Incorporating stochastic gene expression, signaling-mediated intercellular interactions, and regulated cell proliferation in models of coordinated tissue development

TL;DR

This paper develops a simplified mathematical model integrating stochastic gene expression, cell signaling, and proliferation to better understand tissue development processes.

Contribution

It introduces a novel framework combining Waddington vector fields and fitness landscapes to model cell differentiation and proliferation.

Findings

The model captures non-gradient dynamics like cycles and entropy production.

It links epigenetic fitness landscapes with Waddington's vector fields.

Application to two gene systems demonstrates model versatility.

Abstract

Formulating quantitative and predictive models for tissue development requires consideration of the complex, stochastic gene expression dynamics, its regulation via cell-to-cell interactions, and cell proliferation. Including all of these processes into a practical mathematical framework requires complex expressions that are difficult to interpret and apply. We construct a simple theory that incorporates intracellular stochastic gene expression dynamics, signaling chemicals that influence these dynamics and mediate cell-cell interactions, and cell proliferation and its accompanying differentiation. Cellular states (genetic and epigenetic) are described by a Waddington vector field that allows for non-gradient dynamics (cycles, entropy production, loss of detailed balance) which is precluded in Waddington potential landscape representations of gene expression dynamics. We define an epigenetic fitness landscape that describes the proliferation of different cell types, and elucidate how this fitness landscape is related to Waddington's vector field. We illustrate the applicability of our framework by analyzing two model systems: an interacting two-gene differentiation process and a spatiotemporal organism model inspired by planaria.