Abstract
Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues and maintaining their functionality. Hence, to maintain in vivo-like behaviour when cells are cultured in vitro, they are often seeded in a gel, which aims to mimic the ECM. In this paper, we present a mathematical model that incorporates cell-gel interactions together with osmotic pressure to study the mechanical behaviour of biological gels. In particular, we consider an experiment where cells are seeded within a gel, which gradually compacts due to forces exerted on it by the cells. Adopting a one-dimensional Cartesian geometry for simplicity, we use a combination of analytical techniques and numerical simulations to investigate how cell traction forces interact with osmotic effects (which can lead to either gel swelling or contraction depending on the gel’s composition). Our results show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e. its chemical potentials) and the strength of the cell traction forces. A novel prediction of our model is that there are cases where the gel oscillates between swelling and contraction; to our knowledge, this behaviour has not been reported in experiments. We also consider how physical parameters like drag and viscosity affect the manner in which the gel evolves.
Highlights
Biological tissues are composed of cells living in extra-cellular matrix, hereafter designated extracellular matrix (ECM) (Iordan et al 2010)
We have presented a new model for cell-induced gel contraction, and studied its behaviour in a 1D Cartesian geometry
This has allowed us to develop a thorough understanding of the conditions under which the gel equilibrates, the conditions affecting the early time behaviour and the stability of the system, and, through numerical solution, the qualitative behaviours that can occur
Summary
Biological tissues are composed of cells living in extra-cellular matrix, hereafter designated ECM (Iordan et al 2010). The Moon and Tranquillo model assumed that the only forces acting on the gel were those exerted by the cells; gels can swell or contract in the absence of cells, for example, due to osmotic effects whereby solvent molecules can enter or leave the gel as a result of differences in the chemical potentials across the gel-solvent interface (Hong et al 2010) This is often studied mathematically using multiphase flow models, in which the behaviour of both the polymer and solvent components of the gel are each accounted for. The multiphase or mixture theory approach provides an obvious framework for modelling the dynamics of gel swelling and contraction, and models of this type have been developed by Keener et al (2011a, b) and Mori et al (2013) They consider a gel consisting of two phases, polymer network and solvent, and present mass balance and momentum balance equations for each phase. We aim to combine their approaches with mechanochemical theory (Murray et al 1983)
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