Learning Boolean Controls in Regulated Metabolic Networks: A Case-Study

Abstract

Many techniques have been developed to infer Boolean regulations from a prior knowledge network and experimental data. Existing methods are able to reverse-engineer Boolean regulations for transcriptional and signaling networks, but they fail to infer regulations that control metabolic networks. This paper provides a formalisation of the inference of regulations for metabolic networks as a satisfiability problem with two levels of quantifiers, and introduces a method based on Answer Set Programming to solve this problem on a small-scale example.

Appendices

A Binarized Metabolic Steady State

Table 3. All the Boolean metabolic steady states admissible for the metabolic network $\mathcal {N}$ show Fig. 1a. The external metabolite Biomass is not shown since its value can be both $0$ and $1$ for each Boolean metabolic steady state. The experimentation column indicates the numbers of the experiments where the Boolean metabolic steady states occurs.

B Experiments and Simulations

Fig. 4.

Simulation made with FlexFlux of the regulated metabolic network in Fig. 1 for each experiment (Table 3a). Time step is set to $0.01$. Reaction domains are $\forall r \in \{ \text {Tc1},\,\text {Tc2} \},\,(l_r,\, u_r) = (0,\, 10.5)$, $\forall r \in \{ \text {Td},\,\text {Te} \},\,(l_r,\, u_r) = (0,\, 12.0)$, $\forall r \in \{ \text {R6},\,\text {R7},\,\text {Rres},\,\text {Growth} \},\,(l_r,\, u_r) = (0,\, 9999)$ and for Oxygen, $(l_r,\, u_r) = (0,\, 15.0)$. The same simulation graphs are obtained using the local function $f_\text {Rres} = \lnot x_\text {RPO2}$ and $f_\text {Rres} = 1$.

Table 4. All the different binarized metabolic steady states of each experiment. They are the input data used to solve the inference problem.