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Energy Function (energy + function)
Kinds of Energy Function Selected AbstractsHuman motion reconstruction from monocular images using genetic algorithmsCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3-4 2004Jianhui Zhao Abstract This paper proposed an optimization approach for human motion recovery from the un-calibrated monocular images containing unlimited human movements. A 3D skeleton human model based on anatomy knowledge is employed with encoded biomechanical constraints for the joints. Energy Function is defined to represent the deviations between projection features and extracted image features. Reconstruction procedure is developed to adjust joints and segments of the human body into their proper positions. Genetic Algorithms are adopted to find the optimal solution effectively in the high dimensional parameter space by simultaneously considering all the parameters of the human model. The experimental results are analysed by Deviation Penalty. Copyright © 2004 John Wiley & Sons, Ltd. [source] Energy functions for FACTS devices with an energy-storage systemEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 5 2007V. Azbe Abstract An energy-storage system (ESS) can provide additional capabilities for FACTS devices in dynamic power-flow control, and in this way improve electric-power system stability. In order to assess their influence on the system's dynamic behavior or to determinate the device's control strategy using direct methods, proper energy functions for these devices are needed. In this paper the energy functions for the whole spectrum of FACTS devices with an ESS have been developed. For each of the devices various energy functions were proposed according to the control strategy applied. The energy functions were constructed as additional terms that can be added to any existing structure-preserving energy function (SPEF). Tests within a single-machine infinite-bus system proved the correctness of the proposed energy functions. The application of new energy functions was demonstrated on the problem of transient-stability assessment. Copyright © 2006 John Wiley & Sons, Ltd. [source] Energy-Based Image DeformationCOMPUTER GRAPHICS FORUM, Issue 5 2009Z. Karni Abstract We present a general approach to shape deformation based on energy minimization, and applications of this approach to the problems of image resizing and 2D shape deformation. Our deformation energy generalizes that found in the prior art, while still admitting an efficient algorithm for its optimization. The key advantage of our energy function is the flexibility with which the set of "legal transformations" may be expressed; these transformations are the ones which are not considered to be distorting. This flexibility allows us to pose the problems of image resizing and 2D shape deformation in a natural way and generate minimally distorted results. It also allows us to strongly reduce undesirable foldovers or self-intersections. Results of both algorithms demonstrate the effectiveness of our approach. [source] Complex-valued multidirectional associative memoryELECTRICAL ENGINEERING IN JAPAN, Issue 1 2007Masaki Kobayashi Abstract Hopfield model is a representative associative memory. It was improved to Bidirectional Associative Memory (BAM) by Kosko and to Multidirectional Associative Memory (MAM) by Hagiwara. They have two layers or multilayers. Since they have symmetric connections between layers, they ensure convergence. MAM can deal with multiples of many patterns, such as (x1,x2,,), where xm is the pattern on layer m. Copyright © 2004 Wiley Periodicals, Inc. Noest, Hirose, and Nemoto proposed complex-value Hopfield model. Lee proposed complex-valued Bidirectional Associative Memory. Zemel proved the rotation invariance of complex-valued Hopfield model. It means that the rotated pattern in also stored. In this paper, the complex-valued Multidirectional Associative Memory is proposed. The rotation invariance is also proved. Moreover it is shown by computer simulation that the differences of angles of given patterns are automatically reduced. At first we define complex-valued Multidirectional Associative Memory. Then we define the energy function of network. With the energy function, we prove that the network ensures convergence. Next, we define the learning law and show the characteristic of recall process. The characteristic means that the differences of angles of given patterns are automatically reduced. Especially we prove the following theorem. In the case that only a multiple of patterns is stored, if patterns with different angles are given to each layer, the differences are automatically reduced. Finally, we investigate whether the differences of angles influence the noise robustness. It is found to reduce the noise robustness, because the input to each layer becomes small. We show this by computer simulations. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(1): 39,45, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20387 [source] A matching method using edges with the rigid body assumptionELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 11 2009Shiho Tanaka Abstract In this paper, we propose the matching method using the edge image with the rigid-body assumption. We introduce the virtual intensity added to the edge image and regard it as the energy function. It is assumed that the objects to match each other are rigid. The edges are repeatedly moved to the direction which the energy function is reduced by parallel translation and rotation. The corresponding point between two images can be found when the function is minimum. Real images include the areas which have no or extreme intensity change. The proposed method is available in those cases since it uses features of the image, that is, the edges. We showed this advantage by experiments on motion estimation. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(11): 28,33, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10148 [source] Experiments on stabilizing receding horizon control of a direct drive manipulatorELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 5 2008Yasunori Kawai Abstract In this paper, the application of receding horizon control to a two-link direct drive robot arm is demonstrated. Instead of terminal constraints, a terminal cost on receding horizon control is used to guarantee stability, because of the computational demand. The key idea of this paper is to apply receding horizon control with a terminal cost derived from the energy function of the robot system. The energy function is defined as the control Lyapunov function by considering inverse optimality. In experimental results, stability and performance are compared with respect to the horizon length by applying receding horizon control and inverse optimal control to the robot arm. © 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(5): 33,40, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10113 [source] Energy functions for FACTS devices with an energy-storage systemEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 5 2007V. Azbe Abstract An energy-storage system (ESS) can provide additional capabilities for FACTS devices in dynamic power-flow control, and in this way improve electric-power system stability. In order to assess their influence on the system's dynamic behavior or to determinate the device's control strategy using direct methods, proper energy functions for these devices are needed. In this paper the energy functions for the whole spectrum of FACTS devices with an ESS have been developed. For each of the devices various energy functions were proposed according to the control strategy applied. The energy functions were constructed as additional terms that can be added to any existing structure-preserving energy function (SPEF). Tests within a single-machine infinite-bus system proved the correctness of the proposed energy functions. The application of new energy functions was demonstrated on the problem of transient-stability assessment. Copyright © 2006 John Wiley & Sons, Ltd. [source] A study on the multiswing instability region using Hopf bifurcation theory considering energy thresholdIEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 3 2006Takao Tsuji Member Abstract Transient stability is treated as one of the important constraints for calculating available transfer capability (ATC), especially in Japan. Therefore, to improve the time required for ATC calculation, development of high-speed transient stability analysis is required. For this analysis, a screening method that can recognize the serious case of fault will be greatly effective to solve the problem. Many screening methods on the first swing instability are proposed these days. However, a method based on multiswing instability has not been developed and its characteristic is not understood clearly. In this paper, the relationship between the nonlinear limit cycle and the energy function of a power system is examined using the Hopf bifurcation theory. A calculation method, which gives the critical transfer capability considering multiswing instability, is proposed. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source] On the numerical treatment of initial strains in biological soft tissuesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006E. Peña Abstract In this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress-free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible ,deformation gradient' field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress-free configuration, while in blood vessels the starting point is usually the load-free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are presented to show the performance of the strategies and to quantify the errors appearing in each of them. Copyright © 2006 John Wiley & Sons, Ltd. [source] A compact dynamic channel assignment scheme based on Hopfield networks for cellular radio systemsINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 1 2009A. Dang Abstract In this paper, a new channel assignment strategy named compact dynamic channel assignment (CDCA) is proposed. The CDCA differs from other strategies by consistently keeping the system in the utmost optimal state, and thus the scheme allows to determine a call succeeding or failing by local information instead of that of the whole network. It employs Hopfield neural networks for optimization which avoids the complicated assessment of channel compactness and guarantees optimum solutions for every assignment. A scheme based on Hopfield neural network is considered before; however, unlike others, in this algorithm an energy function is derived in such a way that for a neuron, the more a channel is currently being allocated in other cells, the more excitation the neuron will acquire, so as to guarantee each cluster using channels as few as possible. Performance measures in terms of the blocking probability, convergence rate and convergence time are obtained to assess the viability of the proposed scheme. Results presented show that the approach significantly reduces stringent requirements of searching space and convergence time. The algorithm is simple and straightforward, hence the efficient algorithm makes the real-time implementation of channel assignment based on neural network feasibility. Copyright © 2008 John Wiley & Sons, Ltd. [source] Texture-based parametric active contour for target detection and trackingINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 3 2009Ali Reza Vard Abstract In recent years, active contour models (ACM) have been considered as powerful tools for image segmentation and object tracking in computer vision and image processing applications. This article presents a new tracking method based on parametric active contour models. In the proposed method, a new pressure energy called "texture pressure energy" is added to the energy function of the parametric active contour model to detect and track a texture target object in a texture background. In this scheme, the texture features of the contour are calculated by a moment-based method. Then, by comparing these features with texture features of the target object, the contour curve is expanded or contracted to be adapted to the object boundaries. Experimental results show that the proposed method is more efficient and accurate in the tracking of objects compare to the traditional ones, when both object and background are textures in nature. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 187,198, 2009 [source] Matching pursuit-based shape representation and recognition using scale-spaceINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2006François Mendels Abstract In this paper, we propose an analytical low-level representation of images, obtained by a decomposition process, namely the matching pursuit (MP) algorithm, as a new way of describing objects through a general continuous description using an affine invariant dictionary of basis function (BFs). This description is used to recognize multiple objects in images. In the learning phase, a template object is decomposed, and the extracted subset of BFs, called meta-atom, gives the description of the object. This description is then naturally extended into the linear scale-space using the definition of our BFs, and thus providing a more general representation of the object. We use this enhanced description as a predefined dictionary of the object to conduct an MP-based shape recognition task into the linear scale-space. The introduction of the scale-space approach improves the robustness of our method: we avoid local minima issues encountered when minimizing a nonconvex energy function. We show results for the detection of complex synthetic shapes, as well as real world (aerial and medical) images. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 162,180, 2006 [source] Matching of uncalibrated stereo images by elastic deformationINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2004Wan-Chiu Li Abstract We propose a method for uncalibrated stereo matching. The method applies gradual elastic deformation to the line segments in a pair of images until they match with each other. By using an energy function and a neighborhood function, matching is performed in a coarse-to-fine manner. Our method gives point correspondences with a low proportion of outliers and is robust in the uncalibrated case (with no need to estimate the epipolar geometry). The computation complexity is proportional to the square of the number of line segments in the images, which is relatively efficient compared with other elaborate methods. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 198,205, 2004; Published online in Wiley Inter-Science (www.interscience.wiley.com). DOI 10.1002/ima.20024 [source] Theoretical investigations on analytical potential energy function and spectroscopic parameters for the state b3,u of dimer 7Li2INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2007De-Heng Shi Abstract The SAC-CI (symmetry-adapted-cluster configuration-interaction) method presented in Gaussian 03 program package is applied to investigate the adiabatic potential energy curves (PECs) of 7Li2(b3,u). These calculations are performed at numbers of basis sets, such as 6-311++G(3df,3pd), 6-311++G(2df,2pd), 6-311++G(df,pd), D95V++, D95(3df,3pd), D95(d,p), cc-PVTZ, 6-311++G and 6-311++G(d,p). All the ab initio calculated points are fitted to the analytic Murrell-Sorbie functions and then used to compute the spectroscopic parameters. The analytic potential energy function (APEF) for this b3,u state is reported. By comparison, the spectroscopic parameters reproduced by the APEF attained at 6-311++G(2df,2pd) are found to be very close to the latest experimental findings. With the APEF obtained at the SAC-CI/6-311++G(2df,2pd) level of theory, a total of 62 vibrational states is found when J = 0. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants for these vibrational states are also reported. The reasonable dissociation limit for this state is deduced using the calculated results at present. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot exampleINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2006Arun D. Mahindrakar Abstract Interconnection and damping assignment passivity-based control is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Hamiltonian structure with a desired energy function,that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. A class of underactuation degree one systems for which the partial differential equations can be explicitly solved,making the procedure truly constructive,was recently reported by the authors. In this brief note, largely motivated by the interesting Acrobot example, we pursue this investigation for two degrees-of-freedom systems where a constant inertia matrix can be assigned. We concentrate then our attention on potential energy shaping and give conditions under which an explicit solution of the associated partial differential equation can be obtained. Using these results we show that it is possible to swing-up the Acrobot from some configuration positions in the lower half plane, provided some conditions on the robot parameters are satisfied. Copyright © 2006 John Wiley & Sons, Ltd. [source] Structural refinement by restrained molecular-dynamics algorithm with small-angle X-ray scattering constraints for a biomoleculeJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2004Masaki Kojima A new algorithm to refine protein structures in solution from small-angle X-ray scattering (SAXS) data was developed based on restrained molecular dynamics (MD). In the method, the sum of squared differences between calculated and observed SAXS intensities was used as a constraint energy function, and the calculation was started from given atomic coordinates, such as those of the crystal. In order to reduce the contribution of the hydration effect to the deviation from the experimental (objective) curve during the dynamics, and purely as an estimate of the efficiency of the algorithm, the calculation was first performed assuming the SAXS curve corresponding to the crystal structure as the objective curve. Next, the calculation was carried out with `real' experimental data, which yielded a structure that satisfied the experimental SAXS curve well. The SAXS data for ribonuclease T1, a single-chain globular protein, were used for the calculation, along with its crystal structure. The results showed that the present algorithm was very effective in the refinement and adjustment of the initial structure so that it could satisfy the objective SAXS data. [source] Identifying and reducing error in cluster-expansion approximations of protein energiesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 16 2010Seungsoo Hahn Abstract Protein design involves searching a vast space for sequences that are compatible with a defined structure. This can pose significant computational challenges. Cluster expansion is a technique that can accelerate the evaluation of protein energies by generating a simple functional relationship between sequence and energy. The method consists of several steps. First, for a given protein structure, a training set of sequences with known energies is generated. Next, this training set is used to expand energy as a function of clusters consisting of single residues, residue pairs, and higher order terms, if required. The accuracy of the sequence-based expansion is monitored and improved using cross-validation testing and iterative inclusion of additional clusters. As a trade-off for evaluation speed, the cluster-expansion approximation causes prediction errors, which can be reduced by including more training sequences, including higher order terms in the expansion, and/or reducing the sequence space described by thecluster expansion. This article analyzes the sources of error and introduces a method whereby accuracy can be improved by judiciously reducing the described sequence space. The method is applied to describe the sequence,stability relationship for several protein structures: coiled-coil dimers and trimers, a PDZ domain, and T4 lysozyme as examples with computationally derived energies, and SH3 domains in amphiphysin-1 and endophilin-1 as examples where the expanded pseudo-energies are obtained from experiments. Our open-source software package Cluster Expansion Version 1.0 allows users to expand their own energy function of interest and thereby apply cluster expansion to custom problems in protein design. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010 [source] Flexible protein-protein docking based on Best-First search algorithmJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2010Efrat Noy Abstract We developed a new high resolution protein-protein docking method based on Best-First search algorithm that loosely imitates protein-protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; "high," "medium," "acceptable," and "incorrect"). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side-chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side-chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein-protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010 [source] Coarse-grained model of nucleic acid basesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2010Maciej Maciejczyk Abstract Atomistic simulations of nucleic acids are prohibitively expensive and, consequently, reduced models of these compounds are of great interest in the field. In this work, we propose a physics-based coarse-grained model of nucleic-acid bases in which each base is represented by several (3,5) interaction centers. van der Waals interactions are modeled by Lennard-Jones spheres with a 12,6 potential energy function. The charge distribution is modeled by a set of electric dipole moments located at the centers of the Lennard-Jones spheres. The method for computing the Lennard-Jones parameters, electric dipole moments (their magnitude and orientation) and positions of the interaction centers is described. Several models with different numbers of interaction centers were tested. The model with three-center cytosine, four-center guanine, four-center thymine, and five-center adenine satisfactorily reproduces the canonical Watson,Crick hydrogen bonding and stacking interaction energies of the all-atom AMBER model. The computation time with the coarse-grained model is reduced seven times compared with that of the all-atom model. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010 [source] New angle-dependent potential energy function for backbone,backbone hydrogen bond in protein,protein interactionsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2010Hwanho Choi Abstract Backbone,backbone hydrogen bonds (BBHBs) are one of the most abundant interactions at the interface of protein,protein complex. Here, we propose an angle-dependent potential energy function for BBHB based on density functional theory (DFT) calculations and the operation of a genetic algorithm to find the optimal parameters in the potential energy function. The angular part of the energy funtion is assumed to be the product of the power series of sine and cosine functions with respect to the two angles associated with BBHB. Two radial functions are taken into account in this study: Morse and Leonard-Jones 12-10 potential functions. Of these two functions under consideration, the former is found to be more accurate than the latter in terms of predicting the binding energies obtained from DFT calculations. The new HB potential function also compares well with the knowledge-based potential derived by applying Boltzmann statistics for a variety of protein,protein complexes in protein data bank. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010 [source] Soft energy function and generic evolutionary method for discriminating native from nonnative protein conformationsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2008Yi-yuan Chiu Abstract We have developed a soft energy function, termed GEMSCORE, for the protein structure prediction, which is one of emergent issues in the computational biology. The GEMSORE consists of the van der Waals, the hydrogen-bonding potential and the solvent potential with 12 parameters which are optimized by using a generic evolutionary method. The GEMSCORE is able to successfully identify 86 native proteins among 96 target proteins on six decoy sets from more 70,000 near-native structures. For these six benchmark datasets, the predictive performance of the GEMSCORE, based on native structure ranking and Z -scores, was superior to eight other energy functions. Our method is based solely on a simple and linear function and thus is considerably faster than other methods that rely on the additional complex calculations. In addition, the GEMSCORE recognized 17 and 2 native structures as the first and the second rank, respectively, among 21 targets in CASP6 (Critical Assessment of Techniques for Protein Structure Prediction). These results suggest that the GEMSCORE is fast and performs well to discriminate between native and nonnative structures from thousands of protein structure candidates. We believe that GEMSCORE is robust and should be a useful energy function for the protein structure prediction. © 2008 Wiley Periodicals, Inc. J Comput Chem 2008 [source] On searching in, sampling of, and dynamically moving through conformational space of biomolecular systems: A reviewJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2008Markus Christen Abstract Methods to search for low-energy conformations, to generate a Boltzmann-weighted ensemble of configurations, or to generate classical-dynamical trajectories for molecular systems in the condensed liquid phase are briefly reviewed with an eye to application to biomolecular systems. After having chosen the degrees of freedom and method to generate molecular configurations, the efficiency of the search or sampling can be enhanced in various ways: (i) efficient calculation of the energy function and forces, (ii) application of a plethora of search enhancement techniques, (iii) use of a biasing potential energy term, and (iv) guiding the sampling using a reaction or transition pathway. The overview of the available methods should help the reader to choose the combination that is most suitable for the biomolecular system, degrees of freedom, interaction function, and molecular or thermodynamic properties of interest. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Can a physics-based, all-atom potential find a protein's native structure among misfolded structures?JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2007Abstract Recent work has shown that physics-based, all-atom energy functions (AMBER, CHARMM, OPLS-AA) and local minimization, when used in scoring, are able to discriminate among native and decoy structures. Yet, there have been only few instances reported of the successful use of physics based potentials in the actual refinement of protein models from a starting conformation to one that ends in structures, which are closer to the native state. An energy function that has a global minimum energy in the protein's native state and a good correlation between energy and native-likeness should be able to drive model structures closer to their native structure during a conformational search. Here, the possible reasons for the discrepancy between the scoring and refinement results for the case of AMBER potential are examined. When the conformational search via molecular dynamics is driven by the AMBER potential for a large set of 150 nonhomologous proteins and their associated decoys, often the native minimum does not appear to be the lowest free energy state. Ways of correcting the potential function in order to make it more suitable for protein model refinement are proposed. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] SODOCK: Swarm optimization for highly flexible protein,ligand dockingJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2007Hung-Ming Chen Abstract Protein,ligand docking can be formulated as a parameter optimization problem associated with an accurate scoring function, which aims to identify the translation, orientation, and conformation of a docked ligand with the lowest energy. The parameter optimization problem for highly flexible ligands with many rotatable bonds is more difficult than that for less flexible ligands using genetic algorithm (GA)-based approaches, due to the large numbers of parameters and high correlations among these parameters. This investigation presents a novel optimization algorithm SODOCK based on particle swarm optimization (PSO) for solving flexible protein,ligand docking problems. To improve efficiency and robustness of PSO, an efficient local search strategy is incorporated into SODOCK. The implementation of SODOCK adopts the environment and energy function of AutoDock 3.05. Computer simulation results reveal that SODOCK is superior to the Lamarckian genetic algorithm (LGA) of AutoDock, in terms of convergence performance, robustness, and obtained energy, especially for highly flexible ligands. The results also reveal that PSO is more suitable than the conventional GA in dealing with flexible docking problems with high correlations among parameters. This investigation also compared SODOCK with four state-of-the-art docking methods, namely GOLD 1.2, DOCK 4.0, FlexX 1.8, and LGA of AutoDock 3.05. SODOCK obtained the smallest RMSD in 19 of 37 cases. The average 2.29 Å of the 37 RMSD values of SODOCK was better than those of other docking programs, which were all above 3.0 Å. © 2006 Wiley Periodicals, Inc. J Comput Chem 28: 612,623, 2007 [source] Electrostatic energies and forces computed without explicit interparticle interactions: A linear time complexity formulationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2005Robert J. Petrella Abstract A rapid method for the calculation of the electrostatic energy of a system without a cutoff is described in which the computational time grows linearly with the number of particles or charges. The inverse of the distance is approximated as a polynomial, which is then transformed into a function whose terms involve individual particles, instead of particle pairs, by a partitioning of the double sum. In this way, the electrostatic energy that is determined by the interparticle interactions is obtained without explicit calculation of these interactions. For systems of positive charges positioned on a face-centered cubic lattice, the calculation of the energy by the new method is shown to be faster than the calculation of the exact energy, in many cases by an order of magnitude, and to be accurate to within 1,2%. The application of this method to increase the accuracy of conventional truncation-based calculations in condensed-phase systems is also demonstrated by combining the approximated long-range electrostatic interactions with the exact short-range interactions in a "hybrid" calculation. For a 20-Å sphere of water molecules, the forces are shown to be six times as accurate using this hybrid method as those calculated with conventional truncation of the electrostatic energy function at 12 Å. This is accomplished with a slight increase in speed, and with a sevenfold increase in speed relative to the exact all-pair calculation. Structures minimized with the hybrid function are shown to be closer to structures minimized with an exact all-pair electrostatic energy function than are those minimized with a conventional 13-Å cutoff-based electrostatic energy function. Comparison of the energies and forces calculated with the exact method illustrate that the absolute errors obtained with standard truncation can be very large. The extension of the current method to other pairwise functions as well as to multibody functions, is described. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 755,787, 2005 [source] Folding funnels: The key to robust protein structure predictionJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2002Corey Hardin Abstract Natural proteins fold because their free energy landscapes are funneled to their native states. The degree to which a model energy function for protein structure prediction can avoid the multiple minima problem and reliably yield at least low-resolution predictions is also dependent on the topography of the energy landscape. We show that the degree of funneling can be quantitatively expressed in terms of a few averaged properties of the landscape. This allows us to optimize simplified energy functions for protein structure prediction even in the absence of homology information. Here we outline the optimization procedure in the context of associative memory energy functions originally introduced for tertiary structure recognition and demonstrate that even partially funneled landscapes lead to qualitatively correct, low-resolution predictions. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 138,146, 2002 [source] Soft protein,protein docking in internal coordinatesPROTEIN SCIENCE, Issue 2 2002Juan Fernández-Recio PDB, Protein Data Bank; ICM, Internal Coordinate Mechanics; RMSD, root-mean-square deviation Abstract The association of two biological macromolecules is a fundamental biological phenomenon and an unsolved theoretical problem. Docking methods for ab initio prediction of association of two independently determined protein structures usually fail when they are applied to a large set of complexes, mostly because of inaccuracies in the scoring function and/or difficulties on simulating the rearrangement of the interface residues on binding. In this work we present an efficient pseudo-Brownian rigid-body docking procedure followed by Biased Probability Monte Carlo Minimization of the ligand interacting side-chains. The use of a soft interaction energy function precalculated on a grid, instead of the explicit energy, drastically increased the speed of the procedure. The method was tested on a benchmark of 24 protein,protein complexes in which the three-dimensional structures of their subunits (bound and free) were available. The rank of the near-native conformation in a list of candidate docking solutions was <20 in 85% of complexes with no major backbone motion on binding. Among them, as many as 7 out of 11 (64%) protease-inhibitor complexes can be successfully predicted as the highest rank conformations. The presented method can be further refined to include the binding site predictions and applied to the structures generated by the structural proteomics projects. All scripts are available on the Web. [source] Modeling of loops in protein structuresPROTEIN SCIENCE, Issue 9 2000András Fiser Abstract Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4,, 8,, and 12,residue loop predictions, respectively, had <2 Å RMSD error for the mainchain N, Ca, C, and O atoms; the average accuracies were 0.59 6 0.05, 1.16 6 0.10, and 2.61 6 0.16 Å, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 Å, the average loop prediction error increased by 180, 25, and 3% for 4,, 8,, and 12,residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling. [source] Energy absorption capacity; a new concept for stability analysis of nonlinear dynamic systems,ASIAN JOURNAL OF CONTROL, Issue 1 2009Ali Akbar Jamshidifar Abstract Stability is the main concern considered for every system. Generally the well-known Lyapunov and input-output stability methods are utilized for the stability analysis of nonlinear systems. These methods face serious difficulties as the size and complexity of the systems increases. In this paper a new approach is presented to overcome this problem by introducing a new concept "Energy Absorption Capacity" (EAC) for every component. The EAC of the system can be derived from its component EACs considering their interaction. It is shown that the stability of every individual component is assured if its EAC has a positive value. The proposed approach is less conservative compared to a Lyapunov-based approach. This is due to its reliance on EAC as the extreme value of energy function rather than the function itself. Some examples are given to support the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Refinement of protein crystal structures using energy restraints derived from linear-scaling quantum mechanicsACTA CRYSTALLOGRAPHICA SECTION D, Issue 3 2005Ning Yu A novel method is proposed in which combined restraints derived from linear-scaling semiempirical quantum-mechanical (QM) calculations and X-ray diffraction data are combined to refine crystal structures of proteins. Its performance has been tested on a small protein molecule, bovine pancreatic trypsin inhibitor (BPTI). The refinement involves minimization of the sum of a geometric energy function and an X-ray target function based on either the least-squares residual or the maximum-likelihood formalism. For comparison, similar refinement runs have also been performed using energy restraints derived from the force field available in the Crystallography & NMR System (CNS) program. The QM refinements were carried out with weights that were varied by several orders of magnitude and the optimal weights were identified by observing the trend in the final free R values, QM heats of formation and coordinate root-mean-square deviations (r.m.s.d.s) from the crystal structure. It is found that the QM weights are typically smaller but generally on the same scale as the molecular-mechanics (MM) weights for the respective X-ray target functions. The crystallographic R, free R, real-space R values and correlation coefficients based on the structures refined with the energy restraints derived from our QM calculations and Engh and Huber parameters are comparable, suggesting that the QM restraints are capable of maintaining reasonable stereochemistry to a similar degree as the force-field parameters. A detailed inspection of the structures refined with the QM and MM energy restraints reveals that one of the common differences between them and the crystal structure is that the strained bond angles in the crystal structure are corrected after energetically restrained refinements. Systematic differences in certain bond lengths between the QM-refined structures and the statistical averages of experimental structures have also been observed and discussed. [source] | ||||||||||||||||||||||