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Geometric and potential driving formation and evolution of biomolecular surfaces

JOURNAL OF MATHEMATICAL BIOLOGY 2009年第2期59卷 193-231页

作者： Bates, P. W. Chen, Zhan Sun, Yuhui Wei, Guo-Wei Zhao, Shan Michigan State Univ Dept Math E Lansing MI 48824 USA Michigan State Univ Dept Elect & Comp Engn E Lansing MI 48824 USA Univ Alabama Dept Math Tuscaloosa AL 35487 USA

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent-solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank-Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.

关键词： Biomolecular surface formation and evolution Mean curvature flow Potential driven geometric flows High order geometric flows Stochastic geometric flows computational algorithm

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computational Scheme for Invariantly Unbiased Estimation of Linear Operators in a Given Class

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computational MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第4期48卷 549-560页

作者： Bulychev, Yu. G. Eliseev, A. V. Rostov Mil Inst Missile Forces Rostov Na Donu 344027 Russia

The values of linear operators of a given class are estimated in the case of measurements including piecewise continuous noise of deterministic structure with unknown parameters. A computational scheme producing unbia... 详细信息

关键词： estimation of linear operators invariance of linear estimates least squares method computational algorithm statistical methods for error estimation

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computational algorithmic procedure of optimal inventory policy involving a negative exponential crashing cost and variable lead time demand

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APPLIED MATHEMATICS AND COMPUTATION 2007年第2期184卷 798-808页

作者： Wu, Jong-Wuu Lee, Wen-Chuan Tsai, Hui-Yin Chang Jung Christian Univ Dept Int Business Tainan 71101 Taiwan Natl Chiayi Univ Dept Appl Math Chiayi 60004 Taiwan Yuanpei Univ Dept Business Adm Hsinchu 300 Taiwan

When the demand of the different customers are not identical in the lead time, we cannot use only a single distribution (such as Ouyang et al. (1996) [L.Y. Ouyang, N.C. Yeh, K.S. Wu, Mixture inventory model with backorders and lost sales for variable lead time, Journal of the Operational Research Society 47 (1996) 829-832] using normal distribution) to describe the demand of the lead time. Hence, in this paper, we extend the models of Ouyang et al. (1996) and Ouyang and Wu (1998) [L.Y. Ouyang, K.S. Wu, A minimax distribution free procedure for mixed inventory model with variable lead time, International Journal of Production Economics 56-57 (1998) 511-516] by considering the mixture of normal distributions and the mixture of free distributions (see Everitt and Hand (1981) [B.S. Everitt, D.J. Hand, Finite Mixture Distribution, Chapman and Hall, London, NY, 1981]), respectively. Moreover, we quote the continuous model which the total crashing cost is related to the lead time by a negative exponential function (such as Ben-Daya and Raouf (1994) [M. Ben-Daya, A. Raouf, Inventory models involving lead time as decision variable, Journal of the Operational Research Society 45 (1994) 579-582]). Finally, we give two algorithmic procedures to find the optimal inventory policy and two numerical examples to illustrate the results. (c) 2006 Elsevier Inc. All rights reserved.

关键词： crashing cost order quantity mixture of distributions backorders lost sales computational algorithm

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Solution of inverse complex problems for multicomponent elliptic parabolic distributed systems

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JOURNAL OF AUTOMATION AND INFORMATION SCIENCES 2008年第5期40卷 1-29页

作者： Sergienko, I. V. Deineka, V. S. Natl Acad Sci Ukraine VM Glushkov Cybernet Inst Kiev Ukraine

For a series of the inverse complex problems of parameters restore for elliptic parabolic multicomponent distributed systems the computational algorithms are proposed for realization of gradient methods on the basis of solution of direct and conjugate problems in weak formulations. The proposed approach eliminates the need for explicit constructing Lagrangian functionals and using Green functions.

关键词： inverse complex problem elliptic parabolic multicomponent distributed system gradient methods computational algorithm direct and conjugate problem in a weak formulation

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Automatic Parallel Generation of Tetrahedral Grids by Using a Domain Decomposition Approach

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computational MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第8期48卷 1367-1375页

作者： Andrae, H. Gluchshenko, O. N. Ivanov, E. G. Kudryavtsev, A. N. Fraunhofer Inst Techno & Wirtschaftsmath D-67663 Kaiserslautern Germany Tech Univ Kaiserslautern Kaiserslautern Germany Russian Acad Sci Khristianovich Inst Theoret & Appl Mech Novosibirsk 630090 Russia

An algorithm for the automatic parallel generation of three-dimensional unstructured grids based on geometric domain decomposition is proposed. A software package based on this algorithm is described. Examples of generating meshes for some application problems on a multiprocessor computer are presented. It is shown that the parallel algorithm can significantly ( by a factor of several tens) reduce the mesh generation time. Moreover, it can easily generate meshes with as many as 5 x 10(7) elements, which can hardly be generated sequentially. Issues concerning the speedup and the improvement of the efficiency of the computations and of the quality of the resulting meshes are discussed.

关键词： tetrahedral grid generation domain decomposition automatic parallel grid generation computational algorithm

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Constructing Open-Loop and Closed-Loop Solutions of Linear-Quadratic Optimal Control Problems

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computational MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第10期48卷 1715-1745页

作者： Gabasov, R. Kirillova, F. M. Pavlenok, N. S. Belarusian State Univ Minsk 220030 BELARUS Belarussian Acad Sci Inst Math Minsk 220072 BELARUS

A linear-quadratic optimal control problem subject to geometric constraints on the controls is studied. Techniques for finding the optimal open-loop control and constructing a closed-loop control are described. The problem solution can include special intervals and sections with chattering modes. The proposed techniques make it possible to find special intervals and construct realizable approximations of unrealizable chattering modes to any degree of accuracy.

关键词： linear-quadratic optimal control problem construction of optimal open-loop control construction of closed-loop control special modes computational algorithm

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Optimal Measurement Feedback Control of Finite-time Continuous Linear Systems

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IFAC Proceedings Volumes 2008年第2期41卷 15339-15344页

作者： Natalia Dmitruk Rolf Findeisen Frank Allgöwer Institute of Mathematics National Academy of Sciences of Belarus Surganovstr. 11 220072 Minsk Belarus Institute for Automation Engineering Otto-von-Guericke Universität Magdeburg Universitätsplatz 2 39016 Magdeburg Germany Institute for Systems Theory and Automatic Control University of Stuttgart Pfaffenwaldring 9 70550 Stuttgart Germany

We consider optimal control of linear continuous time systems subject to constrained inputs based on output measurements that are subject to set-membership uncertainties. The objective is to steer the system in a fixed finite-time to a given polyhedral set while minimizing a linear terminal cost function. To achieve this objective a min-max optimal control strategy is proposed, taking into account that at future time instants new measurement information is available for feedback. The proposed strategy coincides with the (computationally intractable) exact min-max dynamic programming solution if all future measurement times are considered. Limiting the number of instants at which the new measurement information is considered we achieve a compromise between the computational efforts for feedback construction and the performance of the closed-loop.

关键词： optimal control linear system constraints continuous time measurements set-membership uncertainty feedback computational algorithm

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Local rolling and tilting capability analysis of fully parallel linear actuated platform-type manipulators

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ADVANCED ROBOTICS 2007年第8期21卷 931-960页

作者： Wang, Li-Chun T. Oen, Ka-Tjun Natl Taiwan Univ Sci & Technol Dept Mech Engn Taipei 106 Taiwan Technol & Sci Inst No Taiwan Dept Mech Engn Taipei 112 Taiwan

Two problems associated with the local rotatability of two types of fully parallel linearly actuated platform manipulators are investigated in this paper. The first problem is to find the physically allowable region that the movable platform can be freely rolled about any given direction at any specified position. The second problem is to evaluate the maximum angle that the movable platform can be tilted about any given position and orientation. The kinematic constraints involved in these problems are the stroke limitation of the linear actuators, the motion constraints of the passive spherical and universal joints, and the interference condition between the supporting limbs. A unified and computationally efficient approach for solving these problems which takes into account all of the kinematic constraints is developed.

关键词： parallel robot rolling capability tilting capability computational algorithm

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Stepwise prediction of conformational discontinuous B-Cell Epitopes using the mapitope algorithm

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PROTEINS-STRUCTURE FUNCTION AND BIOINFORMATICS 2007年第1期68卷 294-304页

作者： Bublil, Erez M. Freund, Natalia Tarnovitski Mayrose, Itay Penn, Osnat Roitburd-Berman, Anna Rubinstein, Nimrod D. Pupko, Tal Gershoni, Jonathan M. Tel Aviv Univ Dept Cell Res & Immunol IL-69978 Tel Aviv Israel

Mapping the epitope of an antibody is of great interest, since it contributes much to our understanding of the mechanisms of molecular recognition and provides the basis for rational vaccine design. Here we present Mapitope, a computer algorithm for epitope mapping. The algorithm input is a set of affinity isolated peptides obtained by screening phage display peptide-libraries with the antibody of interest. The output is usually 1-3 epitope candidates on the surface of the atomic structure of the antigen. We have systematically tested the performance of Mapitope by assessing the effect of the algorithm parameters on the final prediction. Thus, we have examined the effect of the statistical threshold (ST) parameter, relating to the frequency distribution and enrichment of amino acid pairs from the isolated peptides and the D (distance) and E (exposure) parameters which relate to the physical parameters of the antigen. Two model systems were analyzed in which the antibody of interest had previously been co-crystallized with the antigen and thus the epitope is a given. The Mapitope algorithm successfully predicted the epitopes in both models. Accordingly, we formulated a stepwise paradigm for the prediction of discontinuous conformational epitopes using peptides obtained from screening phage display libraries. We applied this paradigm to successfully predict the epitope of the Trastuzumab antibody on the surface of the Her-2/neu receptor in a third model system.

关键词： antibody combinatorial phage display peptide library computational algorithm epitope mapping vaccine

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Comparative Analysis of Regulatory Motif Discovery Tools for Transcription Factor Binding Sites

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Genomics, Proteomics & Bioinformatics 2007年第2期5卷 131-142页

作者： Wei Wei Xiao-Dan Yu Department of Pathobiology Center of Computational Biology Institute of Basic Medical Sciences Beijing100850 China

In the post-genomic era, identification of specific regulatory motifs or transcription factor binding sites （TFBSs） in non-coding DNA sequences, which is essential to elucidate transcriptional regulatory networks, has emerged as an obstacle that frustrates many researchers. Consequently, numerous motif discovery tools and correlated databases have been applied to solving this problem. However, these existing methods, based on different computational algorithms, show diverse motif prediction efficiency in non-coding DNA sequences. Therefore, understanding the similarities and differences of computational algorithms and enriching the motif discovery literatures are important for users to choose the most appropriate one among the online available tools. Moreover, there still lacks credible criterion to assess motif discovery tools and instructions for researchers to choose the best according to their own projects. Thus integration of the related resources might be a good approach to improve accuracy of the application. Recent studies integrate regulatory motif discovery tools with experimental methods to offer a complementary approach for researchers, and also provide a much-needed model for current researches on transcriptional regulatory networks. Here we present a comparative analysis of regulatory motif discovery tools for TFBSs.

关键词： motif TFBS non-coding DNA sequence computational algorithm motif discovery tool

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