Analysis methods for comparison of multiple molecular dynamics trajectories: applications to protein unfolding pathways and denatured ensembles

Abstract

In molecular dynamics simulations of protein unfolding, the pathway of one protein molecule is studied at a time. In contrast, experimental denaturation studies sample from large ensembles of molecules passing from the native to unfolded state. If reasonable comparisons with experiment are to be made, then the generality of the simulations needs to be confirmed by performing multiple unfolding simulations. Given that protein unfolding trajectories are very complicated functions of the proteins and the environment, comparing different trajectories, even under the same conditions, is not straightforward. Several methods are presented here that attempt to accomplish this task at different levels of complexity. The simpler methods are geometry based and make use of the root-mean-squared deviations between structures, while the more complicated methods are based on the time variation of the various properties of the system during the unfolding process. These methods are applied to multiple simulations of three different proteins, bovine pancreatic trypsin inhibitor, chymotrypsin inhibitor 2, and barnase. In general, for these three proteins protein unfolding proceeded via expansion of the core and fraying of secondary structure to yield the major transition state. Once past the transition state, the trajectories for a given protein diverged as the protein lost further secondary and tertiary structure by a variety of mechanisms. Although the unfolding pathways diverged, similar conformations were populated in the denatured state even when the unfolding occurred via different pathways. The multitude of different pathways leading to the denatured state agrees with the funnel description of protein folding. Although the pathways differed in conformational space, the physical properties of the conformations were often similar, highlighting the danger of assuming that similar observed properties imply similar conformations. In fact, there may be many different “conformational pathways” of unfolding that fit within a preferred “property space pathway”.