Megasphaera elsdenii has been considered as an interesting hexanoic acid producer because of its capability to utilize a variety of carbons sources. However, the cellular metabolism and physiology of M. elsdenii still remain uncharacterized. Therefore, in order to better understand hexanoic acid synthetic metabolism in M. elsdenii, we newly reconstructed its genome-scale metabolic model, iME375, which accounts for 375 genes, 521 reactions, and 443 metabolites. A constraint-based analysis was then employed to evaluate cell growth under various conditions. Subsequently, a flux ratio analysis was conducted to understand the mechanism of bifurcated hexanoic acid synthetic pathways, including the typical fatty acid synthetic pathway via acetyl-CoA and the TCA cycle in a counterclockwise direction through succinate. The resultant metabolic states showed that the highest hexanoic acid production could be achieved when the balanced fractional contribution via acetyl-CoA and succinate in reductive TCA cycle was formed in various cell growth rates. The highest hexanoic acid production was maintained in the most perturbed flux ratio, as phosphoenolpyruvate carboxykinase (pck) enables the bifurcated pathway to form consistent fluxes. Finally, organic acid consuming simulations suggested that succinate can increase both biomass formation and hexanoic acid production.Hexanoic acid and its derivatives have been recently recognized as value-added materials and can be synthesized by several microbes. Of them,  Clostridium kluyveri synthesizes hexanoic acid by fermenting ethanol with acetate or succinate [Rhodospirillum rubrum and Clostridium scatologenes are other hexanoic acid producers utilizing pyruvic acid and methanol as carbon sources, respectively [Megasphaera elsdenii fueled by glucose, maltose, and sucrose. Among such potential producers, M. elsdenii has noticeable advantages, as it can consume diverse carbohydrates such as starch, mannitol, glucose, maltose, and sucrose, which are economic carbon sources [Hexanoic acid and its derivatives are generally used for the production of artificial flavors and food additives, as well as plastics, rubber, transportation fuel, and pharmaceuticals ,2,3,4. Auccinate . Rhodospectively ,7. Furth sources , and als sources  and sucr sources , respectM. elsdenii, which is anaerobic Gram-negative bacterium found in rumen of cattle, sheep, and the human gut. In this regard, constraint-based metabolic modeling and in silico analysis have been appreciated as one of the attractive techniques to characterize it; a multitude of genome-scale metabolic models (GSMMs) have been built for elucidating the cellular physiology of various organisms. However, only a handful of GSMMs for volatile fatty acid (VFA) derivative producers are available to date, including Clostridium acetobutylicum, producing butyric acid and butanol [Clostridium beijerinckii for butanol production [Clostridium spp. Thus, we believe anaerobic bacteria producing higher value C6 compounds (hexanoic acid and hexanol) can be further characterized by resorting to this in silico modeling approach. To this end, we reconstructed a manually curated GSMM of M. elsdenii based on its genome annotation, which is poorly studied, although it has high biotechnological potentials [In order to enhance the titre further toward an industrial scale, it is highly required to systematically understand the cellular behavior under various environmental and genetic conditions, as well as the relevant metabolic states to the hexanoic acid synthetic pathway in  butanol , and Clooduction . Both motentials . SubsequM. elsdenii was reconstructed based on a genome sequence of M. elsdenii DSM20460 [The genome-scale metabolic network model of DSM20460  by usingDSM20460 . An initDSM20460  and BiocDSM20460 . Then, tDSM20460 ,13,14. Tin silico flux analysis, is composed of several building blocks such as amino acids, nucleic acids, and fatty acids. The building block synthetic reactions represent polymerizations of each metabolite precursor. The amino acids and phospholipid compositions were obtained from previous studies [E. coli [The formulation of the biomass, which is an important prerequisite for  studies ,16, whil studies . The ove[E. coli . DetaileM. elsdenii by employing constraint-based flux analysis under various culture conditions, as described elsewhere [We simulated the cellular metabolism of lsewhere ,19. The ijS is the stoichiometric coefficient of metabolite i involved in reaction j; jv refers to the specific rate of metabolic reaction j; and the reaction capacity is constrained using parameters jminv and jmaxv, representing the lower and upper bounds of reaction j, respectively. We describe jminv = −inf and jmaxv = inf as reversible reactions, or jminv = 0 and jmaxv = inf as irreversible reactions. Z denotes the cellular objective of all of the metabolic reactions, where the relative fluxes are determined by coefficient jc. The COBRA toolbox was used to solve the constraint-based flux analysis [Subject to the following:analysis .in silico resulting cell growth of the mutant is zero. The gene essentiality test was carried out using the COBRA toolbox [The gene essentiality analysis was conducted by evaluating the maximal biomass formation rate while constraining the relevant reactions to be zero under a defined glucose uptake rate. The gene is classified to be essential for cell growth when the  toolbox .In order to examine the fractional contribution for hexanoic acid production in a furcated pathway, we performed a flux ratio analysis using the COBRA toolbox. First, the model was simulated to investigate the flux distribution of the bifurcated pathway with hexanoic acid production in different cell growing states, by fixing the specific glucose uptake rate and growth rate while setting the hexanoic acid synthetic reaction as the objective function. Subsequently, in each specific growth rate, nine different flux ratios  were tested to check for changes in the flux distribution. M. elsdenii (iME375) was reconstructed, followed by model refinement. A number of network gaps were filled by adding suitable metabolic reactions based on the information obtained from metabolic pathway databases  and literature sources. For example, the draft model contained a few gaps in the synthetic pathway of propionic acid, which is the major fermentation product from lactate in M. elsdenii. Thus, we added the reactions corresponding to lactate racemase and lactoyl-CoA dehydratase for the conversion of d-lactate into l-lactate, and the dehydration of lactoyl-CoA to acryloyl-CoA, respectively, according to previous studies [M. elsdenii is able to grow on all of these carbon sources, we added new transport reactions based on the information available from the KEGG and Biocyc databases. The genome-scale metabolic network of  studies ,22. The M. elsdenii, including the glycolysis, tricarboxylic acid (TCA) cycle, pentose phosphate pathway (PPP), amino acids, and fatty acids synthetic pathways. Notably, the glycolysis and PPP are complete, but the TCA cycle is incomplete, as the gene of 2-oxoglutarate dehydrogenase was not found. The synthetic pathways of 20 amino acids and VFAs are also depicted in M. elsdenii, iME375, accounts for 375 genes , 521 metabolic reactions, and 443 metabolites. In iME375, all of the 521 reactions were classified into six major subsystems, namely: amino acids, carbohydrates, cofactors and vitamins, energy, lipids, and nucleotides metabolisms. Among them, amino acids metabolism constitutes the largest part of metabolic reactions, followed by cofactors and vitamins metabolisms , NADH:ferredoxin oxidoreductase (rnfA-E) and 4-hydroxybutyryl-CoA dehydratase (abfD) as compared to M. elsdenii. On the other hand, C. acetobutylicum has butyrate–acetoacetate CoA transferase (CA_P0163 and 0164) instead of acetyl-CoA hydrolase/transferase. As such, the coenzyme A (CoA) of butyryl-CoA is transferred to acetoacetate and the carbon chain elongation is terminated. In M. elsdenii, the butyryl-CoA (C4) is elongated to 3-oxohexanoyl-CoA (C6) by transferring the acetyl (C2) group from acetyl-CoA via acetyl-CoA C-acetyltransferase, or is converted to butyric acid by utilizing acetate (C2) as the CoA acceptor via acetyl-CoA hydrolase/transferase. However, C. acetobutylicum produces butyric acid (C4) and butanol (C4) through butyrate-acetoacetate CoA transferase and butanol dehydrogenase during acidogenic and solventogenic phases, respectively. Unlike M. elsdenii, acetoacetate (C4) is involved in CoA transferase in C. acetobutylicum. Thus, we suggest that the existence of the three enzymes  and the substrate specificity of other enzymes, such as thlA, hbd, crt, and cat, which contribute to acyl-CoA elongation, may affect the carbon length of the final product in M. elsdenii. The VFA synthetic pathways of n detail . The homM. elsdenii is closer to E. coli than C. acetobutylicum  in M. elsdenii, according to a previous study [The exchange fluxes of essential minerals and nutrients such as NOnditions . The grous study . To minimize the influence of other nutrients in the culture medium, such as amino acids or trace amounts of carbon sources, which can help cell growth during the early exponential phase, we used experimental data during the late exponential phase in three different experiments for simulation. Remarkably, all of the simulated biomass formation rates were highly consistent with the observed growth rates, within the acceptable error range of 10% .M. elsdenii under a glucose minimal medium condition by deleting each gene at a time (see Methods), allowing us to identify lethal genes for further genetic engineering in order to enhance productivity. The genes were classified into the following three types: completely essential genes (genes that are required for cellular growth), partially essential genes , and non-essential genes (genes that are not required for cellular growth). There were 221 and 24 reactions, corresponding to 182 and 21 genes, that were predicted to be essential and partially essential, respectively. Most of the amino acid, riboflavin, and coenzyme A synthetic genes are completely essential. Interestingly, VFA synthetic genes are non-essential or partially essential, as most VFA forming reactions are catalyzed by isozymes. Hexanoic acid synthetic reactions via succinate, acetate formation reactions, and butyryl-CoA:acetate CoA transferase are partially essential. In anaerobic microorganisms, acetate is known as one of the key metabolites that can accept electrons from other redox cofactors involved in butyric and hexanoic acid synthesis [M. elsdenii also requires acetate and protons as electron acceptors to generate energy and balance the intracellular redox potential by converting them to acetyl-CoA and H2, respectively [We conducted a gene essentiality analysis of ynthesis . Like otectively .M. elsdenii. We found two possible routes via acetyl-CoA (Route A) and oxaloacetate (Route B), in order to convert from pyruvate to crotonyl-CoA, which is further catalyzed to synthesize hexanoic acid. Route A is initiated with the oxidative decarboxylation of pyruvate to acetyl-CoA and CO2 by utilizing pyruvate–ferredoxin oxidoreductase (pfo), which is commonly found in anaerobic organisms. A part of acetyl-CoA is converted to acetate by generating ATP; the acetoacetyl-CoA (C4) is produced by condensing 2 mol of the remaining acetyl-CoA (C2), and further is catalyzed toward crotonyl-CoA. In Route B, M. elsdenii synthesizes oxaloacetate (C4) from pyruvate (C3) and HCO3 (C1) via pyruvate carboxylate (pyc). Succinate is then produced from oxaloacetate by running the TCA cycle in a reductive (counterclockwise) direction. Note that the reductive TCA cycle, from oxaloacetate to succinate, is also present in C. acetobutylicum [bcd/etfAB), and in turn elongated to hexanoyl-CoA (C6) by combining with acetyl-CoA.utylicum . Crotony2 loss—one 6C product (hexanoic acid) requires three molecules of pyruvate (3C * 3 = 9C), while wasting three carbon atoms as CO2. However, a more comprehensive comparison of Routes A and B should be made in terms of other energetically expensive consumables such as ATP, acetyl-CoA, and reducing equivalents (NADH).Routes A and B are decomposing and composing pathways, respectively. In Route A, the C3 metabolite is divided into C1 and C2 metabolites. Two molecules of the C2 metabolite are then integrated to build a C4 metabolite. Thus, two molecules of the C1 metabolite are withdrawn to synthesize one molecule of the C4 metabolite. However, in Route B, the C3 metabolite is combined with the C1 metabolite to synthesize a C4 metabolite. Route A is less efficient with respect to the C-balance because of CO2 via pfo, while reducing ferredoxin. A portion of CO2 is fixed with H2O in order to produce HCO3 and a proton via carbonate dehydratase, and the residual CO2 secretes it out of cell. While producing 1 crotonyl-CoA from 2 acetyl-CoA, 1 NADH is oxidized (reaction 1).Pyruvate is divided into acetyl-CoA and COOne crotonyl-CoA is synthesized from pyruvate through succinate in a reductive direction, while oxidizing 5 NADH and reducing 1 ferredoxin (Reaction 2).bcd/etfAB, while 1 crotonyl-CoA is converted to butyryl-CoA. The enzymes that catalyze for synthesizing hexanoyl-CoA from butyryl-CoA are the same as those that participated in butyryl-CoA synthesis from acetyl-CoA. Then, 2 reduced ferredoxin and 5 NAD+ are generated via the hexanoyl-CoA synthetic pathway from crotonyl-CoA according to Reaction 3  by reduced ferredoxin and NAD+ to regenerate the necessary NADH. The rnf complex couples proton translocation with the oxidation of ferredoxin and reduction of NAD+. The proton gradient, which is generated by the rnf complex, is a driving force for synthesizing ATP via ATPase (atpA-I). The resulting fluxes of Reactions 1, 2, and 3 allowed for the cell to make a balance of reduced ferredoxin and oxidized NAD in order to produce the required amounts of ATP and NADH. The excess electrons, which were not oxidized through the rnf complex, are delivered to H+ via hydrogenase (hyd) for H2 formation. The reduced molecular hydrogen (H2) is then secreted.Flux is driven through the NADH:ferredoxin oxidoreductase  acceptor, while butyric and hexanoic acid are converted from butyryl-CoA and hexanoyl-CoA, respectively. Therefore, it is also important to synthesize an adequate amount of acetate to produce the maximal yield of hexanoic acid in M. elsdenii since it is composed of many pathways such as 2 types of crotonyl-CoA synthesis, fatty acid elongation, CO2 fixation, electron transfer and ATP synthesis. In addition, the FBA result of iME375 by fixing the glucose uptake rate of 5 mmol g−1 DCW h−1 and maximizing the hexanoic acid synthetic reaction showed that 3.51 mmol g−1 DCW h−1 of hexanoic acid was produced by using both of the above-mentioned pathways. The flux values of Routes A and B were 2.97 mmol g−1 DCW h−1 and 0.54 mmol g−1 DCW h−1, respectively. In order to further investigate the effect of the specific cell growth rate and flux ratio of Route A to Route B on hexanoic acid productivity, we conducted the flux ratio analysis in different cell growing rates  and pyruvate:ferredoxin oxidoreductase (pfo) with nine different ratios . The highest hexanoic acid production rate was maintained through most of the flux ratios (pck) helps to form consistent flux through Route B. Unlike the results of other specific growth rates, at 0.6 h−1, a slight increase (6%) of hexanoic acid production was observed when setting the flux ratio as 5:1. Based on the result of the flux ratio analysis, we could guess that the hexanoic acid productivity may not be increased simply by the knockdown of pfo or the overexpression of pyc. Thus, in order to find the potential metabolic engineering targets for improving the productivity of the target metabolite, a comprehensive understanding of the microorganism and the in silico strain design methods would be needed.Flux ratio analysis was further performed in each cell growth rate by changing the flux ratio of pyruvate carboxylase , albeit the carbon yield of this flux is lower than in Route B  for balancing the redox potentials. On the other hand, hexanoic acid is produced only through Route B at a maximum specific growth rate condition. The additional flux ratio analysis suggested that a simple gene knockdown or overexpression may not be suitable for improving the target metabolite in this system. In future, we expect to further improve our understanding of M. elsdenii when the metabolic model is integrated with high throughput -omics data.In this study, we reconstructed a genome-scale metabolic model of hexanoic acid synthetic bacteria


Escherichia coli str. K-12 substr. MG1655 (iJO1366), we found that RIPTiDe correctly identifies context-specific metabolic pathway activity without supervision or knowledge of specific media conditions. We also assessed the application of RIPTiDe to in vivo metatranscriptomic data where E. coli was present at high abundances, and found that our approach also effectively predicts metabolic behaviors of host-associated bacteria. In the setting of human health, understanding metabolic changes within bacteria in environments where growth substrate availability is difficult to quantify can have large downstream impacts on our ability to elucidate molecular drivers of disease-associated dysbiosis across the microbiota. Our results indicate that RIPTiDe may have potential to provide understanding of context-specific metabolism of bacteria within complex communities.The metabolic responses of bacteria to dynamic extracellular conditions drives not only the behavior of single species, but also entire communities of microbes. Over the last decade, genome-scale metabolic network reconstructions have assisted in our appreciation of important metabolic determinants of bacterial physiology. These network models have been a powerful force in understanding the metabolic capacity that species may utilize in order to succeed in an environment. Increasingly, an understanding of context-specific metabolism is critical for elucidating metabolic drivers of larger phenotypes and disease. However, previous approaches to use network models in concert with omics data to better characterize experimental systems have met challenges due to assumptions necessary by the various integration platforms or due to large input data requirements. With these challenges in mind, we developed RIPTiDe (Reaction Inclusion by Parsimony and Transcript Distribution) which uses both transcriptomic abundances and parsimony of overall flux to identify the most cost-effective usage of metabolism that also best reflects the cell’s investments into transcription. Additionally, in biological samples where it is difficult to quantify specific growth conditions, it becomes critical to develop methods that require lower amounts of user intervention in order to generate accurate metabolic predictions. Utilizing a metabolic network reconstruction for the model organism  Escherichia coli, we demonstrate that this new approach correctly predicts patterns of metabolism utilizing a variety of both in vitro and in vivo transcriptomes. This platform could be important for revealing context-specific bacterial phenotypes in line with governing principles of adaptive evolution, that drive disease manifestation or interactions between microbes.Transcriptomic analyses of bacteria have become instrumental to our understanding of their responses to changes in their environment. While traditional analyses have been informative, leveraging these datasets within genome-scale metabolic network reconstructions (GENREs) can provide greatly improved context for shifts in pathway utilization and downstream/upstream ramifications for changes in metabolic regulation. Many previous techniques for GENRE transcript integration have focused on creating maximum consensus with input datasets, but these approaches were recently shown to generate less accurate metabolic predictions than a transcript-agnostic method of flux minimization (pFBA), which identifies the most efficient/economic patterns of metabolism given certain growth constraints. Despite this success, growth conditions are not always easily quantifiable and highlights the need for novel platforms that build from these findings. Our new method, RIPTiDe, combines these concepts and utilizes overall minimization of flux weighted by transcriptomic analysis to identify the most energy efficient pathways to achieve growth that include more highly transcribed enzymes, without previous insight into extracellular conditions. Utilizing a well-studied GENRE from  Metabolic plasticity is critical for bacterial survival in changing environments, and fundamental to stable microbial communities ,2. In thGENREs have also become strong platforms for providing context to multiple forms of high-throughput omics data, allowing for the study of whole-network changes in metabolism due to upstream/downstream shifts in enzyme activity . To thisNumerous approaches to integrating transcriptomic data into GENREs primarily focus on identifying reactions associated with defined cutoffs of gene transcription or change, then maximizing flux through those reactions with many transcripts and minimizing flux through those reactions associated with genes with fewer transcripts –21. WhilSaccharomyces metabolism, pFBA alone with constraints on metabolic inputs was found to be able to largely outperform several other methods in predicting metabolic network behavior under various growth conditions despite not utilizing any transcriptomic data for these predictions [Escherichia coli grown in defined in vitro conditions have shown that levels of transcript were only predictive for roughly half of the concentrations of the corresponding enzymes in the cell [in situ biology.Recently, parsimonious Flux Balance Analysis (pFBA) was developed, which seeks to minimize the flux associated with each reaction in the model while maintaining optimum flux through the objective function . In essedictions . Recentldictions . These sthe cell ,34. In rthe cell . As arbithe cell , and absthe cell , we chosE. coli str. K-12 substr. MG1655. Transcriptomic data from multiple distinct in vitro growth conditions were compared against each other as well as the base implementation of pFBA. RIPTiDe was able to accurately discern context-specific phenotypes including growth rates that closely match experimentally measured values under the same conditions, as well as gene essentiality predictions in metabolic pathways relevant to the corresponding media. The platform was subsequently tested utilizing in vivo metatranscriptomic sequence data from clindamycin-treated mouse cecal content where E. coli is the dominant member of the bacterial community [in vivo RIPTiDe-contextualized model simulated significantly slower growth than in aerobic rich media and more central metabolites were produced intracellularly when in competition with other bacterial species. These combined analyses validated our methodology by correctly uncovering context-specific biological trends, and previously unappreciated host-associated behaviors of E. coli. Furthermore, this technique could present a powerful tool for the study of the microbiota through the simultaneous unsupervised contextualization of omics data from multiple organisms within the same community.We call this combined method RIPTiDe, or Reaction Inclusion by Parsimony and Transcript Distribution. RIPTiDe was then tested on the most well curated GENRE of the highly studied model organism ommunity . When coRIPTiDe relies on sequential optimization steps, guided by transcript abundances in order to identify the most efficient usage of metabolism that also reflects an organism’s transcriptional state . The reqAs with pFBA, reversible reactions are split into pairs of irreversible reactions carrying non-negative flux. Coefficients are subsequently transferred to the corresponding metabolic reactions for each gene. Reactions are then assembled into a single new equation which is set as the cellular objective where the magnitude of the linear coefficient drives the amount of flux carried by each reaction. Reactions without genes are assigned the median score to not be incorrectly penalized, nor overly biased to their inclusion. Larger coefficients correspond to the reaction receiving a larger weight per unit of flux during optimal growth, which would therefore be favored less when minimizing the overall sum of weights times flux for a given objective function. In this way, we were able to minimize overall flux subject to the transcript-guided linear coefficients added by RIPTiDe. Within the transcript abundance distribution, progressively smaller linear coefficients are assigned to genes with increased transcription . With anThe scope of feasible solution states in a GENRE typically out-scales the number of realistic metabolic states of the cell by a large magnitude . PlacingNear optimal flux through the objective function is set as a constraint ≧80%, .Linear coefficients are assigned as constraints to each reaction based on transcriptomic abundance of the associated gene-enzyme assignments. In cases where multiple gene products contribute to the same reaction, the lowest coefficient/largest weight among them is selected.Total sum of weights times fluxes in the model is minimized subject to previously outlined constraints.Standard flux balance analysis then identifies inactivated subnetworks (zero flux) which are subsequently removed from the model. Orphaned genes and metabolites are then pruned.Inverse linear coefficients within the original provided range are calculated and assigned for each reaction. Flux sampling is performed on the constrained and reduced model to find most likely pathway utilization patterns while maintaining 80% of the objective function.The resultant pruned model has a dramatically more focused, biologically feasible, metabolic solution space that has been adequately sampled for feasible metabolic states . Unlike To test RIPTiDe, we created a small, flux-consistent metabolic network reconstruction with two compartments and generation of ATP (in arbitrary units) as the cellular objective function. The model has two separate means of accomplishing this goal; either through glycolysis where glucose is the primary substrate, or Stickland fermentation which requires pairs of amino acids in coupled redox reactions to create energy . In natuAs a means to determine the context specificity of RIPTiDe output models, we then generated two distinct simulated transcript abundance distributions that each reflected elevated transcription of a single pathway . In Fig E. coli strain K-12 substr. MG1655 [in vitro media conditions including aerobic LB rich media, aerobic M9+glucose defined minimal media, and anaerobic M9+glucose defined minimal media. Each dataset was collected at approximately the same mid-exponential phase of growth [E. coli is a facultative anaerobe with known differences in metabolism between these lifestyles that we hoped to capture with RIPTiDe [To perform a thorough evaluation of our approach, we utilized the genome-scale metabolic network reconstruction iJO1366 , for the model organism . MG1655 . This GE. MG1655 . Leveragf growth ,48, and  RIPTiDe .E. coli K-12 growing in aerobic LB rich media. We elected to assess an array of distinct GENRE+transcriptome integration algorithms; including GIMME, iMAT, CORDA, MBA, and RegrEx [E. coli K-12 growing in LB rich media [in silico. Only after altering extracellular metabolite availability to reflect LB media components are all genes found to be essential across all platforms  from each other group as it has access to all possible growth substrates which combined allow for faster growth and distinct patterns of metabolism. A striking relationship emerged when RIPTiDe flux distributions were compared with those from media-constrained models, revealing that these groups were highly correlated. Importantly, no difference  was found when RIPTiDe was applied to the model with M9+glucose media constraints contrasted against results from RIPTiDe-generated flux samples without media constraints  as was the case with GIMME and CORDA-produced models. These results collectively indicated that RIPTiDe is also able to approximate the media condition from which the transcriptome was collected. This feature will likely be especially useful when growth conditions are much more difficult to quantify, as in environmental samples or in vivo.To evaluate how closely RIPTiDe-based predictions reflect predictions when media conditions are known, we performed NMDS ordination analysis of Bray-Curtis dissimilarities between common exchange reaction flux distribution samples from iJO1366 with and without constraints on available substrates compared with RIPTiDe-generated flux samples with no defined media . For thestraints . A similnditions . These dnditions . Growth r growth . Additioehaviors –54. ConvE. coli grown in M9 minimal media (aerobic & anaerobic), which supported that RIPTiDe was able to identify general biological trends that are conserved between similar media conditions. Interestingly, the next largest group was the intersection between Maximum Parsimony and LB rich media, which may reflect that growth in an environment with surplus growth nutrients is partially analogous to the artificial state of minimal cellular investment. These distinctions in network topology were further crystallized by conditional gene essentiality between the RIPTiDe-contextualized models (necessary for at least 1% of optimum growth). It is important to note that genes found to be essential during these analyses do not necessarily correspond with survival of E. coli, only that these genes may be critical to the optimal metabolic strategy under the associated conditions [in vitro transcriptomes , and also constrained to achieve at least 80% of the optimal objective function value. We first assessed the impact that each transcriptome had on the components of each model created by RIPTiDe. Different topologies of reaction inclusion were found among each of the contextualized models; however none were completely unique and a core set of metabolic reactions were necessary for optimal growth across all conditions  resulted in a bacterial community composed of >90% E. coli [in vivo transcript abundance distribution reflected the same negative binomial type as those derived from in vitro transcriptomes mapped to the same E. coli K-12 MG1655 genome , but more specifically between those bacteria grown in M9 minimal media and those found using LB rich media or in vivo transcriptomes . These results implied distinct metabolic strategies necessary for growth during resource scarcity or surplus, and these patterns were captured by RIPTiDe. Although similar, no group of flux distributions entirely overlapped another and indicated that although numerous reactions and metabolites are shared between all context-specific models, they are utilized significantly differently to manage growth across media conditions and supported differential metabolism is likely necessary to cope with distinct environments.Finally, we sought to test the utility of RIPTiDe for capturing metabolic behavior of bacteria from within host-associated communities of microorganisms. Computational analysis of a discrete bacterial species within a complex environment as a member of a larger microbial community has been historically difficult . To addr E. coli . To begi5 genome . This re5 genome  & S2 Fig5 genome . This anin vivo or LB rich media transcriptomes as they were more similar during unsupervised learning analysis. Aside from one environment being highly aerobic and the other largely anaerobic, previous research on E. coli physiology during growth in liquid LB concluded that the bacterium utilizes amino acids that are simple to metabolize for growth early on, then switches to other substrates in a diauxic-like growth pattern. LB broth has also been shown to have only modest levels of usable carbohydrate growth substrates, increasing the importance of amino acid catabolism for E. coli [in vivo amino acids and simple sugars are contested resources in the cecum as the majority are already absorbed by the host or used by other microbes upstream in the GI tract, making these growth conditions extremely different [in vivo, and 5 of these were peptides or peptide conjugates  are at elevated concentrations [Next, we contrasted the RIPTiDe models generated using  E. coli . Additioifferent . As an anjugates . Carbohyal phase . Indeed, microbe . AdditioLB media . ContinuLB media  on the slian gut . Putresctrations . AltogetIn order to survive in a given environment, an organism must express the appropriate forms of metabolism to cope with changing conditions. Production of transcript and protein is metabolically expensive, and over-production likely puts the cell at risk if further perturbation is placed on the system . Althougin vitro and in vivo metabolic phenotypes with reasonably high accuracy. In addition to these predictions, our method does not require prior knowledge of active metabolic subnetworks which can preclude work with understudied or uncultured species that cannot or have not been grown or characterized in isolation. Furthermore, the ability to accurately capture the context-specific metabolism of bacteria when media conditions are not easily defined will be an important component for the discovery of metabolic behaviors of microbes in complex environments or novel host-microbe metabolic interactions. Some possible limitations of RIPTiDe do exist however. First, as RIPTiDe relies on the distribution associated with shotgun transcriptomic sequencing, it is less suited for other types of omic data in its current form [in vitro and in vivo conditions, producing models that closely mirror known biological phenotypes. Additionally, RIPTiDe run time scales linearly with GENRE size and compartmentalization  techniques, avoiding computational demand brought on by mixed integer linear programming (MILP) approaches and making it compatible with all popular solvers (GLPK was used in this study). Optimal flux through the objective function was set as a constraint with a 20% range of allowed variation . Following sensitivity testing, this level was found to result in models which best achieved high growth rates while reaching acceptable levels of correlation with input transcriptomes  assignment of gene g, the reads-per-million normalized transcript abundance of gene Tg within the sorted  transcript abundance distribution is divided by the largest abundance Tmax this distribution. These gw values are then assigned to their corresponding reactions to generate a distribution of linear coefficients rwsampling and the maximum weight among reactions in each gene reaction rule (GPR) is assigned to all associated reactions. The sum of the minimum and maximum weights within gw is calculated and then the inverse weight is determined based on the weight associated with reaction r in rwsampling, creating a second distribution of reaction weights rwpruning.For reaction weight virrev. Linear coefficients wr for each vector can now be integrated and an objective function is then defined to minimize that total of flux across the entire model. These steps are all performed subject to a lower bound on the biomass flux  set to a fraction  of the previously identified maximum biomass flux (max vobjective) and mass-balance constraints. Optimization (standard FBA) is performed and reactions found in the solution to have <1x10-6 flux are then removed from the model (the threshold is adjustable by the user). The model is then checked for orphaned genes and metabolites, which are subsequently removed as well.As in parsimonious-FBA, each reversible reaction is separated into individual forward and reverse reactions rwsampling linear coefficient assignments. The overall sum of flux is then maximized. The assembly of the large function of weighted reaction fluxes is performed with symengine (https://github.com/symengine/symengine):In order to adequately explore intracellular flux through the remaining reactions, previous coefficients are reassigned to remaining reactions using the rwsampling) are then assigned to the corresponding irreversible reactions virrev. Flux sampling was then performed with the Gapsplit sampler using standard parameters and 500 samples (https://github.com/jensenlab/gapsplit) [p-value between median absolute flux and their associated linear coefficient during flux sampling for all reactions (Coefficients (apsplit) . Flux vaapsplit) . An overeactions .https://github.com/mjenior/Jenior_RIPTiDe_PLOSCompBio_2019github.com/csbl/Jenior_RIPTiDe_2020.The example model used for initial RIPTiDe testing consists of 16 reactions  and 14 metabolites across 2 compartments (extracellular and intracellular). The intracellular demand reaction for ATP generation was utilized as the objective. Simulated transcriptomes are shown in Escherichia coli K-12 MG1655 genes using Bowtie2 [broadinstitute.github.io/picard/). The remaining mappings were converted to idxstats format using SAMtools [In vivo untargeted metabolomic data were generated for a previous study [Sequenceread processing was performed as described previously in ,8. In su Bowtie2 . MarkDupSAMtools , and theus study .https://github.com/SchlossLab/Jenior_Metatranscriptomics_mSphere_2018/tree/lab_computer/data/metabolome. https://paperpile.com/c/vZ3H0e/ECBShttps://opencobra.github.io/cobratoolbox/stable/) using the specified thresholds. For both MBA and RegrEx, a flux consistent model was used based on the requirements for the integration algorithms. CORDA (v0.4.2) and RegRx were downloaded and installed on 12-1-2019.GIMME , iMAT 1, MBA 2020, CORDAAll statistical analysis was performed using R (v3.2.0). Significant differences between flux distributions and metabolite concentrations were determined by Wilcoxon signed-rank test with Benjamini-Hochberg correction. Principle Component Analysis and Non-Metric Multidimensional Scaling of sampled flux distributions was performed using the vegan package . Machinehttps://github.com/mjenior/riptide and also as a full package (v2.8.0) from the Python Package Index (https://pypi.org/project/riptide/). Complete analysis associated with this study is available in a Jupyter notebook hosted on a GitHub repository along with all other data and code associated with this study (https://github.com/mjenior/Jenior_RIPTiDe_PLOSCompBio_2019https://github.com/csbl/Jenior_RIPTiDe_2020).As previously stated, RIPTiDe is freely available for download at S1 FigComputed doubling time from biomass reaction objective value following FBA analysis of each contextualized model . Result from the unconstrained model is listed along the top axis. Biomass objective flux was constrained to ≧80% of the optimal flux value prior to identifying the state of Maximum Parsimony as it is during RIPTiDe contextualization.(TIF)Click here for additional data file.S2 Fig(A) Valine, (B) Deoxyuridine, (C) and Methionine. Significant differences were determined by Wilcoxon signed-rank test.Concentrations quantified with liquid chromatography mass-spectrometry previously . Compari(TIF)Click here for additional data file.S3 Fig(A) Spearman correlation results between RIPTiDe linear coefficients from flux sampling and median absolute values from sampled flux ranges from in vivo transcriptome. Assigned linear coefficients are significantly correlated with their associated absolute reaction activities. Correlation results are referred to as concordance in the output of RIPTiDe. (B) Run time in seconds with increasing metabolic network reconstruction size. Using RIPTiDe, each GENRE  was integrated with a simulated transcriptome of 1.0 transcript for all genes. Multicellular eukaryotic models include mouse (iMM1415), golden hamster (iCHOv1), and human (Recon3D). The relationship between model size and RIPTiDe run time fits a linear model . These analyses were completed using an Intel Core i7-7Y75 CPU @ 1.30GHz × 4 processor and 15.4 GB of memory.(TIF)Click here for additional data file.S4 Figin vivo and LB rich media RIPTiDe-contextualized transcriptomes of E. coli.Mean Decrease Accuracy for an optimal subset of 20 reactions determined by AUC Random Forest that flux levels differentiate the distributions from shared reactions between (TIF)Click here for additional data file.S5 Fig(A) M9+glucose anaerobic and (B) LB aerobic. Significant differences between constrained objective flux only and all other groups determined by PERMANOVA. The dissimilarity of RIPTiDe-generated flux samples in these analyses highlight context-specific metabolic patterns that were unobservable through other methods.NMDS ordination of Bray-Curtis dissimilarities between flux samples for each version of iJO1366 in (TIF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.


To further challenge our approach, we also do the reverse: estimate the magnitude of changes in drug-target binding based on antibiotic dose-response curves. We overexpress target molecules to infer changes in antibiotic-target binding from changes in antimicrobial efficacy of ciprofloxacin with 92–94% accuracy. To test the generality of our approach, we use the beta-lactam ampicillin to predict target molecule occupancy at MIC from antimicrobial action with 90% accuracy. Finally, we apply COMBAT to predict antibiotic concentrations that can select for resistance due to novel resistance mutations. Using ciprofloxacin and ampicillin as well defined test cases, our work demonstrates that drug-target binding is a major predictor of bacterial responses to antibiotics. This is surprising because antibiotic action involves many additional effects downstream of drug-target binding. In addition, COMBAT provides a framework to inform optimal antibiotic dose levels that maximize efficacy and minimize the rise of resistant mutants.Antibiotic resistance is rising and we urgently need to gain a better quantitative understanding of how antibiotics act, which in turn would also speed up the development of new antibiotics. Here, we describe a computational model  that can quantitatively predict antibiotic dose-response relationships. Our goal is dual: We address a fundamental biological question and investigate how drug-target binding shapes antibiotic action. We also create a tool that can predict antibiotic efficacy a priori. COMBAT requires measurable biochemical parameters of drug-target interaction and can be directly fitted to time-kill curves. As a proof-of-concept, we first investigate the utility of COMBAT with antibiotics belonging to the widely used quinolone class. COMBAT can predict antibiotic efficacy in clinical isolates for quinolones from drug affinity (R Antibiotic efficacy is traditionally assessed with a single value, the minimal inhibitory concentration, despite its limited predictive power. Dose-response curves that assess efficacy over a range of antibiotic concentrations are promising, but extremely work intensive. Using the well-characterized antibiotics ciprofloxacin and ampicillin as proof-of-concept, we provide a mathematical framework that allows predicting optimal dosing of antibiotics based on drug-target binding parameters. These could be measured early in drug development and can also change when bacteria become resistant. Thus, we can predict the probability that resistant strains are selected at a given dosing regimen without isolating and testing a multitude of resistant strains. Predicting optimal dosing with early accessible experimental data can reduce the prevalent trial-and-error approaches and thereby the number of antibiotic candidates that fail late in drug development. The rise of antibiotic resistance represents an urgent public health threat. In order to effectively combat the spread of antibiotic resistance, we must optimize the use of existing drugs and develop new drugs that are effective against drug-resistant strains. Accordingly, methods to improve antibiotic dose levels to i) maximize efficacy against susceptible strains and ii) minimize resistance evolution play a key role in our defense against antibiotic resistant pathogens.It is noteworthy that dosing strategies for treatment of susceptible strains  [The next challenge to successfully designing antibiotic treatment arises when the experimental information is integrated into mathematical pharmacodynamic models that then predict efficacy under realistic, fluctuating concentrations in patients. Pharmacodynamic models from 1910 (E-models)  are stil-models) –21. HoweIn this report, we describe a mechanistic computational modeling framework  that allows us to predict full pharmacodynamic profiles based solely on accessible biochemical parameters describing drug-target interaction. These parameters can be determined early in drug development. We use this framework to investigate how changes in drug target binding, either due to improvements in existing antibiotics or due to resistance mutations in bacteria, affect antibiotic efficacy. We first show that COMBAT accurately predicts bacterial susceptibility as a function of drug-target binding and, conversely, allows inference of these biochemical parameters on the basis of observed patterns of bacterial growth suppression or killing. We then use COMBAT to predict the susceptibility of newly arising resistant variants based on the molecular mechanism of resistance and determine the resistance selection window.KD ~10−4–10−7 M) but are of similar molecular sizes and have a similar mode of action [To investigate how biochemical changes in antibiotic action modifies bacterial susceptibility, we explored how the affinity of antibiotics to their target affects the MIC. We compared the MICs of quinolones, an antibiotic class in which individual antibiotics have a wide range of affinities to one of their targets, gyrase  drug-target binding occurs much more quickly than bacterial replication, ii) the antibiotic concentration remains constant and iii) that during the 18 hours of an MIC assay, the concentration gradient of the drug inside and outside the cell has equilibrated. Under these assumptions, the MIC can be expressed as the MIC . Accordip < 0.018) linear correlation between MIC and KD in all species, confirming the qualitative model prediction.While it was encouraging that our model can qualitatively predict MIC changes, our aim was to quantitatively predict antibiotic treatment performance. The simplified model assumes that the binding kinetics are much faster than bacterial replication, which may not be true in all cases. To expand the generalizability of the model, we extended the modeling framework to allow that bacterial replication may occur in a similar time frame as drug-target binding events.θ target molecules per cell with a system of θ + 1  ordinary differential equations (ODEs). This system increases in complexity with the number of target molecules and makes fitting the model to data computationally too demanding for most settings. To simplify this prior approach, we developed new mathematical models based on partial differential equations (PDEs), where a single equation describes all bacteria simultaneously. The sum of bacteria within all target occupancy states over time can be described by a time kill curve  describes the binding and unbinding of antibiotics to their targets and predicts how such binding dynamics affects bacterial replication and death . In prevll curve , during ll curve . This cull curve .kf) and unbinding (kr) to bacterial target molecules , 31, and2 = 0.93, r(x) and death as a function of target occupancy δ(x) based on the fit obtained in E. coli .E. coli. We then quantified these biochemical changes by fitting COMBAT to corresponding time-kill curves and compared them to the experimental results. Ciprofloxacin acts on gyrase A2B2 tetramers [E. coli strain for which both gyrase A and gyrase B are under the control of a single inducible promoter (PlacZ), such that the amount of gyrase A2B2 tetramer can be experimentally manipulated [Having shown that COMBAT can quantitatively fit experimental data on antibiotic action within biologically plausible parameters, we continued to test the predictive ability of the model. Given our hypothesis that modifications in antibiotic-target interactions lead to predictable changes in bacterial susceptibility, we experimentally induced changes in the antibiotic-target interaction of ciprofloxacin in etramers . We usedipulated . We measE. coli more susceptible to ciprofloxacin [2B2, to vary. We assumed that the only change between the different conditions was the amount of target. We further assumed that the relationship between bound target and bacterial replication or death did not differ between the control strain containing a mock plasmid (no IPTG) and the experiments with overexpression   . Fig 5C Staphylococcus aureus (84–99%)[Having established that COMBAT can also adequately capture the pharmacodynamics of ampicillin, we next tested whether we can estimate experimentally determined target occupancy at the MIC. Our estimated mean occupancy considering both living and dead bacteria is 89% , a value (84–99%).KD, have more profound effects than changes in target molecule content, bacterial reaction to increasingly bound target (i.e. δ(x) and r(x)), or changes in target molecule content. We also predict that the individual binding rates kr and kf, and not just the ratio of these terms, the KD, are important factors in efficiency. The faster a drug binds, the more efficient we predicted it will be. One intuitive explanation for the observation that kf drives efficacy is that a slow binding fails to rapidly interfere with bacterial replication, which may allow for the production of additional target molecules and thereby reduce the ratio of free antibiotic to target molecules.It is possible to vary all parameters in COMBAT and explore their effect. We used this to test how hypothetical chemical changes to ampicillin or ciprofloxacin would affect antibiotic efficacy –S11 Fig.Resistant; 15 min, MICResistant; 45 min, MICResistant; 18 h). In all cases, the bacterial population first increases and then decreases slowly. This may have consequences for the selection of resistant strains. Finally, we illustrate how COMBAT can be used to explore how the molecular mechanisms of resistance mutations affect antibiotic concentrations at which resistance can emerge, i.e., the resistance selection window. We compared predicted net growth rates as a function of ciprofloxacin concentrations for a wild-type strain and an archetypal resistant strain. For this analysis, we assumed that the resistant strain has a 100x slower drug-target binding rate  and thaThus, we estimate that sustained levels of 1.27-7mg/L would safeguard against resistance. While ciprofloxacin plasma concentrations typically reach concentrations of 2mg/L after oral uptake and 6mg/L after intravenous administration , levels Optimizing dosing levels of antibiotics is important for maximizing drug efficacy against wild-type strains as well as for minimizing the rise of resistant mutants. Antibiotic efficacy is traditionally described by a single value, the minimal inhibitory concentration (MIC), which has limited predictive power , 8. In ma priori. Recent studies have reported methods to predict MICs from whole genome sequencing data [a priori how chemical changes to an antibiotic structure or novel resistance mutations affect bacterial growth at a given antibiotic concentration.Because of the experimental effort, pharmacodynamic profiles for either novel drug candidates or novel resistant strains are often not obtained. Thus, we need a transferrable framework that allows quantitative predictions based on parameters that can be determined ing data , 47. HowHere, we accurately predict antibiotic action on the basis of accessible biochemical parameters of drug-target interaction. Our computational model, COMBAT provides a framework to predict the efficacy of compounds based on drug-target affinity, target number, and target occupancy. These parameters may change both when improving antibiotic lead structures as well as when bacteria evolve resistance. Importantly, they can be measured early in drug development and may even be a by-product of target-based drug discovery . When thIn previous work, for example on antipsychotics , antivirIn drug development, our mechanistic modeling approach provides insight into which chemical characteristics of drugs may be useful targets for modification. For example, our sensitivity analyses indicate that antibiotics with a similar affinity but faster binding inactivate bacteria more quickly and therefore prevent replication and production of more target molecules, which would change the ratio of antibiotic to target. Furthermore, because e.g. antibiotic binding and unbinding rates can be determined early in the drug development process, such insight can help the transition to preclinical and clinical dosing trials. This may contribute to reducing bottlenecks between these phases of drug development and thereby save money and time.Avoiding antibiotic concentrations that select for resistance is challenging for two reasons. First, the differences in the pharmacodynamic curves of wild-type and resistant strains are not trivial. Resistance can affect not only the MIC, but also the maximal kill rate at high drug concentrations and the steepness of the dose-response curve . TherefoCOMBAT offers insight into determinants of the resistance selection window and builds transferrable knowledge that allows estimating useful dose ranges. In concordance with a recent meta-analysis of experimental data , our senGood quantitative estimates on the dose-response relationship of new drugs would also help defining the therapeutic window, i.e. the range of drug concentrations at which the drug is effective but not yet toxic. For example in ciprofloxacin, the doses found necessary to prevent resistance after marketing were found to be toxic , and an de novo resistance evolution.Our quantitative work can help to identify optimal dosing strategies at constant antibiotic concentrations for homogeneous bacterial populations. These measures are commonly used to assess antibiotic efficacy. In addition, previous work has demonstrated that drug-target binding models outperform traditional pharmacodynamic models for the fluctuating concentrations that actually occur in patients , 51. To COMBAT incorporates the binding and unbinding of antibiotics to their targets and describes how target binding affects bacterial replication and death. This work extends the model developed in . COMBAT A, assuming that the time needed for drug molecules to enter bacterial cells is negligible. We model ciprofloxacin  and ampθ. The binding process is defined by the formula A + T ⇌ x, where the intracellular antibiotic molecules A react with target molecules T at a rate kf and form an antibiotic-target molecule complex x, where values for x range between 0 and θ. If the reaction is reversible, the complex dissociates with a rate kr.We describe the action of antibiotics as a binding and unbinding process to bacterial target molecules . For simkf is the association rate, Vtot is the volume in which the experiment is performed, nA is Avogadro’s number, kr is the dissociation rate, Bi is the number of bacteria with i bound targets, and θ is the total number of targets.In , the assx ∈ ℛ. Under this continuity assumption, we consider the bacterial cells as a function of x and the time t, thereby reducing the total number of equations to two.This approach requires the use of a large number of ordinary differential equations, (0 + 1) for the bacterial population and one for the antibiotic concentration. To generalize this approach, we assume that the variable of bound targets is a real number x ∈ ℛ), we can rewrite the binding kinetics in the formvr = krx can be considered as two velocities, i.e., the derivative of the bound targets with respect to the time Under the continuity approximation (r(x), is dependent on the number of bound target molecules x. The function r(x) is a monotonically decreasing function of x, such that fewer bacteria replicate as more target is bound. r(0) is the maximum replication rate, corresponding to the replication rate of bacteria in absence of antibiotics. Thus, r(x) describes the bacteriostatic action of the antibiotics, i.e., the effect of the antibiotic on bacterial replication.We assume that the replication rate of bacteria, K. At that point, the replication term of the equation isK, and 0 ≤ Flim ≤ 1.Replication ceases as the total bacterial population approaches the carrying capacity x bound target molecules of the mother cell to its progeny is described by a hypergeometric sampling of n molecules from x bound and 2θ−x unbound molecules. Under the continuity assumption, we generalize the concept of hypergeometric distribution. Because the hypergeometric distribution is a function of combinations and because a combination is defined as function of factorials, we can use Γ functions in place of factorials and redefine a continuous hypergeometric distribution as a function of Γ functions. A Γ function isζ is a complex number. In this way, the distribution can be expressed as a probability density function of continuous variables. The amount of newborn bacteria is given by the term r(x)BFlim(t). We assume that bound target molecules are distributed randomly between mother and daughter cells, with each of them inheriting 50% upon division on average. This means that twice the amount of newborn cells must be redistributed along x to account for the random distribution process. For example, if a mother cell with 4 bound targets divides, we have two daughter cells, each with a number of bound targets between 0 and 4 (their sum has to be 4), following the generalized hypergeometric distribution. For simplicity, we define S to be a function related to the replication rate that depends on the number of bacteria with a number of bound target molecules ranging between x and θ, their specific replication rate r(x), and the fraction of their daughter cells expected to inherit x antibiotic-target complexes h:We assume that the total number of target molecules doubles at replication, such that each daughter cell has the same number as the mother cell. We also assume that the total number of drug-target complexes is preserved in the replication and that the distribution of δ(x) depends on the number of bound target molecules. The function δ(x) is assumed to be a monotonically increasing function of x, where δ(θ) is the maximum death rate, when all targets in the bacteria have been bound by antibiotics. The shape of this function describes the bactericidal action of the antibiotic.The death rate function r(x) and/or the death rate δ(x) can be obtained by fitting COMBAT to time-kill curves of bacterial populations after antibiotic exposure. The sigmoidal shape of r(x) and δ(x) can be written as:xrth is the replication rate threshold, xdth is the death rate threshold, and both represent the point where the sigmoidal function reaches ½ of its maximum. γr and γd represent the shape parameters of the replication and death rate functions, respectively. These factors determine the steepness around the inflection point. When they are extreme, the relationship approaches a linear or a step function.We consider several potential functional forms of the relationship between the percentage of bound targets and replication and death rates, because the exact mechanisms how target occupancy affects bacteria is unknown . We use B is the number of bacteria.Putting these components together, the full equation describing a bacterial population is:The free antibiotic concentration results from mass conservation, i.e., all antibiotic molecules associating with their target are subtracted and all dissociating antibiotic molecules are added. kr = 0. To reflect the recovery of target molecules, we substituted the dissociation rate kr in the equation describing the bacterial population with the deacetylation rate ka, as described in [Beta-lactams acetylate their target molecules (PBPs) and thereby inhibit cell wall synthesis. The acetylation of PBPs consumes beta-lactams. However, PBPs can recover through deacetylation. We modified the term of drug-target dissociation in the equation describing antibiotic concentrations , and setribed in .t = 0, we assume that all bacteria have zero bound targets (x = 0), and the initial concentration of bacteria is B = 0, x > 0, and B = B0.At x = 0, x = θ), we specify that the outgoing velocities are zero. For x = 0, i.e. no bound target molecules, the unbinding velocity vr = 0, and in x = θ, i.e. all targets are bound, the binding velocity vf =0. When the replication term at x = 0 and the death term at x = θ are known, we can solve the partial differential equation with two ordinary differential equations at the boundaries. They are similar to the equations at x = 0 and at x = θ described by Abel zur Wiesch et al. [At the boundaries of the partial differential equation  and the spatial approximation vr < 0). For the time approximation of both the PDEs and the ODEs, we used the forward approximation To solve our system of differential equations, we used a first-order upwind scheme. Specifically, we used the spatial approximation Bn+1-BnΔt. We also2 and B2, respectively, which in turn bind to each other to form the tetramer TR [We assumed that gyrases A and B first homo-dimerize to Aramer TR . The fol2B2 tetramers (~100) per wild type bacterial cell [4 sets of six parameters in k−3, … k3) in a Latin hypercube approach from a biologically plausible range where the association rates are between 107–109 M-1 s-1 and the dissociation rates between 10−3–10−1 s-1 [4 estimates for each of the six experimental replicates quantifying gyrase A and B  and 10 μM (mild induction) or 100 μM (strong induction) of isopropyl β-D-1-thiogalactopyranoside (IPTG)  when necessary. BW25113   were used to determine the minimal and maximal kill rate, respectively. Samples were taken immediately prior to addition of the antibiotic and in ~20 min intervals or after 45 min, respectively. Samples were washed once in phosphate buffered saline (PBS) before colony forming units (CFUs) were determined for each sample by plating a 1:10 dilution series in PBS on LB agar plates.Overnight cultures of BW25113 or SoA3329 and SoA3330 were diluted 1:1000 in pre-warmed LB or LB-Cm and LB-Cm-IPTG, respectively, and grown with shaking to OD600 = 1 were harvested by centrifugation. Pelleted cells were lysed at room temperature for 20 min using B-PER bacterial protein extraction reagent  supplemented with 100 μg/mL lysozyme, 5 units/mL DNaseI  and 100 μM/mL PMSF . Samples were stored at -80°C until further use.To quantify the relative amount of GyrAB, samples of SoA3329 and SoA3330 were collected after 45 min of drug treatment as described above. An equal number of cells corresponding to 1 mL culture at ODSamples were heated to 70°C for 10 min after addition of 1x Bolt sample reducing agent  and 1x fluorescent compatible sample buffer . Proteins in whole-cell lysates were separated on 4–15% Mini-Protean TGX Precast gels  and transferred to 0.2 μm Nitrocellulose membranes .E. coli CRP, 664304, Nordic Biosite antibodies) were diluted 1:250, 1:250, and 1:2,000 in Odyssey blocking buffer-TBS, respectively. The blocked membranes were incubated with the appropriate primary antibodies overnight at 4°C, washed 4x for 15 min each in TBS-T solution , and incubated for 2 h at room temperature with fluorescent labelled secondary antibodies  in Odyssey blocking buffer-TBS. Finally, the membranes were washed 4x for 15 min each in TBS-T solution and imaged at 700 nm and 800 nm using a Li-Cor Odyssey Sa scanning system.Membranes were blocked in Odyssey blocking buffer-TBS  for at least one hour at room temperature. Primary antibodies raised against GyrA , GyrB , and CRP , and death, δ(x), on target occupancy for antibiotics with bacteriostatic, bactericidal or mixed action. Solid lines indicate a sigmoidal relationship, dotted lines indicate a step function, dashed lines indicate a linear relationship, and dash-dotted lines indicate independence, i.e. a constant replication or death rate. The left panels, show the replication rates (blue), the right panels show the death rates (red). The top panels, show rates for a bacteriostatic drug, the middle panels, show rates for a bactericidal drug, and the bottom panels, show rates for a drug with mixed effects. The sum of the replication and death rates at certain target occupancies gives the net growth or decline rate of the bacterial population.These graphs show which functions were used to fit the dependence of bacterial replication, (TIF)Click here for additional data file.S2 Figa, b, E. coli expressing gyrA and gyrB under control of the same IPTG-inducible promoter (SoA3329) grown in the presence of 10 μM IPTG (mild overexpression) and 100 μM IPTG (strong overexpression). A control strain containing a mock plasmid (SoA3330), representing wild-type GyrAB levels, was grown in the absence of inducer. Whole cell lysates were separated on a SDS-PAGE gel, blotted, and detected with specific fluorescent antibodies against GyrA (green), GyrB (green) and CRP (red). CRP (cAMP receptor protein) was used as loading control.(TIF)Click here for additional data file.S3 Figkf . a, Net growth rate —log10)/18 h) as function of drug concentration for different values of the binding rate kf (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the corresponding MICs. b, Sensitivity of the MIC to kf obtained from simulations in (a). The color code indicates the MIC corresponding to the simulation with the same color in (a).We use the model fitted to experimental data to explore the sensitivity of our results to changes in (TIF)Click here for additional data file.S4 Figkr . a, Net growth rate —log10)/18 h) as function of drug concentration for different values of the binding rate kr (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. b, Sensitivity of the MIC to kr obtained from simulations in (a). The color code indicates the MIC corresponding to the simulation with the same color in (a).We use the model fitted to experimental data to explore the sensitivity of our results to changes in (TIF)Click here for additional data file.S5 Figkr and kf  while keeping the ratio between kf and kr, the affinity KD, constant. a, shows the net growth rate —log10)/18 h) as function of drug concentration for different values of the turnover rate. The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. b, Sensitivity of the MIC to turnover rate obtained from simulations in (a). The color code indicates the MIC corresponding to the simulation with the same color in (a).We use the model fitted to experimental data to explore the sensitivity of our results to changes in the turnover rate of the drug-target complex. We changed (TIF)Click here for additional data file.S6 Figr(x). We change the value of bound target at which we obtain a half-maximal replication rate, x1/2. a, Functions connecting bacterial replication rates r(x) to percentage of bound target molecules with different half-maximal replication rates. b, Net growth rate —log10)/18 h) as function of drug concentration for different values of x1/2 (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. c, Sensitivity of the MIC to r(x) obtained from simulations in (b). The color code indicates the MIC corresponding to the simulation with the same color in (a&b).We use the model fitted to experimental data to explore the sensitivity of our results to changes in the replication rate with increasingly bound target (TIF)Click here for additional data file.S7 Figδ(x). We change the value of bound target at which we obtain a half-maximal death rate, x1/2. a, Functions connecting bacterial death rates δ(x) to percentage of bound target molecules with different half-maximal death rates. b, Net growth rate —log10)/18 h) as function of drug concentration for different values of x1/2 (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. c, Sensitivity of the MIC to δ(x) obtained from simulations in (b). The color code indicates the MIC corresponding to the simulation with the same color in (a&b).We use the model fitted to experimental data to explore the sensitivity of our results to changes in the death rate with increasingly bound target (TIF)Click here for additional data file.S8 Figkf . a, Net growth rate —log10)/18 h) as function of drug concentration for different values of the binding rate kf (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. b, Sensitivity of the MIC to kf obtained from simulations in (a). The color code indicates the MIC corresponding to the simulation with the same color in (a).We use the model fitted to experimental data Fi  to explo(TIF)Click here for additional data file.S9 Figka . a, Net growth rate —log10)/18 h) as function of drug concentration for different values of the binding rate ka (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. b, Sensitivity of the MIC to ka obtained from simulations in (a). The color code indicates the MIC corresponding to the simulation with the same color in (a).We use the model fitted to experimental data  to explo(TIF)Click here for additional data file.S10 Figka and kf  while keeping the ration of ka/kf constant. a, Net growth rate —log10)/18 h) as function of drug concentration for different values of the turnover rate (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. b, Sensitivity of the MIC to turnover rate obtained from simulations in (a). The color code indicates the MIC corresponding to the simulation with the same color in (a).We use the model fitted to experimental data  to explo(TIF)Click here for additional data file.S11 Figδ(x). We change the value of bound target at which we obtain a half-maximal death rate, x1/2 (see legend). a, Functions connecting bacterial death rates δ(x) to percentage of bound target molecules with different half-maximal replication rates x1/2 (see legend). b, Net growth rate —log10)/18 h) as function of drug concentration for different values of δ(x) (see legend). The dotted horizontal line indicates zero net growth. The intersections of the simulated dose-response curves with this line indicate the respective MICs. c, Sensitivity of the MIC to δ(x) obtained from simulations in (b). The color code indicates the MIC corresponding to the simulation with the same color in (a&b).We use the model fitted to experimental data  to explo(TIF)Click here for additional data file.S12 Figkf) 100-fold and imparts a 15% fitness cost. The dotted horizontal line represents no net growth. The first vertical dotted line indicates where the resistant strain becomes fitter than the wild-type (the start of the competitive resistance selection window), the solid vertical line indicates the MIC of the wild-type , and the dashed vertical line indicates the MIC of the resistant strain, above which selection for resistance should be minimal because both growth of the wild-type and the resistant strain is inhibited.The drug concentration of ampicillin is shown on the x-axes, and the average bacterial net growth rate over 18 h is given on the y-axes. The blue line represents the wild-type strain based on the fits shown in (TIF)Click here for additional data file.S13 FigV1. From there, it can enter the peripheral “tissue” compartment, characterized by the apparent volume V2, with a rate k12. Conversely, the drug can also re-enter the plasma compartment with a rate k21. From the plasma compartment, the drug is eliminated with a rate k10.We simulate plasma and tissue concentrations of ampicillin with a two-compartment pharmacokinetic model. This model described intravenous drug input into the “plasma” compartment, which has an apparent volume of (TIF)Click here for additional data file.S14 Figa, Simulated drug concentrations in the tissue  compartment of a two compartment pharmacokinetic model over two days. The dotted black line indicates the MIC of the pathogen (2.6 mg/L). b, Pathogen load in the tissue compartment in response to fluctuating drug concentrations predicted by COMBAT over the same timeframe.Two modes of drug administrations, 2 g of drug per day given as single, 5 min i.v. infusions (blue line) and 2 g of drug per day given as continuous i.v. infusion (red line), are simulated. (TIF)Click here for additional data file.S1 Tablekr and association rate kf, KD, diverge by more than an order of magnitude in the literature, we chose to fit the association rate kf as a free parameter in our model while constraining KD to remain within the published range .To our knowledge, the association rate for ciprofloxacin has not been determined directly. Because the values of the ratio of dissociation rate (DOCX)Click here for additional data file.S2 Tabler(x) and the death rate δ(x) as a function of the number of bound targets.(DOCX)Click here for additional data file.S3 Table2B2 show the estimated tetramer levels resulting from each measurement. For the GyrA2B2 tetramer estimation, we sampled 104 sets association and dissociation rates from a uniform distribution within their reported limits (Latin hypercube approach). We report the standard deviation for each estimate. We give summary estimates in the last row of the table.(m) indicates mild overexpression, (s) indicates strong overexpression. Columns headed GyrA and GyrB show the experimentally determined overexpression as fold expression compared to the wild type. The columns headed GyrA(DOCX)Click here for additional data file.S4 Tableδ(x) as an exponential function of the number of bound targets δ(x) = a3 eb3x + c3.(DOCX)Click here for additional data file.S5 TableThe parameters were obtained from .(DOCX)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.