Stochastic Binary Modeling of Cells in Continuous Time as an Alternative to Biochemical Reaction Equations

TL;DR

This paper introduces a stochastic binary modeling approach for cellular dynamics in continuous time, offering an alternative to traditional biochemical reaction equations by simplifying molecular states to binary variables and enabling analytical solutions.

Contribution

The authors present a novel coarse-grained stochastic framework that models cellular behavior with binary states and linear differential equations, providing a new analytical tool for cell dynamics.

Findings

Analytical representation of cell states via linear differential equations

Demonstration of the model with multiple biological examples

Efficient prediction of molecular state trajectories over time

Abstract

We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic process, while reducing each biochemical quantity to a binary value at the level of individual cells. The system can be analytically represented by a finite set of ordinary linear differential equations, which provides a continuous time course prediction of each molecular state. In this letter, we introduce our formalism and demonstrate it with several examples.