Designing overall stoichiometric conversions and intervening metabolic reactions

Existing computational tools for de novo metabolic pathway assembly, either based on mixed integer linear programming techniques or graph-search applications, generally only find linear pathways connecting the source to the target metabolite. The overall stoichiometry of conversion along with alternate co-reactant (or co-product) combinations is not part of the pathway design. Therefore, global carbon and energy efficiency is in essence fixed with no opportunities to identify more efficient routes for recycling carbon flux closer to the thermodynamic limit. Here, we introduce a two-stage computational procedure that both identifies the optimum overall stoichiometry (i.e., optStoic) and selects for (non-)native reactions (i.e., minRxn/minFlux) that maximize carbon, energy or price efficiency while satisfying thermodynamic feasibility requirements. Implementation for recent pathway design studies identified non-intuitive designs with improved efficiencies. Specifically, multiple alternatives for non-oxidative glycolysis are generated and non-intuitive ways of co-utilizing carbon dioxide with methanol are revealed for the production of C2+ metabolites with higher carbon efficiency.

: Six alternate network designs for conversion of glucose to acetate with 100% carbon efficiency. The full description of the abbreviated reaction (in upper case) and metabolite (in lower case) names is listed in Supplementary Data Files S3 and S4, respectively. The molar flux values for each reaction are shown in italics under the reaction names.
We next explored whether it is possible to construct the entire pathway in a single organism (see Methods) unlike the engineered NOG pathway that requires at least one heterologous enzyme (i.e., either FPK or XPK). Figure S1e illustrates one such design with reactions from only clostridial species such as C. ljungdahlii 4 or thermophilic organisms such as Moorella thermoacetica 5 . Here, the EMP pathway is combined with the Wood-Ljungdahl cycle to fix the CO 2 lost in the conversion of pyruvate (pyr) to acetyl-CoA. Two pyr molecules (from one glucose molecule) are decarboxylated by the pyr ferredoxin oxidoreductase enzyme (PFOR) 6 to acetyl-CoA and CO 2 . Subsequently, one CO 2 molecule enters the western branch of Wood-Ljungdahl  Wood-Ljungdahl we can in principle provide four ATP molecules (see Figure S1e). An alternate pathway (see Figure S1f) with a maximum generation of three ATP molecules can also be constructed using enzyme in the ED pathway. Here, the serine metabolism is utilized instead of the western branch to generate methf. However, practical hurdles in fixing all the CO 2 released in pyruvate decarboxylation (PFOR) and glycine cleavage (GLYCL) may make these pathways difficult to engineer.
Case study 2: Co-utilization of methanol and carbon dioxide to C 2+ compounds Optimization formulations minRxn/minFlux revealed that the optimal reaction networks for each conversion involved a common core of reactions that initially convert the C 1 substrates to an intermediate product (i.e., acetyl-CoA), which was subsequently routed towards the final product.
As a result, the first example (acetate production) spans alternate routes of fixing CO 2 with methanol to acetyl-CoA (and acetate). Each one of the identified networks is subsequently coupled with additional reactions to synthesize the three other target products (i.e., 3hydroxybuyrate, 2-ketoisovalerate and phloroglucinol). The optimal network for converting methanol and CO 2 to acetate is divided into two modules (see Figure S2a). The first module condenses four molecules of CO 2 and methanol to synthesize four acetyl-CoA molecules using a combination of methylotropic and Wood-Ljungdahl pathway enzymes. The methyl group of methanol is transferred to Corrinoid protein by CoM-Corrinoid methyltransferases (MTA) 7  The design shown in Figure S2a requires the fewest number of reactions, however, the oxygensensitive nature of the Wood-Ljungdahl enzymes (MTA, ACS) 10 could be a practical concern.
The second synthetic design (see Figure S2b) uses histidine degradation metabolism 12 14 is the only additional reaction required to fix an additional formaldehyde molecule with xu5p, and subsequently cleave it to glycerone. Subsequently, glycerone follows lactate metabolism to acetaldehyde (acald) (in Lactate Aldolase (LA)), and oxidation of acetaldehyde completes the network.
A third design using predominantly E. coli reactions was also identified ( Figure S2c). Here, half of the formaldehyde (from methanol) is fixed in the modified RuMP cycle and the rest is fixed along with CO 2 in a functional reversal of the glyoxylate shunt 15 . C 1 metabolism in the serine pathway is combined with serine-glyoxylate aminotransferase (SERAT) 16 to fix the remaining formaldehyde to glyoxylate and produce hydroxypyruvate (hpyr). Phosphoenolpyruvate (pep), from the reduction of hpyr in glycerate metabolism, fixes atmospheric CO 2 in the anaplerotic pep carboxylase enzyme (PPC). This flux is routed through malyl-CoA (in ATP-driven malate thiokinase (MTK) 15 ) producing acetyl-CoA and glyoxylate through the malyl-CoA ligase (MCL). As all the reactions in this design are either native to E. coli or have been successfully expressed in prior studies (MTK, MCL) 15 , it has the fewest potential barriers for its implementation.
Each one of these cyclic routes can be combined with additional paths to route acetyl-CoA flux towards other target chemicals. Figure S3a, b and c show routes for converting methanol and CO 2 to a C 4 , a C 5 and a C 6 product, respectively. Pathways for 3-hydroxybutyrate (3hbut) recapitulate existing engineered routes through acetoacetyl-CoA 17,18 while also proposing additional synthetic designs that utilize succinate synthesis (through a modified TCA cycle) and metabolism (through -oxidation reversal) routes (see Figure S3a). In addition to thiamine-dependent valine synthesis for 2-ketoisovalerate (2kiv) production 19 , an alternate route linking -oxidation reversal with valine degradation is also identified (see Figure S3b). Here, n-butanoyl-CoA in the C 4oxidation cycle is isomerized to isobutyryl-CoA (ibutcoa) in iso-butyryl-CoA mutase (ICM) 20 .
Reversal of 2-ketoisovalerate oxidoreductase (KIVDH) in the valine degradation pathway converts ibutcoa to the target product. In the case of phloroglucinol (phgl) production, however, the traditional pathway using malonyl-CoA metabolism 21 was not identified by minFlux as the acetyl-CoA carboxylase (ACCOAC) step requires three additional ATP thus violating the overall energy balance fixed in optStoic. Instead, acetyl-CoA was converted to hydroxyl-butyryl-CoA    Figure S5c). Upon excluding them an alternate mechanism was identified by minFlux where HSO 3 is converted to S 2 O 3 2− through the oxidation of mercaptopyrvate (to pyruvate) by sulfurtransferases found in E. coli 27 (see Figure S5c).   Figure S4 shows three alternate routes for the conversion of three molecules of methane and one molecule of CO 2 to two acetate molecules with Fe 3+ /Fe 2+ as the terminal electron acceptor. The smallest network (see Figure S4a)  all found in most methanogenic archaea and some methanotrophs 28 . However, in order to maintain the 1:1 ratio of methane and CO 2 in the ACS reaction, one molecule of methane is oxidized to CO 2 in a complex three-step cyclic route involving a functional reversal of the eastern branch of the Wood-Ljungdahl pathway (see Figure S4a). Alternate routes for oxidizing methane were also found that directly oxidize methyl-CoM to CO 2 based on the methylamine cycle (see Figure S4b). The third design (see Figure S4c) bypasses the ACS and MTBA reactions by combining the two cycles describes in Figures S4a and b. Interestingly all the recruited enzymes (except for the terminal electron acceptors) are present in most anaerobic methanogens. This case study demonstrates how cofactor balances can become the dominant factor in synthetic pathway design. For example, the net reduction of 5-methyl thf to 5,10-methylene thf is accomplished by two reactions running in opposite directions involving nad and ferredoxin cofactors ( Figure S4a) to maintain overall balance of cofactors. Figure S5 illustrates a few of the existing (in blue) and newly identified strategies (in green) for the production of four platform chemicals (i.e., 2,3-butanediol, 3-hydroxypropionate, 1-butanol and 1,3-propanediol 29,30 ) each utilizing a different electron acceptor. For example, 2,3-butanediol (23but) is produced from acetyl-CoA by first converting it to pyruvate (using pyruvate-ferredoxin oxidoreductase (PFOR) 6 ) with subsequent dimerization to 2-acetolactate (alac) (see Figure S5a).
Decarboxylation of alac followed by reduction of acetoin (actn) produces 2,3-butanediol. While existing pathways (from pyruvate 31 ) lose two carbon atoms for each molecule of 23but, the identified pathway ( Figure S5a in blue) preserves all carbon as lost CO 2 is fixed back in the PFOR step. It is interesting to note that the identified pathway uses the same enzymes (except the MTA reaction) recruited for converting CO to 23bdo in a recent study performed on three separate acetogenic Clostridial species 32 and functionally expressed in E. coli 33 . An alternate pathway was also identified (see Figure S5a in green) where acetyl-CoA is ultimately converted to acetoin through the reversal of acetoin dehydrogenase (ACNDH) found in acetoin consuming bacteria such as E. aerogenes 34 . Three separate pathways were identified for 3-hydroxypropionate (3hp) production all of which have been explored previously [35][36][37] (see Figure S5b). Similarly, the shortest route for 1-butanol production ( Figure S5c) recapitulates existing strategies involving condensation of two molecules of acetyl-CoA by the accoa acetyltransferase (ACTR) followed by a functional reversal of theoxidation pathway [38][39][40] . A so far unexplored pathway is also suggested that combines the oxidative branch of TCA cycle with succinate-semialdehyde metabolism to reach 1-butanol (see Figure S5c in green). For 1,3-propanediol (13pdo) (see Figure S5d), the only identified pathway converts acetyl-CoA to pyruvate which is reduced back to glyceraldehyde-3-phosphate (g3p) through gluconeogenesis. Glycerol, from g3p, is subsequently reduced to 13pdo in three steps by the native in some Clostridia 41 Figure S5d in red) were absent in our database. Upon inclusion of the metabolite and the reactions, minFlux could identify this pathway as an alternate more energy efficient route for 13pdo production.

Comparison of optStoic+minRxn/minFlux derived designs with other pathway design tools
We compared the optimal pathways identified by our approach with two existing pathway searching tools (Chou et al 44