Dynamical models, chemo-mechanical coupling and numerical recipes for some soft biological systems

Living cells actively sense and respond to a vast variety of biochemical and mechanical signals whose strong interplay regulates most of cellular physical properties. Advances in the field of mechanobiology suggest that changes in cell mechanics, ECM structure, or molecular mechanisms by which cells respond to mechanical signals, also known as mechano-transduction, play an important role in many biological events from nutrients intake and adhesion up to mutation and differentiation. Also, biomechanics is exploited across multiple length and time scales by so allowing the understanding and explanation of the key feedback mechanisms regulating both cellular events, say at the microscopic scale, as well as the overall behavior of cell population, tissues and organs at higher spatial scales. In this regard, multiphysics approaches and chemo-mechanical coupling can be fruitfully exploited to describe the complex evolution of cell and tissue environments by including the fundamental role that mechanics plays in governing cellular activities and interactions among many biological constituents. With this in mind, different living systems can be modeled to estimate how evolving dynamics impact the remodeling and functionality of their structures through experiencing large deformations and continuously re-distributing the internal stresses. Focusing on modeling the response of complex systems at the cellular level, the case of plasma membranes has been analyzed to study the crosstalk between chemical events and the morphological and mechanical adaptation of the bilayer, which directly influence membrane selectivity and cell-ECM communication. In fact, the plasma membrane appears as a highly dynamic and heterogeneous environment exhibiting a strong coupling between biochemical events and structural re-organization, in which lipids order transitions and their micro-mechanical interplay with transmembrane proteins induce membrane conformational changes. It is reasonable to assume the lipid membrane as a visco-hyperelastic body that exhibit both in-plane fluidity and elasticity in which molecules migration and diffusion give rise to ordered lipid microdomains, rich of signaling proteins, named lipid rafts. These islands are characterized by high stiffness and viscosity as well as reduced diffusive walkways and coalescence phenomena of proteins, so locally altering the bilayer dynamics in terms of mechano-signaling and intra-cellular processes. Therefore, a full multiphysics coupling between the mechanical work performed by the proteins on the surrounding lipids and the kinetics of phase changes becomes manifest. Through complex interspecific dynamics, the spatio-temporal evolution of lipid rafts has been investigated in depth by focusing on the phenomena of co-localization and synergy between proteins’ activation and raft formation. This may be beneficial for studying some key mechanisms at the basis of communication between cell-cell and cell-ECM, which are essential to steer the evolution of some collective systems at higher scales. In this regard, cell mechanical properties have a fundamental role for their development, differentiation, physiology, and disease. The cytoskeleton plays a major role in these activities being identified as the cell load bearing structure. Hence, it can be modelled in the framework of Continuum Mechanics as a tensegrity structure obeying self-equilibrium principia. In this framework, it is proposed a predictive mathematical model that quantifies the overall forces sensed by the system in order to have a measure of the stiffness and of the adhesion strength of the cell. Moreover, at the macroscopic tissue level, complex interspecific dynamical models also enable to gain further insights into interactions between different cell populations governing mass development in inhomogeneous microenvironments as the tumor stroma. In fact, through spatio-temporal equations incorporating cell proliferation rates and biochemical interactions among species, it is possible to predict the effectiveness of the immune system response as a result of the competition between the characteristic times of cancer cell growth and the activity rates of the other cell species. By then providing enriched in silico platforms in which the mechanical response of some biological systems and the spatio-temporal dynamics of their main constituents are all put in full coupling by means of multiple types of bio-chemo-mechanical interactions, it is possible to shed light on how living environments can evolve towards different fates either in normal or abnormal conditions. This will contribute to better elucidate the complex physics governing many biological processes and to possibly explore new mechanics-based therapeutic strategies through theoretical predictions obtained from multiscale approaches in coherence with experimental evidence.