# Generic Lifeware subjects for a Phd Thesis or a Post-Doc position

# Specific subjects of Internships for Master's degree or Engineering Schools, and for PhD theses below:

### Positive feedback loops and multistationarity in reaction systems

Contact : Sylvain Soliman

Abstract : The main objective of this internship is to evaluate the recent results [1] about stronger necessary conditions for multistationarity than those of Thomas [3] / Soulé [2]. The test models will come from the literature and from the BioModels database. The first task will be to find which models did fill the Thomas / Soulé necessary conditions, then which do fit the stronger conditions. For the conditions relying on the composition of graph transformations, heuristic search will probably be necessary. Once the models identified, going back to the original articles and determining what was known about the stationary states of the model will allow us to evaluate the real output of the method.

Titre: Boucles de rétroaction positive et multistationarité dans des systèmes de réactions

Résumé : L’objectif principal du stage est d’évaluer les récents résultats [1] sur des conditions nécessaires pour la multistationnarité plus strictes que celles de Thomas [3] / Soulé [2]. Les modèles de tests pourront provenir de la littérature ou de la base de modèles BioModels. Il s’agira dans un premier temps de vérifier quels modèles remplissent les conditions initiales de Thomas/Soulé, puis de vérifier avec les conditions plus strictes. Pour les conditions les plus avancées nécessitant des compositions de transformations de graphe, il sera sans doute nécessaire de procéder de manière heuristique. Une fois des modèles identifiés, il s’agira de comparer avec les articles d’origine afin de déterminer si la multistationnarité était déjà connue/supposée.

Références :

[1] Sylvain Soliman. A stronger necessary condition for the multistationarity of chemical reaction networks. to appear in the Bulletin of Mathematical Biology, September 2013.

[2] Christophe Soulé. Graphic requirements for multistationarity. ComplexUs, 1 :123–133, 2003.

[3] René Thomas. On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Springer Ser. Synergetics, 9 :180–193, 1981.

### Automated reasoning on orders of magnitude in biochemical reaction systems

Contact: François Fages

Model reduction is a central topic in dynamical systems theory, for reducing the complexity of ODE 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, in the domain of computational systems biology, the biochemical reaction systems that are developed need novel methods for comparing and reducing them on the very large scale of model repositories (thousands of models of several tenths to hundreds of molecular species and reactions).

The subgraph epimorphism (SEPI) theory that we have developed provides a graph-theoretic notion of model reduction and modules that fits very well with current practice in systems biology, where models are developed at different levels of details which can be automatically compared on the reaction graph, through operations of deletions or merge of species or reactions, i.e. SEPI morphisms [1]. Computing SEPIs makes it possible to detect model reduction relationships between models in model repositories like BioModels [2]. However that purely structural concept of model reduction does not take into account the kinetics of the reactions and is limited to detecing model reductions in model repositories, not finding meaningful reductions of a given dynamical model.

Tropicalization is a mathematical method for analysing polynomial equations in the (min,+) or (max,plus) semiring [3]. The intuitive idea is to reason on the order of magnitude of concentrations and kinetic parameters. Constraint Logic Programming can be used to identify the tropical equilibrations of dominating monomials and reactions in a network, and then to systematically separate timescales and reduce a model in different regions of the phase space corresponding to different regimes for which a simplified can be given (Quasi Steady State or Quasi Equilibrium assumptions) [4].

The subject of this internship is to develop the model reduction method based on tropical equilibrations and state precise approximation results (e.g. using Tikhonov theorem) about, first, the different regimes of simple examples like Michaelis-Menten enzymatic reaction, and then to scale-up to reaction models of several tenths of variables. The method will be implemented in our modeling environment Biocham [5].

References:

[1] Steven Gay, François Fages, Thierry Martinez, Sylvain Soliman, Christine Solnon. On the subgraph Epimorphism Problem. Discrete Applied Mathematics, 162:214–228, 2014.

[2] Steven Gay, Sylvain Soliman, François Fages. A Graphical Method for Reducing and Relating Models in Systems Biology. Bioinformatics, 26(18):i575–i581, 2010.

[3] Stéphane Gaubert. Two lectures on max-plus algebra, S. Gaubert, Proceedings of the 26th Spring School of Theoretical Computer Science, Algèbres Max-Plus et applications en informatique et automatique", Ile de Noirmoutier, 4-7 mai, pages 83--147, 1998.

[4] Sylvain Soliman, François Fages, Ovidiu Radulescu. A constraint solving approach to model reduction by tropical equilibration. Algorithms for Molecular Biology, 9(24), 2014.

[5] Biocham v4 web page and reference manual.

### Algorithmic complexity of analog computation in the cell

Contact: François Fages

The computational viewpoint at cell biology leads to the analysis of biochemical reaction systems as programs, and to the use of formal methods to reason about their behaviours. This is the foundation of our modeling environment Biocham [1]. Furthermore, advancements in synthetic biology have resulted in the implementation of biochemical systems of increasing complexity within either living cells or cell-free vesicles. For instance, oscillators, toggle switches, logic gates, band pass filters, and analog circuits have been designed and implemented in living cells, while digital circuits, neural networks, and switchable memories have been demonstrated in cell-free systems. In these developments, computer-aided design, simulation, verification and robustness analysis, are crucial steps before any implementation with either real enzymes or DNA.

One major difficulty in this enterprise of deciphering the biochemical interaction networks is the importance of analog computation in the cell. While gene activation can be well approximated by all-or-nothing boolean transitions, this is not the case for many activation of protein complexes and the time taken by these transformations is important for many signalling and control tasks. Recent results in the theory of computability over the reals [2,3] and the algorithmic complexity of analog computation [4] provide novel concepts to speak of the algorithmic complexity of natural biochemical reaction systems and compare it to engineered circuits.

Along these lines, we have started the implementation, in Biocham, of a biochemical compiler [5] which takes as input a specification of the input-output relation, given by a mathematical function, polynomial differential equation or mixed analog digital programs, and produces a set of elementary reactions that implement the specification. Our first experiments on the MAPK signaling network and its specification by a sigmoid function show a better computational complexity for the natural MAPK circuit than the

The purpose of this internship is to specify the function of natural reaction circuits in the cell, evaluate the computational complexity of natural and synthesized circuits, compare them and develop methods to improve the reaction code generated by our compiler. In course, we expect fundamental advances on our understanding of the cell biochemical machinery.

References:

[1] Biocham web page and reference manual.

[2] Olivier Bournez, Manuel L Campagnolo, Daniel S Gra ̧ca, and Emmanuel Hainry. The general purpose analog computer and computable analysis are two equivalent paradigms of analog com- putation. In International Conference on Theory and Applications of Models of Computation, pages 631–643. Springer, 2006.

[3] D.S. Gra ̧ca and J.F. Costa. Analog computers and recursive functions over the reals. Journal of Complexity, 19(5) :644–664, 2003.

[4] Amaury Pouly. Continuous models of computation : from computability to complexity. PhD thesis, Ecole Polytechnique, July 2015.

[5] Guillaume Le Guludec. Compilateur biochimique. Rapport de stage M2, MPRI, 2016. Inria Saclay.

### Machine learning biochemical models from temporal data

Contact: François Fages

In the domain of computational systems biology, the building of biochemical interaction models is still an art and a bottleneck to analyze new data and deal with new applications in biology and medecine. The first attempts to automate the building or revision of reaction systems from temporal logic properties [1] fail short to scale-up beyond a tenth of reactions. Influence systems are a simpler formalism [2] which may be more suited to model inference. Techniques such as Answer Set Programming have already shown some success in the domain of gene regulatory networks or signaling networks [3].

The subject of this internship is to develop new machine learning method by restricting ourselves to positive influence systems and taking benefit from their monotonicity properties [2].

The implementation will be done in Biocham v4 [4]and the evaluation will be done on models of the literature.

References:

[1] Laurence Calzone, Nathalie Chabrier-Rivier, François Fages, Sylvain Soliman. Machine learning biochemical networks from temporal logic properties. In Transactions on Computational Systems Biology VI, pages 68–94, volume 4220 of Lecture Notes in BioInformatics. Springer-Verlag, 2006.

[2] François Fages, Thierry Martinez, David Rosenblueth, Sylvain Soliman. Influence Systems vs Reaction Systems. In CMSB'16: Proceedings of the fourteenth international conference on Computational Methods in Systems Biology, volume 9859 of Lecture Notes in BioInformatics. Springer-Verlag, 2016.

[3] Videla et al. Learning Boolean logic models of signaling networks with ASP. Theoretical Computer Science Volume 599, 27 September 2015, Pages 79–101

[4] Biocham v4 web page and reference manual.

# Other subjects of Internships "stages" for Licence degree or Engineering Schools:

### Static analyses and visualization of biochemical reaction systems

Contact: François Fages

In the domain of computational systems biology, biochemical reaction diagrams are a central medium of communication between biologists and modellers. Unfortunately in this context, automatic graph visualization tools such as GraphViz [1] do not produce well-organized diagrams, and manual edition tools such as Cell Designers are preferred.

The purpose of this internship is to explore the use of static analyzers of reaction systems to extract information relevant to the "logical" drawing of biochemical reaction networks. More specifically, we propose to explore the use of the static analyzers of our modeling software, the Biochemical Abstract Machine (Biocham) [2], to design placement constraints for tools like GraphViz. For instance, the computation of linear conservation laws (i.e. Petri net P-invariants [3]) in Biocham provide information on groups of molecules that are transformed but conserved under their different forms and that could be preferably drawn on the same line. The use of dynamic analyzers, e.g. relying on numerical simulation, will be considered also if necessary [3].

References:

[1] GraphViz http://www.graphviz.org

[2] Biocham v4 http://lifeware.inria.fr/biocham/

[3] François Fages. AI in Biological Modeling. To appear in A Guided Tour of Artificial Intelligence Research. Springer-Verlag, 2017. preprint