Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.

Understanding how local protein modifications, such as binding small-molecule ligands, can trigger and regulate large-scale motions of large protein domains is a major open issue in molecular biology. We address various aspects of this problem by analyzing and comparing atomistic simulations of Hsp90 family representatives for which crystal structures of the full length protein are available: mammalian Grp94, yeast Hsp90 and E.coli HtpG. These chaperones are studied in complex with the natural ligands ATP, ADP and in the Apo state. Common key aspects of their functional dynamics are elucidated with a novel multi-scale comparison of their internal dynamics. Starting from the atomic resolution investigation of internal fluctuations and geometric strain patterns, a novel analysis of domain dynamics is developed. The results reveal that the ligand-dependent structural modulations mostly consist of relative rigid-like movements of a limited number of quasi-rigid domains, shared by the three proteins. Two common primary hinges for such movements are identified. The first hinge, whose functional role has been demonstrated by several experimental approaches, is located at the boundary between the N-terminal and Middle-domains. The second hinge is located at the end of a three-helix bundle in the Middle-domain and unfolds/unpacks going from the ATP- to the ADP-state. This latter site could represent a promising novel druggable allosteric site common to all chaperones. Understanding the connections between structure, binding, dynamics and function in proteins is one of the most fascinating problems in biology and is actively investigated experimentally and computationally. In the latter context, significant advancements are possible by exposing the causal link between the fine atomic-scale protein-ligand interactions and the large-scale protein motions. One ideal avenue to explore this relationship is given by proteins of the Hsp90 chaperones family. Their dynamics is regulated by ATP binding and hydrolysis, which activates the onset of large-scale, functional conformational changes. Herein, we concentrated on three homologs with markedly different structural organization—mammalian Grp94, yeast Hsp90 and prokaryotic HtpG—and developed a novel computational multiscale approach to detect and characterize the salient traits of the functionally-oriented internal dynamics of the three chaperones. The comparative analysis, which exploits a novel highly simplified, yet viable, description of the protein internal dynamics, highlights fundamental mechanical aspects that preside the ligand-dependent conformational arrangements in all chaperones. For the three molecules, two corresponding regions are singled out as ligand-susceptible hinges for the large-scale internal motion. On the basis of this and other evidence it is suggested that these regions represent functionally relevant druggable substructures in the discovery of novel allosteric modulators.

In the last few decades, computer simulations have become a fundamental tool in the field of soft matter science, allowing researchers to investigate the properties of a large variety of systems. Nonetheless, even the most powerful computational resources presently available are, in general, sufficient to simulate complex biomolecules only for a few nanoseconds. This limitation is often circumvented by using coarse-grained models, in which only a subset of the system’s degrees of freedom is retained; for an effective and insightful use of these simplified models; however, an appropriate parametrization of the interactions is of fundamental importance. Additionally, in many cases the removal of fine-grained details in a specific, small region of the system would destroy relevant features; such cases can be treated using dual-resolution simulation methods, where a subregion of the system is described with high resolution, and a coarse-grained representation is employed in the rest of the simulation domain. In this review we discuss the basic notions of coarse-graining theory, presenting the most common methodologies employed to build low-resolution descriptions of a system and putting particular emphasis on their similarities and differences. The AdResS and H-AdResS adaptive resolution simulation schemes are reported as examples of dual-resolution approaches, especially focusing in particular on their theoretical background.

Knotted proteins, because of their ability to fold reversibly in the same topologically entangled conformation, are the object of an increasing number of experimental and theoretical studies. The aim of the present investigation is to assess, on the basis of presently available structural data, the extent to which knotted proteins are isolated instances in sequence or structure space, and to use comparative schemes to understand whether specific protein segments can be associated to the occurrence of a knot in the native state. A significant sequence homology is found among a sizeable group of knotted and unknotted proteins. In this family, knotted members occupy a primary sub-branch of the phylogenetic tree and differ from unknotted ones only by additional loop segments. These “knot-promoting” loops, whose virtual bridging eliminates the knot, are found in various types of knotted proteins. Valuable insight into how knots form, or are encoded, in proteins could be obtained by targeting these regions in future computational studies or excision experiments. Out of the tens of thousands of known protein structures, only a few hundred are knotted. The latter epitomize, better than unknotted proteins, the degree of coordinated motion of the backbone required to fold reversibly in a specific native conformation, which indeed must contain a precise knot in a specific protein region. In the present work we search for salient features associated to protein “knottedness” through a systematic sequence and structure comparison of knotted and unknotted protein chains. A significant sequence relatedness is found within a sizeable group of knotted and unknotted proteins. Their tree of sequence relatedness suggests that the knotted entries all diverged from a specific evolutionary event. The systematic structural comparison further indicates that the knottedness of several different types of proteins is likely ascribable to the presence of short “knot-promoting” loops. These segments, whose bridging eliminates the knot, are natural candidates for future experimental/computational studies aimed at clarifying whether the global knotted state of a protein is influenced by specific regions of the primary sequence.

We present an accurate and efficient method to obtain Kirkwood-Buff (KB) integrals in the thermodynamic limit from small-sized molecular dynamics simulations. By introducing finite size effects into integral equations of statistical mechanics, we derive an analytical expression connecting the KB integrals of the bulk system with the fluctuations of the number of molecules in the corresponding closed system. We validate the method by calculating the activity coefficients of aqueous urea mixtures and the KB integrals of Lennard-Jones fluids. Moreover, our results demonstrate how to identify simulation conditions under which computer simulations reach the thermodynamic limit.