Long Timestep Dynamics of Peptides by the Dynamics Driver Approach


Previous experience with the Langevin/implicit-Euler scheme for dynamics ("LI") on model systems (butane, water) has shown that LI is numerically stable for timesteps in the 5-20 fs range but quenches high-frequency modes. To explore applications to polypeptides, we apply LI to model systems (several  dipeptides, a tetrapeptide, and a 13-residue oligoalanine) and also develop a new dynamics driver approach ("DA"). The DA scheme, based on LI, addresses the important issue of proper sampling, which is unlikely to be solved  by small-timestep integration methods or implicit methods with intrinsic damping at room temperature, such as LI. Equilibrium averages, time-dependent molecular properties, and sampling trends at room temperature are reported for both LI and DA dynamics simulations, which are then compared  to those generated by a standard explicit discretization of the Langevin equation with a 1 fs timestep. We find that LI's quenching effects are severe on both the fast and slow  (due to vibrational coupling) frequency modes of all-atom polypeptides and lead to more restricted dynamics at moderate timesteps (40 fs). The DA approach empirically counteracts these damping effects by adding random atomic perturbations to the coordinates at each step (before the minimization of a dynamics function). By restricting the energetic fluctuations and controlling  the kinetic energy, we are able with a 60 fs timestep to generate continuous trajectories that sample more of the relevant conformational space and also reproduce reasonably Boltzmann statistics. Although the timescale for transition may be accelerated by the DA approach, the transitional information obtained for the alanine dipeptide and the tetrapeptide is consistent with that obtained by several other theoretical approaches that focus specifically on the determination of pathways. While the trajectory for oligoalanine by the explicit scheme over the nanosecond timeframe remains in the vicinity of the full R-helix starting structure, and a high-temperature (600ºK) MD trajectory departs slowly from the  helical structure, the DA-generated trajectory for the same CPU time exhibits unfolding and refolding  and reveals a range of conformations with an intermediate helix content. Significantly, this range of states is more consistent  with spectroscopic experiments on small peptides, as well as the cooperative two-state model for helix coil transition. The good, near-Boltzmann statistics reported for the smaller systems above, in combination with  the interesting oligoalanine results, suggest that DA is a promising tool for efficiently exploring conformational spaces of biomolecules and exploring folding/unfolding processes of polypeptides. 

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