Molecular Dynamics

MD simulation (discussed in detail in Chap. 12) propagates physically realistic trajectories by applying Newton’s equations of motion iteratively to allow atom movement, and is thus the most faithful method depicting atomistically what is occurring in proteins. The method is therefore often used for the study of protein folding pathways (Duan and Kollman 1998; Freddolino et al. 2010). The massive computational cost of long simulations is a major challenge with this method, since the incremental time scale is usually in the order of femtoseconds (10 ¹⁵ s) while the fastest folding time of small proteins are on timescales of several microseconds (for folding model systems) or in the millisecond range (more typically). From the standpoint of search efficiency, molecular dynamics simulations are guaranteed to propagate some motion after each energy/force evaluation, but the steps that are taken are very small; in contrast, as described in the preceding section, Monte Carlo simulations may make larger steps, but not all steps will be accepted after energy evaluation. The relative sampling efficiency of the methods is thus dependent on the acceptance rate of Monte Carlo moves; with modern move sets (see, e.g., Fig. 1.5) Monte Carlo sampling of protein conformational space tends to be much more efficient. Thus, the application of molecular dynamics simulations using atomistic models is reserved for cases where the topic of interest is the folding process, rather than the folded structure per se. One unusual strength of MD sampling compared with Monte Carlo is that MD can accommodate the presence of explicit water much more readily, which might prove useful in the rare cases where implicit solvent models are directly responsible for failed structure predictions (Zhou 2003).

In addition, molecular dynamics simulations have been successfully applied in protein structure prediction using a variety of coarse-grained models, in which the computational complexity is substantially reduced and the folding accelerated due to the simulation of a smaller system with a less rugged energetic landscape, but of course with reduced resolution (Tozzini 2005; Hills and Brooks 2009). In addition, when a low-resolution model is available, MD simulations are often carried out for structure refinement since the conformational changes are assumed to be small (Zhang et al. 2011; Miijalili and Feig 2013). Sampling in molecular dynamics simulations of protein folding may be enhanced using similar methods to those in Monte Carlo simulations, e.g. through the use of replica exchange simulations (Sugita and Okamoto 1999), but at the price of complicating the interpretation of folding kinetics and pathways. One particularly promising enhanced sampling method for future protein folding simulations and structure prediction is accelerated molecular dynamics (aMD) (Hamelberg et al. 2004), which applies a bias to lower the relative height of barriers on the potential energy surface. In a recent application, aMD allowed the prediction of the folded structures and folding free energy landscapes of a set of four commonly used model proteins with 10-100 fold less computational effort than unbiased simulations (Miao et al. 2015), providing promise for future applications to study folding pathways and equilibriums.