Extracting cellular automaton rules from physical Langevin equation models for single and collective cell migration

Area of Science:

• Computational Biology
• Biophysics
• Mathematical Modeling

Background:

• Cellular automata (CA) are widely used for biological modeling, with lattice-gas cellular automata (LGCA) specifically applied to cell migration.
• Current LGCA models often rely on phenomenologically chosen interaction rules, limiting their biological accuracy.
• Bridging the gap between abstract CA models and biophysical reality is crucial for advancing computational biology.

Purpose of the Study:

• To develop a method for deriving LGCA interaction rules from physics-based Langevin equations.
• To apply this method to models of single cell movement and collective cell migration, including polar and nematic alignment.
• To compare the derived LGCA models with their Langevin counterparts to assess agreement and identify areas for improvement.

Main Methods:

• Derivation of LGCA transition probability rules from the steady-state distribution of off-lattice Fokker-Planck equations.
• Modeling of single cell movement using Langevin equations.
• Modeling of collective cell migration with polar and nematic alignment mechanisms via Langevin equations.
• Comparison of alignment order parameters between Langevin and derived LGCA models.

Main Results:

• A systematic method was established to derive LGCA rules from Langevin equations.
• Discrepancies in alignment order parameters were observed between Langevin and derived LGCA models across different parameter spaces.
• The study identified specific conditions and parameter ranges where the derived LGCA models accurately reflect the underlying Langevin dynamics.

Conclusions:

• The developed method provides a physically-grounded approach to constructing biologically relevant LGCA models.
• Further refinements and extensions to the CA rule derivation methodology are proposed to improve model accuracy.
• This work facilitates more accurate computational modeling of complex cellular behaviors like migration and alignment.