Petri nets formalism facilitates analysis of complex biomolecular structural data

Molecular dynamics (MD) simulation is a popular method of protein and nucleic acids research. Current MD output trajectories are huge files and therefore they are hard to analyze. Petri nets (PNs) is a mathematical modeling language that allows for concise, graphical representation of complex data. We have developed a few algorithms for PNs generation from such large MD trajectories. One of them, called the One Place One Conformation (OPOC) algorithm, is presented in a greater detail. In the OPOC algorithm one biomolecular conformation corresponds to one PN place and a transition occurring in PN graph is related to a change between biomolecules conformations. As case studies three simulations are analyzed: an enforced steered MD (SMD) dissociation of a transthyretin protein tetramer into dimers, the SMD dissociation of an antibody-antigen complex and a classical MD simulation of transthyretin. We show that PNs reproduce events hidden in MD trajectories and enable observations of the conformational space features hard-to-see by the other clustering methods. Thus, a fundamental process of biomolecular data classification may be optimized using the PN approach.

[1]  W. Nowak,et al.  Molecular basis of lateral force spectroscopy nano-diagnostics: computational unbinding of autism related chemokine MCP-1 from IgG antibody , 2013, Journal of Molecular Modeling.

[2]  Berk Hess,et al.  GROMACS 3.0: a package for molecular simulation and trajectory analysis , 2001 .

[3]  Andreas Prlic,et al.  Sequence analysis , 2003 .

[4]  Holger Gohlke,et al.  The Amber biomolecular simulation programs , 2005, J. Comput. Chem..

[5]  Rafal Jakubowski,et al.  Computational studies of TTR related amyloidosis: exploration of conformational space through petri net-based algorithm , 2014 .

[6]  H. Berendsen,et al.  Essential dynamics of proteins , 1993, Proteins.

[7]  Angel E García,et al.  High-resolution reversible folding of hyperstable RNA tetraloops using molecular dynamics simulations , 2013, Proceedings of the National Academy of Sciences.

[8]  P. Tavan,et al.  Ligand Binding: Molecular Mechanics Calculation of the Streptavidin-Biotin Rupture Force , 1996, Science.

[9]  C Sander,et al.  Mapping the Protein Universe , 1996, Science.

[10]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[11]  K Schulten,et al.  VMD: visual molecular dynamics. , 1996, Journal of molecular graphics.

[12]  Adam Godzik,et al.  Flexible structure alignment by chaining aligned fragment pairs allowing twists , 2003, ECCB.

[13]  Wieslaw Nowak,et al.  Petri Nets Approach to Modeling of Immune System and Autism , 2012, ICARIS.

[14]  Qinggang Zhang,et al.  Insights into drug resistance of mutations D30N and I50V to HIV-1 protease inhibitor TMC-114: Free energy calculation and molecular dynamic simulation , 2010, Journal of molecular modeling.

[15]  K. Lindorff-Larsen,et al.  Structure and dynamics of an unfolded protein examined by molecular dynamics simulation. , 2012, Journal of the American Chemical Society.

[16]  Wolfgang Reisig Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[17]  Monika Heiner,et al.  Snoopy - a unifying Petri net framework to investigate biomolecular networks , 2010, Bioinform..

[18]  J. P. Grossman,et al.  Biomolecular simulation: a computational microscope for molecular biology. , 2012, Annual review of biophysics.

[19]  H. V. van Vlijmen,et al.  Structure activity relationships of monocyte chemoattractant proteins in complex with a blocking antibody. , 2006, Protein engineering, design & selection : PEDS.

[20]  Jianpeng Ma,et al.  CHARMM: The biomolecular simulation program , 2009, J. Comput. Chem..

[21]  P E Bourne,et al.  Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. , 1998, Protein engineering.

[22]  Laxmikant V. Kalé,et al.  Scalable molecular dynamics with NAMD , 2005, J. Comput. Chem..

[23]  Jianyin Shao,et al.  Clustering Molecular Dynamics Trajectories: 1. Characterizing the Performance of Different Clustering Algorithms. , 2007, Journal of chemical theory and computation.

[24]  I. Jolliffe Principal Component Analysis , 2002 .

[25]  A. Godzik The structural alignment between two proteins: Is there a unique answer? , 1996, Protein science : a publication of the Protein Society.

[26]  M. Sternberg,et al.  On the prediction of protein structure: The significance of the root-mean-square deviation. , 1980, Journal of molecular biology.

[27]  A. Wojtczak,et al.  Structure of a new polymorphic monoclinic form of human transthyretin at 3 A resolution reveals a mixed complex between unliganded and T4-bound tetramers of TTR. , 2001, Acta crystallographica. Section D, Biological crystallography.