A model checking approach to the parameter estimation of biochemical pathways

Model checking has historically been an important tool to verify models of a wide variety of systems. Typically a model has to exhibit certain properties to be classed ‘acceptable’. In this work we use model checking in a new setting; parameter estimation. We characterise the desired behaviour of a model in a temporal logic property and alter the model to make it conform to the property (determined through model checking). We have implemented a computational system called MC2(GA) which pairs a model checker with a genetic algorithm. To drive parameter estimation, the fitness of set of parameters in a model is the inverse of the distance between its actual behaviour and the desired behaviour. The model checker used is the simulation-based Monte Carlo Model Checker for Probabilistic Linear-time Temporal Logic with numerical constraints, MC2(PLTLc). Numerical constraints as well as the overall probability of the behaviour expressed in temporal logic are used to minimise the behavioural distance. We define the theory underlying our parameter estimation approach in both the stochastic and continuous worlds. We apply our approach to biochemical systems and present an illustrative example where we estimate the kinetic rate constants in a continuous model of a signalling pathway

Model Revision from Temporal Logic Properties in Computational Systems Biology

International audienceSystems biologists build models of bio-molecular processes from knowledge acquired both at the gene and protein levels, and at the phenotype level through experiments done in wildlife and mutated organisms. In this chapter, we present qualitative and quantitative logic learning tools, and illustrate how they can be useful to the modeler. We focus on biochemical reaction models written in the Systems Biology Markup Language SBML, and interpreted in the Biochemical Abstract Machine BIOCHAM. We first present a model revision algorithm for inferring reaction rules from biological properties expressed in temporal logic. Then we discuss the representations of kinetic models with ordinary differential equations (ODEs) and with stochastic logic programs (SLPs), and describe a parameter search algorithm for finding parameter values satisfying quantitative temporal properties. These methods are illustrated by a simple model of the cell cycle control, and by an application to the modelling of the conditions of synchronization in period of the cell cycle by the circadian cycle

(Mathematical) Logic for Systems Biology (Invited Paper)

International audienceWe advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including a sequent calculus presentation enjoying cut-elimination and focusing), and should come with (certified) proof tools. Beyond providing a reliable framework, this allows the adequate encodings of our biological systems. We present two candidate logics (two modal extensions of linear logic, called HyLL and SELL), along with biological examples. The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq. Future works includes using automatic provers, which would extend existing automatic provers for linear logic. This should enable us to specify and study more realistic examples in systems biology, biomedicine (diagnosis and prognosis), and eventually neuroscience

Reversibility in Chemical Reactions

open access bookIn this chapter we give an overview of techniques for the modelling and reasoning about reversibility of systems, including outof- causal-order reversibility, as it appears in chemical reactions. We consider the autoprotolysis of water reaction, and model it with the Calculus of Covalent Bonding, the Bonding Calculus, and Reversing Petri Nets. This exercise demonstrates that the formalisms, developed for expressing advanced forms of reversibility, are able to model autoprotolysis of water very accurately. Characteristics and expressiveness of the three formalisms are discussed and illustrated

Constraint solving in uncertain and dynamic environments - a survey

International audienceThis article follows a tutorial, given by the authors on dynamic constraint solving at CP 2003 (Ninth International Conference on Principles and Practice of Constraint Programming) in Kinsale, Ireland. It aims at offering an overview of the main approaches and techniques that have been proposed in the domain of constraint satisfaction to deal with uncertain and dynamic environments

Metabolomic profiles of hepatocellular carcinoma in a European prospective cohort

Background: Hepatocellular carcinoma (HCC), the most prevalent form of liver cancer, is difficult to diagnose and has limited treatment options with a low survival rate. Aside from a few key risk factors, such as hepatitis, high alcohol consumption, smoking, obesity, and diabetes, there is incomplete etiologic understanding of the disease and little progress in identification of early risk biomarkers. Methods: To address these aspects, an untargeted nuclear magnetic resonance metabolomic approach was applied to pre-diagnostic serum samples obtained from first incident, primary HCC cases (n = 114) and matched controls (n = 222) identified from amongst the participants of a large European prospective cohort. Results: A metabolic pattern associated with HCC risk comprised of perturbations in fatty acid oxidation and amino acid, lipid, and carbohydrate metabolism was observed. Sixteen metabolites of either endogenous or exogenous origin were found to be significantly associated with HCC risk. The influence of hepatitis infection and potential liver damage was assessed, and further analyses were made to distinguish patterns of early or later diagnosis. Conclusion: Our results show clear metabolic alterations from early stages of HCC development with application for better etiologic understanding, prevention, and early detection of this increasingly common cancer.This work was supported by the French National Cancer Institute (L’Institut National du Cancer; INCA; grant number 2009-139; PI: M. Jenab). AF received financial support (BDI fellowship) from the Centre National de la Recherche Scientifique (CNRS) and Bruker Biospin. The coordination of EPIC is financially supported by the European Commission (DG-SANCO) and the International Agency for Research on Cancer. The national cohorts are supported by Danish Cancer Society (Denmark); Ligue Contre le Cancer, Institut Gustave Roussy, Mutuelle Générale de l’Education Nationale, and Institut National de la Santé et de la Recherche Médicale (INSERM) (France); Deutsche Krebshilfe, Deutsches Krebsforschungszentrum (DKFZ), and Federal Ministry of Education and Research (Germany); Hellenic Health Foundation (Greece); Italian Association for Research on Cancer (AIRC), National Research Council, Associazione Italiana per la Ricerca sul Cancro-AIRC-Italy, and AIRE-ONLUS Ragusa, AVIS Ragusa, Sicilian Government (Italy); Dutch Ministry of Public Health, Welfare and Sports (VWS), Netherlands Cancer Registry (NKR), LK Research Funds, Dutch Prevention Funds, Dutch ZON (Zorg Onderzoek Nederland), World Cancer Research Fund (WCRF), and Statistics Netherlands (the Netherlands); European Research Council (ERC; grant number ERC-2009-AdG 232997) and Nordforsk, and Nordic Center of Excellence Programme on Food, Nutrition and Health (Norway); Health Research Fund (FIS), Regional Governments of Andalucía, Asturias, Basque Country, Murcia (No. 6236) and Navarra, and ISCIII RETIC (RD06/0020) (Spain); Swedish Cancer Society, Swedish Scientific Council, and Regional Government of Skåne and Västerbotten (Sweden); Cancer Research UK, Medical Research Council, Stroke Association, British Heart Foundation, Department of Health, Food Standards Agency, and Wellcome Trust (UK)

Moment Semantics for Reversible Rule-Based Systems

International audienceWe develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the 'no-dangling-edge' condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree