Biology subjects

Ruth E Baker

Publications and source records attributed to Ruth E Baker.

9 recordsLinked to original sources

bioRxiv2016

Numerical Analysis of the Immersed Boundary Method for Cell-Based Simulation

Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behaviour, models that consider cells as individual objects are becoming a common tool to study how processes at the single-cell level affect collective dynamics and determine tissue size, shape and function. However, there often remains no comprehensive account of these models, their method of solution, computational implementation or analysis of parameter scaling, hindering our ability to utilise and accurately compare different models. Here we present an effcient, open-source implementation of the immersed boundary method (IBM), tailored to simulate the dynamics of cell populations. This approach considers the dynamics of elastic membranes, representing cell boundaries, immersed in a viscous Newtonian fluid. The IBM enables complex and emergent cell shape dynamics, spatially heterogeneous cell properties and precise control of growth mechanisms. We solve the model numerically using an established algorithm, based on the fast Fourier transform, providing full details of all technical aspects of our implementation. The implementation is undertaken within Chaste, an open-source C++ library that allows one to easily change constitutive assumptions. Our implementation scales linearly with time step, and subquadratically with mesh spacing and immersed boundary node spacing. We identify the relationship between the immersed boundary node spacing and fluid mesh spacing required to ensure fluid volume conservation within immersed boundaries, and the scaling of cell membrane stiffness and cell-cell interaction strength required when refining the immersed boundary discretization. This study provides a recipe allowing consistent parametrisation of IBM models.

Systems Biology↗

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↗

bioRxiv2016

Robust cell tracking in epithelial tissues through identification of maximum common subgraphs

Tracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Characterising cell growth, proliferation, intercalation and apoptosis in epithelia helps us to understand how morphogenetic processes such as tissue invagination and extension are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells entering or leaving the field of view between frames, cell neighbour exchanges, cell removals and cell divisions. However, current tracking methods for epithelial sheets are not robust to large morphogenetic deformations and require significant manual interventions. Here, we present a novel algorithm for epithelial cell tracking, exploiting the graph-theoretic concept of a maximum common subgraph to track cells between frames of a video. Our algorithm does not require the adjustment of tissue-specific parameters, and scales in sub-quadratic time with tissue size. It does not rely on precise positional information, permitting large cell movements between frames and enabling tracking in datasets acquired at low temporal resolution due to experimental constraints such as photoxicity. To demonstrate the method, we perform tracking on the Drosophila embryonic epidermis and compare cell-cell rearrangements to previous studies in other tissues. Our implementation is open source and generally applicable to epithelial tissues.

Bioengineering↗

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↗

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

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↗

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↗