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

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.

14 pages, 5 figures

References in corpus (15)

• Anomalous transport in the crowded world of biological cells
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Motility-driven glass and jamming transitions in biological tissues
• Anomalous dynamics of cell migration
• Exact distributions for stochastic gene expression models with bursting and feedback
• Symmetric vs asymmetric stem cell divisions: an adaptation against cancer?
• Realization of Waddington's Metaphor: Potential Landscape, Quasi-potential, A-type Integral and Beyond
• Small protein number effects in stochastic models of autoregulated bursty gene expression
• A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations
• A kinetic theory for age-structured stochastic birth-death processes
• A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration
• Exact steady-state distributions of multispecies birth-death-immigration processes: effects of mutations and carrying capacity on diversity
• Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation
• Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions
• Kinetic theories of state- and generation-dependent cell populations