ArticleProceedings of the National Academy of Sciences of the United States of America1998
Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets.
Article in Proceedings of the National Academy of Sciences of the United States of America, 1998. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 71 papers.
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71 citing papers in PubMed.
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- Deciphering plasmid replication dynamics: a computational approach to predict ColE1-like plasmid copy number.Journal of the Royal Society, Interface · 2025Article
- From single cells to communities: Mathematical perspectives on bacterial quorum sensing.Computational and structural biotechnology journal · 2025Review
- Advances in modeling cellular state dynamics: integrating omics data and predictive techniques.Animal cells and systems · 2025Review
- Automatic construction of Petri net models for computational simulations of molecular interaction network.NPJ systems biology and applications · 2024Article
- MGDrivE 3: A decoupled vector-human framework for epidemiological simulation of mosquito genetic control tools and their surveillance.PLoS computational biology · 2024Article
- Stochastic model of vesicular stomatitis virus replication reveals mutational effects on virion production.PLoS computational biology · 2024Article
- Expansions to the MGDrivE suite for simulating the efficacy of novel gene-drive constructs in the control of mosquito-borne diseases.BMC research notes · 2023Article
- Machine Learning Guided Batched Design of a Bacterial Ribosome Binding Site.ACS synthetic biology · 2022Article
- Kinetic Modeling ofMetabolites · 2022Review
- Tracing the footsteps of autophagy in computational biology.Briefings in bioinformatics · 2021Article
- MGDrivE 2: A simulation framework for gene drive systems incorporating seasonality and epidemiological dynamics.PLoS computational biology · 2021Article
- Mathematical Models of Plasmid Population Dynamics.Frontiers in microbiology · 2021Review
- Nets-within-nets for modeling emergent patterns in ontogenetic processes.Computational and structural biotechnology journal · 2021Article
- A Role of Inflammation and Immunity in Essential Hypertension-Modeled and Analyzed Using Petri Nets.International journal of molecular sciences · 2020Article
- Recent advances in biomedical simulations: a manifesto for model engineering.F1000Research · 2019Review
- Modeling and Simulating the Aerobic Carbon Metabolism of a Green Microalga Using Petri Nets and New Concepts of VANESA.Journal of integrative bioinformatics · 2018Article
11 more citing papers are in PubMed but not listed here.
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Abstract
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.
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