Stochastic Petri net modeling of wave sequences in cardiac arrhythmias

Chin, T. M.; Willsky, Alan S.

doi:10.1016/0010-4809(89)90022-0

Cited by 7 publications

(3 citation statements)

References 10 publications

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“…Specifically, a stochastic Petri net (SPN) modeling formalism was employed. Petri nets have been used to model biological systems (Chin and Willsky, 1989;Peccoud, 1998, 1999;Ouchi and Tazaki, 1998;Reddy et al, 1993). SPNs are effective for modeling event-driven processes for continuous-time, discrete-space, distributed systems (Marsan et al, 1995).…”

Section: Model Developmentmentioning

confidence: 99%

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ³²‐targeted antisense

Srivastava

Peterson

Bentley

2001

Biotech & Bioengineering

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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.

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Section: Model Developmentmentioning

confidence: 99%

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ³²‐targeted antisense

Srivastava

Peterson

Bentley

2001

Biotech & Bioengineering

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“…Under such conditions, the inherently stochastic nature of the ensuing processes may give rise to dynamics that differ significantly from those predicted by deterministic models. There are many examples of stochastic biological models in the literature (Chin & Willsky, 1989;McAdams & Arkin, 1997;Arkin et al, 1998;Goss & Peccoud, 1998;Srivastava et al, 2001), as well as examples comparing deterministic and stochastic kinetics of simple biochemical systems ( ! Erdi & T !…”

Section: Introductionmentioning

confidence: 99%

Stochastic vs. Deterministic Modeling of Intracellular Viral Kinetics

Srivastava

Summers

et al. 2002

Journal of Theoretical Biology

174

167

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Within its host cell, a complex coupling of transcription, translation, genome replication, assembly, and virus release processes determines the growth rate of a virus. Mathematical models that account for these processes can provide insights into the understanding as to how the overall growth cycle depends on its constituent reactions. Deterministic models based on ordinary differential equations can capture essential relationships among virus constituents. However, an infection may be initiated by a single virus particle that delivers its genome, a single molecule of DNA or RNA, to its host cell. Under such conditions, a stochastic model that allows for inherent fluctuations in the levels of viral constituents may yield qualitatively different behavior. To compare modeling approaches, we developed a simple model of the intracellular kinetics of a generic virus, which could be implemented deterministically or stochastically. The model accounted for reactions that synthesized and depleted viral nucleic acids and structural proteins. Linear stability analysis of the deterministic model showed the existence of two nodes, one stable and one unstable. Individual stochastic simulation runs could access and remain at the unstable node. In addition, deterministic and averaged stochastic simulations yielded different transient kinetics and different steady-state levels of viral components, particularly for low multiplicities of infection (MOI), where few virus particles initiate the infection. Furthermore, a bimodal population distribution of viral components was observed for low MOI stochastic simulations. The existence of a low-level infected subpopulation of cells, which could act as a viral reservoir, suggested a potential mechanism of viral persistence.

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“…The number of Petri Net-based models regarding the ECG is limited despite the expressive power, readability, and convenience of Petri Nets as one of the formal specification techniques [9]. In [7], a framework for modelling the electrical events using stochastic Petri Nets was presented. Nevertheless, this study focused solely on P and R waves.…”

Section: Environmentmentioning

confidence: 99%

Modeling Cardiac Pacemakers With Timed Coloured Petri Nets And Related Tools

Assiri

Janicki

2022

Preprint

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Stochastic Petri net modeling of wave sequences in cardiac arrhythmias

Cited by 7 publications

References 10 publications

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ³²‐targeted antisense

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ³²‐targeted antisense

Stochastic vs. Deterministic Modeling of Intracellular Viral Kinetics

Modeling Cardiac Pacemakers With Timed Coloured Petri Nets And Related Tools

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Stochastic Petri net modeling of wave sequences in cardiac arrhythmias

Cited by 7 publications

References 10 publications

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ32‐targeted antisense

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ32‐targeted antisense

Stochastic vs. Deterministic Modeling of Intracellular Viral Kinetics

Modeling Cardiac Pacemakers With Timed Coloured Petri Nets And Related Tools

Contact Info

Product

Resources

About

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ³²‐targeted antisense

Stochastic kinetic analysis of the Escherichia coli stress circuit using σ³²‐targeted antisense