Influence of nucleus deformability on cell entry into cylindrical structures

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.

A multiphase model of tumour segregation in situ by a heterogeneous extracellular matrix

“…Unfortunately, to our knowledge there are no quantitative experiments that can help in evaluating neither A 1 nor n. However, some hints can be obtained by the simulations given in [25,26]. Also the threshold value A 0 in general can not be taken constant, because as shown in [8,25,26], it depends…”

“…The latter dependence is a measurement of the force that the cell passively experiences due to the pressure of the other cells, or is able to exert by itself attaching and pulling on the ECM fibres in order to pass through the ECM pore. Therefore, in general this last contribution will depend on the density of integrins expressed at the membrane, on the density of adhesive sites on the ECM, and on the active force due to myosin activation [8].…”

“…In order to do that we will refer to the experimental results by Wolf et al [30] and also to the outcomes of the mathematical models describing the motion of single cells interacting with virtual regular ECMs and microchannels [8,25,26,27] based on other experimental behaviours [12,13,24]. As already stated, in growth phenomena it is possible to neglect in m c the contribution due to the interaction between cell and interstitial fluid with respect to the one between cells and ECM, so that m c = m cm .…”

“…On the basis of these experiments and of energy arguments Giverso et al [8] identified a criterium of penetration involving the comparison of the ratio of adhesion forces exerted by the cells and nucleus stiffness with a given function of the ratio of the microchannel size with respect to the nucleus diameter. In particular, if the size ratio is too restrictive, then the cell cannot penetrate into the micro-channel.…”

Relevance of Cell-ECM Interactions: From a Biological Perspective to the Mathematical Modeling

“…In [2] we proposed a set of models dealing with cell migratory ability and migratory mode in highly confined matrix structures. The underlying biological motivation is that the nucleus is a very voluminous and stiff subcellular organelle, thereby constituting a steric hindrance for cell migration in tight and dense ECM networks.…”