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.

In this work, we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell–cell interactions. This is important as cell–cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work, therefore, describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell–cell adhesion or repulsion are known to play a significant role.

A key feature of cell migration is how cell movement is affected by cell-cell interactions. Furthermore, many cell migratory processes such as neural crest stem cell migration [Thomas and Erickson, 2008; McLennan et al., 2012] occur on growing domains or in the presence of a chemoattractant. Therefore, it is important to study interactions between migrating cells in the context of domain growth and directed motility. Here we compare discrete and continuum models describing the spatial and temporal evolution of a cell population for different types of cell-cell interactions on static and growing domains. We suggest that cell-cell interactions can be inferred from population density characteristics in the presence of motility bias, and these population density characteristics for different cell-cell interactions are conserved on both static and growing domains. We also study the expected displacement of a tagged cell, and show that different types of cell-cell interactions can give rise to cell trajectories with different characteristics. These characteristics are conserved in the presence of domain growth, however, they are diminished in the presence of motility bias. Our results are relevant for researchers who study the existence and role of cell-cell interactions in biological systems, so far as we suggest that different types of cell-cell interactions could be identified from cell density and trajectory data.

Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviors, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.

Mathematical models describing cell movement and proliferation are important tools in developmental biology research. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner.