Collado-Vides, J., Hofestadt, R., Mavrovouniotis, M.L., and Michal, G.. "Modeling and simulation of gene regulation and metabolic pathways." Biosystems. 49
(1).
1999.
pp. 79-82.
[ .pdf ] [ PubMed ]
Keywords: *Gene Expression Regulation ; *Metabolism ; *Models Genetic
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
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
Hofestadt, R. and Thelen, S.. "Quantitative modeling of biochemical networks." In Silico Biol. 1
(1).
1998.
pp. 39-53.
[ PubMed ] [ WebSite ]
Today different database systems for molecular structures (genes and proteins) and metabolic pathways are available. All these systems are characterized by the static data representation. For progress in biotechnology the dynamic representation of this data is important. The metabolism can be characterized as a complex biochemical network. Different models for the quantitative simulation of biochemical networks are discussed, but no useful formalization is available. This paper shows that the theory of Petrinets is useful for the quantitative modeling of biochemical networks.
Keywords: *Biochemistry ; Biotechnology ; Catalysis ; Computational Biology ; *Computer Simulation ; Databases Factual ; Glycolysis ; Models Biological ; Protein Engineering
Kuffner, R., Zimmer, R., and Lengauer, T.. "Pathway analysis in metabolic databases via differential metabolic display (DMD)." Bioinformatics. 16
(9).
2000.
pp. 825-36.
[ .pdf ] [ PubMed ] [ WebSite ]
MOTIVATION: A number of metabolic databases are available electronically, some with features for querying and visualizing metabolic pathways and regulatory networks. We present a unifying, systematic approach based on PETRI nets for storing, displaying, comparing, searching and simulating such nets from a number of different sources. RESULTS: Information from each data source is extracted and compiled into a PETRI net. Such PETRI nets then allow to investigate the (differential) content in metabolic databases, to map and integrate genomic information and functional annotations, to compare sequence and metabolic databases with respect to their functional annotations, and to define, generate and search paths and pathways in nets. We present an algorithm to systematically generate all pathways satisfying additional constraints in such PETRI nets. Finally, based on the set of valid pathways, so-called differential metabolic displays (DMDs) are introduced to exhibit specific differences between biological systems, i.e. different developmental states, disease states, or different organisms, on the level of paths and pathways. DMDs will be useful for target finding and function prediction, especially in the context of the interpretation of expression data.
Keywords: *Algorithms ; Catalysis ; Computational Biology_*methods ; Computer Simulation ; *Data Display ; *Databases Factual ; Enzymes_genetics ; Enzymes_metabolism ; Glycolysis ; Metabolism_*physiology ; Mycoplasma_metabolism ; Yeasts_metabolism
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
Oliveira, J.S., Bailey, C.G., Jones-Oliveira, J.B., and Dixon, D.A.. "An algebraic-combinatorial model for the identification and mapping of biochemical pathways." Bull Math Biol. 63
(6).
2001.
pp. 1163-96.
[ .pdf ] [ PubMed ]
We develop the mathematical machinery for the construction of an algebraic-combinatorial model using Petri nets to construct an oriented matroid representation of biochemical pathways. For demonstration purposes, we use a model metabolic pathway example from the literature to derive a general biochemical reaction network model. The biomolecular networks define a connectivity matrix that identifies a linear representation of a Petri net. The sub-circuits that span a reaction network are subject to flux conservation laws. The conservation laws correspond to algebraic-combinatorial dual invariants, that are called S- (state) and T- (transition) invariants. Each invariant has an associated minimum support. We show that every minimum support of a Petri net invariant defines a unique signed sub-circuit representation. We prove that the family of signed sub-circuits has an implicit order that defines an oriented matroid. The oriented matroid is then used to identify the feasible sub-circuit pathways that span the biochemical network as the positive cycles in a hyper-digraph.
Keywords: Linear Models ; Mathematical Computing ; *Models Biological ; *Models Chemical
Peleg, M., Yeh, I., and Altman, R.B.. "Modelling biological processes using workflow and Petri Net models." Bioinformatics. 18
(6).
2002.
pp. 825-37.
[ .pdf ] [ PubMed ] [ WebSite ]
MOTIVATION: Biological processes can be considered at many levels of detail, ranging from atomic mechanism to general processes such as cell division, cell adhesion or cell invasion. The experimental study of protein function and gene regulation typically provides information at many levels. The representation of hierarchical process knowledge in biology is therefore a major challenge for bioinformatics. To represent high-level processes in the context of their component functions, we have developed a graphical knowledge model for biological processes that supports methods for qualitative reasoning. RESULTS: We assessed eleven diverse models that were developed in the fields of software engineering, business, and biology, to evaluate their suitability for representing and simulating biological processes. Based on this assessment, we combined the best aspects of two models: Workflow/Petri Net and a biological concept model. The Workflow model can represent nesting and ordering of processes, the structural components that participate in the processes, and the roles that they play. It also maps to Petri Nets, which allow verification of formal properties and qualitative simulation. The biological concept model, TAMBIS, provides a framework for describing biological entities that can be mapped to the workflow model. We tested our model by representing malaria parasites invading host erythrocytes, and composed queries, in five general classes, to discover relationships among processes and structural components. We used reachability analysis to answer queries about the dynamic aspects of the model. AVAILABILITY: The model is available at http://smi.stanford.edu/projects/helix/pubs/process-model/.
Reddy, V.N., Liebman, M.N., and Mavrovouniotis, M.L.. "Qualitative analysis of biochemical reaction systems." Comput Biol Med. 26
(1).
1996.
pp. 9-24.
[ PubMed ]
The qualitative analysis of biochemical reaction systems is presented. A discrete event systems approach is used to represent and analyze bioreaction pathways. The approach is based on Petri nets, which are particularly suited to modeling stoichiometric transformations, i.e. the inter-conversion of metabolites in fixed proportions. The properties and methods for the analysis of Petri nets, along with their interpretation for biochemical systems, are presented. As an example, the combined glycolytic and pentose phosphate pathway of the erythrocyte cell is presented to illustrate the concepts of the methodology.
Keywords: Biochemistry ; *Computer Simulation ; Erythrocytes_*physiology ; Glycolysis_*physiology ; Human ; Models Theoretical ; Pentosephosphate Pathway_*physiology
Reddy, V.N., Mavrovouniotis, M.L., and Liebman, M.N.. "Petri net representations in metabolic pathways." Proc Int Conf Intell Syst Mol Biol.
vol. 1.
1993.
pp. 328-36.
[ PubMed ]
The present methods for representing metabolic pathways are limited in their ability to handle complex systems, incorporate new information, and to provide for drawing qualitative conclusions from the structure of pathways. The theory of Petri nets is introduced as a tool for computer-implementable representation of pathways. Petri nets have the potential to overcome the present limitations, and through a multitude of properties, enable the preliminary qualitative analysis of pathways.
Keywords: *Computer Simulation ; Fructose_metabolism ; Liver_metabolism ; *Metabolism ; *Models Biological
Rana, O.F.. "Automating parallel implementation of neural learning algorithms." Int J Neural Syst. 10
(3).
2000.
pp. 227-41.
[ PubMed ]
Neural learning algorithms generally involve a number of identical processing units, which are fully or partially connected, and involve an update function, such as a ramp, a sigmoid or a Gaussian function for instance. Some variations also exist, where units can be heterogeneous, or where an alternative update technique is employed, such as a pulse stream generator. Associated with connections are numerical values that must be adjusted using a learning rule, and and dictated by parameters that are learning rule specific, such as momentum, a learning rate, a temperature, amongst others. Usually, neural learning algorithms involve local updates, and a global interaction between units is often discouraged, except in instances where units are fully connected, or involve synchronous updates. In all of these instances, concurrency within a neural algorithm cannot be fully exploited without a suitable implementation strategy. A design scheme is described for translating a neural learning algorithm from inception to implementation on a parallel machine using PVM or MPI libraries, or onto programmable logic such as FPGAs. A designer must first describe the algorithm using a specialised Neural Language, from which a Petri net (PN) model is constructed automatically for verification, and building a performance model. The PN model can be used to study issues such as synchronisation points, resource sharing and concurrency within a learning rule. Specialised constructs are provided to enable a designer to express various aspects of a learning rule, such as the number and connectivity of neural nodes, the interconnection strategies, and information flows required by the learning algorithm. A scheduling and mapping strategy is then used to translate this PN model onto a multiprocessor template. We demonstrate our technique using a Kohonen and backpropagation learning rules, implemented on a loosely coupled workstation cluster, and a dedicated parallel machine, with PVM libraries.
Keywords: *Algorithms ; Artificial Intelligence ; Computers ; Models Neurological ; *Neural Networks (Computer) ; Programming Languages
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
Schuster, S., Pfeiffer, T., Moldenhauer, F., Koch, I., and Dandekar, T.. "Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae." Bioinformatics. 18
(2).
2002.
pp. 351-61.
[ PubMed ] [ WebSite ]
MOTIVATION: Reconstructing and analyzing the metabolic map of microorganisms is an important challenge in bioinformatics. Pathway analysis of large metabolic networks meets with the problem of combinatorial explosion of pathways. Therefore, appropriate algorithms for an automated decomposition of these networks into smaller subsystems are needed. RESULTS: A decomposition algorithm for metabolic networks based on the local connectivity of metabolites is presented. Interrelations of this algorithm with alternative methods proposed in the literature and the theory of small world networks are discussed. The applicability of our method is illustrated by an analysis of the metabolism of Mycoplasma pneumoniae, which is an organism of considerable medical interest. The decomposition gives rise to 19 subnetworks. Three of these are here discussed in biochemical terms: arginine degradation, the tetrahydrofolate system, and nucleotide metabolism. The interrelations of pathway analysis of biochemical networks with Petri net theory are outlined.
Keywords: Algorithms ; Arginine_metabolism ; Computational Biology ; *Metabolism ; Models Biological ; Mycoplasma pneumoniae_*metabolism ; Nucleotides_metabolism ; *Software
Sharov, A.A.. "Self-reproducing systems: structure, niche relations and evolution." Biosystems. 25
(4).
1991.
pp. 237-49.
[ PubMed ]
A formal definition of a self-reproducing system is proposed using Petri nets. A potential self-reproducing system is a set of places in the Petri net such that the number of tokens in each place increases due to some sequence of internal transitions (a transition is called internal to the marked subset of places if at least one of its starting places and one of its terminating places belongs to that subset). An actual self-reproducing system is a system that compensates the outflow of its components by reproduction. In a suitable environment every potential self-reproducing system becomes an actual one. Each Petri net can be considered as an ecosystem with the web of ecological niches bound together with trophic and other relations. The stationary dynamics of the ecosystem is characterized by the set of filled niches. The process of evolution is described in terms of niche composition change. Perspectives of the theory of self-reproducing systems in biology are discussed.
Keywords: *Evolution ; Models Biological ; Reproduction ; Selection (Genetics) ; Systems Theory