Using stochastic dynamics to validate runtimes of protein simulations

We use short molecular dynamics simulations ($\sim$200 cpu-hr, using NAMD) of individual bonds between capsid proteins to microscopically determine coarse-grained elastic parameters of entire virus capsids. In particular, we treat each protein (or for larger proteins, each domain) as a rigid body described by a 6-vector of translational and orientational degrees of freedom, $x_i(t)$. We then model the evolution of the relative positions as an overdamped random walk, $\dot x_i(t) = -\Gamma_{ij}K_{jk}(x_k(t)-\bar x_k) + \zeta_i(t)$, where $\zeta_i(t)$ are random variables satisfying $\langle\zeta_i(t)\zeta_j(t')\rangle = 2\Gamma_{ij}T\delta(t-t')$. Our goal is to determine the stiffness matrix $K_{ij}$, but this requires long-time data to measure accurately. We therefore measure the noise matrix $2\Gamma_{ij}T$, which depends on much shorter timescales, and compute the relaxation times by diagonalizing $\Gamma^{\frac12}K\Gamma^{\frac12}$. Although we use biologically relevant configurations in each simulation, we have taken the domains out of their full context by simulating one pair at a time, and therefore external stresses are missing, which we measure from the drift and compensate for in subsequent simulations. Finally, we apply this technique to the HIV capsid protein.