Systems and methods of use of regulatory network machines

Abstract

A regulatory network machine, including: a dissipative dynamic system as a regulatory network including a plurality of nodes and directed edges, in which the plurality of edges connects at least two nodes in the plurality of nodes, and the plurality of edges determines how the connected nodes interact, in which the dissipative dynamic system occupies an initial state; a plurality of inputs to the dissipative dynamic system, in which applying an input in the plurality of inputs to the dissipative dynamic system transitions the dynamic system from the initial state to corresponding equilibrium state, in which the corresponding equilibrium state is based on the input in the plurality of inputs and the initial state; and a finite state machine which includes a record of the plurality of inputs, the corresponding equilibrium state to each input in the plurality of inputs, and a map of possible transitions between equilibrium states.

Description

Tufts T002882 WO.PCT Quarles 166118.01558SYSTEMS AND METHODS OF USE OF REGULATORY NETWORK MACHINESCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 63 / 721,912, filed November 18, 2024, and U.S. Provisional Application No. 63 / 778,838, filed March 27, 2025, each of which is incorporated herein by reference in its entirety for all purposes.BACKGROUND

[0002] Regulatory networks describe collectives of entities (e.g., proteins) that regulate each other’s level (e.g., via protein regulation of gene expression) and are a class of dissipative dynamic system. Regulatory networks are generally viewed as mechanistic systems, in which topology must be altered to effect change to system outputs. There exists a need to reconceptualize regulatory networks in order to better understand how a network can respond to inputs, or outside stimulus, without change to the topology of the network itself. This has implications for biomedicine and synthetic biology.SUMMARY

[0003] Disclosed herein are methods and systems for a regulatory network machine, and modeling a system. In various embodiments, the methods and systems may include one or more of the following.

[0004] In one aspect, a regulatory network machine is disclosed. The regulatory network machine includes: a dissipative dynamic system including a plurality of nodes and a plurality of directed edges, a plurality of inputs that can be applied to the dissipative dynamic system; and a finite state machine (FSM) comprising the equilibrium states of the regulatory network and directed edges representing the transition between equilibrium states occurring under a specific applied input that induces a change between system states. In some embodiments, nodes represent the level of a phy si cal / chemi cal property (e.g., the concentration of a protein) and edges represent the influence of one node’s property on the expression of another (e.g., the concentration of one protein regulates the expression of another protein through genetic interaction); the plurality of directed edges may connect at least two nodes, and the plurality ofTufts T002882 WO.PCT Quarles 166118.01558edges may determine how the connected nodes interact. Applying an input in the plurality of inputs to the regulatory network may transition the dissipative dynamic system into a corresponding equilibrium state. The NFSM may include a record of the plurality of inputs, the corresponding equilibrium state to each input in the plurality of inputs, and a map of possible transitions between equilibrium states. The FSM provides a mapping detailing which equilibrium state transitions occur with the application of different inputs, where transitions between equilibrium states may depend on both the specific equilibrium state considered and the specific input applied.

[0005] In another aspect, a method of modeling a system is disclosed. The method includes: building a dissipative dynamic system of interest (e.g., a signaling network known to regulate cancer cell properties) including a plurality of nodes and directed edges representing the regulatory interactions between nodes; determining a plurality of inputs to the dissipative dynamic system; applying an input in the plurality of inputs to the dynamic system as it occupies each of its equilibrium states; and outputting a finite state machine that maps all the transitions between each equilibrium state for each applied input. In the regulatory network, the plurality of edges may connect at least two nodes in a directed fashion, where the level of one node exerts a regulatory influence on the level of another node, and the plurality of edges may determine how the connected nodes interact. The specific input, applied to the system when it occupies one equilibrium state, may push the regulatory network into a corresponding equilibrium state, where the transition between equilibrium states may depend on both the initial equilibrium state and the specific input applied. The FSM therefore provides a mapping of possible transitions between equilibrium states under the application of each input, and may show path-dependencies, pathirreversibilities, cycles, and unreachable equilibrium states occurring under patterns of applied inputs.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. 1 shows a schematic of the persuadability spectrum. In a persuadable system, simple information signals (e.g., pharmaceuticals, treats, words) can activate inherent competencies in a system to get it to emit a desired behavior, or to perform a desired function. In contrast to persuadability, a programmable system is one in which detailed information is used toTufts T002882 WO.PCT Quarles 166118.01558precisely specify (e.g., micromanage) how a system should behave in response to different conditions and in general comes at more effort and expense than being able to persuade a system to emit desired behavior.

[0007] FIGS. 2A-2F show complete RNM for the MAPK Cancer Cell Fate Network of Grieco et. al. (74) The MAPK Cancer Cell Fate GRN (FIG. 2A) has been decomposed into: (i) an input node layer (‘DNA damage’, ‘EGFR stimulus’, ‘FGFR3 stimulus’, ‘TGFBR stimulus’, see (FIG. 2B); (ii) a network core (all non-input and non-output nodes in FIG. 2A, not shown); and (iii) an output node layer (‘Apoptosis’, ‘Growth Arrest’ and ‘Proliferation’ nodes in FIG. 2C), representing the output responses of the network that form 15 unique equilibrium states (FIG. 2C). Each input node variable represents an information bit, which taken together, form 16 input "words" where the color bar indicates expression levels (FIG. 2B). Each equilibrium output state is associated with an equilibrium type (e.g., point attractor, limit cycle, and to a unique expression patterns of all output nodes (FIG. 2C, where color bar indicates expression levels). Nodes in A are color coded to their hierarchical level (115). We further associate output equilibrium states with no apoptosis, low cell cycle arrest, and high proliferation as indicative of the cancer cell state (e.g., ‘Apoptosis’=0, ‘Growth Arrest’ =0, and ‘Proliferation’ = 1 represents the ideal cancer state with closest state matches indicated in FIG. 2B), whereas limit cycle cell states that cycle through proliferation, cell cycle arrest, and apoptosis expression regimes are indicative of the health cell state (FIG. 2B). The pathway analysis of the G-NFSM showing sustained input interventions leading from a cancer-like State 2 to healthy States 9, 10, 11, and 12 is shown in FIG. 2D, where node color indicates the Euclidean distance of the equilibrium output state from the idealized cancer state. The complete set of E-NFSMs for the system are shown in FIG. 2E, indicating temporary stimuli can lead to permanent transition to a cancer state (sub-graphs ‘Held at 18’ and ‘Held at 110’ in FIG. 2E), but that there are no temporary stimuli that can treat cancer. The full G-NFSM for the system is shown in FIG. 2F, revealing all held interventions that allow for access and movement between states.

[0008] FIGS. 3A-3H show analogue computing uses dynamic systems to perform individual computations (FIG. 3 A and FIG. 3B) as well as coordinated computational programs (FIG. 3C and FIG. 3D) that can be analogized to a hybrid Turing-Hopfield digital computing machine (FIG. 3F, FIG. 3G, and FIG. 3H). Here dynamic systems with two time-dependentTufts T002882 WO.PCT Quarles 166118.01558variables, ‘HO’ and ‘Hl’, are considered. An analogue computation is defined as a trajectory in state space, where the input is represented by initial conditions (orange, green, and blue circles in FIG. 3A), the computational process is the direction-field-guided time-evolution of the system (orange, green, and blue trajectories in FIG. 3 A) and the output is the resulting system state (black dot in FIG. 3 A). While the system in A functions as a homeostat, the time-evolution of the same system can be used as a counter that activates a process a number of times before ceasing (FIG. 3B). Our RNM model goes further to create a computational program using externally-set inputs to a dynamic system (‘10’ and ‘13’ in FIG. 3C) to select subsets of the system’s full state space (planes in FIG. 3C). This has the effect of driving analogue computations between equilibrium points of two state-space subsets with each change in the applied input state, creating a computational trajectory that spans the two state sub-spaces (green line in FIG. 3C). This allows the dynamic system to occupy multiple different equilibrium points, and to transition between these different equilibria under the influence of an applied input state, which can be organized into a state transition diagram we call the G-NFSM (FIG. 3E). Our RNM model can be analogized to a hybrid Turing-Hopfield digital computing machine (FIG. 3F, FIG.3G, and FIG. 3H), which, like a classical Turing machine, is fed a tape of input state symbols (FIG. 3F) that are read by a read-head moving to the right in time (FIG. 3F). Yet, like a Hopfield network, the system also has associative memory, such that each state represents a pattern of output variables, which are the computational output (FIG. 3F and FIG. 3G). A detailed comparison of the properties of Turing, Hopfield, and Regulatory Network Machines is summarized in Table 2.

[0009] FIGS. 4A-4G show core characteristics of monostable RNM computational programs. FIG. 4A shows a simple 3-node regulatory network and FIG. 4E shows a visualizable complete state space. The regulatory network studied is shown in panel FIG. 4A, with input states of the system shown in FIG. 4B, and the two output states in FIG. 4C. The G-NFSM for the system is shown in FIG. 4D. As the full state space of this system can be visualized, we can see how the transitions of the G-NFSM arise in response to applied inputs (FIG. 4E and FIG. 4F). The complete state space of the dynamic system has dimensions made of the probability of HO expression, the probability of Hl expression, and the probability of the input SO (FIG. 4E). Setting S0=0.0 or 80=1.0 selects two regions of the complete state space (two state sub-spaces),Tufts T002882 WO.PCT Quarles 166118.01558which each have a slice of the full direction field (FIG. 4E and FIG. 4F). The output states, State 0 and State 1 can be seen as individual equilibrium points on each state sub-space plane (labeled circles ‘0’ and ‘ 1’ in FIG. 4E and FIG. 4F). At time t=0.0, the system starts in an initial condition equivalent to state 0 (‘t0’ in FIG. 4E, FIG. 4F, and FIG. 4G) with input S0=0.0 applied and held (equivalent to stating that input state 10 is applied and held); in this configuration the system is in a stable equilibrium and will not change in time (FIG. 4G). At time tl=60, the input state is changed to II (equivalent to changing S0=1.0), which injects the system into the second state sub-space (see FIG. 4E), where it is no longer in equilibrium (see tl of FIG. 4E and FIG. 4F). The system follows the direction field of the new state sub-space plane to a new equilibrium (see t2 of FIG. 4E, FIG. 4F, and FIG. 4G). As there is only one equilibrium state in each state subspace plane, the system output state is reversible to the original condition when the input state is changed back to 10 (see t3 and t4 of FIG. 4E, FIG. 4F, and FIG. 4G).

[0010] FIGS. 5A-5H show core characteristics of multistable RNM. Core characteristics of multistable RNM are shown using a simple 3-node regulatory network (FIG. 5A) with a visualizable complete state space (FIG. 5E). The regulatory network is shown in FIG. 5A, the two input states in FIG. 5B, and the four output states in FIG. 5C. The G-NFSM is shown in FIG.5D. We found that in some cases this system responds to transient application of input states with permanent changes to output state and therefore also has an E-NFSM (FIG. 5E). As the full state space of this system can be visualized, we can see how the transitions of the G-NFSM and E-NFSM arise in response to a sequence of applied inputs (FIG. 5F and FIG. 5G). The complete state space of the dynamic system has dimensions made of the probability of HO expression, the probability of Hl expression, and the probability of the input SO (FIG. 5E). Setting S0=0.0 or 80=1.0 selects two regions of the complete state space (two state sub-spaces), where each plane contains a functional slice of the full direction field (FIG. 5F and FIG. 5G). The multiple output states are individual equilibrium points on each state sub-space plane (labeled circles ‘O’, ‘1’, ‘2’ and ‘3’ in FIG. 5E and FIG. 5F). Note that plane selected by S0=0.0 (input state 10) contains three unique equilibrium points and is therefore a multistable state sub-space. At time t=0.0, the system starts in an initial condition equivalent to State 1 (‘t0’ in FIG. 5F, FIG. 5G, and FIG. 5H) with input S0=0.0 (10) applied and held; in this configuration the system is in a stable equilibrium and will not change in time (FIG. 5H). At time tl=60, the input state is changed toTufts T002882 WO.PCT Quarles 166118.01558Il (equivalent to changing S0=1.0), which injects the system into the second state sub-space (see F), where it is no longer in equilibrium (see tl of FIG. 5F and FIG. 5G). The system follows the direction field of the new state sub-space plane to a new equilibrium, which corresponds to State 3 (see t2 of FIG. 5F, FIG. 5G, and FIG. 5H). At t3 S0=1.0 (input 10) is reapplied and the system is re-injected into the original state sub-space, however, the system output tracks to a new output State 2 due to its new location in the state sub-space and the presence of multiple equilibria altering the direction fields (see t3 and t4 of FIG. 5F, FIG. 5G, and FIG. 5H).

[0011] FIGS. 6A-6D show NFSM predict the emission of categorically different behaviors associated with certain input states, creating a map of both levels and modes of system behavior. Here a cyclic regulatory network (FIG. 6A) with five unique output states in association with eight input states (FIG. 6B) forms a monostable NFSM with a limit cycle attractor as output State 1 (where all other states have point attractors) (FIG. 6C). Examining its behavior over time, starting the system in State 0 and holding with input state 10, then changing to input state 14, leads to a transition from a monotonically stable pattern of gene expression to a genetic oscillator, while input state 14 is applied and held (FIG. 6D). The genetic oscillation ceases when the input state is reverted to 10 (FIG. 6D). The behavior of the system is predicted by the G-NFSM, which shows the point attractor of the start state, State 0 (indicated by a black arrow and bold green halo in FIG. 6C) predicted to transition to the limit cycle of State 1 (indicated by thin green halo in FIG. 6C) via a transition induced by 14, and to proceed back from State 1 to State 0 via a transition induced by input 10 (FIG. 6C). The transitions are shown highlighted in light green (FIG. 6C).

[0012] FIGS. 7A-7F show stem cell differentiation in response to transient exposure to morphogens is a context-dependent, event-driven state transition in a multistable RNM system. The ESC regulatory network modeled in this example is shown in FIG. 7A. High levels of NANOG, OCT4, and SOX2 are known to correspond with undifferentiated ESC (corresponding to output State 6, FIG. 7B), whereas differentiation towards a neuroectoderm lineage occurs when levels of NANOG and OCT4 drop, leaving SOX2 high (corresponding to output State 1, FIG. 7B), and differentiation towards a mesoendoderm lineage occurs when levels of NANOG and SOX2 drop, leaving OCT4 high (corresponding to output State 3, FIG. 7B). Our RNM analysis of the ESC network in FIG. 7A indicates it is a multistable system with seven uniqueTufts T002882 WO.PCT Quarles 166118.01558output states (FIG. 7B), both a G-NFSM (FIG. 7C) and an E-NFSM (FIG. 7D), and a high average Intelligence Potential of 1.64 (see “Full Chain” network of Table 1). The biological observation of high NANOG, OCT4, and SOX2 in undifferentiated ESC indicates that the biological system starts in State 6 (marked with a black block arrow and bold green highlight in FIG. 7C). The G-NFSM suggests that both States 1 and 3 are accessible from State 6 via application of input 16 and 15, respectively (trajectories highlighted in pink in FIG. 7C).However, State 6 exists in monostable context 10; therefore, while transient application of 16 or 15 leads to transition of the system to State 1 or State 3, it is not a permanent change, and the system reverts to State 6 once input 16 or 15 are removed (FIG. 7E). The E-NFSM shows us that it is only in context 14 that a permanent change of the system from State 6 to States 1 or 3 can be achieved from a transient application of the same 16 or 15 inputs, with respective paths highlighted in green (FIG. 7C and FIG. 7D). In the time evolution of the system shown in FIG.7F, we see that by first switching to State 4 with the application of 14, a transient exposure to 15 now leads to a permanent switch of the system to State 3 even with a return to the original held context established by 14 (FIG. 7F).

[0013] FIGS. 8A-8H show multiple - apparently identical - systems can show dramatically different responses to the same intervention yet are deterministically described within the RNM framework. The regulatory network modeled in this example is shown in panel FIG. 8A, which was found to have 7 unique output states (FIG. 8B) and to have a G-NFSM (FIG. 8C) and multiple E-NFSM (FIG. 8D). The G-NFSM shows four transitions from State 5 to four unique states (State 0, State2, State 4, and State 6) happening with the application of the same input state 17 (bold arrows of FIG. 8C). The E-NFSMs show four different input contexts (for systems with a baseline-normal held input state of 10, II, 14 and 15) where State 5 transitions to another state under input 17 (bold arrows of FIG. 8D). In time-course studies, we find that systems with a held input state of 15 (FIG. 8E), 10 (FIG. 8F), 14 (FIG. 8G) and II (FIG. 8H) are initially stable in State 5, as predicted by the G-NFSM and E-NFSMs. Subsequent transient application of input 17 to each of the four systems leads to four different final states (FIG. 8E, FIG. 8F, FIG. 8G and FIG. 8H), as predicted by the E-NFSMs (FIG. 8D).

[0014] FIGS. 9A-9H shows osmoadaptive set-point control is an analogue computational system naturally “computing” the correct response required to maintain cell volume (volcell) at aTufts T002882 WO.PCT Quarles 166118.01558target value for a wide range of environmental conditions. Here the same physical process of osmotic-pressure-induced cell volume change is compared in an inanimate vesicle (FIG. 9A) and in an osmoadapted yeast cell (FIG. 9B). The dimensions of the systems’ full state spaces are the internal cell osmolytes (ni), cell volume (volcell), and environmental osmolyte concentrations (mo) (FIG. 9C - FIG. 9H). In the yeast cell, the osmotic process interacts with a regulatory network involving a sensor for cell volume via membrane strain (PhoQ), which conveys information regarding cell volume through to the HOG-MAPK signaling pathway, thereby altering levels of intracellular glycerol, which contributes to, and therefore allows the cell to change, total internal cell osmolytes (FIG. 9B). For each initial system state (an example initial state is given by the small green dot in FIG. 9F and FIG. 9H) the system dynamics naturally “compute” a new state (large green dot in FIG. 9F and FIG. 9H) by simply evolving in time under the system dynamics (green trajectory of FIG. 9F and FIG. 9H). The direction field of the inanimate vesicle maintains a surface of equilibrium states (shown as the dotted black line in FIG. 9E and FIG. 9F), meaning there is a range of possible equilibrium state vesicle volumes for different environmental osmolyte concentrations and starting system states. In contrast, the yeast system’s direction field is in the form of an attractive limit cycle with a single equilibrium state appearing as a central point corresponding to the system’s desired target volume (FIG. 9G and FIG. 9H, where equilibrium state / target volume are indicated by the large green dot). In 3D, the direction field for the yeast system is cylindrically-shaped, meaning the attractive limit cycle will converge to the consistent target cell volume for a wide range of environmental and internal osmolyte concentrations, thereby demonstrating that the system has excellent control of cell volume (FIG. 9B).

[0015] FIGS. 10A-10C show G-NFSM is useful as a detailed set of instructions specifying which inputs engage the specific output states of signaling networks important in disease processes, such as the cross-regulation network between PAM, RAS / ERK, and Wnt / b-catenin (adapted from Fig. 7 of Glaviano et al. (73)) The regulatory network in FIG. 10A specifies activation / inhibition interactions between biologically-relevant input, hub, and effector nodes, making it a suitable candidate for our RNM framework. A set of input states were defined from the input nodes (FIG. 10B), and three unique output states were returned from our analysis, which are shown with respect to effector node levels in FIG. 10B. Our analysis also determinedTufts T002882 WO.PCT Quarles 166118.01558that the dynamic system for this regulatory network is monostable, with a 1 : 1 reversible mapping between each input and output state, leading to a fully-connected G-NFSM (FIG. IOC), no E-NFSM on account of its monostability, and a low Intelligence Potential of 0.8 (see ‘ AKT Net’ in Table 1). The G-NFSM specifies the exact input states (as labels on transition arrows) that will result in the desired output state (FIG. 10C), which are intrinsic to the system and can be accessed without having to alter the network topology.

[0016] FIGS. 11A-11F show direct comparison between RNM of Continuous vs.Boolean GRN models shows nearly perfect correspondence between the two modeling approaches. The same GRN network is modeled in both the Boolean (FIG. 11 A) and Continuous (FIG. 11D) cases, with the same returned set of equilibrium states for the Boolean (FIG. 11B) and Continuous (FIG. HE) cases (when the states of the continuous model are rounded up to 0.0 or 1.0). The G-NFSM and E-NFSMs, which indicate input-driven transitions between the equilibrium states, are also almost identical, where here the E-NFSMs of the Boolean (FIG. 11C) and Continuous (FIG. 1 IF) GRN models are shown. The input states of this system are identical between the Boolean and Continuous GRN models and not shown.

[0017] FIGS. 12A-12C show close correspondences exist between direction fields of continuous models of GRN based on differential equations, and State Transition Graphs (STG) of Boolean models of GRN. Direction fields and STG are compared for simple GRN with FIG.12A) double activator relationship, FIG. 12B) an activator and inhibitor relationship, which produces a limit cycle in both direction fields and STG, and FIG. 12C) a double inhibitor relationship, which produces two point attractors at (0,1) and (1,1) and a metastable saddle point at (0.5, 0.5) in both direction fields and STG. For STG, cyclic patterns of activity average to the correct dynamic equilibrium state seen in the continuous model, e.g., persistent switching between states (0, 1) and (1,0) in the STG of FIG. 12A) represent a metastable saddle point at their average, (0.5, 0.5) , while persistent cycling through states (0,0), (0,1), (1,1), (1,0) represents a limit cycle at the state average of (0.5, 0.5).

[0018] FIG. 13 shows networks studied in Intelligence Potential investigation with results summarized in Table 2.Tufts T002882 WO.PCT Quarles 166118.01558

[0019] FIG. 14 shows activator and inhibitor interaction function based on a Hill Equation base function that specifies the rate of change of the probability of node expression in the network.

[0020] FIG. 15 shows activator and inhibitor interaction function based on a Logistic Equation base function that specifies the rate of change of the probability of node expression in the network.

[0021] FIG. 16 shows an example regulatory network, where nodes Ho and Hl each have two regulatory inputs, used for demonstrating options for combining multiple regulatory inputs.

[0022] FIG. 17 shows an example of a fully analytical solution for the equilibrium state of a network when the network is parameterized using the Hill function formalism.

[0023] FIG. 18 shows steady-state cell volumes for cells with different perimeters (e.g., plant cell wall, yeast cell wall, and mammalian plasma membrane) for models without osmoadaptation.

[0024] FIGS. 19A-19D show osmotic cell volume changes in different topological regimes. Top shows the concept of the different deformation regimes with volume change, where FIG. 19B shows an undeformed cell, FIG. 19A shows the cell where and FIG. 19C shows the cell where elastic deformation is occurring. FIG. 19D shows steady state cell volume for a variety of cell types as a function of environmental osmolyte concentration for cell without osmoregulation.

[0025] FIG. 20 shows response functions showing modulation of glycerol production (inhibitor curve) and glycerol efflux (activator curve) by membrane strain.

[0026] FIGS. 21A-21C show illustration of the osmoadapted cell's ability to maintain its volume at a setpoint. FIG. 21A shows the environmental osmolyte concentration as a function of time, FIG. 2 IB shows the cell volume as a function of time, and FIG. 21C shows the intracellular glycerol concentration as a function of time.

[0027] FIG. 22 shows an illustration showing general concept of using RNMs to detect and characterize GRN equilibrium states, determine input-driven output transitions, and read inputs that transition the GRN to desired stable outputs.Tufts T002882 WO.PCT Quarles 166118.01558

[0028] FIG. 23A shows a schematic of a method of modeling a system.

[0029] FIG. 23B shows a method for outputting an FSM.

[0030] FIG. 24 shows a schematic of a computer system.DETAILED DESCRIPTION

[0031] The disclosures of any these patents, patent applications, and publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art as known to those skilled therein as of the date of the invention described and claimed herein. The instant disclosure will govern in the instance that there is any inconsistency between the patents, patent applications, and publications and this disclosure.

[0032] Before any embodiments of the disclosure are explained in detail, it is to be understood that the disclosure is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The disclosure is capable of other embodiments and of being practiced or of being carried out in various ways.

[0033] It is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

[0034] In accordance with some embodiments of the disclosed subject matter, mechanisms (which can include, for example, systems and methods) for a regulatory network machine are provided.

[0035] Regulatory networks, such as gene regulatory networks (GRNs), are important for efforts in biomedicine and synthetic biology. They have classically been viewed as mechanistic, ‘clockwork-like’ systems, assumed to require direct changes to network topology via genetic modification to effect significant, stable changes in their output functions. This perspective limits therapeutic approaches, suggesting a need for alternative conceptual framing. Here, it is shown that regulatory networks can behave as analog computational agents to perform sophisticated information processing, driven by patterns of stimulus inputs, without a change in networkTufts T002882 WO.PCT Quarles 166118.01558topology. New conceptual and computational frameworks for working with regulatory networks, call the Regulatory Network Machine (RNM), are described herein. Given a regulatory network model, the RNM framework enables the construction of detailed maps that embody the “software-like” nature of a regulatory network, providing easy identification of the specific interventions necessary to achieve desired outcomes. The use of the RNM framework helps to gain insights into important biological examples including yeast osmoadaptation, PI3K / AKT / mTor cross-signaling cascades, and embryonic stem cell differentiation. System-level outcomes can be induced in a biological system without requiring genetic rewiring. The RNM approach also elucidates system factors that support the innate computational capabilities of regulatory networks, and ascertains the interventions that provide the most control for the least amount of effort. The insights gained from the RNM framework can be used to expand the horizons of biomedicine, providing an effective avenue to move beyond “single-factor, single treatment” and “one-constant-dose” biomedical paradigms.

[0036] A regulatory network refers to a system of interconnected elements that regulate each other’s activity with a defined functional connectivity map. A Regulatory Network Machine (RNM) is made up of a regulatory network, a set of input states, and a Network Finite State Machine (NFSM).

[0037] The regulatory network may be a dissipative dynamic system, made up of elements (e.g., edges and nodes) which interact with each other based on a set of rules or equations. A dynamic system can be described by a set of equations which estimate how the variables in the system (e.g., edges and nodes) change over time, and how the variables interact. The dynamic system can be viewed as occupying a state space, wherein the state space is defined by set of equations describing the system at a given point in time. In some embodiments, the dynamic system is governed by a set of differential equations. In some embodiments, the differential equations are non-linear partial differential equations.

[0038] In some embodiments, a system may be a mathematical model. A system may be an established model of a known system (e.g., a specific gene regulatory system). In other embodiments, a system may be experimentally queried (e.g., determined based on experimental results).Tufts T002882 WO.PCT Quarles 166118.01558

[0039] Elements of a dynamic system may be referred to as nodes, and nodes are connected by edges. The edges connecting two nodes determine how the nodes interact with one another. For instance, an edge connecting node A and node B can determine that node A inhibits the activity of node B. A gene regulatory network (GRN) refers to a set of gene products corresponding to a biological system. Multiple nodes can influence a single node; the way these influences interact is determined by the network’s dynamics. For instance, multiple inhibiting interactions can be referred to as multiplicative.

[0040] Nodes may be input / sensor nodes (e.g., capable of receiving outside information, such as an external input), internal / hub nodes (e.g., are not capable of directly receiving or outputting external information), or output / effector nodes (e.g., provides responses). Input, internal, and output nodes all interact with one another. An input refers to a force that is enacted upon the system (in a biological system, an input may refer to morphogens, growth factors, and physical properties such as light, temperature, or pressure). An internal node refers to a node that is impacted by an input node, but is not directly impacted by an external input. In a biological system, an internal node could refer to genes or molecular components. An output node influences the external environment. A network includes a plurality of nodes; in general, a network includes a plurality of input nodes, a plurality of internal nodes, and a plurality of output nodes.

[0041] An “input event” or “input” refers to a perturbation to the system. An input refers to an action on the input nodes, rather than changing the input nodes themselves. An input may be sustained (e.g., applied and held for a duration in time). Sustained inputs may also be referred to as “context-defining inputs.” An input may be transient (e.g., temporarily applied to a system, and then removed from the system). A system may be perturbed (e.g., moved out of an initial state or initial equilibrium state) by an input. A system may return to its initial state after the input is removed; this is referred to as a transient event. Alternatively, a system may be permanently altered by an input.

[0042] In some embodiments, an input may have a binary value, corresponding to the presence of absence of an input. Alternatively, the binary value may correspond to high or low presence of the input. A network may be continuous (e.g., real-valued). In some embodiments, anTufts T002882 WO.PCT Quarles 166118.01558input may have a discrete value selected from a continuous range of variables corresponding to the degree of presence of the input.

[0043] A state refers to the status of the elements of a regulatory network. A state can be described by the mathematical equations that govern the regulatory network. A sub-state refers to the status of a node of a regulatory network. A system can transition between states in response to inputs and interactions between nodes of the system. A state may also be referred to as a space or sub-space. A trajectory refers to a record of the states and transitions between states a network undergoes over time. A regulatory network has an initial state. Once an input is enacted on the network, the regulatory network progresses through intermediate states and eventually comes to an equilibrium state or final state.

[0044] Equilibrium refers to a state of balance or stability. A system of equilibrium does not exhibit net change over time. An equilibrium can either be static (no change) or dynamic (brief changes without net change over a period of time). A system may trend towards an equilibrium state. An input may “push” a system out of an equilibrium state. An input may “push” or “transition” a system towards a different equilibrium state than the system occupied prior to the input being applied.

[0045] A given system may have “internal” and “external” states. An internal state accounts for the sub-state of every node and edge of the system, including internal nodes. An output state accounts for the state of the external nodes as a subset of all nodes in the system (e.g., it ignores the sub-states of internal nodes). More than one internal state can have the same output state. Therefore, a system may have more internal states than it does external states.

[0046] In some embodiments, external states can be grouped together into “effector” states. For instance, in the case of a cancer model, an “effector” may be defined as cell proliferation, growth arrest, and apoptosis. External states may then be grouped together based on whether they share an effector state.

[0047] In some embodiments, a first input is applied to a dynamic system and results in the dynamic system occupying a first equilibrium state. In some embodiments, a second input is applied to the dynamic system which pushes the dynamic system into a second equilibrium state. In some embodiments, the second equilibrium state is the same as the first equilibrium state; inTufts T002882 WO.PCT Quarles 166118.01558other embodiments, the second equilibrium state is a different state than the first.“Corresponding” does not necessarily imply a 1:1 mapping of a first state to a second state. A system may be “monostable,” in which a given input has a single corresponding equilibrium state. In some embodiments, multiple inputs have the same corresponding equilibrium states. In these cases, the second equilibrium state is a single equilibrium state. In some embodiments, a system may be “multi stable,” in which a single input may have multiple corresponding equilibrium states. In these cases, the second equilibrium state may be more than one state.

[0048] A finite state machine may be a mathematical model used to record states and transitions between states. A network finite state machine may include a record of the plurality of inputs, a corresponding equilibrium state to each input in the plurality of inputs, and a map of possible transitions between equilibrium states. A network finite state machine may be used to construct a state transition diagram. A network finite state machine may also be used to predict dynamics or behaviors of a system when it is in a particular state. A general NFSM (G-NFSM) refers to an NFSM of a network in response to a context-defining or sustained input. An even-driven NFSM (E-NFSM) an NFSM of a network in response to a transient input. A finite state machine may represent all possible transitions between equilibrium states for each equilibrium state and each input, showing path-dependencies, cycles, and irreversibilities in the ability to reach equilibrium states under patterns of input.

[0049] In some embodiments, the network finite state machine may be used to predict the behaviors of the dynamic system when the dynamic system occupies a particular state. A behavior refers to a function, or output, of the dynamic system.

[0050] In some embodiments, a finite state machine may be used to determine distances between different external states. For instance, it can calculate the Euclidean distance between two external states (such as a cancer state to a non-cancer state). This allows one to assess how difficult or easy it might be to push a system into a different external state.

[0051] In some embodiments, the finite state machine may be used to calculate an intelligence potential of the regulatory network machine. The intelligence potential may be based on at least one of a multi state ratio or a context ratio.Tufts T002882 WO.PCT Quarles 166118.01558

[0052] In some embodiments, the dynamic system may be tested to determine how persuadable the system is. Persuadable refers to the degree to which a system transitions in response to information signals. For instance, information signals may activate inherent competencies in the system. Highly persuadable systems exhibit complex, autonomous responses to low-information content signals. Minimally persuadable systems exhibit little to not responses to low-information content signals.

[0053] In some embodiments, the regulatory network machine can be used to model a biological system. For instance, the dynamic system can correspond to a biological system. In some embodiments, the biological system corresponds to yeast osmoadaptation, P13K / AKT / mTor cross-signaling cascades, or embryonic stem cell differentiation. In some embodiments, the inputs can correspond to environmental variables. In some embodiments, the environmental variables correspond to morphogens, growth factors, light, temperature, pH, or pressure.

[0054] In some embodiments, systems and methods described herein can be used to find ways to control systems. For instance, the systems and methods described herein can be used to investigate biological systems, and may be used to develop treatment for a disease, increase longevity, repair a birth defect, induce the bioengineering of in vitro living constructs (like biobots or synthetic biology construct), or induce regeneration of an injured or missing organ or appendage, such as biological systems. The regulatory network machine can determine whether a transient input (e.g., a single or short-term dose of medicine) can have long-term or permanent effects (e.g., on health of a subject). In other embodiments, the systems and methods described herein may be used to investigate non-biological systems, including but not limited to, power grids, organizational charts, economic networks, and logistics and distribution networks. The regulatory network machine can help determine how to effect permanent changes in a multistable system. This has applications in stem cell differentiation, medicine, synthetic biology, and more.

[0055] In some embodiments, an initial state based on a biological system may be based on data from a subject. For instance, a sample (e.g., a blood sample, urine sample, tissue sample, biopsy, liquid biopsy, etc.) may be collected from a subject and analyzed to measure interpretable values (e.g., using a DNA microarray or other similar methods). Those measured values may beTufts T002882 WO.PCT Quarles 166118.01558used to determine an initial state of the system. That initial state can then be related to an output state. One example is shown in FIG. 13; the vertical axis of the plot shows factors that can be measured, and the horizontal axis are output states.

[0056] The measured interpretable values may be based on multi-omic analysis and / or patient health indicators. For instance, the values may be based on genomics, transcriptomics, proteomics, metabolomics, or epigenomics. The values may also be based on measures of hormone levels, enzyme levels, organ function, or other patient health indicators.

[0057] In some embodiments, output states may exist on a range from “health” to “disease” states. States can be grouped together based on where they exist on the spectrum of health to disease. The spectrum may be defined based on one or more effector states. For instance, if the system is a cancer system, an output state may be assessed for whether it is associated with apoptosis, growth arrest, and proliferation; output states that are associated with these characteristics may be grouped together as “cancer” or “disease” states. In contrast, output states that are not associated with apoptosis, growth arrest, or proliferation may be grouped together as “normal” states.” It is important to note that these clusters do not need to be binary. For instance, a spectrum of “health” to “disease” may include normal states, pre-cancer, early cancer, cancer, and metastatic cancer.

[0058] EXAMPLES

[0059] Overview

[0060] Gene regulatory networks (GRNs) are critically important for efforts in biomedicine and biotechnology. It has classically been assumed that GRNs require direct changes to network topology to effect significant, stable changes in their output functions. This perspective limits therapeutic approaches, suggesting a need for alternative conceptual framing. Here we show how GRNs can behave as analog computational agents capable of performing sophisticated information processing, and how to achieve stable changes to GRN output without requiring a change in network topology. We achieve this by introducing and developing a new framework for working with GRNs called the Regulatory Network Machine (RNM). Our RNM framework encapsulates the combination of: 1) a dissipative dynamic system, where here we focus on computationally modeled GRNs; 2) a set of inputs to the system that can be externallyTufts T002882 WO.PCT Quarles 166118.01558set or measured; 3) system output states with identifiable relevance to biotechnological or biomedical objectives; and 4) Network Finite State Machines (NFSMs), which are maps detailing how the system changes equilibrium state in response to patterns of applied inputs. As an extension to attractor landscape analysis, the NFSMs are detailed, input-driven state-transition maps that embody the “software-like” nature of the GRN, providing easy identification of the specific applied interventions necessary to achieve desired, stable biological outcomes, without requiring direct changes to network topology via genetic engineering. With pertinence to basal cognition, biological information processing, and various biomedical and biotechnological objectives, we specify analysis techniques for NFSMs that identify path-dependencies, pathdegeneracies, irreversibilities, and cycles, which we further demonstrate to be the fundamental basis for “intelligent” behaviors. We illustrate the use of our RNM framework in important biological examples including yeast osmoadaptation, PI3K / AKT / mT0R cross-signaling cascades, embryonic stem cell differentiation (OCT4-SOX2-NANOG signaling), and in cancer renormalization therapy (MAPK signaling cascades in cancer). Ultimately, insights gained from our RNM framework can expand the horizons of biomedicine, providing an effective avenue to move beyond “single-factor, single treatment” and “one-constant-dose” biomedical paradigms.

[0061] Introduction

[0062] Surviving and thriving in highly dynamic, stochastic environments requires living systems to be adept at sensing environmental conditions, processing the information obtained from the senses, and implementing a response that is maximally effective for the organism's survival. As even single cell organisms lacking central nervous systems are capable of sophisticated, context-dependent information processing and finely-tuned process control in stochastic environments, it becomes critical to understand how these capabilities may be instantiated in biological materials and control mechanisms.

[0063] For example, a yeast cell can sense a plethora of environmental characteristics and respond in surprisingly complex and nuanced ways, including the ability to anticipate future events with survival- enhancing responses. Likewise, single cells in a developing multicellular organism sense transient morphogenic cues and respond by developing permanent and significant changes to gene expression profiles, representing their differentiation into differentTufts T002882 WO.PCT Quarles 166118.01558cell lineages and types. In a mature organism, a transient event such as wounding can initiate tightly-regulated, multi-step wound-healing or regeneration responses involving sophisticated cascades of activity that restore the initial (healed) state of the organism. In all of these cases, the same control schemes take an “experience” - that is, input information obtained from the internal / external environment via sensors / receptors - and processes that information to engage a survival-appropriate response through changes in the expression or activity of its own components. Alternatively, under other circumstances dysregulation can occur, wherein an organism’s state transitions from one of “health”, where the structural and functional properties of the organism are stable and life-promoting, to one of “disease”, where disorganization and disruption of physical structures and processes occurs. A precise and detailed understanding of what this transition means, how it happens, and how to effectively move from the state of disease and back to one of health has not been defined.

[0064] As regulatory networks, GRNs are collectives of molecular regulators, including protein-based transcription-factor gene products, which up- or down-regulate each other’s expressions in a defined functional connectivity map. GRNs serve a major role in regulating the behavior of single cells, multicellular tissues, organs, and organisms, and are therefore recognized as critically important targets of inquiry for evolutionary developmental biology, biomedicine, bioengineering, and synthetic biology. It is essential to understand how to predict their behaviors, and how to manipulate these networks to induce desired biological outcomes. These networks are well-recognized to have emergent properties, yet their control remains challenging, with a number of new perspectives emerging on their system-level regulation. Therefore, frameworks that elucidate and focus our understanding of information processing by GRN are acutely needed in biological and biomedical fields.

[0065] A gradualist approach considers the essential problem-solving strategies that lifeforms utilized to thrive and survive prior to the evolution of advanced brains. We envision a continuum of advances in the information-processing capacities of a system, which we call the Persuadability Spectrum, FIG. 1. A system is “persuadable” to the degree to which concise information signals (e.g., pharmaceuticals, food rewards, words) can activate inherent competencies in a system to get it to emit a desired behavior, or to perform a desired function. Highly persuadable systems offer complex, autonomous responses to low information-contentTufts T002882 WO.PCT Quarles 166118.01558trigger prompts. Mechanistic physical systems, such as gears, present on one extrema of the continuum (FIG. 1). If one desires a change of function (“behavior”), these systems cannot be persuaded to change; rather, change in their output can only occur with alteration of their hardware (e.g., by changing their physical make-up). On the other extreme are human beings, whose behavior can be radically changed by a brief communication encoding a rationally or emotionally persuasive argument that alters values, beliefs, and / or feelings (FIG. 1). We propose that between these extremes lies a rich panoply of intermediate agents, including biological networks such as GRNs, which can be controlled by signals, stimuli, and training, without needing to directly alter the physical substratum of the agent.

[0066] Here we develop a conceptual framework, and related computational system, for working with GRNs as persuadable agents. Regulatory networks such as GRNs have classically been assumed to be mechanistic, “clockwork-like” systems requiring direct and permanent changes to network topology via genetic modification to effect stable changes in GRN output. However, gene therapy is still a significant barrier for biomedical interventions; moreover, the inverse problem of discovering how to modify a genetic network to achieve a desired set of responses is extremely challenging, motivating the search for different ways to predict and control GRN behavior. Our assertion is that such a priori assumptions are unwarranted and unnecessarily limit advances in our fundamental understanding and productive work in the fields of both basal intelligence and biomedicine. In contrast, we hypothesize GRNs to be “persuadable”, which, if true, opens the door to an entirely novel and powerful set of strategies for their manipulation.

[0067] Our general view is of regulatory networks, including GRNs, as a class of dissipative dynamic system (see Box 1 for definitions), which can exist in one of multiple possible equilibrium states (Box 1) at a time, where the collective state of all nodes in the network is a state of the GRN (FIGS. 2A-2F). Persuasion of the GRN system requires the capability to define and apply inputs to the GRN network, which are precisely the concise information signals that can activate inherent competencies in the GRN system and are therefore a requirement for persuasive control of the GRN (FIG. 2B). The input signals to the GRN system may be of a chemical (e.g., chemical, biochemical, morphogen) or physical (e.g., light, pressure, temperature) nature (FIG. 2B). As a dissipative dynamic system, the application of an inputTufts T002882 WO.PCT Quarles 166118.01558signal, of sufficient strength and duration, causes the GRN to exist as (e.g., occupy) one of its equilibrium states (FIG. 2C). The states of the GRN are patterns of gene expression (FIG. 2C), which are known to be directly associated with biological outcomes, and therefore, the GRN states are essentially synonymous with important cell and organism states, examples including cell phenotype (e.g., “embryonic stem cell” or “fibroblast”), the health status of the cell (e.g., “cancer” or “normal”), or different physiological modalities (e.g., “stress response” versus “resting response”). The overall technical objective of persuading the GRN system is to identify patterns of input stimuli that can transition the GRN system from the occupation of one (undesirable, e.g., diseased) equilibrium state to another (desirable, e.g., healthy) output state without requiring a modification of the network structure. Moreover, we wish to identify patterns of input stimuli that can make this transition permanent after the input stimulus is removed, which enables new avenues of research such as movement beyond the paradigm of “one constant dose” medicine.

[0068] We use computational modeling of GRNs to identify the equilibrium state that the GRN system transitions to in response to each input signal applied to the system when it starts in each equilibrium state. We use this set of equilibrium state transitions induced by input signals to build Network-associated Finite State Machines (NFSMs). Finite State Machines (FSMs) are universal models of sequential logic (Box 1), and therefore, the NFSM of a GRN is a mapping of the sequential logic that the GRN system can exhibit. Note that while a NFSM may appear superficially similar to a GRN, the NFSM is not a regulatory network model like a GRN; rather, it is a map detailing how an equilibrium state of the GRN system can be reached given a pattern of input stimuli applied to the system when it starts from a specific initial equilibrium state. Importantly, we have found that many systems do not have a 1 : 1 correspondence between an equilibrium state and the application of an input signal, and that in contrast, the NFSM highlights previously undetectable path-dependencies, path-irreversibilities, modes of system behavior (e.g., stable versus oscillatory), cycles, and unreachable equilibrium states occurring under patterns of applied inputs, which all underpin “intelligent” behavior exhibited by a GRN-regulated cell system.

[0069] Taken together, our complete computational framework is called the Regulatory Network Machine (RNM) and is designed for optimal persuasive control of GRN. The RNMTufts T002882 WO.PCT Quarles 166118.01558consists of: 1) a dissipative dynamic system, which may be a real-world system queried experimentally, or a system studied using computational modeling (here we focus on computationally modeled GRNs); 2) a set of input states that can be applied to the dissipative dynamic system, which have the capacity to alter the behavior of the system; 3) system equilibrium states with identifiable relevance to biomedical or biotechnological objectives; and 4) Network Finite State Machines (NFSMs) comprised of the input signal induced transitions between equilibrium states of the dissipative dynamic system (here the equilibrium states of the GRN).

[0070] Ultimately, while it is well-known that regulatory networks can perform functions such as state-switching, memory of state, counting, and timing, it remains unclear how these networks can perform the context-dependent, multi-step, information-processing and event-driven process control seen in real living organisms. Moreover, a formalized understanding of what it means to “persuade” a regulatory network, and how to optimally and systematically achieve such persuasion, does not yet exist. Here we use our RNM framework to specifically illustrate various biological cases, including what it means for a biological system to perform analogue “computations” to arrive at survival-appropriate responses in a stochastically-changing environment; how, given a regulatory network, a RNM model can be constructed and used to predict prompts that elicit desired behaviors from the system and can be used to inform disease treatment; and how some RNMs elucidate characteristics of smart, persuadable systems and can pinpoint the origins and implications of context-dependent behaviors. Overall, our work is an extremely tractable minimal system offering a route to both move beyond classical paradigms of biomedicine (e.g., “one constant dose” and “single factor, single treatment” doctrines) and to understand how larger kinds of proto-cognitive systems may emerge from smaller components.

[0071] Theory

[0072] While our RNM framework will work with any dissipative dynamic system, here we focus on GRN due to the extensive biomedical and biotechnological applications. The GRN can be modeled using any method that returns the equilibrium state(s) of the system that occur in response to a stimulus / perturbation. We use two complementary methods to computationally model GRNs: 1) as continuous systems described by coupled non-linear differential equations,Tufts T002882 WO.PCT Quarles 166118.01558which offers a high level of accuracy, yet requires more intensive computation; and 2) as simplified, yet highly computationally efficient, Boolean networks, where a Boolean model of a regulatory network simplifies the values that a single node can occupy to be equal to 0 or 1, and the regulatory activities of nodes upon other nodes are handled using logical functions. Our GRN models are described in detail in the Method Details section. We directly compare the results of the Continuous and Boolean models when each are used with the same underlying GRN in our RNM framework and find excellent comparability between both modeling techniques (FIG. 11 A- 1 IF and Table 3).

[0073] The GRN utilized in our RNM may be any network comprised of nodes that assume different factor levels, where nodes interact with each other via directed edges representing activation (represented by a blue edge ending in a dot) and inhibition (represented by a red edge ending with a bar) relationships. Note that our RNM framework can utilize any GRN modeling method that returns the equilibrium state of the GRN in response to an applied input / stimulus / perturbation and is not limited to the continuous partial differential or Boolean models we have utilized herein.

[0074] Dissipative Dynamic Systems as Analogue Computing Agents

[0075] In essence, a computational device is one that maps a system from an input state to an output state, where the internal operations involved in going from the input to the output are described as the computational process (62), see Box 1 and FIG. 3 A for additional details. While there is no formal definition of what constitutes analogue computation (Box 1), the view we adopt here is of the dissipative dynamic system as an analogue computer, where computations are understood in terms of what happens in the state space of the system in response to inputs as perturbations, as described in (62) and shown in FIG. 3 A. In our RNM framework, the dissipative dynamic system is of a chemical nature, comprised of dynamically interacting biomolecular, protein, and genetic components represented by a regulatory network (i.e., by a GRN).

[0076] Dynamic systems, including GRNs, can be described using differential equations estimating how the variables defining the system change in time, and their relationships to one another. By imagining that the values of each system variable can be represented along an axis,Tufts T002882 WO.PCT Quarles 166118.01558each variable can thereby form a dimension of a metaphorical space, where each point in the space is one possible state of the system (FIG. 3A). This metaphorical space represents an important concept called the state space (Box 1). At each point in state space, the set of differential equations describing the system specifies a rate of change for each system variable, which can be depicted as a vector showing the direction and magnitude of change at a point in state space. A vector field called the direction field (Box 1) can thereby be created by computing instantaneous rate of change vectors at each point in the state space (FIG. 3A). The system’s evolution in time from one point of the state space to another is then naturally prescribed by the direction field (FIG. 3A).

[0077] The direction field can be analogized to the currents of a river, where the present state of the system is akin to a leaf afloat on the river’s surface, and the leaf’s trajectory in time depends on the characteristics of the currents that carry it along. The form of the direction field (river’s currents) determines how the network’s state (leaf floating on one place in the river) will be drawn towards different regions of the state space (river as a whole), providing an indication of how the system state will evolve in time, if it becomes stalled or trapped in certain areas, and if so, how stable this entrapment is. The entrapment of the system in a certain state is formally called an equilibrium state (Box 1). Importantly, the direction field leading to the equilibrium can assume different forms, leading to different stability and other characteristics of the equilibrium.

[0078] The stability characteristic of an equilibrium describes how the network responds to a perturbation that takes it away from the equilibrium. For example, an asymptotically-stable equilibrium returns to the equilibrium point - as if drawn back by a force field - even when a moderately strong perturbation occurs (FIGS. 12A-12C). In contrast, a meta-stable equilibrium such as a saddle point moves away from the equilibrium when exposed to even a small disturbance (FIGS. 12A-12C). Several types of equilibrium dynamics and stability characteristics are commonly observed in the state space of dissipative dynamic systems, including: asymptotically-stable point attractors; asymptotically stable limit cycle attractors, which oscillate several times with decreasing amplitude before reaching a stable equilibrium; cyclic limit cycle attractors with sustained oscillations, and metastable saddle-point attractors, see FIGS. 12A-12C for additional details and examples. Details regarding our algorithms forTufts T002882 WO.PCT Quarles 166118.01558detecting and characterizing equilibria in Continuous and Boolean GRN models can be found in Method Details.

[0079] Analogous concepts to the above-described state space and direction fields also exist for the simplified Boolean network models, where individual nodes of the regulatory network are restricted to values of 0 or 1, and regulatory interactions between nodes are modeled using logic functions (see Method Details, FIGS. 12A-12C for details). A Boolean network with N nodes has 2N total possible states in its state space. Boolean Network dynamics are commonly analyzed using State Transition Graphs (STGs), which are also referred to as the “attractor landscape.” The STG or attractor landscape shows how each possible system state spontaneously moves towards the equilibrium states of the system (FIGS. 12A-12C). In this, the STG of a GRN modeled as a Boolean network is a simplification of the full direction field obtained from the continuous, partial differentiation model of the GRN (FIGS. 12A-12C). Note that for both the STG of Boolean Networks and the direction fields of continuous models, the attractor landscape of the system is generated without applying a specific input state to the system, and transitions between states happens spontaneously as non-equilibrium states naturally transition to equilibrium states with the progression of time (FIGS. 12A-12C).

[0080] Having now reviewed fundamental concepts of dissipative dynamic systems theory, the basic concept of a dissipative dynamic system as an analogue computing agent can be appreciated in its most trivial embodiment by visualizing a system’s direction field (FIG. 3A). The computational input to the system may correspond to the initial state of the system (orange, green, and blue dots in FIG. 3A), where the analogue “computation” is performed simply by allowing the system to spontaneously follow the direction field of the state space as a temporal evolution, with the system ultimately becoming entrained by an equilibrium. The set of system variable values associated with the equilibrium represents the output of the analogue computation, and the trajectory taken along the direction field represents the computational process. The orange, green, and blue trajectories in FIG. 3A represent the analogue computational process for a simple system and the black dot in FIG. 3 A represents the output state as the single equilibrium point of the system. The direction field is therefore instrumental in understanding how analogue computing via dissipative dynamic systems works, and the full “computational strategy” of the dynamic system is embodied in the form of the direction fieldTufts T002882 WO.PCT Quarles 166118.01558(FIG. 3 A). Note that as the STGs of Boolean networks are analogous to direction fields, the spontaneous transitions indicated by the STG also represent the input-output relations and computational strategy of the system (FIGS. 12A-12C).

[0081] While FIG. 3A shows an example of an individual analogue computation from an unstable to an equilibrium point, to work with regulatory networks as persuadable information-processing agents, a more sophisticated tool is required. Specifically, we require a framework that can specify how individual analogue computations can come together into what we could refer to as an analogue computational program. A crucial difference between standard attractor landscape analysis and our RNM framework is that our framework identifies and maps non-spontaneous, input signal driven analogue computations between two equilibrium states of the dissipative dynamic system, whereas attractor landscape analysis works with spontaneous transitions between all possible states of the system. In a Boolean model this means an attractor landscape model works with all 2N states, which may be prohibitively large (for N=53 GRN nodes this is 9x1015 states), whereas our RNM framework refines the focus to only equilibrium states, which tend to number less than 100, even in complex networks and represent the timestable output of the GRN system.

[0082] Regulatory Network Machines: A tool to work with regulatory networks as persuadable agents

[0083] Here we develop the basic concepts underlying the RNM concept, with two simple examples of RNMs shown in FIGS. 4A-4G and 5A-5H. The RNM is comprised of multiple elements including: a regulatory network (FIGS. 4A-4G and 5A-5H); a set of input states representing the “vocabulary” that can be utilized to “persuade” the system into modes of activity (FIGS. 4B and 5B); a set of stable output states representing the set of inherent competencies (the behavioral repertoire) that may be activated by the vocabulary through persuasion (FIGS. 4C and 5C); and the NFSM maps specifying how each element of the system’s input vocabulary can be used to persuade the system from one stable behavioral pattern to another (FIGS. 4D, 5D, 5E). The NFSM of a regulatory network are maps showing if transitions between equilibrium states are possible, and if so, precisely how the system can be persuaded into a specific stable output state from an initial stable state using the available inputTufts T002882 WO.PCT Quarles 166118.01558state vocabulary. Note that the NFSM also predicts the stable behavioral dynamics that are emitted by the system when it is in a particular equilibrium state (e.g., which kind of equilibrium the direction field pattern generates), allowing for the persuasive activation of - not only monotonic patterns of gene expression - but also of stable dynamic behaviors such as genetic oscillators, which arise naturally from the nonlinear system dynamics (FIGS. 6A-6C).

[0084] A key aspect of our RNM framework is the assertion that the network is not an isolated entity with homogeneous node types; rather, we ultimately need to consider heterogeneous networks that are interfaced with an environment via sensors endowing the network with the ability to observe / experience / sample the environment, and where the network can change state to adopt a response to the environment, see comprehensive example in FIGS.2A-2F, with other good examples from the literature found in. We thereby distinguish between input, internal, and output nodes of the system, which may all involve different types of agents acting in the network (FIGS. 2A-2F). This heterogeneity, wherein levels of some internal nodes of the network (e.g., gene expression levels) may be influenced by sensing agents such as transmembrane receptors, and in turn, where the levels of internal nodes exert an influence on the environment via potentiating outputs, is a natural aspect of most biological. For example, most signaling cascades involve trans-membrane receptors that sense environmental variables (e.g., variables external to the network) such as morphogens, growth factors, and physical properties such as light, temperature, or pressure (the inputs), which are capable of influencing genetic expression (the state of internal network nodes) to elicit survival-enhancing responses (output nodes) in relation to environmental variable values. For maximum comparability with digital computational systems and simplicity, regardless of whether our model is discrete or continuous, we fix the value of each input node to binary values of 0 or 1, representing a high or low presence of the respective factor; therefore, the input state space of our model is discrete rather than continuous. However, this is an artificial restriction, and the value of input nodes can assume continuous levels of resolution, as needed.

[0085] An essential aspect of our RNM framework is that the application of an input signal selects a state sub-space, or alternatively an attractor sub-landscape, that contains a direction field and associated equilibrium states unique to the specific input signal. For the case of Boolean Networks, the state sub-space associated with a specific input is represented by aTufts T002882 WO.PCT Quarles 166118.01558STG instead of a direction field. This concept of sub-space selection by application of a specific input state can be visualized in the simple systems of FIGS. 4E and 5F. While the complete state space of our RNM framework is spanned by dimensions created by values of all nodes of the network, the input nodes become instrumental in selecting modules of possible system output (FIGS. 4A-4Gand FIGS. 5A-5H).

[0086] This use of input states to select state sub-spaces allows for a natural representation of how the network functions as an information-processing entity capable of emitting non-trivial behavior sequences in response to patterns of sensed experience and allows us to formalize two major functions (visualized in FIGS. 4A-4G and FIGS. 5A-5H). Primarily, the application of an input signal changes the selection of the state sub-space, and therefore, the input changes the direction field and the possible equilibrium states present in the sub-space. When the input signal is applied and held for a sufficient duration, the system will spontaneously track to one of the equilibria in the state sub-space, and while there are no further changes to the nature of the input signal, the system will remain in that equilibrium. However, when there is a change in the input signal applied to the system, the selected state sub-space changes, and the system is injected from its equilibrium location in the original state sub-space, to a corresponding location in the new state sub-space (this can be visualized in the low-dimensional systems of FIGS. 4E and 5F). Yet with this change in the input signal, the location of the system in the new state sub-space may no longer be an equilibrium, and the system will spontaneously track to a new equilibrium, depending on the nature of the direction field in the new state sub-space (FIGS.4E and 5F). This means that a change in the input state initiates an analogue computational process as a trajectory that traverses, both within and between two sub-spaces (see the green line in FIGS. 4E and 5F), and allows for the input state to act as the agent that induces a transition between two system states. This also allows the input signal to access different modes of analogue computation within each sub-space, as the computational strategy of the system is embedded in the morphology of the sub-space’s direction field (FIG. 3 A).

[0087] We also identify two distinct classes of RNM: (i) a monostable class where there is only one equilibrium state in each sub-space (see FIGS. 4A-4G) and (ii) a multistable class where there is at least one sub-space that contains multiple equilibria (see FIGS. 5A-5H). As we shall demonstrate in examples, multistability endows RNM with the capacity to exhibit behaviorTufts T002882 WO.PCT Quarles 166118.01558that depends on experience (e.g., FIGS. 7A-7F) and to “recognize” context (e.g., FIGS. 8A-8H). If the system is monostable (Box 1 and FIGS. 4A-4G), meaning there is only one equilibrium state in each of the state sub-spaces, then there is necessarily a 1 : 1 correspondence between the input signal applied to the system and the equilibrium state occupied, as the direction field in the state sub-space will always track to the single equilibrium state independent of the starting position of the system in the state space (FIGS. 4A-4G and Method Details). However, if at least two of the system’s state sub-spaces are multistable (Box 1 and FIGS. 5A-5H), exhibiting more than one equilibrium state in the sub-space, then upon change of input signal, the location of the system in the new, multi-stable state space may track to one of several possible equilibria, depending on the location of the newly injected point in the new state space (FIG. 5F). The nature of path-dependency and context-dependent behavior in the system’s behavior is founded on these sub-space multi-stabilities, as tracking to a specific equilibrium state in a multi-stable sub-space can introduce irreversibilities, as it may no longer be possible to return to specific areas of other multi-stable state sub-spaces (see FIGS. 5A-5H). Therefore, multi-stable systems enable non-trivial transitions between different equilibria in response to different sequences of applied inputs and are the origin of more complex behavioral patterns (FIGS. 5A-5H).

[0088] We further distinguish between inputs that are transient perturbations to the system, which we refer to as input events (Box 1), and those input states that are applied and held for a duration in time, which we refer to as the system’s context-defining inputs (Box 1). By system context we specifically refer to the state sub-space that is selected when an input state is applied and held (e.g., the sub-space planes in FIGS. 4E and 5F each represent a unique context that is accessed by the applied input state). As each context may comprise radically different direction field patterns and equilibria, this means categorically different computational processes and output responses may become available for each context-defining input (see FIGS. 5F and 5G). Biologically, we take a context-defining input to represent the case where the applied input state remains relatively stable in time. For example, a cell in a body experiences “normal” physiological conditions pertaining to a regulated body temperature, levels of various salts in the extracellular media, and so on. In contrast, we distinguish an input event to be a transient deviation from this baseline context of “normal conditions”, for example, the temporary incidence of a very hot environment can generate hyperthermia and dehydration, altering variousTufts T002882 WO.PCT Quarles 166118.01558parameters from what can be considered the physiological baseline, or a morphogen may be present for only a relatively short period of time during development. In our RNM framework, when an input state is transiently applied, yet is then returned to the original input state, the transient input is taken to act as a perturbing event, which may possibly change the state of the system by removing the system from one equilibrium in a multi-stable sub-space, temporarily transitioning the system to an alternative equilibrium in a new sub-space, yet upon returning the original multi-stable sub-space the original equilibrium cannot be accessed and therefore a new equilibrium is occupied, leading to an irreversibility (FIGS. 5A-5H).

[0089] The progression of the regulatory network system in time is governed by a set of non-linear partial differential equations (see Method Details), where the full output of the system is the value of all internal nodes when the system nears an equilibrium. Note since only certain nodes interact directly with an external process, for simplicity and conciseness, we categorize nodes with zero out-degree as the set of output nodes (FIGS. 2A-2F). This convention is commonly followed in the literature in studies using regulatory networks to work with experimental biological systems (73,74). We emphasize that as the network may comprise a large number of output nodes, each unique, stable network equilibrium state represents a categorically different pattern of activity (e.g., gene expression), and therefore, a categorically different response and action taken by the network (FIGS. 2A-2F). The set of outputs may represent a variety of outcomes such as the categorically different gene expressions of differentiated cell types in an organism (e.g., the different gene expressions of fibroblasts, stem cells, and neurons), different metabolic modes (e.g., ketosis versus glycolysis), or other modes such as the physiological stress state versus the resting state response.

[0090] Working from the basis of our RNM framework, we have developed another tool we call the Network Finite State Machine (NFSM) that maps the emitted behaviors of the GRN system in response to applied inputs and is therefore a map of the sequential logic program of the GRN. We distinguish between two different types of NFSM: 1) the general NFSM (G-NFSM) that maps all possible transitions from each equilibrium state and each applied input signal to induce a transition to a new equilibrium state; and 2) the event-driven NFSM (E-NFSM), which shows irreversible state transitions occurring for transiently applied input signals in a context-defining input (FIG. 5E). Please see the Method Details for the operational steps toTufts T002882 WO.PCT Quarles 166118.01558create the G-NFSM and E-NFSM from any GRN (or, more generally, any dissipative dynamic system). Once the NFSMs associated with the GRN have been generated, pathway analyses can be performed on the NFSM to identify “persuasive” routes to accessing desired output states from an initial state (e.g., to move from a “disease” equilibrium state to one of “health”). Cycles analysis on the NFSMs can identify multi-stage processes in the system and how to engage them (e g., a wound-healing multi-step process). Please see Method Details for steps to utilize the G-NFSM and E-NFSM in biomedical and biotechnological applications.

[0091] Having outlined our RNM framework for working with regulatory networks as persuadable information-processing entities, we next examine several cases, including those of real biological networks, to demonstrate the utility of the analogue computing and RNM frameworks.

[0092] Results

[0093] Biological systems use analogue methods to “compute” correct responses to environmental challenges

[0094] We first explored a case-study of yeast osmoadaptation, where we show how a biological system successfully uses analogue computing to solve an environmental challenge. We also looked at identifying fundamental differences between how biological systems and human engineers solve a challenge such as maintaining an important variable at a target value (a set-point control problem), as recognizing these differences is the first step in improving our ability to work more effectively with biological systems through better understanding of their fundamental operations.

[0095] Human engineers use devices such as Proportional-Integral-Derivative (PID) controllers that employ digital computation to perform a function such as set-point control. A PID controller requires a physical memory to store information, a physical central processing unit (CPU) to perform digital computations, a software program that provides specific instructions on what to read / write to memory and which digital calculations are required to produce an output, connections to take input from a physical sensor that measures the process variable, and connections to an effector device that can receive computed output from the PID controller to influence some external process that changes the level of the process variable (84).Tufts T002882 WO.PCT Quarles 166118.01558The PID controller uses these elements to solve a set-point control problem by: i) using the sensor to measure the present state of the process variable, ii) using digital computing to calculate the error signal as the difference between the measured value of the process variable and the desired set-point value that is stored in physical memory of the controller, iii) using its physical memory to store a history of the error signal, and iv) using the error signal and its value stored at past times to compute an output signal in terms of the PID algorithm using digital computation and an algorithm specified by software. The PID’s algorithm computes output as the sum of a component proportional to the error signal, and numerically estimated integrals and derivatives involving the error signal. Finally, the PID controller sends the digitally computed output signal to the effector to attempt to alter the value of the process variable in a way that maintains it at the set-point value.

[0096] To illustrate the fundamental differences between human engineered PID controllers and biological systems, we considered yeast cell osmoadaptation as our case study - a classic, well-studied example of biological set-point control. Details of our osmoadaptation model can be found in Method Details, Osmoadaptation Model Mathematics. Osmoadaptive setpoint control provides an excellent example of an analogue computational system naturally “computing” the correct response required to maintain cell volume (volcell) at a target value for a wide range of environmental conditions (FIGS. 9A-9H). Here the same physical process of osmotic-pressure-induced cell volume change is further compared in an inanimate vesicle (FIG.9A) and in an osmoadapted yeast cell (FIG. 9B). The dimensions of the systems’ complete state spaces are the internal cell osmolytes (ni), cell volume (volcell), and environmental osmolyte concentrations (mo) (FIGS. 9C-H). In the yeast cell, the osmotic process interacts with a regulatory network involving a sensor for cell volume via membrane strain (PhoQ), which conveys information regarding cell volume through to the HOG-MAPK signaling pathway, thereby altering levels of intracellular glycerol, which contributes to, and therefore allows the cell to change, total internal cell osmolytes (FIG. 9B).

[0097] We see that due to the intrinsic dynamics of the system, for each initial system state (an example initial state is given by the green dot in FIGS. 9F and 9H), the system dynamics naturally “compute” a new state (large green dot in FIGS. 9F and H) by simply evolving in time under the system dynamics (green trajectory of FIGS. 9F and H).Tufts T002882 WO.PCT Quarles 166118.01558

[0098] The direction field of the non-living vesicle maintains a surface of equilibrium states (shown as the dotted black line in FIGS. 9E and F), meaning there is a range of possible equilibrium vesicle volumes for different environmental osmolyte concentrations and starting system states; therefore, there is no way the vesicle can maintain a single target volume in the face of different environmental osmolarities. In contrast, the yeast system’s direction field is in the form of an attractive limit cycle with a single equilibrium state appearing as a central point corresponding to the system’s desired target volume (FIGS. 9G and H, where equilibrium / target volume are indicated by the large green dot). Moreover, visualizing the yeast system’s complete state space in 3D, we see that the direction field for the yeast system is cylindrically shaped, meaning the attractive limit cycle will converge to the consistent target cell volume for a wide range of environmental and internal osmolyte concentrations, thereby demonstrating that the system has excellent control of cell volume (FIG. 9B).

[0099] In striking contrast to how a digital PID controller works, we see from the above example that by using analogue computing, the biological system has no need for a physical memory to store the set-point value; rather, the set-point value is an inherent aspect of the system dynamics, and can be considered to be “stored” abstractly in the system’s direction field as the equilibrium point of a limit cycle attractor (e.g., the large green circle terminating the green trajectory in FIGS. 9G and H). The biological system also has no need for a central processing unit (CPU) to perform computations of an error signal or output variable, nor for physical memory to store a history of the error signal, nor for any software to specify a computational algorithm. Instead, as can be recognized by visualizing the direction fields of the osmoadapted yeast model (FIGS. 9D, G, and H), that the system dynamics naturally utilize the present state of the biological system, in combination with the sensed process variable, to spontaneously evolve in a manner that naturally embodies an appropriate response to an environmental challenge such as high extracellular osmolarity.

[0100] We note that in contrast to a digital computation, the above example also illustrates how analogue computations embody sophisticated modules of holistic functional competency. However, while the analogue computing responses of the biological system are remarkable due to their ability to function without requiring a physical memory storage strategy nor a CPU, a key difficulty in working with analogue computing is the inherent difficulty toTufts T002882 WO.PCT Quarles 166118.01558change the function of the system (e.g., to reprogram existing computational capabilities). To reprogram the characteristics of a specific analogue computation (e.g., to alter the set-point value of the cell’s target volume) requires editing the system’s direction field, which in turn necessitates a change to the biological hardware. This is entirely unlike the ease of inputting a new set-point value into a PID’s software module, as it is unclear how to perform the required editing to achieve the desired results.

[0101] We therefore note that, as this model of osmoadaptation has only one stable state corresponding to the set-point target value, at the level of individual functions and behaviors (e.g., at the level of individual analogue computations), this system is technically neither programmable nor persuadable to alternative behavioral outcomes. However, we next consider systems with dynamics that allow for multiple equilibrium states associated with different inputs to see how input stimuli can be used to select analogue computing modules from a meta-network of possibilities (e.g., the NFSM), which we highlight as the act of using persuasion on regulatory networks taken from real-world biological systems.

[0102] The G-NFSM is a map guiding persuasion of regulatory networks

[0103] We next demonstrate how the G-NFSM is highly useful as a detailed set of instructions capable of specifying which inputs engage the specific output states of signaling networks important in disease processes. We chose the cross-regulation regulatory network between P13K / AKT / mTor, RAS / ERK, and Wnt / -catenin as an example (73). The regulatory network shown in FIG. 10A, adapted from Fig. 7 of (73), specifies activation / inhibition interactions between biologically relevant input, hub, and effector nodes, making it a suitable candidate for our RNM framework. A set of input states were defined from the input nodes of the network (FIG. 10B), and three unique output states were returned from our equilibrium search analysis, which are shown in FIG. 10C.

[0104] Our analysis also determined that the dynamic system for the PI3K / AKT / mTor, RAS / ERK, and Wnt / p-catenin network is monostable, which means there is a 1:1, fully reversible mapping between each input and output state, as monostability means there is only one output state in each state sub-space (see FIGS. 4A-4G), leading to a fully-connected G-NFSM (FIG. 10C), no E-NFSM on account of its monostability, and a low Intelligence PotentialTufts T002882 WO.PCT Quarles 166118.01558of 1.0 (see ‘ART Net’ in Table 1). Our analysis indicates that despite the appearance of apparent complexity in the signaling network, any regulatory network that does not have nodes engaged in cycles of interaction is necessarily monostable as mathematically there is only one solution possible for each set of input values (see Method Details, Directed Acyclic GRNS). For a monostable network, there is no dependency of state transition on the history of inputs; therefore, any state can be reached from any other state with the application of the appropriate input.

[0105] The G-NFSM specifies the exact input signals (as labels on transition arrows) that will result in each possible stable output equilibrium state (FIG. 10C), and therefore, the G-NFSM shows precisely which input signal needs to be applied and held to obtain a desired emitted behavior. Note that the equilibrium states are intrinsic to the system and can be accessed without having to alter the network topology, therefore, this network is persuadable. We see that for this PI3K / AKT / mTor, RAS / ERK, and Wnt / -catenin cross-regulation network, the G-NFSM of the RNM provides the necessary information to persuade the system to any desired output equilibrium state. For example, if state 0 represents a disease state, while state 1 represents one of health, we can see that “persuading” the system from one of disease to one of health requires applying and holding input state 10. By using the RNM approach, we also determine that since the system is monostable and there is a 1:1 correspondence between an input signal and the resulting output equilibrium, there is no possibility in the case of this network for a transient intervention to effect a permanent change in output (e.g., one-constant-dose therapy is required to maintain the desired output state). Moreover, we recognize that the results apply to all monostable networks, which includes all regulatory networks that are directed acyclic graphs lacking cycles (see Method Details: Directed Acyclic GRNs).

[0106] However, our preliminary analysis determined that not all networks are monostable, and that multistability - the property of a state sub-space containing multiple equilibrium states (see FIGS. 5A-5H) - endows a RNM with higher-order features such as the ability to have future behavior depend on past experiences and the ability to exhibit different behaviors to the same input signal depending on context. Therefore, our next biological case study examines the multistable OCT4-SOX2-NANOG transcription factor network involved in direct lineage specification of embryonic stem cells (ESC).Tufts T002882 WO.PCT Quarles 166118.01558

[0107] Feature of smart, persuadable regulatory networks

[0108] Here we show a simple real -world example of how a RNM can parameterize stem cell differentiation in response to a transient exposure to a morphogen is a context-dependent, event-driven state transitions (FIGS. 7A-7F). While multi stability has previously been suggested to account for the cell differentiation process, RNMs provide a framework enabling organized, systematic work with this concept (FIGS. 7A-7F). In essence we are showing how multistable RNMs can have future behavior depend on their past experience to maintain a long-lasting, or even permanent, change to their outputs and future responses after a transient experience.

[0109] The transcription factors OCT4, SOX2, and NANOG are well known to form a tightly interacting network motif responsible for lineage specification in embryonic stem cells (ESC), with the specific ESC regulatory network modeled in this example shown in FIG. 7A. High levels of NANOG, OCT4, and SOX2 are known to correspond with undifferentiated ESC (corresponding to output State 6, FIG. 7B), whereas differentiation towards a neuroectoderm lineage occurs when levels of NANOG and OCT4 drop, leaving SOX2 high (corresponding to output State 1, FIG. 7B). Differentiation towards a mesoendoderm lineage occurs when levels of NANOG and SOX2 drop, leaving OCT4 high (corresponding to output State 3, FIG. 7B). In this example, application of different input states corresponds to the presence of morphogens that actuate the input effects. Our RNM analysis of the ESC network in A indicates it is a multistable system with seven unique output states (FIG. 7B), both a G-NFSM (FIG. 7C) and E-NFSMs (FIG. 7D), and a high average Intelligence Potential of 1.64 (see “Full Chain” network of Table 1).

[0110] The biological observation of high NANOG, OCT4, and SOX2 in undifferentiated ESC indicates that undifferentiated ESC must start in State 6 (marked with a black block arrow and bold green highlight in FIG. 7C). The G-NFSM suggests that both States 1 and 3 are accessible from State 6 via application of input 16 and 15, respectively (trajectories highlighted in pink in FIG. 7C). However, State 6 exists in monostable context 10; therefore, while transient application of 16 or 15 leads to transition of the system to State 1 or State 3, it is not a permanent change, and the system reverts to State 6 once input 16 or 15 are removed (FIG.7E).Tufts T002882 WO.PCT Quarles 166118.01558

[0111] From the E-NFSM, we see that a non-trivial input context exists for input 14 when it is held as the “normal” baseline input for the system (FIG. 7D). The E-NFSM shows us that it is only in context 14 that a permanent change of the system from State 6 to States 1 or 3 can be achieved from a transient application of the same 16 or 15 inputs, with respective paths highlighted in green (FIGS. 7C and D). In the time evolution of the system shown in FIG. 7F, we see that by first switching to State 4 with the application of 14, a transient exposure to 15 now leads to a permanent switch of the system to State 3 even with a return to the original held context established by 14 (FIG. 7F). Similarly, a system first switched from State 6 to State 4 with the application of 14 with a transient exposure to 16 will permanently switch to State 1 even with a return to the original held context established by 14.

[0112] This example illustrates the importance of baseline context in multistable systems by showing how the same morphogen can only successfully induce differentiation in the correct context. Moreover, the RNM specifies precisely how to use input states to set different contexts to see desired permanent results. Moving beyond the case of stem cell differentiation, this example also has important implications for medicine, as it demonstrates how a transient course of a medicine can offer successful long-term treatment of certain diseases by effecting permanent changes in a multistable system.

[0113] RNMs pinpoint an origin of highly variable biological responses

[0114] In our next example we show how the RNM framework can help us understand how multiple - apparently identical - systems can show dramatically different responses to the same intervention. The regulatory network modeled in this example is shown in FIG. 8A, which was found to have 7 unique output states (FIG. 8B) and to have a G-NFSM (FIG. 8C) and multiple E-NFSM (FIG. 8D). The G-NFSM shows four transitions from State 5 to four unique states (State 0, State2, State 4, and State 6) happening with the application of the same input state 17 (bold arrows of FIG. 8C). The E-NFSMs show four different input contexts (for systems with a baseline-normal held input state of 10, II, 14 and 15) where State 5 transitions to another state under input 17 (bold arrows of FIG. 8D). In time-course studies, we find that systems with a held input state of 15 (FIG. 8E), 10 (FIG. 8F), 14 (FIG. 8G) and II (FIG. 8H) are initially stable in State 5, as predicted by the G-NFSM and E-NFSMs. Subsequent transient application of input 17Tufts T002882 WO.PCT Quarles 166118.01558to each of the four systems leads to four different final states (FIGS. 8E, F, G and H), as predicted by the E-NFSMs (FIG. 8D).

[0115] This example shows that it is possible to use the RNM framework to identify nonspecific elements of the system (e.g., the combination of input factors SO, SI, and S2 that create the different contexts 10, II, 14 and 15 in the FIGS. 8A-8H example) that lead to categorically different responses to the same perturbing event / intervention (e.g., 17 in the FIGS. 8A-8H example). This is significant, as a real-life situation may entail multiple patients who appear to have similar levels of key factors in their blood work (therefore being equivalent to the four systems shown here that start in State 5, see FIGS. 8A-8H) and yet these patients may each show dramatically different responses to a pharmaceutical treatment. The RNM framework opens up the possibility to identify and control for these apparently extraneous factors (e.g., the fact that the four systems are actually under different input contexts) to minimize undesirable variation in biological responses to an intervention.

[0116] RNMs Elucidate Strategies in Cancer Renormalization Therapy

[0117] Our results detail how RNM analysis can be used to identify specified treatment strategies to transition cells from a disease state back to a healthy state. When applied to cancer, this concept of inducing a transition between diseased to healthy cell states is known as “cancer renormalization”. We used the “MAPK Cancer Cell Fate” Boolean Network model from, see FIG. 2A, sourced from the Cell Collective model database, as an experimentally-verified Boolean GRN model that specifies input nodes (‘DNA damage’, ‘EGFR stimulus’, ‘FGFR3 stimulus’, ‘TGFBR stimulus’, see FIG. 2B) and output nodes (‘Apoptosis’, ‘Growth Arrest’ and ‘Proliferation’ nodes in FIG. 2C), in addition to 46 internal nodes with numerous internal feedback cycles (FIG. 2A). Each input node variable represents an information bit, which taken together, form 16 input states, labeled 10 through 115 (FIG. 2B). Our RNM analysis found that 15 unique equilibrium output states (labeled State 0 through State 14, FIG. 2C) were possible for all of the possible applied inputs and determined the relationships between the equilibrium output state transitions and the applied inputs using techniques to generate both E-NFSMs (FIG. 2E) and G-NFSM (FIG. 2F). Interestingly, all equilibrium output states in the system are predicted to be limit cycles (except for States 0 and 1), which would spontaneously and cyclically passTufts T002882 WO.PCT Quarles 166118.01558through different modalities of a cell cycle rather than remain fixed as a monotonic gene expression.

[0118] The descriptive nature of the output nodes in this model allows for easy definitions of the ideal cancer state as one in which apoptosis is inhibited but proliferation is maximized (e.g., Cancer State = ‘Apoptosis’=0, ‘Growth Arrest’ =0, and ‘Proliferation’ =1), versus a normal cell state which can cycle through all of the outputs (e.g., Normal State = ‘ Apoptosis’=0.33, ‘Growth Arrest’ =0.33, and ‘Proliferation’=0.33). From the definition of the idealized cancer state, we calculated the Euclidean distance between each of the 15 equilibrium output states and the ideal cancer state, finding that States 1, 2, and 3 were closest to the ideal cancer state, that States 4 and 5 were akin to a pre-cancerous state, and that the remaining States 6 through 14 could be interpreted as normal, healthy cells demonstrating both programmed proliferation and cell death. Pathway analysis of the G-NFSM map allows for automatic identification of persistent therapies that can be trialed to persuasively transition cancer cells back to a healthy state. The pathway analysis of the G-NFSM showing sustained input interventions leading from a cancer-like State 2 to healthy States 9, 10, 11, and 12 is shown in FIG. 2D, indicating that while inputs 18 and 110 sustain a cancer state in this model, inputs 14 through 17 and 112 through 114 are all candidate therapeutic interventions.

[0119] The E-NFSMs of FIG. 2E provide insights into whether it is possible for transient therapies to induce permanent outcomes in this model system. E-NFSM results show that under a sustained exposure to held inputs (baseline context) 18 or 110, a pre-cancerous State 5 irreversibly proceeds to a cancerous State 2 or 3 after a temporary exposure to various input events (FIG. 2E). These results imply that once cancer develops, there is no way to persuade the cell to return to a normal state using a transient intervention without a change in network topology. However, we learned from G-NFSM analysis of this model that cancer is maintained only in the 18 and 110 contexts, which feature high EGFR in isolation, or EGFR and FGFR3 with no other stimuli. The role of 18 and 110 in sustaining cancer states is consistent with the results discovered by Grieco et. al. in working with this same Boolean network model. However, our G-NFSM also makes clear predictions for a wide array of cancer renormalization strategies, including the application of 14, 15, 16, 17, 112, 113, and 14 (see FIG. 2D with input states shown in FIG. 2B). Overall, we show how the G-NFSM and E-NFSMs of our RNM framework provide aTufts T002882 WO.PCT Quarles 166118.01558clear and comprehensive map of the sequential logic embedded in the dynamics of a complex GRN dynamic system, leading to clear and efficient exposure of treatment strategies and possibilities that remain hidden in other analysis techniques.

[0120] Discussion

[0121] Here we presented and developed the novel conceptual and computational framework of Regulatory Network Machines, thereby enabling work with GRNs as persuadable entities capable of context-dependent information processing and behavioral output that depends on past experiences.

[0122] Notably, our RNM framework builds upon a well-known analysis method used to study regulatory networks called Attractor Landscape Analysis. Attractor Landscape Analysis is a technique, typically used with Boolean network models), that maps out spontaneous transitions from non-stable states to equilibrium states of a network for a single applied input state. While the STG of an attractor landscape analysis may superficially appear similar to our NFSMs, there are crucial differences to be noted. The STG shows how any starting state of the system naturally and spontaneously moves towards different kinds of equilibrium states in the attractor landscape defined when one input state is applied to the system (FIGS. 12A-12C), and the STG is a discrete version of the continuous direction field concept (FIGS. 12A-12C). There are no labels on the edges of the STG, as there is nothing that drives the transition between states; these transitions happen naturally and spontaneously due to internal system dynamics. In our RNM framework, the application of an input state to the network is also associated with an attractor landscape (here, an attractor sub-landscape or state sub-space); however, we see that different input states generate categorically different attractor landscape sub-spaces (FIGS. 4E and 5F visualize this in two simple examples). In contrast to the STG, the NFSM maps non-spontaneous transitions between equilibria within and between different attractor sub-spaces, where transitions occur only as different input signals are applied to the system (FIGS. 12A-12C). In contrast to the STG, edge labels in the NFSM specify the input signal that is applied to induce the transition between two equilibrium states, and the states of the NFSM represent only equilibrium states and exclude all other states. By dealing only with the stable equilibrium states, our NFSM also offers a major advantage over attractor landscape models that work with all 2N states, which may beTufts T002882 WO.PCT Quarles 166118.01558prohibitively large (for N=53 GRN nodes this is 9x1015 states), whereas our RNM framework refines the focus to only equilibrium states, which tend to number less than 1000 (in the examples presented here, to less than 20), even in complex networks. Thus, the NFSM produces a map of the effects that patterns of input have on the stable outputs of the system, where, as we have seen in biological case examples, path-dependencies and cycles in the NFSM are crucial for supporting advanced behaviors.

[0123] Through our RNM framework, we have shown how a regulatory network with fixed topology can take different “experiences” as input information obtained from the internal / external environment and use analogue computation to process this information to engage a range of responses through changes in the expression or activity of its own nodes, which are represented by output equilibrium states. The RNM framework thereby demonstrates how a GRN can be understood to be a persuadable system in which concise information signals (e.g., input signal states) can activate inherent competencies (e.g., output states) to get the system to emit a desired behavior or perform a desired function. In this framework, we can thereby contextualize “health” and “disease” as different possible output states that an organism may occupy, where the NFSMs of the RNM framework provide maps indicating which specific interventions are most likely to result in transitions between health and disease states, and how the intervention needs to be applied (e.g., constantly, or if a transient course of treatment will effect a permanent change of state). Here, this process was demonstrated in detail using the MAPK Cancer Cell Fate network (FIGS. 2A-2F).

[0124] In working with various biological case studies, we have identified system multistability as a key criteria distinguishing “smart” RNMs that can leam from experience (or alternatively, that can change permanently after a transient event, FIGS. 7A-7F) and perform context-dependent behaviors where different outcome behavior is observed from systems in the same initial state but experiencing different baseline conditions (FIGS. 8A-8H) from those that have more simplistic 1:1 relationships between inputs and outputs (FIGS. 10A-10C). The RNM framework thereby shows how, if we have accurate regulatory network models, we can enhance biomedicine in two ways. First, it suggests that we can use RNM with accurate regulatory network models to move beyond the “one-constant-dose” paradigm in medicine through the identification of specific factors in multistable RNM systems that allow the system to respondTufts T002882 WO.PCT Quarles 166118.01558permanently to a transient intervention (FIGS. 7A-7F). Secondly, the RMN framework opens up the possibility to identify and control for apparently extraneous factors existing in input contexts to minimize undesirable variation in patient responses to an intervention (FIGS. 8A-8H).

[0125] We have also provided some illustrations of the analogue computing characteristics of biological systems controlled by regulatory networks, which highlight characteristics that are in striking contrast to how human-made digital systems, such as PID controllers, function (FIGS. 9A-9H). By shifting our focus to see a biological system as one that employs analogue computing, we see that the biological system has no need for a physical memory to store information, such as the set-point value of a homeostat; rather, the set-point value is an inherent aspect of the system dynamics, and can be considered to be stored abstractly in the system’s direction field as the equilibrium point of a limit cycle attractor (e.g., the large green circle terminating the green trajectory in FIGS. 9G and H). The biological system also has no need for a central processing unit (CPU) to perform algorithmic computations of system variables such as error signals and the magnitude of behavioral responses. Instead, the system dynamics naturally utilize the present state of the biological system and sensed environmental variables to spontaneously evolve in a manner that naturally embodies an appropriate response to an environmental challenge such as high extracellular osmolarity (FIGS. 9A-9H).

[0126] Computationally, our RNM model can be analogized to a hybrid Turing-Hopfield digital computing machine (FIGS. 3F, 3G, and 3H), which, like a classical Turing machine, is fed a tape of input state symbols (FIG. 3F) that are read by a read-head moving to the right in time (FIG. 3F). The tape represents the sensed experience of the dynamic system in time. Like a classical Turing machine, the RNM can store a memory of state and runs a program specified by a state transition diagram (FIG. 3F), which specifies which state to progress to, given its present state and the input symbol read from the tape (FIG. 3F and Box 1). Yet, like a Hopfield network, the system also has associative memory, such that each state represents a pattern of output variables, which are the computational output (FIGS. 3F and 3G and Box 1). The result is a progression of initial and final system output states with each input state applied in time (FIG.3H). A detailed comparison of the properties of Turing, Hopfield, and Regulatory Network Machines is summarized in Table 2.Tufts T002882 WO.PCT Quarles 166118.01558

[0127] Our RNM framework is also related to connectivist computational approaches to intelligence that utilize artificial neural networks (ANNs), in particular to Physics Informed Neural Networks (PINNs) and Reservoir Computing. Similar to GRNs, an ANN consists of a network of nodes that interact with each other via connecting edges, where the ANN processes information by transforming an input signal into an output signal. Some ANNs learn a set inputoutput relationships contained in a dataset through training algorithms, which alter the ANN network topology (e.g., change the connecting edges between nodes). APINN is an artificial neural network that has been partially trained on differential equations representing the laws of physics (e.g., the neural network may be trained on the Navier-Stokes equations describing fluid dynamics). This allows the PINN to embed the knowledge of the physics (e.g., Navier-Stokes equations) and to thereby capture the correct solution in a specific problem area (e.g., a fluid dynamics problem) with a minimal amount of new training data. Working from the analogue computing perspective developed herein, the GRN of our RNM framework could also be said to be naturally trained (e g., the GRN topology is naturally shaped) with regards to knowledge of physical systems through the processes of a biological organism’s continuous physical experience and evolution through natural selection, which is the “programming” that enables effective analogue computing responses to environmental challenges (e.g., osmomolarity shocks). Our framework also parallels Reservoir Computing, which is based on the concept that input stimuli perturb the state of a multi-stable, network-based computational reservoir, sending the reservoir to certain attractor states. Unlike in traditional ANNs, but similar to our RNM framework, in reservoir computing the edges of the reservoir network do not change, and the system relies on the memory and other complex dynamics of its multi-stable “computational reservoir” to achieve information processing results.

[0128] While here we have focused on GRNs, our RNM approach has a high degree of general applicability (e.g., universality). The RNM framework has only three general dependencies to function: 1) the system of study must be a dissipative dynamic system; 2) the system must be able to accept inputs and produce stable outputs; and 3) a systematic methodology must be followed to generate all of the transitions of the NFSM of the RNM (see Method Details for details). Examples of regulatory networks that are dissipative dynamic systems that will work with our RNM framework are: transcription factor networks, metabolicTufts T002882 WO.PCT Quarles 166118.01558and chemical reaction networks, bioelectric networks, neural networks, ecological food webs, human economic systems, and mixed signaling / regulatory networks comprised of a variety of entities.

[0129] Overall, the RNM framework provides the essential elements required to understand a regulatory network as a persuadable entity, where for any given regulatory network, an RNM details what specifically needs to be done to persuade a system to desired modes of activity. The RNM framework also determines the limitations to persuading any given system by indicating the level of function at which it is necessary to reprogram the system by changing its hardware (e.g., alter its physical make up). In this, there are numerous applications of our RNM framework in biomedical and bioengineering. The RNM can be used to address drug habituation (the loss of pharmacological efficacy over time), where the G-NFSM can be used to identify new strategies to achieve a “healed” state from the habituated state using an alternative pharmacological strategy. Also, the RNM can work to solve drug sensitization (functional pharmaceuticals that cannot be given for therapeutically necessary time periods because their side-effects build over time), where the E-NFSM of our RNM can be used to identify if and how transient applications of pharmaceuticals can induce permanent outcomes. In regenerative medicine and injury, the G-NFSM and E-NFSMs can be used to determine how to persuade GRNs to trigger complex repair cascades. As we have shown here, in cancer the G-NFSM and E-NFSM can be used to identify strategies to shift complex, system-level behavioral profiles toward cooperativity with tissue homeostasis. There are also applications in bioengineering, where the G-NFSM and E-NFSM can be used to identify strategies to achieve desired outcomes, such as increased yeast resistance to ethanol concentrations to improve bio-ethanol yields.

[0130] By working with regulatory networks as analogue computational systems, and with the introduction of our RNM framework, we have shown how to generate maps evidencing the “software-like” nature of a regulatory network, providing easy identification of the specific interventions necessary to achieve desired outcomes. Importantly, we have shown how systemlevel outcomes such as cancer normalization can be induced in a biological system without requiring genetic rewiring, and in cases that are too complex to directly micromanage. Our RNM approach determines the behavior and capabilities of regulatory networks, elucidating their innate computational capabilities and ascertaining the interventions that will provide the mostTufts T002882 WO.PCT Quarles 166118.01558control for the least amount of effort (or side effects). Ultimately, the view of regulatory networks as analogue computers described by RNMs expands horizons in our understanding and treatment of disease.

[0131] Conclusions

[0132] As with all frameworks in network science, the results of RNM analysis are only as good as the regulatory network model on which the RNM is based, so care must be taken to utilize good starting GRN models. Obtaining accurate regulatory network models for multistable dynamic systems may be highly dependent on experimental design and the inference method. However, it is worth highlighting that as the accuracy of our RNM framework does indeed hinge on the accuracy of an underlying regulatory network model, we have undertaken significant efforts to select regulatory networks that are suitable for the RNM, have already undergone experimental verification, and also have relevance to important biological or biomedical cases, these are: 1) the well-known HOG-MAPK signaling network of yeast osmoadaptation; 2) the cross-regulation network between PAM, RAS / ERK, and Wnt / p-Catenin, which is known to govern many processes including cancer transformation; 3) the NANOG / OCT4 / SOX2 network that has undergone extensive experimental study by many research groups for its role in stem cell differentiation and cancer; and 4) the MAPK Cancer Cell Fate network.

[0133] Regarding the computational efficiency and capabilities of our RNM framework, here we have utilized two different computational models of GRN. We have employed continuous models of GRN described by nonlinear differential equations, which maximize biorealism and accuracy, yet do not offer computationally efficient modeling capacity. We have also used Boolean Network computational models of the GRNs, which offer exceptional computational efficiency, yet may sacrifice accuracy in GRNs with large numbers of cycles and high hierarchical incoherence. We have found that Boolean Networks are up to 400 times faster at computing GRN outputs than our continuous model utilizing differential equations (Table 3), with excellent comparison to continuous models for GRNs (FIG. 11). In future work, we aim to identify parallelization techniques to improve on the computational efficiency of the continuous partial differential equation model of the GRN.Tufts T002882 WO.PCT Quarles 166118.01558

[0134] We view this work as a complement to efforts to understand gene regulatory networks as computational and proto-cognitive media, and to help explain remarkable and still poorly-understood ways in which tissues can adaptively respond to novel stressors.

[0135] The RNM framework provides the essential elements required to understand a regulatory network as a persuadable entity, where for any given regulatory network, an RNM details what specifically needs to be done to persuade a system to desired modes of activity. The RNM framework also determines the limitations to persuading any given system by indicating the level of function at which it is necessary to reprogram the system by changing its hardware (e.g., alter its physical make up).

[0136] By working with regulatory networks as analogue computational systems, and with the introduction of our RNM framework, we have shown how to generate maps evidencing the “software- like” nature of a regulatory network, providing easy identification of the specific interventions necessary to achieve desired outcomes. Importantly, we have shown how systemlevel outcomes can be induced in a biological system without requiring genetic rewiring, and in cases that are too complex to directly micromanage. Our RNM approach determines the behavior and capabilities of regulatory networks, elucidating their innate computational capabilities and ascertaining the interventions that will provide the most control for the least amount of effort (or side effects). Ultimately, the view of regulatory networks as analogue computers described by RNMs expands horizons in our understanding and treatment of disease.

[0137] Method Details

[0138] General Computational Strategy

[0139] The core of each Regulatory Network Machine (RNM) is a dissipative dynamic system, which in our examples is taken to be a Gene Regulatory Network (GRN). Here we utilized computational models of GRNs, and trialed both continuous partial differential equation models (“Continuous Models”) and discrete Boolean network models (“Boolean Models”) of the GRNs. All of our models were constructed in the Python language. First, both Continuous and Boolean GRN models were constructed using the symbolic mathematics package Sympy to create fully analytic computational models and, in the Continuous Model case, fully analytic derivatives were computed and used to generate Jacobians and Hessians for use in equilibriumTufts T002882 WO.PCT Quarles 166118.01558state searches in the GRN model. In the case of the Continuous Models, where possible, these symbolic models were also simplified using analytical techniques to reduce the number of equations, and in some cases, to find complete solutions. For all GRN cases reported herein, except the MAPK Cancer Cell Fate GRN, both Continuous and Boolean models were utilized and the Continuous model results shown in all figures. The MAPK Cancer Cell Fate GRN was the only exception, which was computed using the Boolean method only.

[0140] In GRN images, a directed edge between two nodes symbolizes the influence of one node level on the dynamics of another, where the influence can be to activate (blue edge terminating in a circle) or inhibit (red edge terminating in a bar) the growth of the influenced node by modulating the growth term in the influenced node’s change rate function (see the growth term dynamics for HO in FIGS. 14 and 15).

[0141] GRN Base Functions

[0142] Continuous GRN Models

[0143] Continuous GRN modeling formalism conformed to well-known standards commonly used for continuous models of GRN. Descriptions of the parameters utilized in Continuous GRN models are summarized in Table 4. The level of each node of our GRNs represents the probability that the gene is expressed at the time point in question, and therefore, the level of each node spans from 0.0 to 1.0. The level of each node in the network changes in time according to a differential equation involving separate growth and decay terms (HO in FIGS.14 and 15), where nodes without any influencing input are seen as inputs controlled by external factors (SO in FIGS. 14 and 15). Our GRN models allowed for the option to choose the use of a Hill function based dynamic equation (FIG. 14), or a Logistic function based dynamic equation (FIG. 15); all models presented in the paper utilized the Hill function model yet little difference was seen between the two function types. Default parameters for models utilized di = 1.0, (Bij = 2.0, and nij = 3.0 for all node expression probability change rate expressions in a network using the Hill function base, and di = 1.0, (Bij = 0.5, and nij = 15.0 for expressions using the Logistic function base.

[0144] Boolean GRN odelsTufts T002882 WO.PCT Quarles 166118.01558

[0145] Boolean GRN modeling formalism conformed to well-known standards commonly used for Boolean models of GRN. The level of each node of our Boolean GRNs was discretized and restricted to the values of 0 (False) or 1 (True). A Boolean GRN with N nodes has 2N states (note these are not necessarily equilibrium states). Each computation of Boolean GRN state iterates from a previous state, where the next state of the network is calculated directly from the previous state according to logic equations at each network node. An activating interaction of one node (e.g., ‘SO’) upon another node (e.g., ‘HO’) is updated simply as HO = SO, whereas an inhibiting interaction of one node (e.g., ‘SO’) upon another node (e.g., ‘HO’) is expressed in terms of the logical “NOT” operator as HO = NOT(SO) or. alternatively, as HO = 1 - SO. As detailed in the next section, the influence of multiple nodes upon another node (e.g., if nodes ‘SO’ and ‘HO’ both influence ‘Hl’), is accomplished using the logical operators “AND” and “OR” to combine multiple influences (e.g., Hl = SO OR HO would mean that Hl is activated by the presence of node SO or by node HO).

[0146] Combining Multiple Regulatory interactions

[0147] In a GRN it’s possible for a single node to be influenced by multiple other nodes, and therefore a strategy must be implemented to combine the effects of multiple influences. A simple example network is shown in FIG. 16, where nodes HO and Hl each have two interactions acting upon them.

[0148] In a Continuous GRN model, multiple influences can be combined multiplicatively, which means to have all interaction terms multiply together in the influenced node’s growth term, as shown in equation El for the network of FIG. 16. In the Boolean case, this combination type is implemented using the “AND” operator.

[0149] (El)Tufts T002882 WO.PCT Quarles 166118.01558

[0150] Alternatively, in a Continuous Model, interactions can be combined additively by adding terms together in the growth term of the influenced node, as shown in equation E2 for the network of FIG. 16. In the Boolean case, this corresponds to combining the terms using an “OR” operator.

[0152] Finally, a mixed scheme can be utilized, wherein inhibitive interactions can be combined in a multiplicative fashion (“AND” operator combination), while activating interactions can be combined in an additive fashion (“OR” operator combination), as shown in E3 for the network of FIG. 16.

[0154] Throughout this work, all models presented utilized the mixed scheme for combining multiple interactions; however, multiplicative, additive, and mixed schemes were all subject to study.

[0155] State Space Equilibrium Search and Characterization

[0156] Our RNM framework requires, ideally all, equilibrium states of the state space to be identified and characterized. For both Continuous and Boolean GRN modeling, state space searches were conducted using a subset of the full network’s nodes, which were selected based on their hierarchical level in the network after excluding the input nodes.Tufts T002882 WO.PCT Quarles 166118.01558

[0157] The hierarchical level of a node in a regulatory network is a numerical measure of how much downstream influence the node has on other nodes in the network and is defined in. Input nodes have the highest hierarchical level in the network, are also nodes with zero in-degree and levels controlled by factors outside of the network and have the greatest influence on the dynamics of all other nodes of the network. Conversely, output nodes have the lowest hierarchical level in the network, are nodes with zero out-degree and have no influence on the dynamics of all other nodes in the network. We found that using only a subset of nodes with the highest hierarchical level (not including the input nodes) as the dimensions of the state space was able to return all of the equilibrium states of the whole network. For example, in the 53 node GRN of the MAPK Cancer Cell Fate network model (FIG. 2), we were able to return all equilibrium states of the network using only 12 nodes with the highest hierarchical level to form the dimensions of the searched state space (these nodes were ‘TGFBR’, ‘SMAD’, ‘TAK1’, ‘TAOK’, ‘ATM’, ‘FGFR3’, ‘GADD45’, ‘EGFR’, GRB2’, ‘PLCG’, ‘PKC’, and ‘MTK1’, see FIG. 2Afor the whole GRN and color-coded node hierarchical level). This means the state space search required 212 = 4096 individual equilibrium search queries instead of 246 = 70x1012 queries required if all internal nodes needed to be used to find all equilibrium states, representing an enormous improvement in computational efficiency and feasibility.

[0158] For the Continuous models, for each input state assigned to the input nodes, and subsequently, for each trial initial value from the state space search set applied to the remaining nodes of the network, Scipy’s root finding algorithm, fsolve, was used to find an equilibrium point. A multi-level rounding scheme was used to round solutions to the nearest tenth (e.g., to 0.1), such that gene expressions that differed by more than 10% would be classified as unique solutions. After finding each equilibrium solution, the stability characteristic of each equilibrium was characterized using characteristics of the eigenvalues of the system’s Jacobian calculated at the equilibrium point. Table 5 describes how the sign and presence of nonzero imaginary components of the eigenvalues was used to characterize the stability of the equilibrium.

[0159] For Boolean models, through comparison with Continuous counterparts (see FIG.11 for an example) we determined that the stability characteristic of equilibrium states in Boolean models can be assessed based on the characteristic of repeated motifs when calculating a sequence of states from an initial starting state. In particular, we found that a single stateTufts T002882 WO.PCT Quarles 166118.01558repeating is equivalent to an asymptotically stable point attractor, that a motif that persistently cycles between two states is equivalent to a meta-stable saddle-point attractor, and that a motif that persistently cycles between more than two states is a limit cycle. In our Boolean models we did not find any attractive limit cycles (all were oscillating limit cycles) in any GRN models. For a Boolean model with a saddle-point or limit cycle attractor, the value of the equilibrium state was taken to be the average of all state values in the repeating motif, which produced results consistent with the Continuous model. We constructed a motif analyzer in our RNM software to automatically identify the motif and characterize the equilibrium state of the Boolean model.

[0160] Network Finite State Machine Build Procedure

[0161] After acquiring a set of unique, stability-characterized equilibrium states (referred to as the matrix Mstates) using the above-described methods, along with a set of input states, in Continuous models, temporal simulation was employed to determine the state transition network of the NFSM. In Boolean models, a sequence of states was calculated and analyzed for each applied input and starting equilibrium state.

[0162] Whether working with a Continuous or Boolean model of a GRN, the G-NFSM and E-NFSM can be created from any GRN (or, more generally, any dissipative dynamic system) through the following four steps:

[0163] 1. Identify the GRN (or dissipative dynamic system) of interest and construct a realistic computational model of the GRN (or of the dissipative dynamic system).

[0164] 2. Identify the input nodes, internal nodes, and the output nodes which ideally relate to important biological phenomenon (e.g., cell proliferation, apoptosis, etc.). We refer to individual input signals as “I#”, whererepresents an integer identifier.

[0165] 3. For each applied input signal, I#, use computational methods (see Method Details) to find and characterize all equilibrium states existing for each state sub-space associated with each input signal. We refer to individual equilibrium states as “Statewhere represents an integer identifier.

[0166] 4. Create the edges of the NFSMs by following a methodology of input signal application and equilibrium state detection. Specifically, apply each input signal, I#, to theTufts T002882 WO.PCT Quarles 166118.01558network (this initially applied input is called the “Held Context I#”) and start the system off in each of the equilibrium states (“Initial State #”) associated with the applied input signal’s subspace. Then, transiently change the applied input signal to be each member of the input signal set (these are each “Input Event I#”). Detect the equilibrium of the system while the Input Event I# is transiently applied (“Transient State #”). Finally, return the input signal back to the original Held Context I# and detect the equilibrium of the system (“Final State #”). The labeled edges of the G-NFSM are, specifically: Initial State # - Input Event I# Transient State #, and Held State # - Held Context I# — Final State. The edges of the E-NFSM are recorded only for the case where the Initial State # is not the same as the Final State #, and are defined in a sub-graph indicating the Held Context I#, specifically: Initial State # - Input Event I# —> Final State #, and describe a transition under the Held Context 1# sub-graph.

[0167] Steps for Applying RNM Analysis to Biomedical Applications

[0168] To utilize our RNM framework in biomedical or biotechnological applications, the following steps can be followed:

[0169] 1. Identify phenomenological biological outcomes represented by the different output node states. For example, in the MARK Cancer Cell Fate GRN model (see FIGS. 2A-2F), we identified states without apoptosis and only proliferation to be indicative of cancer states, and other states that cycle through proliferation, cell cycle arrest, and apoptosis to be indicative of “normal” cell states (FIG. 2C).

[0170] 2. Categorize the system’s equilibrium output states in terms of the ideal biological outcome states defined in Step 1. For the MAPK Cancer Cell Fate model, this was done by using the Euclidean distance from each equilibrium state and the idealized state to find the closest match (FIGS. 2A-2F).

[0171] 3 Use path analysis on the G-NFSM to identify the input states that work to support each of the desired biological outcomes, or alternatively, that can transition the system from an undesirable to desirable state (FIGS. 2A-2F). These input states are potential therapeutics in the system.Tufts T002882 WO.PCT Quarles 166118.01558

[0172] 4. Examine the E-NFSM to determine if it is possible to move beyond “one constant dose” medicine and use transient application of an input intervention to achieve a permanent transition to a desired biological outcome equilibrium state.

[0173] Estimating the Intelligence Potential of Regulatory Networks

[0174] We developed a metric to estimate the intelligence potential (IP) of regulatory network studied in the RNM framework (Box 1). We define the IP of a network as the sum of two parameters: i) the Multistate Ratio, (MR) and ii) the Context Ratio (CR). The MR is defined as the total number of output equilibrium states, scaled by the number of input signals. The CR is defined as the total number of non-trivial input contexts (N Contexts) scaled by the number of input signals, where a non-trivial input context is defined as an input-specified state sub-space containing more than one equilibrium (i.e., a multistable state sub-space). A system with nontrivial input contexts is multistable and therefore capable of maintaining memory of state and emitting context-dependent behaviors.

[0175] By definition, a monostable network has at most one equilibrium per input context and can therefore have a maximum number of output states equal to the number of input states, for a maximum MR=1.0. In contrast, multistability allows multiple states to be present in any input context, leading to MRs greater than 1.0. The CR of a monostable network is 0.0 by definition, as there are no multistable sub-spaces. Note that state degeneracy (the case where the same state is present in multiple input contexts) leads to MRs less than 1.0. A multistable system can have a maximum number of non-trivial input contexts equal to the number of input states, for a maximum CR of 1.0.

[0176] We studied several network topologies, calculated their average IP, and examined the IP as a function of different network properties (see Table 1). We found that the intelligence potential of a regulatory network is loosely related to the number of network cycles and the hierarchical incoherence (Box 1) of the regulatory network, but unrelated to the total number of nodes, edges or the maximum in-degree of nodes in the network. The form of networks included in this analysis are shown in FIG. 13, and analysis was performed on 15 unique networks of each class, each with different randomly generated edge interaction types (e.g., different unique combinations of activators and inhibitors).Tufts T002882 WO.PCT Quarles 166118.01558

[0177] Directed Acyclic GRNS: Evidence for Guaranteed Mono-stability and Fully Analytical Solutions

[0178] As GRNs were constructed using symbolic mathematics, it was possible to use computer algebra to look for simplifications to the set of differential equations (e.g., dimensionality reduction), which in some cases lead to the determination of fully analytical solutions. It was found that when using the Hill function base (example shown in FIG. 14), any regulatory network that is free of cycles (e.g., networks that are Directed Acyclic Graphs, DAGs) have a single, fully analytical solution determining the steady- state value of each node in terms of input node values. No analytical solutions were found when using the Logistic function base. An example of a network with a complete analytical solution is shown in FIG. 17, where the steady-state (equilibrium) expression probability of the two nodes ‘p0’ and ‘pl’ are uniquely specified by the level of input node ‘p2’ and the set of interaction edge parameters |3ij and nij for the network parameterized using Hill functions. For any value of parameters and the state of the input node ‘p2’, there is only one unique solution. We found this to be the case for all DAGs studied.

[0179] Osmoadapation Model Mathematics

[0180] Here we detail our computational model of yeast osmoadaptation. Our model is comprised of a physical component that describes the dynamic change of volume of a cell with water movements mediated by transmembrane osmotic pressure gradients, which can be applied to a variety of cell types including inanimate vesicles, plant cells, and mammalian cells. A second component of our model is a regulatory scheme based on yeast HOG-MAPK osmoadaptation, which interacts with the physical osmotic volume increase to help the cell maintain its volume at a set-point value against stochastic changes in environmental osmolarity. All parameters and variables of our model are summarized in Table S4. In the following we derive our complete osmoadaptation model from first principles.

[0181] We begin by defining the osmolarity inside the cell (mi) in terms of the total moles of osmolytes in the cell (« / ):Tufts T002882 WO.PCT Quarles 166118.01558[01821 The transmembrane osmotic pressure gradient (Posmo) can be defined in terms of the difference in osmolarity between the inside and outside (mo) of the cell. Note we assume that the osmolarity outside :

[0183] In our model, the cell volume will change with osmotic pressure driven transmembrane water flow. Therefore, we wish to write the osmotic pressure gradient in terms of the cell volume variable by substituting El into E2:

[0184] First we consider the case where the present cell volume (volcell) is less than the undeformed cell volume (volcello ) and where the cell is wrinkling with volume loss and therefore does not encounter mechanical resistance to volume changes. In this case where volceii < volceiio , osmotic transmembrane water flow into the cell occurs via flow channels and can be described by:"""

[0185] Substituting in equation E3 to E4 we obtain an expression for transmembrane water flow in terms of osmolyte gradients and the present cell volume:Tufts T002882 WO.PCT Quarles 166118.01558"

[0186] Multiplying the transmembrane linear flow rate by the area over which water flows (which is equal to the number of water channels multiplied by the cross-sectional area of a water channel) we obtain a volume flow rate, which is equivalent to the rate of cell volume change with transmembrane osmotic water flow:

[0187] Substituting in E5 to E6 we obtain the differential equation for the case where VOlcell VOlcello

[0188] Steady-state volume for the case where volcell < volceiio can be found by solving E7 for voLeii when the volcell change rate is equal to zero, which yields:

[0189] For the regime where volcell >= volceiio and the cell is changing volume from an elastically deformed state that results in mechanical resistance to stretch the membrane or cell wall as volume expands, we need to consider that the mechanical structure of the cell wall or membrane may resist deforming under an osmotic pressure due to the generation of a mechanical pressure. Hoop stress of a cylindrically shaped cell is one way to account for these mechanical factors, where Pmd is the pressure inducing the stressTufts T002882 WO.PCT Quarles 166118.01558

[0190] In the circumferential direction hoop stress of a cylindrically shaped cell is described by:

[0191] In the longitudinal (axial) direction hoop stress is described by:

[0192] Hoop strain in the circumferential direction is described by:

[0193] While hoop strain in the longitudinal direction is described by:&

[0194] Substituting in E9 and E10 into Ell we obtain:

[0195] And substituting in E9 and E10 into E12 we obtain:>Tufts T002882 WO.PCT Quarles 166118.01558

[0196] Displacement in the circumferential direction is represented by:

[0197] And displacement in the longitudinal / axial direction is represented by:

[0198] An expression for the volume of the cell in terms of the unstrained volume and the circumferential and longitudinal strains is:

[0199] Substituting in El 5 and El 6 into El 7 we obtain:

[0200] For simplicity, if we assume the Poisson’s ratio is v=0.5, then:(El 9)

[0201] Solving E19 for the inducing pressure, PM>

[0202] In the case where the cell is expanding against structural resistance (volcell >= volo), the structural pressure PM (analogous to Turgor pressure) provides a resistance to theTufts T002882 WO.PCT Quarles 166118.01558osmotic pressure Posmo, possibly limiting osmotic water influx as the cell pressurizes with turgor pressure. Mathematically, this is represented as:

[0203] Substituting in E20 and E3 into E21, and then substituting the resulting expression for water influx into E6, we obtain the differential equation for the case where volcell ->=VOlcello :> >

[0204] Solving E22 for the steady state volcell, which occurs when the change in cell volume is equal to zero, provides the expression:>

[0206] The above derivations provide us with cell volume change expressions for a system without an osmoadaptive regulatory network for two regimes: 1) the volcell < vo eiio regime occurring when the osmotic gradient favors water efflux from the cell to the environment, the cell volume is assumed to shrink without mechanical resistance to decreasing volume and is described by E7, and 2) the volcell >= volcdio regime occurring when the osmotic gradient favors water influx from the environment to the cell, the cell volume is assumed to expand with mechanical resistance created by the properties of the cell membrane or wall which induces mechanical pressure that opposes further water influx, and is described by E22. Steady-state cell volumes for cells with different perimeters (e.g., plant cell wall, yeast cell wall, and mammalian plasma membrane) are shown for models without osmoadaptation in FIG. 18.Tufts T002882 WO.PCT Quarles 166118.01558

[0207] The final component of our osmoadaptation model incorporated bio-realistic regulatory network-based control components into the osmotic volume change through implementation of a simplified yeast HOG-MAPK pathway.

[0208] Firstly, the moles of osmolytes inside the osmoadapted cell was assumed to be the combination of a fixed base level plus the moles of glycerol in the cell:

[0209] The molarity (i.e., moles per liter) of glycerol in the cell was taken to be the product of a decay and growth term, where glycerol decay is mediated by membrane strain activation of glycerol efflux transporters (parameterized by Ki, bi,see Table S4) while glycerol production is activated by membrane strain via the SLN1 strain sensor activation of the HOG-MAPK pathway (parameterized by K2, b2, and sO2, see Table 6):

[0210] The response curves for the growth and decay of glycerol production with membrane strain are shown in FIG. 19A-19D, while the ability of a cell to maintain its volume near a setpoint value against an osmotic challenge is shown in FIG. 20A-20C.

[0211] Box 1

[0212] Analogue Computing: A computational method that uses continuous physical phenomena, such as electrical voltages or mechanical movements, to represent and manipulate data. Unlike digital computing, which represents information in discrete bits, analog computing operates on continuous signals. This approach can be highly efficient for certain types ofTufts T002882 WO.PCT Quarles 166118.01558problems, particularly those involving differential equations and simulations of dynamic systems.

[0213] Asymptotically-Stable: A system is considered asymptotically stable if, given an initial condition sufficiently close to an equilibrium point, the system's state will converge to that equilibrium point as time approaches infinity. In simpler terms, it means that the system will eventually settle down to a steady state, regardless of small disturbances. This concept is crucial in various fields, including control theory, physics, and engineering, where it's used to analyze the stability of systems and design controllers to stabilize them.

[0214] Attractor: A set of states towards which a system tends to evolve. It's a sort of "magnetic" point or region in the system's phase space that pulls the system's trajectory toward it. Attractors can be simple, like a single point (a fixed point attractor), or more complex, like a closed loop (a periodic attractor). In chaotic systems, attractors can be intricate geometric shapes known as strange attractors.

[0215] Context: The circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed. It encompasses the surrounding environment, background information, and relevant factors that influence meaning and interpretation. In the realm of language, context helps determine the specific meaning of words and phrases. In broader terms, it refers to the social, cultural, historical, or political setting within which something occurs. Understanding context is crucial for effective communication, problemsolving, and decision-making.

[0216] Compute: To determine something, often using mathematical methods or a computer. It involves processing information and performing operations to arrive at a specific result. For example, one might compute the area of a circle, the average of a set of numbers, or the solution to a complex equation.

[0217] Context Ratio: Used in the estimate of the Intelligence Potential of a Regulatory Network Machine, the context ratio (CR) is the total number of non-trivial input contexts (N Contexts) scaled by the number of input states, where a non-trivial input context is an input-specified state sub-space containing more than one equilibrium (i.e., a multistable sub-state).Tufts T002882 WO.PCT Quarles 166118.01558

[0218] Dissipative Dynamic System: A system that loses energy over time, leading to a reduction in its overall activity. This energy loss can be due to various factors such as friction, heat dissipation, or other forms of energy transfer. As a result, the system's trajectories converge towards a smaller region in its phase space, often referred to as an attractor. Dissipative systems are common in nature and engineering. Examples include mechanical systems with friction, electrical circuits with resistance, and biological systems that lose energy through metabolism.

[0219] Direction Field: An array of directions defined at each point in state space that indicates the trajectory / time evolution of the system from that specific state point (FIG. 1). When the system is at any point / state in the state space, the direction field is akin to a force field that directs the evolution of the system to another state. The direction field of the state space is akin to a leaf (system state) moving along on the currents of a river (direction field). The direction field allows for visualization and understanding of the different characteristics of the dynamic system, including attractors and limit cycles (cyclic attractors).

[0220] Equilibrium: A state of balance or stability. In a system at equilibrium, there is no net change over time. Equilibrium can be either static (no change) or dynamic (continuous change without a net change).

[0221] Finite State Machine: A mathematical model of computation used to design algorithms. It's a simple machine with a finite number of states. At any given time, the machine exists in exactly one of these states. When the machine receives an input, it transitions from its current state to another state, or remains in the same state. This transition is determined by a set of rules defined for the FSM. The machine can also produce an output based on its current state and the input it receives. FSMs are widely used in computer science and engineering to model various systems, from simple traffic lights to complex computer programs.

[0222] Gene Regulatory Network: A complex system of interconnected genes and their regulatory elements. Regulatory elements, such as transcription factors, which are in turn proteins expressed by genes, control the expression of other genes, determining when and how much of a particular protein is produced. GRNs are essential for cellular processes and the development of organisms.Tufts T002882 WO.PCT Quarles 166118.01558

[0223] Hierarchical Incoherence: A calculated parameter of a network that gives insight to its topology, where low hierarchical incoherence means that all its vertices have approximately the same hierarchical level and that the network is therefore influenced by a large percentage of its vertices. In contrast, low hierarchical incoherence means that there are distinct hierarchical levels and that the network is therefore influenced by a small percentage of its vertices.

[0224] Hopfield Network: A type of recurrent artificial neural network that can be used as an associative memory. It consists of a single layer of interconnected neurons, where each neuron is connected to every other neuron. These connections have weights that are adjusted during training. The network operates by iteratively updating the state of each neuron based on the weighted sum of its inputs. This process continues until the network reaches a stable state, which represents a stored memory pattern. Hopfield networks are known for their ability to recall patterns even when presented with noisy or incomplete input. They have applications in various fields, including pattern recognition, optimization, and content- addressable memory.

[0225] Intelligence Potential: For a Regulatory Network Machine, the intelligence potential (IP) estimates the capability of the network to output diverse behaviors in response to stimuli, maintaining memory of state, and emitting context-dependent behaviors. The IP of a network is the sum of the Multistate Ratio (MR) and the Context Ratio (CR).

[0226] Meta-Stable: A state of a system that is not in its lowest energy state, but is stable enough to persist for a relatively long time. It's like a ball balanced on a hilltop: it's not the lowest point (the valley), but it can stay there unless disturbed. A small disturbance can cause the system to transition to a more stable state. For example, a diamond is metastable at room temperature and pressure: it's not the most stable form of carbon, but it can exist for a very long time without changing.

[0227] Multistate Ratio: Used in the estimate of the Intelligence Potential of a Regulatory Network Machine, the multistate ratio (MR) is the total number of output states, scaled by the number of input states.

[0228] Osmoadaptation: The ability of an organism to survive and acclimatize to changes in its environmental osmolarity. Osmoadaptation involves physiological sensors (typically surface receptors) that alert the system to changes in osmolarity and transduce the signal toTufts T002882 WO.PCT Quarles 166118.01558activate appropriate cellular responses. Activated cellular responses ultimately activate appropriate actuators / effectors that achieve the goal state of appropriate directed water flow across the cell, thereby maintaining cell volume homeostasis against the osmotic challenge.

[0229] Persuasion: As we use the term here, persuasion involves using communication techniques to transition a system such that it adopts a particular state or take a specific action.

[0230] Setpoint Control: A control strategy used to maintain a system at a desired value. It involves measuring the current state of the system, comparing it to the desired setpoint, and then adjusting the system's inputs to minimize the difference between the two.

[0231] State Space: Commonly used in dynamical systems and control theory, state space, also known as phase space, is a conceptual metaphor to physical space where all possible states of the system are represented as points in the state space. The evolution of the system in time progresses along trajectories in the state space, which helps to visualize and characterize the full characteristics of the system. A continuous, spatial representation for the states of a system facilitate the use of conceptual tools related to navigation and problem-solving by agents with various degrees of context-sensitive control.

[0232] Turing Machine: A formalism for computation that clearly separates the concept of a machine (a device with discrete states and a known, deterministic transition between those states) and data (an information stream that both guides the machine’s behavior and is itself modified by the machine). The Turing Machine metaphor introduced the general concept of programmability (and the distinction between software and hardware) because its function can be radically altered by the information content of the input data without needing to change the design or components of the machine.

[0233] Tufts T002882 WO.PCT Quarles 166118.01558

[0234] TABLE 1. Estimating the intelligence potential (IP) of various regulatory networks.Tufts T002882 WO.PCT Quarles 166118.01558Tufts T002882 WO.PCT Quarles 166118.01558

[0235] TABLE 2. Feature comparison between classical Turing Machines, Hopfield Networks, and Regulatory Network Machines (RNMs), which are a hybrid model between Turing Machines and Hopfield Networks.

[0236] TABLE 3. Comparison of computational time and equilibrium state match error between Boolean and Continuous models of GRN. The GRN used in this analysis are shown in FIG. 13.< << <Tufts T002882 WO.PCT Quarles 166118.01558& >>

[0237] TABLE 4. Description of parameters used in regulatory network models.

[0238] TABLE 5. Characterizing the stability of an equilibrium from the eigenvalues of the Jacobian at the equilibrium, used to characterize equilibrium stability in Continuous models of GRN.Tufts T002882 WO.PCT Quarles 166118.01558&Tufts T002882 WO.PCT Quarles 166118.01558

[0239] TABLE 6: Description of all param eters / variables utilized in the yeast osmoadaptation model.

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[0369] Illustrative Embodiments of Methods and Systems Described Herein

[0370] FIG. 23 A shows an example process 2300 to model a system. At step 2302, a dissipative dynamic system is built. Building a dissipative dynamic system can include identifying a known system, or defining a new dissipative dynamic system (e.g., based on experimental results). The dynamic system may be a regulatory network that includes a plurality of nodes and a plurality of directed edges. At step 2304, a plurality of inputs may be determined. At step 2306, an input in the plurality of inputs may be applied to the dynamic system. Applying an input to the system when it is in one equilibrium state may transition the dynamic system to a corresponding equilibrium state, where the state to which the system transitions may depend on both the initial equilibrium state and the input applied to the system in that state. At step 2308, a finite state machine is output. The network finite state machine may include a record of theTufts T002882 WO.PCT Quarles 166118.01558plurality of inputs, the corresponding equilibrium state to each input in the plurality of inputs, and a map of possible transitions between equilibrium states. The FSM may be a map representing the possible transitions between equilibrium states for each equilibrium states, showing path-dependencies, cycles, and irreversibilities in the ability to reach equilibrium states under patterns of input.

[0371] FIG. 23B shows an example process 2300B to output a network finite state machine that is tied to experimental data regarding the health of a patient. At 2310, a regulatory network is built / identified / modeled as a dissipative dynamic system. At 2312, a plurality of inputs is identified. At 2314, the process identifies a plurality of unique equilibrium internal / output states. At 2316, the process begins with the dissipative dynamic system in each equilibrium input / output state. Each input in the plurality of inputs from 2312 is applied to each equilibrium input / output state from 2314. The process then determines which equilibrium internal / output state the system transitions to. At 2318, the process outputs a network finite state machine.

[0372] Separately, at 2320, a patient is identified or selected. At 2322, the process collects multiomics patient data. At 2324, the process identifies internal or output states related to patient condition (e.g., “disease” vs. “healthy”). The states may be based on the multiomics data collected at 2322. At 2326, the output network finite state machine from 2318 is used to identify inputs that transition the system between states (e.g., what transitions the system from “healthy” to “disease,” or from “disease” to “healthy”).

[0373] At 2310, the dissipative dynamic system may be built based on the multi omic patient data, as well as a disease of interest (e.g., a disease the patient as 2320 is diagnosed with or is suspected of having). The plurality of inputs identified at 2312, may correspond to the multiomic patient data from 2322.

[0374] In FIG. 24, an example 2400 of a system (e.g., a data processing system) for modeling a system in accordance with some embodiments of the disclosed subject matter is shown.

[0375] In some embodiments, computing device 2404 and / or server 2416 can be any suitable computing device or combination of devices, such as a desktop computer, a laptopTufts T002882 WO.PCT Quarles 166118.01558computer, a smartphone, a tablet computer, a wearable computer, a server computer, a virtual machine being executed by a physical computing device, etc. As described herein, system 2400 can present information about the characterized protein to a user (e.g., a researcher and / or a physician).

[0376] In some embodiments, communication network 2402 can be any suitable communication network or combination of communication networks. In some embodiments, communication network 2402 can be any suitable communication network or combination of communication networks. For example, communication network 2402 can include a Wi-Fi network (which can include one or more wireless routers, one or more switches, etc.), a peer-to-peer network (e.g., a Bluetooth network), a cellular network (e.g., a 4G network, a 5G network, etc., complying with any suitable standard, such as CDMA, GSM, LTE, LTE Advanced, WiMAX, etc.), a wired network, etc. In some embodiments, communication network 2402 can be a local area network, a wide area network, a public network (e.g., the Internet), a private or semi-private network (e.g., a corporate or university intranet), any other suitable type of network, or any suitable combination of networks. Communications links shown in FIG. 24 can each be any suitable communications link or combination of communications links, such as wired links, fiber optic links, Wi-Fi links, Bluetooth links, cellular links, etc.

[0377] FIG. 24 additionally shows an example of hardware that can be used to implement computing device 2404 and server 2416 in accordance with some embodiments of the disclosed subject matter. In some embodiments, computing device 2404 can be used to execute one or more set of instructions to identify a behavioral catalog. In other embodiments, computing device 2404 can be used to identify therapeutic interventions. In still other embodiments, computing device 2404 can be used to identify a configuration of parameter of a gene regulatory network to perform a desired function.

[0378] As shown in FIG. 24, computing device 2404 can include one or more hardware processor 2406, one or more displays 2408, one or more inputs 2410, one or more communications 2412, and / or memory 2414. In some embodiments, processor 2406 can be any suitable hardware processor or combination of processors, such as central processing unit, a graphics processing unit, etc. In some embodiments, display 2408 can include any suitableTufts T002882 WO.PCT Quarles 166118.01558display devices, such as a computer monitor, a touchscreen, a television, etc. In some embodiments, inputs 2410 can include any suitable input device and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, etc.

[0379] In some embodiments, communication systems 2412 can include any suitable hardware, firmware, and / or software for communicating information over communication network 2402 and / or any other suitable communication networks. For example, communications systems 2412 can include one or more transceivers, one or more communication chips and / or chip sets, etc. In a more particular example, communications systems 2412 can include hardware, firmware and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, etc.

[0380] In some embodiments, memory 2414 can include any suitable storage device or devices that can be used to store instructions, values, etc., that can be used, for example, by processor 2406 to present content using display 2408, to communicate with server 2416 via communications system(s) 2412, etc.

[0381] Memory 2414 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 2414 can include RAM, ROM, EEPROM, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, etc. In some embodiments, memory 2414 can have encoded thereon a computer program for controlling operation of computing device 2404. In such embodiments, processor 2406 can execute at least a portion of the computer program to present content (e.g., images, user interfaces, graphics, tables, etc.), receive content from server 2416, transmit information to server 2416, etc.

[0382] In some embodiments, server 2416 can include a processor 2418, a display 2420, one or more inputs 2422, one or more communications systems 2424, and / or memory 2426. In some embodiments, processor 2418 can be any suitable hardware processor or combination of processors, such as a central processing unit, a graphics processing unit, etc. In some embodiments, display 2420 can include any suitable display devices, such as a computer monitor, a touchscreen, a television, etc. In some embodiments, inputs 2422 can include anyTufts T002882 WO.PCT Quarles 166118.01558suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, etc.

[0383] In some embodiments, communications systems 2424 can include any suitable hardware, firmware, and / or software for communicating information over communication network 2402 and / or any other suitable communication networks. For example, communications systems 2424 can include one or more transceivers, one or more communication chips and / or chip sets, etc. In a more particular example, communications systems 2424 can include hardware, firmware and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, etc.

[0384] In some embodiments, memory 2426 can include any suitable storage device or devices that can be used to store instructions, values, etc., that can be used, for example, by processor 2418 to present content using display 2420, to communicate with one or more computing devices 2404, etc. Memory 2426 can include any suitable volatile memory, nonvolatile memory, storage, or any suitable combination thereof. For example, memory 2426 can include RAM, ROM, EEPROM, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, etc. In some embodiments, memory 2426 can have encoded thereon a server program for controlling operation of server 2416. In such embodiments, processor 2418 can execute at least a portion of the server program to transmit information and / or content (e.g., results of a tissue identification and / or classification, a user interface, etc.) to one or more computing devices 2404, receive information and / or content from one or more computing devices 2404, receive instructions from one or more devices (e.g., a personal computer, a laptop computer, a tablet computer, a smartphone, etc.), etc.

[0385] In some embodiments, any suitable computer readable media can be used for storing instructions for performing the functions and / or processes described herein. For example, in some embodiments, computer readable media can be transitory or non-transitory. For example, non-transitory computer readable media can include media such as magnetic media (such as hard disks, floppy disks, etc.), optical media (such as compact discs, digital video discs, Blu-ray discs, etc.), semiconductor media (such as RAM, Flash memory, electrically programmable read only memory (EPROM), electrically erasable programmable read onlyTufts T002882 WO.PCT Quarles 166118.01558memory (EEPROM), etc.), any suitable media that is not fleeting or devoid of any semblance of permanence during transmission, and / or any suitable tangible media. As another example, transitory computer readable media can include signals on networks, in wires, conductors, optical fibers, circuits, or any suitable media that is fleeting and devoid of any semblance of permanence during transmission, and / or any suitable intangible media.

[0386] A number of references to patent and non-patent documents are made throughout the publication, each of which is herein incorporated by reference in its entirety.

[0387] Thus, while the invention has been described above in connection with particular embodiments and examples, the invention is not necessarily so limited, and that numerous other embodiments, examples, uses, modifications and departures from the embodiments, examples and uses are intended to be encompassed by the claims attached hereto.

Claims

Tufts T002882 WO.PCT Quarles 166118.01558CLAIMSWhat is claimed is:

1. A regulatory network machine, comprising:a dissipative dynamic system as a regulatory network comprising a plurality of nodes and a plurality of directed edges,wherein the plurality of edges connects at least two nodes in the plurality of nodes, and the plurality of edges determines how the connected nodes interact,wherein the dissipative dynamic system occupies an initial state;a plurality of inputs to the dissipative dynamic system,wherein applying an input in the plurality of inputs to the dissipative dynamic system transitions the dynamic system from the initial state to corresponding equilibrium state, wherein the corresponding equilibrium state is based on the input in the plurality of inputs and the initial state; anda finite state machine (FSM), wherein the FSM comprises a record of the plurality of inputs, the corresponding equilibrium state to each input in the plurality of inputs, and a map of possible transitions between equilibrium states.

2. The regulatory network machine of claim 1, wherein the dissipative dynamic system is governed by a set of differential equations or logic functions.

3. The regulatory network machine of claim 2, wherein the set of differential equations comprise non-linear partial differential equations.

4. The regulatory network machine of claim 2 or 3, wherein the logic functions comprise Boolean logic functions.

5. The regulatory network machine of any one of claims 1-4, wherein the plurality of nodes comprises input nodes, internal nodes, and output nodes.Tufts T002882 WO.PCT Quarles 166118.015586. The regulatory network machine of any one of claims 1-5, wherein at least one input in the plurality of inputs is a sustained input to the dynamic system.

7. The regulatory network machine of any one of claims 1-6, wherein at least one input in the plurality of inputs is a transient input to the dynamic system.

8. The regulatory network machine of any one of claims 1-7, wherein each input in the plurality of inputs has a binary value corresponding to a high or low presence of the input.

9. The regulatory network machine of any one of claims 1-8, wherein each input in the plurality of inputs is selected from a continuous range of variables corresponding to a degree of presence of the input.

10. The regulatory network machine of any one of claims 1-9, wherein a first input in the plurality of transitions the dynamic system into a first equilibrium state, and a change in the plurality of inputs to a second input transitions the dynamic system into a second equilibrium state.

11. The regulatory network machine of any one of claims 1-10, wherein the corresponding equilibrium state for an initial state and a given input comprises more than one equilibrium state.

12. The regulatory network machine of any one of claims 1-11, wherein the corresponding equilibrium state for an initial state and a given input is a single equilibrium state.

13. The regulatory network machine of any one of claims 1-12, wherein the FSM is further configured to predict behaviors of the dynamic system when the dynamic system occupies a particular equilibrium state and is subjected to a specific input.Tufts T002882 WO.PCT Quarles 166118.0155814. The regulatory network machine of any one of claims 1-13, wherein the FSM is used to calculate an intelligence potential of the regulatory network machine based on at least one of a multistate ratio or a context ratio.

15. The regulatory network machine of any one of claims 1-14, wherein the plurality of inputs corresponds to environmental variables.

16. The regulatory network machine of claim 15, wherein the environmental variables correspond to at least one of physical properties, osmotic conditions, temperature, light, pH, chemical properties / exposure, oxygen levels, exposure to toxins / pollutants, biochemical factors, signaling molecules, hormones, nutrients, morphogens, bioelectric characteristics, or growth factors.

17. The regulatory network machine of any one of claims 1-16, wherein the dynamic system corresponds to at least one of diseases, cancers, wound healing, tissue regeneration, embryonic stem cell differentiation, aging, development, yeast osmoadaptation, P13K / AKT / mTor crosssignaling cascades, embryonic stem cell differentiation, power grids, organizational charts, economic networks, or logistics / distribution networks.

18. The method of any one of claims 1-17, wherein the corresponding equilibrium state for an initial state and a given input comprises more than one equilibrium state.

19. A method for developing a treatment for a disease comprising utilizing the regulatory network machine of any one of claims 1-18.

20. The method of claim 19, wherein developing the treatment comprises identifying at least one therapeutic agent and a dosing regimen for the at least one therapeutic agent.Tufts T002882 WO.PCT Quarles 166118.0155821. The method of claim 19 or 20, wherein the treatment is selected from at least one of pharmaceutical therapy, immunotherapy, gene therapy, antibody therapy, chemotherapy, or radiation therapy.

22. A method for diagnosing a subject with a disease comprising utilizing the regulatory network machine of any one of claims 1-21.

23. The method of claim 22, wherein the method further comprises:obtaining sample from the subject;analyzing the sample to determine the expression of a plurality of features in the sample, wherein the plurality of features corresponds to a plurality of nodes in the system.

24. The method of claim 23, wherein analyzing the sample comprises analyzing at least one of genomics, transcriptomics, proteomics, metabolomics, epigenomics, measures of hormone levels, measures of enzyme levels, measures of organ function, or patient health indicators.

25. The method of claim 23 or 24, wherein the sample comprises at least one of a blood sample, urine sample, tissue sample, biopsy, or liquid biopsy.

26. A method of modeling a system, comprising:building a dissipative dynamic system as a regulatory network comprising a plurality of nodes and a plurality of edges,wherein the plurality of edges connects at least two nodes, and the plurality of edges determines how the connected nodes interact,wherein the dissipative dynamic system occupies an initial state;determining a plurality of inputs to the dynamic system;applying an input in the plurality of inputs to the dynamic system,wherein applying an input in the plurality of inputs to the dissipative dynamic system transitions the dynamic system from the initial state to a corresponding equilibrium state,Tufts T002882 WO.PCT Quarles 166118.01558wherein the corresponding equilibrium state is based on the input in the plurality of inputs and the initial state; andoutputting a finite state machine (FSM), wherein the FSM comprises a record of the plurality of inputs, the corresponding equilibrium state to each input in the plurality of inputs, and a map of possible transitions between equilibrium states.

27. The method of claim 26, wherein the dynamic system is governed by a set of differential equations or logical functions28. The method of claim 27, wherein the differential equations comprise non-linear partial differential equations.

29. The method of claim 27 or 28, wherein the logic functions are Boolean logic functions.

30. The method of any one of claims 26-29, wherein the plurality of nodes comprises input nodes, internal nodes, and output nodes.

31. The method of claims 26-30, wherein at least one input in the plurality of inputs is a sustained input to the dynamic system.

32. The method of claims 26-31, wherein at least one input in the plurality of inputs is a transient input to the dynamic system.

33. The method of claims 26-32, wherein each input in the plurality of inputs has a binary value corresponding to a high or low presence of the input.

34. The method of claims 26-32, wherein each input in the plurality of inputs is selected from a continuous range of variables corresponding to a degree of presence of the input.Tufts T002882 WO.PCT Quarles 166118.0155835. The method of claims 26-34, wherein a first input in the plurality of inputs transitions the dynamic system into a first equilibrium state, and a change in the plurality of inputs to a second input transitions the dynamic system into a second equilibrium state.

36. The method of claims 26-35, wherein the corresponding equilibrium state for an initial state and a given input is a single equilibrium state.

37. The method of claims 26-36, wherein the method further comprises predicting behaviors of the dynamic system when the dynamic system occupies a particular equilibrium state and is subjected to a specific input.

38. The method of any one of claims 26-37, wherein the method further comprises calculating an intelligence potential of the RNM based on at least one of a multistate ratio or a context ratio.

39. The method of any one of claims 26-38, wherein the plurality of inputs corresponds to environmental variables.

40. The method of claim 39, wherein the environmental variables corresponds to at least one of physical properties, osmotic conditions, temperature, light, pH, chemical properties / exposure, oxygen levels, exposure to toxins / pollutants, biochemical factors, signaling molecules, hormones, nutrients, morphogens, or growth factors.

41. The method of any one of claims 26-40, wherein the dynamic system corresponds to at least one of diseases, cancers, wound healing, tissue regeneration, embryonic stem cell differentiation, aging, development, yeast osmoadaptation, P13K / AKT / mTor cross-signaling cascades, embryonic stem cell differentiation, power grids, organizational charts, economic networks, or logistics / distribution networks.Tufts T002882 WO.PCT Quarles 166118.0155842. The method of any one of claims 26-41, wherein the method further comprises developing a treatment for a disease based on the modeled system.

43. The method of claim 42, wherein developing a treatment for a disease comprises identifying at least one therapeutic agent and a dosing regiment for the at least one therapeutic agent.

44. The method of claim 42 or 43, wherein the treatment is selected from at least one of pharmaceutical therapy, immunotherapy, gene therapy, antibody therapy, chemotherapy, or radiation therapy.

45. The method of any one of claims 26-44, wherein the method further comprises diagnosing a subject with a disease.

46. The method of claim 45, further comprising:obtaining a sample from the subject;analyzing the sample to measure a plurality of features;determine the initial state of the system, wherein the plurality of input nodes corresponds to the plurality of measured features.

47. The method of claim 46, wherein analyzing the sample comprises analyzing at least one of genomics, transcriptomics, proteomics, metabolomics, epigenomics, measures of hormone levels, measures of enzyme levels, measures of organ function, or patient health indicators.

48. The method of claim 46 or 47, wherein the sample comprises at least one of a blood sample, urine sample, tissue sample, biopsy, or liquid biopsy.

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