Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

TRIM32 regulates skeletal muscle stem cell differentiation and is necessary for normal adult muscle regeneration

Limb girdle muscular dystrophy type 2H (LGMD2H) is an inherited autosomal recessive disease of skeletal muscle caused by a mutation in the TRIM32 gene. Currently its pathogenesis is entirely unclear. Typically the regeneration process of adult skeletal muscle during growth or following injury is controlled by a tissue specific stem cell population termed satellite cells. Given that TRIM32 regulates the fate of mammalian neural progenitor cells through controlling their differentiation, we asked whether TRIM32 could also be essential for the regulation of myogenic stem cells. Here we demonstrate for the first time that TRIM32 is expressed in the skeletal muscle stem cell lineage of adult mice, and that in the absence of TRIM32, myogenic differentiation is disrupted. Moreover, we show that the ubiquitin ligase TRIM32 controls this process through the regulation of c-Myc, a similar mechanism to that previously observed in neural progenitors. Importantly we show that loss of TRIM32 function induces a LGMD2H-like phenotype and strongly affects muscle regeneration in vivo. Our studies implicate that the loss of TRIM32 results in dysfunctional muscle stem cells which could contribute to the development of LGMD2H.