Comparing chemical reaction networks: A categorical and algorithmic perspective

Cardelli, Luca; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea

doi:10.1016/j.tcs.2017.12.018

Cited by 11 publications

(19 citation statements)

References 42 publications

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“…The main features of our approach are: (i) a compact encoding of an individual, which exploits information about the structure of an influence network and about necessary conditions for the existence of an emulation; and (ii) the design of a fitness function that uses the BDE partition-refinement algorithm to measure the distance between the individual and a possible emulation. We apply our algorithm to the influence networks first introduced in [4] and then algorithmically analyzed with CAGE [7]. With a prototype implementation, we find that EGAC recovers previously found emulations.…”

Section: Introductionmentioning

confidence: 78%

“…We performed three kinds of experiments. First, we studied the soundness of EGAC by comparing it against the exact CAGE algorithm of [7]. Then, we performed scalability experiments by considering networks of larger size which could not be handled by CAGE.…”

Section: Resultsmentioning

confidence: 99%

“…Also, there might be more than one emulation among two CRNs. This is overcome in [7] where the authors provide an algorithm, CAGE, that uses the largest-BDE computation as an inner step and returns all possible emulations among two CRNs. This is done by first computing all possible BDEs of the union CRN, filtered through the above two characterizing properties.…”

Section: Emulationmentioning

confidence: 99%

“…In addition to the exact algorithm, a bounded version (hereafter called bCAGE) is discussed in [7] which provides an under-approximation of the set of all BDEs with the aim of reducing memory consumption. With our domain-specific EGAC we encode domain-specific knowledge directly in the algorithm, showing its effectiveness with respect to both CAGE and bCAGE when applied to discovering emulations for influence networks.…”

Section: Emulationmentioning

confidence: 99%

“…Instead, finding all possible emulations between two CRNs is possible through an algorithm, CAGE, that computes all BDEs (which thus will contain all emulations) [7]. However often emulations may be a small fraction thereof.…”

Section: Introductionmentioning

confidence: 99%

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Discovering relations between chemical reaction networks (CRNs) is a relevant problem in computational systems biology for model reduction, to explain if a given system can be seen as an abstraction of another one; and for model comparison, useful to establish an evolutionary path from simpler networks to more complex ones. This is also related to foundational issues in computer science regarding program equivalence, in light of the established interpretation of a CRN as a kernel programming language for concurrency. Criteria for deciding if two CRNs can be formally related have been recently developed, but these require that a candidate mapping be provided. Automatically finding candidate mappings is very hard in general since the search space essentially consists of all possible partitions of a set. In this paper we tackle this problem by developing a genetic algorithm for a class of CRNs called influence networks, which can be used to model a variety of biological systems including cell-cycle switches and gene networks. An extensive numerical evaluation shows that our approach can successfully establish relations between influence networks from the literature which cannot be found by exact algorithms due to their large computational requirements.

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Section: Introductionmentioning

confidence: 78%

Section: Resultsmentioning

confidence: 99%

Section: Emulationmentioning

confidence: 99%

Section: Emulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reducing Boolean Networks with Backward Boolean Equivalence

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Syntactic Markovian Bisimulation for Chemical Reaction Networks

Cardelli

Tribastone

Tschaikowski

et al. 2017

Lecture Notes in Computer Science

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In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.

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Comparing chemical reaction networks: A categorical and algorithmic perspective

Cited by 11 publications

References 42 publications

Egac

Egac

Reducing Boolean Networks with Backward Boolean Equivalence

Syntactic Markovian Bisimulation for Chemical Reaction Networks

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