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Modelling and analysis of gene regulatory networks,
 Nat Rev Mol Cell Biol
, 2008
"... The genome encodes thousands of genes whose pro ducts enable cell survival and numerous cellular func tions. The amounts and the temporal pattern in which these products appear in the cell are crucial to the pro cesses of life. Gene regulatory networks govern the levels of these gene products. A ge ..."
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Cited by 118 (2 self)
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The genome encodes thousands of genes whose pro ducts enable cell survival and numerous cellular func tions. The amounts and the temporal pattern in which these products appear in the cell are crucial to the pro cesses of life. Gene regulatory networks govern the levels of these gene products. A gene regulatory net work is the collection of molecular species and their inter actions, which together control geneproduct abundance. Numerous cellular processes are affected by regulatory networks. Innovations in experimental methods have ena bled largescale studies of gene regulatory networks and can reveal the mechanisms that underlie them. Consequently, biologists must come to grips with extremely complex networks and must analyse and integrate great quantities of experimental data. Essential to this challenge are computational tools, which can answer various questions: what is the full range of behaviours that this system exhibits under different conditions? What changes are expected in the dynamics of the system if certain parts stop functioning? How robust is the system under extreme conditions? Various computational models have been developed for regulatory network analysis. These models can be roughly divided into three classes. The first class, logi cal models, describes regulatory networks qualitatively. They allow users to obtain a basic understanding of the different functionalities of a given network under dif ferent conditions. Their qualitative nature makes them flexible and easy to fit to biological phenomena, although they can only answer qualitative questions. To under stand and manipulate behaviours that depend on finer timing and exact molecular concentrations, a second class of models was developed continuous models. For example, to simulate the effects of dietary restriction on yeast cells under different nutrient concentrations 1 , users must resort to the finer resolution of continuous models. A third class of models was introduced follow ing the observation that the functionality of regulatory networks is often affected by noise. As the majority of these models account for interactions between individual molecules, they are referred to here as singlemolecule level models. Singlemolecule level models explain the relationship between stochasticity and gene regulation. Predictive computational models of regulatory net works are expected to benefit several fields. In medi cine, mechanisms of diseases that are characterized by dysfunction of regulatory processes can be elucidated. Biotechnological projects can benefit from predictive models that will replace some tedious and costly lab experiments. And, computational analysis may con tribute to basic biological research, for example, by explaining developmental mechanisms or new aspects of the evolutionary process. Here we review the available methodologies for mod elling and analysing regulatory networks. These meth odologies have already proved to be a valuable research tool, both for the development of network models and for the analysis of their functionality. We discuss their relative advantages and limitations, and outline some open questions regarding regulatory networks, includ ing how structure, dynamics and functionality relate to each other, how organisms use regulatory networks to adapt to their environments, and the interplay between regulatory networks and other cellular processes, such as metabolism. Stochasticity The property of a system whose behaviour depends on probabilities. In a model with stochasticity, a single initial state can evolve into several different trajectories, each with an associated probability. Modelling and analysis of gene regulatory networks Guy Karlebach and Ron Shamir Abstract  Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.
Necessary conditions for multistationarity in discrete dynamical systems
, 2007
"... R. Thomas conjectured, twenty years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar ..."
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Cited by 35 (12 self)
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R. Thomas conjectured, twenty years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar approach, we generalize the result to discrete dynamical systems, and by focusing on the asynchronous dynamics that R. Thomas used in the course of his analysis of genetic networks, we obtain a more general variant of the R. Thomas ’ conjecture. In this way, we get a necessary condition for genetic networks to lead to differentiation.
Detecting Inconsistencies in Large Biological Networks with Answer Set Programming
, 2008
"... We introduce an approach to detecting inconsistencies in large biological networks by using Answer Set Programming. To this end, we build upon a recently proposed notion of consistency between biochemical/genetic reactions and highthroughput profiles of cell activity. We then present an approach ba ..."
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Cited by 28 (13 self)
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We introduce an approach to detecting inconsistencies in large biological networks by using Answer Set Programming. To this end, we build upon a recently proposed notion of consistency between biochemical/genetic reactions and highthroughput profiles of cell activity. We then present an approach based on Answer Set Programming to check the consistency of largescale data sets. Moreover, we extend this methodology to provide explanations for inconsistencies in the data by determining minimal representations of conflicts. In practice, this can be used to identify unreliable data or to indicate missing reactions.
Uncovering operational interactions in genetic networks using asynchronous boolean dynamics
 in "J. Theor. Biol
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Negative circuits and sustained oscillations in asynchronous automata networks
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From logical regulatory graphs to standard Petri nets: Dynamical roles and functionality of feedback circuits
 WEAKNESSES OF SELECTED MODELING METHODS USED IN SYSTEMS BIOLOGY CIRCUITS. TRANSACTIONS ON COMPUTATIONAL SYSTEMS BIOLOGY VII, LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Logical modelling and Petri nets constitute two complementary approaches for the dynamical modelling of biological regulatory networks. Leaning on a translation of logical models into standard Petri nets, we propose a formalisation of the notion of circuit functionality in the Petri net framework. ..."
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Cited by 16 (7 self)
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Logical modelling and Petri nets constitute two complementary approaches for the dynamical modelling of biological regulatory networks. Leaning on a translation of logical models into standard Petri nets, we propose a formalisation of the notion of circuit functionality in the Petri net framework. This approach is illustrated with the modelling and analysis of a molecular regulatory network involved in the control of Thlymphocyte differentiation.
Temporal constraints in the logical analysis of regulatory networks
 Theoretical Computer Science
"... Starting from the logical description of gene regulatory networks developed by R. Thomas, we introduce an enhanced modelling approach based on timed automata. We obtain a refined qualitative description of the dynamical behaviour by exploiting not only information on ratios of kinetic parameters re ..."
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Cited by 12 (2 self)
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Starting from the logical description of gene regulatory networks developed by R. Thomas, we introduce an enhanced modelling approach based on timed automata. We obtain a refined qualitative description of the dynamical behaviour by exploiting not only information on ratios of kinetic parameters related to synthesis and decay, but also constraints on the time delays associated with the operations of the system. We develop a formal framework for handling such temporal constraints using timed automata, discuss the relationship with the original Thomas formalism, and demonstrate the potential of our approach by analysing an illustrative gene regulatory network of bacteriophage λ. 1
Positive circuits and maximal number of fixed points in discrete dynamical systems
 Discrete Appl. Math
, 2009
"... We consider a product X of n finite intervals of integers, a map F from X to itself, the asynchronous state transition graph Γ(F) on X that Thomas proposed as a model for the dynamics of a network of n genes, and the interaction graph G(F) that describes the topology of the system in terms of positi ..."
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Cited by 12 (3 self)
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We consider a product X of n finite intervals of integers, a map F from X to itself, the asynchronous state transition graph Γ(F) on X that Thomas proposed as a model for the dynamics of a network of n genes, and the interaction graph G(F) that describes the topology of the system in terms of positive and negative interactions between its n components. Then, we establish an upper bound on the number of fixed points for F, and more generally on the number of attractors in Γ(F), which only depends on X and on the topology of the positive circuits of G(F). This result generalizes the following discrete version of Thomas ’ conjecture recently proved by Richard and Comet: If G(F) has no positive circuit, then Γ(F) has a unique attractor. This result also generalizes a result on the maximal number of fixed points in Boolean networks obtained by Aracena, Demongeot and Goles. The interest of this work in the context of gene network modeling is briefly discussed.
On differentiation and homeostatic behaviours of Boolean dynamical systems
 of Lecture Notes in Computer Science
, 2007
"... Abstract. We study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in [10] are stable under projection, and this en ..."
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Cited by 11 (6 self)
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Abstract. We study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in [10] are stable under projection, and this enables us to relax the assumptions under which they are valid. More precisely, we relate here the presence of a positive (resp. negative) circuit in a regulatory graph to a more general form of biological differentiation (resp. of homeostasis). 1
From minimal signed circuits to the dynamics of Boolean regulatory networks
, 2008
"... It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (involved in homeostasis). Rules propose ..."
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Cited by 10 (5 self)
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It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (involved in homeostasis). Rules proposed by the biologist R. Thomas assert that these circuits are necessary for such dynamical properties. These rules have been studied by several authors. Their obvious interest is that they relate the rather simple information contained in the structure of the network (signed circuits) to its much more complex dynamical behaviour. We prove in this article a nontrivial converse of these rules, namely that certain positive or negative circuits in a regulatory graph are actually sufficient for the observation of a restricted form of the corresponding dynamical property, differentiation or homeostasis. More precisely, the crucial property that we require is that the circuit be globally minimal. We then apply these results to the vertebrate immune system, and show that the 2 minimal functional positive circuits of the model indeed behave as modules which combine to explain the presence of the 3 stable states corresponding to the Th0, Th1 and Th2 cells.