Modeling the mechanobioelectricity of cell clusters
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ORIGINAL PAPER
Modeling the mechanobioelectricity of cell clusters Alessandro Leronni1 Received: 24 September 2020 / Accepted: 16 October 2020 © The Author(s) 2020
Abstract We propose a continuum finite strain theory for the interplay between the bioelectricity and the poromechanics of a cell cluster. Specifically, we refer to a cluster of closely packed cells, whose mechanics is governed by a polymer network of cytoskeletal filaments joined by anchoring junctions, modeled through compressible hyperelasticity. The cluster is saturated with a solution of water and ions. We account for water and ion transport in the intercellular spaces, between cells through gap junctions, and across cell membranes through aquaporins and ion channels. Water fluxes result from the contributions due to osmosis, electro-osmosis, and water pressure, while ion fluxes encompass electro-diffusive and convective terms. We consider both the cases of permeable and impermeable cluster boundary, the latter simulating the presence of sealing tight junctions. We solve the coupled governing equations for a one-dimensional axisymmetric benchmark through finite elements, thus determining the spatiotemporal evolution of the intracellular and extracellular ion concentrations, setting the membrane potential, and water concentrations, establishing the cluster deformation. When suitably complemented with genetic, biochemical, and growth dynamics, we expect this model to become a useful instrument for investigating specific aspects of developmental mechanobioelectricity. Keywords Bioelectricity · Poromechanics · Electro-diffusion · Osmosis · Electro-osmosis · Membrane potential
1 Introduction Recent endeavors have documented that, alongside genetic and biochemical cues, bioelectrical and mechanical signaling is important for development (McCaig et al. 2005; Mammoto and Ingber 2010). In particular, bioelectricity deals with the study of the ion redistribution within a network of non-excitable cells and its environment, modulating the membrane potential (Levin et al. 2017). The latter qualifies as both a key readout and regulator of several developmental processes, such as proliferation and differentiation (Sundelacruz et al. 2009), at the single cell level, and symmetry breaking (Levin et al. 2002), wound healing and regeneration (Levin 2007), and cancer progression (Chernet and Levin 2013), at the tissue level. In addition to experimentation through ion channels manipulation, deciphering the bioelectrical dynamics * Alessandro Leronni [email protected] 1
Department of Civil, Environmental, Architectural Engineering and Mathematics (DICATAM), University of Brescia, Via Branze, 43, 25123 Brescia, Italy
requires ad hoc simulators. The BioElectric Tissue Simulation Engine (BETSE), a finite volume code proposed by Pietak and Levin (2016), allows one to predict the spatiotemporal evolution of the ion concentrations and membrane potential within a cluster of closely packed cells, in response to a perturbation of the bioelectric state. Later, BETSE has
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