Abstracting the Differential Semantics of Rule-Based Models: Exact and Automated Model Reduction

Danos, Vincent; Feret, Jérôme; Fontana, Walter; Harmer, Russell; Krivine, Jean

doi:10.1109/lics.2010.44

Cited by 68 publications

(75 citation statements)

References 53 publications

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“…We are not aware of general automated approaches to ODE equivalences as done in this paper, though there is a large literature of techniques in domain-specific situations. The combinatorial explosion of CRN biochemical models has spurred considerable research in this area, e.g., [15,16,20,24,25,28,35,36]. The fragmentation approach for κ identifies a coarse-grained ODE system for models with mass-action semantics through sums of variables; this is weaker than an equivalence relation over species, because one variable may appear in more than one block (a fragment) [28,36].…”

Section: Introductionmentioning

confidence: 99%

Symbolic computation of differential equivalences

Cardelli

Tribastone

Tschaikowski

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Ordinary differential equations (ODEs) are widespread in many natural sciences including chemistry, ecology, and systems biology, and in disciplines such as control theory and electrical engineering. Building on the celebrated molecules-as-processes paradigm, they have become increasingly popular in computer science, with highlevel languages and formal methods such as Petri nets, process algebra, and rule-based systems that are interpreted as ODEs.We consider the problem of comparing and minimizing ODEs automatically. Influenced by traditional approaches in the theory of programming, we propose differential equivalence relations. We study them for a basic intermediate language, for which we have decidability results, that can be targeted by a class of highlevel specifications. An ODE implicitly represents an uncountable state space, hence reasoning techniques cannot be borrowed from established domains such as probabilistic programs with finite-state Markov chain semantics. We provide novel symbolic procedures to check an equivalence and compute the largest one via partition refinement algorithms that use satisfiability modulo theories.We illustrate the generality of our framework by showing that differential equivalences include (i) well-known notions for the minimization of continuous-time Markov chains (lumpability), (ii) bisimulations for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics. With a prototype implementation we are able to detect equivalences in biochemical models from the literature that cannot be reduced using competing automatic techniques.

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Section: Introductionmentioning

confidence: 99%

Symbolic computation of differential equivalences

Cardelli

Tribastone

Tschaikowski

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…For example, abstract interpretation has been already applied to Kappa [11] to reduce, under some circumstances, the number of chemical species and reactions resulting from a translation from Kappa to standard chemistry similar to the one we have presented in this paper. In order to apply such techniques in κ F , it is necessary to check their applicability in the presence of the functional rate.…”

Section: Resultsmentioning

confidence: 99%

Complex Functional Rates in Rule-Based Languages for Biochemistry

Versari

Zavattaro

2012

Lecture Notes in Computer Science

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Rule-based languages (like, for example, Kappa, BioNetGen, and BioCham) have emerged as successful models for the representation, analysis, and simulation of bio-chemical systems. In particular Kappa, although based on reactions, differs from traditional chemistry as it allows for a graph-like 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 Kappa-calculus in which rates are defined as functions of the actually involved complexes.

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“…In informatics, they have been receiving increasing attention due to the powerful analogy between computational processes and molecular systems [21], leading to a wealth of cross-fertilization that has produced, to cite a few, foundational results on the computational power of CRNs (e.g., [14,27]), languages for the specification of complex biomolecular systems [9], and model-reduction techniques based on traditional approaches within theoretical computer science such as abstract interpretation [10] and bisimulation [4,15].…”

Section: Introductionmentioning

confidence: 99%

“…Unlike many model-reduction approaches for CRNs (e.g., [1,7,8,10]) or control systems (see [26] and references therein) BDE cannot be seen as an instance of that framework. Hence, its geometric interpretation is a new result in its own right.…”

Section: Introductionmentioning

confidence: 99%

Comparing chemical reaction networks: A categorical and algorithmic perspective

Cardelli

Tribastone

Tschaikowski

et al. 2019

Theoretical Computer Science

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We study chemical reaction networks (CRNs) as a kernel language for concurrency models with semantics based on ordinary differential equations. We investigate the problem of comparing two CRNs, i.e., to decide whether the trajectories of a source CRN can be matched by a target CRN under an appropriate choice of initial conditions. Using a categorical framework, we extend and relate model-comparison approaches based on structural (syntactic) and on dynamical (semantic) properties of a CRN, proving their equivalence. Then, we provide an algorithm to compare CRNs, running linearly in time with respect to the cardinality of all possible comparisons. Finally, we apply our results to biological models from the literature.

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Abstracting the Differential Semantics of Rule-Based Models: Exact and Automated Model Reduction

Cited by 68 publications

References 53 publications

Symbolic computation of differential equivalences

Symbolic computation of differential equivalences

Complex Functional Rates in Rule-Based Languages for Biochemistry

Comparing chemical reaction networks: A categorical and algorithmic perspective

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