Kinetic profiling of metabolic specialists demonstratesstability and consistency of in vivo enzymeturnover numbersDavid Heckmanna1

Anaamika Campeaub Colton J Lloyda Patrick V Phaneufa Ying Hefnera

Marvic Carrillo-Terrazasb Adam M Feistac David J Gonzalezb and Bernhard O Palssonac1

aDepartment of Bioengineering University of California San Diego La Jolla CA 92093 bDepartment of Pharmacology Skaggs School of Pharmacy andPharmaceutical Sciences University of California San Diego La Jolla CA 92093 and cThe Novo Nordisk Foundation Center for Biosustainability TechnicalUniversity of Denmark 2800 Lyngby Denmark

Edited by Athel Cornish-Bowden Institut de Microbiologie de la Meacutediterraneacutee CNRS Marseille France and accepted by Editorial Board Member Alan RFersht July 28 2020 (received for review February 11 2020)

Enzyme turnover numbers (kcats) are essential for a quantitativeunderstanding of cells Because kcats are traditionally measured inlow-throughput assays they can be inconsistent labor-intensive toobtain and can miss in vivo effects We use a data-driven approachto estimate in vivo kcats using metabolic specialist Escherichia colistrains that resulted from gene knockouts in central metabolismfollowed by metabolic optimization via laboratory evolution Bycombining absolute proteomics with fluxomics data we find thatin vivo kcats are robust against genetic perturbations suggestingthat metabolic adaptation to gene loss is mostly achieved throughother mechanisms like gene-regulatory changes Combining ma-chine learning and genome-scale metabolic models we show thatthe obtained in vivo kcats predict unseen proteomics data with muchhigher precision than in vitro kcats The results demonstrate thatin vivo kcats can solve the problem of inconsistent and low-coverage parameterizations of genome-scale cellular models

in vivo | turnover number | proteomics | kcat | gene knockout

Enzyme catalytic rates are crucial for understanding manyproperties of living systems like growth proteome allocation

stress and dynamic responses to perturbation The turnovernumber of an enzyme kcat describes the maximal rate at which anenzymersquos catalytic site can catalyze a reaction Knowledge of kcathas traditionally been a bottleneck in the quantitative under-standing of cells mainly because kcats have historically beenobtained in labor-intensive low-throughput in vitro assays Thesubstantial effort required for in vitro assays is likely the reasonwhy even in model organisms only a small fraction of cellularenzymes has a measured kcat (1) Furthermore in vitro kcat esti-mates for the same enzyme that are found in databases are fre-quently very inconsistent when different literature sources arecompared (2) probably because different experimental protocolsare used Furthermore in vitro conditions can miss importantin vivo effects like posttranslational modifications cellularcrowding or metabolite concentrations The latter points hamperthe utilization of in vitro kcats in genome-scale metabolic modelsIn order to address the problems of low-throughput acquisition

and in vivominusin vitro discrepancies Davidi et al (3) combinedproteomics data and flux predictions to estimate in vivo turnovernumbers based on apparent catalytic rate (kapp) Davidi et al (3)integrated published Escherichia coli proteomics datasets within silico flux predictions in multiple growth conditions and showedthat the resulting maximum apparent catalytic rate (kappmax)across growth conditions is significantly correlated with in vitrokcats Thus kappmax has the potential to overcome the problem ofinconsistent conditions low coverage and in vitrominusin vivo dis-crepancies that hampers the use of in vitro kcats in large models ofmetabolism However it is unclear whether kappmax is a stablesystem parameter that is robust to perturbation and how muchexperimental procedures bias the estimation of kappmax Absolute

proteomic quantification techniques are still suffering from highvariation and previous estimates of kcat were based on in silicoflux predictions rather than 13C fluxomics data Furthermore kcatis expected to scale with growth rate (4) As many experimentalconditions in the literature data used in Davidi et al (3) resulted inlow growth rates the effective number of datasets contributing tokappmax is low Finally if kappmax is a useful estimator of in vivokcat it should improve the predictive capability of metabolicmodels on data that was not used to obtain kappmax that is theperformance on a test setHere we present an approach for estimating kcat in vivo

(Fig 1) We combined proteomic profiling with fluxomics data toestimate in vivo kcats in E coli strains that have undergone strongphysiological perturbations via knockout (KO) of metabolicgenes To obtain strains with high growth rates for which kappapproaches kappmax adaptive laboratory evolution (ALE) (5)was used on the metabolic KO strains We profiled 21 strainsrepresenting metabolic specialists with diverse flux profiles thatare able to obtain high growth rates (6ndash9) With this data-drivenapproach we show that in vivo kcats are stable and robust togenetic perturbations and that they can be used in genome-scale

Significance

Enzyme kinetic parameters are crucial for a quantitative under-standing of metabolism but traditionally have to be measuredin laborious low-throughput assays To solve this problem theenzyme turnover number kcat can be estimated in vivo but it isunclear whether in vivo estimates represent stable systems pa-rameters that can be used for metabolic modeling We presentthe data-driven estimation of in vivo kcats using proteomics andflux data of metabolic knock out strains of Escherichia coli Ourresults show that in vivo kcats are stable parameters that can beused for metabolic modeling We use the estimated in vivo kcatsto parameterize metabolic models and show that model per-formance for gene expression predictions increases drasticallycompared to in vitro parameters

Author contributions DH AC DJG and BOP designed research DH AC CJLPVP YH MC-T and AMF performed research DH CJL PVP and AMF ana-lyzed data and DH and BOP wrote the paper

The authors declare no competing interest

This article is a PNAS Direct Submission AC-B is a guest editor invited by theEditorial Board

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 40 (CC BY-NC-ND)1To whom correspondence may be addressed Email davidheckmannhhude orpalssonucsdedu

This article contains supporting information online at httpswwwpnasorglookupsuppldoi101073pnas2001562117-DCSupplemental

First published September 1 2020

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models to obtain a high predictive performance for unseenprotein abundance data

ResultsQuantifying In Vivo Kinetics in Metabolic Specialists In theorykappmax will approach kcat in vivo if a condition is found in whichthe respective enzyme is utilized at full efficiency In order toachieve strong genetic perturbations of enzyme usage we usedgene KO strains for the phosphotransferase system (PTS)(ptsHIcrr ref 6) the phosphoglucose isomerase (pgi ref 8)triosephosphate isomerase (tpiA ref 7) and succinate dehy-drogenase (sdhCB ref 9) As kapp increases with growth rate (4)we used KO strains that were optimized for growth on glucoseminimal medium via ALE (6ndash9) experiments In addition tothese KO strains we utilized a wild-type (WT) MG1655 strainthat was subjected to ALE (6ndash10) As evolution is not a deter-ministic process ALE endpoints differ in genotype and we in-cluded a total of 21 strains that resulted from replicates of ALEexperiments (ie four endpoint strains for ptsHIcrr eight for pgifour for tpiA three for sdhCB and two WT controls) and thatwere representative for the respective endpoint population Wesubjected the selected strains to genome sequencing and usedthe resulting sequences as reference proteomes in liquid chro-matography with tandem mass spectrometry (LC-MSMS) pro-teomics (see Materials and Methods) Absolute quantification ofbiological duplicates was achieved via calibration to the UPS2standard and the top3 metric (11 12) which estimates proteinabundance based on the average intensity of the three bestionizing peptides Measured protein abundances show a medianR2 of 091 between biological replicates and a median number of2076 proteins were detected per strain (SI Appendix Table S1)The obtained protein abundance vectors cluster by the geneticbackground of the strain used for ALE (SI Appendix Fig S1)This result indicates that protein levels have adjusted in a spe-cific pattern to compensate for the respective gene KO (see refs6ndash9 for details on the transcript level)

Gene KO and ALE Cause Diversity in Enzyme Usage We integratedthe measured protein abundances with 13C metabolic flux anal-ysis (MFA) fluxomics data (6ndash9) to calculate apparent catalyticrates in the 21 strains as the ratio of flux and protein abundanceLike in Davidi et al (3) we only calculated kapp for homomericenzymes and reactions that are not catalyzed by multiple isoen-zymes to allow a specific mapping of proteins to reactions Thisapproach resulted in a median number of 258 enzymes per strainfor which we were able to calculate kapp The resulting apparentcatalytic rates largely cluster by the genotype of the KO strain(Fig 2A) confirming that enzyme usage was indeed perturbed bythe respective KOs Across the 21 strains the maximum ob-served kapp of an enzyme is on average 44 times larger than thesmallest observed kapp (Fig 2B) This result indicates that con-siderable variation in enzyme usage was caused by the metabolicgene KO To exclude the possibility that experimental variationcauses this apparent diversity in enzyme usage we compared theSD of kapp in biological replicates (mean on log10 scale = 007) tothe SD measured across the 21 strains (mean on log10 scale =018) We found that the variation caused by KOs and ALE issignificantly larger than that caused by experimental variation(P lt 2e-16 n1 = 5177 n2 = 311 Wilcoxon rank sum test)

In Vivo Turnover Numbers Are Stable and Consistent We estimatedin vivo kcat for a given enzyme as the maximum of kapp (kappmax)in the 21 KO strains This approach was similar to Davidi et al(3) who estimated in vivo kcats as the maximum kapp over dif-ferent growth conditions Due to incomplete substrate saturationand backward flux the apparent catalytic rate of an enzyme issmaller than the in vivo kcat It is thus unclear whether kappmax isa stable property of the system that can be used in metabolicmodels to give reliable predictions Furthermore absolute pro-teomics data and fluxomics data come with significant experi-mental uncertainties and biases that could prevent kappmax frombeing useful in modeling applicationsEven though our protocol perturbed enzyme kapp via gene KO

and ALE whereas Davidi et al (3) used differences in growth

Fig 1 Approach for obtaining kcat in vivo from metabolic specialists KO of enzymes in central metabolism was followed by ALE to obtain 21 strains that haddiverse flux profiles while achieving high growth rates (6ndash9) Fluxomics and proteomics data were then integrated for the evolved strains to obtain themaximum kapp across the 21 strains (kappmax) for each enzyme that could be mapped uniquely The obtained kappmax vector was then extrapolated to genomescale via supervised machine learning and used to parameterize genome-scale metabolic models The resulting genome-scale models were then validated onunseen proteomics data

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conditions to achieve variation in enzyme usage we found a veryhigh agreement between kappmax from the two sources (R2 = 09Fig 3A) We used a parametric bootstrap procedure to quantifythe uncertainty in our kappmax estimations (see Materials andMethods) We found that 42 (88 out of 210) of comparablevalues estimated by Davidi et al (3) fall into the 95 CIs of thekappmax values obtained in this study A clear outlier is the re-action FAD reductase (FADRx Fig 3A) This discrepancy iscaused by the different methods of flux estimation While pro-tein abundances of FAD reductase are relatively similar in therespective conditions for which the maximum kapp was measured[protein abundance is 2 times lower in Davidi et al (3)] fluxthrough the FADRx reaction in parsimonious flux balanceanalysis (FBA) (13) is 1000 times higher than the flux estimatedin 13C MFAIt is worth noting that the mutations observed in the ALE

strains are mostly regulatory in nature with almost no structuralchanges in the homomeric enzymes examined in this study (seeDataset S1D and refs 6ndash9 and 14 for details) One exception is

the enzyme isocitrate dehydrogenase which has shown a veryhigh level of convergence for a coding sequence mutation(R395C) in seven out of the eight evolved pgi KO strains Wefound no significant difference in kappmax compared to thekappmax of isocitrate dehydrogenase reported by Davidi et al (3)(P = 028 n = 500 parametric bootstrap) suggesting that thestructural mutation does not increase the in vivo catalyticefficiencyIn order to understand the relationship of kappmax from KO

strains with kcat in vitro we compared kappmax with a dataset ofkcat in vitro that was compiled by Davidi et al (3) for that pur-pose This in vitro dataset originates from a variety of literaturesources and thus varying assay conditions (3) While kappmaxfrom KO strains is very consistent with kappmax from differentgrowth conditions the correlation with kcat in vitro is significantlylower (R2 = 059 Fig 3C) and only 26 (32 out of 125) of thein vitro values fall into the 95 CIs of kappmax A similar lowcorrelation with in vitro kcat was found in the kappmax estimatespublished by Davidi et al (3) (R2 = 059 Fig 3D)In summary although we obtained kappmax from a genetic

perturbation rather than variation in growth conditions and used13C fluxomics data instead of in silico flux and despite proteo-mics and flux data being subject to significant noise we foundvery high agreement between kappmax from the two sources

Using Machine Learning to Extrapolate to the Genome Scale Theproblem of low coverage that is associated with kcat in vitro is alsopresent in kappmax Not all protein abundance can be mapped toenzymes uniquely and proteomics experiments still suffer fromcoverage issues The final set of kappmax values includes 325 en-zymes (Fig 3B) This coverage is 27 higher than that found inDavidi et al (3) mostly because we used 13C fluxomics data thattends to have a higher sensitivity than the in silico method (par-simonious FBA ref 13) used by Davidi et al (3) In order tovalidate the estimated in vivo turnover numbers in a genome-scalemodel that contains over 3000 direction-specific reactions we firstneeded to extrapolate the data to the genome scale We usedsupervised machine learning on a diverse enzyme dataset (15) thatincludes data on enzyme network context enzyme three-dimensional structure and enzyme biochemistry to achieve thisgoal An ensemble model of an elastic net random forest andneural network (15) showed good performance in cross-validationfor the in vivo turnover numbers where the highest performancewas achieved for kappmax that was obtained from the 21 KO strains(Fig 4) Taking the maximum of kappmax from this study and thatof Davidi et al (3) did not improve model performance eventhough it resulted in the largest training set

Validation of Turnover Numbers in Mechanistic Models The enzymeturnover number is a major determinant of gene expressionlevels as it sets a lower limit on the enzyme concentration re-quired to maintain a given flux Turnover numbers are success-fully used in genome-scale metabolic models to constrainmetabolic fluxes by a limited cellular protein budget (16ndash18) orthe balance of translation and dilution of proteins (19ndash21) Thekappmax obtained from diverse growth conditions was previouslyused successfully in genome-scale metabolic models showingthat the performance of protein abundance predictions ofmodels using kappmax was significantly higher than that of modelsusing in vitro kcats (15) A major drawback of this analysis lies inthe validation of the metabolic model which used data (22) thatwas also utilized in obtaining kappmax (3) posing the risk ofcircular reasoning through data leakage If kappmax is a stableproperty of in vivo enzyme catalysis it is expected to yield a highperformance in metabolic models on unseen data that is kappmax-based models should generalize wellTo test this hypothesis we parameterized two genome-scale

modeling algorithms of proteome-limited metabolism a metabolic

A

B

Fig 2 Apparent catalytic rates cluster by genetic background and exhibitdiversity across strains (A) Data on kapp in each of the 21 strains projectedonto the first two principal components Only reactionminusstrain combinationsfor which kapp was available in all strains were used resulting in 214 reac-tions used in the analysis Data were centered and scaled before conductingprincipal component analysis (B) Distribution of ranges of kapp across reac-tions The log2 of the ratio between the highest and the lowest kapp perreaction is shown

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modeling with enzyme kinetics (MOMENT) model (16) and anintegrated model of metabolism and macromolecular expression(ME model) (19) with kappmax obtained from KO strains We thenused the model to predict enzyme abundance data under variousgrowth conditions published by Schmidt et al (22) a dataset thatwas not used to obtain kappmax in this study For comparison weincluded model parameterization based on kcat in vitro with kappmax

from Davidi et al (3) and the maximum of kappmax obtained in thisstudy and that of Davidi et al (3) We found that the performanceof kappmax from KO strains on the Schmidt et al (22) data is verysimilar to that of Davidi et al (3) The average root-mean-squareerror (RMSE) on log10 scale is 4 higher for the MOMENTmodeland 12 lower for the ME model even though the Schmidt et al(22) data were used to obtain kappmax in Davidi et al (3) (Fig 5 andSI Appendix Fig S2) This good performance on unseen dataconfirms that in vivo kcat are stable against genetic perturbation andconsistent across experimental protocolsWe further found that kappmax outperforms kcat in vitro in

MOMENT and ME models across all growth conditions (Fig 5)When comparing median-imputed kcat parameterizations tothose using supervised machine learning we found that machine

learning reduces RMSE on log10 scale by 38 for kappmax and10 for kcat in vitro confirming the utility of this approach (15)

DiscussionA large-scale characterization of the kinetic parameters thatgovern metabolism termed the kinetome (1) has been a majorhurdle in our quantitative understanding of cellular behavior (123 24) Previous efforts to use kcat which represents a majorfraction of the kinetome at the genome scale either utilizedin vitro data (16 18) or fitted kinetic parameters to physiologicaldata (4 25 26) While the parameterization with in vitro kcatscan suffer from varying assay protocols low throughput andpotentially missing in vivo effects parameter fitting is frequentlyunderdetermined and leads to nonunique solutions that cannotbe expected to generalize well when used in new conditions Theuse of proteomics data and flux predictions on homomeric en-zymes (3) for which proteome abundances can be assigneduniquely is a promising approach that could solve many short-comings of in vitro data and fitting approaches While it wasshown that this approximation of in vivo kcat kappmax exhibits adecent correlation with kcat in vitro it is unclear whether kappmaxcaptures an upper bound on enzymatic rate that is stable with

26115 210

KO ALE Davidiet al

A B

C D

Fig 3 Estimates of in vivo turnover numbers are consistent (A) Comparison between kappmax obtained from KO strains (this study) and kappmax from growthconditions (3) MAE mean absolute error (B) Number of reactions for which kappmax was obtained in KO strains (this study) and varying growth conditions (3)(C) Comparison between kappmax obtained from KO strains and in vitro kcats (D) Comparison between kappmax obtained from KO strains and in vitro kcats (3)Horizontal lines are 95 CIs determined by 500 parametric bootstrap samples (see Materials and Methods) Points are marked red when the compared valuefalls into the 95 CI of kappmax from KO strains and are colored blue if the compared value does not fall into the CI Points are labeled with reaction IDs asgiven in the iJO1366 reconstruction (51) if the values differ by more than one order of magnitude Data on kcat in vitro shown in C and D were taken fromDavidi et al (3) to allow for comparison between the studies Davidi et al (3) obtained this in vitro dataset from the Braunschweig Enzyme Database(BRENDA) (52) and utilized the maximal kcat in cases where multiple sources were available for the same enzyme

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respect to genetic perturbations and consistent across experi-mental procedures These properties are prerequisites for theapplication of kappmax in metabolic modelsWe found that in vivo turnover numbers that are obtained

from KO strains are surprisingly consistent between very differ-ent protocols (Fig 3) Specifically the protocol we used to obtainkappmax shows the following differences compared to that ofDavidi et al (3) 1) kapp is not perturbed by growth conditionsbut by genetic KOs 2) we used 13C MFA fluxomics data insteadof in silico data from parsimonious FBA 3) we utilized pro-teomics data that were obtained with a single LC-MSMS pro-tocol avoiding batch effects and 4) all data were obtained underbatch growth that promotes high growth rates increasing kapp(4) Given these differences in the two approaches to obtain

kappmax the high agreement between the two methods indicatesa high stability and consistency of in vivo kcatsThe high stability of in vivo kcats indicates that the adaptation

of the strains during ALE does not lead to drastic increases inin vivo kcats This hypothesis is supported by the relatively lownumber of convergent mutations in the coding regions of en-zymes (Dataset S1D) Short-term metabolic evolution appears tobe governed by changes in gene regulation rather than changesin enzyme efficiencies at least in the case of the homomericenzymes investigated in this studyWhy does kappmax exhibit a high consistency where in con-

trast in vitro kcats often show a low agreement between differentsources (2) In the context of large metabolic models in vitrokcats are typically obtained from hundreds of different publica-tions that are collected in databases Thus it is usually not

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Fig 4 Performance of machine learning models on different sources of turnover numbers The performance is estimated in five-times repeated five-foldcross-validation in elastic net random forest and a neural network (15) (see Materials and Methods) Data for kcat in vitro were taken from Heckmannet al (15)

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possible to obtain data that use uniform experimental protocolsthat mimic the in vivo situation of interest In contrast kappmax isobtained from a small number of proteomics and flux datasetsthat were ideally obtained on the same instruments thusavoiding batch effects Furthermore there is some indicationthat metabolite levels in vivo tend to saturate many enzymes(27) Such a high saturation might allow for conditions of highenzyme saturation to be found even with a relatively smallnumber of system perturbations

Some sources of uncertainty remain in the kappmax values pre-sented in this study The 13C MFA data that we used were obtainedfor the endpoint populations of the respective ALE experiments(6ndash9) whereas we used clonal samples for proteomics experimentsWhile we chose clones that represented the most dominant muta-tions found in the endpoint populations flux distributions could beaffected by uncommon mutations Furthermore 13C MFA data canyield high coverage (28) but it still relies heavily on the quality ofthe underlying network model which could bias analyses

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Acetate(n=215)

Fructose(n=213)

Fumarate(n=214)

Galactose(n=220)

Glucosamine(n=217)

Glucose(n=220)

Glycerol(n=213)

LB(n=138)

Mannose(n=214)

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Succinate(n=219)

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Fig 5 Performance of turnover number vectors in mechanistic models of proteome allocation The MOMENT algorithm and an ME model were parame-terized with different sources of turnover numbers [including Davidi et al (3)] Growth on different carbon sources was simulated with the two algorithms topredict relative protein weight fractions of metabolic enzymes The protein abundance predictions were then compared to proteomics data in the respectivegrowth condition published by Schmidt et al (22) using the RMSE on log10 scale Machine learning model predictions were based on the protocol introducedby Heckmann et al (15) but all models were newly trained on the data produced in this study (Dataset S1)

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Because not all enzymes can be mapped to a reaction uniquelyand proteomics data still suffer from incomplete coveragekappmax has a low coverage of the metabolic network and cannotbe readily used in genome-scale models Based on mechanisticknowledge of factors that shape enzyme turnover numbers (2 2930) supervised machine learning was previously used success-fully to extrapolate in vivo kcats to the genome scale (15) Wefind a slightly lower error in cross-validation on kappmax obtainedfrom KO strains compared to kappmax from varying growthconditions (3) this slight increase in performance may lie in theincreased size of the training set as we were able to obtain 38more kappmax values due to the use of 13C MFA data Thisfinding is consistent with previously computed learning curves ofkappmax on the Davidi et al (3) dataset that showed that a do-main of diminishing returns in model performance is reachedwith respect to the size of the training set (15)We find that metabolic models that are parameterized with

the kappmax values we obtained from KO strains lead to verygood predictive performance on unseen proteomics data Thisperformance in mechanistic models supports the hypothesis thatkappmax indeed represents a stable property of the system that iskcat in vivo Thus kappmax can enable genome-scale metabolicmodels that generalize well to unseen conditionsWhile kinetic parameters remain difficult to obtain the stable

and consistent properties of in vivo kcats support the notion thatthese parameters can improve the predictive capabilities ofmetabolic models significantly and thus enable better quantita-tive understanding of the cell Finally the high stability of in vivokcats suggests that short-term metabolic evolution is governed bychanges in gene expression rather than adaptation at the level ofenzyme kinetics

Materials and MethodsStrain Genomic Sequencing Genomic DNA of ALE endpoint clones was iso-lated using bead agitation in 96-well plates as outlined previously (31)Paired-end whole-genome DNA sequencing libraries were generated with aKapa HyperPlus library prep kit (Kapa Biosystems) and run on an IlluminaHiSeq 4000 platform with a HiSeq SBS kit 150 base pair reads The gener-ated DNA sequencing fastq files were processed with the breseq computa-tional pipeline (version 0320) (32) and aligned to an E coli K12 MG1655reference genome (33) to identify mutations DNA sequencing quality con-trol was accomplished using the software AfterQC (version 097) (34)

Cloneswere chosen in order to represent the high-frequency alleles found inthe endpoint populations of the respective ALE experiments DNA sequenceswere used to create reference proteomes for proteomics experimentsdescribed below

Sample Preparation For each strain 3 mL of culture was grown overnight at37 degC with shaking in M9 medium (4 g of glucose Lminus1) (35) with trace ele-ments (36) and then passed twice the following days in 15 mL of media at37 degC from optical density (OD) 005 to 01 to OD 10 to 15 For the exper-iment 100 mL of culture with initial OD600 (OD at a wavelength of 600 nm) =01 was grown in flasks with stirring in a water bath at 37 degC When culturesreached OD600 = 06 40 mL of culture was collected and immediately put onice The cells were pelleted by centrifuge at 5000 rpm at 4 degC for 20 min Cellpellets were then washed with 20 mL of cold phosphate-buffered saline(PBS) buffer three times and centrifuged at 5000 rpm for 20 min at 4 degCPellets were transferred into 15-mL microcentrifuge tubes and centrifugedat 8000 rpm at 4 degC for 10 min Remaining PBS buffer was removed andpellets of proteomic samples were frozen at minus80 degC

Sample Lysis for Proteomics Frozen samples were immersed in a lysis buffercomprising 75 mM NaCl (Sigma Aldrich) 3 sodium dodecyl sulfate (Fisher Sci-entific) 1mMsodium fluoride (VWR International LLC) 1mM β-glycerophosphate(Sigma Aldrich) 1 mM sodium orthovanadate 10 mM sodium pyrophosphate(VWR International LLC) 1 mM phenylmethylsulfonyl fluoride (Fisher Scientific)50 mM Hepes (Fisher Scientific) pH 85 and 1times complete ethylenediaminetetra-acetic acid-free protease inhibitor mixture Samples were subjected to rapidmixing and probe sonication using a Q500 QSonica sonicator (Qsonica) equippedwith a 16-mmmicrotip at amplitude 20 Samples were subjected to three cyclesof 10 s of sonication followed by 10 s of rest with a total sonication time of 50 s

Protein Abundance Quantitation Total protein abundance was determinedusing a bicinchoninic acid Protein Assay Kit (Pierce) as recommended by themanufacturer

Peptide Isolation Six milligrams of protein was aliquoted for each sampleSample volume was brought up to 20 mL in a solution of 4 M Urea + 50 mMHepes pH = 85 Disulfide bonds were reduced in 5 mM dithiothreitol (DTT)for 30 min at 56 degC Reduced disulfide bonds were alkylated in 15 mM ofiodoacetamide in a darkened room-temperature environment for 20 minThe alkylation reaction was quenched via the addition of the original vol-ume of DTT for 15 min in a darkened environment at room temperatureProteins were next precipitated from solution via the addition of 5 μL of100 wtvol trichloroacetic acid Samples were mixed and incubated on icefor 10 min Samples were subjected to centrifugation at 16000 times g for 5 minat 4 degC The supernatant was removed and sample pellets were gentlywashed in 50 μL of ice-cold acetone Following the wash step samples weresubjected to centrifugation at 16000 times g at 4 degC The acetone wash wasrepeated and the final supernatant was removed Protein pellets were driedon a heating block at 56 degC for 15 min and pellets were resuspended in asolution of 1 M Urea + 50 mM Hepes pH = 85 The UPS2 standard (Sigma)was reconstituted as follows Twenty milliliters of a solution of 4 M Urea +50 mM Hepes pH = 85 was added to the tube The sample tube was sub-jected to vortexing and water bath sonication for 5 min each The standardwas subjected to reduction and alkylation using methods described aboveThe sample was next diluted in a solution of 50 mM Hepes pH = 85 suchthat the final concentration of Urea was 1 M Then 088 mg of the proteinstandard was spiked into each experimental sample and samples weresubjected to a two-step digestion process First samples were digested using66 μg of LysC at room temperature overnight shaking Next protein wasdigested in 165 μg of sequencing-grade trypsin (Promega) for 6 h at 37 degCDigestion reactions were terminated via the addition of 33 μL of 10 tri-fluoroacetic acid (TFA) and were brought up to a sample volume of 300 μLof 01 TFA Samples were subjected to centrifugation at 16000 times g for5 min and desalted with in-house-packed desalting columns using methodsadapted from previously published studies (37 38) Following desaltingsamples were lyophilized and then stored at minus80 degC until further use

LC-MSMS Samples were resuspended in a solution of 5 acetonitrile (ACN)and 5 formic acid (FA) Samples were subjected to vigorous vortexing andwater bath sonication Samples were analyzed on an Orbitrap Fusion MassSpectrometer with in-line Easy NanoLC (Thermo) in technical triplicateSamples were run on an increasing gradient from 6 to 25 ACN + 0125FA for 70 min then 100 ACN + 0125 FA for 10 min One milligram ofeach sample was loaded onto an in-houseminuspulled and minuspacked glass capil-lary column heated to 60 degC The column measured 30 cm in length withouter diameter of 360 mm and inner diameter of 100 mm The tip waspacked with C4 resin with diameter of 5 mm to 05 cm then with C18 resinwith diameter of 3 mm an additional 05 cm The remainder of the columnup to 30 cm was packed with C18 resin with diameter of 18 mm Electro-spray ionization was achieved via the application of 2000 V to a T-junctionconnecting sample waste and column capillary termini The mass spec-trometer was run in positive polarity mode MS1 scans were performed inthe Orbitrap with a scan range of 375 mz to 1500 mz with resolution of120000 Automatic gain control (AGC) was set to 5 times 105 with maximum ioninject time of 100 ms Dynamic exclusion was performed at 30-s durationTop n was used for fragment ion isolation with n = 10 The decision treeoption was used for fragment ion analysis Ions with charge state of 2 wereisolated between 375 mz and 1500 mz and ions with charge states 3 to 6were isolated between 600 mz and 1500 mz Precursor ions were frag-mented using fixed Collision-Induced Dissociation Fragment ion detectionoccurred in the linear ion trap and data were collected in profile modeTarget AGC was set to 1 times 104

Technical triplicate spectral data were searched against a customizedreference proteome comprising the reference proteome of the respectivestrain (see above) appended to the UPS2 fasta sequences (Sigma) usingProteome Discoverer 21 (Thermo) Spectral matching and in silico decoydatabase construction was performed using the SEQUEST algorithm (39)Precursor ion mass tolerance was set to 50 parts per million Fragment ionmass tolerance was set to 06 Da Trypsin was specified as the digestingenzyme and two missed cleavages were allowed Peptide length toleratedwas set to 6 to 144 amino acids Dynamic modification included oxidation ofmethionine (+15995 Da) and static modification included carbamidome-thylation of cysteine residues (+57021 Da) A false-discovery rate of 1 wasapplied during spectral searches

23188 | wwwpnasorgcgidoi101073pnas2001562117 Heckmann et al

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Protein Abundance Estimation In order to estimate absolute protein abun-dance the top3 metric was calculated for each protein as the average of thethree highest peptide areas (11 12) Robust linear regression (as imple-mented in the Modern Applied Statistics with S (MASS) package ref 40) wasused to calibrate top3 with the UPS2 standard according to the followingmodel to obtain the amount of loaded protein A

log10 A( ) = a + bthinsp log10 top3( )In order to obtain abundance relative to cell dry weight (C) we use a constantratio γ = 1394 μmolmiddotgDWminus1 (41)

Ci = γAi

sumjAj

Calculation of kappmax For each biological replicate apparent catalytic rateskapp were calculated as the ratio of protein abundance and measured flux if1) the protein abundance surpassed 50 pmolmiddotgDWminus1 and 2) the estimatedflux was at least 4 times larger than the range of the 95 CI and larger than100 fmolmiddotgDWminus1 hminus1 and the 95 CI did not include zero as defined inMcCloskey et al (28)

For each of the two biological replicates per strain kappmax was calculatedas the maximum kappmax across the 21 strains Finally the average kappmax

over the two replicates was calculated and used in the presented analyses

Parametric Bootstrap for kappmax We used a parametric bootstrap approachto estimate how experimental variability in proteomics and fluxomics dataaffects kappmax For each enzyme we assumed protein abundance to benormally distributed with mean and SD estimated from the biological rep-licates for the respective enzyme In cases where only one biological repli-cate was available due to lack of detection in the MSMS we imputed themissing SD with a linear regression of SD (on log scale) against meanabundance (on log scale) for all available enzymes Variability in flux datafor the respective reaction was also assumed to take a normal distributionwhere we used the SD estimated in the MFA procedure that resulted frommultiple MFA model reruns on biological triplicates (as described in refs6ndash9) For each reaction 500 bootstrap samples were simulated based on theparameterized normal distributions of protein abundance and flux for thatreaction and these samples were used to calculate 95 CIs for kappmax

Machine Learning Turnover numbers were extrapolated to the genome scaleusing the machine learning approach published previously (15) In this su-pervised machine learning procedure enzyme features on enzyme networkcontext enzyme structure biochemical mechanism and in the case of kcatin vitro assay conditions were utilized (15) These enzyme features werelabeled with the kappmax values estimated in this study and an ensemblemodel of elastic net random forest and neural network was trained usingthe caret package (42) and h2o (43) The ensemble used an average of thepredictions of the three individual models Model hyperparameters werechosen in five-times repeated cross-validation (one repetition in the case ofneural networks) based on the RMSE metric as reported in Heckmann et al(15) For the neural networks random discrete search was used for optimi-zation of hyperparameters (15)

MOMENT Modeling Validation of different turnover number vectors in theMOMENT model was conducted as described in Heckmann et al (15) In theMOMENT algorithm a flux distribution is computed that maximizes straingrowth rate subject to constraints on the total protein budget of the cell(16) In order to constrain fluxes based on enzyme usage the algorithmrequires kcat parameters (16) Here we use the respective vectors of kcat fromdifferent sources to parameterize MOMENT and thus to predict proteinabundances that were experimentally determined by Schmidt et al (22) Thegenome-scale metabolic model iML1515 (44) was used in the R (45) packagessybil (46) and sybilccFBA (47) to construct linear programming problems thatwere solved in IBM CPLEX version 127

ME Modeling To complement the MOMENT-based validation of the com-puted turnover numbers a similar validation approach was employed withthe iJL1678b-ME genome-scale model of E coli metabolism and gene ex-pression (48) The ME model contains a detailed description of the cellrsquos geneexpression machinery that is not contained in the MOMENT model The kappswere mapped to iJL1678b-ME as previously described (15) However the MEmodel kapps were adjusted due to a key difference that lies in the way thatthe MOMENT and ME model resource allocation models apply enzymeconstraints MOMENT accounts for each unique protein contained within acatalytic enzyme whereas the ME model formulation accounts for thecomplete number of protein subunits in an enzyme As a result the mac-romolecular ldquocostrdquo of catalyzing a reaction in the ME model is often notablyhigher than in MOMENT To account for this the kapps in the ME model wereadjusted by scaling each kapp by the number of protein subunits divided bythe number of unique proteins

The ME model was solved in quad precision using the qMINOS solver (49)and a bisection algorithm (50) to determine the maximum feasible modelgrowth rate within a tolerance of of 10minus12 All proteins in a solution with acomputed synthesis greater than zero copies per cell were compared toexperimentally measured protein abundances Since the ME model accountsfor the activity of many proteins outside of the scope of the kapp predictionmethod only those that overlap with predicted kapps were considered

Data Availability Results of genome sequencing and mutation calling weredeposited to ALEdb (aledborg) as part of the ldquoCentral Carbon Knockout (CCK)projectrdquo MS-based proteomic data can be found on the ProteomeXchangeConsortium (httpproteomecentralproteomexchangeorg) with the datasetidentifier PXD015344 Inferred protein abundances MFA fluxes and resultingkapps are available as Dataset S1A Sets of kappmax are available as Dataset S1BA table of kcat in vitro and kappmax extrapolated with machine learning modelsor the median is available as Dataset S1C A mutation table of the strains usedin this study is available as Dataset S1D Source code in R and Python used forproducing the analyses presented in this article is available in GitHub underhttpsgithubcomSBRGKinetome_profiling All study data are included in thearticle and SI Appendix

ACKNOWLEDGMENTS This work was funded by the Novo Nordisk Founda-tion Grant NNF10CC1016517We thank Dan Davidi and Douglas McCloskey forinsightful discussions Lars Nielsen for insightful comments on the manuscriptand Marc Abrams for proofreading the manuscript

1 A Nilsson J Nielsen B O Palsson Metabolic models of protein allocation call for the

kinetome Cell Syst 5 538ndash541 (2017)2 A Bar-Even et al The moderately efficient enzyme Evolutionary and physicochem-

ical trends shaping enzyme parameters Biochemistry 50 4402ndash4410 (2011)3 D Davidi et al Global characterization of in vivo enzyme catalytic rates and their

correspondence to in vitro kcat measurements Proc Natl Acad Sci USA 113

3401ndash3406 (2016)4 A Goelzer et al Quantitative prediction of genome-wide resource allocation in

bacteria Metab Eng 32 232ndash243 (2015)5 T E Sandberg M J Salazar L L Weng B O Palsson A M Feist The emergence of

adaptive laboratory evolution as an efficient tool for biological discovery and in-

dustrial biotechnology Metab Eng 56 1ndash16 (2019)6 D McCloskey et al Adaptive laboratory evolution resolves energy depletion to

maintain high aromatic metabolite phenotypes in Escherichia coli strains lacking the

phosphotransferase system Metab Eng 48 233ndash242 (2018)7 D McCloskey et al Adaptation to the coupling of glycolysis to toxic methylglyoxal

production in tpiA deletion strains of Escherichia coli requires synchronized and

counterintuitive genetic changes Metab Eng 48 82ndash93 (2018)8 D McCloskey et al Multiple optimal phenotypes overcome redox and glycolytic in-

termediate metabolite imbalances in Escherichia coli pgi knockout evolutions Appl

Environ Microbiol 84 e00823-18 (2018)

9 D McCloskey et al Growth adaptation of gnd and sdhCB Escherichia coli deletionstrains diverges from a similar initial perturbation of the transcriptome Front Mi-crobiol 9 1793 (2018)

10 R A LaCroix et al Use of adaptive laboratory evolution to discover key mutationsenabling rapid growth of Escherichia coli K-12 MG1655 on glucose minimal mediumAppl Environ Microbiol 81 17ndash30 (2015)

11 J C Silva M V Gorenstein G-Z Li J P C Vissers S J Geromanos Absolutequantification of proteins by LCMSE A virtue of parallel MS acquisition Mol CellProteomics 5 144ndash156 (2006)

12 E Ahrneacute L Molzahn T Glatter A Schmidt Critical assessment of proteome-widelabel-free absolute abundance estimation strategies Proteomics 13 2567ndash2578(2013)

13 H-G Holzhuumltter The principle of flux minimization and its application to estimatestationary fluxes in metabolic networks Eur J Biochem 271 2905ndash2922 (2004)

14 D McCloskey et al Evolution of gene knockout strains of E coli reveal regulatoryarchitectures governed by metabolism Nat Commun 9 3796 (2018)

15 D Heckmann et al Machine learning applied to enzyme turnover numbers revealsprotein structural correlates and improves metabolic models Nat Commun 9 5252(2018)

16 R Adadi B Volkmer R Milo M Heinemann T Shlomi Prediction of microbialgrowth rate versus biomass yield by a metabolic network with kinetic parametersPLOS Comput Biol 8 e1002575 (2012)

Heckmann et al PNAS | September 15 2020 | vol 117 | no 37 | 23189

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17 Q K Beg et al Intracellular crowding defines the mode and sequence of substrateuptake by Escherichia coli and constrains its metabolic activity Proc Natl Acad SciUSA 104 12663ndash12668 (2007)

18 B J Saacutenchez et al Improving the phenotype predictions of a yeast genome-scalemetabolic model by incorporating enzymatic constraints Mol Syst Biol 13 935(2017)

19 J A Lerman et al In silico method for modelling metabolism and gene productexpression at genome scale Nat Commun 3 929 (2012)

20 E J OrsquoBrien J A Lerman R L Chang D R Hyduke B Oslash Palsson Genome-scalemodels of metabolism and gene expression extend and refine growth phenotypeprediction Mol Syst Biol 9 693 (2013)

21 L Yang J T Yurkovich Z A King B O Palsson Modeling the multi-scale mecha-nisms of macromolecular resource allocation Curr Opin Microbiol 45 8ndash15 (2018)

22 A Schmidt et al The quantitative and condition-dependent Escherichia coli pro-teome Nat Biotechnol 34 104ndash110 (2016)

23 D Davidi R Milo Lessons on enzyme kinetics from quantitative proteomics CurrOpin Biotechnol 46 81ndash89 (2017)

24 K van Eunen B M Bakker The importance and challenges of in vivo-like enzymekinetics Perspect Sci 1 126ndash130 (2014)

25 A Ebrahim et al Multi-omic data integration enables discovery of hidden biologicalregularities Nat Commun 7 13091 (2016)

26 A Khodayari C D Maranas A genome-scale Escherichia coli kinetic metabolic modelk-ecoli457 satisfying flux data for multiple mutant strains Nat Commun 7 13806(2016)

27 B D Bennett et al Absolute metabolite concentrations and implied enzyme activesite occupancy in Escherichia coli Nat Chem Biol 5 593ndash599 (2009)

28 D McCloskey J D Young S Xu B O Palsson A M Feist Modeling method forincreased precision and scope of directly measurable fluxes at a genome-scale AnalChem 88 3844ndash3852 (2016)

29 D Heckmann D C Zielinski B O Palsson Modeling genome-wide enzyme evolutionpredicts strong epistasis underlying catalytic turnover rates Nat Commun 9 5270(2018)

30 D Davidi L M Longo J Jabłonska R Milo D S Tawfik A birdrsquos-eye view of enzymeevolution Chemical physicochemical and physiological considerations Chem Rev118 8786ndash8797 (2018)

31 C Marotz et al DNA extraction for streamlined metagenomics of diverse environ-mental samples Biotechniques 62 290ndash293 (2017)

32 D E Deatherage J E Barrick Identification of mutations in laboratory-evolved mi-crobes from next-generation sequencing data using breseq Methods Mol Biol 1151165ndash188 (2014)

33 P Phaneuf SBRGbop27refseq Zenodo httpsdoiorg105281zenodo1301236 Ac-cessed 28 August 2020

34 S Chen et al AfterQC Automatic filtering trimming error removing and quality

control for fastq data BMC Bioinf 18 (suppl 3) 80 (2017)35 J Sambrook D W Russell Molecular Cloning A Laboratory Manual (Cold Spring

Harbor Laboratory Press ed 3 2001)36 S S Fong et al In silico design and adaptive evolution of Escherichia coli for pro-

duction of lactic acid Biotechnol Bioeng 91 643ndash648 (2005)37 J D Lapek Jr M K Lewinski J M Wozniak J Guatelli D J Gonzalez Quantitative

temporal viromics of an inducible HIV-1 model yields insight to global host targets

and phospho-dynamics associated with protein Vpr Mol Cell Proteomics 16

1447ndash1461 (2017)38 J Rappsilber Y Ishihama M Mann Stop and go extraction tips for matrix-assisted

laser desorptionionization nanoelectrospray and LCMS sample pretreatment in

proteomics Anal Chem 75 663ndash670 (2003)39 J K Eng A L McCormack J R Yates An approach to correlate tandemmass spectral

data of peptides with amino acid sequences in a protein database J Am Soc Mass

Spectrom 5 976ndash989 (1994)40 W N Venables B D Ripley Modern Applied Statistics with S (Springer ed 5 2002)41 F C Neidhardt et al Escherichia coli and Salmonella Cellular and Molecular Biology

(ASM Press ed 2 1996)42 M Kuhn Others caret package J Stat Softw 28 1ndash26 (2008)43 A Candel V Parmar E LeDell A Arora Deep Learning with H2O (H2Oai Inc 2016)44 J M Monk et al iML1515 a knowledgebase that computes Escherichia coli traits

Nat Biotechnol 35 904ndash908 (2017)45 R Core Team R A Language and Environment for Statistical Computing (R Foun-

dation for Statistical Computing Vienna Austria 2017)46 G Gelius-Dietrich A A Desouki C J Fritzemeier M J Lercher SybilmdashEfficient

constraint-based modelling in R BMC Syst Biol 7 125 (2013)47 A A Desouki sybilccFBA Cost Constrained FLux Balance Analysis MetabOlic Mod-

eling with ENzyme kineTics (MOMENT) version 200 httpsCRANR-projectorg

package=sybilccFBA Accessed 28 August 202048 C J Lloyd et al COBRAme A computational framework for genome-scale models of

metabolism and gene expression PLoS Comput Biol 14 e1006302 (2018)49 D Ma et al Reliable and efficient solution of genome-scale models of metabolism

and macromolecular expression Sci Rep 7 40863 (2017)50 L Yang et al solveME Fast and reliable solution of nonlinear ME models BMC Bi-

oinf 17 391 (2016)51 J D Orth et al A comprehensive genome-scale reconstruction of Escherichia coli

metabolismndash2011 Mol Syst Biol 7 535 (2011)52 I Schomburg et al BRENDA the enzyme database Updates and major new devel-

opments Nucleic Acids Res 32 D431ndashD433 (2004)

23190 | wwwpnasorgcgidoi101073pnas2001562117 Heckmann et al

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