Coarse-grained modelling of protein structure and internal dynamics: comparative methods and applications

The first chapter is devoted to a brief summary of the basic techniques commonly used to characterise protein's internal dynamics, and to perform those primary analyses which are the basis for our further developments. To this purpose we recall the basics of Principal Component Analysis of the covariance matrix of molecular dynamics (MD) trajectories. The overview is aimed at motivating and justifying a posteriori the introduction of coarse-grained models of proteins. In the second chapter we shall discuss dynamical features shared by different conformers of a protein. We'll review previously obtained results, concerning the universality of the vibrational spectrum of globular proteins and the self-similar free energy landscape of specific molecules, namely the G-protein and Adk. Finally, a novel technique will be discussed, based on the theory of Random Matrices, to extract the robust collective coordinates in a set of protein conformers by comparison with a stochastic reference model. The third chapter reports on an extensive investigation of protein internal dynamics modelled in terms of the relative displacement of quasi-rigid groups of amino acids. Making use of the results obtained in the previous chapters, we shall discuss the development of a strategy to optimally partition a protein in units, or domains, whose internal strain is negligible compared to their relative uctuation. These partitions will be used in turn to characterise the dynamical properties of proteins in the framework of a simplified, coarse-grained, description of their motion. In the fourth chapter we shall report on the possibility to use the collective uctuations of proteins as a guide to recognise relationships between them that may not be captured as significant when sequence or structural alignment methods are used. We shall review a method to perform the superposition of two proteins optimising the similarity of the structures as well as the dynamical consistency of the aligned regions; then, we shall next discuss a generalisation of this scheme to accelerate the dynamics-based alignment, in the perspective of dataset-wide applications. Finally, the fifth chapter focuses on a different topic, namely the occurrence of topologically-entangled states (knots) in proteins. Specifically, we shall investigate the sequence and structural properties of knotted proteins, reporting on an exhaustive dataset-wide comparison with unknotted ones. The correspondence, or the lack thereof, between knotted and unknotted proteins allowed us to identify, in knotted chains, small segments of the backbone whose `virtual' excision results in an unknotted structure. These `knot-promoting' loops are thus hypothesised to be involved in the formation of the protein knot, which in turn is likely to cover some role in the biological function of the knotted proteins.