The response of cells during spreading and motility is dictated by several multi-physics events, which are triggered by
extracellular cues and occur at different time-scales. For this sake, it is not completely appropriate to provide a cell with
classical notions of the mechanics of materials, as for "rheology" or "mechanical response". Rather, a cell is an alive system
with constituents that show a reproducible response, as for the contractility for single stress fibers or for the mechanical
response of a biopolymer actin network, but that reorganize in response to external cues in a non-exactly-predictable and
reproducible way.
Whereas uncountable papers have been published on the biology of cells spreading, motility and the relocation of proteins on advecting lipid membranes, the mathematical modeling definitely lags behind experiments and overall received much less attention. Although nowadays a widespread literature in mechanobiology exists, the relocation of proteins and their interaction with the reorganizing cytoskeleton in the biological phenomena mentioned above is still an ongoing research topic, let alone the formulation of efficient algorithms and computational solvers for three-dimensional simulations.
In our work, we attempt at defining a multi-physics scheme for the modeling of cells spreading, motility and the relocation of proteins on advecting lipid membranes, framing the mathematical setting within the mechanics and thermodynamics of continua, stemming from seminal works and accounting for recent literature, either connected to the endocytosis of virus in human and animal cells or ligand-receptor mediated raft formation, chemotaxis, surface-associated caveolae mechanotransduction.
The general framework that we have been developing applies to growth and remodeling, too, falling within the category of the theory of finite growth.
The multiscale scenario of cell viscoelasticity
Although the free energy scenario is rather clear, a specialization of the constitutive equations has not been attempted for the lamellipodia filament network and microtubules in the literature, to the best of our knowledge. The hindrance stands in the multiscale scenario of cell viscoelasticity:
while the mechanical behavior and properties of single intermediate filaments, actin filaments, and microtubules has been nowadays quite clarified, at least in terms of relative stiffness and strengths, bundles of the filaments, their response, polymerization, shape and time evolution is hard to be captured by comprehensive models at the "macroscopic" scale through appropriate free energies. As a consequence, the ability of models to capture the mechanics of fundamental cellular processes (as chemotaxis, cell sprouting, junction and differentiation, endocytosis and exocytosis to cite a few) still requires abundant research before gaining predicting capabilities in simulations. This is the framework of our work.
The cytoskeleton, an interconnected network of regulatory proteins and filamentous biological polymers, undergoes massive reorganization during cell deformation, especially after cell rolling and adhesion and in mediating, sensing and transduction of mechanical cues from the micro-environment.
Homogenized models for the mechanical response of a cell shall condense in effective properties the: i) polymerisation/depolimerisation of filaments; ii) the process of cross-linking that determine the architecture of cytoskeletal filaments; iii) the passive mechanical properties of the cytosol. The thermodynamics of statistically-based continuum theories for polymers with transient networks appears to be a valuable candidate for the selection of free energies.
At present however, such a comprehensive model has not yet been proposed for the pseudopodia driven cell motion.
We care for education
The challenges faced by modern society most often do not come in disciplinary packages. They are complex and
as such require an integrated response, calling for interdisciplinary actions. Unfortunately, whereas multidisciplinary endeavors offer
a large variety of opportunities, they also entail significant complexity due to the usually unfamiliar scientific backgrounds of
participants, their dissimilar mindsets and methodological approaches, and last but not least to the disconnected contents and
languages. These major limitations obstruct the
way to scientific integration in the academic community and negatively impact the deployment of training strategies for young
researchers.
Based on this evidence, we care for education and propose innovative training avenues for bachelor, undergrads, graduate students.
