Efficiency estimates for electromicrobial production of branched-chain hydrocarbons

Summary In electromicrobial production (EMP), electricity is used as microbial energy to produce complex molecules starting from simple compounds like CO2. The aviation industry requires sustainable fuel alternatives that can meet demands for high-altitude performance and modern emissions standards. EMP of jet fuel components provides a unique opportunity to generate fuel blends compatible with modern engines producing net-neutral emissions. Branched-chain hydrocarbons modulate the boiling and freezing points of liquid fuels at high altitudes. In this study, we analyze the pathways necessary to generate branched-chain hydrocarbons in vivo utilizing extracellular electron uptake (EEU) and H2-oxidation for electron delivery, the Calvin cycle for CO2-fixation and the aldehyde deformolating oxygenase decarboxylation pathway. We find the maximum electrical-to-fuel energy conversion efficiencies to be 40.0−4.4+0.6% and 39.8−4.5+0.7%. For a model blend containing straight-chain, branched-chain, and terpenoid components, increasing the fraction of branched-chain alkanes from zero to 47% only lowers the electrical energy conversion efficiency from 40.1−4.5+0.7% to 39.5−4.6+0.7%.


INTRODUCTION
The industrial-scale synthesis of carbon-neutral hydrocarbon fuels that are drop-in compatible with present-day internal combustion and jet engines is one of the biggest challenges in the decarbonization of the world's energy infrastructure.Corn ethanol can be safely blended into gasoline up to a fraction of z10-15%.However, the widespread use of high fractions of ethanol in fuel blends is unfeasible as it lacks the high boiling and low freezing points needed in many applications, especially aviation. 1This difficulty has motivated the production of kerosenegrade biofuel blends.Third-generation algal biofuels show promise for use in aviation, but the upscaling of algal fuels is challenging and faces many hurdles to commercial acceptance. 2 For alternative fuels to be established as commonplace, their properties must be as close to those of conventional fuels as possible.
In addition to straight-chain alkanes and terpenoids, branched-chain hydrocarbons are key components of traditional jet fuels.In Jet A-1, branched-chain hydrocarbons are used to raise the boiling and lower the freezing points while burning almost as cleanly as straight-chain alkanes. 3Although terpenoids (whose electromicrobial synthesis was described by us previously 4 ) could achieve similar boiling increases and freezing point reductions, they also create significant soot deposition during combustion. 5Production of a library of branched-chain hydrocarbons could permit synthesis of blends that closely match the composition and physico-chemical properties of fossil-derived kerosene, while also burning cleanly.Furthermore, gasoline containing a high fraction of isoalkanes (one type of branched-chain alkanes) could burn much cleaner than conventional gasoline. 6lectromicrobial production (EMP) could enable highly efficient production of carbon-neutral drop-in biofuels.][9][10][11][12][13][14][15][16] EMP has allowed for microbes that assimilate electrochemically reduced CO 2 like formate 14,17 and acetate; 16 H 2 -oxidizing, CO 2 -fixing systems like the Bionic Leaf; 18,19 microbe-semiconductor hybrids; 20 and microbes that can directly absorb electricity through processes like extracellular electron uptake (EEU). 8,21,22Lab-scale demonstrations of EMP already have effective solar-to-chemical energy conversion efficiencies exceeding all forms of terrestrial photosynthesis. 19,235][26] This high efficiency mitigates many of the concerns about competition for land created by first-and second-generation biofuels. 27,28Furthermore, a large library of metabolic pathways for the biological synthesis of branched-chain hydrocarbons has been established 3,6,[29][30][31][32] that could allow the production of jet fuel blends much closer in composition to Jet A-1 than algae-derived biofuels (reviewed in Adesina et al. 33 and Sheppard et al. 34 ).
In this work we extend our earlier predictions of EMP efficiency 8,25,26,34 to make minimum energy cost and upper-limit production efficiency estimates of single-and multi-branched hydrocarbons powered by H 2 -oxidation 18,19 or EEU, 8,21,22 with carbon supplied by in vivo CO 2 -fixation with the Calvin cycle.We then calculate the production efficiency of drop-in fuel blends of increasing branched-chain content.

Electromicrobial production of jet fuel components
We predict upper limit efficiencies for the EMP of branched-chain hydrocarbons.These predictions set an upper bound on the performance of a set of highly engineered microorganisms created for production of drop-in jet fuel components.Below we summarize all of the key equations utilized in this article.For detailed derivations see Salimijazi et al. 8 and our subsequent work that builds upon this theory. 25,26,34All model parameters are shown in Table 1, and all symbols used in this article are shown in Table S1.
As in earlier work, we assume access to a reservoir of CO 2 .Reducing power for the regeneration of NAD(P)H and ATP are provided via oxidation of electrochemically reduced H 2 (Figure 1B part 1) by EEU from a diffusible intermediary (such as flavins or anthra(hydra) quinone-2,6-disulfonate (AHDS red /AQDS ox )) or through a conductive biofilm or direct contact with a cathode (Figure 1B part 2).We assume that the energy requirements for microbial maintenance are negligible at maximum efficiency, allowing the cell to operate as a ''bag of enzymes''. 8,38ydrocarbon molecules with an energy-per-molecule, E HC , are produced a rate of Ṅ HC molecules per second.The amount of energy needed to produce a mole of hydrocarbon, L EP , 8,25 L EP = P e;T N A 0 N $ HC ; (Equation 1) where P e;T is the power input to the system and N A is the Avogadro constant.Thus, the minimum energy input into the bio-electrochemical system is, where DU e.cell is the potential difference across the bio-electrochemical cell (note we have changed this from DU cell in earlier work for clarity), e is the fundamental charge, and n ep is the number of electrons needed to synthesize a molecule of the product from CO 2 .The whole-cell voltage is one of the biggest determinants of EMP efficiency.In H 2 -oxidation systems, we make the assumption that the whole-cell voltage, DU e.cell , is 2V (the optimal applied voltage for the Bionic Leaf device 19 ).However, it is not clear if this very low whole-cell voltage can be  S2 No. NAD(P)H for product n p, NADH See Table S2 No. Fd red for product n p, Fd See Table S2 Product energy density (J molecule À1 ) E HC See Table S3 Model parameters used in this article are based upon model parameters used in a previous analysis of the electromicrobial production of the biofuel butanol. 8A sensitivity analysis was performed for all key parameters in this work. 8chieved in a scaled-up system, possibly due to mass transport issues.Increasing this value will reduce the efficiencies quoted here.For example, increasing DU e.cell from 2V to 3V will reduce the efficiency by a factor of 2/3.A similar reduction will be seen for EEU-mediated systems.Furthermore, the efficiency of energy conversion from input power to final product is, (Equation 3) When utilizing in vivo carbon-fixation (Figure 1A), the upper limit of electrical-to-chemical efficiency is equivalent to the energy carried per molecule of hydrocarbon, E HC , relative to the amount of energy needed to move the charge for product synthesis across the bio-electrochemical cell (en ep DU e.cell ), 8 h EP % E HC À en ep DU e:cell Á : (Equation 4) (B) Mechanism by which electricity sources can be used to power microbial production, using either H 2 -oxidation or extracellular electron uptake (EEU).
(C) In the first, H 2 is electrochemically reduced on a cathode, transferred to the microbe by diffusion or stirring, and is enzymatically oxidized.In the second mechanism, extracellular electron uptake (EEU), electrons are transferred from a cathode (i) along a microbial nanowire (part of a conductive biofilm), (ii) by a reduced medium potential redox shuttle like a quinone or flavin, or (iii, not shown) by direct contact of the cell with the cathode and are then oxidized at the cell surface by the extracellular electron transfer (EET) complex.From the thermodynamic perspective considered in this article, these mechanisms of EEU are equivalent.Electrons are then transported to the inner membrane where reverse electron transport is used to regenerate NAD(P)H, reduced Ferredoxin (not shown), and ATP. 8,21,39This schematic is modified from our earlier work on the synthesis of the straight-chain alkane and terpenoid components of jet fuels. 34n this article we calculate the number of electrons needed for production of a hydrocarbon by in vivo CO 2 -fixation (n ep ) with electron uptake both by H 2 -oxidation and EEU. 8 For electron delivery by H 2 , where n p, NADH , n p, Fd , and n p, ATP are the number of NAD(P)H, reduced ferredoxin, and ATP needed for product synthesis; DG ATP/ADP is the Gibbs free energy for regeneration of ATP; DU membrane is the potential difference between the cytoplasmic and periplasmic faces of the inner membrane (the host of the electron transport chain); U H2 is the redox potential of H 2 -oxidation; and U acceptor is the redox potential of the terminal electron acceptor (usually O 2 ).
For electron delivery by EEU, (Equation 6) where U NADH is the redox potential of NAD(P)H reduction; U Q is the redox potential of menaquinone reduction; and U Fd is the redox potential of ferredoxin reduction.

ATP, NAD(P)H, and reduced ferredoxin demands for jet fuel component electromicrobial production
The ATP, NADP(H), and reduced ferredoxin requirements for individual molecules in a jet fuel blend are calculated by flux balance analysis.Pathways for the production of the straight-chain alkane and terpenoid components of jet fuel were compiled by us in a recent article. 34ike straight-chain alkanes, branched-chain alkanes are produced by the Type II fatty acid synthase (FAS) system followed by decarboxylation. 3Branches are introduced into the growing fatty acid by incorporation of unconventional methylated initiator and lengthener molecules. 3n overview of branched-chain alkane synthesis is shown in Figure 2. Synthesis pathways for methylated initiators and lengtheners are shown in   2. In wild-type cells, the incorporation of methylated initiators and lengtheners into fatty acids is kept at low levels and are limited by one of several regulatory enzymes native to these systems. 3,40Downregulation of these native regulatory enzymes can promote methylated initiator production and a high output of branched-chain hydrocarbons.From this start point, we are able to generate singlebranched compounds of any length with odd or even methylation patterns as shown in Figure 3. Full pathways for the synthesis of a panel of individual branched-chain alkane compounds (shown in Figure 4) are compiled from listings of reactions in the Kyoto Encyclopedia of Genes and Genomes (KEGG) [41][42][43] 44 Briefly, we consider a chemical species number rate of change vector, ṅ ṅ, that encodes the rate of change of number of the reactant molecules over a single cycle of the reaction network; a stoichiometric matrix S p that encodes the number of reactants made or consumed in every reaction in the network; and a flux vector v that encodes the number of times each reaction is used in the network.Reactant molecules are denoted as inputs (e.g., CO 2 , ATP, NAD(P)H), outputs (e.g., H 2 O), intermediates, or the target molecule (e.g., the alkane to be synthesized).2][43] The (S)-methylmalonyl-[acp] pathway is mediated by either Propionyl-CoA Carboxylase (PCC) or the downregulation of the regulatory enzyme Methylmalonyl-CoA Demethylase (MMCD) that traditionally prevents (S)-methylmalonyl-CoA formation from Acetyl-CoA Carboxylase.Pathways are depicted in Figure 3.
under the constraint that the number of each intermediate chemical species does not change over a reaction cycle, and that the number of target molecules increases by 1, output or the target : (Equation 8) The calculated stoichiometries for the synthesis of each branched-chain hydrocarbon considered in this article are listed in Table S2.The stoichiometries for each molecule are then combined with their molecular weights and energies per molecule (listed in Table S3) to calculate the energy input and production efficiency (FIG-4A&B.PY; FIG-4A&B.PY, results shown in Figure 4).The energy inputs and conversion efficiencies for jet fuel blends are calculated by a weighted average of the energy inputs and efficiencies of the individual components (Figure 5).

Restrictions of branched-chain formation
Due to the limits of FAS, we are unable to produce adjacently methylated branched-chain alkanes.Given the molecular structure of malonyl-CoA, a methyl group can only be added to every second carbon during lengthening.This prevents the preparation of some single-methyland multi-methylated-branched-chains.Nonetheless, FAS allows us to produce a great variety of compounds that allow us to more closely mimic the composition of traditional jet fuel blends.
Increasing the fraction of branched-chain hydrocarbons in a jet fuel blend by 10% lowers conversion efficiency by 0.1% We next calculated how the introduction of branched-chain alkanes into a jet fuel blend would change the energy production costs and energy conversion efficiency (Figure 5).We compared a previously conceived blend containing 85% straight-chain alkanes (C 10 -C 16 ) and 15% terpenoids (pinene, limonene, farnesene, bisabolene, and geraniol), 34 with two additional blends incorporating our branched-chain hydrocarbons (C 8 -C 10 backbone).The energy conversion efficiency for H 2 -driven production of the original blend is 40:1 +0:7 À 4:5 %.

DISCUSSION
Herein, we calculate conversion efficiencies of a panel of 13 single-branched and 11 multi-branched hydrocarbons with backbone lengths between C 5 and C 10 , using H 2 -oxidation or EEU for electron delivery.Figures 4A and 4C show the energy required to produce a mole of each hydrocarbon, and Figures 4B and 4D show the electrical-and solar-to-chemical conversion efficiency for each molecule.Figure 5 shows the energy costs and production efficiencies of jet fuel blends containing increasing amounts of branched-chain alkanes.(C) Energy input required for multi-branched-chain alkane biosynthesis using the Calvin CO 2 -fixation cycle with the ADO alkane termination pathway.(D) Energy conversion efficiency of multi-branched-chain alkane compound biosynthesis on left axis.Solar conversion efficiency compared to C 3 , C 4 , algae, and H 2 -mediated electromicrobial production of glucose on right axis, lines corresponding to those in (B).A sensitivity analysis by Salimijazi et al. 8 found that the biggest source of uncertainty in the energy input and efficiency calculation is the potential difference across the inner membrane of the cell (DU membrane ).Estimates for the trans-membrane voltage range from 80 mV (BioNumber ID 45 (BNID) 10408284 to 270 mV (BNID 107135), with a most likely value of 140 mV (BNIDs 109774, 103386, and 109775).The central value (thick blue or red bar) corresponds to 140 mV.Our sensitivity analysis found that DU membrane = 280 mV produces lower efficiencies (hence a higher energy input), while DU membrane = 80 mV produces higher efficiencies (and hence lower energy inputs). 8The right axis in (A and C) shows the minimum cost of that solar electricity, assuming that the United States Department of Energy's cost target of 3 ¢ per kWh by 2030 can be achieved. 46The right axes in (B and D) show the solar-to-product energy conversion efficiency, assuming the system is supplied by a perfectly efficient singlejunction Si solar photovoltaic (solar to electrical efficiency of 32.9%. 47For comparison, we have marked the upper limit solar-to-biomass energy conversion efficiencies of C 3 , C 4 , 48,49 algal photosynthesis, 50 and upper limit electromicrobial production conversion efficiency of glucose using H 2 -oxidation and the Calvin cycle 25 4C&D.PY in the EMP-TO-BRANCHED-JET online code repository. 44e observe a general trend of increased energy cost with increased chain length.However, changing the position of the methylation sites can change the energy cost of synthesis.For example, the production of 3-M 1 -hexane is more expensive than 2-M 1 -hexane (see Figure 2C).This difference in energy is due to the higher energy cost for production of the (S)-methyl-malonyl-[acp] lengthener needed to install the branch in 3-M 1 -hexane, versus the cost of the 2-methyl-propionyl-[acp] initiator needed to install the branch in 2-M 1 -hexane.The high cost of (S)-methyl-malonyl-[acp], which adds 2 carbons to backbone, is due to the high energy cost of synthesis, requiring 15 ATP and 7 NADH (7.5 ATP C À1 and 3.5 NADH C À1 ).In contrast, 2-methyl-propionyl-[acp] adds 3 carbons to the backbone and requires 14 ATP and 10 NADH (4.6 ATP C À1 and 3.3 NADH C À1 ).
The production efficiency of odd-length alkanes with a branch on the second carbon is lower than that for even-length alkanes with the branch in the same place.Odd-alkanes with a branch on the second carbon need to be initiated with energy-expensive 3-methyl-butanoyl-[acp].On the other hand, even-length alkanes with the branch in the same place need to be initiated with energy-cheap 2-methyl-propionyl-[acp] (see 2-M 1 -pentane and 2-M 1 -hexane an example in Figure 2C).Synthesis of 2-methyl-propionyl-[acp] in total costs 14 ATP and 10 NADH and adds 3 carbons to backbone (4.6 ATP C À1 and 3.3 NADH C À1 ).In contrast, 3-methyl-butanoyl-[acp] adds 4 carbons to the backbone, but requires 21 ATP and 14 NADH (5.25 ATP C À1 and 3.5 NADH C À1 ).
The efficiency of production of straight-chain alkanes ranges from 35:8 +1:7 À 4:2 % for hexane to 40:8 +0:7 À 4:5 % for hexadecane. 34Though similar to the efficiencies of our branched-chains, our straight-chains appear to have slightly higher efficiencies across the board, likely a result of higher combustion energies for compounds of similar carbon length.In all cases, if the electricity for production of these alkanes is derived from a perfectly efficient solar photovoltaic, 47 then their production efficiency exceeds the efficiency of all forms of photosynthesis (see the right hand axis in Figure 4B).
As with single-branched-chain alkanes there is a general increase in energy requirement with multi-branched-chain hydrocarbon length.Furthermore, as with single-branched-chain alkanes, the choice of initiator molecule and the sites of branching cause notable differences in energy cost.The drop of energy required for 3,5-dimethyl octane over 2,4-dimethyl octane can be attributed to this cause.Here, 3,5-dimethyl octane obtains its branches entirely from the use of (S)-methylmalonyl-[acp], which is energetically unfavorable given its use of propionyl-[acp] in production.In contrast, 2,4-M 2 -octane requires the initial production of 2-methyl-propionyl-[acp], and further utilization of (S)-methylmalonyl-[acp]. 2-methyl-propionyl-[acp] is less energetically expensive to produce and thus costs less than (S)-methylmalonyl-[acp] alone.Therefore, though both molecules are chemically similar and combust similarly, they differ in production cost by $ 600 kJ mol À 1 .

Limitations of the study
We can already foresee significant challenges on the way to achieving the solar-to-fuel and electrical-to-fuel efficiencies predicted in this article.These challenges, and their effect on efficiency, are hard to predict but could come from space-time yields, kinetics and other process parameters not considered here.In an earlier work, 8 we noted the effect of H 2 solubility and of biofilm conductivity on the kinetics of the EMPprocess and their subsequent effect on efficiency. 8If CO 2 -concentration is required for the EMP process, this could result in an additional efficiency cost (especially in the future when point CO 2 sources like coal-and natural gas-fired power plants will hopefully be retired). 54,55owever, we do not believe the challenges of realizing something close to our predicted efficiencies are insurmountable.For example, in 1961, Shockley and Quiesser made their estimate of the upper limit of the efficiency of solar photovoltaics when the highest reported efficiency of a PV device was z4%. 56Today, just a little over 60 years later, the technology is beginning to reach full maturity with efficiencies approaching 30% 57 (the theoretical maximum is 33% 58 ), and costs that are exponentially reducing (Swanson's law 59 ).We can similarly envision that the cost (and perhaps the efficiency) of CO 2 -concentration technologies will drop rapidly due to learning-by-doing. 60While we may not know how to solve all of the engineering challenges of EMP, this article indicates that if they can be solved, the payoff could be significant.This article also allows the reader to separate which engineering interventions will have a big pay-off from those that will not.We believe this will be a particularly strong source of motivation and reassurance for young scientists working in the field.First, as we noted in the results, we assume that the very low whole-cell voltages achieved at lab-scale can be consistently achieved when scaled-up.It is likely that this may not be initially feasible due to mass transport considerations.Likewise, limitations of carbon-fixing metabolism may also limit the achievable efficiency due to photorespiration and reduce efficiency by z 25%. 48 very low whole-cell voltage could be achieved (perhaps even at large scale) using high salinity electrolytes.This would necessitate the use of an EMP organism that could tolerate high salinity.While most organisms used in EMP (especially those operated by EEU) are poorly tolerant of salinity, the highly engineerable Vibrio natriegens was recently discovered to be EEU-capable and is well known for being halophilic. 61The high natural tolerance to salinity and high evolvability of V. natriegens creates the possibility of operating an EMP system at very low whole-cell voltages and high efficiencies.These losses could also be reduced by creative reactor design as well.
Next, use of the Calvin cycle (as we consider in this article) is likely to cause efficiency losses due to photorespiration. 48Again, however, creative engineering could reduce these losses.Operating RuBisCO inside of a carbon concentrating mechanism like a carboxysome 62 or bacterial nanocompartment 63 could significantly reduce the oxygenation activity of RuBisCO, allowing the system efficiency to operate much closer to our theoretical maximum efficiency.Furthermore, swapping the entire carbon fixation cycle could eliminate oxygenation entirely.For instance, the 3HP-4HB cycle 17 relies upon the Phosphoenol Pyruvate (PEP) carboxylase that does not suffer from the same oxygenation side reaction as RuBisCO, again allowing a much higher theoretical efficiency to be achieved.If a compartmentalization system can be implemented that completely shields enzymes from O 2 , then we could operate O 2 -sensitive pathways like the Wood-Ljungdahl pathway that could achieve very high efficiencies. 4,8,25For example, in our earlier work on the synthesis of blends of straight-chain alkanes and terpenoids, swapping the Calvin cycle for the Wood-Ljngdahl pathway raised the energy conversion efficiency of a jet fuel blend from 40.1% to 49.2%. 4ate, yield, and titer are important concerns for EMP systems. 64For the production of branched-chain alkanes, many lessons can be learned from gram-negative bacteria that accumulate branched-chain lipids in their cell membranes, such as B. subtilis. 65aking this work a reality will require extensive metabolic engineering and synthetic biology, concerning both the creation of novel and potentially toxic pathways for producing hydrocarbons in combination with the engineering of radical new hosts for EMP.However, we have established that the high theoretical efficiency of EMP justifies doing this engineering in the hopes of creating viable, sustainable biofuels for demanding applications like aviation.Further, by using EMP to create a library of diverse, branched hydrocarbons that go beyond simple unbranched alkanes, we can create a repository of fuel components which when blended can replicate the desirable attribute of today's fuels, furthering the cause of biofuels ultimately sourced from renewable electricity and CO 2 .

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

Figure 1 .
Figure 1.Schematic of electromicrobial production of jet fuel components (A) In the article we just consider electromicrobial production systems that use the Calvin-Benson-Bassham (CBB) cycle for in vivo CO 2 -fixation and hydrocarbon synthesis.(B)Mechanism by which electricity sources can be used to power microbial production, using either H 2 -oxidation or extracellular electron uptake (EEU).(C) In the first, H 2 is electrochemically reduced on a cathode, transferred to the microbe by diffusion or stirring, and is enzymatically oxidized.In the second mechanism, extracellular electron uptake (EEU), electrons are transferred from a cathode (i) along a microbial nanowire (part of a conductive biofilm), (ii) by a reduced medium potential redox shuttle like a quinone or flavin, or (iii, not shown) by direct contact of the cell with the cathode and are then oxidized at the cell surface by the extracellular electron transfer (EET) complex.From the thermodynamic perspective considered in this article, these mechanisms of EEU are equivalent.Electrons are then transported to the inner membrane where reverse electron transport is used to regenerate NAD(P)H, reduced Ferredoxin (not shown), and ATP.8,21,39This schematic is modified from our earlier work on the synthesis of the straight-chain alkane and terpenoid components of jet fuels.34

Figure 2 .
Figure 2. Mechanics for branched-chain alkane production Branched-chain alkanes are synthesized by the same Type II fatty acid synthase (FAS) system as straight-chain alkanes, 34 but branches are added with additional initiator and lengthener molecules.(A) Initiators for branched-chain alkane synthesis.Acetyl-[acp] (acp: acyl-carrier protein) and propionyl-[acp] are also used as initiators for synthesis of even and odd chain-length straight-chain alkanes by Type II fatty acid synthase. 342-methyl-propionyl-[acp] and 3-methyl-butanoyl-[acp] are used exclusively for branchedchain alkanes by Type II fatty acid synthase.(B) Lengtheners for branched-chain alkane synthesis.Malonyl-[acp] is used to add two additional carbons to a growing straight-or branched-chain alkane.(S)methylmalonyl-[acp] is used to add a branch to a growing branched-chain alkane.In all cases considered in this article, the last carbon in the alkane is by a termination reaction catalyzed by the well known aldehyde deformolating oxygenase (ADO) pathway.(C) Composition of example branched-chain alkane molecules shown in Figure 4. Synthesis pathways for initiators and lengtheners are shown in Figure 3. Pathways are shown in Table2.Note that the position of the branch is normally measured from the bottom (the start of synthesis) of the molecule, but in the case of 3-M 1 -hexane and 5-M 1 -decane it is measured from the top of the chain.

Figure 3
Figure 3 and Table2.In wild-type cells, the incorporation of methylated initiators and lengtheners into fatty acids is kept at low levels and are limited by one of several regulatory enzymes native to these systems.3,40Downregulation of these native regulatory enzymes can promote methylated initiator production and a high output of branched-chain hydrocarbons.From this start point, we are able to generate singlebranched compounds of any length with odd or even methylation patterns as shown in Figure3.Full pathways for the synthesis of a panel of individual branched-chain alkane compounds (shown in Figure4) are compiled from listings of reactions in the Kyoto Encyclopedia of Genes and Genomes (KEGG)[41][42][43] in the input files to the INFO-FIG 4A&B.PY, INFO-FIG 4C&D.PY codes in the EMP-TO-BRANCHED-JET repository. 44The overall stoichiometric matrix (S p ) for synthesis of each alkane using the Calvin-Benson-Bassham cycle was calculated by the INFO-FIG 4A&B.PY and INFO-FIG 4C&D.PY codes.44Briefly, we consider a chemical species number rate of change vector, ṅ ṅ, that encodes the rate of change of number of the reactant molecules over a single cycle of the reaction network; a stoichiometric matrix S p that encodes the number of reactants made or consumed in every reaction in the network; and a flux vector v that encodes the number of times each reaction is used in the network.Reactant molecules are denoted as inputs (e.g., CO 2 , ATP, NAD(P)H), outputs (e.g., H 2 O), intermediates, or the target molecule (e.g., the alkane to be synthesized).For the purposes of this thermodynamic analysis, we consider NADH and NADPH to be equivalent as they Figure 3 and Table2.In wild-type cells, the incorporation of methylated initiators and lengtheners into fatty acids is kept at low levels and are limited by one of several regulatory enzymes native to these systems.3,40Downregulation of these native regulatory enzymes can promote methylated initiator production and a high output of branched-chain hydrocarbons.From this start point, we are able to generate singlebranched compounds of any length with odd or even methylation patterns as shown in Figure3.Full pathways for the synthesis of a panel of individual branched-chain alkane compounds (shown in Figure4) are compiled from listings of reactions in the Kyoto Encyclopedia of Genes and Genomes (KEGG)[41][42][43] in the input files to the INFO-FIG 4A&B.PY, INFO-FIG 4C&D.PY codes in the EMP-TO-BRANCHED-JET repository. 44The overall stoichiometric matrix (S p ) for synthesis of each alkane using the Calvin-Benson-Bassham cycle was calculated by the INFO-FIG 4A&B.PY and INFO-FIG 4C&D.PY codes.44Briefly, we consider a chemical species number rate of change vector, ṅ ṅ, that encodes the rate of change of number of the reactant molecules over a single cycle of the reaction network; a stoichiometric matrix S p that encodes the number of reactants made or consumed in every reaction in the network; and a flux vector v that encodes the number of times each reaction is used in the network.Reactant molecules are denoted as inputs (e.g., CO 2 , ATP, NAD(P)H), outputs (e.g., H 2 O), intermediates, or the target molecule (e.g., the alkane to be synthesized).For the purposes of this thermodynamic analysis, we consider NADH and NADPH to be equivalent as they

Figure 4 .
Figure 4. Electrical energy requirements and energy conversion efficiencies for single-and multi-branched-chain alkane production yields maximum efficiencies of 40.0% and 39.9%, respectively (A) Energy input for single-branched-chain fatty alkane biosynthesis using the Calvin CO 2 -fixation cycle with the ADO alkane termination pathway.(B) Energy conversion efficiency of single-branched-chain from solar cell on left axis.Solar conversion efficiency compared to C 3 , C 4 , algae, and H 2 -mediated electromicrobial production of glucose on right axis, lines corresponding to those in (D).(C)Energy input required for multi-branched-chain alkane biosynthesis using the Calvin CO 2 -fixation cycle with the ADO alkane termination pathway.(D) Energy conversion efficiency of multi-branched-chain alkane compound biosynthesis on left axis.Solar conversion efficiency compared to C 3 , C 4 , algae, and H 2 -mediated electromicrobial production of glucose on right axis, lines corresponding to those in (B).A sensitivity analysis by Salimijazi et al.8 found that the biggest source of uncertainty in the energy input and efficiency calculation is the potential difference across the inner membrane of the cell (DU membrane ).Estimates for the trans-membrane voltage range from 80 mV (BioNumber ID45 (BNID) 10408284 to 270 mV (BNID 107135), with a most likely value of 140 mV (BNIDs 109774, 103386, and 109775).The central value (thick blue or red bar) corresponds to 140 mV.Our sensitivity analysis found that DU membrane = 280 mV produces lower efficiencies (hence a higher energy input), while DU membrane = 80 mV produces higher efficiencies (and hence lower energy inputs).8The right axis in (A and C) shows the minimum cost of that solar electricity, assuming that the United States Department of Energy's cost target of 3 ¢ per kWh by 2030 can be achieved.46The right axes in (B and D) show the solar-to-product energy conversion efficiency, assuming the system is supplied by a perfectly efficient singlejunction Si solar photovoltaic (solar to electrical efficiency of 32.9%.47For comparison, we have marked the upper limit solar-to-biomass energy conversion efficiencies of C 3 , C 4 ,48,49 algal photosynthesis,50 and upper limit electromicrobial production conversion efficiency of glucose using H 2 -oxidation and the Calvin cycle25 on the right axes of (B and D).This figure can be reproduced by running the codes INFO-FIG-4A&B.PY, INFO-FIG-4C&D.PY, FIG-4A&B.PY, and FIG-4C&D.PY in the EMP-TO-BRANCHED-JET online code repository.44 Figure 4. Electrical energy requirements and energy conversion efficiencies for single-and multi-branched-chain alkane production yields maximum efficiencies of 40.0% and 39.9%, respectively (A) Energy input for single-branched-chain fatty alkane biosynthesis using the Calvin CO 2 -fixation cycle with the ADO alkane termination pathway.(B) Energy conversion efficiency of single-branched-chain from solar cell on left axis.Solar conversion efficiency compared to C 3 , C 4 , algae, and H 2 -mediated electromicrobial production of glucose on right axis, lines corresponding to those in (D).(C)Energy input required for multi-branched-chain alkane biosynthesis using the Calvin CO 2 -fixation cycle with the ADO alkane termination pathway.(D) Energy conversion efficiency of multi-branched-chain alkane compound biosynthesis on left axis.Solar conversion efficiency compared to C 3 , C 4 , algae, and H 2 -mediated electromicrobial production of glucose on right axis, lines corresponding to those in (B).A sensitivity analysis by Salimijazi et al.8 found that the biggest source of uncertainty in the energy input and efficiency calculation is the potential difference across the inner membrane of the cell (DU membrane ).Estimates for the trans-membrane voltage range from 80 mV (BioNumber ID45 (BNID) 10408284 to 270 mV (BNID 107135), with a most likely value of 140 mV (BNIDs 109774, 103386, and 109775).The central value (thick blue or red bar) corresponds to 140 mV.Our sensitivity analysis found that DU membrane = 280 mV produces lower efficiencies (hence a higher energy input), while DU membrane = 80 mV produces higher efficiencies (and hence lower energy inputs).8The right axis in (A and C) shows the minimum cost of that solar electricity, assuming that the United States Department of Energy's cost target of 3 ¢ per kWh by 2030 can be achieved.46The right axes in (B and D) show the solar-to-product energy conversion efficiency, assuming the system is supplied by a perfectly efficient singlejunction Si solar photovoltaic (solar to electrical efficiency of 32.9%.47For comparison, we have marked the upper limit solar-to-biomass energy conversion efficiencies of C 3 , C 4 ,48,49 algal photosynthesis,50 and upper limit electromicrobial production conversion efficiency of glucose using H 2 -oxidation and the Calvin cycle25 on the right axes of (B and D).This figure can be reproduced by running the codes INFO-FIG-4A&B.PY, INFO-FIG-4C&D.PY, FIG-4A&B.PY, and FIG-4C&D.PY in the EMP-TO-BRANCHED-JET online code repository.44

Figure 5 .
Figure 5. Adding branched-chain hydrocarbons to a fuel blend lowers production efficiencies by only $0.1% for every 10% branched-chains added Effect of increasing branched chain content on (A) energy input for, and (B) energy conversion efficiency of production of a model jet fuel blend containing equimolar proportions of straight-chains | terpenoids | and branched-chains.Right axes in (A) and (B) and lines in (B) correspond to those in Figure 4.The central value (thick blue or red bar) corresponds to the most likely value of the trans-membrane (DU membrane ) voltage of 140 mV.Meanwhile, DU membrane = 280 mV produces lower efficiencies (hence a higher energy input), while DU membrane = 80 mV produces higher efficiencies (and hence lower energy inputs). 8This figure can be reproduced by running the codes INFO-FIG-5A&B.PY, and FIG-5A&B.PY in the EMP-TO-BRANCHED-JET online code repository.44

Table 1 .
Electromicrobial jet fuel production model parameters

Table 2 .
Reactions for synthesis of initiator and lengthener molecules used for branched-chain alkane production

TABLE
d RESOURCE AVAILABILITY B Lead contact B Materials availability B Data and code availability d METHOD DETAILS