Biology subjects

Matthew J Simpson

Publications and source records attributed to Matthew J Simpson.

5 recordsLinked to original sources

bioRxiv2016

Logistic proliferation of cells in scratch assays is delayed

Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell mono-layer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction-diffusion models have been calibrated to data from scratch as-says. These models typically include a logistic source term to model carrying capacity-limited proliferation, however the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay, and we focus on the proliferation of these cells far away from the scratch. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the evolution of the cell density as a function of time reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. The per capita growth rate in the proliferation assay decreases, approximately linearly, with density in the proliferation assay suggesting that the logistic growth model is valid for the entire duration of the proliferation assay. However, the per capita growth rate in the scratch assay increases with density when the density is sufficiently small in the scratch assay, suggesting that the logistic growth model does not apply. Instead, guided by data, we find that there are two phases of proliferation in a scratch assay. At short time we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. Accounting for the differences in the growth and disturbance phase, we obtain biologically realistic estimates of the proliferation rate and carrying capacity density. In contrast, simply calibrating the solution of the logistic growth equation to all data from the scratch assays, we obtain an excellent match between the data and the model, but the parameter estimates vary wildly and are not biologically realistic. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.

Biophysics↗

bioRxiv2016

Accelerating computational Bayesian inference for stochastic biochemical reaction network models using multilevel Monte Carlo sampling

Investigating the behavior of stochastic models of biochemical reactionnetworks generally relies upon numerical stochastic simulation methods to generate many realizations of the model. For many practical applications, such numerical simulation can be computationally expensive. The statistical inference of reaction rate parameters based on observed data is, however, a significantly greater computational challenge; often relying upon likelihood-free methods such as approximate Bayesian computation, that requirethe generation of millions of individual stochastic realizations. In this study, we investigate a new approach to computational inference, based on multilevel Monte Carlo sampling: we approximate the posterior cumulative distribution function through a combination of model samples taken over a range of acceptance thresholds. We demonstrate this approach using a variety of discrete-state, continuous-time Markov models of biochemical reactionnetworks. Results show that a computational gain over standard rejection schemes of up to an order of magnitude is achievable without significant loss in estimator accuracy.\n\nAuthor SummaryWe develop a new method to infer the reaction rate parameters for stochastic models of biochemical reaction networks. Standard computational approaches, based on numerical simulations, are often used to estimate parameters. These computational approaches, however, are extremely expensive, potentially requiring millions of simulations. To alleviate this issue, we apply a different method of sampling allowing us to find an optimal trade-off between performance and accuracy. Our approach is approximately one order of magnitude faster than standard methods, without significant loss in accuracy.

Systems Biology↗

bioRxiv2015

Quantifying transport in crowded biochemical environments

Transport of cells and biochemical molecules often takes place in crowded, heterogeneous environments. As such, it is important we understand how to quantify crowded transport phenomena, and the possibilities of extracting transport coefficients from limited observations. We employ a volume-excluding random walk model on a square lattice where different fractions of lattice sites are filled with inert, immobile obstacles to investigate whether it is possible to estimate parameters associated with transport when crowding is present. By collecting and analysing data obtained on multiple spatial scales we demonstrate that commonly used models of motility within crowded environments can be used to reliably predict our random walk data. However, infeasibly large amounts of data are needed to estimate transport parameters, and quantitative estimates may differ depending on the spatial scale on which they are collected. We also demonstrate that in models of crowded environments there is a relatively large region of the parameter space within which it is difficult to distinguish between the \"best fit\" parameter values. This suggests commonly used descriptions of transport within crowded systems may not be appropriate, and that we should be careful in choosing models to represent the effects of crowding upon motility within biochemical systems.

Biophysics↗

bioRxiv2014

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: Criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0 < x < L(t), where L(t) is the length of the growing domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Biophysics↗

bioRxiv2014

Choosing an appropriate modelling framework for analysing multispecies co-culture cell biology experiments

In vitro cell biology assays play a crucial role in informing our understanding of the migratory, proliferative and invasive properties of many cell types in different biological contexts. While mono-culture assays involve the study of a population of cells composed of a single cell type, co-culture assays study a population of cells composed of multiple cell types (or subpopulations of cells). Such co-culture assays can provide more realistic insights into many biological processes including tissue repair, tissue regeneration and malignant spreading. Typically, system parameters, such as motility and proliferation rates, are estimated by calibrating a mathematical or computational model to the observed experimental data. However, parameter estimates can be highly sensitive to the choice of model and modelling framework. This observation motivates us to consider the fundamental question of how we can best choose a model to facilitate accurate parameter estimation for a particular assay. In this work we describe three mathematical models of mono-culture and co-culture assays that include different levels of spatial detail. We study various spatial summary statistics to explore if they can be used to distinguish between the suitability of each model over a range of parameter space. Our results for mono-culture experiments are promising, in that we suggest two spatial statistics that can be used to direct model choice. However, co-culture experiments are far more challenging: we show that these same spatial statistics which provide useful insight into mono-culture systems are insufficient for co-culture systems. Therefore, we conclude that great care ought to be exercised when estimating the parameters of co-culture assays.

Cell Biology↗