Computational method for highly-constrained molecular dynamics of rigid bodies: coarse-grained simulation of auxetic two-dimensional protein crystals

TL;DR

This paper introduces a novel molecular dynamics simulation method for highly-constrained rigid body systems, specifically applied to auxetic two-dimensional protein crystals, enabling long-time dynamics analysis and revealing unique mechanical behaviors.

Contribution

It extends MD protocols to include complex constraints and collision detection, providing the first long-timescale simulation of protein crystal dynamics.

Findings

Persistent motional interdependence among protein subunits

Non-holonomic constraints increase network inhomogeneity

Simulation reveals promising mechanical properties of protein crystals

Abstract

The increasing number of protein-based metamaterials demands reliable and efficient theoretical and computational 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. Our MD methodology extends the well-known protocols SHAKE and RATTLE to include highly non-linear holonomic and non-holonomic constraints, with emphasis on collision detection and response between anisotropic rigid bodies. The presented method enables the simulation of long-time dynamics with reasonably large time-steps. The data extracted from the simulations allow the characterization of the dynamical correlations featured by the protein subunits, which show a persistent motional interdependence across the array. On the other hand, non-holonomic constraints (collisions between subunits) increase the number of inhomogeneous deformations of the network, thus driving it away from an isotropic response. Our work provides the first long-timescale simulation of the dynamics of protein crystals and offers insights into promising mechanical properties afforded by these materials.