MOCCASIN: converting MATLAB ODE models to SBML

MATLAB is popular in biological research for creating and simulating models that use ordinary differential equations (ODEs). However, sharing or using these models outside of MATLAB is often problematic. A community standard such as Systems Biology Markup Language (SBML) can serve as a neutral exchange format, but translating models from MATLAB to SBML can be challenging—especially for legacy models not written with translation in mind. We developed MOCCASIN (Model ODE Converter for Creating Automated SBML INteroperability) to help. MOCCASIN can convert ODE-based MATLAB models of biochemical reaction networks into the SBML format

On Estimating Derivatives of Input Signals in Biochemistry

The online estimation of the derivative of an input signal is widespread in control theory and engineering. In the realm of chemical reaction networks (CRN), this raises however a number of specific issues on the different ways to achieve it. A CRN pattern for implementing a derivative block has already been proposed for the PID control of biochemical processes, and proved correct using Tikhonov's limit theorem. In this paper, we give a detailed mathematical analysis of that CRN, thus clarifying the computed quantity and quantifying the error done as a function of the reaction kinetic parameters. In a synthetic biology perspective, we show how this can be used to design error correcting terms to compute online functions involving derivatives with CRNs. In the systems biology perspective, we give the list of models in BioModels containing (in the sense of subgraph epimorphisms) the core derivative CRN, most of which being models of oscillators and control systems in the cell, and discuss in detail two such examples: one model of the circadian clock and one model of a bistable switch

Solving Subgraph Epimorphism Problems using CLP and SAT

International audienceIn this work, we compare CLP and SAT solvers on the NP-complete problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized as the existence of a sequence of vertex, species or reaction, deletion and merge operations which transforms a first reaction graph into a second graph. This problem is in turn equivalent to the existence of a subgraph (corresponding to delete operations) epimorphism (i.e. surjective homomorphism, corresponding to merge operations) from the first graph to the second. We show how subgraph epimorphism problems can be modeled as Boolean constraint satisfaction problems, and we compare CLP and SAT solvers on a large benchmark of reaction graphs from systems biology

Graph matching, theory and SAT implementation

International audienceIn systems biology, large biochemical reaction networks can either be represented by bipartitegraphs or by systems of ordinary differential equations. Modelers want to determine the existenceof reductions between those reaction networks. Because, it is not possible to decide this existencewith equation systems, a previous thesis [1] focussed on graph structures. A subgraph epimorphism(SEPI) framework was developed and gave results close to biologists’ expectations.Three main difficulties of the SEPI framework have been identified. First, establishing whethertwo models are linked through a SEPI is complex and computationally expensive. Second, thenumber of SEPIs found can be huge, making the analysis of SEPI sets between two given graphsvery difficult for biologists. Finally, some existing SEPIs do not have a biological interpretation.This diploma thesis led to three combined ways to improve the framework. One way consisted toredefine the decision problem into an optimisation problem to restrict the set of solutions. Asecond way was to determine, together with biologists, restrictions on one of the framework’soperations in order to filter irrelevant reductions. Lastly, a preprocessing step has been introduced,consisting of rewriting graphs according to subgraph isomorphism relations. The impact ofthese three combined implementations has been evaluated on models of the BioModels database.Results demonstrated that it contributed to make the SEPI framework more relevant, efficientand functional

Solving hard subgraph problems in parallel

This thesis improves the state of the art in exact, practical algorithms for finding subgraphs. We study maximum clique, subgraph isomorphism, and maximum common subgraph problems. These are widely applicable: within computing science, subgraph problems arise in document clustering, computer vision, the design of communication protocols, model checking, compiler code generation, malware detection, cryptography, and robotics; beyond, applications occur in biochemistry, electrical engineering, mathematics, law enforcement, fraud detection, fault diagnosis, manufacturing, and sociology. We therefore consider both the ``pure'' forms of these problems, and variants with labels and other domain-specific constraints. Although subgraph-finding should theoretically be hard, the constraint-based search algorithms we discuss can easily solve real-world instances involving graphs with thousands of vertices, and millions of edges. We therefore ask: is it possible to generate ``really hard'' instances for these problems, and if so, what can we learn? By extending research into combinatorial phase transition phenomena, we develop a better understanding of branching heuristics, as well as highlighting a serious flaw in the design of graph database systems. This thesis also demonstrates how to exploit two of the kinds of parallelism offered by current computer hardware. Bit parallelism allows us to carry out operations on whole sets of vertices in a single instruction---this is largely routine. Thread parallelism, to make use of the multiple cores offered by all modern processors, is more complex. We suggest three desirable performance characteristics that we would like when introducing thread parallelism: lack of risk (parallel cannot be exponentially slower than sequential), scalability (adding more processing cores cannot make runtimes worse), and reproducibility (the same instance on the same hardware will take roughly the same time every time it is run). We then detail the difficulties in guaranteeing these characteristics when using modern algorithmic techniques. Besides ensuring that parallelism cannot make things worse, we also increase the likelihood of it making things better. We compare randomised work stealing to new tailored strategies, and perform experiments to identify the factors contributing to good speedups. We show that whilst load balancing is difficult, the primary factor influencing the results is the interaction between branching heuristics and parallelism. By using parallelism to explicitly offset the commitment made to weak early branching choices, we obtain parallel subgraph solvers which are substantially and consistently better than the best sequential algorithms

On the subgraph Epimorphism Problem

International audienceIn this paper we study the problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized as the existence of a sequence of vertex deletion and merge operations that transforms a first reaction graph into a second graph. This problem is in turn equivalent to the existence of a subgraph (corresponding to delete operations) epimorphism (i.e. surjective homomorphism, corresponding to merge operations) from the first graph to the second. In this paper, we study theoretical properties of subgraph epimorphisms in general directedgraphs. We first characterize subgraph epimorphisms (SEPI), subgraph isomorphisms (SISO) and graph epimorphisms (EPI) in terms of graph transformation operations. Then we study the graph distance measures induced by these transformations. We show that they define metrics on graphs and compare them. On the algorithmic side, we show that the SEPI existence problem is NP-complete by reduction of SAT, and present a constraint satisfaction algorithm that has been successfully used to solve practical SEPI problems on a large benchmark of reaction graphs from systems biology

On the subgraph Epimorphism Problem

International audienceIn this paper we study the problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized as the existence of a sequence of vertex deletion and merge operations that transforms a first reaction graph into a second graph. This problem is in turn equivalent to the existence of a subgraph (corresponding to delete operations) epimorphism (i.e. surjective homomorphism, corresponding to merge operations) from the first graph to the second. In this paper, we study theoretical properties of subgraph epimorphisms in general directedgraphs. We first characterize subgraph epimorphisms (SEPI), subgraph isomorphisms (SISO) and graph epimorphisms (EPI) in terms of graph transformation operations. Then we study the graph distance measures induced by these transformations. We show that they define metrics on graphs and compare them. On the algorithmic side, we show that the SEPI existence problem is NP-complete by reduction of SAT, and present a constraint satisfaction algorithm that has been successfully used to solve practical SEPI problems on a large benchmark of reaction graphs from systems biology