Figure 1.
Bi-level approaches considering additions and deletions.
(A) Simplified representation of the existing OptStrain procedure and an illustrative example. Step 1 adds a minimum number of reactions from a universal database that yields the maximal increase in theoretical maximum production (TMP). Step 2 identifies reaction deletions in the augmented network identified in Step 1 that couple biomass and biochemical production. (B) SimOptStrain with simultaneous gene deletion and non-native reaction addition, and illustrative examples. Solution s1 shows an example of reaction additions, which do not increase the TMP, that improve biochemical production at the maximum growth rate when combined with gene deletions. Solution s2 is an example of reaction additions that yield a suboptimal increase in the TMP, while solution s3 is a case where the number of added reactions is not necessarily the minimum. Solutions s1, s2, and s3 could only be found using SimOptStrain.
Figure 2.
BiMOMA – a direct mixed-integer programming approach for quadratic bi-level strain design.
The MOMA inner problem, a convex quadratic program, is converted to its optimality conditions using strong duality. The resulting BiMOMA problem is a single level mixed-integer quadratically constrained program.
Figure 3.
Analysis of dual variables for reaction removals using dual LP of FBA.
Maximum (downward triangle) and minimum (upward triangle) of observed dual variable values for each reaction sorted by the standard deviation. The values of dual variables were obtained from 1,000,000 samples of 10 gene knockouts in glucose anaerobic condition using the iAF1260 metabolic model of E. coli.
Figure 4.
Performance of different search methods.
(A) Predicted acetate production yields in glucose anaerobic conditions for E. coli strains designed using our MIP techniques or a local search method. (B) Cumulative CPU times for our MIP techniques (○) and a local search method (□). For both panels, cases using α = 0% TMP (light blue) or 0.5% TMP (blue) were solved to optimality and α = 0.005% TMP (dark blue) was solved with a node limit of 104 (TMP = 2.56 mol acetate produced/mol glucose consumed).
Table 1.
Best gene deletion strategies identified by OptORF using our MIP techniques for acetate production under glucose anaerobic condition.
Figure 5.
Product yields for E. coli strains designed to generate different products.
Different colors indicate OptKnock (light grey), OptGene (grey), and OptORF (dark grey). The numbers on the x-axis correspond to the number of reaction deletions identified (or maximum allowed if no strategy was found) by OptKnock and OptGene [30], or gene deletions (equivalent reaction deletions listed in parentheses) identified by OptORF (this study). The product yields for OptKnock and OptGene were taken from an earlier study [30] and re-calculated based on TMP values without a minimum growth requirement. A missing bar indicates that no strategy was previously found.
Figure 6.
Fluxes involving NADPH production/consumption and central metabolism.
The top numbers are for wild-type and the bottom numbers are for a predicted succinate producing strain (ΔsdhC Δgnd ΔglyA+EC 1.2.1.52+EC 2.1.3.1 reactions). (A) Metabolic pathways producing or consuming NADPH are shown. The numbers are percentages of the total NADPH produced or consumed, where 100% is 15.7 mmol gDW−1 h−1 for wild-type (first line) and 7.3 mmol gDW−1 h−1 for succinate producing strain (second line). gDW stands for gram dry weight. Abbreviations of metabolites: Glu, glutamate; Gln, glutamine; Ile, isoleucine; Leu, leucine; Lys, lysine; Thr, threonine; Val, valine. (B) Metabolic fluxes and genes associated with each reaction in the central metabolic networks are shown. Blue arrows indicate removed native E. coli reactions, and red arrows indicate added non-native reactions. The numbers are relative fluxes normalized with respect to the total glucose uptake rate (100% is 10 mmol glucose gDW−1 h−1). Abbreviations of metabolites (‘_ext’ indicates extracellular): AC, acetate; ACCOA, acetyl-CoA; ACTP, acetyl phosphate; AKG, 2-oxoglutarate; CIT, citrate; FUM, fumarate; G6P, glucose 6-phosphate; GLC, glucose; ICIT, isocitrate; MAL, malate; MALCOA, malonyl-CoA; OAA, oxaloacetate; PEP, phosphoenolpyruvate; PYR, pyruvate; SUCC, succinate; SUCCOA, succinyl-CoA.
Table 2.
Gene deletion and reaction addition strategies identified by SimOptStrain for succinate production under glucose aerobic condition.
Table 3.
Gene deletion and reaction addition strategies identified by SimOptStrain for glycerol production under glucose aerobic condition.
Figure 7.
Improvements in product yields in glucose aerobic conditions for E. coli strains designed using BiMOMA.
(A) Pyruvate and (B) Glutamate. The best BiMOMA strategies (○) were identified for k = 1 to 5 using a penalty of 0.5% TMP, and were combined with a local search (□) with search sizes of 2 or 3. BiMOMA+local search size of 2 starts from the best BiMOMA solutions for k = 2 and 3; and BiMOMA+local search size of 3 starts from the best BiMOMA solutions for k = 3, 4, and 5. A sequential search was also performed, which is a local search with search size of 1 starting from the best k = 1 solution.
Table 4.
Top gene deletion strategies identified by BiMOMA (k<5) or BiMOMA+Local Search (k>5) for pyruvate production under glucose aerobic condition.
Table 5.
Top gene deletion strategies identified by BiMOMA (k<5) or BiMOMA+Local Search (k>5) for glutamate production under glucose aerobic condition.