Bridging the Atomic and Coarse-Grained Descriptions of Collective Motions in Proteins

Protein structures are carefully "designed" to balance the need of thermodynamical stability with the necessity of sustaining conformational changes and efficiently interconverting among different functionally relevant conformers. This subtle equilibrium reverberates in the complexity of the free-energy landscape which is endowed by a variety of local minima of varying depth and breadth corresponding to the salient structural states of the molecules. In this chapter we will present some concepts and computational algorithms that can be used to characterize the internal dynamics of proteins and relate it to their "functional mechanics". We will apply these concepts to the analysis of a molecular dynamics simulation of adenylate kinase, a protein for which the structural rearrangement is known to be crucial for the accomplishment of its biological function. We will show how, despite the structural heterogeneity of the explored conformational ensemble, the generalized directions accounting for conformational fluctuations within and across the visited conformational substates are robust and can be described by a limited set of collective coordinates. Finally, as a term of comparison, we will show that in the case of HIV-1 Transactivator of Transcription (TAT), a naturally unstructured protein, the lack of any hierarchical organization of the free-energy minima results in a poor consistency of the essential dynamical spaces sampled during the dynamical evolution of the system.