a Merkel cell cancer, and a hematologic malignancy.

[0172] V. Kits

[0173] Provided herein are kits including comprising therapeutic agents (e.g., a pan-RAF inhibitor (e.g., belvarafenib) and / or a MEK inhibitor (e.g., a MEK inhibitor) for treating an individual or patient with a disease or disorder (e.g., a proliferative cell disorder (e.g., cancer (e.g., colorectal cancer, ovarian cancer, lung cancer, pancreatic cancer, and skin cancer (e.g., melanoma))) according to the methods described herein, particularly by administering the therapeutic agents according to optimized in vivo dosages determined according to the methods described herein.

[0174] The kits may additionally include instructions and / or package inserts that describe protocols for administering the therapeutic agents according to the optimized in vivo dosages determined according to the methods described herein

[0175] EXAMPLES

[0176] The following examples are provided to illustrate, but not to limit the presently claimed invention.

[0177] Example 1. Computational Modeling of Drug Response Identifies Mutant-Specific Constraints for Dosing panRAF and MEK Inhibitors in Melanoma

[0178] 1. Summary of Study

[0179] Pre-clinical in vitro cell line drug response data and computational modeling of signal transduction and of pharmacokinetics were leveraged to elucidate distinct dose requirements for the combination of pan-RAF and MEK inhibitors in melanoma. The findings revealed a more synergistic but narrower dosing landscape in NRAS vs. BRAF mutant melanoma, which was linked to a mechanism of adaptive resistance through negative feedback. Further, the analysis suggested the importance of drug dosing strategies to optimize synergy based on mutational context yet highlights the real-world challenges of maintaining a narrow dose range. This approach established a framework for translational investigation of drug responses in the refinement of combination therapy, balancing the potential for synergy and practical feasibility in cancer treatment planning.

[0180] 2. Abstract of Study

[0181] Purpose: This study explored the potential of pre-clinical in vitro cell line response data and computational modeling in identifying the optimal dosage requirements of pan-RAF (Belvarafenib) and MEK (Cobimetinib) inhibitors in melanoma treatment. This research was motivated by the need to close the knowledge gap around selecting effective dosing strategies to maximize their potential.

[0182] Results: In a drug combination screen of 43 melanoma cell lines, specific dosage landscapes of panRAF and MEK inhibitors were identified for NRAS vs. BRAF mutant melanomas. Both experienced benefits, but with a notably more synergistic and narrow dosage range for NRAS mutant melanoma (mean Bliss score of 0.27 in NRAS vs. 0.1 in BRAF mutants). Computational modeling and follow-up molecular experiments attributed the difference to a mechanism of adaptive resistance by negative feedback. The in vivo translatability of in vitro dose-response maps were validated by predicting tumor growth in xenografts with high accuracy in capturing cytostatic and cytotoxic responses. The pharmacokinetic and tumor growth data from Phase 1 clinical trials of Belvarafenib with Cobimetinib were analyzed to show that the synergy requirement imposed stricter precision dose constraints in NRAS mutant melanoma patients.

[0183] Conclusion: Leveraging pre-clinical data and computational modeling, the present approach provides dosage strategies that can optimize synergy in drug combinations. Overall, this work presented a framework to aid dose selection in drug combinations.

[0184] 3. Introduction

[0185] Cancer is a disease marked by abnormal cell growth and the potential to spread and cause death. Despite its complexities, cancers often carry vulnerabilities that make them susceptible to targeted treatments. Precision medicine provides a promising approach to exploit these vulnerabilities and effectively kill cancer cells. However, designing effective targeted therapies is not straightforward. The dynamic nature of cancer cells enables them to adapt and develop resistance mechanisms, often rendering single-drug treatments less effective. As a response, the medical field has turned towards combined drug regimens, simultaneously targeting multiple vulnerabilities in cancer cells. Identifying effective drug combinations, however, is only one part of the puzzle. The dosing regimens of these combinations that yield maximal benefit while maintaining tolerability must also be determined. Current approaches to delineate these aspects often fall short.

[0186] In vitro drug screens using cancer cell lines can assist the identification of drug combinations that act beneficially on lines exhibiting traits of interest. However, such screens have significant limitations, which may lead to the omission of drug doses from the benefit assessment. This can lead to an inaccurate assessment of clinical potentials and a mischaracterization of biomarkers, particularly in situations where cancer populations exhibit responses at distinct effective dose ranges. The reasons for these limitations are both practical and conceptual. A practical limitation is the lack of computational frameworks for easily manipulating large-scale dose-response data and extracting dose-specific information. A more profound conceptual limitation is the unclear translatability of in vitro drug responses to in vivo settings.

[0187] While dose-response experiments with cell lines provide insightful data on drug impact, their phenomenological nature limits mechanistic understanding. Thus, methods able to link dose-response data to molecular measurements and information on protein structures and networks are needed. In this study, a framework was deployed that combined pre-clinical in vitro cell line drug response data and computational modeling of signal transduction and pharmacokinetics to unravel the dose requirements for using pan-RAF and MEK inhibition for melanoma treatment. Unlike first-generation RAF inhibitors that have limited efficacy in blocking RAF dimer signaling, small-molecule ATP-competitive panRAF inhibitors, such as Belvarafenib, are capable of targeting RAF dimers. The approach was applied to unravel how the combination of panRAF and MEK inhibition impacted different mutational contexts and to identify effective drug regimens for clinical use.

[0188] 4. Materials and Methods

[0189] 4. 1. Drug Combination Screen

[0190] The drugs were obtained via in-house synthesis or purchased from commercial vendors. A fully automated transfer system by Nova Technology (Innovate Engineering, 9 Merry Ln, East Hanover, NJ 07936, USA) was used to transfer the material from a dry library, solubilize them with DMSO, and then log the solutions into a compound management system. A high-throughput liquid chromatography mass spectrometry / ultraviolet absorbance / charged aerosol detector / chemiluminescent nitrogen detector (LCMS / UV / CAD / CLND) system was used to verify the identity, purity, and concentration of drugs used in the Genentech Cell Line Screening Initiative (gCSI) screens. The LCMS / UV / CAD / CLND system consisted of an LCMS / UV system (Shimadzu, 7102 Riverwood Drive Columbia, MD 21046, USA) with an LC-30AD solvent pump, 2020 MS, a SH-30AC autosampler, an SP-M30A UV detector, and a CTO-20A column oven; a CORONA™ VEO™ RS CAD (Thermo Scientific, 168 Third Avenue. Waltham, MA 02451 , USA); and a model 8060 CLND. Drugs with lower than 80% purity and 20% below expected concentration were excluded. An ECHO® 555 acoustic drop ejection (ADE) liquid handler (Labcyte, 170 Rose Orchard Way San Jose, CA 95134, USA) was fully integrated in the ultra-high-throughput screening (uHTS) system to dispense DMSO solubilized compounds. Nine-point dose-response curves at 1 :3 dilution were generated using ADE as a means of transferring library compounds at ultra-low volume (in nanoliter scale) to achieve direct dilution of the compounds. The starting doses for Vemurafenib, Belvarafenib, and Cobimetinib were 10, 10, and 5 pM, respectively. The uHTS system delivered assay-ready daughter plates at a concentration of 31 ,000. A DMSO backfill step was performed to achieve an equal volume of DMSO in each well. Assay-ready drug plates were stored at -80 °C until the day of compound addition and subjected to a single freeze-thaw cycle. The use of ADE technology limited the final DMSO concentration in assay plates to 0.1%, which had a negligible effect on cell growth. Seeding densities were optimized for each cell line to obtain 70-80% confluence after 6 days. The cells were plated into 384-well plates (Greiner, Bad Haller Str. 32, 4550 Kremsmunster, Austria, 781091 ) and then treated with the compound the following day in a final DMSO concentration of 0.1%. The relative numbers of viable cells were measured by luminescence using CELLTITER-GLO® (Promega, 2800 Woods Hollow Road Madison, Wl 53711 , USA, G7573).

[0191] 4.2. Higher Drug Dose Resolution Combination Responses

[0192] Higher drug dose-resolved 10 x 10 drug combination responses were generated, which centered around clinically relevant doses for 5 cell lines: A375, IPC-298, MEL-JUSO, SK-MEL-2, and SK-MEL-30. The seeding densities were optimized to obtain 70-80% confluence after 6 days. The cells were seeded into 384-well plates 24 hours prior to compound addition and treated with the compound the following day (final DMSO concentration of 0.1%). The compound stocks, 10 mM in DMSO, were supplied by Genentech Compound Management. Belvarafenib and Cobimetinib were dosed using an HP 300 automatic dose dispenser as a 10 x 10 combinatorial drug matrix with serial dose dilutions starting from 1 to 0.002 pM for Belvarafenib and 0.5 to 0.002 pM for Cobimetinib. After 120 hours, relative numbers of viable cells were measured using CELLTITER-GLO® (Promega, G7573).

[0193] 4.3. Western Blots

[0194] Anti-MEK1 (12671 , western blot (WB) 1 :1000), anti-pMEK (S217 / S221 ) rabbit monoclonal antibody (mAb) (41 G9) (9154, WB 1 :1000), anti-ERK (9107, WB 1 :1000), and anti-pERK (T202 / Y204) (9101 , WB 1 :1000) were purchased from Cell Signaling Technology (3 Trask Ln, Beverly, MA 01915, USA). Infrared (IR)-conjugated secondary antibodies, Goat anti-Mouse 680LT (926-68020, WB: 1 :10,000), and Goat anti-Rabbit 800CW (926-32211 , WB: 1 :10,000) were purchased from Li-Cor (4647 Superior St, Lincoln, NE 68504, USA). All Western blots were scanned on Li-Cor ODYSSEY® CLX using duplexed IR-conjugated secondary antibodies.

[0195] SK-MEL-28, A-375, and SK-MEL-2 were obtained from American Type Culture Collection (ATCC). IPC-298 and MEL-JUSO were obtained from Deutsche Sammlung von Mikroorganismen und Zellkulturen (DSMZ). The cell lines were maintained in the recommended media and supplemented with 10% heat-inactivated fetal bovine serum (FBS) (HyClone, 925 W 1800 S, Logan, UT 84321 , USA, SH3007003HI), 1 x GLUTAMAX™ (Gibco, 168 Third Avenue. Waltham, MA 02451 , USA, 35050-061 ), and 1 x Penicillin-Streptomycin (Gibco, 15140-122).

[0196] Immunoblotting was performed using standard methods. The cells were briefly washed in ice-cold phosphate buffered saline (PBS) and lysed in the following lysis buffer (1% NP-40, 50 mM Tris, pH 7.8, 150 mM NaCI, and 5 mM EDTA) plus a protease inhibitor mixture (COMPLETE™ mini tablets; Roche Applied Science, Grenzacherstrasse 124, 4058 Basel, Switzerland, 11836170001 ) and phosphatase inhibitor mix (ThermoFisher Scientific, 168 Third Avenue. Waltham, MA 02451 , USA, 78420). The lysates were centrifuged at 15,000 rpm for 10 min at 4 °C, and the protein concentration was determined by BCA (ThermoFisher Scientific, 23227). Equal amounts of protein were resolved by sodium dodecyl sulfatepolyacrylamide gel electrophoresis (SDS-PAGE) on NUPAGE™, 4-12% Bis-Tris Gels (ThermoFisher Scientific, WG-1403) and transferred to a nitrocellulose membrane (Bio-Rad, 1000 Alfred Nobel Dr, Hercules, CA 94547, USA, 170-4159). After blocking in a blocking buffer (Li-Cor, 927-40000), the membranes were incubated with the indicated primary antibodies and analyzed by the addition of secondary antibodies IRDYE® 680LT Goat anti-Mouse IgG (Li-Cor, 926-68050) or IRDYE® 800CW Goat anti-Rabbit IgG (Li-Cor, 926-32211 ). The membranes were visualized on a Li-Cor ODYSSEY® CLx Scanner.

[0197] 4.4. Immunofluorescence and High-Content Imaging

[0198] The cells were washed twice with 1 x PBS and fixed with 4% paraformaldehyde (PFA) for 15 min at 25 °C. To remove PFA, the cells were washed with 1 x PBS three times, and PFA was quenched by incubating the cells with 50 mM NFUCI for 10 min at 25 °C. The cells were then rinsed twice with PBS and permeabilized with ice-cold methanol for 10 min at -20 °C. Following permeabilization, the cells were first incubated with a blocking buffer for 1 hour at room temperature (1 x PBS / 5% normal serum / 0.3% TRITON™ X-100), followed by overnight incubation with the primary antibody against phospho-ERK (Cell Signaling Technology, catalog no. 4370S) at 1 :800 dilution at 4 °C. The next day, the cells were washed three times with 1 x PBS and incubated for one hour at room temperature with the secondary antibody (Jackson ImmunoResearch Laboratories, 872 W Baltimore Pike, West Grove, PA 19390, USA, catalog no. 711 -606-152). To stain the nucleus and cell body, the cells were incubated with NUCBLUE™ Fixed Cell READYPROBES™ Reagent (catalog number: R37606) and HCS CELLMASK™ Blue Stain (catalog number: H32720) for 20 min at room temperature. Finally, the cells were washed three times with 1 x PBS and imaged on the Opera PHENIX™ high-content screening (HCS) machine (PerkinElmer, 710 Bridgeport Ave, Shelton, CT 06484, USA) using the 40x water immersion objective using confocal modality. Analysis and quantification were conducted on HARMONY™ (PerkinElmer) software.

[0199] 4.5. Tumor Volume Experiments in Xenografts

[0200] G03083045.23-6 (free base of GDC-5573, Lot 23-6; hereafter referred to as Belvarafenib) was provided to Genentech as a solution at concentrations of 3.3 mg / mL and 6.6 mg / mL (expressed as free- base equivalents) in 5% dimethyl sulfide / 5% CREMOPHOR® EL. Cobimetinib (GDC-0973, Lot 150-10) was provided by Genentech as a solution at concentrations of 1 .1 mg / mL (expressed as free-base equivalents) in 0.5% (w / v) methylcellulose / 0.2% TWEEN® 80. All concentrations were calculated based on a mean body weight of 22 g for the NCr.nude mouse strain used in this study. The vehicle controls were 5% dimethyl sulfide / 5% CREMOPHOR®EL and 0.5% (w / v) methylcellulose / 0.2% TWEEN® 80. Test articles were stored in a refrigerator set to maintain a temperature range of 4-7 °C. All treatments and vehicle control dosing solutions were prepared once a week for three weeks.

[0201] Female NCr.nude mice that were 6-7 weeks old were obtained from Taconic Biosciences (New York, NY, USA), weighing an average of 22 g. The mice were housed at Genentech in standard rodent micro-isolator cages and were acclimated to the study conditions at least 3 days before tumor cell implantation. Only animals that appeared to be healthy and that were free of obvious abnormalities were used for the study.

[0202] Human melanoma IPC-298 cells were obtained from the ATCC (Rockville, MD, USA), harboring NRAS Q61 L mutation. The cells were cultured in vitro, harvested in log-phase growth, and resuspended in Hank’s Balanced Salt Solution (HBSS) containing MATRIGEL® (BD Biosciences; San Jose, CA, USA) at a 1 :1 ratio. The cells were then implanted subcutaneously in the right lateral thorax of 140 NCr.nude mice. Each mouse was injected with 20 x 106cells in a volume of 100 mL. Tumors were monitored until they reached a mean tumor volume of 250-300 mm3. Mice were distributed into six groups based on tumor volume, with n = 10 mice per group. The mean tumor volume across all six groups was 240 mm3at the initiation of dosing.

[0203] Mice were given vehicles (100 pL 5% DMSO / 5% CREMOPHOR® EL (CremEL) and 100 pL 0.5% methylcellulose (MCT)), 15 mg / kg or 30 mg / kg Belvarafenib (expressed as free-base equivalents) and 5 mg / kg Cobimetinib (expressed as free-base equivalents). All treatments were administered on a daily basis (QD) orally (PO) by gavage for 21 days in a volume of 100 mL for Belvarafenib or Cobimetinib. Tumor sizes and mouse body weights were recorded twice weekly over the course of the study. Mice were promptly euthanized when tumor volume exceeded 2000 mm3or if body weight loss was >20% of their starting weight.

[0204] All drug concentrations were calculated based on a mean body weight of 22 g for the NCr.nude mouse strain used in this study. The study design is summarized in Table 1 below. Tumor volumes were measured in two dimensions (length and width) using Ultra Cal-IV calipers (model 54-10-111 ; Fred V. Fowler Co.; Newton, MA, USA) and analyzed using Excel, version 14.2.5 (Microsoft Corporation; Redmond, WA, USA). The tumor volume was calculated with the following formula: tumor size (mm3) = (longer measurement x shorter measurement2) x 0.5. Animal body weights were measured using an ADVENTURER™ Pro AV812 scale (Ohaus Corporation; Pine Brook, NJ, USA). Percent weight change was calculated using the following formula: body weight change (%) = [(current body weight / in itial body weight) - 1 ) x 100].

[0205] Table 1. Study Design for xenograft experiment.

[0206] Vehicle controls were 5% dimethyl sulfide / 5% CREMOPHOR® EL (100 pL) + 0.5% (w / v) methylcellulose; 0.2% TWEEN® 80 (100 pL).aDose levels and concentrations were expressed as free-base equivalents and were dosed once daily (QD) for 21 days.

[0207] F = female; Cone. = concentration; PO = orally; QD = once daily.

[0208] Percent animal weight was tracked for each individual animal while on study, and the percent change in body weight for each group was calculated and plotted (FIGS. 8A and 8B). A generalized additive mixed model (GAMM) was employed to analyze the transformed tumor volumes over time. As tumors generally exhibit exponential growth, tumor volumes were subjected to natural log transformation before analysis. Changes in tumor volumes over time in each group were described by fits (i.e., regression splines with auto-generated spline bases) generated using customized functions in R version 3.4.2 (28 September 2017) (R Development Core Team 2008; R Foundation for Statistical Computing; Vienna, Austria). For assessment of gene expression in harvested tumors, total RNA was extracted from xenograft tumor tissue using RNEASY® Plus Mini kits (Qiagen, Qiagen Str. 1 , 40724 Hilden, Germany) following the manufacturer’s instructions. RNA quantity was determined using a NANODROP™ spectrophotometer (Thermo Fisher Scientific). Transcriptional readouts were assessed using a Fluidigm BIOMARK™ HD System (Standard BioTools, 2 Tower PI Suite 2000, South San Francisco, CA 94080, USA) according to the manufacturer’s recommendations. RNA (100 ng) was subjected to cDNA synthesis and pre-amplification using the High-Capacity cDNA RT Kit and TAQMAN™ PreAmp Master Mix (Thermo Fisher Scientific) per the manufacturer’s protocol. Following amplification, the samples were diluted 1 :4 with Tris EDTA pH 8.0 and qPCR was conducted using a Fluidigm 96.96 DYNAMIC ARRAY™ and the Fluidigm BIOMARK™ HD System (Standard BioTools) according to the manufacturer’s recommendations. Cycle threshold (Ct) values were converted to fold changes or percentages in relative expression values (2-<AACt>) by subtracting the mean of the housekeeping reference genes from the mean of each target gene followed by subtraction of the mean vehicle ACt from the mean sample ACt.

[0209] Blood was harvested from mice treated for 4 days and 3 hours after the last dosing to quantify the free concentrations of drugs in plasma. Briefly, the concentration of Belvarafenib and Cobimetinib in each sample was determined using a non-validated LC-MS / MS method using labeled internal standards (Cobimetinib: 13C6, Belvarafenib: d5) with qualified curve ranges (Cobimetinib: 1 .00 to 100 ng / mL with 2000 ng / mL dilution quality control (QC), Belvarafenib: 5.00 to 5000 ng / mL with 75,000 ng / mL dilution QC) using specific columns (Cobimetinib: WATERS™ Xbridge C18, 50 x 2.1 mm, 3.5 urn, Belvarafenib: Phenomenex ONYX™ Monolithic C18, 50 x 2.0 mm) and MS / MS transition ranges (Cobimetinib: 532.2- 249.1 , Belvarafenib: 479.1-328.0, 13C6 Cobimetinib: 538.2-255.1 , Belvarafenib-d5: 484.1-333.1 ). The lower limit of quantitation (LLOQ) was 1 .00 ng / mL for Cobimetinib and 5.00 ng / mL for Belvarafenib. Free plasma concentrations were calculated by multiplying the plasma concentration in each sample with the fraction unbound in plasma.

[0210] 4.6. Computational Dynamic Modeling of MAPK Signaling

[0211] The MARM2 model is written in the PySB framework and describes interactions of the EGFR / MAPK signaling pathway. The model, along with relevant parameters, trained on a range of conditions with MEK and RAF inhibitors, was obtained from Frohlich, F. and Gerosa, L. et al. A curation step was performed wherein unnecessary species and their associated model components were removed. The pan-RAF inhibitor Belvarafenib was implemented by setting ep_RAF_RAF_mod_RAFi_double_ddG = 0, removing the reduction in binding affinity of a type 1 .5 RAF inhibitor (Vemurafenib) to a partially inhibited RAF dimer. For NRAS Q61 mutants, the hydrolysis rate of NRAS GTP, catalyze_NF1_RAS_gdp_kcatr, was reduced by a factor of 10, and the stability of CRAF dimers, ep_RAF_RAF_mod_RASgtp_double_ddG, was reduced by a factor of 5. Furthermore, since CRAF is the dominant RAF species in NRAS Q61 , BRAF was removed in order to greatly reduce the model size and computation times. The reduced tendency for phosphorylated CRAF to bind to RAS and form dimers is an important negative feedback mechanism, which is referred to as pRAF feedback. To better understand the impacts of this feedback, an extra NRAS Q61 model was generated with the feedback removed. Through this process, three models were obtained: BRAF V600E, NRAS Q61 with pRAF feedback, and NRAS Q61 without pRAF feedback.

[0212] Each model was converted to a set of ordinary differential equations (ODEs) using BioNetGen (BNG) and then simulated until a steady state was reached. The steady state was achieved when the relative change in all species was less than 0.1 % over a period of at least 4 hours. For the steady-state dose-responses, 100 inhibitor dose conditions were generated from 10 Cobimetinib doses (0 pM and 9 doses from 10-2.75 pM to 100 pM) and 10 Belvarafenib doses (0 pM and 9 doses from 10-2.25 pM to 100.5 pM). The initial steady-state system was subjected to one of these dose conditions and then simulated until the steady state was reached. The full simulation times for all conditions were as follows: BRAF V600E — 475 s, NRAS Q61 without pRAF feedback — 474 s, and NRAS Q61 with pRAF feedback — 330 s (ran on MACBOOK PRO™ with M2 Max chip). Bliss values were then generated from the steadystate values using the synergy Python library. For the time course responses, the initial steady-state system was simulated for 24 hours and then dosed with Cobimetinib (0.5 pM) and either 0 or 133 nM of Belvarafenib. The system was then simulated for 8 additional hours. The full simulation times were as follows: NRAS Q61 without pRAF feedback — 32 s, NRAS Q61 with pRAF feedback — 32 s, and BRAF V600E— 27 s (ran on MACBOOK PRO™ with M2 Max chip).

[0213] 4.7. Analysis of Drug Dose-Responses

[0214] Cell viability data were processed to relative viability to obtain single-agent fits and metrics (e.g., IC50, maximum effect (Emax), and area under curve (AUC)), as well as drug combination fits and metrics such as highest single agent (HSA) and Bliss scores. Briefly, single-agent fits for each drug and cell line were obtained using the drm fitting function from the drc R package using a three-parameter (LL.3u) or a four-parameter (LL.4) log-logistic function that relates drug dose to relative viability. For drug combination data, HSA and Bliss scores were calculated as the average of the 10% highest HSA and Bliss excess values observed across the full dose ranges tested, respectively. HSA and Bliss excess values for each dose combination tested were calculated by subtracting the observed response against the expected response under the HSA and Bliss models. As an observed response, a smoothened version of the experimental drug combination matrix of relative viability obtained by fitting dose-response curves along every fixed dose of each drug and averaging the fitted values was used. The HSA expectation matrix was calculated by selecting for each dose combination the maximum response of each individual agent in the observed response. The Bliss expectation was calculated using the Bliss independence formula given as the sum of the responses of the individual drugs minus their product. Data import, processing, and calculations were performed using the R package gDR.

[0215] 4.8. Projection of In Vivo Free Drug Concentrations on In Vitro Growth Responses

[0216] Nominal drug concentrations associated with growth viability responses were converted to free drug concentrations in order to project the free drug concentrations measured in vivo in mice or patients. Briefly, nominal drug concentrations were multiplied by the fraction unbound (fu) of Belvarafenib and Cobimetinib, which was measured to be 0.034 in 10% FBS media and estimated to be 0.068 in 5% FBS media for Belvarafenib and measured to be 0.196 in 10% FBS media and 0.3 in 5% FBS media for Cobimetinib. To estimate the viability of responses or Bliss excess values at corresponding in vivo free drug doses, the matrix with corresponding dose-matrix responses with units converted to free drug concentrations was interpolated using the function interp2 from the pracma R package.

[0217] 4.9. Prediction of Tumor Growth Inhibition in Xenografts

[0218] The normalized growth rate inhibition (GR) metric was calculated from the relative viability of IPC- 298 cells treated with a combination of Belvarafenib and Cobimetinib by setting an experimentally measured untreated doubling time of 60 hours using the gDR package. The resulting GR metric was converted to control-normalized growth rates, i.e., the growth rate of treated cells divided by the growth rate of the control cells. The growth rate of the control-treated IPC-298 xenograft tumors was calculated using the doubling time of 18 days estimated from measured tumor volumes to be 0.0385 day-1. Using free drug concentrations measured in mice for Belvarafenib and Cobimetinib, corresponding control- normalized growth rates were estimated from the in vitro matrix dose-response. The control-normalized growth rates were multiplied by the baseline tumor growth to predict the growth rate achieved by tumors at any given dosing regimen. The obtained growth rates were used in an exponential growth model to simulate tumor volumes in time and compared to experimental data.

[0219] 4.10. Pharmacokinetic (PK) Modeling of Drug Concentrations in Patients

[0220] Synthetic PK profiles were generated for Belvarafenib and Cobimetinib, which recapitulated the population level PK variability expected for each respective compound. For each compound, 500 synthetic PK profiles were generated at each of the following dosing regimens (Belva: 50 mg QD, 100 mg twice daily (BID), 200 mg BID, and 400 mg BID; Cobi: 20 mg once every other day (QOD), 20 mg QD, 40 mg QD, and 60 mg QD). These simulations were performed in R 4.1 .1 using mrgsolve based on the published population PK (popPK) model for Cobimetinib and a popPK model developed on the available individual time-concentration profiles from n = 243 patients treated with Belvarafenib in clinical trial reference Nos. NCT03118817, NCT02405065, and NCT03284502. Both models were developed using the non-linear mixed effects approach as implemented in NONMEM. Simulations were conducted until steady state, after which the drug levels were recorded for use. In particular, of the 30 days of simulation, days 22-26 were saved for analysis, providing at least two complete cycles of drug concentrations for each condition. Simulated plasma total drug concentrations in ng / mL were divided by the corresponding molecular weight (Belvarafenib = 478.93 g / mol, Cobimetinib = 531 .3 g / mol) to obtain total drug concentrations in pM. These were multiplied by the fraction unbound in plasma measured at 0.00258 for Belvarafenib and 0.052 for Cobimetinib.

[0221] 4.11. Clinical Tumor Growth Simulations

[0222] A clinical tumor growth inhibition (TGI) model was used to describe the tumor dynamics of patients treated in clinical trial reference Nos. NCT03118817 and NCT03284502. This model was developed using the population approach as implemented in NONMEM version 7.5.0. The model that best described the observed tumor dynamics was a biexponential growth model. In this model, tumor dynamics evolve from an estimated initial tumor size TSo, with key treatment-related parameters describing the tumor growth rate constant (KG) (1 / week) and tumor shrinkage rate constants (KS) (1 / week). Individual empirical Bayesian estimates (EBEs) for KG and KS were summarized in melanoma patients and stratified by mutational status. Model-based tumor dynamics were simulated for 1 year for each of these groups based on the mean KG and KS for the group given the same TSo = 50. 5. Results

[0223] 5. 1. PanRAF and MEK Inhibition Is Additive in the BRAF Mutant Cell Line but Synergistic in the NRAS Mutant Cell Line

[0224] An in vitro drug screen was performed to assess the dose-response of 43 melanoma cell lines treated with the type 1 .5 “first-generation” RAF inhibitor Vemurafenib and the type 2 “panRAF” inhibitor Belvarafenib combined with the allosteric MEK inhibitor Cobimetinib. These clinical-grade inhibitors are considered highly selective for their target kinase(s). Drug responses were measured using the CELLTITER-GLO® cell viability assay in a 9-by-9 drug combination matrix design with half-log dilution series starting at the top concentrations of 10 pM for Vemurafenib and Belvarafenib and 5 pM for Cobimetinib. Cell viability readouts were processed using the gDR R package to obtain relative viability and calculate the half-maximal inhibitory concentrations (IC50) (FIG. 1 A) and Bliss scores (FIG. 1 B) as metrics of single-agent potency and combination benefit, respectively. As expected and serving as a control, Vemurafenib as a single agent was found to only inhibit melanoma lines carrying BRAF V600E / K mutations, which signal as BRAF monomers and are thus sensitive to type 1 .5 RAF inhibitors that specifically inhibit RAF monomers (FIG. 1 A). In addition to the BRAF V600E / K mutant lines, Belvarafenib also inhibited most melanoma lines with a NRAS hotspot mutation (specifically Q61 R, Q61 K, Q61 V, and Q61 L) or the wild type for RAS / RAF proteins. These mutational contexts are believed to signal through RAF dimers and are thus sensitive to type 2 RAF inhibitors that block dimeric signaling (FIG. 1 A). The MEK inhibitor Cobimetinib inhibited the growth of most cell lines, validating their broad dependency on MAPK signaling, but interestingly, had a much higher potency on cell lines carrying the BRAF V600E / K mutation (log 10 mean= -1 .66 uM, std = 0.6) than the NRAS mutation (log 10 mean = -1 .08 uM, std = 0.39) or RAS / RAF wild type (Iog10 mean = -0.68 uM, std = 0.82) (FIG. 1 A).

[0225] This difference in Cobimetinib’s single-agent potency appeared to extend to the way it combined with Belvarafenib, as quantified by the Bliss scores (FIG. 1 B). The combination of Belvarafenib and Cobimetinib presented Bliss scores around zero for most BRAF V600E / K cell lines but positive Bliss scores in most NRAS mutant or RAS / RAF wild-type lines (FIG. 1 B). Bliss scores were calculated as the highest difference between experimentally observed and theoretically expected relative viability based on Bliss independence. With values closer to zero, the Bliss scores for BRAF V600E / K melanoma lines (mean = 0.10, std = 0.06) showed that Belvarafenib and Cobimetinib inhibition was mostly additive. High Bliss scores for the NRAS mutant (mean = 0.27, std = 0.12) and RAS / RAF wild-type lines (mean = 0.25, std = 0.12) highlighted a synergistic reduction in relative viability compared to single-agent responses at the same doses. There was a small number of BRAF mutant lines (5 / 32) that showed synergistic pharmacological responses similar to NRAS mutant lines. The dose range at which the maximal benefit was achieved can be visualized by showing relative viability and Bliss excess calculated at each drug dose combination, as shown for representative BRAF and NRAS mutant cell lines (FIG. 1 C). While Bliss excess showed drug additivity across the entire dose-response landscape in BRAF V600E / K lines, NRAS mutant melanoma lines presented a narrow concentration range in which the combination of panRAF and MEK inhibitors was highly synergized in inhibiting cancer growth (FIG. 1 C). 5.2. Upregulation of MEK Phosphorylation in NR AS Q61 but Not in BRAF V600 Contexts Is Linked with Synergy to panRAF and MEK Inhibitors

[0226] The different ways in which panRAF and MEK inhibitors combined in NRAS vs. BRAF mutant melanomas may have likely originated from the distinct pathway rewiring caused by these oncogenic mutations. NRAS Q61 is believed to signal through RAS-dependent RAF dimers that are sensitive to negative feedback operating on RAFs (FIG. 2A). Instead, BRAF V600E / K signals as RAS-independent RAF monomers that are insensitive to upstream negative feedback (FIG. 2B).

[0227] To confirm the engagement of negative feedback in NRAS Q61 , but not BRAF V600 contexts, Western blot experiments were performed with MEL-JUSO (FIG. 2C) and A-375 cell lines (FIG. 2D) to measure the phosphorylation status of the MEK and ERK kinases upon inhibition with Cobimetinib, with or without a single dose of Belvarafenib. ERK phosphorylation, the functional output of the MAPK signaling cascade, revealed a trend similar to relative viability readouts: as a single agent, Cobimetinib had lower potency and a shallower dose-response on the NRAS Q61 line MEL-JUSO than the BRAF V600 line A-375 (FIGS. 2C, 2D, and 9). Moreover, when combined with a fixed dose of Belvarafenib, it showed synergy in reducing ERK phosphorylation in the MEL-JUSO lines but was additive in the A375 line.

[0228] MEK phosphorylation measurements were used as a proxy to assess the relief of upstream negative feedback on MAPK signaling. It is believed that upon MEK inhibition, negative feedback release can be observed as a paradoxical increase in pMEK due to higher upstream signaling. At doses as low as 10 nM, Cobimetinib was found to induce an increase in MEK phosphorylation in the MEL-JUSO cell line while causing a decrease in the A-375 cell line. Interestingly, the synergy observed between Belvarafenib and Cobimetinib appeared to saturate at the dose of 50 nM Cobimetinib, which corresponds to full engagement of the negative feedback, as shown by the higher MEK phosphorylation in the Cobimetinib single-agent treatment (FIGS. 2C and 2D). Paradoxical activation of MEK phosphorylation caused by Cobimetinib was abolished by adding Belvarafenib, likely due to a counteracting of the negative feedback relief on RAF dimers (FIGS. 2C and 2D). These results supported the hypothesis that the negative feedback relief observed through pMEK upregulation was linked to the differential response of the NRAS Q61 and BRAF V600E lines to Cobimetinib and in combination with Belvarafenib.

[0229] 5.3. Computational Model of MAPK Signaling Implicates Negative Feedback in the Response of NRAS and BRAF Mutant Melanoma Lines to panRAF and MEK Inhibitors

[0230] To ground this hypothesis on a quantitative framework and disentangle mechanisms of drug synergy, a modified computational model of MAPK signaling was generated that could be instantiated with a BRAF V600 or a NRAS Q61 oncogenic driver. Briefly, a previously missing negative feedback was implemented that links ERK phosphorylation with an inhibitory phosphorylation of RAF. This phosphorylation reduces the ability for RAF to bind to RAS, dimerize, and facilitate signaling. In order to quantitatively assess whether pRAF feedback is capable of explaining the above observations and to better understand the consequences, the BRAF V600E and NRAS Q61 with the pRAF feedback models described in Section 4.6 above were used. These models indeed captured the observations made for Western blotting data (FIG. 2E). The NRAS Q61 model exhibited a strong increase in pMEK under single- agent Cobimetinib, which was significantly diminished with the addition of Belvarafenib while single-agent Cobimetinib was effective on the BRAF V600E model. For an NRAS Q61 model with the pRAF feedback removed, there was little to no increase in pMEK in response to Cobimetinib (FIGS. 10A and 10B), offering support to the hypothesis that negative feedback was key for differential drug responses between NRAS and BRAF mutant tumors.

[0231] Next, the model was used to simulate a full drug combination matrix response for Belvarafenib and Cobimetinib. A dose range focused on the area of synergy was sampled and used to predict MEK and ERK phosphorylation responses in the BRAF V600 and NRAS Q61 contexts (FIGS. 3A and 3B). The model predicted that in those dose ranges, ERK phosphorylation would be strongly inhibited in the BRAF V600 context by both single agents and in combination. Conversely, it would only strongly inhibit pERK by synergy in the NRAS Q61 context, with a paradoxical activation of pMEK by Cobimetinib. To validate model predictions, immunofluorescence-based microscopy was used to quantify ERK phosphorylation in the A-375 and MEL-JUSO cell lines across a 6-by-6 dose dilution matrix of Cobimetinib and Belvarafenib, finding that it accurately and quantitatively matched model predictions (FIG. 3C). This suggested that the synergistic rather than additive response to panRAF and MEK inhibition observed in NRAS mutant vs. BRAF mutant melanoma was driven by the sensitivity to negative feedback of the former compared to the latter. Moreover, drug responses were determined by the degree of inhibition of ERK phosphorylation that was directly translated into cell viability.

[0232] 5.4. In Vitro Drug Dose-Responses Assessed at Clinically Relevant Concentrations Can Accurately Predict Inhibition of Tumor Growth In Vivo

[0233] A direct translatability was not obvious as several parameters were different between in vitro and in vivo settings, such as microenvironment, growth dynamics, cellular states, pharmacokinetic profiles, drug distribution, etc. To directly test translatability, a computational methodology was devised to predict in vivo tumor volume responses using in vitro dose-responses and in vivo drug concentrations as inputs. This methodology was applied to predict the tumor responses of IPC-298 melanoma cells grafted in the flanks of mice treated for 21 days with clinically relevant doses of Belvarafenib and Cobimetinib (FIGS. 4A and 4B).

[0234] First, the in vitro relative viability of IPC-298 cells was reassessed using a 10-by-10 dose matrix of Belvarafenib and Cobimetinib with concentration ranges that better match in vivo relevant doses (FIG. 4A). This provided a more refined map on which to score growth inhibition at in vivo drug concentrations compared to the large drug screen. Subsequently, relative viabilitywas converted into growth rate inhibition using the growth inhibition rate (GR) metric. Briefly, the baseline doubling rate of IPC-298 cells (60 hours) was used to back-calculate initial seeding cell numbers and calculate the growth rate inhibition at every Belvarafenib and Cobimetinib dose (FIG. 4A). GR values between one and zero quantify a degree of growth arrest; zero indicates complete stasis, and negative values indicate net cell loss (FIG. 4A). Then, nominal drug concentrations were convered to free drug concentrations by multiplying the fraction unbound (fu) in the serum of each drug (Belvarafenib fu = 0.034, Cobimetinib fu = 0.196).

[0235] Second, the dose-response matrix was projected onto the free drug concentrations measured in the plasma of mice treated with 15 mg / kg (free drug = 8 nM) or 30 mg / kg (free drug = 20 nM) of Belvarafenib or 5 mg / kg (free drug = 3 nM) of Cobimetinib QD for 3 days and measured 3 hours post last dose. This allowed estimation of the growth rate inhibition expected from the in vitro data at the corresponding free drug concentrations for single-agent and combination treatments (FIG. 4A). Finally, the baseline growth rate was calculated of IPC-298 xenografts in mice treated with vehicle QD for 21 days and scaled the growth rate according to the corresponding in vitro growth rate inhibition at each dose regimen. This allowed prediction of the steady-state tumor volume progressions that should be achieved in vivo (FIG. 4B). A comparison with the tumor volume growth experimentally measured in mice treated for 21 days showed an accurate prediction of the tumor growth dynamics (FIG. 4B). As single agents, Belvarafenib achieved partial and complete cytostasis at 15 mg / kg and 30 mg / kg, respectively, while Cobimetinib achieved little to no tumor growth inhibition at 5 mg / kg (FIG. 4B). The addition of 5 mg / kg of Cobimetinib to 15 mg / kg and 30 mg / kg Belvarafenib shifted tumor control from cytostatic to cytotoxic (FIG. 4B), proving that synergy scored in the in vitro setting quantitatively translated into in vivo responses. The expression of genes measured at the end of treatment confirmed that improved tumor control is linked to a stronger inhibition of genes that reported on the activity of MAPK signaling (e.g., FOSL1 , DUSP6, and SPRY4). This confirmed the mechanistic basis for synergy previously identified using in vitro experiments and computational modeling (FIG. 10B).

[0236] 5.5. Drug Levels Required for Additive and Synergistic Responses in NRAS and BRAF Mutant Melanoma Can Be Achieved Clinically

[0237] In order to evaluate the clinically relevant concentrations of Belvarafenib and Cobimetinib, the average and standard deviation of free drug concentrations were calculated from the respective clinical PK models under 16 dose regimens (4 unique dose schemes for each drug) using the simulated responses from days 22 to 26, as described in Section 4.10 above. The average predicted in vitro drug combinations were converted to free drug concentrations and projected onto the in vitro responses as described in Section 4.8 above (FIG. 5A). This approach was used on both the A-375 (BRAF V600E) and IPC-298 (NRAS Q61 ) cell lines to obtain the GR metric and Bliss excess values for these two mutational contexts at clinically relevant concentrations.

[0238] In the BRAF mutant context, all but the weakest clinically realized combinations of Belvarafenib and Cobimetinib performed similarly, inhibiting tumor growth, as shown by the corresponding GR metric values, without significant synergistic effects, as shown by low Bliss excess values (FIG. 5B, upper left panel). As a result, it was concluded that in the BRAF V600E lines, there was little motivation to achieve precise drug combination levels in the patient. For these lines, a drug regimen of intermediate intensity should be sufficient to inhibit tumor growth. Conversely, the choice of drug regimen had a greater impact on the extent of growth inhibition in the NRAS mutant context (FIG. 5B, lower right panel). Strong tumor inhibition was either achieved with potent Belvarafenib (at 400 mg QD) or Cobimetinib (at 60 mg DQ) single-agent activity or by synergy achieved at intermediate doses, with the highest synergy with good tumor control observed for 100 mg BID Belvarafenib and 20 or 40 mg QD Cobimetinib. This showed that the mutational context created a different need for dosing of the two combination agents, where leveraging synergy in NRAS mutant melanoma was better achieved at intermediate doses of Cobimetinib that lower the requirement of Belvarafenib to synergize. 5.6. Pharmacokinetic Variability in Patients Highlights Precision Requirement for Synergistic Responses in NR AS Mutant Melanoma Tumors

[0239] The role that the patient-to-patient variability in pharmacokinetic profiles has in leveraging synergistic vs. additive responses was assessed. The PK models in this study provide the drug levels for individual, virtual patients, which enables us to develop a map from each patient’s PK profile to a distribution of drug effects that the patient experiences, i.e. , GR metric and Bliss excess values. To accomplish this, the patient’s free drug concentrations were obtained once per hour over the course of 48 hours (FIG. 11 ) and then projected these concentrations onto the GR metric and Bliss scores of each mutational context in the same way the average free drug levels were projected in Section 5.5 above. Doing this for multiple patients revealed the impacts of patient-to-patient variation as well as the effects resulting from the temporal variation of drug levels (FIG. 6A). From this, it was observed that a single drug regimen can generate different responses within a population.

[0240] This indicated a significant challenge for treatments; a given regimen might, for example, work well for one patient but have less effect for another. In order to gain a better understanding of which regimens consistently result in high benefit / low tumor growth across all patients and times, the full distribution of predicted effects that resulted from a given drug regimen (FIG. 6B) was examined. It was found that BRAF V600E tumors lacked significant synergy (low Bliss excess) but still achieved consistently strong tumor suppression (high GR values) from drug regimens with as low dosing as Belvarafenib 100 mg QD and Cobimetinib 20 mg QD. Therefore, it was concluded that drug additivity imposed no strict requirements on the precision of dosing in this mutational context.

[0241] Conversely, NRAS Q61 tumors were seen to achieve tumor control by having significant synergy (high Bliss excess) in drug combinations that leveraged partial single-agent MEK inhibition in the 20 or, even better, 40 mg QD regimen, which combined well with doses as low as 50 mg QD and 100 mg BID of Belvarafenib. The distribution of growth inhibition measured by GR and synergy by Bliss excess visualized via violin plots showed, however, that combinations with 50 mg QD Belvarafenib suffered from incomplete responses due to the large variability in free drug concentrations in individual patients. This happened because combinations with 50 mg QD Belvarafenib lay very close to the synergy boundary in the dose landscape and fluctuations brought the response outside of the synergistic regimens (FIGS. 6A and 6B). Of all the synergistic combinations, Cobimetinib at 40 mg QD with Belvarafenib at 100 mg BID seemed to achieve consistent tumor control with lower patient-to-patient variability and moderate single agent-activities, thus representing an ideal drug-sparing synergistic point in the dose landscape. This underscored the importance of using dose regimens with high synergy when treating NRAS Q61 tumors to achieve strong effects while minimizing the effect of pharmacokinetic fluctuations.

[0242] 5.7. Clinical Trials Support Distinct Combinability of panRAF and MEK Inhibitors in BRAF and NRAS Mutant Patients

[0243] To ascertain the validity of insights from modeling and experiments, limited data available from Phase 1 clinical trials combining Belvarafenib and Cobimetinib in the treatment of melanoma patients were analyzed. A clinical tumor growth inhibition (TGI) model was fitted to describe the tumor dynamics of patients treated in clinical trials NCT03118817 and NCT03284502, as described in Section 4.11 above. The model described the observed tumor dynamics with a biexponential growth model with tumor dynamics evolving for one year from the estimated initial tumor size, with tumor growth rate and tumor shrinkage rate constants summarized in melanoma patients and stratified by mutational status (FIG. 7A). The simulations provided support for the differential contribution of increasing Cobimetinib dose in the BRAF mutant vs. NRAS mutant setting. The supralinear impact on growth from increasing Cobimetinib doses on the NRAS mutant tumors subjected to a constant Belvarafenib dose (FIGS. 7B and 12, lower panel) indicated the presence of synergistic effects. While the more linear impact on growth from increasing Cobimetinib doses on the BRAF mutant tumor subjected to a constant Belvarafenib dose (FIGS. 7B and 12, upper panel) indicated that the drugs were acting in a more additive fashion. This synergy appeared to be important for reaching the desired effects in NRAS mutant tumors, with a combination of Cobimetinib and Belvarafenib outperforming single-agent Belvarafenib at suppressing tumor growth.

[0244] Clinical data allowed assess of other key information for the design of drug combinations not included in the analysis, namely if tolerability is a relevant issue that constrains drug regimens. In the clinical trial NCT03284502, the regimen of Belvarafenib 200 mg BID continuously and Cobimetinib 40 mg QD 21 / 7 led to three dose-limiting toxicities (DLTs) (G3 colitis, G3 diarrhea, and G3 nausea) in two patients. These and other reported treatment-emergent toxicities (“dermatitis acneiform, diarrhea, constipation, and increase in blood creatine phosphokinase”) suggested on-target toxicity on wild-type MAPK signaling. Consequently, Cobimetinib was reduced to 20 mg QD while Belvarafenib was dose- escalated to 300 mg BID, which did not result in DLTs. The analysis described in FIG. 6B showed that at 200 mg BID Belvarafenib and 40 mg QD Cobimetinib, Belvarafenib and Cobimetinib were already both substantially active as single agents in NRAS mutant cells, suggesting that the combination was not leveraging synergy as effectively and was likely impinging on wild-type MAPK signaling. Increasing Belvarafenib to 300 mg BID while reducing Cobimetinib to 20 mg QD shifted the contribution to mostly Belvarafenib as a single agent, likely reducing toxicity but also losing synergistic effects on NRAS mutant tumors. The analysis suggested that maintaining Cobimetinib at 40 mg QD or QOD while reducing Belvarafenib to as low as 50-100 mg QD / BID was an alternative approach to de-escalate dose intensity which might better leverage the synergy of tumor inhibition without invoking strong single-agent effects, the possible culprits of toxicity. This regimen of intermediate Cobimetinib dose and low Belvarafenib dose remains untested in the clinic.

[0245] 6. Conclusions

[0246] In this study, the use of pre-clinical cell line drug response data alongside computational modeling was explored to determine the optimal dosages of pan-RAF (Belvarafenib) and MEK (Cobimetinib) inhibitors for melanoma treatment. The main finding was that the two main oncogenic drivers in melanoma, BRAF V600 and NRAS Q61 hotspot mutations, resulted in different underlying signaling biologies requiring different treatment regimens using the same drugs. It was shown that most combinatorial dose regimens achievable in the clinic were effective for treating BRAF mutant melanoma thanks to the higher single-agent potency and drug additivity, whereas NRAS mutant melanoma required more precise dosing to harness drug synergy, posing practical implementation challenges due to interpatient pharmacokinetic variability.

[0247] The research underscored that precision medicine should aim to not only identify the most effective drug combination for a given indication but also tailor dosing regimens to match the pathway biology driven by mutational mechanisms, among other biologic factors. In these contexts, the need for precision dosing becomes imperative, demanding thorough examination within both pre-clinical and translational research frameworks. By introducing a novel methodological approach, the study seeks to tackle the challenges associated with implementing precision dosing strategies, propelling the efforts to enhance the personalization of cancer treatment.

[0248] EMBODIMENTS

[0249] Some embodiments of the technology described herein can be defined according to any of the following numbered embodiments:

[0250] 1 . A method of determining one or more in vitro combination dosages each comprising a first in vitro dosage of a first therapeutic agent and a second in vitro dosage of a second therapeutic agent for inhibiting growth or inducing cell death of a cancer cell line comprising a cancer:

[0251] (a) administering a dilution matrix comprising a first dilution series of the first therapeutic agent and a second dilution series of the second therapeutic agent to the cancer cell line; and

[0252] (b) determining an excess over bliss score (bliss excess) for each element of the dilution matrix based on a growth inhibition assay or cytotoxicity assay, wherein the one or more in vitro combination dosages are the elements of the dilution matrix having a positive bliss excess.

[0253] 2. The method of embodiment 1 , wherein the positive bliss excess is from 0.2 to 1 .

[0254] 3. The method of embodiment 2, wherein the positive bliss excess is from 0.5 to 1 .

[0255] 4. The method of embodiment 3, wherein the positive bliss excess is from 0.7 to 1 .

[0256] 5. The method of any one of embodiments 1 -4, wherein the bliss excess is determined from steady state dose-responses determined for each element of the dilution matrix.

[0257] 6. The method of any one of embodiments 1 -5, wherein the steady state dose-responses are determined using a set of ordinary differential equations (ODEs).

[0258] 7. The method of embodiment 6, wherein the set of ODEs are generated using BioNetGen 2.2.

[0259] 8. The method of embodiment 6 or 7, wherein the set of ODEs are generated using a model of a biological pathway comprising the cancer, the first therapeutic agent, and the second therapeutic agent.

[0260] 9. The method of embodiment 8, wherein the biological pathway is an EGFR / MAPK signaling pathway.

[0261] 10. The method of embodiment 9, wherein the model is a second-generation MAPK Adaptive Resistance Model (MARM2.0).

[0262] 11 . The method of any one of embodiments 6-10, wherein the steady state dose-responses are when the relative change of all species in the set of ODEs is less than 0.1% over a period of at least 4 hours. 12. The method of any one of embodiments 1 -1 1 , wherein the first dilution series comprises 4 to 20 doses.

[0263] 13. The method of embodiment 12, wherein the first dilution series comprises 10 doses.

[0264] 14. The method of any one of embodiments 1 -13, wherein the second dilution series comprises 4 to 20 doses.

[0265] 15. The method of embodiment 14, wherein the second dilution series comprises 10 doses.

[0266] 16. The method of any one of embodiments 1 -15, wherein the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

[0267] 17. The method of embodiment 16, wherein the skin cancer is melanoma.

[0268] 18. The method of embodiment 17, wherein the cancer cell line comprises UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC- 62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0269] 19. The method of embodiment 17, wherein the melanoma comprises a mutation of a biomarker gene.

[0270] 20. The method of embodiment 19, wherein the melanoma comprises a BRAF mutation or an NRAS mutation.

[0271] 21 . The method of embodiment 20, wherein the BRAF mutation is a V600E mutation.

[0272] 22. The method of embodiment 21 , wherein the cancer cell line comprises WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, CGLG800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242I, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

[0273] 23. The method of embodiment 20, wherein the NRAS mutation is a Q61 hotspot mutation.

[0274] 24. The method of embodiment 23, wherein the cancer cell line comprises SK-MEL-30, SK-MEL- 2, MEL-JUSO, or Hs852.T.

[0275] 25. The method of any one of embodiments 1 -24, wherein the one or more in vitro combination dosages are determined using a growth inhibition assay.

[0276] 26. The method of any one of embodiments 1 -24, wherein the one or more in vitro combination dosages are determined using a cytotoxicity assay.

[0277] 27. The method of any one of embodiments 1 -26, wherein the first therapeutic agent comprises a small molecule inhibitor, a protein, a nucleic acid, or a CAR-T cell.

[0278] 28. The method of embodiment 27, wherein the first therapeutic agent comprises a MEK inhibitor.

[0279] 29. The method of embodiment 28, wherein the first therapeutic agent comprises cobimetinib. 30. The method of any one of embodiments 1 -29, wherein the second therapeutic agent comprises a small molecule inhibitor, a protein, a nucleic acid, or a CAR-T cell.

[0280] 31 . The method of embodiment 30, wherein the second therapeutic agent comprises a pan-RAF inhibitor.

[0281] 32. The method of embodiment 31 , wherein the second therapeutic agent comprises belvarafenib.

[0282] 33. A method of determining one or more combination in vivo dosages each comprising a first in vivo dosage of a first therapeutic agent and a second in vivo dosage of a second therapeutic agent for treating a cancer comprising converting the one or more in vitro combination dosages determined in any one of embodiments 1 -32 to the one or more combination in vivo dosages based on the plasma free drug concentrations of the first therapeutic agent administered according to a dilution series to a subject and the plasma free drug concentrations of the second therapeutic agent administered according to a dilution series to a subject.

[0283] 34. The method of embodiment 33, wherein the subject is a mouse or a human.

[0284] 35. A method of treating a cancer in an individual by administering a first therapeutic agent and a second therapeutic agent according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0285] 36. A first therapeutic agent for use in the manufacture of a medicament for treating a cancer in an individual, wherein the first therapeutic agent is to be administered in combination with a second therapeutic agent, and wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0286] 37. A second therapeutic agent for use in the manufacture of a medicament for treating a cancer in an individual, wherein the second therapeutic agent is to be administered in combination with a first therapeutic agent, and wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0287] 38. A first therapeutic agent and a second therapeutic agent for use in the manufacture of a medicament for treating a cancer in an individual, wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0288] 39. A first therapeutic agent for use in treating a cancer in an individual, wherein the first therapeutic agent is to be administered in combination with a second therapeutic agent, and wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0289] 40. A second therapeutic agent for use in treating a cancer in an individual, wherein the second therapeutic agent is to be administered in combination with a first therapeutic agent, and wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34. 41 . A first therapeutic agent and a second therapeutic agent for use in treating a cancer in an individual, wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0290] 42. Use of a first therapeutic agent in treating a cancer in an individual, wherein the first therapeutic agent is to be administered in combination with a second therapeutic agent, and wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0291] 43. Use of a second therapeutic agent in treating a cancer in an individual, wherein the second therapeutic agent is to be administered in combination with a first therapeutic agent, and wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0292] 44. Use of a first therapeutic agent and a second therapeutic agent in treating a cancer in an individual, wherein the first therapeutic agent and the second therapeutic agent are to be administered to the individual according to any one of the one or more combination in vivo dosages determined in embodiment 33 or 34.

[0293] 45. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of any one of embodiments 35-44, wherein the individual is a human.

[0294] 46. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of any one of embodiments 35-45, wherein the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

[0295] 47. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of embodiment 46, wherein the skin cancer is melanoma.

[0296] 48. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of embodiment 47, wherein the melanoma comprises a mutation of a biomarker gene.

[0297] 49. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of embodiment 48, wherein the melanoma comprises a BRAF mutation or an NRAS mutation.

[0298] 50. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of embodiment 49, wherein the BRAF mutation is a V600E mutation. 51 . The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of embodiment 49, wherein the NRAS mutation is a Q61 hotspot mutation.

[0299] 52. The method, first therapeutic agent for use, second therapeutic agent for use, first therapeutic agent and second therapeutic agent for use, or use of any one of embodiments 35-51 , wherein the first therapeutic agent and the second therapeutic agent exhibit a synergistic effect when administered to the individual according to the one of the one or more combination in vivo dosages.

[0300] Other Embodiments Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity of understanding, the descriptions and examples should not be construed as limiting the scope of the invention. The disclosures of all patent and scientific literature cited herein are expressly incorporated in their entirety by reference.

Claims

WHAT IS CLAIMED IS:1 . A method of determining one or more in vitro combination dosages each comprising a first in vitro dosage of a first therapeutic agent and a second in vitro dosage of a second therapeutic agent for inhibiting growth or inducing cell death of a cancer cell line comprising a cancer:(a) administering a dilution matrix comprising a first dilution series of the first therapeutic agent and a second dilution series of the second therapeutic agent to the cancer cell line; and(b) determining an excess over bliss score (bliss excess) for each element of the dilution matrix based on a growth inhibition assay or cytotoxicity assay, wherein the one or more in vitro combination dosages are the elements of the dilution matrix having a positive bliss excess.

2. The method of claim 1 , wherein the positive bliss excess is from 0.2 to 1 .

3. The method of claim 2, wherein the positive bliss excess is from 0.5 to 1 .

4. The method of claim 3, wherein the positive bliss excess is from 0.7 to 1 .

5. The method of any one of claims 1 -4, wherein the bliss excess is determined from steady state dose-responses determined for each element of the dilution matrix.

6. The method of any one of claims 1 -5, wherein the steady state dose-responses are determined using a set of ordinary differential equations (ODEs).

7. The method of claim 6, wherein the set of ODEs are generated using BioNetGen 2.2.

8. The method of claim 6 or 7, wherein the set of ODEs are generated using a model of a biological pathway comprising the cancer, the first therapeutic agent, and the second therapeutic agent.

9. The method of claim 8, wherein the biological pathway is an EGFR / MAPK signaling pathway.

10. The method of claim 9, wherein the model is a second-generation MAPK Adaptive Resistance Model (MARM2.0).11 . The method of any one of claims 6-10, wherein the steady state dose-responses are when the relative change of all species in the set of ODEs is less than 0.1% over a period of at least 4 hours.

12. The method of any one of claims 1 -1 1 , wherein the first dilution series comprises 4 to 20 doses.

13. The method of claim 12, wherein the first dilution series comprises 10 doses.

14. The method of any one of claims 1 -13, wherein the second dilution series comprises 4 to 20 doses.

15. The method of claim 14, wherein the second dilution series comprises 10 doses.

16. The method of any one of claims 1 -15, wherein the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

17. The method of claim 16, wherein the skin cancer is melanoma.

18. The method of claim 17, wherein the cancer cell line comprises UACC-257, HT-144, HSC-5, A-431 , A-253, A388, HSC-1 , SK-MEL-30, SK-MEL-2, MEL-JUSO, Hs852.T, WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242L, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

19. The method of claim 17, wherein the melanoma comprises a mutation of a biomarker gene.

20. The method of claim 19, wherein the melanoma comprises a BRAF mutation or an NRAS mutation.21 . The method of claim 20, wherein the BRAF mutation is a V600E mutation.

22. The method of claim 21 , wherein the cancer cell line comprises WM-266-4, UACC-62, RVH-421 , SK-MEL-24, COLO858, MMAc, SK23-mel, COLO857, HMY-1 , A-375, COLO829, G-361 , HCC1498, SK-MEL-28, COLO800, COLO853, MEL-HO, SK-MEL-1 , UCSD-242I, 928mel, SK-MEL-3, 501 A, COLO849, MDA-MB-435, Hs695T, 624mel, IGR-1 , A2058, SK-MEL-31 , Hs294T, RPMI-7951 , or IGR-39.

23. The method of claim 20, wherein the NRAS mutation is a Q61 hotspot mutation.

24. The method of claim 23, wherein the cancer cell line comprises SK-MEL-30, SK-MEL-2, MEL-JUSO, or Hs852.T.

25. The method of any one of claims 1 -24, wherein the one or more in vitro combination dosages are determined using a growth inhibition assay.

26. The method of any one of claims 1 -24, wherein the one or more in vitro combination dosages are determined using a cytotoxicity assay.

27. The method of any one of claims 1 -26, wherein the first therapeutic agent comprises a small molecule inhibitor, a protein, a nucleic acid, or a CAR-T cell.

28. The method of claim 27, wherein the first therapeutic agent comprises a MEK inhibitor.

29. The method of claim 28, wherein the first therapeutic agent comprises cobimetinib.

30. The method of any one of claims 1 -29, wherein the second therapeutic agent comprises a small molecule inhibitor, a protein, a nucleic acid, or a CAR-T cell.31 . The method of claim 30, wherein the second therapeutic agent comprises a pan-RAF inhibitor.

32. The method of claim 31 , wherein the second therapeutic agent comprises belvarafenib.

33. A method of determining one or more combination in vivo dosages each comprising a first in vivo dosage of a first therapeutic agent and a second in vivo dosage of a second therapeutic agent for treating a cancer comprising converting the one or more in vitro combination dosages determined in any one of claims 1 -32 to the one or more combination in vivo dosages based on the plasma free drug concentrations of the first therapeutic agent administered according to a dilution series to a subject and the plasma free drug concentrations of the second therapeutic agent administered according to a dilution series to a subject.

34. The method of claim 33, wherein the subject is a mouse or a human.

35. A method of treating a cancer in an individual by administering a first therapeutic agent and a second therapeutic agent according to any one of the one or more combination in vivo dosages determined in claim 33 or 34.

36. The method of claim 35, wherein the individual is a human.

37. The method of claim 35 or 36, wherein the cancer is a blastoma, a colorectal cancer, an ovarian cancer, a lung cancer, a pancreatic cancer, a skin cancer, a kidney cancer, a bladder cancer, a breast cancer, a gastric cancer, an esophageal cancer, an esophageal cancer, a head and neck cancer, a thyroid cancer, a sarcoma, a prostate cancer, a testicular cancer, a uterine cancer, a bone cancer, a brain cancer, an endometrial cancer, a cervical cancer, a thymic carcinoma, or a blood cancer.

38. The method of claim 37, wherein the skin cancer is melanoma.

39. The method of claim 38, wherein the melanoma comprises a mutation of a biomarker gene.

40. The method of claim 39, wherein the melanoma comprises a BRAF mutation or an NRAS mutation.41 . The method of claim 40, wherein the BRAF mutation is a V600E mutation.

42. The method of claim 40, wherein the NRAS mutation is a Q61 hotspot mutation.

43. The method of any one of claims 35-42, wherein the first therapeutic agent and the second therapeutic agent exhibit a synergistic effect when administered to the individual according to the one of the one or more combination in vivo dosages.