Developing time constraints in Petri net models of biochemical processes via computation structure modeling

Computation structure modeling can be applied to a model of a biochemical process. We present an application of computation structure model analysis to a published Petri net model of part of an inflammation process. From this computation structure model and published experimental data we develop a timing constraint. Because the number of possible biochemical reactions in the human cell is distressingly large, recognizing existing constraints upon what reactions can occur, such as when potential reactants are sequestered in different compartments, or steric constraints prohibit docking, provides needed reduction of these possibilities. Modeling with networks, including Petri nets, is common in systems biology and constraint application can be visualized acting upon these graphs, pruning subtrees from a network of possibilities. The technique is complementary to stochastic simulations algorithms and to T and P-invariant analysis of Petri nets. We apply the modeling technique to spliceosome acting on C9ORF72 intronic hexanucleotide repeats, to illustrate one effect of this repeat on splicing.

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

[2]  Taylor L. Booth,et al.  Software performance modeling using computation structures , 1975, IEEE Transactions on Software Engineering.

[3]  D. Floreano,et al.  Revealing strengths and weaknesses of methods for gene network inference , 2010, Proceedings of the National Academy of Sciences.

[4]  M. P. Tosi,et al.  Introduction To Liquid State Physics , 2002 .

[5]  C. Koch.  Modular Biological Complexity , 2012, Science.

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

[7]  M. Carmo-Fonseca,et al.  Imaging dynamic interactions between spliceosomal proteins and pre-mRNA in living cells. , 2014, Methods.

[8]  Masao Nagasaki,et al.  Constructing biological pathway models with hybrid functional petri nets. , 2011, Studies in health technology and informatics.

[10]  Ina Koch,et al.  Modeling of the U1 snRNP assembly pathway in alternative splicing in human cells using Petri nets , 2009, Comput. Biol. Chem..

[11]  W. S. Hlavacek,et al.  A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity. , 2006, Bio Systems.

[12]  Andrea Sackmann,et al.  Modeling the process of human body iron homeostasis using a variant of timed Petri nets , 2009, Discret. Appl. Math..

[13]  Monika Heiner,et al.  Understanding Network Behavior by Structured Representations of Transition Invariants , 2009, Algorithmic Bioprocesses.

[14]  Dov Dori,et al.  Conceptual Model-Based Systems Biology: Mapping Knowledge and Discovering Gaps in the mRNA Transcription Cycle , 2012, PloS one.

[15]  Masao Nagasaki,et al.  Cell Illustrator 4.0: A Computational Platform for Systems Biology , 2010, Silico Biol..

[16]  Lily Shiue,et al.  Competition between pre-mRNAs for the splicing machinery drives global regulation of splicing. , 2013, Molecular cell.

[17]  Chuan Yi Tang,et al.  Computational modeling with forward and reverse engineering links signaling network and genomic regulatory responses: NF-κB signaling-induced gene expression responses in inflammation , 2010, BMC Bioinformatics.

[18]  Alexander Bockmayr,et al.  A Lattice-Theoretic Framework for Metabolic Pathway Analysis , 2013, CMSB.

[19]  Ina Koch,et al.  Petri net modelling of gene regulation of the Duchenne muscular dystrophy , 2008, Biosyst..

[20]  C. Will,et al.  Inhibition of RNA Helicase Brr2 by the C-Terminal Tail of the Spliceosomal Protein Prp8 , 2013, Science.

[21]  Annegret Wagler,et al.  Encoding the dynamics of deterministic systems , 2011, Math. Methods Oper. Res..

[22]  V. Murthy,et al.  Dendritic spines , 1998 .

[23]  D. Gillespie.  Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[24]  Fumiaki Tanaka,et al.  Spliceosome integrity is defective in the motor neuron diseases ALS and SMA , 2013, EMBO molecular medicine.

[25]  Wolfgang Reisig,et al.  Modeling in Systems Biology, The Petri Net Approach , 2010, Computational Biology.

[26]  Ruth Nussinov,et al.  Structure and dynamics of molecular networks: A novel paradigm of drug discovery. A comprehensive review , 2012, Pharmacology & therapeutics.

[27]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[28]  Smectic ordering in liquid-crystal-aerosil dispersions. II. Scaling analysis. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Claudine Chaouiya,et al.  Discrete Modelling: Petri Net and Logical Approaches , 2010 .

[30]  Lars Kotthoff,et al.  Qualitative modelling via constraint programming , 2012, Constraints.

[31]  Ashish Tiwari,et al.  Computing minimal nutrient sets from metabolic networks via linear constraint solving , 2013, BMC Bioinformatics.

[32]  José Braga,et al.  A Stochastic View of Spliceosome Assembly and Recycling in the Nucleus , 2007, PLoS Comput. Biol..

[33]  A. Marquis Gacy,et al.  Trinucleotide repeats that expand in human disease form hairpin structures in vitro , 1995, Cell.

[34]  M. Andersen,et al.  Ultrasensitive response motifs: basic amplifiers in molecular signalling networks , 2013, Open Biology.

[35]  P. Hobza.  Chapter 20 – Potential Energy and Free Energy Surfaces of Floppy Systems. Ab initio Calculations and Molecular Dynamics Simulations , 1999 .