An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

Dyson, Rosemary; Green, J. E. F.; Whiteley, Jonathan; Byrne, Helen M.

doi:10.1007/s00285-015-0927-7

Cited by 34 publications

(35 citation statements)

References 64 publications

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“…Other approaches based on mechano-chemical models [13], continuum [14,15], and continuum-discrete modelling [16], have tackled this issue. For example, Dyson et al have used a multiphase approach to show how fibres embedded in the tissue matrix may bias cell movement and how cell movement may deform the fibres [17]. However, none of these models couples the mechanical stress that the endothelial cells experience to their growth, proliferation and the phenotype of their daughter cells.…”

Section: Introductionmentioning

confidence: 99%

3D hybrid modelling of vascular network formation

Perfahl

Hughes

Alarcón

et al. 2017

Journal of Theoretical Biology

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We develop an off-lattice, agent-based model to describe vasculogenesis, the de novo formation of blood vessels from endothelial progenitor cells during development. The endothelial cells that comprise our vessel network are viewed as linearly elastic spheres that move in response to the forces they experience. We distinguish two types of endothelial cells: vessel elements are contained within the network and tip cells are located at the ends of vessels. Tip cells move in response to mechanical forces caused by interactions with neighbouring vessel elements and the local tissue environment, chemotactic forces and a persistence force which accounts for their tendency to continue moving in the same direction. Vessel elements are subject to similar mechanical forces but are insensitive to chemotaxis. An angular persistence force representing interactions with the local tissue is introduced to stabilise buckling instabilities caused by cell proliferation. Only vessel elements proliferate, at rates which depend on their degree of stretch: elongated elements have increased rates of proliferation, and compressed elements have reduced rates. Following division, the fate of the new cell depends on the local mechanical environment: the probability of forming a new sprout is increased if the parent vessel is highly compressed and the probability of being incorporated into the parent vessel increased if the parent is stretched. Simulation results reveal that our hybrid model can reproduce the key qualitative features of vasculogenesis. Extensive parameter sensitivity analyses show that significant changes in network size and morphology are induced by varying the chemotactic sensitivity of tip cells, and the sensitivities of the proliferation rate and the sprouting probability to mechanical stretch. Varying the chemotactic sensitivity directly influences the directionality of the networks. The degree of branching, and thereby the density of the networks, is influenced by the sprouting probability. Glyphs that simultaneously depict several network properties are introduced to show how these and other network quantities change over time and also as model parameters vary. We also show how equivalent glyphs constructed from in vivo data could be used to discriminate between normal and tumour vasculature and, in the longer term, for model validation. We conclude that our biomechanical hybrid model can generate vascular networks that are qualitatively similar to those generated from in vitro and in vivo experiments.

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Section: Introductionmentioning

confidence: 99%

3D hybrid modelling of vascular network formation

Perfahl

Hughes

Alarcón

et al. 2017

Journal of Theoretical Biology

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“…Cancer cells lose their ability to regulate genome stability which leads to further genetic changes and tumour development (Khalique et al, 2007). Over the last three decades it has been shown experimentally that tumours consist of heterogeneous populations of cells, which are the result of genetic instability (Stackpole, 1983; 3 of 36 new mathematical models of parabolic type have been derived to describe these cell-cell and cell-matrix adhesion processes (Armstrong et al, 2006;Dyson et al, 2016;Gerisch & Chaplain, 2008;Gerisch & Painter, 2010;Green et al, 2010;Painter et al, 2015). Since these models incorporate the assumption that cells at position x bind/unbind to/from other cells at position x ± s (for some s > 0 within cells sensing radius), they are generally nonlocal.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

Buono

Eftimie

2016

Springer Proceedings in Mathematics &Amp; Statistics

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[Date] Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.

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“…This is often done by means of partial differential equations (PDEs) describing the temporal change in the density of cells. An example of such a model is the fluid-type model developed by Dyson et al (2016). They model collagen, culture medium and cells as a three-phase mixture, resulting in a system of partial differential equations for the respective densities.…”

Section: Existing Mathematical Models Of Cell Migrationmentioning

confidence: 99%

The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration

2020

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The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.

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An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

Cited by 34 publications

References 64 publications

3D hybrid modelling of vascular network formation

3D hybrid modelling of vascular network formation

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration

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