Wang-Landau molecular dynamics technique to search for low-energy conformational space of proteins

Multicanonical molecular dynamics (MD) is a powerful technique for sampling conformations on rugged potential surfaces such as protein. However, it is notoriously difficult to estimate the multicanonical temperature effectively. Wang and Landau developed a convenient method for estimating the density of states based on a multicanonical Monte Carlo method. In their method, the density of states is calculated autonomously during a simulation. In this paper we develop a set of techniques to effectively apply the Wang-Landau method to MD simulations. In the multicanonical MD, the estimation of the derivative of the density of states is critical. In order to estimate it accurately, we devise two original improvements. First, the correction for the density of states is made smooth by using the Gaussian distribution obtained by a short canonical simulation. Second, an approximation is applied to the derivative, which is based on the Gaussian distribution and the multiple weighted histogram technique. A test of this method was performed with small polypeptides, Met-enkephalin and Trp-cage, and it is demonstrated that Wang-Landau MD is consistent with replica exchange MD but can sample much larger conformational space.Comment: 8 pages, 7 figures, accepted for publication in Physical Review

Relevant distance between two different instances of the same potential energy in protein folding

In the context of complex systems and, particularly, of protein folding, a physically meaningful distance is defined which allows to make useful statistical statements about the way in which energy differences are modified when two different instances of the same potential-energy function are used. When the two instances arise from the fact that different algorithms or different approximations are used, the distance herein defined may be used to evaluate the relative accuracy of the two methods. When the difference is due to a change in the free parameters of which the potential depends on, the distance can be used to quantify, in each region of parameter space, the robustness of the modeling to such a change and this, in turn, may be used to assess the significance of a parameters' fit. Both cases are illustrated with a practical example: the study of the Poisson-based solvation energy in the Trp-Cage protein (PDB code 1L2Y).Comment: 20 pages, 6 figures, LaTeX file, elsart style. v1: Aknowledgments modified. v2: y-values of fig. 5 and 6 corrected. v3: Journal-ref added, aknowledgements modified and fig. 1 and 2 correcte

A physically meaningful method for the comparison of potential energy functions

In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient r has no units and allows only semi-quantitative statements to be made. Those that do have units of energy and whose value may be compared to a physically relevant scale, such as the root mean square deviation (RMSD), the mean error of the energies (ER), the standard deviation of the error (SDER) or the mean absolute error (AER), overestimate the distance between potentials. Moreover, their precise statistical meaning is far from clear. In this article, a new measure of the distance between potential energy functions is defined which overcomes the aforementioned difficulties. In addition, its precise physical meaning is discussed, the important issue of its additivity is investigated and some possible applications are proposed. Finally, two of these applications are illustrated with practical examples: the study of the van der Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y) and the comparison of different levels of the theory in the ab initio study of the Ramachandran map of the model peptide HCO-L-Ala-NH2.Comment: 30 pages, 7 figures, LaTeX, BibTeX. v2: A misspelling in the author's name has been corrected. v3: A new application of the method has been added at the end of section 9 and minor modifications have also been made in other sections. v4: Journal reference and minor corrections adde

Genetically encoded photocross-linkers determine the biological binding site of exendin-4 peptide in the N-terminal domain of the intact human glucagon-like peptide-1 receptor (GLP-1R)

The glucagon-like peptide-1 receptor (GLP-1R) is a key therapeutic target in the management of type II diabetes mellitus, with actions including regulation of insulin biosynthesis and secretion, promotion of satiety, and preservation of β-cell mass. Like most class B G protein-coupled receptors (GPCRs), there is limited knowledge linking biological activity of the GLP-1R with the molecular structure of an intact, full-length, and functional receptor·ligand complex. In this study, we have utilized genetic code expansion to site-specifically incorporate the photoactive amino acid p-azido-l-phenylalanine (azF) into N-terminal residues of a full-length functional human GLP-1R in mammalian cells. UV-mediated photolysis of azF was then carried out to induce targeted photocross-linking to determine the proximity of the azido group in the mutant receptor with the peptide exendin-4. Cross-linking data were compared directly with the crystal structure of the isolated N-terminal extracellular domain of the GLP-1R in complex with exendin(9–39), revealing both similarities as well as distinct differences in the mode of interaction. Generation of a molecular model to accommodate the photocross-linking constraints highlights the potential influence of environmental conditions on the conformation of the receptor·peptide complex, including folding dynamics of the peptide and formation of dimeric and higher order oligomeric receptor multimers. These data demonstrate that crystal structures of isolated receptor regions may not give a complete reflection of peptide/receptor interactions and should be combined with additional experimental constraints to reveal peptide/receptor interactions occurring in the dynamic, native, and full-length receptor state

Four small puzzles that Rosetta doesn't solve

A complete macromolecule modeling package must be able to solve the simplest structure prediction problems. Despite recent successes in high resolution structure modeling and design, the Rosetta software suite fares poorly on deceptively small protein and RNA puzzles, some as small as four residues. To illustrate these problems, this manuscript presents extensive Rosetta results for four well-defined test cases: the 20-residue mini-protein Trp cage, an even smaller disulfide-stabilized conotoxin, the reactive loop of a serine protease inhibitor, and a UUCG RNA tetraloop. In contrast to previous Rosetta studies, several lines of evidence indicate that conformational sampling is not the major bottleneck in modeling these small systems. Instead, approximations and omissions in the Rosetta all-atom energy function currently preclude discriminating experimentally observed conformations from de novo models at atomic resolution. These molecular "puzzles" should serve as useful model systems for developers wishing to make foundational improvements to this powerful modeling suite.Comment: Published in PLoS One as a manuscript for the RosettaCon 2010 Special Collectio

Folding Trp-cage to NMR resolution native structure using a coarse-grained model

We develop a coarse-grained protein model with a simplified amino acid interaction potential. We perform discrete molecular dynamics folding simulations of a small 20 residue protein - Trp-cage - from a fully extended conformation. We demonstrate the ability of the Trp-cage model to consistently reach conformations within 2angstrom backbone root-mean-square distance (RMSD) from the corresponding NMR structures. The minimum RMSD of Trp-cage conformations in the simulation can be smaller than 1.00angstrom. Our findings suggest that, at least for the case of Trp-cage, a detailed all-atom protein model with a physical molecular mechanics force field is not necessary to reach the native state of a protein. Our results also suggest that the success folding Trp-cage in our simulations and in the reported all-atom molecular mechanics simulations studies may be mainly due to the special stabilizing features specific to this miniprotein.Comment: 30 pages, 6 figures, and 4 table

Gateway to offending behaviour: permission-giving thoughts of online users of child sexual exploitation material.

The endorsement of permission-giving thoughts, or so-called cognitive distortions, has been discussed as a contributing factor in sexually abusive behaviour. The current study set out to explore the thinking patterns of offenders who have used/downloaded child sexual exploitation material (CSEM), based on a survey of professionals. A thematic analysis elicited four overarching themes, namely the Perceived Nature of Children (perception of children portrayed in CSEM, as well as children in general), Non-sexual Engagement with CSEM (motivating factors that are not inherently sexual in nature), Denial of Harm (perception of the level of harm caused by CSEM), and Expression of a General Sexual Preference (general interest in deviant sexual behaviour). These themes aid to explore the differences and similarities between contact and non-contact offenders and to improve the understanding of the role of permission-giving thoughts in this offending. Results are discussed in terms of their theoretical significance and future implications