时间模型的随机模拟

Question

我想对一个速率常数随时间变化的模型进行随机模拟。我不知道有任何支持时间相关速率常数的随机模拟器。

到目前为止，我已经尝试使用 Python（stochpy 和 gillespy2）和 Matlab（Simbiology）。

我正在尝试为下面编写的简单模型执行此操作（代码在 Matlab (Simbiology) 中运行）。我的问题是：在这个模型中，我如何使 k1 与时间相关，例如在随机模拟期间使 k1 随时间线性变化？

% Create a new model
model = sbiomodel('GeneExpressionModel');

% Add reactions for gene expression
reaction1 = addreaction(model, 'Gene -> Gene + mRNA');
reaction2 = addreaction(model, 'mRNA -> mRNA + Protein');
reaction3 = addreaction(model, 'mRNA -> null');
reaction4 = addreaction(model, 'Protein -> null');

% Set reaction rate constants
kineticLaw1 = addkineticlaw(reaction1, 'MassAction');
kineticLaw2 = addkineticlaw(reaction2, 'MassAction');
kineticLaw3 = addkineticlaw(reaction3, 'MassAction');
kineticLaw4 = addkineticlaw(reaction4, 'MassAction');

% Add parameters for reaction rate constants
p1 = addparameter(kineticLaw1, 'k1', 'Value', 0.1);
p2 = addparameter(kineticLaw2, 'k2', 'Value', 0.05);
p3 = addparameter(kineticLaw3, 'k3', 'Value', 0.01);
p4 = addparameter(kineticLaw4, 'k4', 'Value', 0.002);

% Set the rate equation for each reaction
kineticLaw1.ParameterVariableNames = {p1.Name};
kineticLaw2.ParameterVariableNames = {p2.Name};
kineticLaw3.ParameterVariableNames = {p3.Name};
kineticLaw4.ParameterVariableNames = {p4.Name};

% Set initial conditions
model.Species(1).InitialAmount = 1;
model.Species(2).InitialAmount = 0;
model.Species(3).InitialAmount = 0;

% Configure the stochastic solver
configSet = getconfigset(model, 'active');
set(configSet, 'SolverType', 'ssa'); % Set the solver to stochastic (Gillespie algorithm)
set(configSet, 'StopTime', 100); % Set the simulation end time

% Run the stochastic simulation
simulationData = sbiosimulate(model);

% Plot the simulation results
figure;
plot(simulationData.Time, simulationData.Data);
xlabel('Time');
ylabel('Species Count');
legend('Gene', 'mRNA', 'Protein');
title('Stochastic Simulation of Gene Expression');