SAT-based metabolics pathways analysis without compilation

Abstract

Elementary flux modes (EFMs) are commonly accepted tools for metabolic network analysis under steady state conditions. They can be defined as the smallest sub-networks enabling the metabolic system to operate in steady state with all irreversible reactions proceeding in the appropriate direction. However, when networks are complex, the number of EFMs quickly leads to a combinatorial explosion, preventing from drawing even simple conclusions from their analysis. Since the concept of EFMs analysis was introduced in 1994, there has been an important and ongoing effort to develop more efficient algorithms. However, these methods share a common bottleneck: they enumerate all the EFMs which make the computation impossible when the metabolic network is large and only few works try to search only EFMs with specific properties. As we will show in this paper, enumerating all the EFMs is not necessary in many cases and it is possible to directly query the network instead with an appropriate tool. For ensuring a good query time, we will rely on a state of the art SAT solver, working on a propositional encoding of EFMs, and enriched with a simple SMT-like solver ensuring EFMs consistency with stoichiometric constraints. We illustrate our new framework by providing experimental evidences of almost immediate answer times on a non trivial metabolic network.