Molecular jamming - the cystine slipknot mechanical clamp in all-atom simulations

A recent survey of 17 134 proteins has identified a new class of proteins which are expected to yield stretching induced force-peaks in the range of 1 nN. Such high force peaks should be due to forcing of a slip-loop through a cystine ring, i.e. by generating a cystine slipknot. The survey has been performed in a simple coarse grained model. Here, we perform all-atom steered molecular dynamics simulations on 15 cystine knot proteins and determine their resistance to stretching. In agreement with previous studies within a coarse grained structure based model, the level of resistance is found to be substantially higher than in proteins in which the mechanical clamp operates through shear. The large stretching forces arise through formation of the cystine slipknot mechanical clamp and the resulting steric jamming. We elucidate the workings of such a clamp in an atomic detail. We also study the behavior of five top strength proteins with the shear-based mechanostability in which no jamming is involved. We show that in the atomic model, the jamming state is relieved by moving one amino acid at a time and there is a choice in the selection of the amino acid that advances the first. In contrast, the coarse grained model also allows for a simultaneous passage of two amino acids

Combining Coarse-Grained Protein Models with Replica-Exchange All-Atom Molecular Dynamics

We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.Comment: 12 pages, 4 figure

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.Comment: 28 pages, 18 figure

Open Boundary Simulations of Proteins and Their Hydration Shells by Hamiltonian Adaptive Resolution Scheme

The recently proposed Hamiltonian Adaptive Resolution Scheme (H-AdResS) allows to perform molecular simulations in an open boundary framework. It allows to change on the fly the resolution of specific subset of molecules (usually the solvent), which are free to diffuse between the atomistic region and the coarse-grained reservoir. So far, the method has been successfully applied to pure liquids. Coupling the H-AdResS methodology to hybrid models of proteins, such as the Molecular Mechanics/Coarse-Grained (MM/CG) scheme, is a promising approach for rigorous calculations of ligand binding free energies in low-resolution protein models. Towards this goal, here we apply for the first time H-AdResS to two atomistic proteins in dual-resolution solvent, proving its ability to reproduce structural and dynamic properties of both the proteins and the solvent, as obtained from atomistic simulations.Comment: This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Chemical Theory and Computation, copyright \c{opyright} American Chemical Society after peer review and technical editing by the publishe

Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge based potentials based on pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities reference ratio distributions deriving from the application of the reference ratio method. This new view is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures

Structure and stability of chiral beta-tapes: a computational coarse-grained approach

We present two coarse-grained models of different levels of detail for the description of beta-sheet tapes obtained from equilibrium self-assembly of short rationally designed oligopeptides in solution. Here we only consider the case of the homopolymer oligopeptides with the identical sidegroups attached, in which the tapes have a helicoid surface with two equivalent sides. The influence of the chirality parameter on the geometrical characteristics, namely the diameter, inter-strand distance and pitch, of the tapes have been investigated. The two models are found to produceequivalent results suggesting a considerable degree of universality in conformations of the tapes.Comment: 24 pages, 5 PS figures. Accepted to J. Chem. Phy

Coarse-grained simulations of RNA and DNA duplexes

Although RNAs play many cellular functions little is known about the dynamics and thermodynamics of these molecules. In principle, all-atom molecular dynamics simulations can investigate these issues, but with current computer facilities, these simulations have been limited to small RNAs and to short times. HiRe-RNA, a recently proposed high-resolution coarse-grained for RNA that captures many geometric details such as base pairing and stacking, is able to fold RNA molecules to near-native structures in a short computational time. So far it had been applied to simple hairpins, and here we present its application to duplexes of a couple dozen nucleotides and show how with our model and with Replica Exchange Molecular Dynamics (REMD) we can easily predict the correct double helix from a completely random configuration and study the dissociation curve. To show the versatility of our model, we present an application to a double stranded DNA molecule as well. A reconstruction algorithm allows us to obtain full atom structures from the coarse-grained model. Through atomistic Molecular Dynamics (MD) we can compare the dynamics starting from a representative structure of a low temperature replica or from the experimental structure, and show how the two are statistically identical, highlighting the validity of a coarse-grained approach for structured RNAs and DNAs.Comment: 28 pages, 11 figure