Computational Methods for the Parallel 3D Simulation of Biochemical Kinetics at the Microscopic Scale

This work takes place in the context of biochemical kinetics simulation for the understanding of complex biological systems such as haemostasis. The classical approach, based on the numerical solving of differential systems, cannot satisfactorily handle local geometrical constraints, such as membrane binding events. To address this problem, we propose a particle-based system in which each molecular species is represented by a three-dimensional entity which diffuses and may undergo reactions. Such a system can be computationaly intensive, since a small time step and a very large number of entities are required to get significant results. Therefore, we propose a model that is suitable for parallel computing and that can especially take advantage of recent multicore and multiprocessor architectures. We present our particle-based system, detail the behaviour of our entities, and describe our parallel computing algorithms. Comparisons between simulations and theoretical results are exposed, as well as a performance evaluation of our algorithms.

[1]  Rui Alves,et al.  Tools for kinetic modeling of biochemical networks , 2006, Nature Biotechnology.

[2]  R. Colman.  Hemostasis and thrombosis: Basic principles and clinical practice , 1987 .

[3]  Carole A. Goble,et al.  Investigating Semantic Similarity Measures Across the Gene Ontology: The Relationship Between Sequence and Annotation , 2003, Bioinform..

[4]  Jijun Tang,et al.  Improving genome rearrangement phylogeny using sequence-style parsimony , 2005, Fifth IEEE Symposium on Bioinformatics and Bioengineering (BIBE'05).

[5]  Breakpoint Phylogenies. , 1997, Genome informatics. Workshop on Genome Informatics.

[6]  Haluk Resat,et al.  Spatial aspects in biological system simulations. , 2011, Methods in enzymology.

[7]  Philip Resnik,et al.  Using Information Content to Evaluate Semantic Similarity in a Taxonomy , 1995, IJCAI.

[8]  C. Lumsden,et al.  Stochastic Simulation of Coupled Reaction-Diffusion Processes , 1996 .

[9]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..

[10]  Vincent Rodin,et al.  Absolute Stability of Chaotic Asynchronous Multi-Interactions Schemes for Solving ODE , 2010 .

[11]  F. Perrin,et al.  Mouvement brownien d'un ellipsoide - I. Dispersion diélectrique pour des molécules ellipsoidales , 1934 .

[12]  M. Lavin,et al.  Venom factor V from the common brown snake escapes hemostatic regulation through procoagulant adaptations. , 2009, Blood.

[13]  Yu Lin,et al.  Bootstrapping phylogenies inferred from rearrangement data , 2011, Algorithms for Molecular Biology.

[14]  S. Colowick,et al.  Methods in Enzymology , Vol , 1966 .

[15]  L. Stougie,et al.  Constructing Level-2 Phylogenetic Networks from Triplets , 2007, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[16]  Tak Wah Lam,et al.  Computing the Unrooted Maximum Agreement Subtree in Sub-quadratic Time , 1996, Nord. J. Comput..

[17]  Tao Ju,et al.  Interactive skeletonization of intensity volumes , 2009, The Visual Computer.

[18]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[19]  Erik De Schutter,et al.  Monte Carlo Methods for Simulating Realistic Synaptic Microphysiology Using MCell , 2000 .

[20]  P. Robinson,et al.  The Human Phenotype Ontology: a tool for annotating and analyzing human hereditary disease. , 2008, American journal of human genetics.

[21]  J. Majewski,et al.  Sexual isolation in bacteria. , 2001, FEMS microbiology letters.

[22]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[23]  Daniel L. Purich,et al.  Handbook of biochemical kinetics , 1999 .

[24]  G. Broze,et al.  Regulation of Extrinsic Pathway Factor Xa Formation by Tissue Factor Pathway Inhibitor* , 1998, The Journal of Biological Chemistry.

[25]  Geppino Pucci,et al.  Universality in VLSI Computation , 2011, ParCo 2011.

[26]  Jijun Tang,et al.  A mixture framework for inferring ancestral gene orders , 2012, BMC Genomics.

[27]  Alexandru Telea,et al.  Skeletonization and Distance Transforms of 3D Volumes Using Graphics Hardware , 2006, DGCI.

[28]  P. Kam,et al.  : 4 , 1898, You Can Cross the Massacre on Foot.

[29]  Dan Gusfield,et al.  A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters , 2005, RECOMB.

[30]  Zhi-Zhong Chen,et al.  Algorithms for Reticulate Networks of Multiple Phylogenetic Trees , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[31]  Fabrice Harrouet.  Designing a Multicore and Multiprocessor Individual-Based Simulation Engine , 2012, IEEE Micro.

[32]  Wing-Kin Sung,et al.  RB-Finder: An Improved Distance-Based Sliding Window Method to Detect Recombination Breakpoints , 2008, J. Comput. Biol..

[33]  Frances S. Turner,et al.  Computational disease gene identification: a concert of methods prioritizes type 2 diabetes and obesity candidate genes , 2006, Nucleic acids research.

[34]  Tandy J. Warnow,et al.  Kaikoura Tree Theorems: Computing the Maximum Agreement Subtree , 1993, Inf. Process. Lett..

[35]  D. Bray,et al.  Stochastic simulation of chemical reactions with spatial resolution and single molecule detail , 2004, Physical biology.

[36]  M. Nei,et al.  A new method of inference of ancestral nucleotide and amino acid sequences. , 1995, Genetics.

[37]  Yu Lin,et al.  Maximum Likelihood Phylogenetic Reconstruction from High-Resolution Whole-Genome Data and a Tree of 68 Eukaryotes , 2012, Pacific Symposium on Biocomputing.

[38]  Wing-Kin Sung,et al.  Algorithms for combining rooted triplets into a galled phylogenetic network , 2005, SODA '05.

[39]  David Padua,et al.  Encyclopedia of Parallel Computing , 2011 .

[40]  Alexandros Stamatakis,et al.  RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models , 2006, Bioinform..

[41]  Catia Pesquita,et al.  Metrics for GO based protein semantic similarity: a systematic evaluation , 2008, BMC Bioinformatics.

[42]  L. Orgel,et al.  Phylogenetic Classification and the Universal Tree , 1999 .

[43]  Bernard B. Suh,et al.  Reconstructing contiguous regions of an ancestral genome. , 2006, Genome research.

[44]  David Sankoff,et al.  Decompositions of Multiple Breakpoint Graphs and Rapid Exact Solutions to the Median Problem , 2008, WABI.

[45]  P. R. ten Wolde,et al.  Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. , 2005, The Journal of chemical physics.

[46]  Tandy J. Warnow,et al.  Reconstructing reticulate evolution in species: theory and practice , 2004, RECOMB.

[47]  Meng Zhang,et al.  Maximum likelihood phylogenetic reconstruction using gene order encodings , 2011, 2011 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB).

[48]  Roger Brent,et al.  Detailed Simulations of Cell Biology with Smoldyn 2.1 , 2010, PLoS Comput. Biol..

[49]  Sébastien Kerdélo.  Méthodes informatiques pour l'expérimentation in virtuo de la cinétique biochimique. Application à la coagulation du sang. (Computer methods for the in virtuo experimentation of biochemical kinetics. Application to the blood coagulation system) , 2006 .

[50]  M. Baker,et al.  Modeling protein structure at near atomic resolutions with Gorgon. , 2011, Journal of structural biology.

[51]  Wing-Kin Sung,et al.  Constructing a Smallest Refining Galled Phylogenetic Network , 2005, RECOMB.

[52]  F. Perrin,et al.  Mouvement Brownien d'un ellipsoide (II). Rotation libre et dépolarisation des fluorescences. Translation et diffusion de molécules ellipsoidales , 1936 .

[53]  Jianpeng Ma,et al.  A Structural-informatics approach for tracing beta-sheets: building pseudo-C(alpha) traces for beta-strands in intermediate-resolution density maps. , 2004, Journal of molecular biology.

[54]  J. Felsenstein.  Evolutionary trees from DNA sequences: A maximum likelihood approach , 2005, Journal of Molecular Evolution.

[55]  P. Bork,et al.  Association of genes to genetically inherited diseases using data mining , 2002, Nature Genetics.

[56]  H. Berg.  Random Walks in Biology , 2018 .

[57]  Yu Lin,et al.  Fast and Accurate Phylogenetic Reconstruction from High-Resolution Whole-Genome Data and a Novel Robustness Estimator , 2010, RECOMB-CG.

[58]  Nicolas Le Novère,et al.  Particle-Based Stochastic Simulation in Systems Biology , 2006 .

[59]  F. Harrouet,et al.  ORis : S'immerger par le langage pour le prototypage d'univers virtuels à base d'entités autonomes , 2000 .

[60]  C. SIAMJ..  SPARSE DYNAMIC PROGRAMMING FOR EVOLUTIONARY-TREE COMPARISON , 1997 .

[61]  David Sankoff,et al.  A consolidation algorithm for genomes fractionated after higher order polyploidization , 2012, BMC Bioinformatics.

[62]  Daniel H. Huson,et al.  Beyond Galled Trees - Decomposition and Computation of Galled Networks , 2007, RECOMB.

[63]  Catia Pesquita,et al.  Evaluating GO-based Semantic Similarity Measures , 2007 .

[64]  Matthew L. Baker,et al.  Computing a Family of Skeletons of Volumetric Models for Shape Description , 2006, GMP.

[65]  T. Bartol,et al.  Monte Carlo Methods for Simulating Realistic Synaptic Microphysiology Using MCell , 2000 .

[66]  MICHEL HABIB,et al.  Constructing a Minimum phylogenetic Network from a Dense triplet Set , 2012, J. Bioinform. Comput. Biol..

[67]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[68]  C. Fraser,et al.  Recombination and the Nature of Bacterial Speciation , 2007, Science.

[69]  S. Plimpton,et al.  ChemCell : a particle-based model of protein chemistry and diffusion in microbial cells. , 2003 .

[70]  Richard Friedberg,et al.  Efficient sorting of genomic permutations by translocation, inversion and block interchange , 2005, Bioinform..

[71]  Wenping Wang,et al.  An algebraic condition for the separation of two ellipsoids , 2001, Comput. Aided Geom. Des..

[72]  Daniel Falush,et al.  Mismatch induced speciation in Salmonella: model and data , 2006, Philosophical Transactions of the Royal Society B: Biological Sciences.

[73]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[74]  N. G. Van Kampen,et al.  Chapter III – STOCHASTIC PROCESSES , 2007 .