Automating the process of model building from experimental data is a very desirable goal to palliate the lack of modellers for many applications. However, despite the spectacular progress of machine learning techniques in data analytics, classification, clustering and prediction making, learning dynamical models from data time-series is still challenging. In this paper we investigate the use of the Probably Approximately Correct (PAC) learning framework of Leslie Valiant as a method for the automated discovery of influence models of biochemical processes from Boolean and stochastic traces […]
Fri, Sep 1, 2017
Experimental observations have put in evidence autonomous self-sustained circadian oscillators in most mammalian cells, and proved the existence of molecular links between the circadian clock and the cell cycle. Some mathematical models have also been built to assess conditions of control of the cell cycle by the circadian clock, with applications to cancer chronotherapy optimization. However, recent studies in individual NIH3T3 fibroblasts have shown an unexpected acceleration of the circadian clock together with the cell cycle when the culture medium is enriched with growth factors, and the absence of such acceleration in confluent cells […]
Thu, Jun 1, 2017
In recent years Systems Biology has become a rich field of study, trying to encompass all the information that has become available thanks to the new high-throughput techniques of biologists.Fifteen years ago, a fundamental breakthrough was the publication of Kurt Kohn’s map of the cell cycle control in mammals. Its similarity with electronic circuits was crucial in both making it impossible for humans to comprehend fully, and in prompting the use of formal methods.Since then however, the networks built by biologists and modellers have continued growing bigger, filled with more and more mechanistic details, especially recently acquired post-transcriptional information, but lacking most of precise kinetic data. Because analysis techniques providing dynamical insights mostly rely on complete kinetic information, what was challenging for the human ten years ago is now a challenge even for computers,In this manuscript we will try to give an account of our work of the last twelve years, centered around the question of model […]
Thu, Dec 1, 2016
Experimental observations have put in evidence autonomous self-sustained circadian oscillators in most mammalian cells, and proved the existence of molecular links between the circadian clock and the cell cycle. Some mathematical models have also been built to assess conditions of control of the cell cycle by the circadian clock. However, recent studies in individual NIH3T3 fibroblasts have shown an unexpected acceleration of the circadian clock together with the cell cycle when the culture medium is enriched with growth factors, and the absence of such acceleration in confluent cells […]
Tue, Nov 1, 2016
In Systems Biology, modelers develop more and more reaction-based models to describe the mechanistic biochemical reactions underlying cell processes. They may also work, however, with a simpler formalism of influence graphs, to merely describe the positive and negative influences between molecular species. The first approach is promoted by reaction model exchange formats such as SBML, and tools like CellDesigner, while the second is supported by other tools that have been historically developed to reason about boolean gene regulatory networks […]
Thu, Sep 1, 2016
Fri, Apr 1, 2016
Experimental observations have put in evidence autonomous self-sustained circadian oscillators in most mammalian cells, and proved the existence of molecular links between the circadian clock and the cell cycle. Several models have been elaborated to assess conditions of control of the cell cycle by the circadian clock, in particular through the regulation by clock genes of Wee1, an inhibitor of the mitosis promoting factor, responsible for a circadian gating of mitosis and cell division period doubling phenomena. However, recent studies in individual NIH3T3 fibroblasts have shown an unexpected acceleration of the circadian clock together with the cell cycle when the milieu is enriched in FBS, the absence of such acceleration in confluent cells, and the absence of any period doubling phenomena […]
Tue, Dec 1, 2015
In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation analysis, etc. However, without requiring any in-formation on the reaction kinetics and parameter values, various qualitative analyses can be performed using the structure of the reactions, provided the reactants, products and mod-ifiers of each reaction are precisely defined […]
Tue, Sep 1, 2015
Constraint programming is traditionally viewed as the combination of two components: a constraint model and a search procedure. In this paper we show that tree search procedures can be fully inter-nalized in the constraint model with a fixed enumeration strategy. This approach has several advantages: 1) it makes search strategies declarative, and modeled as constraint satisfaction problems; 2) it makes it possible to express search strategies in existing front-end modeling languages supporting reified constraints without any extension ; 3) it opens up constraint propagation algorithms to search constraints and to the implementation of novel search procedures based on constraint propagation […]
Wed, Jul 1, 2015
Wed, Apr 1, 2015
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While singular perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these methods is in the computation of tropical equilibrations […]
Mon, Dec 1, 2014
Best student paper award
Sat, Nov 1, 2014
In 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 […]
Wed, Jan 1, 2014
Biochemical reaction networks grow bigger and bigger, fed by the high-throughput data provided by biologists and bred in open repositories of models allowing merging and evolution. Nevertheless, since the available data is still very far from permitting the identification of the increasing number of kinetic parameters of such models, the necessity of structural analyses for describing the dynamics of chemical networks appears stronger every day. Using the structural information, notably from the stoichiometric matrix, of a biochemical reaction system, we state a more strict version of the famous Thomas' necessary condition for multistability […]
Fri, Nov 1, 2013
In 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 […]
Sun, Sep 1, 2013
Models of biochemical systems presented as a set of formal reaction rules with kinetic expressions can be interpreted with different semantics: as either deterministic Ordinary Differential Equations, stochastic continuous-time Markov Chains, Petri nets or Boolean transition systems. While the formal composition of reaction models can be syntactically defined as the (multiset) union of the reactions, the hybrid composition of models in different formalisms is a largely open issue. In this paper, we show that the combination of reaction rules with conditional events, as the ones already present in SBML, does provide the expressive power of hybrid automata and can be used in a non standard way to give meaning to the hybrid composition of heterogeneous models of biochemical processes […]
Sun, Sep 1, 2013
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system, and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these tropicalization methods is in the computation of tropical equilibrations […]
Sun, Sep 1, 2013
Background We present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. The use of Petri nets to manipulate Systems Biology models and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, for instance in the context of module decomposition. Results In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc […]
Sat, Dec 1, 2012
Global constraints were introduced two decades ago as a means to model some core aspects of combinatorial problems with one single constraint for which an efficient domain filtering algorithm can be provided, possibly using a complete change of representation. However, global constraints are just constraint schemas on which one would like to apply usual constraint operations such as reification, i.e. checking entailment, disentailment and negating the constraint […]
Mon, Oct 1, 2012
Mon, Oct 1, 2012