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85
Temporal Logic Analysis of Gene Networks under Parameter Uncertainty
 SPECIAL ISSUE ON SYSTEMS BIOLOGY – TRANS. CIRCUITS AND SYSTEMS I / TRANS. AUTOMATIC CONTROL
"... The lack of precise numerical information for the values of biological parameters severely limits the development and analysis of models of genetic regulatory networks. To deal with this problem, we propose a method for the analysis of genetic regulatory networks under parameter uncertainty. We con ..."
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Cited by 18 (3 self)
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The lack of precise numerical information for the values of biological parameters severely limits the development and analysis of models of genetic regulatory networks. To deal with this problem, we propose a method for the analysis of genetic regulatory networks under parameter uncertainty. We consider models based on piecewisemultiaffine differential equations, dynamical properties expressed in temporal logic, and intervals for the values of uncertain parameters. The problem is then either to guarantee that the system satisfies the expected properties for every possible parameter value – the corresponding parameter set is then called valid – or to find valid subsets of a given parameter set. The proposed method uses discrete abstractions and model checking, and allows for efficient search of the parameter space. However, the abstraction process creates spurious behaviors in the abstract systems, along which time does not progress. Consequently, the verification of liveness properties, expressing that something will eventually happen, and implicitly assuming progress of time, often fails. A solution to this second problem is proposed using the notion of transient regions. This approach has been implemented in a tool for robust verification of gene networks (RoVerGeNe) and applied to the tuning of a synthetic network built in E. coli.
R.: Model checking liveness properties of genetic regulatory networks
"... Abstract. Recent studies have demonstrated the possibility to build genetic regulatory networks that confer a desired behavior to a living organism. However, the design of these networks is difficult, notably because of uncertainties on parameter values. In previous work, we proposed an approach t ..."
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Abstract. Recent studies have demonstrated the possibility to build genetic regulatory networks that confer a desired behavior to a living organism. However, the design of these networks is difficult, notably because of uncertainties on parameter values. In previous work, we proposed an approach to analyze genetic regulatory networks with parameter uncertainties. In this approach, the models are based on piecewisemultiaffine (PMA) differential equations, the specifications are expressed in temporal logic, and uncertain parameters are given by intervals. Abstractions are used to obtain finite discrete representations of the dynamics of the system, amenable to model checking. However, the abstraction process creates spurious behaviors along which time does not progress, called timeconverging behaviors. Consequently, the verification of liveness properties, expressing that something will eventually happen, and implicitly assuming progress of time, often fails. In this work, we extend our previous approach to enforce progress of time. More precisely, we define transient regions as subsets of the state space left in finite time by every solution trajectory, show how they can be used to rule out timeconverging behaviors, and provide sufficient conditions for their identification in PMA systems. This approach is implemented in RoVerGeNe and applied to the analysis of a network build in the bacterium E. coli. 1
A mathematical framework for the control of piecewise affine models of gene networks
, 2007
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Analysis of lactose metabolism in E.coli using reachability analysis of hybrid systems
 IEE PROCEEDINGS  SYSTEMS BIOLOGY
, 2007
"... We propose an abstraction method for medium scale biomolecular networks, based on hybrid dynamical systems with continuous multiaffine dynamics. This abstraction method follows naturally from the notion of approximating nonlinear rate laws with continuous piecewise linear functions and can be easil ..."
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Cited by 14 (3 self)
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We propose an abstraction method for medium scale biomolecular networks, based on hybrid dynamical systems with continuous multiaffine dynamics. This abstraction method follows naturally from the notion of approximating nonlinear rate laws with continuous piecewise linear functions and can be easily automated. An efficient reachability algorithm is possible for the resulting class of hybrid systems. We construct an approximation for an ordinary differential equation model of the lac operon, and show that our abstraction passes the same experimental tests that were used to validate the original model. The wellstudied biological system exhibits bistability and switching behavior, arising from positive feedback in the expression mechanism of the lac operon. The switching property of the lac system is an example of the major qualitative features that are the building blocks of higher level, more coarsegrained descriptions. Our approach is useful in helping correctly identify such properties and in connecting them to the underlying molecular dynamical details. We use reachability analysis together with the knowledge of the steady state structure to identify ranges of parameter values for which the system maintains the bistable switching property.
Approximating Continuous Systems by Timed Automata
"... In this work we develop a new technique for overapproximating (in the sense of timed trace inclusion) continuous dynamical systems by timed automata. This technique refines commonlyused discrete abstractions which are often too coarse to be useful. The essence of our technique is the partition of ..."
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Cited by 13 (1 self)
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In this work we develop a new technique for overapproximating (in the sense of timed trace inclusion) continuous dynamical systems by timed automata. This technique refines commonlyused discrete abstractions which are often too coarse to be useful. The essence of our technique is the partition of the state space into cubes and the allocation of a clock for each dimension. This allows us to get much better approximations of the behavior. We specialize this technique to multiaffine systems, a class of nonlinear systems of primary importance for the analysis of biochemical systems and demonstrate its applicability on an example taken from synthetic biology.
Continuous Valuations of Temporal Logic Specifications with applications to Parameter Optimization and Robustness Measures
, 2009
"... Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like modelchecking help solving, in the qualitative but also in the quantitative case. In this article we define a continuous degree of satis ..."
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Cited by 12 (1 self)
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Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like modelchecking help solving, in the qualitative but also in the quantitative case. In this article we define a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with stateoftheart evolutionary optimization methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signaling cascade.
A symbolic approach to controlling piecewise affine systems
 In IEEE Conference on Decision and Control (CDC’10
, 2010
"... Abstract — We present a computational framework for automatic synthesis of a feedback control strategy for a piecewise affine (PWA) system from a specification given as a Linear Temporal Logic (LTL) formula over an arbitrary set of linear predicates in its state variables. Our approach consists of t ..."
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Cited by 9 (5 self)
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Abstract — We present a computational framework for automatic synthesis of a feedback control strategy for a piecewise affine (PWA) system from a specification given as a Linear Temporal Logic (LTL) formula over an arbitrary set of linear predicates in its state variables. Our approach consists of two main steps. First, by defining appropriate partitions for its state and input spaces, we construct a finite abstraction of the PWA system in the form of a control transition system. Second, by leveraging ideas and techniques from Rabin games and LTL model checking, we develop an algorithm to generate a control strategy for the finite abstraction. While provably correct and robust to small perturbations in both state measurements and applied inputs, the overall procedure is conservative and expensive. The proposed algorithms have been implemented and are available for download. Illustrative examples are included. I.
Microarray analysis of gene expression: considerations in data mining and statistical treatment
 PHYSIOL GENOMICS
, 2006
"... DNA microarray represents a powerful tool in biomedical discoveries. Harnessing the potential of this technology depends on the development and appropriate use of data mining and statistical tools. Significant current advances have made microarray data mining more versatile. Researchers are no long ..."
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Cited by 8 (0 self)
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DNA microarray represents a powerful tool in biomedical discoveries. Harnessing the potential of this technology depends on the development and appropriate use of data mining and statistical tools. Significant current advances have made microarray data mining more versatile. Researchers are no longer limited to default choices that generate suboptimal results. Conflicting results in repeated experiments can be resolved through attention to the statistical details. In the current dynamic environment, there are many choices and potential pitfalls for researchers who intend to incorporate microarrays as a research tool. This review is intended to provide a simple framework to understand the choices and identify the pitfalls. Specifically, this review article discusses the choice of microarray platform, preprocessing raw data, differential expression and validation, clustering, annotation and functional characterization of genes, and pathway construction in light of emergent concepts and tools.
Subtilin production by Bacillus subtilis: Stochastic hybrid models and parameter identification
 IEEE Transactions on Circuits and Systems I – IEEE Transactions on Automatic Control
, 2008
"... This paper presents methods for the parameter identification of a model of subtilin production by Bacillus subtilis. Based on a stochastic hybrid model, identification is split in two subproblems: estimation of the genetic network regulating subtilin production from gene expression data, and estima ..."
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Cited by 7 (1 self)
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This paper presents methods for the parameter identification of a model of subtilin production by Bacillus subtilis. Based on a stochastic hybrid model, identification is split in two subproblems: estimation of the genetic network regulating subtilin production from gene expression data, and estimation of population dynamics based on nutrient and population level data. Techniques for identification of switching dynamics from sparse and irregularly sampled observations are developed and applied to simulated data. Numerical results are provided to show the effectiveness of our methods.
Modelling and analysing genetic networks: From Boolean networks to Petri nets
 CMSB’06, LNCS 4210
, 2006
"... Abstract. In order to understand complex genetic regulatory networks researchers require automated formal modelling techniques that provide appropriate analysis tools. In this paper we propose a new qualitative model for genetic regulatory networks based on Petri nets and detail a process for automa ..."
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Cited by 7 (1 self)
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Abstract. In order to understand complex genetic regulatory networks researchers require automated formal modelling techniques that provide appropriate analysis tools. In this paper we propose a new qualitative model for genetic regulatory networks based on Petri nets and detail a process for automatically constructing these models using logic minimization. We take as our starting point the Boolean network approach in which regulatory entities are viewed abstractly as binary switches. The idea is to extract terms representing a Boolean network using logic minimization and to then directly translate these terms into appropriate Petri net control structures. The resulting compact Petri net model addresses a number of shortcomings associated with Boolean networks and is particularly suited to analysis using the wide range of Petri net tools. We demonstrate our approach by presenting a detailed case study in which the genetic regulatory network underlying the nutritional stress response in Escherichia coli is modelled and analysed. 1