Bridging the Gap between Stochastic and Deterministic Regimes in the Kinetic Simulations of the Biochemical Reaction Networks

Puchałka, Jacek; Kierzek, Andrzej M.

doi:10.1016/s0006-3495(04)74207-1

Cited by 147 publications

(117 citation statements)

References 35 publications

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“…Yet we believe that our work represents a step forward towards a formal study of constructive dynamical system. [9]. In an organization, only names of new molecular species are printed that are not present in an organization below.…”

Section: Resultsmentioning

confidence: 99%

“…In a reactive flow system all molecules are usedup by first-order reactions of the form {k} → ∅ (dilution). But as opposed to the previous system, we allow arbitrary additional reactions in R. This is a typical situation for chemical flow reactors or bacteria that grow [9]. In a reactive flow system , semi-organizations are not necessarily organizations, as in the reversible reaction example shown before.…”

Section: Different Reaction Systemsmentioning

confidence: 99%

“…Our investigation of planetary photo-chemistries [10] and bacterial metabolism (which will be published elsewhere), revealed lattices of organizations that vanish when the networks are randomized, indicating a non-trivial structure. Here, in order to give an impression, we show a lattice of organizations obtained from a model of the central sugar metabolism of E.coli by Puchalka and Kierzek [9]. The model consists of 92 species and 197 reactions, including gene expression, signal transduction, transport, and enzymatic activities.…”

Section: Organizations In Real Systemsmentioning

confidence: 99%

“…The input molecules, chosen according to ref. [9], include the external food set (Glcex, Glyex, Lacex) and all promoters (see suppl. material).…”

Section: Organizations In Real Systemsmentioning

confidence: 99%

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Chemical Organisation Theory

2007

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Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory consists of two parts. The first part introduces the concept of a chemical organization as a closed and mass-maintaining set of components. This concept allows to map a complex (reaction) network to the set of organizations, providing a new view on the system's structure. The second part connects dynamics with the set of organizations, which allows to map a movement of the system in state space to a movement in the set of organizations.Our world is changing, qualitatively and quantitatively. The characteristics of its dynamics can be as simple as in the case of a friction-less swinging pendulum, or as complex as the dynamical process that results in the creative apparition of novel ideas or entities. We might characterize the nature of a dynamical process according to its level of novelty production. For example, the friction-less swinging pendulum implies a process where the novelty is only quantitative. Whereas the process of biological evolution is highly creative and generates qualitative novelties, which then spread in a quantitative way.Fontana and Buss [1] called processes and systems that display the production of novelty, constructive (dynamical) processes and constructive (dynamical) systems, respectively. Constructive systems can be found on all levels of scientific abstraction: in nuclear physics, where the collision of atoms or subatomic particles leads to the creation of new particles; in molecular chemistry, where molecules can react to form new molecules; or in social systems, where communication can lead to new communication [2]. As a result of a combinatorial explosion, it is easy to create something that is new, e.g., a molecule or a poem that is unique in the whole known universe. Nevertheless, it should be noted that novelty is relative. Whether something is considered to be new or not, depends on what is already there. Thence it follows that whether a system 1 Both authors contributed equally.

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Section: Resultsmentioning

confidence: 99%

Section: Different Reaction Systemsmentioning

confidence: 99%

Section: Organizations In Real Systemsmentioning

confidence: 99%

“…The input molecules, chosen according to ref. [9], include the external food set (Glcex, Glyex, Lacex) and all promoters (see suppl. material).…”

Section: Organizations In Real Systemsmentioning

confidence: 99%

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Chemical Organisation Theory

2007

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“…Attempts to model such HYBRID SYSTEMS currently focus on automated parsing of networks into stochastic and deterministic regimes. These efforts have resulted in simulation software such as H-GENESIS and STOCK [59,60]. …”

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confidence: 99%

Computational approaches for modeling regulatory cellular networks

Eungdamrong

Iyengar

2004

Trends in Cell Biology

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Cellular components interact with each other to form networks that process information and evoke biological responses. A deep understanding of the behavior of these networks requires the development and analysis of mathematical models. In this article, different types of mathematical representations for modeling signaling networks are described, and the advantages and disadvantages of each type are discussed. Two experimentally well-studied signaling networks are then used as examples to illustrate the insight that could be gained through modeling. Finally, the modeling approach is expanded to describe how signaling networks might regulate cellular machines and evoke phenotypic behaviors.During the past two decades, substantial progress has been made in understanding the biochemical properties of cellular components, in addition to the organization of various molecular machines such as those involved in transcription and motility. From these studies of components and pathways, the design principles underlying cellular networks have emerged [1,2]. However, a substantial number of experiments is still needed to build up thè parts list' for a cell and to specify `parts function' in terms of cellular location, dynamics and regulatory organization. Because of the sheer number of components and interactions, the analysis of regulatory interactions is not easily achieved through intuition; even pathways and networks with few components are configured into systems that display complex behaviors. Hence, it is becoming increasingly clear that quantitative descriptions that lead to predictive models can be of great use in analyzing signaling pathways.Models of regulatory networks can be developed at various levels. Each level has its value. The simplest models of regulatory pathways and networks depict them as connections maps (http://stke.sciencemag.org), which are useful starting points for detailed analyses of signaling pathways. Although many signaling pathways have been identified by the study of binary reactions, connections are increasingly deduced from high-throughput experimental analyses of both protein-protein interactions [3][4][5][6] and protein location and expression patterns [7,8]. However, these connection maps are largely qualitative and, hence, only limited mathematical analysis can be undertaken. Such analyses often fall along the line of statistical correlations (`clustering'), which reveals co-regulation of each component [9], or an analysis of how the components are connected, which describes the statistical properties of the network as a whole [10][11][12]. An advantage of these models is that they can be developed for large numbers of components and interactions, and are useful in obtaining an To understand how extracellular signals evoke dynamic cellular responses, an analysis of the chemical reactions that constitute a biological system is needed. Typically, such models are built in three stages. First, a biochemical scheme that depicts the chemical reactions between the components in the...

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Simulation of biochemical networks

Kierzek

2005

Encyclopedia of Genetics, Genomics, Proteomics and Bioinformatics

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Advances in experimental techniques of molecular biology motivate attempts to mathematically model complex biochemical reaction networks occurring in the cell. Usually, the models are so complex that they cannot be solved analytically and so computer simulations must be employed. Biochemical reaction networks may be expressed as a system of differential equations, thus allowing standard algorithms and software packages to be used in the simulation. Frequently, the lack of precise model parameters prevents quantitative studies of the system dynamics. In such cases, qualitative simulations using logical formalism or the study of flux distribution of the stationary state may be performed. The methods mentioned above are deterministic and do not take into account stochastic fluctuations resulting from the fact that biochemical processes occur in very small volumes. Various Monte Carlo approaches are used to account for the stochastic effects in the dynamics of biochemical reaction networks. Recent advances in these methods allow simulations of systems composed of reactions varying by many orders of magnitude in their rates and the number of molecules involved. Simulations explicitly incorporating positional information on the spatial clustering of membrane receptors have also been performed.

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Bridging the Gap between Stochastic and Deterministic Regimes in the Kinetic Simulations of the Biochemical Reaction Networks

Cited by 147 publications

References 35 publications

Chemical Organisation Theory

Chemical Organisation Theory

Computational approaches for modeling regulatory cellular networks

Simulation of biochemical networks

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