Formal molecular biology

Danos, Vincent; Laneve, Cosimo

doi:10.1016/j.tcs.2004.03.065

Cited by 410 publications

(384 citation statements)

References 20 publications

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“…transition systems by either process calculi [22,45,46,47,48], rules [33,10,9], Petri nets [26,29], etc..., but also for formalizing the biological properties of the system known from biological experiments under various conditions, opens a whole avenue of research for designing automated reasoning tools inspired from circuit and program verification to help the modeler [15]. The temporal logics CTL (Computation Tree Logic), LTL (Linear Time Logic) and PLTL (Probabilistic LTL) with numerical constraints are used in the three semantics of reaction models, respectively, in the boolean semantics, the differential semantics and the stochastic semantics.…”

Section: Corollary 3 the Differential Influence Graph Of A Reaction mentioning

confidence: 99%

Formal Cell Biology in Biocham

Fages

Soliman

Formal Methods for Computational Systems Biology

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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 semi-qualitative semi-quantitative properties of the boolean and differential semantics of reaction models, and that model-checking 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.

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Section: Corollary 3 the Differential Influence Graph Of A Reaction mentioning

confidence: 99%

Formal Cell Biology in Biocham

Fages

Soliman

Formal Methods for Computational Systems Biology

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“…Kappa [8], a stochastic rewriting approach for graphs representing molecular structures, is a case in point. For a particular class of (hyper)graphs and finely tuned constraints on rules and matches, its techniques for refinement, simulation and analysis [5,9] are significantly more powerful than those for standard (stochastic) graph transformations.…”

Section: Introductionmentioning

confidence: 99%

Transformation and Refinement of Rigid Structures

Danos

Heckel

Sobociński

2014

Graph Transformation

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Abstract. Stochastic rule-based models of networks and biological systems are hard to construct and analyse. Refinements help to produce systems at the right level of abstraction, enable analysis techniques and mappings to other formalisms. Rigidity is a property of graphs introduced in Kappa to support stochastic refinement, allowing to preserve the number of matches for rules in the refined system. In this paper: 1) we propose a notion of rigidity in an axiomatic setting based on adhesive categories; 2) we show how the rewriting of rigid structures can be defined systematically by requiring matches to be open maps reflecting structural features which ensure that rigidity is preserved; and 3) we obtain in our setting a notion of refinement which generalises that in Kappa, and allows a rule to be partitioned into a set of rules which are collectively equivalent to the original. We illustrate our approach with an example of a social network with dynamic topology.

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“…The paradigm of chemical reactions is predominant in programming languages used for modeling and simulation in systems biology [6,9,3,19,1]. Chemical reactions are advantageous in that they can be given both, a continuous semantics in terms of ordinary differential equations (odes) as well as a stochastic semantics in terms of continuous time Markov chains (ctmcs).…”

Section: Introductionmentioning

confidence: 99%

“…Biochemical reactions in the κ-calculus are widely accepted as a useful modeling language for systems biology [4,12,5,6]. The underlying idea is to model biochemical reactions as graph rewrite rules.…”

Section: Introductionmentioning

confidence: 99%

Biochemical Reaction Rules with Constraints

John

Lhoussaine

Niehren

et al. 2011

Programming Languages and Systems

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Abstract. We propose React(C ), an expressive programming language for stochastic modeling and simulation in systems biology that is based on biochemical reactions with constraints. We prove that React(C ) can express the stochastic π-calculus, in contrast to previous rule-based programming languages, and further illustrate the high expressiveness of React(C ). We present a stochastic simulator for React(C ) independently of the choice of the constraint language C . Our simulator decides for a given reaction rule whether it can be applied to the current biochemical solution. We show that this decision problem is NP-complete for arbitrary constraint systems C and that it can be solved in polynomial time for rules of bounded arity. In practice, we propose to solve this problem by constraint programming.

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Formal molecular biology

Cited by 410 publications

References 20 publications

Formal Cell Biology in Biocham

Formal Cell Biology in Biocham

Transformation and Refinement of Rigid Structures

Biochemical Reaction Rules with Constraints

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