Many models in Systems Biology are described as Ordinary Differential Equations (ODEs), which allow for numerical integration, bifurcation analyses, parameter sensitivity analyses, etc. However, before fixing the kinetics and parameter values and going to simulations, various analyses can be performed based only on the structure of the model. This approach has rapidly developed in Systems Biology in the last decade, with for instance, the analyses of structural invariants in Petri net representation, model reductions by subgraph epimorphims, qualitative attractors in logical dynamics or temporal logic properties by analogy to circuit and program verification. These complementary analysis tools do not rely on kinetic information, but on the structure of the model with reactions.

In , , we present a symbolic computation algorithm for inferring a reaction model from an ODE system, based a general compatibility condition between the kinetic expression and the structure of a reaction, and report on its use for automatically curating the writing in SBML of the models in the respository biomodels.net. SBML is now a standard for sharing and publishing reaction models. However, since SBML does not enforce any coherence between the structure and the kinetics of a reaction, an ODE model can be transcribed in SBML without reflecting the real structure of the reactions, hereby invalidating many structural analyses. We show that the automatic writing in SBML of the models of biomodels.net allows us to reduce the percentage of models with a non well-formed reaction from 66% to 28%.

Petri nets are a simple formalism for modeling concurrent computation. Recently, they have emerged as a promising tool for modeling and analyzing biochemical interaction networks, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be large and complex, which makes their study difficult and computationally challenging.

In , we focus on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species. We present a Boolean model and two constraint-based methods for enumerating all minimal siphons and traps of a Petri net, by iterating the resolution of Boolean satisfiability problems executed with either a SAT solver or a CLP(B) program. We compare the performances of these methods with respect to a state-of-the-art algorithm from the Petri net community. On a benchmark with 80 Petri nets from the Petriweb database and 403 Petri nets from curated biological models of the Biomodels database, we show that miniSAT and CLP(B) solvers are overall both faster by two orders of magnitude with respect to the dedicated algorithm. Furthermore, we analyse why these programs perform so well on even very large biological models and show a polynomial time complexity result for Petri nets of fixed treewidth, using a similar theorem for constraint satisfaction problems with bounded treewidth constraint graphs.

In we present a method to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. This analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc. thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri nets correspond to well-known techniques in constraint solving, like symmetry-breaking. A simple implementation based on GNU-Prolog's finite domain solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment and in the independent tool Nicotine. Some illustrative examples and benchmarks are provided.

The operations of deleting and merging vertices are natural operations for reducing a graph. While graph reductions through a sequence of vertex deletions (resp. mergings) characterize subgraph isomorphisms (resp. graph epimorphisms), sequences of both vertex deletion and merging operations characterize subgraph epimorphisms. Our proposal is thus to use subgraph epimorphism for comparing graphs in applications in systems biology and image analysis, when a more flexible notion than the classical notion of subgraph isomorphism is required.

In collaboration with Christine Solnon (INSA Lyon), we have developed the theory of subgraph epimorphisms. We have defined the SEPI, EPI and SISO distances between two graphs as the size of the largest SEPI (resp. EPI, SISO) lower bound graphs. These distances are equal to the minimum number of respectively vertex deletion and/or merging operations that are necessary to obtain isomorphic graphs. They are also metrics on graphs and we have $d_d\ge d_{md}$ and $d_m\ge d_{md}$. From a computational point of view, we have shown that the existence of a SEPI between two graphs is an NP-complete problem and have presented a constraint satisfaction algorithm for solving it.

Our algorithm is implemented in BIOCHAM and is currently improved for better performance on large graphs and generalized as a SEPI graph constraint propagation algorithm for computing SEPI lower and upper bounds.

Our method for solving temporal logic constraints in first-order linear time logic LTL($R_{\text{lin}}$), opens up the field of model-checking to optimization through the definition of a continuous degree of satisfaction for temporal logic formulae. This satisfaction degree can be used in a number of ways, e.g. as a fitness function with continuous optimization methods to find unknown parameter values in a model, to perform sensitivity analyses and compute the robustness of a system w.r.t. a temporal property and a perturbation of the parameters. or to find control parameters.

This approach is implemented in BIOCHAM and is one unique feature of this modeling environment. In this implementation, the continuous optimization procedure we use is the Covariance Matrix Adaptation Evolutionary Strategy CMAES of Nikolaus Hansen from the EPI TAO. A parallel version of Biocham implements this method on the Jade cluster of 10000 cores at GENCI for running our most challenging parameter search problems.

This year, in collaboration with Fernando Buarque, we have explored another continuous optimization method of the family of Particle Swarm Optimization (PSO), called Fish School Optimization (FSS). In , we report on our first results which are encouraging for using FSS for decreasing the sensitivity of the method to initial conditions and being able to maintain several swarms of solutions.

Recent advances in cancer chronotherapy techniques support the evidence that there exist imortant links between the cell cycle and the circadian clock genes. One purpose for modeling these links is to better understand how to efficiently target malignant cells depending on the phase of the day and patient characterictics. This is at the heart of our participation in collaboration with the EPI BANG in the EraNet SysBio project C5Sys, follow up of the former EU STREP project TEMPO.

This year we have investigated the effect of transcription inhibition during mitosis, as a reverse coupling from the cell cycle to the circadian clock. We use temporal logic constraints and the parallel version of BIOCHAM for parameter search, running on the Jade cluster of 10000 processors at the GENCI CINES, to couple dynamical models in high dimension and fit models to experimental data time series obtained in Franck Delaunay's lab in Nice, CNRS.

Extrinsic apoptosis is a programmed cell death triggered by external ligands, such as the TNF-related apoptosis inducing ligand (TRAIL). Depending on the cell line, the specific molecular mechanisms leading to cell death may significantly differ. Precise characterization of these differences is crucial for understanding and exploiting extrinsic apoptosis. Cells show distinct behaviors on several aspects of apoptosis, including (i) the relative order of caspases activation, (ii) the necessity of Mitochondria Outer Membrane Permeabilization (MOMP) for effector caspase activation, and (iii) the survival of cell lines overexpressing Bcl2, leading to classification of cell lines into two groups (type I and type II). In , we challenge this type I/II cell line classification. We encode the three aforementioned distinguishing behaviors in a formal language, called signal temporal logic (STL), and use it to extensively test the validity of a previously-proposed model of TRAIL-induced apoptosis with respect to experimental observations made on different cell lines. Then, STL-guided parameter search is used to solve the few inconsistencies found between model and data. We show that these three criteria do not define consistent cell line classifications in type I or type II, and suggest mutants that are predicted to exhibit ambivalent behaviors. In particular, this finding sheds light on the role of a feedback loop between caspases, and reconciliates two apparently-conflicting views regarding the importance of either upstream or downstream processes for cell type determination. More generally, our work suggests that rather than being considered as defining criteria for cell type classification, these three distinguishing behaviors should be merely considered as type I or II features. On the methodological point of view, this work illustrates the biological relevance of STL-diagrams, STL population data, and STL-guided parameter search. Such tools are well adapted to the ever-increasing availability of heterogeneous knowledge on complex signal transduction pathways.

Gene expression plays a central role in the orchestration of cellular processes. The use of inducible promoters to change the expression level of a gene from its physiological level has significantly contributed to the understanding of the functioning of regulatory networks. However, from a quantitative point of view, their use is limited to short-term, population-scale studies to average out cell-to-cell variability and gene expression noise and limit the nonpredictable effects of internal feedback loops that may antagonize the inducer action. In this project, in collaboration with the Hersen Lab at MSC (Paris Diderot University), we show that, by implementing an external feedback loop, one can tightly control the expression of a gene over many cell generations with quantitative accuracy. To reach this goal, we developed a platform for real-time, closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmostress responsive promoter and playing with the osmolarity of the cells environment, we show that long-term control can, indeed, be achieved for both time-constant and time-varying target profiles at the population and even the single-cell levels . Importantly, we provide evidence that real-time control can dynamically limit the effects of gene expression stochasticity. We anticipate that our method will be useful to quantitatively probe the dynamic properties of cellular processes and drive complex, synthetically engineered networks.

Targeted integration of multi-unit genetic payloads would greatly benefit elucidating complex cellular mechanisms and implementing new functions in mammalian cells. Current technologies are however time-consuming and require tedious post-integration controls. To address this problem, we propose a modular framework to assemble large multi-unit genetic payloads and target their integration into either one or both alleles of a chromosomal locus of choice. To achieve this, we combine in a two-step process the customizable targeting properties of homing endonucleases with the efficiency and specificity of a large serine recombinase. We have demonstrated that an optimized version of BxB1 recombinase allows the targeted integration of large genetic circuits (up to 7 transcription units, 60kb) into a preintegrated landing pad in the AAVS1 locus, with a significant increase in efficiency compared to other site-specific recombination systems (integration in 10% of transfected cells without selection) . By reducing the time and efforts to generate large populations of isogenic stable cell lines adapted to study multi-component genetic systems, our framework is a valuable tool for mammalian synthetic biology and offers great potential for a broad range of biotechnology and therapeutic applications.

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. This is currently not the case in state-of-the-art tools and was not considered in the global constraint catalog until recently. In , we propose a general framework for reifying global constraints and apply it to some important constraints of the catalog, such as the cumulative constraint for instance. We show that several global constraints that were believed to be hard to negate can in fact be efficiently negated, and that entailment and disentailment can be efficiently tested. We also point out some new global constraints that are worth studying from this point of view and provide some performance figures obtained with an implementation in Choco.

This scheme is currently used for compiling the Rules2CP constraint modeling language to Choco, and to internalize search in CSPs through constraint reification.

Metros are able to generate electricity on a metro line by braking. This energy is immediately available in the third rail and is lost if no metro in the neighbourhood can consume it. It is thus possible to decrease the total energy consumption of a metro line by synchronizing the accelerations and braking of the metros. In , , we propose a classification of energy optimization timetable problems and we present a model for optimizing energy consumption which does not significantly alter the quality of service, by subtly modifying dwell times. We show however that this optimization problem is NP-hard. We present a hybrid genetic/linear programming algorithm for computing the distribution of braking metros. In this hybridization, the objective function is computed by a linear program and by a heuristic, and the dwell times are modified by a genetic algorithm. On a typical example with real data, the savings exceed 7%. Furthermore, on a benchmark of the literature for a simpler problem, we discuss the results obtained with our genetic algorithm, a tabu search algorithm and the mixed integer linear program used by the authors.