Hybrid models of the cell cycle molecular machinery

TL;DR

This paper introduces a novel approach using tropical geometry to simplify and analyze hybrid models of the cell cycle, which combine continuous and discrete dynamics to represent cellular processes.

Contribution

It presents a new method inspired by tropical geometry for reducing, hybridizing, and analyzing complex cell cycle models based on polynomial or rational ODEs.

Findings

Enables reduction of complex cell cycle models

Facilitates hybridization of continuous and discrete dynamics

Provides analytical tools for cell cycle regulation

Abstract

Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off some molecular interactions, simulating cell progression through a series of functioning modes. The advancement through the cell cycle is the archetype of such an organized sequence of events. We present an approach, inspired from tropical geometry ideas, allowing to reduce, hybridize and analyse cell cycle models consisting of polynomial or rational ordinary differential equations.