104 research outputs found

    A virtual pebble game to ensemble average graph rigidity

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    Previous works have demonstrated that protein rigidity is related to thermodynamic stability, especially under conditions that favor formation of native structure. Mechanical network rigidity properties of a single conformation are efficiently calculated using the in- teger Pebble Game (PG) algorithm. However, thermodynamic properties require averaging over many samples from the ensemble of accessible conformations, leading to fluctuations within the network. We have developed a mean field Virtual Pebble Game (VPG) that provides a probabilistic description of the interaction network, meaning that sampling is not required. We extensively test the VPG algorithm over a variety of body-bar networks created on disordered lattices, from these calculations we fully characterize the network conditions under which the performance of the VPG offers the best solution. The VPG provides a satisfactory description of the ensemble averaged PG properties, especially in regions removed from the rigidity transition where ensemble fluctuations are greatest. In further experiments, we characterized the VPG across a structurally nonredundant dataset of 272 proteins. Using quantitative and visual assessments of the rigidity characterizations, the VPG results are shown to accurately reflect the ensemble averaged PG properties. That is, the fluctuating interaction network is well represented by a single calculation that re- places density functions with average values, thus speeding up the desired calculation by several orders of magnitude. Finally, we propose a new algorithm that is based on the combination of PG and VPG to balance the amount of sampling and mean field treatment. While offering interesting results, this approach needs to be further optimized to fully lever- age its utility. All these results positions the VPG as an efficient alternative to understand the mechanical role that chemical interactions play in maintaining protein stability

    Calculating Ensemble Averaged Descriptions of Protein Rigidity without Sampling

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    Previous works have demonstrated that protein rigidity is related to thermodynamic stability, especially under conditions that favor formation of native structure. Mechanical network rigidity properties of a single conformation are efficiently calculated using the integer body-bar Pebble Game (PG) algorithm. However, thermodynamic properties require averaging over many samples from the ensemble of accessible conformations to accurately account for fluctuations in network topology. We have developed a mean field Virtual Pebble Game (VPG) that represents the ensemble of networks by a single effective network. That is, all possible number of distance constraints (or bars) that can form between a pair of rigid bodies is replaced by the average number. The resulting effective network is viewed as having weighted edges, where the weight of an edge quantifies its capacity to absorb degrees of freedom. The VPG is interpreted as a flow problem on this effective network, which eliminates the need to sample. Across a nonredundant dataset of 272 protein structures, we apply the VPG to proteins for the first time. Our results show numerically and visually that the rigidity characterizations of the VPG accurately reflect the ensemble averaged properties. This result positions the VPG as an efficient alternative to understand the mechanical role that chemical interactions play in maintaining protein stability

    Rigidity and flexibility of biological networks

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    The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is given. We also briefly discuss the network aspects of cytoskeletal tensegrity. Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks. Our summary raises the possibility that the concepts of flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl

    Mechanistic insights into allosteric regulation of the A2A adenosine G protein-coupled receptor by physiological cations.

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    Cations play key roles in regulating G-protein-coupled receptors (GPCRs), although their mechanisms are poorly understood. Here, 19F NMR is used to delineate the effects of cations on functional states of the adenosine A2A GPCR. While Na+ reinforces an inactive ensemble and a partial-agonist stabilized state, Ca2+ and Mg2+ shift the equilibrium toward active states. Positive allosteric effects of divalent cations are more pronounced with agonist and a G-protein-derived peptide. In cell membranes, divalent cations enhance both the affinity and fraction of the high affinity agonist-bound state. Molecular dynamics simulations suggest high concentrations of divalent cations bridge specific extracellular acidic residues, bringing TM5 and TM6 together at the extracellular surface and allosterically driving open the G-protein-binding cleft as shown by rigidity-transmission allostery theory. An understanding of cation allostery should enable the design of allosteric agents and enhance our understanding of GPCR regulation in the cellular milieu

    Sublinear Computation Paradigm

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    This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms

    Conformational Ensemble Generation via Constraint-based Rigid-body Dynamics Guided by the Elastic Network Model

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    Conformational selection is the idea that proteins traverse positions on the conformational space represented by their potential energy landscape, and in particular positions considered as local energy minima. Conformational selection a useful concept in ligand binding studies and in exploring the behavior of protein structures within that energy landscape. Often, research that explores protein function requires the generation of conformational ensembles, or collections of protein conformations from a single structure. We describe a method of conformational ensemble generation that uses joint-constrained rigid-body dynamics (an approach that allows for explicit consideration of rigidity) and the elastic network model (providing structurally derived directional guides for the rigid-body model). We test our model on a selection of unbound proteins and examine the structural validity of the resulting ensembles, as well as the ability of such an approach to generate conformations with structural overlaps close to the ligand-bound versions of the proteins

    Rigidity Analysis for Modeling Protein Motion

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    Protein structure and motion plays an essential role in nearly all forms of life. Understanding both protein folding and protein conformational change can bring deeper insight to many biochemical processes and even into some devastating diseases thought to be the result of protein misfolding. Experimental methods are currently unable to capture detailed, large-scale motions. Traditional computational approaches (e.g., molecular dynamics and Monte Carlo simulations) are too expensive to simulate time periods long enough for anything but small peptide fragments. This research aims to model such molecular movement using a motion framework originally developed for robotic applications called the Probabilistic Roadmap Method. The Probabilistic Roadmap Method builds a graph, or roadmap, to model the connectivity of the movable object?s valid motion space. We previously applied this methodology to study protein folding and obtained promising results for several small proteins. Here, we extend our existing protein folding framework to handle larger proteins and to study a broader range of motion problems. We present a methodology for incrementally constructing roadmaps until they satisfy a set of evaluation criteria. We show the generality of this scheme by providing evaluation criteria for two types of motion problems: protein folding and protein transitions. Incremental Map Generation eliminates the burden of selecting a sampling density which in practice is highly sensitive to the protein under study and difficult to select. We also generalize the roadmap construction process to be biased towards multiple conformations of interest thereby allowing it to model transitions, i.e., motions between multiple known conformations, instead of just folding to a single known conformation. We provide evidence that this generalized motion framework models large-scale conformational change more realistically than competing methods. We use rigidity theory to increase the efficiency of roadmap construction by introducing a new sampling scheme and new distance metrics. It is only with these rigidity-based techniques that we were able to detect subtle folding differences between a set of structurally similar proteins. We also use it to study several problems related to protein motion including distinguishing secondary structure formation order, modeling hydrogen exchange, and folding core identification. We compare our results to both experimental data and other computational methods

    An Interfacial Thermodynamics Model for Protein Stability

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