Raffaello Potestio

Hamiltonian Adaptive Resolution Simulation for Molecular Liquids

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.

Coarse-Grained Description of Protein Internal Dynamics: An Optimal Strategy for Decomposing Proteins in Rigid Subunits

The possibility of accurately describing the internal dynamics of proteins, in terms of movements of a few approximately-rigid subparts, is an appealing biophysical problem with important implications for the analysis and interpretation of data from experiments or numerical simulations. The problem is tackled here by means of a novel variational approach that exploits information about equilibrium fluctuations of interresidues distances, provided, e.g., by atomistic molecular dynamics simulations or coarse-grained models. No contiguity in primary sequence or in space is enforced a priori for amino acids grouped in the same rigid unit. The identification of the rigid protein moduli, or dynamical domains, provides valuable insight into functionally oriented aspects of protein internal dynamics. To illustrate this point, we first discuss the decomposition of adenylate kinase and HIV-1 protease and then extend the investigation to several representatives of the hydrolase enzymatic class. The known catalytic site of these enzymes is found to be preferentially located close to the boundary separating the two primary dynamical subdomains.

Corresponding Functional Dynamics across the Hsp90 Chaperone Family: Insights from a Multiscale Analysis of MD Simulations

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.

Knotted vs. unknotted proteins: evidence of knot-promoting loops.

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.

Computer Simulations of Soft Matter: Linking the Scales

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.

Adaptive resolution simulation of a biomolecule and its hydration shell: Structural and dynamical properties

A fully atomistic modelling of many biophysical and biochemical processes at biologically relevant length- and time scales is beyond our reach with current computational resources, and one approach to overcome this difficulty is the use of multiscale simulation techniques. In such simulations, when system properties necessitate a boundary between resolutions that falls within the solvent region, one can use an approach such as the Adaptive Resolution Scheme (AdResS), in which solvent particles change their resolution on the fly during the simulation. Here, we apply the existing AdResS methodology to biomolecular systems, simulating a fully atomistic protein with an atomistic hydration shell, solvated in a coarse-grained particle reservoir and heat bath. Using as a test case an aqueous solution of the regulatory protein ubiquitin, we first confirm the validity of the AdResS approach for such systems, via an examination of protein and solvent structural and dynamical properties. We then demonstrate how, in addition to providing a computational speedup, such a multiscale AdResS approach can yield otherwise inaccessible physical insights into biomolecular function. We use our methodology to show that protein structure and dynamics can still be correctly modelled using only a few shells of atomistic water molecules. We also discuss aspects of the AdResS methodology peculiar to biomolecular simulations.

Statistical mechanics of Hamiltonian adaptive resolution simulations

The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.

PiSQRD: a web server for decomposing proteins into quasi-rigid dynamical domains

SUMMARY The PiSQRD web resource can be used to subdivide protein structures in quasi-rigid dynamical domains. The latter are groups of amino acids behaving as approximately rigid units in the course of protein equilibrium fluctuations. The PiSQRD server takes as input a biomolecular structure and the desired fraction of protein internal fluctuations that must be accounted for by the relative rigid-body motion of the dynamical domains. Next, the lowest energy modes of fluctuation of the protein (optionally provided by the user) are calculated and used to identify the rigid subunits. The resulting optimal subdivision is returned through a web page containing both interactive graphics and detailed data output. AVAILABILITY The PiSQRD web server, which requires Java, is available free of charge for academic users at http://pisqrd.escience-lab.org.

Advantages and challenges in coupling an ideal gas to atomistic models in adaptive resolution simulations

In adaptive resolution simulations, molecular fluids are modeled employing different levels of resolution in different subregions of the system. When traveling from one region to the other, particles change their resolution on the fly. One of the main advantages of such approaches is the computational efficiency gained in the coarse-grained region. In this respect the best coarse-grained system to employ in the low resolution region would be the ideal gas, making intermolecular force calculations in the coarse-grained subdomain redundant. In this case, however, a smooth coupling is challenging due to the high energetic imbalance between typical liquids and a system of non-interacting particles. In the present work, we investigate this approach, using as a test case the most biologically relevant fluid, water. We demonstrate that a successful coupling of water to the ideal gas can be achieved with current adaptive resolution methods, and discuss the issues that remain to be addressed.

Nuclear Quantum Effects in Water: A Multiscale Study

We outline a method to investigate the role of nuclear quantum effects in liquid water making use of a force field derived from ab initio simulations. Starting from a first-principles molecular dynamics simulation, we obtain an effective force field for bulk liquid water using the force-matching technique. After validating that our effective model reproduces the key structural and dynamic properties of the reference system, we use it to perform path integral simulations to investigate the role played by nuclear quantum effects on bulk water, probing radial distribution functions, vibrational spectra, and hydrogen bond fluctuations. Our approach offers a practical route to derive ab initio quality molecular models to study quantum effects at a low computational cost.