An alpha radionuclide drug in-vitro cell response prediction method and system based on multi-module mathematical modeling and a medium

Abstract

The application discloses an alpha-nucleus drug in-vitro cell reaction prediction method and system based on multi-module mathematical modeling and a medium, the method comprises four sequentially connected modules of basic parameter input, pharmacokinetic prediction, cell absorption dose calculation and biological effect prediction, integrates a three-compartment kinetic model, a microdose point kernel convolution and a DNA damage repair kinetic model, and realizes quantitative simulation of a whole chain from drug distribution, microscopic energy deposition to cell survival. The application overcomes defects of an existing experience model, such as inability to accurately reflect high LET characteristics of alpha particles, neglecting bystander effects and repair kinetics, and significantly improves prediction accuracy. The method can quickly simulate the curative effect of different drugs, cell lines and dose schemes on a computer, greatly reduces research and development cost and period, and provides an efficient theoretical tool for new drug screening and dose optimization.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of radiobiology and mathematical modeling, specifically to a method, system, and medium for predicting the in vitro cellular response of α-nucleoside drugs based on multi-module mathematical modeling. Background Technology

[0002] Targeted Alpha Therapy (TAT) is a cutting-edge direction in the field of radiotherapy. Utilizing the unique physical properties of alpha particles—high linear energy transfer and short range—it can efficiently kill tumor cells while minimizing radiation damage to surrounding normal tissues, demonstrating significant clinical application potential, especially in the treatment of micrometastases and scattered tumors.

[0003] However, current preclinical evaluation systems for the efficacy and safety of alpha-nucleoside drugs still heavily rely on traditional and relatively primitive in vitro cell experiments and animal models. These methods have significant and inherent limitations in terms of predictive accuracy, efficiency, and systematicity, becoming a key bottleneck restricting the rapid development of this class of novel drugs. The shortcomings of existing technologies are not isolated but permeate the entire chain from physical dose calculation to biological effect assessment, specifically manifested in the following aspects:

[0004] (1) Limitations of empirical dose-response models: Currently, the prediction of in vitro cell viability largely relies on empirical mathematical models based on the average absorbed dose (Gy), such as the linear quadratic (LQ) model. These models originate from studies of low-LET radiation (such as X-rays and gamma rays), and their basic assumption is that energy deposition is uniform and the biological effect is only related to the total dose. However, the energy deposition of alpha particles is highly localized and random, and its micro-dose distribution is extremely non-uniform. Directly applying the LQ model or similar empirical models cannot accurately reflect the unique biological effects of high-LET radiation, such as significantly higher relative bioefficacy (RBE) and lower oxygen enhancement ratio (OER), leading to a systematic bias between the predicted cell viability and experimental observations, and failing to provide reliable quantitative guidance for high-LET alpha radionuclide therapy.

[0005] (2) Inaccuracies in applying macroscopic dosimetry to the microscopic scale: Traditional radiation dosimetry calculations are usually based on macroscopic average doses at the organ or tissue level. When applied to the cellular or even subcellular scale, this averaging method seriously ignores the discrete distribution characteristics of alpha particle tracks, the geometric relationship between the cell nucleus and the radiation source (such as the localization of isotopes on the cell membrane, cytoplasm, or nucleus), and the dose heterogeneity within the cell population. A cell may be hit by multiple alpha particles and die, while its neighboring cells may survive because they were not hit. This "all or nothing" dose distribution characteristic makes it impossible for average dose-based assessment methods to accurately correlate with the final biological effect, thus making it difficult to guide personalized drug dosage optimization and failing to truly reflect the microscopic efficacy of treatment.

[0006] (3) Lack of or oversimplification in modeling key biological processes: Most existing computational models are driven by physical doses, oversimplifying or completely ignoring the subsequent complex biological response processes. They fail to integrate the dynamic uptake, internalization, and metabolism of drugs between the culture medium and different compartments (membrane, cytoplasm, nucleus) of cells, and cannot simulate the real-world scenario of drug concentration changes over time. Alpha particles mainly induce complex DNA double-strand breaks (DSBs). Existing models generally lack modeling of the dynamic process of DSB induction and subsequent repair through non-homologous end joining (NHEJ) and homologous recombination (HR), and cannot reflect the impact of differences in repair capabilities of different cell lines on the final survival rate. In alpha radionuclide therapy, the "bystander effect"—where irradiated cells release signaling molecules to induce biological effects in neighboring unirradiated cells—is significant, and this effect can significantly expand the actual biological killing range. Most existing models do not take this key mechanism into account, resulting in a serious underestimation of the effects at the cell population level.

[0007] (4) Cost and efficiency bottlenecks in the R&D process: Due to the lack of theoretical tools that can reliably predict efficacy, the screening of new drugs and the optimization of dosage regimens rely heavily on a large number of repetitive and lengthy in vitro clonogenic experiments and animal experiments. This "trial and error" R&D model not only consumes high financial and time costs, but also limits the number of drug candidates and dosage regimens that can be fully evaluated, becoming one of the key bottlenecks restricting the rapid development of alpha nucleoside drugs. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a method, system, and medium for predicting in vitro cellular responses of alpha-nucleoside drugs based on multi-module mathematical modeling. This overcomes the deficiencies of existing technologies and enables accurate and efficient simulation of in vitro cellular responses of alpha-nucleoside drugs on a computer before conducting time-consuming and laborious experiments. This provides strong theoretical support and guidance for early drug screening, dosimetric optimization, and research on biological effects mechanisms.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A method for predicting the in vitro cellular response of alpha-nucleoside drugs based on multi-module mathematical modeling includes the following steps:

[0011] Step S1: Receive and initialize the parameters required for the simulation, including experimental environment parameters, radionuclide parameters, drug and target information parameters, and cell line parameters;

[0012] Step S2: Based on the parameters input in Step S1, the spatiotemporal distribution of α-nucleoside drugs in the culture medium, cell membrane and cytoplasm is dynamically simulated by using a multi-compartment kinetic model, and the data of the change of radioactivity in each compartment over time are output.

[0013] Step S3: Based on the radioactivity distribution data output in Step S2, the absorbed dose rate of each cell nucleus is calculated using the principles of microdosimetry and the dose point kernel convolution method.

[0014] Step S4: Based on the nuclear uptake dose rate output in Step S3, the dynamic changes in the number of DNA double-strand breaks in the cell population are simulated by integrating DNA damage kinetics, repair kinetics, and bystander effect, and finally the predicted results of cell survival rate or number of surviving cells over time are output.

[0015] Preferably, in step S2, the multi-compartment kinetic model is a three-compartment kinetic model, which simulates the dynamic distribution of the radionuclide drug inside and outside the cell using the following set of differential equations:

[0016] ;

[0017] ;

[0018] ;

[0019] in, The concentration of radionuclide drugs in the culture medium; The concentration of nucleoside drugs in the cytoplasm; This represents the number of target receptors that have been bound on a single cell. The total number of all target receptors on a single cell; This refers to the volume of the culture medium. Total number of cultured cells; Volume of a single cell; This represents the binding rate constant between the targeting vector and the cell surface targeting receptor; This represents the dissociation rate constant between the targeting vector and the cell surface targeting receptor; is the endocytosis rate constant of the cell surface targeting carrier-receptor complex; This is the degradation rate constant of the intracellular targeting carrier-receptor complex within the cell.

[0020] Preferably, step S2 further includes a step of converting chemical concentration into radioactivity, specifically achieved through the following formula:

[0021] ;

[0022] ;

[0023] ;

[0024] in, , , These are the radioactivity levels of the culture medium, cytoplasm, and cell membrane, respectively. , The initial radioactivity and chemical concentration of the radiopharmaceutical in the culture medium; is the attenuation coefficient of the radioactive nuclide.

[0025] Preferably, in step S3, the absorbed dose rate of each cell nucleus It is calculated by summing the integrals of the following parts:

[0026] The contribution of intracellular radionuclides to their own nucleus;

[0027] The contribution of radioactive isotopes on the cell membrane to the cell nucleus;

[0028] The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus;

[0029] The contribution of radionuclides in the culture medium to the cell nucleus.

[0030] Preferably, in step S3, the absorbed dose rate of each cell nucleus It is calculated using the following formula:

[0031] ;

[0032] in, The contribution of radionuclides in the cytoplasm and cell membrane of one's own cells to the cell nucleus; The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus; The contribution of radionuclides in the culture medium to the cell nucleus; Let be the dose point kernel function, where , representing the Euclidean distance between the source and the target; The location of the radioactive source in space. The target location is the coordinate of the center of the cell nucleus. For cell nucleus mass.

[0033] Preferably, in calculating the absorbed dose rate of the cell nucleus, a piecewise variable step size strategy is used for numerical integration, specifically:

[0034] In the near-field region, which is 0 to 2 micrometers from the cell nucleus, a fine grid step size of 0.1 micrometers is used;

[0035] In the mid-field region, 2 to 20 micrometers from the cell nucleus, a medium grid step size of 0.5 to 1.0 micrometers is used;

[0036] Within 20 micrometers of the cell nucleus to the cutoff radius In the far field region, a coarse grid step size of 1 to 5 micrometers is used;

[0037] Among them, the cutoff radius Determined by a preset dose-energy cumulative contribution criterion:

[0038] ;

[0039] in, Take 0.01 or 0.001.

[0040] Preferably, in step S4, the number of DNA double-strand breaks... The rate of change is described by the following equation:

[0041] ;

[0042] in, , representing the radiation-induced DSB rate; The direct radiation-induced DSB damage coefficient;

[0043] This indicates that the DSB rate is induced by the bystander effect; The bystander signal-induced DSB injury coefficient, The concentration of bystander signaling factor in the culture medium;

[0044] The concentration of bystander signaling factors The rate of change is described by the following equation:

[0045] ;

[0046] in, The rate constant is generated for the bystander effect signal. The bystander effect signal decay rate constant;

[0047] , representing the DSB repair rate through the fast and slow repair pathways; the rate of change in the number of DSBs entering the fast and slow repair pathways are respectively:

[0048] ;

[0049] ;

[0050] in, , These represent the number of DSBs entering the fast and slow repair pathways, respectively. , These are the rate constants for the fast and slow repair pathways, respectively. , The ratio of DSB repair pathways via fast and slow repair methods, and .

[0051] Preferably, before or during step S1, a parameter fitting step is further included to fit the unknown parameters in the model using an optimization algorithm, including:

[0052] Pharmacokinetic parameters were fitted based on time-series data from cellular uptake experiments.

[0053] Radiation sensitivity parameters were fitted based on cell survival curves, conditioned medium experiments, or γ-H2AX focal kinetic data.

[0054] The present invention also discloses an in vitro cellular response prediction system for α-nucleoside drugs for performing the above-described method, comprising:

[0055] The basic parameter input module, used to receive and store initialization parameters, is configured as follows:

[0056] Provides a human-computer interaction interface or data interface for receiving initial parameters input by the user or loading initial parameters from an external database; stores and manages a built-in database containing the physical properties of radionuclides and the biological properties of cell lines; integrates and initializes the received and called parameters to provide a complete scene definition for subsequent simulation calculations;

[0057] The pharmacokinetic prediction module, communicatively connected to the basic parameter input module, is used to perform multi-compartment kinetic simulations; it is configured as follows:

[0058] Receive initial parameters from the basic parameter input module; run a multi-compartment pharmacokinetic mathematical model, which describes the dynamic transfer process of α-nucleoside drugs in the culture medium, cell membrane, and cytoplasm through a set of coupled differential equations; execute a numerical integration algorithm to solve the differential equations and obtain the spatiotemporal distribution of drug concentration and radioactivity in each compartment; output radioactivity distribution data to the cell uptake dose calculation module.

[0059] A cell absorption dose calculation module, communicatively connected to the pharmacokinetics prediction module, is used to calculate the microscopic dose distribution; it is configured as follows:

[0060] Receives spatiotemporal distribution data of radioactivity from the pharmacokinetics prediction module; calls the pre-generated radioactive particle dose point kernel function stored in the database; performs microdosimetry calculations based on dose point kernel convolution integrals, and adopts a piecewise variable step size numerical integration strategy to balance computational efficiency and accuracy; calculates and outputs the absorbed dose rate data of each cell nucleus to the biological effect prediction module.

[0061] A biological effect prediction module, communicatively connected to the cell uptake dose calculation module, is used to predict cell survival; it is configured as follows:

[0062] Receives absorbed dose rate data of cell nuclei from the cell absorbed dose calculation module; runs a biodynamic model that integrates radiation-induced DNA damage, bystander effect, and DNA damage repair dynamics, which is described by a set of coupled differential equations; executes a numerical integration algorithm to solve the biodynamic differential equations to dynamically simulate the changes in the number of DNA damage and the number of viable cells in the cell population; and outputs the final cell survival prediction results.

[0063] The parameter fitting module, communicatively connected to the basic parameter input module, is used to optimize model parameters based on experimental data. It is configured as follows:

[0064] Receive experimental measurement data provided by the user; invoke the optimization algorithm to iteratively optimize and estimate the unknown parameters in the pharmacokinetic or biokinetic model, using the experimental measurement data as the target; feed back the optimal parameter values ​​obtained from the fitting and store them in the built-in database of the basic parameter input module for use in prediction calculations.

[0065] The present invention also discloses a computer-readable storage medium, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the above-described method.

[0066] This invention provides a method for predicting the in vitro cellular response of alpha nucleoside drugs based on multi-module mathematical modeling, offering the following advantages: By seamlessly connecting five modules—basic parameter input, pharmacokinetics, microdositology, biological effects, and parameter fitting—a unified, end-to-end, multi-module coupled mathematical framework is constructed. This framework begins with drug binding to cells and progressively simulates its internalization and distribution, microscale energy deposition, initial DNA damage and repair, intercellular signal transduction, and ultimately, cell survival. This allows the model to more realistically reflect the complete pathway and complex biological logic of alpha nucleoside drug action. Furthermore, by introducing microdositology and dose-point kernel convolution methods based on Monte Carlo simulations, the distorted average dose assumption is completely eliminated, accurately reproducing the discreteness, randomness, and high LET characteristics of alpha particle tracks. Moreover, by integrating DSB dual-pathway repair kinetics and a quantitative bystander effect model, the model can simulate the "shoulder" of the cell survival curve, hypersensitivity in the low-dose region, and the amplified swarm kill effect caused by the bystander effect. In addition, this invention can not only output the final cell survival rate, but also reveal the dynamic changes in the intermediate process. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of this invention or the prior art will be briefly introduced below.

[0068] Figure 1 A schematic diagram of the in vitro cellular response prediction system for α-nucleoside drugs of the present invention;

[0069] Figure 2 A schematic diagram of the three-compartment model of pharmacokinetics in this invention. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0071] Example 1, as Figures 1-2 As shown, this invention provides a method for predicting the in vitro cellular response of α-nucleoside drugs based on multi-module mathematical modeling. This embodiment uses the prediction of radiopharmaceutical […]. 225 Taking the in vitro efficacy of Ac]PSMA-617 in the human prostate cancer cell line PC-3 as an example, the specific steps include:

[0072] Step S1: Receive and initialize the parameters required for the simulation, including experimental environment parameters, radionuclide parameters, drug and target information parameters, and cell line parameters; specifically including:

[0073] S1.1: Input experimental environment parameters:

[0074] Culture medium volume Set to 2 mL.

[0075] Total number of implanted cells Set to 1×10 5 Each cell.

[0076] Cell proliferation rate constant The value was calculated based on the PC-3 cell doubling time (e.g., 24 hours) and set at 1.0 × 10⁻⁶. -5 S -1 .

[0077] The diameter of the petri dish was set to 35 mm.

[0078] Laying time Set to 24 hours.

[0079] Drug incubation time Set to 24 hours.

[0080] S1.2: Input radionuclide parameters:

[0081] The user selects "Ac-225" from the system's built-in database. The system automatically retrieves its physical properties: half-life (9.92 days), complete decay chain information (including daughter nuclei such as Fr-221 and At-217 and their branching ratios), and the energy spectra of all alpha particles in the decay chain (such as 5.83 MeV, 7.07 MeV, etc.) and emission probabilities.

[0082] S1.3: Input drug and target information parameters:

[0083] Targeting vector: Select "PSMA-617".

[0084] Initial chemical concentration Set to 10 nM.

[0085] Initial radioactivity Set to 50 kBq / mL.

[0086] S1.4: Input cell line parameters:

[0087] The user selects "PC-3 (human prostate cancer cell line)" from the system's built-in cell bank. The system automatically loads the preset parameters for this cell line.

[0088] Morphological parameters: cell radius =10μm, nuclear radius =6μm.

[0089] Radiation sensitivity parameters (if known): such as the radiation-induced direct induced basal body (DSB) coefficient. = 20 DSB / Gy.

[0090] In this embodiment, if the system's built-in database lacks PC-3 cells and [ 225 If specific parameters of the interaction between Ac]PSMA-617 are obtained, the parameter fitting module will be activated to guide the user to fit the unknown parameters by inputting experimental data. Specifically, this includes:

[0091] (1) Fitting of pharmacokinetic parameters: If , , , , Unknown, user input: PC-3 cell pairs obtained at different time points (e.g., 0, 0.5, 1, 3, 8, 24 hours) using a gamma counter or fluorescence microscopy. 225 The uptake data of PSMA-617 (or PSMA-617 labeled with other radionuclides or fluorescent probes) were obtained. Then, a nonlinear least squares method was used to automatically fit the optimal binding rate constant, aiming to minimize the residual between the model-predicted cellular uptake curve and the experimental measurements. Dissociation rate constant Internalization rate constant Degradation rate constant and the total number of cell surface receptors .

[0092] (2) Radiation sensitivity and repair parameter fitting: If , , , , For unknown reasons, the user inputs three sets of experimental data: 1) PC-3 cell survival curves after irradiation with different doses of alpha particles (using an alpha particle irradiation device or an alpha nuclide drug with known pharmacokinetics); 2) Time-kinetic data of DSB focus formation and disappearance measured by γ-H2AX immunofluorescence staining after PC-3 cells irradiated with different doses of alpha particles; 3) Survival rate of unirradiated cells cultured in conditioned medium (conditioning medium) of PC-3 cells irradiated with different doses and times of alpha particles, or time-kinetic data of DSB focus formation and disappearance measured by γ-H2AX immunofluorescence staining. Subsequently, the Markov chain Monte Carlo method is used to simultaneously optimize the bystander signal generation rate constant. Bystander injury coefficient Fast repair rate constant Slow repair rate constant and the proportion of repair methods , These parameters minimize the error between the model's final predicted cell viability and the experimental measurement.

[0093] Finally, the fitted parameters are stored in the system's built-in database.

[0094] Step S2: Based on the parameters of Step S1, the spatiotemporal distribution of the α-nucleoside drug in the culture medium, cell membrane, and cytoplasm is dynamically simulated using a multi-compartment kinetic model, and the data on the change of radioactivity in each compartment over time are output; specifically including:

[0095] S2.1: Model Initialization:

[0096] Set initial conditions: , , .

[0097] Calculate the cell number at the start of the simulation (i.e., when the drug is added): .

[0098] S2.2: Numerical solution of the dynamic equations:

[0099] Using the fourth-order Runge-Kutta method, with time step Numerical integration was performed on the following three-zone model differential equation system, with a total simulation time of [missing information]. =24 hours.

[0100] ;

[0101] ;

[0102] ;

[0103] in, The concentration of radionuclide drugs in the culture medium; The concentration of nucleoside drugs in the cytoplasm; This represents the number of target receptors that have been bound on a single cell. The total number of all target receptors on a single cell; This refers to the volume of the culture medium. Total number of cultured cells; Volume of a single cell; This represents the binding rate constant between the targeting vector and the cell surface targeting receptor; This represents the dissociation rate constant between the targeting vector and the cell surface targeting receptor; is the endocytosis rate constant of the cell surface targeting carrier-receptor complex; This is the degradation rate constant of the intracellular targeting carrier-receptor complex within the cell.

[0104] S2.3: Radioactivity conversion:

[0105] At each time step, the chemical concentration is converted into radioactivity and radionuclide decay is taken into account:

[0106] ;

[0107] ;

[0108] ;

[0109] in, , , These are the radioactivity levels of the culture medium, cytoplasm, and cell membrane, respectively. , The initial radioactivity and chemical concentration of the radiopharmaceutical in the culture medium; is the attenuation coefficient of the radioactive nuclide.

[0110] S2.4: Output:

[0111] Final output , , The three time-series curves accurately describe the spatiotemporal distribution of the radioactive source in the culture system, providing a "source term" for the next dose calculation.

[0112] This step enables the prediction of the spatial and temporal distribution of drugs in the culture system, reflecting the influence of different receptor binding characteristics on intracellular radioactive accumulation.

[0113] Step S3: Based on the radioactivity distribution data output in Step S2, calculate the absorbed dose rate for each cell nucleus using the principles of microdosimetry and the dose-point kernel convolution method; specifically including:

[0114] S3.1: Dosage point preparation:

[0115] The dose point kernel function of alpha particles and their secondary particles in an aqueous medium at different energies was pre-calculated using Monte Carlo tools (such as Geant4). And store it as a lookup table.

[0116] Calling the pre-generated dose-point kernel function of Ac-225 and all its daughter nuclei in water for alpha particles The dose-point kernel function of the nuclide was calculated by weighted summation of the energy deposition of each stage of the Ac-225 decay chain. ;

[0117] S3.2: Dose rate calculation:

[0118] For each cell nucleus in the culture system, calculate its absorbed dose rate at time t. ; Nucleus uptake rate The study divided the energy deposition component into three parts: intrinsic dose within the cell, contribution from neighboring cells, and scattering from the culture medium. Using the spatiotemporal distribution curve of the radionuclide drug obtained from the α-radionuclide drug pharmacokinetics module as the source term, a weighted sum of the energy deposition components for each part was calculated.

[0119] ;

[0120] in, The contribution of radionuclides in the cytoplasm and cell membrane of one's own cells to the cell nucleus; The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus; The contribution of radionuclides in the culture medium to the cell nucleus; Let be the dose point kernel function, where , representing the Euclidean distance between the source and the target; The location of the radioactive source in space. The target location is the coordinate of the center of the cell nucleus. For cell nucleus mass.

[0121] S3.3: Computational Optimization (Piecewise Variable Step Size Integration):

[0122] To balance computational accuracy and efficiency, a piecewise variable stride strategy is adopted for the convolution integral:

[0123] Near field area (0-2) ): Use a fine mesh. To accurately capture the high dose gradient of alpha particles within an extremely short range.

[0124] Midfield (2-20) ): Use a medium grid. .

[0125] Far field region (20 - ): Use a coarse grid. The cutoff radius Determined by a preset dose-energy cumulative contribution criterion: Ensure that 99% of the dose contribution is included.

[0126] Step S4: Cells exposed to alpha particles can induce DNA double-strand breaks (DSBs), considered a major initial event in the subsequent series of biological effects following alpha irradiation. Their generation and clearance are primarily influenced by direct radiation induction, bystander effect induction, and DNA damage repair. This step, based on the nuclear uptake dose rate output in Step S3, integrates DNA damage kinetics, repair kinetics, and the bystander effect to simulate the dynamic changes in the number of DNA double-strand breaks in the cell population, ultimately outputting a predicted result of cell viability or the number of surviving cells over time. Specifically, this includes:

[0127] S4.1 Construction and solution of dynamic equations:

[0128] Cell nuclear dose rate As input, together with the cell line-specific parameters defined in step S1, a system of ordinary differential equations describing DSB dynamics and cell survival is constructed.

[0129] The fourth-order Runge-Kutta method was also used for the solution, and the simulation time covered from drug addition (t=0) to the end of the observation (t=0). The entire process of ).

[0130] S4.2 Core Dynamics Process:

[0131] (1) DSB generation and repair:

[0132] Direct DSB generation: ;in, The direct radiation-induced DSB damage coefficient.

[0133] Bystander effect (DSB) generation: Irradiated cells can secrete bystander signaling factors, such as reactive nitrogen, reactive oxygen species, and exosomes, into the culture medium. These secreted bystander signals can further induce cellular DNA damage. This invention assumes that the cultured cells are uniformly distributed in the culture dish, and that the bystander signaling factors generated after irradiation diffuse rapidly. The concentration of bystander signals in the culture medium... The rate of bystander signaling factor secretion and degradation by cells is influenced by the rate at which bystander signaling factors are secreted, and the rate of bystander signaling factor secretion is directly proportional to the induced DSB damage.

[0134] ;

[0135] in, The rate constant is generated for the bystander effect signal. Let be the bystander effect signal decay rate constant.

[0136] By solving the bystander signal concentration The equation, calculate ;in, The bystander signal-induced DSB damage coefficient.

[0137] DSB Repair Dynamics: Proportioning Newly Generated DSBs , Assigned to the fast (NHEJ) and slow (HR) repair pathways, respectively, at rate constants. , Perform repairs. The total repair rate is the sum of the two. Specifically: ;

[0138] in, , These represent the number of DSBs entering the fast and slow repair pathways, respectively. , These are the repair rate constants for the fast and slow repair pathways, respectively;

[0139] ;

[0140] ;

[0141] in, , The ratio of fast to slow repair pathways, and .

[0142] The final equation for the rate of change of the number of DSBs is as follows: .

[0143] (2) Cell survival calculation:

[0144] Final cell count The changes are determined by both proliferation and DSB-dependent mortality:

[0145] ;

[0146] in This is the cell proliferation rate constant. This is a sensitivity constant for a specific cell line.

[0147] S5.3 Final Output and Result Analysis:

[0148] After the module finishes running, it outputs the cell survival score over the entire simulation period. The dynamic change curve and experimental observation points (usually) The final survival rate of α-nucleotides can be obtained. Simultaneously, users can obtain dynamic data from all intermediate processes, such as drug distribution curves, historical nuclear dose rates, changes in DSB counts, and bystander signal concentrations. This data is extremely valuable for a deeper understanding of the mechanism of action of α-nucleotides and for optimizing dosing regimens.

[0149] This invention constructs a unified mathematical framework that is end-to-end and multi-module coupled. Starting with drug-cell binding, this framework progressively simulates the internalization and distribution of the drug, microscale energy deposition, initial DNA damage and repair, intercellular signal transduction, and ultimately, cell survival. This allows the model to more realistically reflect the complete pathway and complex biological logic of alpha-nucleoside drug action, solving the fundamental problem of "model isolation" in existing technologies and providing an unprecedented holistic perspective for understanding its mechanism of action. Furthermore, by introducing microdosimetry and dose-point kernel convolution methods based on Monte Carlo simulations, the distorted average dose assumption is completely eliminated, enabling accurate reproduction of the discreteness, randomness, and high LET characteristics of alpha particle tracks. Moreover, by integrating DSB dual-pathway (NHEJ / HR) repair kinetics and a quantitative bystander effect model, the model can simulate the "shoulder" of the cell survival curve (reflecting sublethal damage repair), hypersensitivity in the low-dose region, and the swarm kill amplification effect brought about by the bystander effect. Compared with traditional LQ models, this model achieves a qualitative leap in its ability to predict the shape of the cell survival curve, especially in capturing high LET radiation characteristics. Furthermore, this invention not only outputs the final cell viability rate but also reveals the dynamic changes in intermediate processes, such as: the dynamic accumulation curves of drugs in different cell compartments; the historical changes in nuclear dose rate over time; the real-time kinetics of DNA double-strand break generation and repair; and the concentration changes and contributions of bystander signaling molecules. These intermediate data provide researchers with a unique and quantitative perspective for a deeper understanding of the mechanism of action of alpha nuclei (how these processes are key determinants of therapeutic efficacy). Simultaneously, the model's precise characterization of the cell-scale dose-response relationship provides crucial theoretical support and a pre-implementation platform for subsequent clinical micro-dosimetry calculations and the optimization of personalized treatment plans, strongly supporting the translation from basic research to clinical application.

[0150] Example 2, as Figure 1 As shown, the present invention also discloses an in vitro cellular response prediction system for α-nucleoside drugs used in the method described in Example 1, comprising:

[0151] The basic parameter input module serves as the system's front-end and data foundation, implemented as a graphical user interface or a standardized data configuration file interface. It is configured to perform the following operations:

[0152] 1) Parameter Receiving and Validation: Provides a form-based interface to guide users to input or select the following four types of parameters:

[0153] Experimental environmental parameters: including culture medium volume Total number of implanted cells Cell proliferation rate constant Petri dish diameter d, plating time Drug incubation time .

[0154] Radionuclide parameters: The user selects the nuclide name (e.g., Ac-225) from the drop-down menu. The system then automatically retrieves the nuclide's half-life, decay chain, decay branch ratios, and energy spectra of the emitted alpha and secondary particles from the built-in nuclide database.

[0155] Drug and target information parameters: including the name of the target carrier (e.g., PSMA-617) and the initial chemical concentration of the drug. (e.g., 1 nM) and initial radioactivity concentration (e.g., 1 kBq / mL).

[0156] Cell line parameters: The user selects the cell line name (e.g., human prostate cancer cells PC-3) from the drop-down menu. The system then retrieves the morphological parameters (e.g., cell radius) of that cell line from the built-in cell line database. Nuclear radius ) and initial radiation sensitivity parameters (such as radiation-induced DSB coefficient) ).

[0157] 2) Data Management: Integrates, formats, and temporarily stores user-input data and data retrieved from the built-in library, providing a unified and standardized initial condition for all subsequent computing modules.

[0158] The pharmacokinetic prediction module is communicatively connected to the basic parameter input module and receives all initialization parameters provided by the basic parameter input module. Its core is a numerical solver configured to perform the following operations:

[0159] 1) Model initialization: Based on the input parameters, set up the three-zone model (see attached diagram). Figure 2 Initial conditions: , , And calculate the initial total number of cells. .

[0160] 2) Numerical solution: The fourth-order Runge-Kutta method is used, with a set time step (e.g., ...). Numerical solution of the following core dynamic differential equations.

[0161] ;

[0162] ;

[0163] ;

[0164] 3) Activity Conversion and Output: After obtaining the chemical concentration in each step, the chemical concentration is converted into radioactivity according to the following formula:

[0165] ;

[0166] ;

[0167] ;

[0168] Finally, the spatiotemporal distribution data of radioactivity over the entire simulation period is output to the next module.

[0169] The cell uptake dose calculation module, communicatively connected to the pharmacokinetics prediction module, is used to receive the spatiotemporal distribution data of radioactivity output by the pharmacokinetics prediction module and calculate the micro-dose distribution. It is configured to perform the following operations:

[0170] 1) Kernel Function Call: Based on the nuclide selected by the user, the system calls the pre-calculated comprehensive dose kernel function for that nuclide from the built-in dose kernel database using a Monte Carlo tool (such as Geant4). ;

[0171] 2) Dose convolution calculation: For a single simulated cell in the culture system, the absorbed dose rate of its cell nucleus is calculated according to the following formula. The uptake rate of the cell nucleus The study divided the energy deposition component into three parts: intrinsic dose within the cell, contribution from neighboring cells, and scattering from the culture medium. Using the spatiotemporal distribution curve of the radionuclide drug obtained from the α-radionuclide drug pharmacokinetics module as the source term, a weighted sum of the energy deposition components for each part was calculated.

[0172] ;

[0173] 3) Efficient integration: When performing convolution integration, a piecewise variable stride strategy and a cutoff radius criterion are adopted to ensure that computational efficiency is optimized while maintaining high accuracy. The final output is the absorbed dose rate data for each cell nucleus at different time points.

[0174] The biological effect prediction module, communicatively connected to the cell uptake dose calculation module, receives the uptake dose rate data of the cell nucleus output by the module and predicts cell survival. It is configured to perform the following operations:

[0175] 1) Kinetic model solution: Run a system of ordinary differential equations that couple DSB kinetics and cell survival, with the model based on the nuclear dose rate. As input, the generation of DSBs (directly related to the bystander effect), dual-pathway DNA repair, and the final cell death / proliferation process are dynamically simulated. This is detailed in Example 1.

[0176] 2) Numerical integration: The same numerical integration method (such as the fourth-order Runge-Kutta method) is used to solve the system of equations. The time step can be kept consistent with the pharmacokinetics module or adjusted according to the speed of the biological process.

[0177] 3) Result Generation and Display: Dynamically calculate and output key intermediate variables (such as...) , ) and the final result and the number of surviving cells A curve showing how the cell survival rate changes over time. The system can visualize and compare the predicted cell survival rate with experimental data.

[0178] The parameter fitting module, acting as a support module, is bidirectionally connected to the basic parameter input module and is used to optimize model parameters based on experimental data. It is configured to perform the following operations:

[0179] 1) Data-driven fitting: When certain parameters (such as those of a new cell line) are in the built-in database... , When any data (such as time-uptake curves, cell survival curves, and γ-H2AX focal kinetic data) is missing, this module is activated. It guides the user to input the corresponding experimental data (such as time-uptake curves, cell survival curves, and γ-H2AX focal kinetic data).

[0180] 2) Optimization algorithm execution: It has multiple built-in optimization algorithms (such as nonlinear least squares method and particle swarm optimization algorithm) to automatically estimate the optimal set of unknown parameters by minimizing the error between the model prediction value and the experimental observation value.

[0181] 3) Database update: The fitted and verified reliable parameters are backfilled into the built-in database of the basic parameter input module to enrich the system knowledge base for subsequent predictions under the same conditions, thereby enabling the system to learn and continuously optimize itself.

[0182] This invention seamlessly integrates five modules—basic parameter input, pharmacokinetics, microdoscopy, biological effects, and parameter fitting—to construct an end-to-end quantitative simulation pipeline encompassing drug delivery, micro-energy deposition, and dynamic biological response. This fundamentally changes the "model silos" state of existing technologies, where processes (such as drug distribution and dosage calculation, and dosage and biological effects) are disconnected. The system automatically uses the output of upstream modules as the input of downstream modules, ensuring the continuity and consistency of the simulation process, thus more realistically reflecting the complex mechanisms of action of alpha-nucleoside drugs. The system's modular design and the built-in database of the basic parameter input module give it strong versatility. Users only need to select or input new parameters through the interface (such as changing the nuclide Ac-225 to Bi-213, changing the target vector, or selecting a different cell line), and the system can automatically call up the corresponding data and complete the simulation of the new scenario without modifying the core code. Furthermore, by introducing the parameter fitting module, the system is upgraded from a static prediction tool to a dynamic learning system. When faced with prediction biases caused by new cell lines or new drugs, the system can use a small amount of experimental data to automatically optimize and update key unknown parameters in the model, so that the model can continuously adapt to the current research object.

[0183] In Embodiment 3, the present invention also discloses a computer-readable storage medium, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the method described in Embodiment 1. The computer-readable storage medium is a non-transitory tangible medium, and its specific implementation forms include, but are not limited to: electronic storage devices, such as solid-state drives, USB flash drives, CF cards, SD cards, etc.; magnetic storage devices, such as hard disks, magnetic disks, etc.; optical storage devices, such as CD-ROMs, DVD-ROMs, Blu-ray discs, etc.; or other forms of storage media known to those skilled in the art. On this medium, a sequence of computer program instructions (i.e., code) for the processor to execute is stored in a physical manner (e.g., magnetic domain orientation, light reflection pits, floating gate transistor charge states, etc.).

[0184] When the storage medium is connected to or installed on a computing device (which includes at least one processor, coupled memory, and necessary input / output interfaces), the computer program stored therein is loaded into memory and executed by the processor, thereby instantiating and running the α-nucleoside drug in vitro cell response prediction system as described in Example 1 on the computing device. The execution of the program specifically implements the following process:

[0185] Step 1: System initialization;

[0186] After the program starts, it first creates and initializes an instance of the basic parameter input module in memory. This instance loads and manages the built-in nuclide and cell line databases, and waits for or receives parameter input from the user.

[0187] Step 2: Modular collaborative prediction;

[0188] After the user completes the parameter configuration and starts the simulation through the graphical interface, the program calls and executes the code of each functional module in a predetermined logical order:

[0189] Calling the pharmacokinetics prediction module code: This part of the code receives parameters, constructs a three-compartment kinetic model, executes a numerical solution algorithm, calculates the spatiotemporal distribution of radioactivity, and stores the result data in a specified area of ​​memory.

[0190] The code that calls the cell absorption dose calculation module reads the output of the pharmacokinetics module from memory, calls the pre-stored dose point kernel function data, performs microdosimetric convolution calculation, obtains the cell nucleus absorption dose rate, and passes the result to the next module.

[0191] The code that calls the biological effects prediction module reads the dose data, runs the biokinetic model, solves the differential equations for DNA damage and repair, bystander effect and cell survival, and finally generates the cell survival prediction results.

[0192] Step 3: Output and Interaction of Results;

[0193] The program presents the final prediction results (such as cell survival curves, intermediate process kinetic diagrams, and data tables) to the user through a graphical user interface.

[0194] When needed, the program can call the parameter fitting module code, which guides the user to input experimental data, executes the optimization algorithm, completes parameter estimation, and updates the built-in database.

[0195] The computer-readable storage medium of this embodiment can solidify a complex, multi-module prediction system into a standardized software product, which can be easily copied, distributed, and installed on any compatible computing device, greatly enhancing the practicality and scalability of the invention. Furthermore, the program instructions in the storage medium ensure that each execution follows the exact same data processing logic and algorithm flow, eliminating errors that may be introduced by human operation and guaranteeing the consistency and repeatability of prediction results, which is crucial for scientific research and new drug review. Users do not need to concern themselves with the underlying complex mathematical models and code implementation; they can obtain professional prediction results simply by operating through the interactive interface. This medium and its program are independent of any specific biological laboratory, allowing computational simulations to be shared and used as a standard service among different teams.

[0196] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the in vitro cellular response of α-nucleoside drugs based on multi-module mathematical modeling, characterized in that: Includes the following steps: Step S1: Receive and initialize the parameters required for the simulation, including experimental environment parameters, radionuclide parameters, target vector parameters, and cell line parameters; Step S2: Based on the parameters input in Step S1, the spatiotemporal distribution of α-nucleoside drugs in the culture medium, cell membrane and cytoplasm is dynamically simulated by using a multi-compartment kinetic model, and the data of the change of radioactivity in each compartment over time are output. Step S3: Based on the radioactivity distribution data output in Step S2, the absorbed dose rate of a single cell nucleus is calculated using the principles of microdosimetry and the dose point kernel convolution method. Step S4: Based on the nuclear uptake rate output in Step S3, the dynamic changes in the number of DNA double-strand breaks in the cell population are simulated by integrating DNA damage kinetics, repair kinetics, and bystander effect, and finally the predicted results of cell survival rate or number of surviving cells over time are output. In step S3, the absorbed dose rate of each cell nucleus It is calculated by summing the integrals of the following parts: The contribution of intracellular radionuclides to their own nucleus; The contribution of radioactive isotopes on the cell membrane to the cell nucleus; The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus; The contribution of radionuclides in the culture medium to the cell nucleus; In step S4, the number of DNA double-strand breaks The rate of change is described by the following equation: ； in, , representing the rate of DSB generation directly induced by radiation; The direct radiation-induced DSB damage coefficient; , representing the DSB rate induced by the bystander effect; The damage coefficient of bystander signal-induced DSB. The concentration of bystander signaling factor in the culture medium; The concentration of the bystander signal factor The rate of change is described by the following equation: ； in, The rate constant is generated for the bystander effect signal. The bystander effect signal decay rate constant; This refers to the volume of the culture medium. Total number of cultured cells; , representing the DSB repair rate through the fast and slow repair pathways; the rate of change in the number of DSBs entering the fast and slow repair pathways are respectively: ； ； in, , These represent the number of DSBs entering the fast and slow repair pathways, respectively. , These are the rate constants for the fast and slow repair pathways, respectively. , The ratio of DSB repair pathways via fast and slow repair methods, and .

2. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In step S2, the multi-compartment kinetic model is a three-compartment kinetic model, which simulates the dynamic distribution of radionuclide drugs inside and outside the cell using the following set of differential equations: ； ； ； in, The concentration of radionuclide drugs in the culture medium; The concentration of nucleoside drugs in the cytoplasm; This represents the number of target receptors that have been bound on a single cell. The total number of all target receptors on a single cell; This refers to the volume of the culture medium. Total number of cultured cells; Volume of a single cell; This represents the binding rate constant between the targeting vector and the cell surface targeting receptor; This represents the dissociation rate constant between the targeting vector and the cell surface targeting receptor; is the endocytosis rate constant of the cell surface targeting carrier-receptor complex; This is the degradation rate constant of the intracellular targeting carrier-receptor complex within the cell.

3. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 2, characterized in that: Step S2 further includes the step of converting chemical concentration into radioactivity, which is specifically achieved through the following formula: ； ； ； in, , , These are the radioactivity levels of the culture medium, cytoplasm, and cell membrane, respectively. , The initial radioactivity and chemical concentration of the radiopharmaceutical in the culture medium; is the attenuation coefficient of the radioactive nuclide.

4. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In step S3, the absorbed dose rate of a single cell nucleus It is calculated using the following formula: ； in, The contribution of radionuclides in the cytoplasm and cell membrane of one's own cells to the cell nucleus; The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus; The contribution of radionuclides in the culture medium to the cell nucleus; Let be the dose point kernel function, where , representing the Euclidean distance between the source and the target; The location of the radioactive source in space. The target location is the coordinate of the center of the cell nucleus. For cell nucleus mass.

5. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In calculating the absorbed dose rate in the cell nucleus, a piecewise variable step size strategy is used for numerical integration, specifically as follows: In the near-field region, which is 0 to 2 micrometers from the cell nucleus, a fine grid step size of 0.1 micrometers is used; In the mid-field region, 2 to 20 micrometers from the cell nucleus, a medium grid step size of 0.5 to 1.0 micrometers is used; Within 20 micrometers of the cell nucleus to the cutoff radius In the far field region, a coarse grid step size of 1 to 5 micrometers is used; Among them, the cutoff radius Determined by a preset dose-energy cumulative contribution criterion: ； in, Take 0.01 or 0.001; This is the dose point kernel function.

6. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: Before or during step S1, a parameter fitting step is also included, which is used to fit the unknown parameters in the model using an optimization algorithm, including: Pharmacokinetic parameters were fitted based on time-series data from cellular uptake experiments. Radiation sensitivity parameters were fitted based on cell survival curves, conditioned medium experiments, or γ-H2AX focal kinetic data.

7. An in vitro cellular response prediction system for α-nucleoside drugs used to perform the method according to any one of claims 1 to 6, characterized in that: include: The basic parameter input module, used to receive and store initialization parameters, is configured as follows: Provides a human-computer interaction interface or data interface for receiving initial parameters input by the user or loading initial parameters from an external database; stores and manages a built-in database containing the physical properties of radionuclides and the biological properties of cell lines; integrates and initializes the received and called parameters to provide a complete scene definition for subsequent simulation calculations; The pharmacokinetic prediction module, communicatively connected to the basic parameter input module, is used to perform multi-compartment kinetic simulations; it is configured as follows: Receive initial parameters from the basic parameter input module; run a multi-compartment pharmacokinetic mathematical model, which describes the dynamic transfer process of α-nucleoside drugs in the culture medium, cell membrane and cytoplasm through a set of coupled differential equations; The numerical integration algorithm is executed to solve the system of differential equations to obtain the spatiotemporal distribution of drug concentration and radioactivity in each compartment; the radioactivity distribution data is output to the cell uptake dose calculation module. A cell absorption dose calculation module, communicatively connected to the pharmacokinetics prediction module, is used to calculate the microscopic dose distribution; it is configured as follows: It receives spatiotemporal distribution data of radioactivity from the pharmacokinetics prediction module; calls the pre-generated radioactive particle dose point kernel function stored in the database; performs microdosimetry calculations based on dose point kernel convolution integrals, and adopts a piecewise variable step size numerical integration strategy to balance computational efficiency and accuracy. Calculate and output the absorbed dose rate data for each cell nucleus to the biological effect prediction module; A biological effect prediction module, communicatively connected to the cell uptake dose calculation module, is used to predict cell survival; it is configured as follows: Receives absorbed dose rate data of the cell nucleus from the cell absorbed dose calculation module; runs a biokinetic model that integrates radiation-induced DNA damage, bystander effect and DNA damage repair dynamics, which is described by a set of coupled differential equations; Numerical integration algorithms are executed to solve the biodynamic differential equations, dynamically simulating the changes in the number of DNA damage and the number of viable cells in the cell population; the final cell survival prediction results are output. The parameter fitting module, which is communicatively connected to the basic parameter input module, is used to optimize model parameters based on experimental data; it is configured as follows: Receive experimental measurement data provided by users; The optimization algorithm is invoked to iteratively optimize and estimate the unknown parameters in the pharmacokinetic or biokinetic model, using experimental measurement data as the target. The optimal parameter values ​​obtained by fitting are fed back and stored in the built-in database of the basic parameter input module for use in prediction calculations.

8. A computer-readable storage medium, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 6.

Images