Article

Adaptive Genetic Robustness of Escherichia coliMetabolic FluxesWei-Chin Ho1 and Jianzhi Zhang1

1Department of Ecology and Evolutionary Biology University of Michigan Ann Arbor

Corresponding author E-mail jianzhiumichedu

Associate editor Meredith Yeager

Abstract

Genetic robustness refers to phenotypic invariance in the face of mutation and is a common characteristic of life but itsevolutionary origin is highly controversial Genetic robustness could be an intrinsic property of biological systems a resultof direct natural selection or a byproduct of selection for environmental robustness To differentiate among thesehypotheses we analyze the metabolic network of Escherichia coli and comparable functional random networksTreating the flux of each reaction as a trait and computationally predicting trait values upon mutations or environmentalshifts we discover that 1) genetic robustness is greater for the actual network than the random networks 2) the geneticrobustness of a trait increases with trait importance and this correlation is stronger in the actual network than in therandom networks and 3) the above result holds even after the control of environmental robustness These findingsdemonstrate an adaptive origin of genetic robustness consistent with the theoretical prediction that under certainconditions direct selection is sufficiently powerful to promote genetic robustness in cellular organisms

Key words environmental robustness metabolic network flux balance analysis evolution natural selection

IntroductionGenetic robustness also known as genetic canalization refersto the ability of a biological system to maintain phenotypicinvariance upon mutation Genetic robustness has been re-ported in many organisms (Rutherford and Lindquist 1998Fares et al 2002 Ciliberti et al 2007 Ho and Zhang 2014 Yanget al 2014) at multiple levels of biological organization(Wagner 2005) and is an important characteristic of lifeThe evolutionary origin of genetic robustness however iscontroversial with three competing hypotheses (de Visseret al 2003 Felix and Barkoulas 2015) The adaptation hypoth-esis states that genetic robustness results from direct positiveselection because mechanisms reducing the phenotypic ef-fects of mutations are favored due to the overall deleteriousnature of mutations (Waddington 1942) Although this hy-pothesis has been supported in digital organisms and viruses(Wilke et al 2001 Sanjuan et al 2007) its validity in cellularorganisms is debated The congruence hypothesis posits thatgenetic robustness is a byproduct of selection for environmen-tal robustness which is the ability to maintain phenotypicinvariance upon environmental perturbations (Meiklejohnand Hartl 2002 de Visser et al 2003) The intrinsic propertyhypothesis asserts that genetic robustness is an intrinsic prop-erty of biological systems (Siegal and Bergman 2002) For ex-ample it was suggested that the genetic robustness oftranscriptional networks originates from the functional con-straint without selection for genetic robustness (Siegal andBergman 2002)

When one mutation affects multiple traits of differentlevels of importance to fitness robustness modifiers that pref-erentially buffer the mutational effects on relatively importanttraits have advantages over modifiers that equally buffer the

mutational effects on all traits (Ho and Zhang 2014)Consequently in the presence of selection for genetic robust-ness genetic robustness is expected to rise with trait impor-tance The population genetic theory of canalization alsopredicts that when trait importance is not too high (sothat there is still sufficient genetic variation) genetic robust-ness should rise with trait importance (Wagner et al 1997)Nevertheless this trend may also exist in the absence of se-lection for genetic robustness if there is selection for environ-mental robustness and if mechanisms for environmentalrobustness also confer genetic robustness (ie the congruencehypothesis) In contrast the intrinsic property hypothesisdoes not predict an increase in genetic robustness withtrait importance Thus examining the correlation betweengenetic robustness and trait importance allows distinguishingthe intrinsic property hypothesis from the other two hypoth-eses which can then be differentiated by computing the par-tial correlation after controlling environmental robustness Ifthe partial correlation remains significant the adaptation hy-pothesis is supported otherwise the congruence hypothesisis supported

Several previous studies tested the adaptation hypothesisusing the above strategy but obtained mixed results possiblybecause the number of traits examined is small the traits arenot randomly sampled the traits are not comparable withone another andor trait importance is not well defined(Stearns and Kawecki 1994 Stearns et al 1995 Houle 1998Proulx et al 2007) We recently applied the same strategy to220 yeast morphological traits and found evidence for theadaptation hypothesis (Ho and Zhang 2014) Although thetraits were plentiful unbiased and comparable the measureof trait importance was based on a correlation between the

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amount of phenotypic change in a trait and the fitnesschange upon gene deletion and is hence indirect (Ho andZhang 2014) Furthermore although the intrinsic propertyhypothesis does not predict a positive correlation betweengenetic robustness and trait importance it remains possiblethat some unknown intrinsic factors create this correlation inthe absence of selection for any robustness For example al-though some evidence for adaptive robustness of gene ex-pression levels was presented (Ho and Zhang 2014) theintrinsic property hypothesis could not be completely ex-cluded Thus it is desirable to test the adaptation hypothesisin a system where direct measures of trait importance areavailable and intrinsic properties can be explicitly scrutinized

To this end we take advantage of the well-developedmathematical analysis of metabolic networks of the modelprokaryote Escherichia coli We treat the flux of each reac-tion in a metabolic network as a trait and use flux balanceanalysis (FBA) (Orth et al 2010) to measure trait impor-tance We then use the method of minimization of meta-bolic adjustment (MOMA) (Segre et al 2002) to quantifyphenotypic alteration upon mutation or environmentalperturbation We compare our findings from the real net-work with those from comparable functional random net-works Our results provide unambiguous computationalevidence for direct selection for the genetic robustness ofmetabolic fluxes in E coli We focus on reaction robustnessrather than fitness robustness in this study because theexistence of multiple reactions allows analyzing the correla-tion between trait importance and genetic robustnesswhich is critical to our differentiation among the hypothesesof adaptation congruence and intrinsic property

Results

Traits and Trait Importance in Metabolic Networks

FBA is a powerful mathematical tool for metabolic networkanalysis Under the steady state assumption FBA maximizesthe biomass production rate (ie cellular fitness) by simulta-neously balancing all metabolic fluxes under a set of fluxconstraints and a given nutritional environment allowingthe prediction of all fluxes as well as the fitness (Orth et al2010) FBA predictions for model organisms such as the bac-terium E coli have been extensively validated experimentally(Ibarra et al 2002 Fong and Palsson 2004 Lewis et al 2010)and have thus been widely used in the study of genotypendashenvironmentndashphenotype relationships (He et al 2010Costenoble et al 2011 Barve et al 2012 Harcombe et al2013 Bordbar et al 2014)

We first applied FBA to the E coli iAF1260 metabolicmodel (Feist et al 2007) under the ldquoglucose environmentrdquowhere the only carbon source is glucose Excluding immutablereactions such as simple diffusions we obtained the wild-typefitness as well as the wild-type fluxes of 362 reactions thathave nonzero fluxes Unless otherwise noted we focused onnonzero flux reactions

We then simulated mutations that caused loss of enzymefunction by setting the flux of the corresponding reaction to0 We used MOMA (Segre et al 2002) to predict the new

fluxes of all other reactions in the network and the fitness ofthe mutant relative to that of the wild type (f) In addition tosatisfying all the constraints in FBA MOMA predicts each fluxand the fitness by minimizing the sum of the squared changeof each flux from its wild-type value over all reactions basedon the premise that the metabolic network undergoes min-imal flux redistribution upon mutation MOMA has beenshown to outperform FBA in predicting fluxes and fitnessupon mutation (Segre et al 2002) After individually con-straining the 362 fluxes to 0 we found that the frequencydistribution of mutant fitness is U-shaped (supplementary figS1A Supplementary Material online) as was previously found(Wloch et al 2001 Sanjuan et al 2004 Wang and Zhang2009a) Note that some f values are extremely small (seesupplementary fig S1B Supplementary Material onlinewhere the distribution of f is plotted in log10 scale) We con-sidered f values lower than 104 to be effectively 0 and re-garded the corresponding reaction as essential By thisdefinition 257 reactions are essential while the remaining105 are nonessential For each nonessential reaction we quan-tified its importance by s = 1f In other words the greaterthe drop in fitness upon the block of a reaction the moreimportant the reaction is

Flux Alteration upon Mutation Correlates withFitness Reduction

The adaptation hypothesis of genetic robustness presumesthat phenotypic changes from the wild type are deleteriousAlthough this presumption appears reasonable and has beenused in various simulation studies (Clark 1991 Rausher 2013)its validity has not been empirically confirmed for the fluxtraits examined here To confirm this presumption for eachof the 105 nonessential reactions we imposed a series of fluxconstraint and used MOMA to estimate the resultant fitnessThat is we reduced the maximal allowed flux of a focal reac-tion by a fraction F where F = 005 010 015 and 1For example if the flux of the focal reaction equals v0 in thewild type its new flux cannot exceed 095v0 when F = 005Consistent with the expected behavior of constraint-basedmetabolic modeling the fitness decreases as F increasesfor each of the 105 nonessential reactions tested (blue linesin fig 1A) The same pattern was observed when essentialreactions were examined (red lines in fig 1A) To test thepresumption that flux alterations from the wild-type valuesare deleterious we examined if the negative correlation be-tween the flux alteration of a focal reaction and fitness existseven when mutations occur to other reactions (ie whennonfocal reactions are constrained) Let k(i) be the fractionalflux change for a nonessential reaction k in a mutant in whichthe flux of reaction i is constrained by F relative to that inthe wild type (see Materials and Methods) For example letk be the reaction PFK (phosphofructokinase) which convertsfructose 6-phosphate to fructose 16-bisphosphate in glycol-ysis When individually constraining all 362 reactions by F =05 we observed that the resultant k(i) and fitness f(i) arenegatively correlated (Spearmanrsquos r=0562 Plt 10300 fig1B) That is no matter which reaction is constrained the

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FIG 1 Changes in metabolic reaction fluxes from the wild-type levels predict fitness decreases (A) FBA-predicted fitness decreases with the rise in theextent to which the flux of a reaction is constrained (F) Each line represents a series of constraints imposed on the flux of one reaction (B) Fitness (f)is negatively correlated with the fractional flux change () for the focal reaction PFK upon the constraining of another reaction at F = 50 Each dotrepresents the result from constraining one reaction (C) Frequency distribution among nonessential focal reactions of Spearmanrsquos correlation coef-ficient (r) between and f under F = 50 (D) Box plot of r between and f at various F In each box plot the lower edge and upper edge of a boxrepresent the first (q1) and third quartiles (q3) respectively The horizontal line inside the box indicates the median (md) The whiskers extend to themost extreme values inside inner fences md 15(q3 q1) The values outside the inner fences (outliers) are plotted by plus signs

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more PFK changes in flux from the wild-type level the lowerthe fitness This result is not unique to PFK but is found foreach nonessential reaction k examined (fig 1C)

Moreover the above finding is not limited to F = 05 Wecalculated r between k(i) and f(i) for each k at every level ofF lt 06 because constraining some essential reactions by60 is lethal (fig 1A) For all F values considered and all k allr values except three are negative (fig 1D) Note that thesethree positive r values occurred under low F values wherethe flux alterations tend to be small and the correlation mea-sures tend to be noisy After we controlled for multiple testingby the conservative Bonferroni correction 989 of the neg-ative r values are significant at the 5 level while none of thepositive r values are significant Together these results sup-port the premise that flux changes from their wild-type levelsare generally deleterious In other words flux invariance uponmutation is beneficial For subsequent analyses we used onlyF = 05 to reduce the computational demand

Genetic Robustness of Escherichia coli Reactions IsSignificantly Higher than Those of Random Networks

Let G be the fractional flux change of a focal reaction from itswild-type level upon a mutation where the subscript Gstands for genetic perturbation We use G to denote themean of G across all mutants in which a nonzero flux reac-tion is constrained by F = 05 We then calculated G themean G across all nonzero flux focal reactions The smallerthe G the greater the average genetic robustness of meta-bolic fluxes We found G to be 0302 for E coli To examine ifE coli metabolic fluxes are more robust to mutation thanexpected by chance we generated 500 random metabolicnetworks that have not been subject to selection for robust-ness and compared them with the E coli metabolic networkThese random networks were generated by the previouslypublished method (Rodrigues and Wagner 2009 Barve andWagner 2013) in which the reactions in the E coli network

were replaced with those randomly picked from the union ofall known metabolic reactions of all organisms one at a timeunder the condition that the network always has nonzerofitness under the glucose environment All these randomnetworks have the same number of reactions as the E colinetwork On average only 363 of E coli reactions allowedfor swapping appeared in a random network This level ofreaction overlap presumably reflects the constraint from theshared function between the E coli network and the randomnetworks We calculated Gfor each of the 500 random net-works after excluding lethal mutations under F = 05 Wefound that only 3 of the 500 random networks have a Gsmaller than that of E coli (fig 2A) indicating that theaverage genetic robustness of metabolic fluxes is significantlygreater in E coli than in comparable random networks (P =0006)

Environmental Robustness of Escherichia coliReactions Is Only Marginally Higher thanThose of Random Networks

We similarly studied environmental robustness Let E be thefractional flux change of a reaction upon an environmentalshift from its level under the glucose environment where thesubscript E stands for environmental perturbation We use E

to denote the mean of E across many environmentalchanges We then calculated E the mean E across all non-zero flux focal reactions The smaller the E the greater theaverage environmental robustness of metabolic fluxes Wesimulated 1000 nutritional environments by supplying arandom combination of 258 different carbon sources (seeMaterials and Methods) and used MOMA to calculate theflux of each reaction We found E to be 0018 for E coliInterestingly we found that 62 of the 500 random networkshave E values smaller than that of E coli (fig 2B) indicatingthat the average environmental robustness of E coli metabolic

FIG 2 Comparison of genetic and environmental robustness between Escherichia coli and random networks (A) Distribution of the average fractionalflux change across all focal reactions and mutants ( G) in 500 random networks The arrow indicates the corresponding value observed in E coli (B)Distribution of the average fractional flux change across all focal reactions and 1000 random nutritional environments ( E) in 500 random networksThe arrow indicates the corresponding value observed in E coli

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fluxes is only marginally significantly greater than the chanceexpectation (P = 0062)

The Intrinsic Property Hypothesis for GeneticRobustness Is Refuted

As mentioned selection for genetic robustness could result inhigher genetic robustness of more important traits To testthis prediction of the adaptation hypothesis we correlatedthe importance of a reaction (s) with its G We consideredonly nonessential reactions as focal reactions in this analysisbecause essential reactions all have s = 1 despite that differentessential reactions may be of different importance We founda strong negative correlation between s and G (Spearmanrsquosr=0859 P = 15 1031 fig 3A) as predicted by theadaptation hypothesis

To examine whether the above trend is truly adaptive orintrinsic we analyzed each of the 500 random networks thesame way we analyzed the E coli network and computed foreach random network Spearmanrsquos r between s and GBecause the number of nonessential reactions with nonzerofluxes varies among random networks r values from differentnetworks are not directly comparable We therefore convertedthe r values of the 500 random networks and the E coli net-work to standard z scores using Fisherrsquos transformation ofz frac14

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiethn 3THORN=106

p where n is the number of nonessential

reactions with nonzero fluxes in the network (Fieller et al1957) We found that the z score is more negative for the Ecoli network than any of the 500 random networks (Plt 0002fig 3B) We further confirmed that among 394 of the 500random networks whose fitness under the glucose environ-ment is higher than that of E coli none has a r that is morenegative than that of E coli Hence the negative correlationbetween s and G observed in E coli is beyond what the

intrinsic property hypothesis can explain natural selectionfor genetic or environmental robustness must be invoked

The Congruence Hypothesis for GeneticRobustness Is Refuted

The congruence hypothesis makes three predictions Firstbecause the hypothesis asserts that environmental robust-ness results from direct selection E and s should be nega-tively correlated in E coli and the correlation should bestronger than what is exhibited in comparable random net-works Second because the hypothesis posits that geneticrobustness and environmental robustness are congruent G

and E should be positively correlated Finally and mostcritically because the hypothesis claims that genetic robust-ness is entirely a byproduct of selection for environmentalrobustness G should no longer correlate with s after thecontrol of E

We examined whether our data are consistent with theabove three predictions of the congruence hypothesisConsistent with the first prediction E is negatively correlatedwith s (r=0890 P = 55 1037 fig 4A) and the corre-lation is significantly stronger than those observed in the 500comparable random networks (Plt 0002 fig 4B) Consistentwith the second prediction we found G to be highly andpositively correlated with E (Spearmanrsquos r= 0911 P = 201041 fig 4C) But contrary to the third prediction the partialcorrelation between G and s after the control of E remainsnegative (Spearmanrsquos r=0252 P = 96 103) and issignificantly stronger than the corresponding values fromthe 500 random networks (P = 0020 fig 4D) Togetherthese results indicate that environmental robustness cannotfully explain genetic robustness In other words the congru-ence hypothesis for the origin of genetic robustness isrejected

FIG 3 The intrinsic hypothesis of genetic robustness is rejected (A) The average fractional flux change for a focal reaction among all mutants ( G)decreases with the rise in reaction importance (s) Each dot represents one focal reaction (B) Frequency distribution of the rank correlation (afterconversion to z) between Gand s in 500 random networks Arrow indicates the corresponding z observed in Escherichia coli

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Results under Single-Carbon-Source Environments

Environmental robustness should be measured under therelevant environments of the species Because of the paucityof such information for E coli in the above analyses we ap-plied 1000 random nutritional environments by using differ-ent combinations of carbon sources which may have resultedin a less reliable estimate of environmental robustness Toexamine the robustness of our results we also used all possi-ble single-carbon-source environments to quantify environ-mental robustness Under the single-carbon-sourceenvironments we found the new E to be 053 muchlarger than the previous E (fig 2B) and G (fig 2A) suggest-ing that on average the single-carbon-source environmentsrepresent severer challenges to E coli than the 1000 randomnutritional environments or flux constraints of F = 05 do

When applying the same analysis using single-carbon-sourceenvironments we found all major results to remain qualita-tively unchanged (fig 5) Because the single-carbon-sourceenvironments are the most extreme environments in termsof carbon source availability and represent all carbon sourcechallenges this finding suggests that our conclusions arerobust to the nutritional environments used and that theresult in figure 4D is not an artifact of much smaller E

than G

Environmental Robustness as a Side Effect of GeneticRobustness

Although E is only marginally significantly smaller in Ecoli than in the random networks (fig 2B) s and E arestrongly correlated in E coli (fig 4A) and this correlation is

FIG 4 The congruence hypothesis of genetic robustness is rejected (A) The average fractional flux change for a focal reaction among all 1000environments examined ( E) decreases with the rise in reaction importance (s) Each dot represents a focal reaction (B) Frequency distribution of therank correlation (after conversion to z) between E and s in 500 random networks Arrow indicates the corresponding z observed in Escherichia coli (C)Average fractional flux change for a focal reaction on mutation and that on environmental change is strongly correlated Each dot represents a focalreaction (D) Frequency distribution of the rank correlation (after conversion to z) between G and s after the control of E among the 500 randomnetworks Arrow indicates the corresponding z observed in E coli

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stronger than that in any of the 500 random networks (fig4B) To examine whether the correlation between s and E is a byproduct of the adaptive genetic robustness weexamined the partial correlation between s and E afterthe control of G Although this partial correlation is stillsignificant (r=0511 P = 28 108) it is no longersignificantly stronger in the E coli network than in therandom networks (P = 0060 supplementary fig S2ASupplementary Material online) This is also true underthe single-carbon-source environments (P = 039 supple-mentary fig S2B Supplementary Material online) Theseresults coupled with those in figure 4 suggest that theenvironmental robustness of E coli metabolic fluxes islikely a byproduct of the adaptive genetic robustness

Capacitor Reactions for Genetic Robustness ofMetabolic Fluxes

What is the genetic mechanism of the genetic robustness ofmetabolic fluxes One approach to this question is to identifyreactions whose removal reduces the genetic robustnessSeveral previous studies used this approach to identify theso-called ldquocapacitorrdquo genes which buffer genetic or environ-mental perturbations (Rutherford and Lindquist 1998 Levyand Siegal 2008 Takahashi 2013) We measured G thedifference in G caused by the removal of an nonessentialreaction The more positive G is the larger the contribu-tion of the removed reaction to the genetic robustness ofmetabolic fluxes To make the comparison fair we only con-sidered 96 reactions whose removal does not alter E coli

FIG 5 Confirmation of results using single-carbon-source environments (A) The average fractional flux change for a focal reaction among 257 single-carbon-source environments examined ( E) decreases with the rise in reaction importance (s) Each dot represents a focal reaction (B) Frequencydistribution of the rank correlation (after conversion to z) between E and s in 500 random networks Arrow indicates the corresponding z observed inEscherichia coli (C) Average fractional flux change for a focal reaction on mutation (G) and that on environmental change ( E) is strongly correlatedEach dot represents a focal reaction (D) Frequency distribution of the rank correlation (after conversion to z) between G and s after the control of E

among the 500 random networks Arrow indicates the corresponding z observed in E coli

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viability for each genetic perturbation considered We foundthat G is positive in all 96 cases (fig 6A) The top 10 ofthe reactions in terms of the associated G values aremarked in figure 6A and these reactions contribute mostto the genetic robustness of E coli metabolic fluxes

It is of particular interest to identify those reactions whoseremoval reduces the strength of the negative correlation be-tween s and G (ie renders r more positive or r larger)Figure 6B shows the frequency distribution of r for thesame 96 reaction removals with those 10 of the reactionshaving the largest r marked Six genes are overlapped be-tween the marked genes in figure 6A and B (marked blue)They are FUM (fumerate) SUCDi (succinate dehydrogenase)PSP_L (phosphoserine phosphatase) PSERT (phosphoserinetransaminase) PGCD (phosphoglycerate dehydrogenase)and PPC (phosphoenolpyruvate carboxylase) FUM andSUCDi are part of the tricarboxylic acid (TCA) cycle whilePSP_L PSERT and PGCD appear in serine anabolism and areclosely related to some metabolites of the TCA cycle (fig 6C)In addition PPC is an anaplerotic reaction replenishing me-tabolites in the TCA cycle that are largely consumed by anab-olism (Nelson and Cox 2008) These observations suggest thebiological importance of the TCA cycle for the genetic robust-ness of E colirsquos metabolic fluxes

Because of the central role of the TCA cycle in aerobicmetabolism one wonders whether the six ldquocapacitorrdquo reac-tions simply reflect an intrinsic property of metabolic net-works We found that these reactions exist in 24 (PSP_L) to39 (FUM) of the 500 random networks examined We quan-tified the contributions of these reactions to the genetic ro-bustness of the random networks by measuring G andr as was conducted for the E coli network Under the samecriteria used for examining the E coli network the number ofusable random networks reduced tolt 5 for three reactions inserine metabolism (PSP_L PSERT and PGCD) and thuscannot be evaluated with any statistical meaning For theother three reactions (FUM PPC and SUCDi) we foundthat G and r are smaller in random networks than inE coli (fig 7) suggesting that at least these three capacitorreactions indeed contribute to genetic robustness beyond therandom expectation

DiscussionSeveral previous studies revealed the genetic robustness ofmetabolic networks by treating the viability as a trait(Edwards and Palsson 2000 Samal et al 2010) but thesestudies did not and could not resolve the evolutionaryorigin of the observed genetic robustness In this work wefirst demonstrated that E coli metabolic fluxes are robust tomutation We then showed that neither the intrinsic propertyhypothesis nor the congruence hypothesis adequately ex-plains the origin of the observed genetic robustness support-ing the hypothesis that direct selection underlies geneticrobustness Our study has several caveats that are worth dis-cussion First FBA and MOMA predictions of fitness and fluxcontain errors In particular MOMA minimizes the sum ofsquared flux changes on mutation or environmental pertur-bation and thus may underestimate actual flux changes

However because our conclusion is based on the comparisonbetween real and random networks that are subject to thesame analyses these errors are not expected to bias our con-clusion although stochastic errors may have reduced the sta-tistical power of our comparison and made our conclusionconservative Second under MOMArsquos criteria large wild-typefluxes are expected to have bigger changes which could biasour results because reaction importance and flux are posi-tively correlated (Spearmanrsquos r= 0626 P = 87 1013)However this bias is presumably removed by using fractionalflux changes in calculating G and E Furthermore the com-parison between the real and random networks shouldremove the potential impact of any remaining bias on ourconclusion Third we mimicked mutation by individuallyconstraining metabolic fluxes by a certain fraction (F)Real mutations of course occur in genes rather than reactionsBecause one gene may affect multiple reactions and one re-action may be catalyzed by multiple isozymes or an enzymemade up of multiple peptides the relationship between genesand reactions is not always one-to-one Nevertheless muta-tional effects on metabolism are usually manifested as differ-ent degrees of flux constraints A mutation may occasionallylead to the gain of a new reaction or rewiring of the metabolicnetwork These possibilities are ignored in our estimate ofgenetic robustness because they are much less frequentthan mutations that result in flux constraints Mutationsmay also lead to a loosened flux constraint which could in-crease rather than decrease fitness These mutations are notconsidered because genetic robustness is about buffering del-eterious mutations and because advantageous mutations areorders of magnitude less common than deleteriousmutations

The intrinsic property hypothesis positing that geneticrobustness is an intrinsic property that arises without selec-tion for robustness was put forward based on observationsmade in simulations of regulatory network evolution (Siegaland Bergman 2002) Interestingly we found that the correla-tion between s and G is significantly negative for 980 ofthe random metabolic networks (nominal Plt 005) suggest-ing that intrinsic origins of a certain degree of genetic robust-ness may be quite common Nonetheless the observedgenetic robustness of E coli metabolic fluxes is well beyondthe intrinsic level (fig 3A) and hence must involve selectionIn this sense genetic robustness may often have both intrinsicand adaptive origins

Similar to genetic robustness the correlation between sand E is significantly negative for 996 of the random met-abolic networks suggesting that environmental robustnesscould arise as an intrinsic property Additional evidence (sup-plementary fig S2 Supplementary Material online) howeversuggests that the environmental robustness of E coli meta-bolic fluxes is likely a side effect of selection for genetic ro-bustness contrary to the congruence hypothesis that geneticrobustness is a byproduct of selection for environmental ro-bustness The congruence hypothesis was proposed becauseenvironmental robustness was thought to be subject tostronger selection than was genetic robustness (Wagneret al 1997 Meiklejohn and Hartl 2002) based on the report

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FIG 6 Removing reactions from the Escherichia coli metabolic network affects how it behaves under genetic perturbations (A) Frequency distributionof G caused by the removal of one of the 96 reactions examined (B) Frequency distribution of r(s G) caused by the removal of one of the 96reactions examined In (A) and (B) reaction names are shown for those in the top 10 of the distributions with the six common reactions in the top10 sets of the two panels marked blue (C) Part of the E coli metabolic network containing the six capacitor reactions The six capacitor reactions aremarked blue The abbreviations of reactions and metabolites follow Feist et al (2007)

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that phenotypic variation caused by environmental pertur-bation is much larger than that caused by mutation (Lynch1988) However this observation may be a consequence ofhigher genetic robustness than environmental robustness in-stead of a cause for stronger selection for environmental ro-bustness than genetic robustness To our knowledge noexperiment has been conducted to differentiate betweenthese two scenarios Consequently whether environmentalrobustness is subject to stronger or weaker selection thangenetic robustness cannot be predicted theoretically

Although we identified capacitor reactions that make rel-atively large contributions to the adaptive genetic robustnessof E colirsquos metabolic fluxes it is worth discussing other pos-sible mechanisms First chaperons such as GroEL in bacteria(Fares et al 2002) and Hsp90 in Drosophila (Rutherford andLindquist 1998) are known to provide genetic and environ-mental robustness by aiding protein folding But the geneticrobustness revealed here is presumably due to somesystemic properties because our analysis does not involvestructurendashfunction relationship of individual proteinsSecond at the network function level increasing thenumber of regulations was shown to enhance the geneticrobustness of a simulated regulatory network (Siegal andBergman 2002) and the power law distribution of node

connectivity was suggested to enhance the metabolic net-work robustness (Jeong et al 2000) However these resultsare not directly applicable to our study because we focus onindividual fluxes rather than the entire network function Forinstance we found no significant correlation between thenumber of reactions that are directly connected to a focalreaction and G of the focal reaction (r=0014 P = 079)Furthermore the E coli network and the random networkshave no significant difference in the number of reactions thatan average reaction is directly connected to although the Ecoli network has a lower G and a stronger correlation be-tween s and G than those of the random networks (supple-mentary fig S3 Supplementary Material online) Third intheory functional redundancy can improve genetic robust-ness Although reactions with various degrees of functionalredundancy are common in the metabolic networks of E colitheir potential backup role is not needed to explain theirevolutionary maintenance (Wang and Zhang 2009a) Inother words functionally redundant reactions are unlikelyto be the primary basis of the observed adaptive genetic ro-bustness Fourth it is known that the flux of a linear meta-bolic pathway is intrinsically robust to concentration changesof the enzymes catalyzing the reactions in the pathway andthat the robustness increases with the pathway length

FIG 7 Removing capacitor reactions does not affect the genetic robustness in random networks as much as in Escherichia coli (A) Frequencydistribution of G in 46 analyzed random networks upon removal of FUM (B) Frequency distribution of r(s G) in 46 analyzed random networksupon removal of FUM (C) Frequency distribution of G in 15 analyzed random networks upon removal of PPC (D) Frequency distribution of r(sG) in 15 analyzed random networks upon removal of PPC (E) Frequency distribution of G in five analyzed random networks upon removal ofSUCDi (F) Frequency distribution of r(s G) in five analyzed random networks upon removal of SUCDi

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(Kacser and Burns 1981 Wang and Zhang 2011) So in prin-ciple natural selection could act on the length of a linearpathway to increase the genetic robustness of its constituentreactions However this mechanism is difficult to test empir-ically because pathways are not easily discernable in a com-plex network (Wang and Zhang 2011)

The present finding of direct selection for genetic robust-ness of E coli metabolic fluxes is consistent with our previousfindings in 220 yeast morphological traits and over 3000 geneexpression traits (Ho and Zhang 2014) suggesting that adap-tive originations of genetic robustness may be widespreadamong different classes of phenotypes These empirical resultssupport the theoretical prediction that under certain condi-tions direct selection is sufficiently powerful to promote ge-netic robustness in cellular organisms (Wagner et al 1997 Hoand Zhang 2014) Our finding not only answers the long-stranding question on the origin of genetic robustness butalso has other implications For instance one important ques-tion in the study of the genotypendashphenotype relationship iswhy different traits are affected by mutations to differentdegrees Our finding provides one explanation that becauseof adaptive selection for genetic robustness modifiers evolveto preferentially buffer the mutational effect on more impor-tant traits In other words the adaptive evolution of geneticrobustness may result in rewiring of the genotypendashphenotypemap and impact the evolutionary trajectory

Materials and Methods

Metabolic Models

We used E coli metabolic network model iAF1260 (Feist et al2007) which includes 2381 reactions and 1039 metabolitesAmong all reactions 2082 are metabolic reactions and 299are exchange reactions allowing the uptake of nutrients fromthe environment The SMBL file of the iAF1260 model wasdownloaded from BiGG (Schellenberger et al 2010) andparsed by COBRA (Becker et al 2007) We chose iAF1260because it outperforms other E coli metabolic models in pre-dicting gene essentiality and other properties (Feist et al2007)

Flux Balance Analysis

Briefly under the steady state assumption FBA formulates alinear programing problem to determine the flux of eachreaction to maximize the production of biomass (Orthet al 2010) Mathematically the objective is to maximizethe flux of the biomass reaction which describes the relativecontributions of various metabolites to the cellular biomassunder the constraints of Sv = 0 and a v b Here v is avector of reaction fluxes S is a matrix describing the stoichio-metric relationships among metabolites in each reaction a isa vector describing the lower bound of each flux and b is avector describing the upper bound of each flux

We used the default a and b in the metabolic model for allreactions to perform FBA This default setting represents theparameters for wild-type cells in a minimal medium withlimited glucose being the sole carbon source and somecommon inorganic compounds such as water oxygen

carbon dioxide and ammonium (Feist et al 2007) Notethat a reaction may be reversible or irreversible For a revers-ible metabolic reaction i the default i frac14 1 and i frac14 1whereas for a reversible metabolic reaction i the defaulti frac14 0 and i frac14 1 The optimized fluxes (v0) of the wild-type model under the glucose environment serve as thebaseline for computing fractional flux changes upon mu-tation or environmental shift

Under the glucose environment the E coli metabolicmodel has 387 nonzero flux reactions Note that some ofthem are simple diffusions of metabolites between differentcellular compartments Because these reactions do not havededicated enzymes and are not ldquomutablerdquo we excluded thesereactions from our data set of traits and used the remaining362 reactions

All linear programing problems were solved by the cplexlpfunction of the IBM ILOG CPLEX Optimizer with MATLABinterface

Minimization of Metabolic Adjustment

The objective of MOMA is to minimize (v v0)2 where v is avector of all reaction fluxes upon a genetic or environmentalperturbation whereas v0 is the corresponding vector for thewild type in the glucose environment described in the previ-ous section The two constraints for FBA are also applied inMOMA All quadratic programing problems were solved bythe cplexqp function of the IBM ILOG CPLEX Optimizer withMATLAB interface

When introducing genetic perturbation to a reaction wealtered its lower bound flux (a) and upper bound flux (b)according to its wild-type flux in the glucose environment (v0)and the fractional flux constraint (F) imposed but kept thea and b of other reactions unchanged For example con-straining a flux by 10 means that the flux of the reactioncannot exceed 90 the wild-type value Specifically if thisreaction is reversible we use 09 j v0 j v 09 j v0 j oth-erwise we use 0 v 09v0

When introducing environmental changes we followedthe approach previously published (Wang and Zhang2009b) to simulate random environments In iAF1260 thereare 258 exchange reactions for 258 carbon sources (Feist et al2007) In each simulation we randomly picked a number q foreach carbon source following an exponential distributionwith mean = 01 Here q is the probability that the carbonsource is available and the actual availability is determinedstochastically based on q Because in the default setting theuptake rate of glucose was set as 10 mmolgDW1h1 (Feistet al 2007) we used the same rate for all organic chemicalswhen they are available In addition in each simulatedrandom environment used we required that E coli and all500 random networks are viable In total 1000 such environ-ments were used The first second and third quartiles of thenumber of carbon sources in a random environment are 2440 and 705 respectively The first second and third quartilesof the number of random environments where a carbonsource exists are 160 180 and 200 respectively

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To examine the robustness of our results we also used 257single-carbon-source environments to mimic environmentalchanges from the glucose environment (fig 5) In this case wedid not require all 501 networks to be viable in an environ-ment because none of the 257 single-carbon-source environ-ments could support all 501 networks

Fractional Flux Change

After calculating the flux of a reaction v from MOMA weused the following formula to calculate fractional flux change() from the flux of the reaction in the wild type under theglucose environment (v0) To make increasing and decreasingfluxes comparable we normalize it in different ways depend-ing on whether v is larger or smaller than v0 A larger meanslarger difference

frac141 v=v0 v lt v0

1 v0=v v v0

(

Random Networks

We used a previously published approach to generate 500random networks (Rodrigues and Wagner 2009 Barve andWagner 2013) We first compiled ldquothe universe of reactionsrdquoby acquiring metabolic reactions listed in the REACTION sec-tion of the KEGG database (Kanehisa and Goto 2000) exceptwhen 1) a reaction appears in the E coli metabolic networkiAF1260 2) a reaction involves polymer subunits with uncer-tain number of atoms 3) a reaction involves glycans 4) areaction involves metabolites without information abouttheir structure and 5) a reaction is unbalanced in mass orcharge Then we combined these reactions with the meta-bolic reactions in iAF1260 (excluding transport reactions) Intotal there are 5001 reactions in the universe of reactionsWhen generating random networks we performed a randomwalk in the space of networks by starting from the E colimetabolic network iAF1260 and iteratively swapping betweena randomly picked reaction from the current network and arandomly picked reaction from the universe of reactions thatis different from any reaction in the current network underthe condition that the current network is viable in the glucoseenvironment Thus the random networks generated have thesame number of reactions as the E coli network but havebeen subject to neither selection for genetic robustness norselection for environmental robustness During the randomwalk we sampled a random network after every 5000 swapsuntil we acquired 500 random networks It is desirable for therandom walk to effectively travel in the whole space with nobias which can be shown by the saturation of the proportionof iAF1260 reactions that are absent from our sampledrandom networks in the time series (supplementary fig S4Supplementary Material online) Among the random net-works the first second and third quartiles of network con-nectivity defined by the number of reactions connecteddirectly with a metabolite averaged across all metabolitesare 334 336 and 338 respectively

Supplementary MaterialSupplementary figures S1ndashS4 are available at MolecularBiology and Evolution online (httpwwwmbeoxfordjour-nalsorg)

Acknowledgments

We thank Xinzhu Wei and Jian-Rong Yang for valuable com-ments This work was supported in part by US NationalInstitutes of Health grant GM103232 and US NationalScience Foundation grant MCB-1329578 to JZ

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Houle D 1998 How should we explain variation in the genetic varianceof traits Genetica 102ndash103241ndash253

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