Reconciling diverse mammalian pigmentation patterns with a fundamental mathematical model

Abstract

Bands of colour extending laterally from the dorsal to ventral trunk are a common feature of mouse chimeras. These stripes were originally taken as evidence of the directed dorsoventral migration of melanoblasts (the embryonic precursors of melanocytes) as they colonize the developing skin. Depigmented ‘belly spots' in mice with mutations in the receptor tyrosine kinase Kit are thought to represent a failure of this colonization, either due to impaired migration or proliferation. Tracing of single melanoblast clones, however, has revealed a diffuse distribution with high levels of axial mixing—hard to reconcile with directed migration. Here we construct an agent-based stochastic model calibrated by experimental measurements to investigate the formation of diffuse clones, chimeric stripes and belly spots. Our observations indicate that melanoblast colonization likely proceeds through a process of undirected migration, proliferation and tissue expansion, and that reduced proliferation is the cause of the belly spots in Kit mutants.

Investigating the Reproducibility of In Vitro Cell Biology Assays Using Mathematical Models

“…Based on the types of simulation domain, discrete random walk models can be further categorised into lattice-based and off-lattice models [28,52,80,109]. For each type of discrete model, individual cells migrate and proliferate depending on a set of rules that are observed from experiments [80,109].…”

“…For each type of discrete model, individual cells migrate and proliferate depending on a set of rules that are observed from experiments [80,109]. For example, in a traditional lattice-based model, cell migration is often incorporated using an unbiased exclusion process with hard-core exclusion representing cell-to-cell crowding [109].…”

“…Johnston et al use the Fisher-Kolmogorov model and the edge detection method to quantify the cell diffusivity, proliferation rate, and carrying capacity of prostate cancer cells from IncuCyte ZOOM TM assays [54]. Mort et al apply a lattice-based discrete model to investigate the formation of diffusion clones, chimeric stripes and belly spots in a mice model [80]. Based on the simulation predictions, they conclude that a depigmented ventral belly spot in mice likely arises due to the decreased cell proliferation [80].…”

“…Mort et al apply a lattice-based discrete model to investigate the formation of diffusion clones, chimeric stripes and belly spots in a mice model [80]. Based on the simulation predictions, they conclude that a depigmented ventral belly spot in mice likely arises due to the decreased cell proliferation [80].…”

“…While lattice-based random walk models are routinely used to mimic certain features in in vitro cell biology assays [80,109], other studies claim that off-lattice models are more biologically realistic [28,52,89]. Compared to lattice-based models, off-lattice models can mimc the change of cell volume during migration and proliferation.…”