Random walker's view of networks whose growth it shapes.

We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker motility rate, the model generates a spectrum of structures situated between well-known limiting cases. We demonstrate that the average degree observed by a walker is a function of its motility rate. Modulating the extent to which the location of node attachment is determined by the walker as opposed to random selection is akin to scaling the speed of the walker and generates new limiting behavior. The model raises questions about energetic and computational resource requirements in a physical instantiation.

Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process.

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.

Variable species densities are induced by volume exclusion interactions upon domain growth.

In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long-term behavior of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behavior, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long-term behavior of multispecies populations and, in certain circumstances, establish spatially varying species densities.

How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations.

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.

Reconciling diverse mammalian pigmentation patterns with a fundamental mathematical model.

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.

Inference of cell-cell interactions from population density characteristics and cell trajectories on static and growing domains.

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.