Connecting Different Approaches for Cell Cycle Modeling: Learning Ordinary Differential Equations from...

Area of Science:

• Computational Biology
• Mathematical Modeling
• Systems Biology

Background:

• Individual-based models (IBMs) in PhysiCell offer detailed cellular simulations.
• Deriving simplified mathematical representations, such as ordinary differential equations (ODEs), can reduce computational burden.
• Hybrid discrete-continuous multiscale systems require efficient modeling approaches.

Purpose of the Study:

• To investigate the feasibility of generating surrogate ODEs from PhysiCell-simulated IBMs.
• To demonstrate the application of machine learning for constructing these surrogate models.
• To assess the accuracy and computational efficiency of the derived surrogate models.

Main Methods:

• Simulated various cell cycle models using the PhysiCell platform.
• Evaluated simulation characteristics including stochasticity, computational cost, and accuracy.
• Applied the sparse identification tool SINDy-SA to identify mathematical structures for surrogate ODEs.

Main Results:

• PhysiCell simulation accuracy and cost depend on parameters like time step and initial population.
• The SINDy-SA framework successfully identified ODE structures for all tested cell cycle models.
• Surrogate models demonstrated potential for reduced computational expense with maintained accuracy.

Conclusions:

• Deriving surrogate ODEs from PhysiCell IBMs is feasible.
• SINDy-SA is an effective tool for constructing these surrogate models.
• This approach aids in modeling hybrid discrete-continuous multiscale systems and developing efficient surrogate models.