Biology subjects

Christian A Yates

Publications and source records attributed to Christian A Yates.

4 recordsLinked to original sources

bioRxiv2016

The effect of domain growth on spatial correlations

Mathematical models describing cell movement and proliferation are important research tools for the understanding of many biological processes. 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.

Systems Biology↗

bioRxiv2016

How domain growth is implemented determines the long term behaviour 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 biological 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 behaviours, 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.

Systems Biology↗

bioRxiv2014

Incorporating pushing in exclusion process models of cell migration

The macroscale movement behaviour of a wide range of isolated migrating cells has been well characterised experimentally. Recently, attention has turned to understanding the behaviour of cells in crowded environments. In such scenarios it is possible for cells to interact mechanistically, inducing neighbouring cells to move in order to make room for their own movements or progeny. Although the behaviour of interacting cells has been modelled extensively through volume-exclusion processes, no models, thus far, have explicitly accounted for the ability of cells to actively displace each other.\n\nIn this work we consider both on and off-lattice volume-exclusion position-jump processes in which cells are explicitly allowed to induce movements in their near neighbours in order to create space for themselves (which we refer to as pushing). From these simple individual-level representations we derive continuum partial differential equations for the average occupancy of the domain. We find that, for limited amounts of pushing, the comparison between the averaged individual-level simulations and the population-level model is nearly as good as in the scenario without pushing but, that for larger and more complicated pushing events the assumptions used to derive the population-level model begin to break down. Interestingly, we find that, in the on-lattice case, the diffusion coefficient of the population-level model is increased by pushing, whereas, for the particular off-lattice model that we investigate, the diffusion coefficient is reduced. We conclude therefore, that it is important to consider carefully the appropriate individual-level model to use when representing complex cell-cell interactions such as pushing.

Systems Biology↗

bioRxiv2014

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 [1, 2] 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.

Systems Biology↗