Computing minimal nutrient sets from metabolic networks via linear constraint solving

Abstract

BackgroundAs more complete genome sequences become available, bioinformatics challenges arise in how to exploit genome sequences to make phenotypic predictions. One type of phenotypic prediction is to determine sets of compounds that will support the growth of a bacterium from the metabolic network inferred from the genome sequence of that organism.ResultsWe present a method for computationally determining alternative growth media for an organism based on its metabolic network and transporter complement. Our method predicted 787 alternative anaerobic minimal nutrient sets for Escherichia coli K–12 MG1655 from the EcoCyc database. The program automatically partitioned the nutrients within these sets into 21 equivalence classes, most of which correspond to compounds serving as sources of carbon, nitrogen, phosphorous, and sulfur, or combinations of these essential elements. The nutrient sets were predicted with 72.5% accuracy as evaluated by comparison with 91 growth experiments. Novel aspects of our approach include (a) exhaustive consideration of all combinations of nutrients rather than assuming that all element sources can substitute for one another(an assumption that can be invalid in general) (b) leveraging the notion of a machinery-duplicating constraint, namely, that all intermediate metabolites used in active reactions must be produced in increasing concentrations to prevent successive dilution from cell division, (c) the use of Satisfiability Modulo Theory solvers rather than Linear Programming solvers, because our approach cannot be formulated as linear programming, (d) the use of Binary Decision Diagrams to produce an efficient implementation.ConclusionsOur method for generating minimal nutrient sets from the metabolic network and transporters of an organism combines linear constraint solving with binary decision diagrams to efficiently produce solution sets to provided growth problems.

Enumeration of minimal stoichiometric precursor sets in metabolic networks

“…A natural question is to compare our results with those obtained in [ 8 ]. Unfortunately, the algorithm of Eker et al [ 8 ] was not publicly available for testing. We nevertheless tried to reproduce the authors’ results by incorporating their definitions in our method, but we were unable to obtain the same results, even using the same Escherichia coli network they made available.…”

“…To our knowledge, there are two algorithms that attempt to enumerate all minimal precursor sets with stoichiometry (henceforth called stoichiometric precursor sets ) [ 7 , 8 ].…”

“…The method of Eker et al [ 8 ] is based on logical and linear constraint solving and on computational boolean algebra. The authors formulated two different constraint models, that were called steady-state and machinery-duplicating .…”

“…

Fig. 1 Network with one source p and one target t illustrating the difference between the two models used by Eker et al [ 8 ], and the limitation of the machinery-duplicating model. The source p is a precursor set for the production of the target if the steady-state model is assumed.

…”

“…sasita enables to enumerate all stoichiometrically feasible minimal precursor sets in both models, steady-state and machinery-duplicating , as in [ 8 ]. A natural question is to compare our results with those obtained in [ 8 ]. Unfortunately, the algorithm of Eker et al [ 8 ] was not publicly available for testing.…”