Analysis of signalling pathways using continuous time Markov chains

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

A Machine Learning approach to Biochemical Reaction Rules Discovery

Beyond numerical simulation, the possibility of performing symbolic computation on bio-molecular interaction networks opens the way to the design of new automated reasoning tools for biologists/modelers. The Biochemical Abstract machine BIOCHAM provides a precise semantics to biomolecular interaction maps as concurrent transition systems. Based on this formal semantics, BIOCHAM offers a compositional rule-based language for modeling biochemical systems, and an original query language based on temporal logic for expressing biological queries about reachability, checkpoints, oscillations or stability. Turning the temporal logic query language into a specification language for expressing the observed behavior of the system (in wild-life and mutated organisms) makes it possible to use machine learning techniques for completing or correcting biological models semi-automatically. Machine learning from temporal logic formulae is quite new however, both from the machine learning perspective and from the Systems Biology perspective. In this paper, we report on the machine learning system of BIOCHAM which allows to discover, on the one hand, interaction rules from a partial model with constraints on the system behavior expressed in temporal logic, and on the other hand, kinetic parameter values from a temporal logic specification with constraints on numerical concentrations

Apprentissage de règles de réactions biochimiques à partir de propriétés en logique temporelle

Avec le développement de langages formels pour modéliser les systèmes d' interactions biomoléculaires, la possibilité d'effectuer des calculs symboliques au delà des simulations numér iques ouvre la voie à la conception de nouveaux outils de raisonnement automatique destinés au biologiste modélisateur. La machine abstraite biochimique BIOCHAM est un environnement logiciel qui offre un langage simple de règles pour modéliser les interactions biomoléculaires et un langage original fondé sur la logique temporelle pour formaliser les propriétés biologiques du système. En s'appuyant sur ces deux langages formels, il devient possible d'utiliser des techniques d'apprentissage automatique pour inférer de nouvelles règles de réaction moléculaire à partir de propriétés temporelles observées. Dans ce contexte, le but est de corriger ou compléter les modèles BIOCHAM semi-automatiquement. Dans cet article, nous décrivons le système d'apprentissage automatique de BIOCHAM, qui permet, d'une part, de trouver de nouvelles règles d'interaction à partir d' un modèle partiel et de contraintes exprimées en logique temporelle, et d'autre part, d'estimer les valeurs de paramètres cinétiques à partir de propriétés formalisées en logique temporelle avec contraintes numériques sur les concentrations ou leurs dérivées

Learning Transition Rules from Temporal Logic Properties

Most of the work on temporal representation issues in Machine Learning deals with the problem of learning/mining temporal patterns from a large set of temporal data. In this paper we investigate the somewhat different problem of learning the behavioral rules of a system from its observed temporal properties formalized in temporal logic. Our interest in this problem arose from Systems Biology and the development of machine learning techniques for learning biochemical reaction rules and kinetic parameters in the Biochemical Abstract Machine BIOCHAM. Our contribution is twofold. First, in the general setting of Kripke structures and concurrent transition systems, we define positive and negative CTL formulae and propose a theory revision algorithm for learning transition rules from a CTL specification. Second, in the setting of hybrid systems which add a continuous dynamics described by differential equations, we show how a similar algorithm can be built to learn parameter values from a constraint LTL specification. In the context of BIOCHAM, which is used as a running example in this paper, we report evaluation results showing the usefulness of this approach and encouraging performance figures

Modular modelling of signalling pathways and their crosstalk

Signalling pathways are well-known abstractions that explain the mechanisms whereby cells respond to signals. Collections of pathways form networks, and interactions between pathways in a network, known as cross-talk, enables further complex signalling behaviours. While there are several formal modelling approaches for signalling pathways, none make cross-talk explicit; the aim of this paper is to define and categorise cross-talk in a rigorous way. We define a modular approach to pathway and network modelling, based on the module construct in the PRISM modelling language, and a set of generic signalling modules. Five different types of cross-talk are defined according to various biologically meaningful combinations of variable sharing, synchronisation labels and reaction renaming. The approach is illustrated with a case-study analysis of cross-talk between the TGF-β, WNT and MAPK pathways

Machine Learning Bio-molecular Interactions from Temporal Logic Properties

With the advent of formal languages for modeling bio-molecu\-lar interaction systems, the design of automated reasoning tools to assist the biologist becomes possible. The biochemical abstract machine BIOCHAM software environment offers a rule-based language to model bio-molecular interactions and an original temporal logic based language to formalize the biological properties of the system. Building on these two formal languages, machine learning techniques can be used to infer new molecular interaction rules from temporal properties. In this context, the aim is to semi-automatically correct or complete models from observed biological properties of the system. Machine learning from temporal logic formulae is quite new however, both from the machine learning perspective and from the Systems Biology perspective. In this paper we present an ad-hoc enumerative method for structural learning from temporal properties and report on the evaluation of this method on formal biological models of the literature

Langages formels dans la machine abstraite biochimique BIOCHAM

International audienceLe développement de langages formels pour modéliser les systèmes biologiques ouvre la voie à la conception de nouveaux outils de raisonnement automatique destinés au biologiste modélisateur. La machine abstraite biochimique BIOCHAM est un environnement logiciel qui offre un langage simple de règles pour modéliser des interactions biomoléculaires, et un lan-gage puissant fondé sur la logique temporelle pour formaliser les propriétés biologiques du sys-tème. En s'appuyant sur ces deux langages formels, il devient possible d'utiliser des techniques d'apprentissage automatique pour inférer de nouvelles règles de réaction, estimer les valeurs des paramètres cinétiques, et corriger ou compléter les modèles semi-automatiquement. Dans cet article, nous décrivons les langages implantés dans BIOCHAM et illustrons l'utilisation du système d'apprentissage automatique sur un modèle simple du contrôle du cycle cellulaire. ABSTRACT. With the advent of formal languages for modeling biological systems, the design of automated reasoning tools to assist the biologist becomes possible. The biochemical abstract machine BIOCHAM software environment offers a rule-based language to model bio-molecular interactions and a powerful temporal logic based language to formalize the biological properties of the system. Building on these two formal languages, machine learning techniques can be used to infer new molecular interaction rules from temporal properties, or to estimate kinetic parameter values, in order to semi-automatically correct or complete models from observed biological properties of the system. In this article we describe the formal languages of BIOCHAM and illustrate, on a simple cell cycle control model, the use of the machine learning system

Trend-based analysis of a population model of the AKAP scaffold protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system

Process algebra modelling styles for biomolecular processes

We investigate how biomolecular processes are modelled in process algebras, focussing on chemical reactions. We consider various modelling styles and how design decisions made in the definition of the process algebra have an impact on how a modelling style can be applied. Our goal is to highlight the often implicit choices that modellers make in choosing a formalism, and illustrate, through the use of examples, how this can affect expressability as well as the type and complexity of the analysis that can be performed

Bio-PEPA: An Extension of the Process Algebra PEPA for Biochemical Networks

AbstractIn this work we introduce Bio-PEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA to deal with some features of biological models, such as stoichiometry and the use of generic kinetic laws. Bio-PEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. Finally, we show a representation of a model, concerning a simple genetic network, in the new language