Reaction-diffusion models for morphological patterning of hESCs

TL;DR

This paper models the self-organized patterning of human embryonic stem cells using reaction-diffusion equations, identifying regimes and conditions for stable pattern formation aligned with experimental observations.

Contribution

It applies activator-inhibitor reaction-diffusion models to hESC patterning, identifying regimes and analyzing stability, bridging mathematical theory with biological experiments.

Findings

Identified three reaction-diffusion regimes for BMP4, Wnt, and Nodal.

Numerical simulations confirmed realistic protein dynamics.

Derived conditions for existence and stability of steady states.

Abstract

In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works. In the first part of the paper we use the activator-inhibitor equations of Gierer and Meinhardt to identify 3 reaction-diffusion regimes for each of the three morphogenic proteins, BMP4, Wnt and Nodal, based on the characteristic features of the dynamic patterning. We identify appropriate boundary conditions which correspond to the experimental setup and perform numerical simulations of the reaction-diffusion (RD) systems, using the finite element approximation, to confirm that the RD systems in these regimes produce realistic dynamics of the protein concentrations. In the second part of the paper we use analytic tools to address the questions of the existence and stability of non-homogeneous steady states for the reaction-diffusion systems of the type considered in the first part of the paper. We find sufficient conditions on the data of the problem under which the system has an universal attractor.