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## Section: New Results

### Going towards control

Combinatorial approach for microbial consortia synthetic design

Synthetic biology has boomed since the early 2000s when it started being shown that it was possible to efficiently synthetise compounds of interest in a much more rapid and effective way by using other organisms than those naturally producing them. However, to thus engineer a single organism, often a microbe, to optimise one or a collection of metabolic tasks may lead to difficulties when attempting to obtain a production system that is efficient, or to avoid toxic effects for the recruited microorganism. The idea of using instead a microbial consortium has thus started being developed in the last decade. This was motivated by the fact that such consortia may perform more complicated functions than could single populations and be more robust to environmental fluctuations. Success is however not always guaranteed. In particular, establishing which consortium is best for the production of a given compound or set thereof remains a great challenge. This is the problem we addressed in a paper accepted this year [16].

We thus introduced an initial model and a method, called MultiPus , that enable to propose a consortium to synthetically produce compounds that are either exogenous to it, or are endogenous but where the interaction among the species in the consortium could improve the production line. In mathematical terms, given a weighted directed hypergraph $ℋ$, the problem is to enumerate all directed sub-hypergraphs whose sets of vertices and of hyperarcs are included in those of $ℋ$, enable to produce the set of targets of interest from a subset of the sources of $ℋ$, and are of minimum weight. We called this the Directed Steiner Hypertree (DSH) problem.

We showed that the main issue in terms of the complexity of the problem comes from the hyperarcs with multiple source vertices (we called those the tentacular hyperarcs), not from the possible multiplicity of the target vertices. This is not the only issue though, and we thus further demonstrated that even when there is only one target that needs to be reached, the problem remains NP-hard. When both parameters, number of tentacular hyperarcs and of targets, are fixed, the problem becomes tractable. We then explored two methods for addressing it. One is a dynamic programming approach, and the other logic programming using ASP (Answer Set Programming). The second was more efficient for now, and the software MultiPus is thus based on it.

As initial validations of the model and of the method, we applied it to two case-studies taken from the literature.

This work was also part of the PhD of Alice Julien-Laferrière defended in December 2016 [1].