Multiscale Analysis of Macromolecular Systems
Doctor of Philosophy
Molecular dynamics (MD) simulation serves as both a supplement to experiments and a predictive tool by revealing details inaccessible to current state-of-the-art experimental techniques. The relevant dynamics in complex macromolecular systems correspond to timescales longer than what can be sampled using MD with standard computational resources. In addition, even if Boltzmann-distributed sampling can be achieved, the definition of good reaction coordinates quantifying the progress of the reaction is non-trivial because of the high degrees of freedom of the system. My doctoral dissertation focuses on these two interrelated issues: the determination of good reaction coordinates and enhanced sampling techniques in the theoretical understanding of macromolecular systems. A new multiscale method, Locally Scaled Diffusion Map (LSDMap), has been introduced to extract the optimal collective reaction coordinates from MD data without a priori knowledge of the system. The method decouples motions with different timescales into a set of reaction coordinates, named diffusion coordinates (DCs). For systems with a seperation of timescales, the first few DCs are sufficient to characterize the slow processes of the system. Reaction rates computed along the 1st DC are in remarkable agreement with the rates measured directly from simulation. LSDMap has been applied to a number of systems, including Alanine Dipeptide, Alanine-12, polymer reversal inside a nanopore, Beta3s and DNA-Anthramycin binding. Based on LSDMap, a new enhanced sampling method, Diffusion Map-directed MD has been introduced by periodically calculating DCs on the fly and restarting the dynamics from the boundary along the 1st DC. The system is more likely to visit new regions of the configuration space instead of being trapped in a local minimum. In particular, the method achieves 3 orders of magnitude speedup over standard MD in the exploration of the configurational space of alanine-12 at 300K. The method is reaction coordinate free and minimally dependent on a priori knowledge of the system. Wide applicability of both LSDMap and its enhanced sampling extension is expected in larger systems, to the extent to allow a comparison with the experimental results, and to make predictions not yet accessible to experiment.
Protein folding; Molecular dynamics; Diffusion map