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Morphisms of reaction networks that couple structure to function
 BMC Systems Biology
"... Background: The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures ..."
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Background: The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures. Results: We define morphisms (mappings) between reaction networks that establish structural connections between them. Some morphisms imply kinetic similarity, and yet their properties can be checked statically on the structure of the networks. In particular we can determine statically that a complex network will emulate a simpler network: it will reproduce its kinetics for all corresponding choices of reaction rates and initial conditions. We use this property to relate the kinetics of many common biological networks of different sizes, also relating them to a fundamental population algorithm. Conclusions: Structural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks.
Biochemical reaction rules with constraints
 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2011
"... 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 picalculus, in contrast to previous rulebased programming languages, and fur ..."
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Cited by 7 (3 self)
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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 picalculus, in contrast to previous rulebased 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 NPcomplete 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.
Graphs, Rewriting and Pathway Reconstruction for RuleBased Models
"... In this paper, we introduce a novel way of constructing concise causal histories (pathways) to represent how specified structures are formed during simulation of systems represented by rulebased models. This is founded on a new, clean, graphbased semantics introduced in the first part of this paper ..."
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In this paper, we introduce a novel way of constructing concise causal histories (pathways) to represent how specified structures are formed during simulation of systems represented by rulebased models. This is founded on a new, clean, graphbased semantics introduced in the first part of this paper for Kappa, a rulebased modelling language that has emerged as a natural description of proteinprotein interactions in molecular biology [1]. The semantics is capable of capturing the whole of Kappa, including subtle sideeffects on deletion of structure, and its structured presentation provides the basis for the translation of techniques to other models. In particular, we give a notion of trajectory compression, which restricts a trace culminating in the production of a given structure to the actions necessary for the structure to occur. This is central to the reconstruction of biochemical pathways due to the failure of traditional techniques to provide adequately concise causal histories, and we expect it to be applicable in a range of other modelling situations.
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.
Forward and Backward Bisimulations for Chemical Reaction Networks
"... We present two quantitative behavioral equivalences over species of a chemical reaction network (CRN) with semantics based on ordinary differential equations. Forward CRN bisimulation identifies a partition where each equivalence class represents the exact sum of the concentrations of the species b ..."
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We present two quantitative behavioral equivalences over species of a chemical reaction network (CRN) with semantics based on ordinary differential equations. Forward CRN bisimulation identifies a partition where each equivalence class represents the exact sum of the concentrations of the species belonging to that class. Backward CRN bisimulation relates species that have identical solutions at all time points when starting from the same initial conditions. Both notions can be checked using only CRN syntactical information, i.e., by inspection of the set of reactions. We provide a unified algorithm that computes the coarsest refinement up to our bisimulations in polynomial time. Further, we give algorithms to compute quotient CRNs induced by a bisimulation. As an application, we find significant reductions in a number of models of biological processes from the literature. In two cases we allow the analysis of benchmark models which would be otherwise intractable due to their memory requirements.
Bigraphical Languages and their Simulation
"... We study bigraphs as a foundation for practical formal languages and the problem of simulating such bigraphical languages. The theory of bigraphs is a foundational, graphical model of concurrent systems focusing on mobility and connectivity. It is a metamodel in the sense that it is parametrized ov ..."
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We study bigraphs as a foundation for practical formal languages and the problem of simulating such bigraphical languages. The theory of bigraphs is a foundational, graphical model of concurrent systems focusing on mobility and connectivity. It is a metamodel in the sense that it is parametrized over a signature and a set of reaction rules which determine the syntax and dynamic semantics, respectively. This allows for rather direct models and, together with a natural yet formal graphical notation and an elegant theory of behavioral equivalence, this makes bigraphs an enticing foundation for practical formal languages. However, the theory of bigraphs is still young. While direct models of many process calculi have been constructed, it is unclear how suitable bigraphs are for more practical formal languages. Also, the generality of bigraphs comes at a price of complexity in the theory and simulation of bigraphical models is nontrivial. A key problem is that of matching: deciding if and how a reaction rule applies to a bigraph. In this dissertation, we study bigraphs and their simulation for two types of practical formal languages: programming languages and languages for cell biology. First, we study programming languages and binding bigraphs, a variant of bigraphs with a facility for modeling the binders found in most programming languages. Building on an existing
Complex Functional Rates in Rulebased Languages for Biochemistry
 Transactions on Computational Systems Biology
"... Rulebased languages (like, for example, Kappa, BioNetGen, and BioCham) have emerged as successful models for the representation, analysis, and simulation of biochemical systems. In particular Kappa, although based on reactions, differs from traditional chemistry as it allows for a graphlike repre ..."
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Rulebased languages (like, for example, Kappa, BioNetGen, and BioCham) have emerged as successful models for the representation, analysis, and simulation of biochemical systems. In particular Kappa, although based on reactions, differs from traditional chemistry as it allows for a graphlike representation of complexes. It follows the “don’t care, don’t write ” approach: a rule contains the description of only those parts of the complexes that are actually involved in a reaction. Hence, given any possible combination of complexes that contain the reactants, such complexes can give rise to the reaction. In this paper we address the problem of extending the “don’t care, don’t write ” approach to cases in which the actual structure of the complexes involved in the reaction could affect it (for instance, the mass of the complexes could influence the rate). The solutions that we propose is κF, an extension of the Kappacalculus in which rates are defined as functions of the actually involved complexes.