Minimal Model for Stem-Cell Differentiation

TL;DR

This paper presents a minimal dynamical systems model of stem-cell differentiation based on two-gene networks, identifying mechanisms for symmetric and asymmetric differentiation, and analyzing their stability and biological relevance.

Contribution

The study introduces a simplified, yet comprehensive, model capturing key differentiation mechanisms through intracellular and intercellular dynamics, highlighting the role of bifurcations and oscillatory behavior.

Findings

Differentiation mechanisms include symmetric Turing-like and asymmetric oscillatory dynamics.

Oscillatory cell states correspond to stem cells capable of proliferation and differentiation.

Cell type ratios are robust due to self-consistent bifurcation parameters.

Abstract

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein expression networks consisting of two genes under cell--cell interactions mediated by the diffusion of a protein. Networks that show cell differentiation are extracted and two forms of symmetric differentiation based on Turing's mechanism and asymmetric differentiation are identified. In the latter network, the intracellular protein levels show oscillatory dynamics at a single-cell level, while cell-to-cell synchronicity of the oscillation is lost with an increase in the number of cells. Differentiation to a fixed-point type behavior follows with a further increase in the number of cells. The cell type with oscillatory dynamics corresponds to a stem cell that can both proliferate and differentiate, while the latter fixed-point type only proliferates. This differentiation is analyzed as a saddle-node bifurcation on an invariant circle, while the number ratio of each cell type is shown to be robust against perturbations due to self-consistent determination of the effective bifurcation parameter as a result of the cell--cell interaction. Complex cell differentiation is designed by combing these simple two-gene networks. The generality of the present differentiation mechanism, as well as its biological relevance, is discussed.