1,721,037 research outputs found
Modelling cell migration strategies in the extracellular matrix
Full text linkThe extracellular matrix (ECM) is a highly organised structure with the capacity to direct cell migration through their tendency to follow matrix fibres, a process known as contact guidance. Amoeboid cell populations migrate in the ECM by making frequent shape changes and have minimal impact on its structure. Mesenchymal cells actively remodel the matrix to generate the space in which they can move. In this paper, these different types of movement are studied through simulation of a continuous transport model. It is shown that the process of contact guidance in a structured ECM can spatially organise cell populations. Furthermore, when combined with ECM remodelling, it can give rise to cellular pattern formation in the form of "cell-chains" or networks without additional environmental cues such as chemoattractants. These results are applied to a simple model for tumour invasion where it is shown that the interactions between invading cells and the ECM structure surrounding the tumour can have a profound impact on the pattern and rate of cell infiltration, including the formation of characteristic "fingering" patterns. The results are further discussed in the context of a variety of relevant processes during embryonic and adult stages. © 2008 Springer-Verlag.</p
The impact of rheotaxis and flow on the aggregation of organisms
Full text linkDispersed populations often need to organize into groups. Chemical attractants provide one means of directing individuals into an aggregate, but whether these structures emerge can depend on various factors, such as there being a sufficiently large population or the response to the attractant being sufficiently sensitive. In an aquatic environment, fluid flow may heavily impact on population distribution and many aquatic organisms adopt a rheotaxis response when exposed to a current, orienting and swimming according to the flow field. Consequently, flow-induced transport could be substantially different for the population members and any aggregating signal they secrete. With the aim of investigating how flows and rheotaxis responses impact on an aquatic population’s ability to form and maintain an aggregated profile, we develop and analyse a mathematical model that incorporates these factors. Through a systematic analysis into the effect of introducing rheotactic behaviour under various forms of environmental flow, we demonstrate that each of flow and rheotaxis can act beneficially or detrimentally on the ability to form and maintain a cluster. Synthesizing these findings, we test a hypothesis that density-dependent rheotaxis may be optimal for group formation and maintenance, in which individuals increase their rheotactic effort as they approach an aggregated state
Trade-offs between chemotaxis and proliferation shape the phenotypic structuring of invading waves
No full textChemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system of equations introduced by Keller and Segel has proven a popular choice in the modelling of such phenomena, but in its original form restricts to a homogeneous population. To account for the possibility of phenotypic heterogeneity, we extend to the case of a population continuously structured across space, time and phenotype, where the latter determines variation in chemotactic responsiveness, proliferation rate, and the level of chemical environment modulation. The extended model considered here comprises a non-local partial differential equation for the local phenotype distribution of cells which is coupled, through an integral term, with a differential equation for the concentration of an attractant, which is sensed and degraded by the cells. In the framework of this model, we concentrate on a chemotaxis/proliferation trade-off scenario, where the cell phenotypes span a spectrum of states from highly-chemotactic but minimally-proliferative to minimally-chemotactic but highly-proliferative. Using a combination of numerical simulation and formal asymptotic analysis, we explore the properties of travelling-wave solutions. The results of our study demonstrate how incorporating phenotypic heterogeneity may lead to a highly-structured wave profile, where cells in different phenotypic states dominate different spatial positions across the invading wave, and clarify how the phenotypic structuring of the wave can be shaped by trade-offs between chemotaxis and proliferation
From random walks to fully anisotropic diffusion models for cell and animal movement
No full textThis chapter provides an introduction on how anisotropic diffusion models can be derived from position-jump and velocity-jump random walks. We show how the availability of measurement data can guide the choice of the appropriate model. We further present two new applications, respectively to cell movement on micro-fabricated surfaces and magnetic compass orientation by sea turtle hatchlings
Navigating the flow: Individual and continuum models for homing in flowing environments
Full text linkNavigation for aquatic and airborne species often takes place in the face of complicated flows, from persistent currents to highly unpredictable storms. Hydrodynamic models are capable of simulating flow dynamics and provide the impetus for much individual-based modelling, in which particlesized individuals are immersed into a flowing medium. These models yield insights on the impact of currents on population distributions from fish eggs to large organisms, yet their computational demands and intractability reduce their capacity to generate the broader, less parameter-specific, insights allowed by traditional continuous approaches. In this paper, we formulate an individual-based model for navigation within a flowing field and apply scaling to derive its corresponding macroscopic and continuous model. We apply it to various movement classes, from drifters that simply go with the flowto navigators that respond to environmental orienteering cues. The utility of the model is demonstrated via its application to 'homing' problems and, in particular, the navigation of the marine green turtle Chelonia mydas to Ascension Island
Mathematical modelling of glioma growth: The use of Diffusion Tensor Imaging (DTI) data to predict the anisotropic pathways of cancer invasion
Full text linkThe nonuniform growth of certain forms of cancer can present significant complications for their treatment, a particularly acute problem in gliomas. A number of experimental results have suggested that invasion is facilitated by the directed movement of cells along the aligned neural fibre tracts that form a large component of the white matter. Diffusion tensor imaging (DTI) provides a window for visualising this anisotropy and gaining insight on the potential invasive pathways. In this paper we develop a mesoscopic model for glioma invasion based on the individual migration pathways of invading cells along the fibre tracts. Via scaling we obtain a macroscopic model that allows us to explore the overall growth of a tumour. To connect DTI data to parameters in the macroscopic model we assume that directional guidance along fibre tracts is described by a bimodal von Mises-Fisher distribution (a normal distribution on a unit sphere) and parametrised according to the directionality and degree of anisotropy in the diffusion tensors. We demonstrate the results in a simple model for glioma growth, exploiting both synthetic and genuine DTI datasets to reveal the potentially crucial role of anisotropic structure on invasion. © 2013 Elsevier Ltd
Pattern formation within phenotype-structured chemotactic populations
Full text linkPopulations can become spatially organized through chemotaxis autoattraction, wherein population members release their own chemoattractant. Standard models of this process usually assume phenotypic homogeneity, but recent studies have shed illumination on the inherent heterogeneity within populations: in terms of chemotactic behaviour, trait heterogeneity can range from the sensitivity to attractant gradients to the rate at which attractants are produced. We propose a framework that accounts for this heterogeneity, extending the standard Keller-Segel model to a non-local formulation in which the population is continuously structured across some phenotype state space. Focusing on autoattraction, we allow both the chemotactic sensitivity and the rate of attractant secretion to vary across the population and suppose members can switch between different phenotype states. We extend classical Turing-type linear stability analyses to determine the impact of phenotypic structuring on pattern formation, showing that the rate of switching influences both the critical condition for self-organization and subsequent pattern dynamics. Scenarios in which the chemotactic sensitivity and attractant secretion are positively or negatively correlated are used to highlight the significance of these results
Spatio-temporal chaos in a chemotaxis model
Full text linkIn this paper we explore the dynamics of a one-dimensional KellerSegel type model for chemotaxis incorporating a logistic cell growth term. We demonstrate the capacity of the model to self-organise into multiple cellular aggregations which, according to position in parameter space, either form a stationary pattern or undergo a sustained spatio-temporal sequence of merging (two aggregations coalesce) and emerging (a new aggregation appears). This spatio-temporal patterning can be further subdivided into either a time-periodic or time-irregular fashion. Numerical explorations into the latter indicate a positive Lyapunov exponent (sensitive dependence to initial conditions) together with a rich bifurcation structure. In particular, we find stationary patterns that bifurcate onto a path of periodic patterns which, prior to the onset of spatio-temporal irregularity, undergo a "periodic-doubling" sequence. Based on these results and comparisons with other systems, we argue that the spatio-temporal irregularity observed here describes a form of spatio-temporal chaos. We discuss briefly our results in the context of previous applications of chemotaxis models, including tumour invasion, embryonic development and ecology. © 2010 Elsevier B.V. All rights reserved
A user's guide to PDE models for chemotaxis
Full text linkMathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399-415, 1970; 30:225- 234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display "auto-aggregation", has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller-Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work. © Springer-Verlag 2008
Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis
Full text linkChemotaxis, the guided migration of cells in response to chemical gradients, is vital to a wide variety of biological processes, including patterning of the slime mold Dictyostelium, embryonic morphogenesis, wound healing, and tumor invasion. Continuous models of chemotaxis have been developed to describe many such systems, yet few have considered the movements within a heterogeneous tissue composed of multiple subpopulations. In this paper, a partial differential equation (PDE) model is developed to describe a tissue formed from two distinct chemotactic populations. For a "crowded" (negligible extracellular space) tissue, it is demonstrated that the model reduces to a simpler one-species system while for an "uncrowded" tissue, it captures both movement of the entire tissue (via cells attaching to/migrating within an extracellular substrate) and the within-tissue rearrangements of the separate cellular subpopulations. The model is applied to explore the sorting of a heterogeneous tissue, where it is shown that differential-chemotaxis not only generates classical sorting patterns previously seen via differential-adhesion, but also demonstrates new classes of behavior. These new phenomena include temporal dynamics consisting of a traveling wave composed of spatially sorted subpopulations reminiscent of Dictyostelium slugs. © 2009 Society for Mathematical Biology.</p
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