Bibliography of: Stochastic Processes

  1. Goss, P.J. and Peccoud, J.. "Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets." Proc Natl Acad Sci U S A. 95 (12). 1998. pp. 6750-5.
    [ .pdf ] [ PubMed ]

    An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the ULTRASAN package is used to present results from numerical analysis and the outcome of simulations.

    Keywords: *Computer Simulation ; Human ; *Models Molecular ; *Molecular Biology ; *Stochastic Processes


  2. Goss, P.J. and Peccoud, J.. "Analysis of the stabilizing effect of Rom on the genetic network controlling ColE1 plasmid replication." Pac Symp Biocomput. 1999. pp. 65-76.
    [ .pdf ] [ PubMed ]

    A stochastic model of ColE1 plasmid replication is presented. It is implemented by using UltraSAN, a simulation tool based on an extension of stochastic Petri nets (SPNs). It allows an exploration of the variation in plasmid number per bacterium, which is not possible using a deterministic model. In particular, the rate at which plasmid-free bacteria arise during bacterial division is explored in some detail since spontaneous plasmid loss is a widely observed empirical phenomenon. The rate of spontaneous plasmid loss provides an evolutionary explanation for the maintainance of Rom protein. The presence of Rom acts to reduce variance in plasmid copy number, thereby reducing the rate of plasmid loss at bacterial division. The ability of stochastic models to link biochemical function with evolutionary considerations is discussed.

    Keywords: Cell Division ; Computational Biology_*methods ; *DNA Replication ; Escherichia coli_*genetics ; Escherichia coli_growth and development ; *Models Genetic ; *Plasmids ; Stochastic Processes


  3. Matsuno, H., Doi, A., Nagasaki, M., and Miyano, S.. "Hybrid Petri net representation of gene regulatory network." Pac Symp Biocomput. 2000. pp. 341-52.
    [ .pdf ] [ PubMed ]

    It is important to provide a representation method of gene regulatory networks which realizes the intuitions of biologists while keeping the universality in its computational ability. In this paper, we propose a method to exploit hybrid Petri net (HPN) for representing gene regulatory networks. The HPN is an extension of Petri nets which have been used to represent many kinds of systems including stochastic ones in the field of computer sciences and engineerings. Since the HPN has continuous and discrete elements, it can easily handle biological factors such as protein and mRNA concentrations. We demonstrate that, by using HPNs, it is possible to translate biological facts into HPNs in a natural manner. It should be also emphasized that a hierarchical approach is taken for our construction of the genetic switch mechanism of lambda phage which is realized by using HPNs. This hierarchical approach with HPNs makes easier the arrangement of the components in the gene regulatory network based on the biological facts and provides us a prospective view of the network. We also show some computational results of the protein dynamics of the lambda phage mechanism that is simulated and observed by implementing the HPN on a currently available tool.

    Keywords: Bacteriophage lambda_genetics ; Bacteriophage lambda_growth and development ; Computer Simulation ; Gene Expression Regulation ; Gene Expression Regulation Viral ; Genes Viral ; *Models Genetic ; Operon ; Repressor Proteins_genetics ; Stochastic Processes ; Viral Proteins_genetics


  4. Srivastava, R., Peterson, M.S., and Bentley, W.E.. "Stochastic kinetic analysis of the Escherichia coli stress circuit using sigma(32)-targeted antisense." Biotechnol Bioeng. 75 (1). 2001. pp. 120-9.
    [ PubMed ]

    A stochastic Petri net model was developed for simulating the sigma(32) stress circuit in E. coli. Transcription factor sigma(32) is the principal regulator of the response of E. coli to heat shock. Stochastic Petri net (SPN) models are well suited for kinetics characterization of fluxes in biochemical pathways. Notably, there exists a one-to-one mapping of model tokens and places to molecules of particular species. Our model was validated against experiments in which ethanol (inducer of heat shock response) and sigma(32)-targeted antisense (downward regulator) were used to perturb the sigma(32) regulatory pathway. The model was also extended to simulate the effects of recombinant protein production. Results show that the stress response depends heavily on the partitioning of sigma(32) within the cell; that is, sigma(32) becomes immediately available to mediate a stress response because it exists primarily in a sequestered, inactive form, complexed with chaperones DnaK, DnaJ, and GrpE. Recombinant proteins, however, also compete for chaperone proteins, particularly when folded improperly. Our simulations indicate that when the expression of recombinant protein has a low requirement for DnaK, DnaJ, and GrpE, the overall sigma(32) levels may drop, but the level of heat shock proteins will increase. Conversely, when the overexpressed recombinant protein has a strong requirement for the chaperones, a severe response is predicted. Interestingly, both cases were observed experimentally.

    Keywords: Antisense Elements (Genetics) ; Computer Simulation ; Escherichia coli_*genetics ; Escherichia coli_*metabolism ; Ethanol ; Gene Expression Regulation Bacterial ; Heat-Shock Proteins_genetics ; Heat-Shock Proteins_metabolism ; *Models Biological ; Recombinant Proteins_genetics ; Sigma Factor_*genetics ; Sigma Factor_*metabolism ; Solvents ; Stochastic Processes