zbMATH — the first resource for mathematics

Petri nets formalism facilitates analysis of complex biomolecular structural data. (English) Zbl 1338.90078
Summary: 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.

90B10 Deterministic network models in operations research
68W99 Algorithms in computer science
92-08 Computational methods for problems pertaining to biology
BioJava; CHARMM; Gromacs; NAMD; VMD
Full Text: DOI
[1] A. Amadei, A.B. Linssen and H.J. Berendsen, Essential dynamics of proteins. Proteins: Structure Function and Bioinform.17 (1993) 412-25. · doi:10.1002/prot.340170408
[2] B.R. Brooks et al. Charmm: the biomolecular simulation program. J. Comput. Chem.30 (2009) 1545-1614. · Zbl 05745476 · doi:10.1002/jcc.21287
[3] D.A. Case, Th. E. Cheatham, T. Darden, H. Gohlke, R. Luo, K.M. Merz, A. Onufriev, C. Simmerling, B. Wang and R.J. Woods, The amber biomolecular simulation programs. J. Comput. Chem.26 (2005) 1668-1688. · Zbl 05429649 · doi:10.1002/jcc.20290
[4] J. Chen, Sh. Zhang, X. Liu and Q. Zhang, Insights into drug resistance of mutations d30n and i50v to hiv-1 protease inhibitor tmc-114: Free energy calculation and molecular dynamic simulation. J. Mol. Mod.16 (2010) 459-468. · doi:10.1007/s00894-009-0553-7
[5] A.A. Chen and A.E. García, High-resolution reversible folding of hyperstable RNA tetraloops using molecular dynamics simulations. Proc. Natl. Acad. Sci.110 (2013) 16820-16825. · doi:10.1073/pnas.1309392110
[6] F.E. Cohen and M.J.E. Sternberg, On the prediction of protein structure: the significance of the root-mean-square deviation. J. Mol. Biol.138 (1980) 321-333. · doi:10.1016/0022-2836(80)90289-2
[7] R.O. Dror, R.M. Dirks, J.P. Grossman, H. Xu and D.E. Shaw, Biomolecular simulation: a computational microscope for molecular biology. Ann. Rev. Biophys.41 (2012) 429-452. · doi:10.1146/annurev-biophys-042910-155245
[8] H. Grubmüller, B. Heymann and P. Tavan, Ligand binding: molecular mechanics calculation of the streptavidin-biotin rupture force. Science271 (1996) 997-999. · doi:10.1126/science.271.5251.997
[9] L. Holm and Ch. Sander, Mapping the protein universe. Science273 (1996) 595-602. · doi:10.1126/science.273.5275.595
[10] R.C.G. Holland et al. Biojava: an open-source framework for bioinformatics. Bioinform.24 (2008) 2096-2097. · Zbl 05511806 · doi:10.1093/bioinformatics/btn397
[11] W. Humphrey, A. Dalke and K. Schulten, Vmd: visual molecular dynamics. J. Mol. Graph.14 (1996) 33-38. · doi:10.1016/0263-7855(96)00018-5
[12] R. Jakubowski, A. Gogolinska, L. Peplowski, P. Skrzyniarz and W. Nowak, Computational studies of ttr related amyloidosis: exploration of conformational space through petri net-based algorithm. TASK Quarterly18 (2014) 289-300.
[13] I. Jolliffe, Principal Component Analysis. Wiley Online Library (2002). · Zbl 1011.62064
[14] E. Lindahl, B. Hess and D.V. Der Spoel, Gromacs 3.0: a package for molecular simulation and trajectory analysis. J. Mol. Mod.7 (2001) 306-317.
[15] K. Lindorff-Larsen, N. Trbovic, P. Maragakis, S. Piana and D.E. Shaw, Structure and dynamics of an unfolded protein examined by molecular dynamics simulation. J. Amer. Chem. Soc.134 (2012) 3787-3791. · doi:10.1021/ja209931w
[16] T. Murata, Petri nets: Properties, analysis and applications. Proc. of IEEE77 (1989) 541-580. · doi:10.1109/5.24143
[17] W. Nowak, Applications of Computational Methods to Simulations of Proteins Dynamics. In Handbook Comput. Chem. Springer (2012) 1127-1153.
[18] J.L. Peterson, Petri nets. ACM Comput. Surveys (CSUR)9 (1977) 223-252. · Zbl 0357.68067 · doi:10.1145/356698.356702
[19] J.C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, Ch. Chipot, R.D. Skeel, L. Kale and K. Schulten, Scalable molecular dynamics with namd. J. Comput. Chem.26 (2005) 1781-1802. · Zbl 05429657 · doi:10.1002/jcc.20289
[20] C. Reid et al. Structure activity relationships of monocyte chemoattractant proteins in complex with a blocking antibody. Protein Engineering Design and Selection19 (2006) 317-324. · doi:10.1093/protein/gzl015
[21] W. Reisig, Petri nets: an introduction, vol. 4. Springer Science & Business Media (2012). · Zbl 0555.68033
[22] Ch. Rohr, W. Marwan and M. Heiner, Snoopya unifying Petri net framework to investigate biomolecular networks. Bioinform.26 (2010) 974-975. · Zbl 05744645 · doi:10.1093/bioinformatics/btq050
[23] A. Godzik, The structural alignment between two proteins: Is there a unique answer? Protein Sci.5 (1996) 1325-1338. · doi:10.1002/pro.5560050711
[24] A. Gogolinska and W. Nowak, Petri nets approach to modeling of immune system and autism. In Artificial Immune Systems. Springer (2012) 86-99.
[25] A. Gogolinska and W. Nowak, Molecular basis of lateral force spectroscopy nano-diagnostics: computational unbinding of autism related chemokine MCP-1 from IgG antibody. J. Mol. Mod.19 (2013) 4773-4780. · doi:10.1007/s00894-013-1972-z
[26] J. Shao, S.W. Tanner, N. Thompson and Th.E. Cheatham, Clustering molecular dynamics trajectories: 1. Characterizing the performance of different clustering algorithms. J. Chem. Theory Comput.3 (2007) 2312-2334. · doi:10.1021/ct700119m
[27] I.N. Shindyalov and Ph.E. Bourne, Protein structure alignment by incremental combinatorial extension (ce) of the optimal path. Protein Engineering11 (1998) 739-747. · doi:10.1093/protein/11.9.739
[28] A. Wojtczak, P. Neumann and V. Cody, Structure of a new polymorphic monoclinic form of human transthyretin at 3 å resolution reveals a mixed complex between unliganded and t4-bound tetramers of TTR. Acta Crystallographica Section D: Biological Crystallography57 (2001) 957-967. · doi:10.1107/S0907444901006047
[29] Y. Ye and A. Godzik, Flexible structure alignment by chaining aligned fragment pairs allowing twists. Bioinform.19 (2003) ii246-ii255.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.