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Modeling and simulation of genetic regulatory systems: A literature review
 Journal of Computational Biology
, 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
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Cited by 477 (10 self)
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In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rulebased formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.
The Systems Biology Markup Language (SBML): a medium for representation and exchange of biochemical network models
 Bioinformatics
, 2003
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A correct abstract machine for the stochastic picalculus
 In Bioconcur’04. ENTCS
, 2004
"... Abstract. This paper presents an abstract machine for a variant of the stochastic picalculus, in order to correctly model the stochastic simulation of biological processes. The abstract machine is proved sound and complete with respect to the calculus, and then used as the basis for implementing a ..."
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Cited by 85 (11 self)
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Abstract. This paper presents an abstract machine for a variant of the stochastic picalculus, in order to correctly model the stochastic simulation of biological processes. The abstract machine is proved sound and complete with respect to the calculus, and then used as the basis for implementing a stochastic simulator. The correctness of the machine helps ensure that the simulator is correctly implemented, giving greater confidence in the simulation results. A graphical representation for the picalculus is also presented, as a potential frontend to the simulator. 1
Hybrid Modeling and Simulation of Biomolecular Networks
 Hybrid Systems: Computation and Control, LNCS 2034
, 2001
"... In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feedback pathways appear t ..."
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Cited by 83 (7 self)
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In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feedback pathways appear to incorporate switches that result in changes in the dynamic behavior of the cell. This paper describes a hybrid systems approach to modeling the intracellular network using continuous di#erential equations to model the feedback mechanisms and modeswitching to describe the changes in the underlying dynamics. We use two case studies to illustrate a modular approach to modeling such networks and describe the architectural and behavioral hierarchy in the underlying models. We describe these models using Charon [2], a language that allows formal description of hybrid systems. We provide preliminary simulation results that demonstrate how our approach can help biologists in their analysis of noisy genetic circuits. Finally we describe our agenda for future work that includes the development of models and simulation for stochastic hybrid systems.
Rulebased Modelling of Cellular Signalling
 Proceedings of the 18 th International Conference on Concurrency Theory (CONCUR’07), Lecture Notes in Computer Science
, 2007
"... Abstract. Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on syste ..."
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Cited by 78 (20 self)
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Abstract. Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agentbased or concurrent languages, such as κ [1–3] or the closely related BioNetGen language [4–10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11, 12]. An exciting aspect of the agentbased approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to κ, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent and rulebased representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience. 1
Probabilistic model checking of complex biological pathways
, 2006
"... Abstract. Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicab ..."
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Cited by 69 (14 self)
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Abstract. Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. 1
BioPEPA: a framework for the modelling and analysis of biological systems
, 2008
"... In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use ..."
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Cited by 58 (21 self)
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In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. The domain of application is the one of biochemical networks. BioPEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. BioPEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered. Finally, we show the translation of three biological models into the new language and we report some analysis results.
Modeling transcriptional control in gene networks—Methods, recent results, and future directions
 Bull Math Biol
"... Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common bioche ..."
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Cited by 55 (0 self)
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Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we compare current methods for modeling genetic networks. A common modeling technique, based on simply modeling genes as ON–OFF switches, is readily implemented and allows rapid numerical simulations. However, this method may predict dynamic solutions that do not correspond to those seen when systems are modeled with a more detailed method using ordinary differential equations. Until now, the majority of gene network modeling studies have focused on determining the types of dynamics that can be generated by common biochemical motifs such as feedback loops or protein oligomerization. For example, these elements can generate multiple stable states for gene product concentrations, statedependent responses to stimuli, circadian rhythms and other oscillations, and optimal stimulus frequencies for maximal transcription. In the future, as new experimental techniques increase the ease of characterization of genetic networks, qualitative modeling will need to be supplanted by quantitative models for specific systems. c © 2000 Society for Mathematical Biology 1.
Analysis of signalling pathways using continuous time Markov chains
 Transactions on Computational Systems Biology
, 2006
"... Abstract. We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK + 03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous ..."
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Cited by 53 (13 self)
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Abstract. We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK + 03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable.