Title: Coarse-grained simulation of auxetic, two-dimensional crystal dynamics,
Abstract: 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.