Protein Folding as Biased Conformational Diffusion

Analysis of molecular dynamics trajectories for a small protein, the villin headpiece subdomain, shows that its internal dynamics can be modeled as a random walk on a bounded high-dimensional lattice where each lattice point corresponds to a protein conformation. The time evolution of the dynamics trajectory can be described as a three-stage process. The first stage, over a very short time scale of 10 fs, is consistent with an all-atoms ballistic flight with an average path length of 0.068 A. The apparent conformational displacement "velocity" of 680 m/s is of similar magnitude to free flight monatomic carbon gas at room temperature. The second stage is unobstructed random walk diffusion in a high-dimensional space for ∼300 fs, average displacement of 0.4 A. In the third stage, at longer times, "harmonic-like" barriers confine the conformational diffusion to a few large-amplitude modes. We use this description to develop a lattice model that can reproduce the time dependence of the root-mean-square displacement (rmsd) along the dynamics trajectory with surprisingly few parameters. The lattice model allows exploration of specific energy landscapes on the folding of the villin headpiece subdomain. For example, we test a simple funnel landscape with a Monte Carlo search in which displacement is biased toward a corner of the lattice space representing the native state. An energy difference of ∼15 kcal/mol between native and unfolded states is sufficient to give a reasonable folding time of 10 μs with two-state kinetics. To our knowledge, these are the first protein-folding simulations that successfully fold the protein using a model with explicit time representation and a stochastic search and without a native-state specific potential function.