Section: Application Domains

Formal models in molecular biology

As mentioned before, our main goal in biology is to characterize groups of genetic actors that control the response of living species capable of facing extreme environments. To focus our developments, applications and collaborations, we have identified three biological questions which deserve integrative studies. Each axis may be considered independently from the others although their combination, a mid-term challenge, will have the best impact in practice towards the long-term perspective of identifying proteins controlling the production of a metabolite of industrial interest. It is illustrated in our presentation for a major algae product: polyunsaturated fatty acids (PUFAs) and their derivatives.

Biological data integration. The first axis of the project (data integration) aims at identifying who is involved in the specific response of a biological system to an environmental stress. Targeted actors will mainly consist in groups of genetic products or biological pathways. For instance, which pathways are implied in the specific production of PUFAs in brown algae? The main work is to represent in a system of logical constraints the full knowledge at hand concerning the genetic or metabolic actors, the available observations and the effects of the system dynamics. To this aim, we focus on the use of Answer Set Programming as we are experienced in modeling with this paradigm and we have a strong partnership with a computer science team leader in the development of dedicated grounders and solvers (Potsdam university). See Sec. 3.1 .

Asymptotic dynamics of a biological system Once a model is built and its main actors are identified, the next step is to clarify how they combine to control the system. This is the second axis of the project. Roughly, the fine tuning of the system response may be of two types. Either it results from the discrete combinatorics of the actors, as the result of a genetic adaptation to extreme environmental conditions or the difference between species is rather at the enzyme-efficiency level. For instance, if Pufa's are found to be produced using a set of pathways specific to brown algae, the work in axis 2 will consist to apply constraint-based combinatorial approaches to select consistent combinations of pathways controlling the metabolite production. Otherwise, if enzymes controlling the production of Pufa's are found to be expressed in other algaes, it suggests that the response of the system is rather governed by a fine quantitative tuning of pathways. In this case, we use symbolic dynamics and average-case analysis of algorithms to weight the respective importance of interactions in observed phenotypes (see Sec. 3.2 and Fig. 2 ). This specific approach is motivated by the quite restricted spectrum of available physiological observations over the asymptotic dynamics of the biological system.

Biological sequence annotation In order to check the accuracy of in-silico predictions, a third research axis of the team is to extract genetic actors responsible of biological pathways of interest in the targeted organism and locate them in the genome. In our guiding example, active proteins implied in Pufa's controlling pathways have to be precisely identified. Actors structures are represented by syntactic models (see Fig. 4 ). We use knowledge-based induction on far instances for the recognition of new members of a given sequence family within non-model genomes (see Fig. 3 ). A main objective is to model enzyme specificity with highly expressive syntactic structures - context-free model - in order to take into account constraints imposed by local domains or long-distance interactions within a protein sequence. See Sec. 3.3 for details.

A posteriori classification of pools of model candidates All the methods presented in the previous section usually result in pools of candidates which equivalently explain the data and knowlegde. These candidates can by dynamical systems, compounds, biological sequences, proteins... In any case, the output of our formal methods generally deserves a a-posteriori investigation and filtering. To that goal, we rely on two classes of symbolic technics: semantic web technologies and Formal Concept Analysis See Sec. 3.4 for details.