Comparative Study by Using Different Numerical Technique for Mathematical Model for Protein Friction and Simulation Code for Cytoskeleton Networks

Abstract

The cellular cytoskeleton is a complex, multiscale network of biopolymers that provides structural integrity and drives cellular motility. Understanding its mechanical behavior requires decoding phenomena such as protein friction, viscoelasticity, and entropic force generation. This paper provides a comparative study of the various numerical techniques and mathematical models used to simulate cytoskeletal networks and cellular mechanics. We evaluate the spatial and temporal bridging of Fully Atomistic Molecular Dynamics (MD), Coarse-Grained Molecular Dynamics (CGMD), Dissipative Particle Dynamics (DPD), and continuum poroviscous models. By introducing specific governing equations—such as the over-damped Langevin dynamics for protein unfolding, the Navier-Stokes formulations for mesoscale fluid dynamics, and the Kelvin-Voigt viscoelastic model for stick-slip cell crawling—this paper synthesizes how these distinct mathematical frameworks decode the intricate mechanotransduction and structural deformation of eukaryotic cells.