Designing optimal cell factories: integer programming couples elementary mode analysis with regulation

Abstract

BackgroundElementary mode (EM) analysis is ideally suited for metabolic engineering as it allows for an unbiased decomposition of metabolic networks in biologically meaningful pathways. Recently, constrained minimal cut sets (cMCS) have been introduced to derive optimal design strategies for strain improvement by using the full potential of EM analysis. However, this approach does not allow for the inclusion of regulatory information.ResultsHere we present an alternative, novel and simple method for the prediction of cMCS, which allows to account for boolean transcriptional regulation. We use binary linear programming and show that the design of a regulated, optimal metabolic network of minimal functionality can be formulated as a standard optimization problem, where EM and regulation show up as constraints. We validated our tool by optimizing ethanol production in E. coli. Our study showed that up to 70% of the predicted cMCS contained non-enzymatic, non-annotated reactions, which are difficult to engineer. These cMCS are automatically excluded by our approach utilizing simple weight functions. Finally, due to efficient preprocessing, the binary program remains computationally feasible.ConclusionsWe used integer programming to predict efficient deletion strategies to metabolically engineer a production organism. Our formulation utilizes the full potential of cMCS but adds additional flexibility to the design process. In particular our method allows to integrate regulatory information into the metabolic design process and explicitly favors experimentally feasible deletions. Our method remains manageable even if millions or potentially billions of EM enter the analysis. We demonstrated that our approach is able to correctly predict the most efficient designs for ethanol production in E. coli.

Which sets of elementary flux modes form thermodynamically feasible flux distributions?

“…Alternative optima and suboptimal solutions λ l with l > 1 (and the corresponding LTCS ℒ 1 ) can be found by successively excluding already existing solutions λ j with j ∈ {1,…, l −1} from the MILP 9. This is achieved by successively adding the constraint$\sum _{i\in Z}{\mathrm{normal\lambda }}_i^l\ge 1,Z=false\{i\mid {\mathrm{\lambda }}_i^l=0\text{for all}j\in \{1,\dots ,l-1\}false\}$ …”

Design of optimally constructed metabolic networks of minimal functionality

“…Only one contributing reaction needs to be deleted to render a steady state flux through this mode infeasible. These two conditions can be used to set up an optimization problem, where x is maximized in such a way that all desired EFMs obey the former condition, while all undesired EFMs are subject to the latter constraint [24]. This approach requires a manual partition of the EFMs into desirable and undesirable modes.…”

“…To check if an EFM is hit by a cut set, we calculated the dot-product between b i and x. If b T i x~jjb i jj then EFM i is not cut by x as none of the reactions contributing to EFM i is affected [24]. If a cut set hits EFM i then b T i xƒjjb i jj{1.…”

“…We have utilized a BIP to calculate cMCSs [24]. In this formulation an EFM i is represented by a binary vector…”

Qualitative Reasoning for Reaction Networks with Partial Kinetic Information

“…Alternatively, pathway analysis approaches [12] rely on the structure of reactions networks, but the combinatorial nature of the problem makes difficult their application to densely interconnected networks. To both methods boolean constraints can be added in order to account for inhibitors that block reactions completely [6]. But blocking inhibitors is not appropriate in deterministic semantics, where the average over blocked and unblocked situations is to be considered.…”