## Model Checking Genetic Regulatory Networks using GNA and CADP (2004)

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Venue: | In: Proceedings of the 11th International SPIN Workshop on Model Checking of Software SPIN’2004 |

Citations: | 39 - 6 self |

### BibTeX

@INPROCEEDINGS{Batt04modelchecking,

author = {Gregory Batt and Calin Belta and Grégory Batt and Calin Belta},

title = {Model Checking Genetic Regulatory Networks using GNA and CADP},

booktitle = {In: Proceedings of the 11th International SPIN Workshop on Model Checking of Software SPIN’2004},

year = {2004},

pages = {158--163},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

who are interested in the interdisciplinary methods and applications relevant to the analysis, design and management of complex systems. 15 St. Mary’s St. Brookline MA 02446 l 617.358.1295 l www.bu.edu/systems

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Citation Context ...ions [6] are used to transpose the problem defined on continuous state and parameter spaces into a problem defined on discrete state and parameter spaces. Algorithmic analysis, notably model-checking =-=[22]-=- is then possible. Conservative approximations are used, such that the parameter sets returned by the procedure are guaranteed to be valid. However, it may fail to correctly identify valid parameter s... |

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Citation Context ...ph of G = (S, →) such that for every pair s, s ′ ∈ S ′ , there exists a path in G ′ from s visiting s ′ . When |S ′ | = 1, the strongly connected component is called trivial. Definition 2 (Simulation =-=[46]-=-). Let T1 = (S1, →1, Π, |=1) and T2 = (S2, →2, Π, |=2) be two transition systems defined on a same set of propositions Π. 3sT2 simulates T1 (denoted by T1 � T2) iff there exists an equivalence relatio... |

422 | Modeling and simulation of genetic regulatory systems: A literature review
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Citation Context ...alysis of the so-called genetic regulatory networks. Arguably, the most widely-used modeling frameworks for the analysis of the dynamics of these networks are based on ordinary differential equations =-=[23, 49]-=-. With few exceptions [25], it is generally assumed that the numerical values of state variables and model parameters are precisely known. However, given the current limitations of experimental measur... |

356 | HyTech: A Model Checker for Hybrid Systems
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Citation Context ... computational techniques supporting these symbolic operations currently apply only to systems having rather simple continuous dynamics, such as timed automaton [20, (P )s21], linear hybrid automaton =-=[22]-=-, piecewise-affine systems [17], or affine hybrid automaton [23]. Alternatively, numerical approaches have been proposed in which parameter uncertainties are captured by means of differential inclusio... |

230 | NuSMV 2: An OpenSource Tool for Symbolic Model Checking
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Citation Context ...) code and exploits the Multi-Parametric Toolbox [41] for polyhedral operations and linear programing, the Matlab Boost Graph Library [32] for graph manipulations, and the CTL/LTL model-checker NuSMV =-=[21]-=-. Given a PMA model, an LTL specification of the property and an initial parameter set, the tool can either simply test whether the given parameter set is valid (Problems 1 and 2), or recursively sear... |

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Citation Context ... Hill function h + and of two approximations: the ramp function r + and the step function s + . We illustrate how a gene network can be represented by a PMA model by means of an example inspired from =-=[29]-=-: the toggle-switch (Figure 2). The toggle-switch is made of two genes, a and b, coding for two repressor proteins, A and B. Protein A (resp. B) represses the expression of gene b 7sI1 A B a Figure 2:... |

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Citation Context ... partition of the state space induced by the piecewise nature of the models and specific properties of multiaffine functions [5] to define an equivalence relation on parameters. Discrete abstractions =-=[6]-=- are used to transpose the problem defined on (infinite) continuous state and parameter spaces into a problem defined on (finite) discrete spaces. Algorithmic analysis by model-checking [7] is then po... |

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Citation Context .... Because of its simplicity, this model is actually piecewise-affine. (d) Known and uncertain parameter values. (e) Bistability property expressed in LTL. the piecewise-affine (PA) models proposed in =-=[13]-=- (see also [9]). However, contrary to the step functions used in PA models, ramp functions capture the graded response of gene expression to continuous changes in effector concentrations. 3.2 Embeddin... |

179 | Recognizing safety and liveness
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Citation Context ...ms is the progress of time: time can progress without upper-bound, that is, time-diverges [5, 51]. This plays a key role for liveness properties, expressing that something good will eventually happen =-=[3]-=-. Examples of liveness properties include those given in Section 3 for mutual exclusion, φ2, and for correct functioning, φ3. 22 > 0 > 0sA general problem encountered when defining the semantics of a ... |

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Citation Context ... A (finite or infinite) transition system T = (S, →, Π, |=) satisfies an LTL formula φ, denoted T |= φ, if every execution of T satisfies the formula φ. Proposition 1 (Simulation weakly preserves LTL =-=[19]-=-). Let T1 and T2 be two transition systems such that T1 � T2 and φ be an LTL formula. If T2 |= φ, then T1 |= φ. 2.2 Affine and multiaffine functions, convex sets and polytopes Definition 5 (Affine fun... |

131 | Qualitative simulation of genetic regulatory networks using piecewise-linear models
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Citation Context ...ltiaffine models of genetic regulatory networks In this section, we present a formalism for modeling genetic regulatory networks. To a large extend, we reuse the notations and the terminology used in =-=[24, 11]-=-. We consider a genetic regulatory network consisting of n genes. The state of the network is given by the vector x = (x1, . . . , xn), where xi is the concentration of the protein encoded by gene i. ... |

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Citation Context ...ls considered here is closely related to the class of uncoupled piecewise affine (PA) differential equation models proposed by Glass and Kauffman [31] (see [45] and [24] for further developments, and =-=[37, 50]-=- for an 8 b I2sxb u2 κa(1 − r + (xb, θ 1 b , θ2 b ) r− (u2, θ 1 u2 , θ2 u2 )) low low κa low high κa high low 0 high high κa Table 1: Ramp functions are used to express the logic of gene regulation: p... |

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Citation Context ...eins and small molecules, called genetic regulatory networks. Understanding how the cellular behavior emerges from these networks of interactions is a central problem in systems and synthetic biology =-=[1, 2]-=-. Arguably, the most widely-used modeling frameworks for the analysis of the dynamics of these networks are based on differential equations [3]. With few exceptions [4], it is generally assumed that t... |

78 | Hybrid modeling and simulation of biomolecular networks
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Citation Context ...3] have also addressed the formal analysis of genetic regulatory networks using model-checking approaches, but they use rather simple rule-based and Boolean models, respectively. Like us, Alur et al. =-=[1]-=-, Antoniotti et al. [2] and Ghosh et al. [9] use hybrid models to analyze biological networks. However, Alur et al. and Antoniotti et al. use numerical instead of qualitative models. The most closely-... |

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Citation Context ...guaranties for dense sets of parameters. Alternatively, exhaustive search or symbolic computations have been used to obtain constraints on parameters of discrete models having finite parameter spaces =-=[26, 27]-=-, or of piecewise-affine models having dense parameter spaces [23]. However, these models do not capture complex genetic regulations with graded responses, as we do in the transcriptional cascade exam... |

69 | An Overview of CADP 2001
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Citation Context ...beled Transition Systems (Ltss) rather than by implementing ad hoc reductions. Therefore, we developed a connection between the qualitative simulator Gna and the widely-used Cadp verification toolbox =-=[8]-=-, which provides the required analysis functionalities on Ltss. The connection is established as follows. Firstly, a dedicated translator converts the state transition graph resulting from qualitative... |

60 | Validation of qualitative models of genetic regulatory networks by model checking: Analysis of the nutritional stress response in Escherichia coli
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Citation Context ...here the recursive search stops. We say that two parameters p and p ′ are equivalent if their associated discrete transition systems TR(p) and TR(p ′ ) are isomorphic. A similar definition is used in =-=[17, 9]-=-. Naturally, a PMA system satisfies the same LTL properties for two equivalent parameters. Definition 4 Let ∼P⊆ P × P be the equivalence relation defined by p ∼P p ′ iff TR(p) = TR(p ′ ). Proposition ... |

60 |
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Citation Context ...n piecewise-linear differential equations, that is well-adapted to the qualitative nature of most available biological data. The method has been implemented in the tool Genetic Network Analyzer (Gna) =-=[6]-=-, which produces a graph of qualitative states and transitions between qualitative states. The graph provides a discrete abstraction of the dynamics of the system. A bottleneck in the application of t... |

59 | Efficient on-the-fly modelchecking for regular alternation-free mu-calculus
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Citation Context ...n Cadp to analyze the behaviour of the biological system. The methodology adopted consists of two steps:s– First, each desired property is expressed as a formula in regular alternationfree µ-calculus =-=[12]-=-, which is the input language of the Evaluator 3.0 model checker of Cadp. This temporal logic is a good compromise between expressive power (it subsumes Ctl and Pdl), user-friendliness (concise formul... |

58 | Analysis of Timed Systems using Timeabstracting Bisimulations
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Citation Context ...sets. 5 Enforcing progress of time for proving liveness properties An implicit requirement for dynamical systems is the progress of time: time can progress without upper-bound, that is, time-diverges =-=[5, 51]-=-. This plays a key role for liveness properties, expressing that something good will eventually happen [3]. Examples of liveness properties include those given in Section 3 for mutual exclusion, φ2, a... |

51 | Symbolic techniques for parametric reasoning about counter and clock systems
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Citation Context ...in A synthesis is inhibited by protein B (r− function) and that its degradation is not regulated. Parameter values are given in Figure 1(d). Synthesis parameters are unknown: (κa, κb) ∈ P = [0, 40] × =-=[0, 20]-=-. For illustrating our purpose, we also consider p1 ∈ P with p1 = (36, 17). This network is known to be bistable: it has two stable equilibrium states, corresponding to protein A and B concentrations ... |

51 | Symbolic model checking of biochemical networks
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Citation Context ...ynamics of the underlying genetic regulatory network. Checking properties of qualitative simulation results using temporal logic was originally proposed by Shults and Kuipers [14]. Chabrier and Fages =-=[4]-=- and Peres and Comet [13] have also addressed the formal analysis of genetic regulatory networks using model-checking approaches, but they use rather simple rule-based and Boolean models, respectively... |

50 | Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta–Notch protein signalling
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Citation Context ...urrently apply only to systems having rather simple continuous dynamics, such as timed automaton [20, (P )s21], linear hybrid automaton [22], piecewise-affine systems [17], or affine hybrid automaton =-=[23]-=-. Alternatively, numerical approaches have been proposed in which parameter uncertainties are captured by means of differential inclusions (e.g. ˙x ∈ hull({f(x, p) | p ∈ P })) [24]. For large paramete... |

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Citation Context ...rnative, discrete formalisms). Here, we use ramp functions instead of the step functions used in PA models. Both are simplifications of the Hill functions often used for representing gene regulations =-=[33, 54]-=- (Figure 1). However, contrary to step functions, ramp functions capture the fact that gene expression increases (decreases) gradually with the activator (inhibitor) concentration. Moreover, technical... |

47 | New generation of UPPAAL
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Citation Context ...cular inevitability properties, are comparatively more difficult to analyze because of the difficulty to enforce the progress of time for these systems [52]. To the best of our knowledge, only Uppaal =-=[15]-=- and RED [52] support the verification of (unbounded) liveness properties, for timed automata. These tools are restricted however to the analysis of a limited class of dynamical system, namely timed a... |

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Citation Context ...ls considered here is closely related to the class of uncoupled piecewise affine (PA) differential equation models proposed by Glass and Kauffman [31] (see [45] and [24] for further developments, and =-=[37, 50]-=- for an 8 b I2sxb u2 κa(1 − r + (xb, θ 1 b , θ2 b ) r− (u2, θ 1 u2 , θ2 u2 )) low low κa low high κa high low 0 high high κa Table 1: Ramp functions are used to express the logic of gene regulation: p... |

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Citation Context ...criptional cascade The method presented in the previous section is applied to the analysis of the steady-state input/output (I/O) behavior of a synthetic transcriptional cascade build and analyzed in =-=[19]-=- (Figure 5(a)). We have developed a PMA model of this system, represented in Figure 5(b). Parameter values were estimated based on experimental data available in [19].saTc TetR LacI CI EYFP tetR lacI ... |

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Citation Context ...m will always (G) remain in such a state. We refer the reader to [10] for a discussion of the use of invariants to express stability in biology. PMA models of gene networks were proposed in [11] (see =-=[12]-=- for a related, piecewise-continuous formalism). The models considered here are also related to 3 This assumption requires that a protein does not regulate its own degradation. In practice, this assum... |

34 | Machine learning biochemical networks from temporal logic properties
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Citation Context ...rconservatism, while preserving efficiency. In the field of systems biology, several approaches use formal verification to analyze uncertain models, often with a focus on parameter identification. In =-=[25, 26]-=-, solution trajectories are computed by numerical simulation for parameter values chosen in specified intervals. Model checking is used to select trajectories satisfying the expected properties. This ... |

31 | Progress on reachability analysis of hybrid systems using predicate abstraction
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Citation Context ...0, with ψi ∈ Ψ. If b is a prefix of b ′ , then Pb ′ ⊆ Pb. The hierarchy between the sets Pb induced by the set-inclusion partial-order is represented in Figure 4 for the cross-inhibition network (see =-=[15, 16]-=- for similar ideas in the context of predicate abstraction). ψ1 =κa − 24 : ψ2 =κb − 12 : ψ3 =κb − 8 : ψ4 =κa − 16 : < 0 P00 < 0 P0 < 0 T ∀ R (P0) �|= φ1 > 0 P01 < 0 > 0 < 0 > 0 Pɛ P1001 = P 2 = P 3 = ... |

31 | Pathway Logic: executable models of biological networks
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Citation Context ...our approach is currently limited to uncertain rate parameters. In the field of systems biology, several approaches based on model checking have been proposed for the analysis of biochemical networks =-=[26, 16, 20, 9, 11]-=-. More specifically, the use of model checking for parameter identification has been proposed for discrete models in [16] and for continuous models in [20]. The discrete models used in [16] provide a ... |

29 | V.: Control of multi-affine systems on rectangles with applications to hybrid biomolecular networks
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Citation Context ... the system will always (G) remain in such a state. We refer the reader to [10] for a discussion of the use of invariants to express stability in biology. PMA models of gene networks were proposed in =-=[11]-=- (see [12] for a related, piecewise-continuous formalism). The models considered here are also related to 3 This assumption requires that a protein does not regulate its own degradation. In practice, ... |

29 | Automated symbolic reachability analysis with application to delta-notch signaling automata
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Citation Context ...f genetic regulatory networks using model-checking approaches, but they use rather simple rule-based and Boolean models, respectively. Like us, Alur et al. [1], Antoniotti et al. [2] and Ghosh et al. =-=[9]-=- use hybrid models to analyze biological networks. However, Alur et al. and Antoniotti et al. use numerical instead of qualitative models. The most closely-related work is the symbolic reachability an... |

27 |
On the relation between effector concentration and the rate of induced enzyme synthesis
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Citation Context ...rnative, discrete formalisms). Here, we use ramp functions instead of the step functions used in PA models. Both are simplifications of the Hill functions often used for representing gene regulations =-=[33, 54]-=- (Figure 1). However, contrary to step functions, ramp functions capture the fact that gene expression increases (decreases) gradually with the activator (inhibitor) concentration. Moreover, technical... |

26 |
The evolution of molecular biology into systems biology
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Citation Context ...c level by a network of interactions between genes, proteins and small molecules. Understanding 1show the cellular behavior emerges from these networks of interactions is a central problem in biology =-=[38, 53]-=-. Recent technological advances, notably for monitoring gene expression [43], provide new opportunities to answer this long-standing question and have renewed the interest for the analysis of the so-c... |

25 | Reachability analysis of multi-affine systems
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Citation Context ...sts at least one common vertex at which the direction of the vector field (fi(v, p)) is in agreement with the relative position of the two rectangles (c ′ i − ci). Similar rules have been proposed in =-=[14]-=-. Consider the two rectangles R11 and R21 in Figure 2(a). They share two vertices: v1 = (θ1 a, 0) and v2 = (θ1 a, θ1 b ). From Proposition 1, there is a transition from R11 to R21, because fa(v1, p1) ... |

23 |
System modeling in cellular biology: from concepts to nuts and bolts
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Citation Context ...is a central problem in systems and synthetic biology [1, 2]. Arguably, the most widely-used modeling frameworks for the analysis of the dynamics of these networks are based on differential equations =-=[3]-=-. With few exceptions [4], it is generally assumed that the numerical values of state variables and model parameters are precisely known. However, given the current limitations of experimental measure... |

22 | Proving properties of continuous systems: qualitative simulation and temporal logic
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(Show Context)
Citation Context ...lable for analyzing the dynamics of the underlying genetic regulatory network. Checking properties of qualitative simulation results using temporal logic was originally proposed by Shults and Kuipers =-=[14]-=-. Chabrier and Fages [4] and Peres and Comet [13] have also addressed the formal analysis of genetic regulatory networks using model-checking approaches, but they use rather simple rule-based and Bool... |

21 |
Forthcoming. Advances in synthetic biology: On the path from prototypes to applications. Curr Opin Biotechnol. Corrected Proof
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Citation Context ...we address here is central in the nascent field of synthetic biology, since most initial attempts at constructing genetic regulatory networks do not result in a system exhibiting the desired behavior =-=[44, 7]-=-. The capacity of the proposed approach to analyze systems of realistic size and give biologically meaningful results was demonstrated on a real application. Second, the proposed approach essentially ... |

19 |
Constructing decidable hybrid systems with velocity bounds
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Citation Context ...of system is motivated by our biological application. However, a theorem similar to, and in fact stronger than, Theorem 1 holds for affine functions on polytopes (with f(P ) = hull({f(v) | v ∈ VP })) =-=[13]-=-, so that our proposed approach would apply as well for similarly-defined continuous piecewise affine systems on polytopes. More generally, for a large class of switched systems, techniques such as th... |

18 | Symbolic parametric safety analysis of linear hybrid systems with bdd-like data-structures - Wang - 2004 |

18 | Taming the complexity of biochemical models through bisimulation and collapsing: theory and practice
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- 2004
(Show Context)
Citation Context ...rconservatism, while preserving efficiency. In the field of systems biology, several approaches use formal verification to analyze uncertain models, often with a focus on parameter identification. In =-=[25, 26]-=-, solution trajectories are computed by numerical simulation for parameter values chosen in specified intervals. Model checking is used to select trajectories satisfying the expected properties. This ... |

17 |
Control of a class of non-linear systems on rectangles
- Belta, Habets
(Show Context)
Citation Context ... valid subsets of a given parameter set.sIn the proposed approach, we use a partition of the state space induced by the piecewise nature of the models and specific properties of multiaffine functions =-=[5]-=- to define an equivalence relation on parameters. Discrete abstractions [6] are used to transpose the problem defined on (infinite) continuous state and parameter spaces into a problem defined on (fin... |

17 |
Molecular interaction maps as information organizers and simulation guides
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(Show Context)
Citation Context ...θ 1 b < θ 2 b < κb/γb < max b Fig.1. (a) Example of a genetic regulatory network of two genes, a and b. The notation follows, in a somewhat simplified form, the graphical conventions proposed by Kohn =-=[11]-=-. (b) Qualitative model, corresponding to the two-gene example, composed of piecewise-linear differential equations (1)-(2) and parameter inequalities (3)-(4). The phase space can be partitioned into ... |

16 |
Tuning genetic control through promoter engineering
- Alper, Fischer, et al.
(Show Context)
Citation Context ...ameter sets. We focus on tuning production rate parameters, since recent experimental techniques have been developed for the controlled modification of transcription or translation efficiencies (e.g. =-=[2]-=-). Accordingly, we left the parameters κlacI , κcI and κeyfp unconstrained - or more precisely in a very large interval - and performed a search for valid parameter sets. A first attempt did not yield... |

15 | Model checking liveness properties of genetic regulatory networks
- Batt, Belta, et al.
- 2007
(Show Context)
Citation Context ...es of similar volumes). Additionally, RoVerGeNe supports an extension of the method presented here, dealing with problems specifically encountered when verifying liveness properties, and described in =-=[8, 18]-=-. 5 Tuning of a transcriptional cascade The method presented in the previous section is applied to the analysis of the steady-state input/output (I/O) behavior of a synthetic transcriptional cascade b... |

15 | Qualitative analysis and verification of hybrid models of genetic regulatory networks : Nutritional stress response
- Batt, Ropers, et al.
- 2005
(Show Context)
Citation Context ...ltiaffine models of genetic regulatory networks In this section, we present a formalism for modeling genetic regulatory networks. To a large extend, we reuse the notations and the terminology used in =-=[24, 11]-=-. We consider a genetic regulatory network consisting of n genes. The state of the network is given by the vector x = (x1, . . . , xn), where xi is the concentration of the protein encoded by gene i. ... |

13 |
Automata-theoretic verification of real-time systems
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- 1996
(Show Context)
Citation Context ...sets. 5 Enforcing progress of time for proving liveness properties An implicit requirement for dynamical systems is the progress of time: time can progress without upper-bound, that is, time-diverges =-=[5, 51]-=-. This plays a key role for liveness properties, expressing that something good will eventually happen [3]. Examples of liveness properties include those given in Section 3 for mutual exclusion, φ2, a... |