Computational Modelling of Nonlinear Calcium Waves

TL;DR

This paper models nonlinear calcium waves in biological systems using a stochastic cellular automaton derived from reaction-diffusion equations, revealing self-organized criticality and complex pattern formation.

Contribution

It introduces a novel stochastic cellular automaton approach for simulating nonlinear calcium waves based on coupled PDEs, linking local calcium distribution to biological positional information.

Findings

Self-organized criticality observed in calcium wave patterns

Both modeling approaches accurately predict wave characteristics

Patterns demonstrate complex, emergent behavior in calcium transport

Abstract

The calcium transport in biological systems is modelled as a reaction-diffusion process. Nonlinear calcium waves are then simulated using a stochastic cellular automaton whose rules are derived from the corresponding coupled partial differential equations. Numerical simulations show self-organized criticality in the complex calcium waves and patterns. Both the stochastic cellular automaton approach and the equation-based simulations can predict the characteristics of calcium waves and complex pattern formation. The implication of locality of calcium distribution with positional information in biological systems is also discussed.