Abstract
The mechanical properties of cell nuclei have been demonstrated to play a fundamental role in cell movement across extracellular networks and micro-channels. In this work, we focus on a mathematical description of a cell entering a cylindrical channel composed of extracellular matrix. An energetic approach is derived in order to obtain a necessary condition for which cells enter cylindrical structures. The nucleus of the cell is treated either (i) as an elastic membrane surrounding a liquid droplet or (ii) as an incompressible elastic material with Neo-Hookean constitutive equation. The results obtained highlight the importance of the interplay between mechanical deformability of the nucleus and the capability of the cell to establish adhesive bonds and generate active forces in the cytoskeleton due to myosin action.
Highlights
Cell migration inside extracellular matrix networks plays a critical role in many physiological and pathological processes
We study how the nucleus deformability can influence the process of a cell entering a 3D extracellular structure, using a continuum description of the cell nucleus
By scaling constant force assumption all distances with Rn and writing all material parameters on the right-hand-side, we identify four dimensionless numbers that represent the ratio between adhesive bond properties and nuclear mechanical parameters
Summary
Cell migration inside extracellular matrix networks plays a critical role in many physiological and pathological processes. Even though the scientific community is becoming aware of the importance of mechanical properties of cells in their process of migration inside porous structures, poor investigations have been carried from the mathematical modelling point of view and mechanical information is generally neglected in the description of cell movements. In vivo, fibre structures and bundles are arranged into really complex networks of strongly varying local densities [57], that create pores and gaps, we simplify the problem, considering the ECM structured in parallel cylindrical channels composed of fibres and bundles that provide directional guidance cues to cells This is a strong assumption of the far more complex real structure of the extracellular environment, but it can be a good approximation for regular scaffolds used in tissue engineering and it helps to make a first step towards the description of the real phenomenon. Results are presented in terms of dimensionless parameters that represent the interplay between adhesive and mechanical properties
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