Geometrical effects in protein nucleation Original Research Article

To understand the importance of protein anisotropy and the influence of translational and rotational degrees of freedom on the nucleation event, we calculate numerically-exact values for the mean encounter time for two non-spherically symmetric molecules to form a cluster, regarded here as a precursor to nucleation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a ‘dimer’ in the sense that each molecule is specified to occupy two lattice sites. The two dimers undergo simultaneously translation and/or rotation, and the mean times for their encounter are determined. Exact numerical results are obtained for small lattices via application of the theory of finite Markov processes, and the results corroborated and extended to large lattices by performing Monte Carlo simulations. These calculations allow one to understand in a detailed way the interplay among geometrical anisotropy, translational and internal (rotational) degrees of freedom and system size in influencing the seminal nucleation event.