An investigation of the influence of extracellular matrix anisotropy and cell-matrix interactions on tissue architecture.
Mechanical interactions between cells and the fibrous extracellular matrix (ECM) in which they reside play a key role in tissue development. Mechanical cues from the environment (such as stress, strain and fibre orientation) regulate a range of cell behaviours, including proliferation, differentiation and motility. In turn, the ECM structure is affected by cells exerting forces on the matrix which result in deformation and fibre realignment. In this paper we develop a mathematical model to investigate this mechanical feedback between cells and the ECM. We consider a three-phase mixture of collagen, culture medium and cells, and formulate a system of partial differential equations which represents conservation of mass and momentum for each phase. This modelling framework takes into account the anisotropic mechanical properties of the collagen gel arising from its fibrous microstructure. We also propose a cell-collagen interaction force which depends upon fibre orientation and collagen density. We use a combination of numerical and analytical techniques to study the influence of cell-ECM interactions on pattern formation in tissues. Our results illustrate the wide range of structures which may be formed, and how those that emerge depend upon the importance of cell-ECM interactions.
School of Mathematics, University of Birmingham, The Watson Building, Edgbaston, Birmingham, B15 2TT, UK.
R J
RJ
Dyson
School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia. edward.green@adelaide.edu.au.
J E F
JE
Green
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK.
J P
JP
Whiteley
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK.|Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road, Oxford, OX2 6GG, UK.
H M
HM
Byrne
D016880:Anisotropy; D002477:Cells / Q000166:cytology / Q000378:metabolism*; D003094:Collagen / Q000378:metabolism; D005109:Extracellular Matrix / Q000378:metabolism*; D008954:Models, Biological
D003094:Collagen
Cell aggregation; Collagen fibres; Mechanics; Multiphase model