Computational methodology for a coarse-grained simulation of auxetic, two-dimensional crystal dynamics

The increasing number of protein-based metamaterials demands reliable and efficient methods to study the physicochemical properties they may display. In this regard, we develop a simulation strategy based on Molecular Dynamics (MD) that addresses the geometric degrees of freedom of an auxetic two-dimensional protein crystal. This model consists of a network of impenetrable rigid squares linked through massless rigid rods, thus featuring a large number of both holonomic and nonholonomic constraints. Our MD methodology is optimized to study highly constrained systems and allows for the simulation of long-time dynamics with reasonably large timesteps. The data extracted from the simulations shows a persistent motional interdependence among the protein subunits in the crystal. We characterize the dynamical correlations featured by these subunits and identify two regimes characterized by their locality or nonlocality, depending on the geometric parameters of the crystal. From the same data, we also calculate the Poisson\rq{}s (longitudinal to axial strain) ratio of the crystal, and learn that, due to holonomic constraints (rigidness of the rod links), the crystal remains auxetic even after significant changes in the original geometry. The nonholonomic ones (collisions between subunits) increase the number of inhomogeneous deformations of the crystal, thus driving it away from an isotropic response. Our work provides the first simulation of the dynamics of protein crystals and offers insights into promising mechanical properties afforded by these materials.