Multi-basin dynamics of a protein in a crystal environment

The dynamics of the small protein crambin is studied in the crystal environment by means of a 5.1 nanoseconds molecular dynamics (MD) simulation. The resulting trajectory is analyzed in terms of a small set of nonlinear dynamical modes that best describe the molecule's fluctuations. These modes are nonlinear in the sense that they describe a trajectory exhibiting multiple transitions among local minima at various timescales. Nonlinear modes are responsible for most of the protein atomic fluctuations. An ultrametric hierarchy of sampled local minima describes the protein trajectory when structures are classified in terms of their interconfigurational mean squared distance. Transitions among minima involve small changes in the relative atomic positions of many atoms in the protein. The character of the MD trajectory fits within the framework of rugged energy landscape dynamics. This MD simulation clarifies the unique statistical features of the barriers between minima in the energy-like configurational landscape. Longer timescale dynamics seem to sample transitions between minima separated by relatively higher barriers. The MD trajectory of the system in configurational space can be described in terms of diffusion of a particle in real space with a waiting time distribution due to partial trapping in shallow minima. A description of the dynamics in terms of an open Newtonian system (the protein) coupled to a stochastic system (the solvent and fast quasiharmonic modes of the protein) reveals that the system loses memory of its configurational space within a few picoseconds. The diffusion of the protein in configurational space is anomalous in the sense that the mean square displacement increases sublinearly with time, i.e., as a power law with an exponent that is smaller than unity.