A Language for Biochemical Systems: Design and Formal Specification

Pedersen, Michael; Plotkin, Gordon

doi:10.1007/978-3-642-11712-1_3

Cited by 31 publications

(32 citation statements)

References 35 publications

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“…Classical examples are concentrations of species in chemical reactions and in biological processes, pressure and temperature in a plant, and voltage and current in an electrical circuit. Much more recently there has been an increasing attention to quantitative models of computation based on ODEs, for example to use formal languages to describe biochemical models [11,14,17,21,26,56,60,66] or as a deterministic approximation for languages with stochastic semantics [21,42,76].…”

Section: Introductionmentioning

confidence: 99%

Symbolic computation of differential equivalences

et al. 2016

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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 high-level 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 high-level 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

et al. 2016

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“…A graphical presentation of rule systems is also needed; in that connection a suitable notion of multilevel Petri net would be useful, even if only for two-level systems, where agents do not occur inside others in populations or rules. Finally, when there is a need for modularisation for large-scale model development, one might wish for a language along the lines of, say, LBS [PP10].…”

Section: Discussionmentioning

confidence: 99%

Coloured stochastic multilevel multiset rewriting

Oury

Plotkin

2011

Proceedings of the 9th International Conference on Computational Methods in Systems Biology

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From the phosphorylation state of a molecule to the volume of a cell, parameters are ubiquitous in systems biology. At the same time, most models involve static or dynamic compartments, for example to separate cells from their environment. We introduce coloured stochastic multilevel multiset rewriting, an expressive formalism for modelling systems with parameters and complex dynamic, multilevel compartment structures, and an extension of both multilevel multiset rewriting and coloured Petri nets. While being very expressive, it allows the direct and natural expression of biological ideas. We give some illustrative examples, demonstrating the use of parameters to handle cell states, position and volume, and variable rates. We further demonstrate the use of rules with complex right-hand sides for reproduction. We regard these examples as paving the way for more biologically relevant models.

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“…Ordinary differential equations (ODEs) are a prominent model of dynamical systems across many branches of science and engineering, and have enjoyed increasing popularity in computer science, for instance, in computational systems biology [13,30,4], as an approximation to large-scale Markov models and as the laws of continuous motion in hybrid systems [7]. This has motivated techniques for the comparison and minimization of ODEs based on behavioral relations, along the lines of other foundational quantitative models of computation, e.g.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

Cardelli

Tribastone

Tschaikowski

et al. 2018

Quantitative Evaluation of Systems

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It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce approximate differential equivalence as a more permissive variant of a recently developed exact counterpart, allowing ODE variables to be related even when they are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differential equivalence; (ii) construct an approximate quotient model from the original one via an appropriate parameter perturbation; and (iii) provide a formal certificate on the quality of the approximation as an error bound, computed as an over-approximation of the reachable set of the perturbed model. Finally, we apply approximate differential equivalences to study the effect of parametric tolerances in models of symmetric electric circuits.

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A Language for Biochemical Systems: Design and Formal Specification

Cited by 31 publications

References 35 publications

Symbolic computation of differential equivalences

Symbolic computation of differential equivalences

Coloured stochastic multilevel multiset rewriting

Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis

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