Detecting Repetitions and Periodicities in Proteins by Tiling the Structural Space

The notion of energy landscapes provides conceptual tools for understanding the complexities of protein folding and function. Energy Landscape Theory indicates that it is much easier to find sequences that satisfy the "Principle of Minimal Frustration" when the folded structure is symmetric (Wolynes, P. G. Symmetry and the Energy Landscapes of Biomolecules. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 14249-14255). Similarly, repeats and structural mosaics may be fundamentally related to landscapes with multiple embedded funnels. Here we present analytical tools to detect and compare structural repetitions in protein molecules. By an exhaustive analysis of the distribution of structural repeats using a robust metric we define those portions of a protein molecule that best describe the overall structure as a tessellation of basic units. The patterns produced by such tessellations provide intuitive representations of the repeating regions and their association towards higher order arrangements. We find that some protein architectures can be described as nearly periodic, while in others clear separations between repetitions exist. Since the method is independent of amino acid sequence information we can identify structural units that can be encoded by a variety of distinct amino acid sequences

Seismotectonic study of the Fergana region (Southern Kyrgyzstan): distribution and kinematics of local seismicity

We present new seismicity and focal-mechanism data for the Fergana basin and surrounding mountain belts in western Kyrgyzstan from a temporary local seismic network. A total of 210 crustal earthquakes with hypocentral depths shallower than 25 km were observed during a 12-month period in 2009/2010. The hypocenter distribution indicates a complex net of seismically active structures. The seismicity derived in this study is mainly concentrated at the edges of the Fergana basin, whereas the observed rate of seismicity within the basin is low. The seismicity at the dominant tectonic feature of the region, the Talas-Fergana fault, is likewise low, so the fault seems to be inactive or locked. To estimate the uncertainties of earthquake locations derived in this study, a strong explosion with known origin time and location is used as a ground truth calibration event which suggests a horizontal and vertical accuracy of about 1 km for our relocations. We derived 35 focal mechanisms using first motion polarities and retrieved a set of nine moment tensor solutions for earthquakes with moment magnitude (Mw) ranging from 3.3 to 4.9 by waveform inversion. The solutions reveal both thrust and strike-slip mechanisms compatible with a NW-SE direction of compression for the Fergana region. Two previously unknown tectonic structures in the Fergana region could be identified, both featuring strike-slip kinematics. The combined analysis of the results derived in this study allowed a detailed insight into the currently active tectonic structures and their kinematics where little information had previously been available

Anisotropic coarse-grained statistical potentials improve the ability to identify native-like protein structures

We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with alpha-helical and beta-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues. Using the local reference frames and histograms of the radial and angular correlation functions for a standard set of non-homologue protein structures, we construct the anisotropic pair potentials. The performance of the orientation dependent potentials was studied using a large database of decoy proteins. The results demonstrate that the new distance and orientation dependent residue-residue potentials present a significantly improved ability to recognize native folds from a set of native and decoy protein structures.Comment: Submitted to "The Journal of Chemical Physics

Replica-Exchange Simulated Tempering Method for Simulations of Frustrated Systems

We propose a new method for the determination of the weight factor for the simulated tempering method. In this method a short replica-exchange simulation is performed and the simulated tempering weight factor is obtained by the multiple-histogram reweighting techniques. The new algorithm is particularly useful for studying frustrated systems with rough energy landscape where the determination of the simulated tempering weight factor by the usual iterative process becomes very difficult. The effectiveness of the method is illustrated by taking an example for protein folding.Comment: 8 pages, (ReVTeX), 5 figures, Chem. Phys. Lett., submitte

Detecting repetitions and periodicities in proteins by tiling the structural space

The notion of energy landscapes provides conceptual tools for understanding the complexities of protein folding and function. Energy landscape theory indicates that it is much easier to find sequences that satisfy the “Principle of Minimal Frustration” when the folded structure is symmetric (Wolynes, P. G. Symmetry and the Energy Landscapes of Biomolecules. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 14249–14255). Similarly, repeats and structural mosaics may be fundamentally related to landscapes with multiple embedded funnels. Here we present analytical tools to detect and compare structural repetitions in protein molecules. By an exhaustive analysis of the distribution of structural repeats using a robust metric, we define those portions of a protein molecule that best describe the overall structure as a tessellation of basic units. The patterns produced by such tessellations provide intuitive representations of the repeating regions and their association toward higher order arrangements. We find that some protein architectures can be described as nearly periodic, while in others clear separations between repetitions exist. Since the method is independent of amino acid sequence information, we can identify structural units that can be encoded by a variety of distinct amino acid sequences.Fil: Parra, Rodrigo Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Espada, Rocío. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Sánchez Miguel, Ignacio Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Sippl, Manfred J.. Universität Salzburg; AustriaFil: Ferreiro, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentin

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

The 2008 Nura earthquake sequence at the Pamir-Tian Shan collision zone, southern Kyrgyzstan

We analyzed the 5 October 2008, Mw 6.6 Nura earthquake, which occurred in the border triangle between Kyrgyzstan, Tajikistan, and China, and its aftershock series based on locally recorded seismic data. More than 3000 aftershocks were detected and located, using a double-difference technique and a regional 3-D velocity model. Moment tensors for the main event and the 42 largest aftershocks were determined by full-waveform inversion of long-period displacement seismograms. The Nura main shock was a shallow (∼3.4 km deep) reverse faulting event and occurred on an approximately east striking rupture plane situated east of the Alai Valley, along the Pamir Frontal Thrust of the Trans Alai Range, the leading edge of the Pamir Thrust System. Its presumed rupture plane dips steeply (∼59°) southward. The aftershocks constitute several distinct clusters that can be attributed to the activation of an array of individual faults including the one that was presumably broken by the main shock. Background seismicity occurred mainly further south, behind the crest of the Trans Alai Range, in an approximately east trending zone of dextral transpressional motion in the interior of the Pamir Thrust System. We show that nearly all reactivated structures lie in regions that experienced an increase in Coulomb stress due to the main shock rupture. The Nura earthquake sequence indicates slip partitioning between north-south shortening that creates large earthquakes along the Pamir Frontal Thrust, and lateral movement in the interior of the Pamir Thrust System.This research was funded by DFG bundle TIPAGE (PAK 443), the CAME project bundle TIPTIMON funded by the German Federal Ministry of Education and Research (support code 03G0809), and GFZ. We acknowledge funding for the Earthquake Task Force deployment by GFZ and the Hannover Rück reinsurance company

Molecular dynamics of C-peptide of ribonuclease A studied by replica-exchange Monte Carlo method and diffusion theory

Generalized-ensemble algorithm and diffusion theory have been combined in order to compute the dynamical properties monitored by nuclear magnetic resonance experiments from efficient and reliable evaluation of statistical averages. Replica-exchange Monte Carlo simulations have been performed with a C-peptide analogue of ribonuclease A, and Smoluchowski diffusion equations have been applied. A fairly good agreement between the calculated and measured $^1$H-NOESY NMR cross peaks has been obtained. The combination of these advanced and continuously improving statistical tools allows the calculation of a wide variety of dynamical properties routinely obtained by experiments.Comment: 17 pages, 5 figures, (LaTeX); Chemical Physics Letters, in pres

Stochastic dynamics simulations in a new generalized ensemble

We develop a formulation for molecular dynamics, Langevin, and hybrid Monte Carlo algorithms in the recently proposed generalized ensemble that is based on a physically motivated realisation of Tsallis weights. The effectiveness of the methods are tested with an energy function for a protein system. Simulations in this generalized ensemble by the three methods are performed for a penta peptide, Met-enkephalin. For each algorithm, it is shown that from only one simulation run one can not only find the global-minimum-energy conformation but also obtain probability distributions in canonical ensemble at any temperature, which allows the calculation of any thermodynamic quantity as a function of temperature.Comment: to appear in Chem. Phy. Let