Ne a gene-specific threshold. To this end, we perform bimodal distribution analysis for each gene over the available conditions and all time-points. Due to the transient (de)activation upon perturbation, genes often show a bimodal distribution in expression values [20], indicating an active and an inactive state. For a gene whose distribution of expression values is a poor match to the bimodal distribution, we use the expression median as a threshold (cf. Additional file 1). Based on these values, we define the weight w of a gene as follows:w=I + - , (1)where z denotes the z-score, is the expression value, and is the determined threshold value. The trivalued indicator I takes values of 1, -1, or 0 if the gene is differentially?Topfer et al. BMC Systems Biology 2012, 6:148 http://www.biomedcentral.com/1752-0509/6/Page 3 ofFigure 1 Schematic depiction of the computational approach. A genome-scale network and time-series transcriptomics data are used to extract time- and condition-specific minimal networks. Data for different environmental conditions are analyzed to weight genes based on differential expression and bimodal distribution analyses. The gene-reaction annotation of the network reconstruction is used to map the weights onto the metabolic model. A minimization approach is applied to extract minimal networks. EFM analysis is conducted on the minimal networks, and the resulting sets of EFMs and the derived fractional appearance profiles are employed to characterize the transitional behavior of the network and of individual reactions, respectively.up- or down-regulated, or shows no differential behavior, respectively. The first term in Equation (1) refers to the differential expression, while the second one combines the normalized difference between the expression value and the gene-specific threshold. We determine weights for transcriptomics data from the cold and heat stress and the control conditions spanning seven time points (0 - 90 min) and map them onto the genome-scale metabolic network reconstruction of E. coli K-12 [21]. If a reaction is annotated with several genes, the AND rule, which accounts for protein complexes, is replaced by using the lowest weight. Moreover, we use the sum of weights if the genes encode isoenzymes and are connected by the OR rule [22]. With this setting, 81 of the reactions in the network can be weighted by experimental data (cf. Additional file 1). Furthermore, annotatedgenes, for Nelfinavir (Mesylate) which the corresponding gene data are missing, are assigned the median weight of all annotated genes. Reactions that are not associated to a gene in the used network PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/6833145 are assigned the median weight over all annotated reactions.Data-driven network reduction--the min-max problemIn the following, we develop a formulation of the problem whose solution yields the minimal network of largest weight, quantifying the compliance with the data. More formally, we determine the minimal number of reactionsNthat maximizej=wj ?vj , where wj and vj are the weightand the flux of reaction j, respectively. The problem can be cast as a bilevel mixed-integer linear program (MILP), Equations (2)-(8), where each reaction j is assigned a?Topfer et al. BMC Systems Biology 2012, 6:148 http://www.biomedcentral.com/1752-0509/6/Page 4 ofBoolean variable yj 0, 1. If yj = 0, reaction j does not carry any flux and is not included in the network; if yj = 1, the reaction carries flux in the range determined by the flux boundaries (Equation (6)). T.