Biology subjects

Alexander George Fletcher

Publications and source records attributed to Alexander George Fletcher.

6 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

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↗

bioRxiv2015

Spatial metrics of tumour vascular organisation predict radiation efficacy in a computational model

Intratumoural heterogeneity is known to contribute to poor therapeutic response. Variations in oxygen tension in particular have been correlated with changes in radiation response in vitro and at the clinical scale with overall survival. Heterogeneity at the microscopic scale in tumour blood vessel architecture has been described, and is one source of the underlying variations in oxygen tension. We endeavour to determine whether histologic scale measures of the erratic distribution of blood vessels within a tumour can be used to predict differing radiation response. Using a two-dimensional hybrid cellular automaton model of tumour growth, we evaluate the effect of vessel distribution on cell survival outcomes of simulated radiation therapy. Using the standard equations for the oxygen enhancement ratio for cell survival probability under differing oxygen tensions, we calculate average radiation effect over a range of different vessel densities and organisations. We go on to quantify the vessel distribution heterogeneity and measure spatial organization using Ripleys L function, a measure designed to detect deviations from spatial homogeneity. We find that under differing regimes of vessel density the correlation coefficient between the measure of spatial organization and radiation effect changes sign. This provides not only a useful way to understand the differences seen in radiation effect for tissues based on vessel architecture, but also an alternate explanation for the vessel normalization hypothesis.\n\nAuthor SummaryIn this paper we use a mathematical model, called a hybrid cellular automaton, to study the effect of different vessel distributions on radiation therapy outcomes at the cellular level. We show that the correlation between radiation outcome and spatial organization of vessels changes signs between relatively low and high vessel density. Specifically, that for relatively low vessel density, radiation efficacy is decreased when vessels are more homogeneously distributed, and the opposite is true, that radiation efficacy is improved, when vessel organisation is normalised in high densities. This result suggests an alteration to the vessel normalization hypothesis which states that normalisation of vascular beds should improve radio- and chemo-therapeutic response, but has failed to be validated in clinical studies. In this alteration, we provide a metric that differentiates between vascular architectures in different density regimes in which the hypothesis holds and does not and that could be used for quantitative histologic analysis of tumours, and for radiation dose personalisation.\n\nAuthor ContributionsConceived and designed the experiments: JGS, AGF, ARAA, PKM\n\nPerformed the experiments: JGS\n\nAnalyzed the data: JGS, AGF, ARAA, PKM\n\nWrote the paper: JGS, AGF, ARAA, PKM

Cancer Biology↗

bioRxiv2015

Evidence of a role for radiation-induced lysosomal damage in non-targeted effects: an experimental and theoretical analysis

A well-known DNA-damaging agent and carcinogen, ionizing radiation (IR) can also exert detrimental effects in cells not directly exposed to it, through \"non-targeted effects\" (NTE). Whilst NTE are known to contribute to radiation-induced damage, their mechanism of induction and propagation remains incompletely understood. To investigate the possible role of lysosomes, key subcellular organelles, in NTE we used acridine orange uptake and relocation methods to monitor lysosomal permeability in irradiated and bystander human fibroblasts. As a potential mediator of lysosomal changes, oxidative stress was measured using the H2DCFDA assay for total reactive oxygen species (ROS). IR was found to induce significant lysosomal permeability in the first hour post irradiation, with reduced permeability persisting up to 24 hours. This occurred in conjunction with an increase in ROS in directly irradiated cells, in contrast with a decrease in ROS in bystander cells. Based on these observations we constructed a simple mathematical model of ROS-induced lysosomal damage, based on a bistable mechanism where a sufficiently strong IR insult can shift a cell from a low ROS, high lysosome to a high ROS, low lysosome state. This has profound cellular implications in radiation response and advances our understanding for the sub-cellular involvement in non-targeted effects.

Cell Biology↗

bioRxiv2015

Capabilities and Limitations of Tissue Size Control Through Passive Mechanical Forces

Embryogenesis is an extraordinarily robust process, exhibiting the ability to control tissue size and repair patterning defects in the face of environmental and genetic perturbations. The size and shape of a developing tissue is a function of the number and size of its constituent cells as well as their geometric packing. How these cellular properties are coordinated at the tissue level to ensure developmental robustness remains a mystery; understanding this process requires studying multiple concurrent processes that make up morphogenesis, including the spatial patterning of cell fates and apoptosis, as well as cell intercalations. In this work, we develop a computational model that aims to understand aspects of the robust pattern repair mechanisms of the Drosophila embryonic epidermal tissues. Size control in this system has previously been shown to rely on the regulation of apoptosis rather than proliferation; however, to date little work has been done to understand the role of cellular mechanics in this process. We employ a vertex model of an embryonic segment to test hypotheses about the emergence of this size control. Comparing the model to previously published data across wild type and genetic perturbations, we show that passive mechanical forces suffice to explain the observed size control in the posterior (P) compartment of a segment. However, observed asymmetries in cell death frequencies across the segment are demonstrated to require patterning of cellular properties in the model. Finally, we show that distinct forms of mechanical regulation in the model may be distinguished by differences in cell shapes in the P compartment, as quantified through experimentally accessible summary statistics, as well as by the tissue recoil after laser ablation experiments.\n\nAuthor SummaryDeveloping embryos are able to grow organs of the correct size even in the face of significant external perturbations. Such robust size control is achieved via tissue-level coordination of cell growth, proliferation, death and rearrangement, through mechanisms that are not well understood. Here, we employ computational modelling to test hypotheses of size control in the developing fruit fly. Segments in the surface tissues of the fruit fly embryo have been shown to achieve the same size even if the number of cells in each segment is perturbed genetically. We show that simple mechanical interactions between the cells of this tissue can recapitulate previously gathered data on tissue sizes and cell numbers. However, this simple model does not capture the experimentally observed spatial variation in cell death rates in this tissue, which may be explained through several adaptations to the model. These distinct adaptations may be distinguished through summary statistics of the tissue behaviour, such as statistics of cell shapes or tissue recoil after cutting. This work demonstrates how computational modelling can help investigate the complex mechanical interactions underlying tissue size and shape, which are important for understanding the underlying causes of birth defects and diseases driven by uncontrolled growth.

Developmental Biology↗

bioRxiv2014

Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly-understood reorientation mechanism in the monoflagellate species Rhodobacter sphaeroides. The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. A further two models also include stochastic reorientations, describing run-and-tumble motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events in R. sphaeroides. This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation.

Microbiology↗