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26
From Reaction Models to Influence Graphs and Back: a Theorem
, 2008
"... Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also more and more employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this paper, we study the ..."
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Cited by 17 (8 self)
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Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also more and more employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this paper, we study the formal relationship between these graphs. We consider systems of biochemical reactions with kinetic expressions, as written in the Systems Biology Markup Language SBML, and interpreted by a system of Ordinary Differential Equations over molecular concentrations. We show that under a general condition of increasing monotonicity of the kinetic expressions, and in absence of both activation and inhibition effects between a pair of molecules, the influence graph inferred from the stoichiometric coefficients of the reactions is equal to the one defined by the signs of the coefficients of the Jacobian matrix. Under these conditions, satisfied by mass action law, MichaelisMenten and Hill kinetics, the influence graph is thus independent of the precise kinetic expressions, and is computable in linear time in the number of reactions. We apply these results to Kohn’s map of the mammalian cell cycle and to the MAPK signalling cascade. Then we propose a syntax for denoting antagonists in reaction rules and generalize our results to this setting.
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
Dynamical Properties of Discrete Reaction Networks
, 2013
"... Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying dis ..."
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Cited by 4 (0 self)
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Reaction networks are commonly used to model the dynamics of populations subject to transformations that follow an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modeling the underlying discrete nondeterministic transitions of stochastic models of reaction networks. In that sense, a proof of nonreachability in a given DRN has immediate implications for any concrete stochastic model based on that DRN, independent of the choice of kinetic laws and constants. Moreover, if we assume that stochastic kinetic rates are given by the massaction law (or any other kinetic law that gives nonvanishing probability to each reaction if the required number of interacting substrates is present), then reachability properties are equivalent in the two settings. The analysis of two types of global dynamical properties of DRNs is addressed: irreducibility, i.e., the ability to reach any discrete state from any other state; and recurrence, i.e., the ability to return to any initial state. Our results consider both the verification of such properties when species are present in a large copy number, and in the general case. The necessary and sufficient conditions obtained involve algebraic conditions on the network reactions which in most cases can be verified using linear programming. Finally, the relationship of DRN irreducibility and recurrence with dynamical properties of stochastic and continuous models of reaction networks is discussed. 1
Knockout Prediction for Reaction Networks with Partial Kinetic Information
, 2012
"... Abstract. In synthetic biology, a common application field for computational methods is the prediction of knockout strategies for reaction networks. Thereby, the major challenge is the lack of information on reaction interpretation, to predict candidates for reaction knockouts, relying only on parti ..."
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Abstract. In synthetic biology, a common application field for computational methods is the prediction of knockout strategies for reaction networks. Thereby, the major challenge is the lack of information on reaction interpretation, to predict candidates for reaction knockouts, relying only on partial kinetic information. We consider the usual deterministic steady state semantics of reaction networks and a few general properties of reaction kinetics. We introduce a novel abstract domain over pairs of real domain values to compute the differences between steady states that are domain allows us to predict correct knockout strategy candidates independent of any particular choice of reaction kinetics. Our predictions remain candidates, since our abstract interpretation overapproximates the solution space. We provide an operational semantics for our abstraction in terms of constraint satisfaction problems and illustrate our approach on a realistic network.
Type Directed Semantics for the Calculus of Looping Sequences
"... Abstract The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. Here we enrich this calculus with a type discipline which preserves some biological properties deriving from the requirement of certain elements, and the rep ..."
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Abstract The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. Here we enrich this calculus with a type discipline which preserves some biological properties deriving from the requirement of certain elements, and the repellency of others. In particular, the type system guarantees the soundness of the application of reduction rules with respect to the elements which are required (all requirements must be satisfied) and to the elements which are excluded (two elements which repel each other cannot occur in the same compartment). As an example, we model the possible interactions (and compatibility) of different blood types with different antigens. The type system does not allow transfusion with incompatible blood types. 1
A stronger necessary condition for the multistationarity of chemical reaction networks
, 2013
"... ..."
Typed Membrane Systems
"... Summary. We introduce and study typing rules and a type inference algorithm for P systems with symport/antiport evolution rules. The main results are given by a subject reduction theorem and the completeness of type inference. We exemplify how the type system is working by presenting a typed descrip ..."
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Summary. We introduce and study typing rules and a type inference algorithm for P systems with symport/antiport evolution rules. The main results are given by a subject reduction theorem and the completeness of type inference. We exemplify how the type system is working by presenting a typed description of the sodiumpotassium pump. 1
Typed Stochastic Semantics for the Calculus of Looping Sequences
, 2012
"... The Stochastic Calculus of Looping Sequences is a quantitative term rewrite formalism suitable to describe the evolution of microbiological systems, taking into account the speed of the described activities. In this paper we propose an operational semantics for this calculus that considers the types ..."
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The Stochastic Calculus of Looping Sequences is a quantitative term rewrite formalism suitable to describe the evolution of microbiological systems, taking into account the speed of the described activities. In this paper we propose an operational semantics for this calculus that considers the types of the species to derive the stochastic evolution of the system. The presence of positive and negative catalysers can modify these speeds. We claim that types provide an abstraction suitable to represent the interaction between elements without specifying exactly the element positions. Our claim is supported through an example modelling the lactose operon.
A Formalism for the Description of Protein Interaction
, 2010
"... The Calculus of Looping Sequences is a formalism for describing evolution of biological systems by means of term rewriting rules. We propose to enrich this calculus by labelling elements of sequences. Since two elements with the same label are considered to be linked, this allows us to represent p ..."
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The Calculus of Looping Sequences is a formalism for describing evolution of biological systems by means of term rewriting rules. We propose to enrich this calculus by labelling elements of sequences. Since two elements with the same label are considered to be linked, this allows us to represent protein interaction at the domain level. Wellformedness of terms are ensured by both a syntactic constraint and a type system: we discuss the differences between these approaches through the description of a biological system, namely the EGF pathway.
Types for BioAmbients
 In FBTC’10, volume 19 of EPTCS
, 2010
"... The BioAmbients calculus is a process algebra suitable for representing compartmentalization, molecular localization and movements between compartments. In this paper we enrich this calculus with a static type system classifying each ambient with group types specifying the kind of compartments in wh ..."
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The BioAmbients calculus is a process algebra suitable for representing compartmentalization, molecular localization and movements between compartments. In this paper we enrich this calculus with a static type system classifying each ambient with group types specifying the kind of compartments in which the ambient can stay. The type system ensures that, in a welltyped process, ambients cannot be nested in a way that violates the type hierarchy. Exploiting the information given by the group types, we also extend the operational semantics of BioAmbients with rules signalling errors that may derive from undesired ambients ’ moves (i.e. merging incompatible tissues). Thus, the signal of errors can help the modeller to detect and locate unwanted situations that may arise in a biological system, and give practical hints on how to avoid the undesired behaviour. 1