Biology subjects

Baker, R. E.

Publications and source records attributed to Baker, R. E..

9 recordsLinked to original sources

bioRxiv2018

A free boundary model of epithelial dynamics

In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In this model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarsegrained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.

systems biology↗

bioRxiv2017

Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics

Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, Mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation, and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

biophysics↗

bioRxiv2017

Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues

The growth and dynamics of epithelial tissues govern many morphogenetic processes in embryonic development. A recent quantitative transition in data acquisition, facilitated by advances in genetic and live-imaging techniques, is paving the way for new insights to these processes. Computational models can help us understand and interpret observations, and then make predictions for future experiments that can distinguish between hypothesised mechanisms. Increasingly, cell-based modelling approaches such as vertex models are being used to help understand the mechanics underlying epithelial morphogenesis. These models typically seek to reproduce qualitative phenomena, such as cell sorting or tissue buckling. However, it remains unclear to what extent quantitative data can be used to constrain these models so that they can then be used to make quantitative, experimentally testable predictions. To address this issue, we perform an in silico study to investigate whether vertex model parameters can be inferred from imaging data, and explore methods to quantify the uncertainty of such estimates. Our approach requires the use of summary statistics to estimate parameters. Here, we focus on summary statistics of cellular packing and of laser ablation experiments, as are commonly reported from imaging studies. We find that including data from repeated experiments is necessary to generate reliable parameter estimates that can facilitate quantitative model predictions.

developmental biology↗

bioRxiv2017

N-terminal sumoylation of centromeric histone H3 variant Cse4 regulates its proteolysis to prevent mislocalization to non-centromeric chromatin

Stringent regulation of cellular levels of evolutionarily conserved centromeric histone H3 variant (CENP-A in humans, CID in flies, Cse4 in yeast) prevents its mislocalization to non-centromeric chromatin. Overexpression and mislocalization of CENP-A has been observed in cancers and leads to aneuploidy in yeast, flies, and human cells. Ubiquitin-mediated proteolysis of Cse4 by E3 ligases such as Psh1 and Sumo-Targeted Ubiquitin Ligase (STUbL) Slx5 prevent mislocalization of Cse4. Previously, we identified Siz1 and Siz2 as the major E3 ligases for sumoylation of Cse4. In this study, we identify lysine 65 (K65) in Cse4 as a SUMO site and show that sumoylation of Cse4 K65 regulates its ubiquitin-mediated proteolysis by Slx5. Strains expressing cse4 K65R exhibit reduced levels of sumoylated and ubiquitinated Cse4 in vivo. Furthermore, co-immunoprecipitation experiments reveal reduced interaction of cse4 K65R with Slx5. Defects in sumoylation of cse4 K65R contribute to increased stability and mislocalization of cse4 K65R under normal physiological conditions. Based on the increased stability of cse4 K65R in psh1{triangleup} strains but not in slx5{triangleup} strains, we conclude that Slx5 targets sumoylated Cse4 K65 for ubiquitination-mediated proteolysis independent of Psh1. In summary, we have identified and characterized the physiological role of Cse4 sumoylation and determined that sumoylation of Cse4 K65 regulates ubiquitin-mediated proteolysis and prevents mislocalization of Cse4 which is required for genome stability.

molecular biology↗

bioRxiv2017

The impact of experimental design choices on parameter inference for models of growing cell colonies

To better understand development, repair and disease progression it is useful to quantify the behaviour of proliferative and motile cell populations as they grow and expand to fill their local environment. Inferring parameters associated with mechanistic models of cell colony growth using quantitative data collected from carefully designed experiments provides a natural means to elucidate the relative contributions of various processes to the growth of the colony. In this work we explore how experimental design impacts our ability to infer parameters for simple models of the growth of proliferative and motile cell populations. We adopt a Bayesian approach, which allows us to characterise the uncertainty associated with estimates of the model parameters. Our results suggest that experimental designs that incorporate initial spatial heterogeneities in cell positions facilitate parameter inference without the requirement of cell tracking, whilst designs that involve uniform initial placement of cells require cell tracking for accurate parameter inference. As cell tracking is an experimental bottleneck in many studies of this type, our recommendations for experimental design provide for significant potential time and cost savings in the analysis of cell colony growth.

cell biology↗

bioRxiv2017

Semblance Of Heterogeneity In Collective Cell Migration

Cell population heterogeneity is increasingly a focus of inquiry in biological research. For example, cell migration studies have investigated the heterogeneity of invasiveness and taxis in development, wound healing, and cancer. However, relatively little effort has been devoted to explore when heterogeneity is mechanistically relevant and how to reliably measure it. Statistical methods from the animal movement literature offer the potential to analyse heterogeneity in collections of cell tracking data. A popular measure of heterogeneity, which we use here as an example, is the distribution of delays in directional cross-correlation. Using a suitably generic, yet minimal, model of collective cell movement in three dimensions, we show how using such measures to quantify heterogeneity in tracking data can result in the inference of heterogeneity where there is none. Our study highlights a potential pitfall in the statistical analysis of cell population heterogeneity, and we argue this can be mitigated by the appropriate choice of null models.\n\nHighlightsO_LIgroups of identical cells appear heterogeneous due to limited sampling and experimental repeatability\nC_LIO_LIheterogeneity bias increases with attraction/repulsion between cells\nC_LIO_LImovement in confined environments decreases apparent heterogeneity\nC_LIO_LIhypothetical applications in neural crest and in vitro cancer systems\nC_LI\n\nIn BriefWe use a mathematical model to show how cell populations can appear heterogeneous in their migratory characteristics, even though they are made up of identically-behaving individual cells. This has important consequences for the study of collective cell migration in areas such as embryo development or cancer invasion.

systems biology↗

bioRxiv2017

Continuum approximations for lattice-free multi-species models of collective cell migration

Abstract\n\nCell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K [≥] 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.

biophysics↗

bioRxiv2017

A new and accurate continuum description of moving fronts

Processes that involve moving fronts of populations are prevalent in ecology and cell biology. A common approach to describe these processes is a lattice-based random walk model, which can include mechanisms such as crowding, birth, death, movement and agent-agent adhesion. However, these models are generally analytically intractable and it is computationally expensive to perform sufficiently many realisations of the model to obtain an estimate of average behaviour that is not dominated by random fluctuations. To avoid these issues, both mean-field and corrected mean-field continuum descriptions of random walk models have been proposed. However, both continuum descriptions are inaccurate outside of limited parameter regimes, and corrected mean-field descriptions cannot be employed to describe moving fronts. Here we present an alternative description in terms of the dynamics of groups of contiguous occupied lattice sites and contiguous vacant lattice sites. Our description provides an accurate prediction of the average random walk behaviour in all parameter regimes. Critically, our description accurately predicts the persistence or extinction of the population in situations where previous continuum descriptions predict the opposite outcome. Furthermore, unlike traditional mean-field models, our approach provides information about the spatial clustering within the population and, subsequently, the moving front.

biophysics↗

bioRxiv2016

Impact of implementation choices on quantitative predictions of cell-based computational models

Cell-based models provide a powerful computational tool for studying the mechanisms underlying the growth and dynamics of biological tissues in health and disease. An increasing amount of quantitative data with cellular resolution has paved the way for the quantitative parameterisation and validation of such models. However, the numerical implementation of cell-based models remains challenging, and little work has been done to understand to what extent implementation choices may influence model predictions. Here, we consider the numerical implementation of a popular class of cell-based models called vertex models, which are often used to study epithelial tissues. In two-dimensional vertex models, a tissue is approximated as a tessellation of polygons and the vertices of these polygons move due to mechanical forces originating from the cells. Such models have been used extensively to study the mechanical regulation of tissue topology in the literature. Here, we analyse how the model predictions may be affected by numerical parameters, such as the size of the time step, and non-physical model parameters, such as length thresholds for cell rearrangement. We find that vertex positions and summary statistics are sensitive to several of these implementation parameters. For example, the predicted tissue size decreases with decreasing cell cycle durations, and cell rearrangement may be suppressed by large time steps. These findings are counter-intuitive and illustrate that model predictions need to be thoroughly analysed and implementation details carefully considered when applying cell-based computational models in a quantitative setting.

biophysics↗