In silico approach to quantify nucleus self-deformation on micropillared substrates

Abstract

Considering the major role of confined cell migration in biological processes and diseases, such as embryogenesis or metastatic cancer, it has become increasingly important to design relevant experimental setups for in vitro studies. Microfluidic devices have recently presented great opportunities in their respect since they offer the possibility to study all the steps from a suspended to a spread, and eventually crawling cell or a cell with highly deformed nucleus. Here, we focus on the nucleus self-deformation over a micropillared substrate. Actin networks have been observed at two locations in this setup: above the nucleus, forming the perinuclear actin cap (PAC), and below the nucleus, surrounding the pillars. We can then wonder which of these contractile networks is responsible for nuclear deformation. The cytoplasm and the nucleus are represented through the superposition of a viscous and a hyperelastic material and follow a series of processes. First, the suspended cell settles on the pillars due to gravity. Second, an adhesive spreading force comes into play, and then, active deformations contract one or both actin domains and consequently the nucleus. Our model is first tested on a flat substrate to validate its global behaviour before being confronted to a micropillared substrate. Overall, the nucleus appears to be mostly pulled towards the pillars, while the mechanical action of the PAC is weak. Eventually, we test the influence of gravity and prove that the gravitational force does not play a role in the final deformation of the nucleus.

Nuclear Stress-Strain State over Micropillars: A Mechanical In silico Study

“…Once the cell approaches the substrate, the contact force f ct applies over a very thin layer corresponding to the intersection between the cell and the substrate. We have shown that f ct can be approximated by a volume force [26] and it can be computed via a penalization technique as follows:…”

“…The latter, which may be discrete [20][21][22] or continuum [15,[23][24][25], allows to investigate the intra-cellular rearrangement or to obtain quantitative results at the global or the local scale. In our previous paper [26], we have proposed an in silico two-dimensional (2D) model which simulates the first three steps (i.e., contact, adhesion and spreading) of the interaction between the cell and the micropillared substrate and provides insights on the mechanisms inducing nuclear deformation. We have been able to determine the role of the gravity and of the actin fibers above and beneath the nucleus responsible for a pushing and a pulling force, respectively.…”

“…In the present paper, we have adapted the model presented in [26] and we have focused on step one only (i.e., contact between the cell and the pillars). The cell and nucleus behaviours are described using specific mechanical tools (i.e., constitutive laws, mechanical properties, fluid and solid phase balance).…”