Subtilin Production by Bacillus Subtilis: Stochastic Hybrid Models and Parameter Identification

Cinquemani, Eugenio; Porreca, Riccardo; Ferrari-Trecate, Giancarlo; Lygeros, John

doi:10.1109/tcsi.2007.911327

Cited by 10 publications

(13 citation statements)

References 32 publications

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“…If hypotheses for the different configurations and discrete events exist, hybrid models can be used to capture such phenomena. In [7], the authors study the problem of genetic network structure identification in a stochastic hybrid modeling framework. They considered a piecewise deterministic model of genetic networks where protein synthesis is triggered by discrete random binding events and follows simple deterministic kinetics.…”

Section: Applications In Systems Biologymentioning

confidence: 99%

Hybrid Systems Modeling for (Cancer) Systems Biology

2015

Preprint

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Abstract-The advent of biological data of increasingly higher resolution in space and time has triggered the use of dynamic models to explain and predict the evolution of biological systems over space and time. Computer-aided system modeling and analysis in biology has led to many new discoveries and explanations that would otherwise be intractable to articulate without the available data and computing power. Nevertheless, the complexity in biology still challenges many labs in capturing studied phenomena in models that are tractable and simple enough to analyze. Moreover, the popular use of ordinary differential equation models have their limitations in that they solely capture continuous dynamics, while we observe many discrete dynamic phenomena in biology such as gene switching or mutations. Hybrid systems modeling provides a framework in which both continuous and discrete dynamics can be simulated and analyzed. Moreover, it provides techniques to develop approximations and abstractions of complex dynamics that are tractable to analyze. I. MOTIVATIONIn biology, many of the dynamic processes that we are interested in studying or affecting with treatments are inherently complex, i.e. nonlinear and varying across time and/or space. In the study of how biological systems behave we can make one important distinction between different dynamic phenomena, i.e. the difference between continuous and discrete dynamics. Continuous state variables model processes that evolve in some continuum, either time and/or space. This can be the evolution of protein expression over time or its diffusion throughout space. Discrete state variables model "sudden" changes or events in a system, such as a binary switch turning on or off, or, more involved, for a cancer cell switching through a sequence of distinct phenotypic states.Ordinary differential equations (ODEs) modeling is generally excepted to be able to capture many physical and biological phenomena quantitatively as we observe them in nature and experiments. On the other hand, logical models like Boolean networks (BNs) seek completely qualitative rather than quantitative models of biological systems. BNs can succeed in capturing high-level discrete phenomena such as activation or deactivation with fewer parameters than their ODE counterpart and can be used to evaluate model structure. However, they cannot capture transient response, only steady state. Unfortunately, ODEs strict use of only continuous state variables is not able to model the discrete dynamics in a system, and vice-versa logical models cannot describe more complicated dynamical evolutions. This motivates the use of hybrid system models, that can capture both continuous dynamics and discrete events. Additionally, trying to capture dynamics that are nonlinear and varying in time or space with one ODE model can lead to expressions that are intractable to simulate and hard to analyze. Instead, one can often get away with modeling an abstraction with simple ODE models that approximate the dynamics locally in space o...

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Section: Applications In Systems Biologymentioning

confidence: 99%

Hybrid Systems Modeling for (Cancer) Systems Biology

2015

Preprint

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“…Related work Identification of piecewise-linear (-affine) hybrid systems has been subject of intensive research, Vidal et al (2002); Ma and Vidal (2005) Grossman and Larson (1995). The application of hybrid systems to modelling complex dynamical systems, originating from biology, and their identification has been a subject of intensive research Casey et al (2005); de Jong (2002); Porreca et al (2010); Koutroumpas et al (2007); Cinquemani et al (2008).…”

Section: Identification Of Pwls and Biological Networkmentioning

confidence: 99%

Identification of Piecewise Linear Models of Complex Dynamical Systems

Westra

Petreczky

Peeters

2011

IFAC Proceedings Volumes

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The paper address the realization and identification problem for a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivated by applications in systems biology.

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“…An important extension would be to include hybrid models as a third category -in addition to " qualitative " and " quantitative " under computational models. Combinations of discrete, deterministic and stochastic models -both within a level of hierarchy or scale as well as across levels -are becoming more prevalent as larger and more complex systems are analyzed [4,12] . Gene regulatory networks, i.e.…”

Section: The Dominance Of Diagrammatic Modelsmentioning

confidence: 99%

“…the complex pathways involving RNA, proteins, etc. involved in the gene interaction, are both a focus of hybrid modelling approaches as well as an emerging theme in the study of complex diseases (including mental illnesses) through genome-wide analysis [4,11] . The dominance of diagrammatic models in other fi elds such as neuroscience and neuropsychiatry is also not surprising.…”

Section: The Dominance Of Diagrammatic Modelsmentioning

confidence: 99%

Concept Maps and Canonical Models in Neuropsychiatry

Marı́n-Sanguino¹,

Rosario²,

Mendoza³

2009

Pharmacopsychiatry

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Most bioscientists engage in informal modelling in their research and explicitly document this activity's results in diagrams or "concept maps". While canonical modelling approaches such as Biochemical Systems Theory (BST) immediately allow the construction of a corresponding system of equations, the problem of determining appropriate parameter values remains. Goel et al. introduced Concept Map Modelling (CMM) as a framework to address this problem through an interactive dialogue between experimenters and modellers. The CMM dialogue extracts the experimenters' implicit knowledge about dynamical behaviour of the parts of the system being modelled in form of rough sketches and verbal statements, e.g. value ranges. These are then used as inputs for parameter and initial value estimates for the symbolic canonical model based on the diagram. Canonical models have the big advantage that a great variety of parameter estimation methods have been developed for them in recent years. The paper discusses the suitability of this approach for neuropsychiatry using recent work of Qi et al. on a canonical model of presynaptic dopamine metabolism. Due to the complexity of systems encountered in neuropsychiatry, hybrid models are often used to complement the canonical models discussed here.

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Subtilin Production by Bacillus Subtilis: Stochastic Hybrid Models and Parameter Identification

Cited by 10 publications

References 32 publications

Hybrid Systems Modeling for (Cancer) Systems Biology

Hybrid Systems Modeling for (Cancer) Systems Biology

Identification of Piecewise Linear Models of Complex Dynamical Systems

Concept Maps and Canonical Models in Neuropsychiatry

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