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Machine learning biochemical networks from temporal logic properties
 Transactions on Computational Systems Biology
, 2006
"... Abstract. One central issue in systems biology is the definition of formal languages for describing complex biochemical systems and their behavior at different levels. The biochemical abstract machine BIOCHAM is based on two formal languages, one rulebased language used for modeling biochemical net ..."
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Cited by 49 (11 self)
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Abstract. One central issue in systems biology is the definition of formal languages for describing complex biochemical systems and their behavior at different levels. The biochemical abstract machine BIOCHAM is based on two formal languages, one rulebased language used for modeling biochemical networks, at three abstraction levels corresponding to three semantics: boolean, concentration and population; and one temporal logic language used for formalizing the biological properties of the system. In this paper, we show how the temporal logic language can be turned into a specification language. We describe two algorithms for inferring reaction rules and kinetic parameter values from a temporal specification formalizing the biological data. Then, with an example of the cell cycle control, we illustrate how these machine learning techniques may be useful to the modeler. 1
Reachability analysis of multiaffine systems
 In Hybrid Systems: Computation and Control, LNCS 3927
, 2006
"... Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initi ..."
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Cited by 31 (4 self)
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Abstract We present a computationally attractive technique to study the reachability of rectangular regions by trajectories of continuous multiaffine systems. The method is iterative. At each step, finer partitions and finite quotients that overapproximate the reachability properties of the initial system are produced. We exploit some convexity properties of multiaffine functions on rectangles to show that the construction of the quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. This methodology can be used for formal analysis of biochemical networks, aircraft and underwater vehicles, where multiaffine models are widely used.
Qualitative analysis and verification of hybrid models of genetic regulatory networks: Nutritional stress response in Escherichia coli
 in Hybrid Systems: Computation and Control
, 2005
"... Abstract. The switchlike character of the dynamics of genetic regulatory networks has attracted much attention from mathematical biologists and researchers on hybrid systems alike. We extend our previous work on a method for the qualitative analysis of hybrid models of genetic regulatory networks, ..."
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Cited by 27 (5 self)
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Abstract. The switchlike character of the dynamics of genetic regulatory networks has attracted much attention from mathematical biologists and researchers on hybrid systems alike. We extend our previous work on a method for the qualitative analysis of hybrid models of genetic regulatory networks, based on a class of piecewiseaffine differential equation (PADE) models, in two directions. First, we present a refinement of the method using a discrete or qualitative abstraction that preserves stronger properties of the dynamics of the PA systems, in particular the sign patterns of the derivatives of the concentration variables. The discrete transition system resulting from the abstraction is a conservative approximation of the dynamics of the PA system and can be computed symbolically. Second, we apply the refined method to a regulatory system whose functioning is not yet wellunderstood by biologists, the nutritional stress response in the bacterium Escherichia coli. 1
European Train Control System: A Case Study in Formal Verification
, 2009
"... Complex physical systems have several degrees of freedom. They only work correctly when their control parameters obey corresponding constraints. Based on the informal specification of the European Train Control System (ETCS), we design a controller for its cooperation protocol. For its free paramet ..."
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Cited by 23 (11 self)
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Complex physical systems have several degrees of freedom. They only work correctly when their control parameters obey corresponding constraints. Based on the informal specification of the European Train Control System (ETCS), we design a controller for its cooperation protocol. For its free parameters, we successively identify constraints that are required to ensure collision freedom. We formally prove the parameter constraints to be sharp by characterizing them equivalently in terms of reachability properties of the hybrid system dynamics. Using our deductive verification tool KeYmaera, we formally verify controllability, safety, liveness, and reactivity properties of the ETCS protocol that entail collision freedom. We prove that the ETCS protocol remains correct even in the presence of perturbation by disturbances in the dynamics. We verify that safety is preserved when a PI controlled speed supervision is used.
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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Cited by 17 (4 self)
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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
Formal Cell Biology in Biocham
"... Abstract. Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this tutorial, we study these ..."
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Cited by 16 (6 self)
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Abstract. Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this tutorial, we study these graphs with formal methods originating from programming theory. We consider systems of biochemical reactions with kinetic expressions, as written in the Systems Biology Markup Language (SBML), and interpreted in the Biochemical Abstract Machine (Biocham) at different levels of abstraction, by either an asynchronous boolean transition system, a continuous time Markov chain, or a system of Ordinary Differential Equations over molecular concentrations. We show that under general conditions satisfied in practice, the activation/inhibition graph is independent of the precise kinetic expressions, and is computable in linear time in the number of reactions. Then we consider the formalization of the biological properties of systems, as observed in experiments, in temporal logics. We show that these logics are expressive enough to capture semiqualitative semiquantitative properties of the boolean and differential semantics of reaction models, and that modelchecking techniques can be used to validate a model w.r.t. its temporal specification, complete it, and search for kinetic parameter values. We illustrate this modelling method with examples on the MAPK signalling cascade, and on Kohn’s map of the mammalian cell cycle. 1
Computing Reachable States for Nonlinear Biological Models
, 2010
"... In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We summarize the stateoftheart for linear systems and then develop a novel algorithm for computing reachable states for n ..."
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Cited by 14 (5 self)
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In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We summarize the stateoftheart for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems. We report experimental results obtained using a prototype implementation applied to several biological models. We believe these results constitute a promising contribution to the analysis of complex models of biological systems.
On the analysis of numerical data time series in temporal logic
 In Proc. CMSB 2007. LNCS/LNBI 4695
, 2007
"... Abstract. Temporal logics and modelchecking techniques have proved successful to respectively express biological properties of complex biochemical systems, and automatically verify their satisfaction in both qualitative and quantitative models. In this paper, we propose a finite time horizon model ..."
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Cited by 13 (1 self)
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Abstract. Temporal logics and modelchecking techniques have proved successful to respectively express biological properties of complex biochemical systems, and automatically verify their satisfaction in both qualitative and quantitative models. In this paper, we propose a finite time horizon modelchecking algorithm for the existential fragment of LTL with numerical constraints over the reals, with the ability to compute the range of values of the real variables occurring in a formula that makes it true in a model. We illustrate this approach for the analysis of biological data time series, provide a set of biologically relevant patterns of formulas, and evaluate them on models of the cell cycle control and MAPK signal transduction. 1
Parameter Synthesis in Nonlinear Dynamical Systems: Application to Systems Biology
"... Abstract. The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic be ..."
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Cited by 12 (0 self)
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Abstract. The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic because in general it is never possible to know/measure the precise state of any biological system due to measurement errors. The parameter synthesis problem is to identify sets of parameters (including initial conditions) for which a given system of nonlinear ODEs does not reach a given set of undesirable states. We present an efficient algorithm for solving this problem that combines sensitivity analysis with an efficient search over initial conditions. It scales to highdimensional models and is exact if the given model is affine. We demonstrate our method on a model of the acute inflammatory response to bacterial infection, and identify initial conditions consistent with 3 biologically relevant outcomes.