Theoretical and computational tools to model multistable gene regulatory networks

TL;DR

This paper reviews theoretical and computational methods for modeling multistable gene regulatory networks, emphasizing their dynamics, heterogeneity, and the application of physics concepts to biological systems.

Contribution

It provides a comprehensive overview of methodologies, tutorials, and literature examples for modeling complex gene regulatory networks with a focus on multistability.

Findings

Highlights the use of statistical physics and non-linear dynamics in gene network modeling

Provides tutorials for simulating biological system models

Identifies current challenges and future directions in the field

Abstract

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.