Accurate and efficient discretizations for stochastic models providing near agent-based spatial resolution at low...

Area of Science:

• Mathematical Biology
• Computational Biology
• Cellular Dynamics

Background:

• Understanding cell proliferation, migration, and death is crucial for organism development and repair.
• Continuum models (e.g., logistic, Fisher-Kolmogorov equations) describe global cell behavior in assays but lack single-cell resolution.
• Agent-based models (ABMs) capture single-cell mechanics but are computationally intensive for large populations.

Purpose of the Study:

• To develop a computationally efficient agent-based model (ABM) that incorporates crowding effects.
• To ensure the proposed ABM aligns with established continuum models (logistic and Fisher-Kolmogorov equations) in relevant parameter regimes.
• To reduce computational storage requirements compared to traditional ABMs.

Main Methods:

• Developed a stochastic agent-based model allowing multiple agents within lattice compartments.
• Proposed a systematic method for determining an optimal compartment size.
• Validated the model's agreement with continuum models for proliferation and scratch assays.

Main Results:

• The compartment-based ABM significantly reduces computational storage.
• The model achieves computational efficiency while maintaining local resolution of agent behavior.
• The model successfully replicates the behavior described by logistic and Fisher-Kolmogorov equations.

Conclusions:

• The proposed compartment-based ABM offers a computationally feasible approach to model large cell populations.
• This model balances computational efficiency, local accuracy, and agreement with continuum theories.
• It provides a valuable tool for analyzing cell proliferation and migration in biological assays.