Genomic Determinants of Protein Folding Thermodynamics in...

doi:10.1016/j.jmb.2004.08.086 J. Mol. Biol. (2004) 343, 1451–1466

Genomic Determinants of Protein FoldingThermodynamics in Prokaryotic Organisms

Ugo Bastolla1*, Andres Moya2, Enrique Viguera1,3 andRoeland C. H. J. van Ham1,4

1Centro de Astrobiologıa(CSIC-INTA), E-28850 Torrejonde Ardoz, Spain

2Institut Cavanilles deBiodiversitat i BiologiaEvolutiva, Universitat deValencia, E-46071 ValenciaSpain

3Departamento de BiologıaCelular y Genetica, Universidadde Malaga, E-29071 MalagaSpain

4Plant Research InternationalPO Box 16, 6700AAWageningen, The Netherlands

0022-2836/$ - see front matter q 2004 E

Abbreviations used: PDB, Proteinprincipal component analysis; KD,E-mail address of the correspond

[email protected]

Here we investigate how thermodynamic properties of orthologousproteins are influenced by the genomic environment in which they evolve.We performed a comparative computational study of 21 protein families in73 prokaryotic species and obtained the following main results. (i) Proteinstability with respect to the unfolded state and with respect to misfoldingare anticorrelated. There appears to be a trade-off between these twoproperties, which cannot be optimized simultaneously. (ii) Foldingthermodynamic parameters are strongly correlated with two genomicfeatures, genome size and GCC composition. In particular, the normalizedenergy gap, an indicator of folding efficiency in statistical mechanicalmodels of protein folding, is smaller in proteins of organisms with a smallgenome size and a compositional bias towards ACT. Such genomicfeatures are characteristic for bacteria with an intracellular lifestyle. Weinterpret these correlations in light of mutation pressure and naturalselection. A mutational bias toward ACTat the DNA level translates into amutational bias toward more hydrophobic (and in general moreinteractive) proteins, a consequence of the structure of the genetic code.Increased hydrophobicity renders proteins more stable against unfoldingbut less stable against misfolding. Proteins with high hydrophobicity andlow stability against misfolding occur in organisms with reduced genomes,like obligate intracellular bacteria. We argue that they are fixed becausethese organisms experience weaker purifying selection due to their smalleffective population sizes. This interpretation is supported by theobservation of a high expression level of chaperones in these bacteria.Our results indicate that the mutational spectrum of a genome andthe strength of selection significantly influence protein folding thermo-dynamics.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: protein folding; molecular evolution; orthologous proteins;intracellular bacteria; mutational bias
*Corresponding author
Introduction

Orthologous proteins expressed in differentorganisms share similar structure and function,but how similar are their thermodynamic proper-ties? In recent years, experimental, computationaland statistical studies have provided importantinsights into the process of protein folding.1 Themain focus in these studies has been the role of thenative state topology, which is known to be highly

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Data Bank; PCA,Kyte & Doolittle.ing author:

conserved through evolution. Comparatively littleattention has been paid to the question howsequence evolution influences the folding proper-ties of proteins. A better understanding of this issuewould be very useful both for testing theoriesof evolutionary change and for improving ourknowledge of protein folding. Genomic projectsnow provide a wealth of evolutionary data that canbe used to address this question.Ohta proposed that the major cause of molecular

evolution in naturally evolving populations is thefixation of slightly deleterious mutations in smallpopulations through random genetic drift.2 Bacteriawith obligatory endosymbiotic or parasitic lifestylein particular are subject to this process because

d.

1452 Genomic Determinants of Protein Folding

transmission bottlenecks during infection of newhosts result in small effective population sizes.Moreover, these bacteria reproduce asexually andlack genetic recombination, factors thought toexacerbate the process of fixation of deleteriousmutation.3 In this light, Moran compared thesubstitution rate of proteins of the aphid endosym-bionts of the species Buchnera aphidicola with thoseof its free-living relative Escherichia coli, and foundthat the former tend to evolve at a faster rate. Sheinterpreted this finding as evidence of the reducedefficacy of selection in endosymbiotic bacteria.4

Furthermore, Lambert & Moran5 showed througha computational analysis that 16 S rRNAs ofobligatory endosymbionts have accumulateddeleterious mutations, resulting in thermo-dynamically less stable molecules than those ofrelated free-living bacteria.

The recent study by Itoh et al.6 confirmed theacceleration of the substitution rate on a genomicscale in intracellular bacteria, but the authorsattributed this effect primarily to higher mutationrates. However, their study was based on a selectionof genes that yielded tree topologies in whichB. aphidicola forms a sister group with E. coli, withHaemophilus influenzae as an outgroup. Genessupporting the alternative topology withB. aphidicola as the outgroup were attributed tolateral gene transfer and excluded from theanalysis. A subsequent phylogenetic analysis byCanbaack et al.7 strongly suggested that the lattertree topology was in fact produced as an artifact oftree reconstruction methods, using genes with anincreased evolutionary rate and strong compo-sitional bias in the B. aphidicola lineage, and thatthe genes selected for the analysis by Itoh et al.6

were the ones most strongly constrained by naturalselection. Without this bias in the genes examined,the acceleration of the substitution rate in endo-symbiotic bacteria is best explained by relaxation ofpurifying selection and host level selection, sincegenes which are essential for the host metabolismevolve more slowly and appear to be moreconstrained.7

In a recent computational study, in theframework of the sequencing of the genome ofB. aphidicola from Baizongia pistacea,8 our groupfound that the normalized energy gap, a crucialindicator of efficient and fast folding, is system-atically lower for proteins encoded in obligateintracellular bacteria than for the orthologousproteins of their free-living relatives. In light ofthe statistical theory of protein folding, thisimplies that slow folding, possible misfolding andaggregation can dramatically reduce protein-folding efficiency in intracellular bacteria. Thatsuch problems may indeed occur is suggested bythe observation of exceptionally high expressionlevels of chaperones in these bacteria,9,10 proteinsthat help other proteins to fold properly and reducethe risk of misfolding. Furthermore, a recent studyhas demonstrated that over-expression of theGroELS chaperone produced a fitness recovery in

an experimental population of E. coli that hadexperienced accumulation of deleterious mutationsby passage through a series of populationalbottlenecks.11

Here, we provide a quantitative relationshipbetween genomic traits and protein thermo-dynamics. To address this issue, it is necessary toadopt a statistical approach and to examine a largesample of organisms and proteins. We extend ourprevious computational study to a total of 21protein families from 73 prokaryotic species, andperform thermodynamic calculations with a newmethod. Since not enough experimental data areavailable for addressing this problem, a compu-tational approach, like the one described here, cangive very valuable insights. We are confident thatour results will stimulate experimental verificationof the evolutionary relationships disclosed here.

The proteins were selected on the basis of thefollowing criteria: (i) family members must bepresent in intracellular bacteria; (ii) they must besoluble globular proteins; (iii) they must have atleast one experimentally known structure; and(iv) they cannot be too large in order to yieldreliable results. These requirements considerablyreduced the number of protein families that couldbe included. However, since each individual familyshowed the same correlations as observed for theentire set of proteins, further increasing the numberof proteins would not have modified our resultsqualitatively.

The computational method is based on a foldrecognition algorithm that uses an effective freeenergy function, without relying on sequencesimilarity. For most globular proteins considered,the effective free energy that we use takes its lowestvalue on the native structure, when this is availableor on structures of proteins homologous to thequery sequence. Moreover, the effective nativeenergy correlates strongly with the unfolding freeenergy measured experimentally for proteins withtwo-states folding thermodynamics. Therefore, thecorrelations presented here are expected to remainvalid if experimental quantities are used instead ofcomputational estimates.

To circumvent the limitations of predicted proteinfolding thermodynamics properties, we have alsocorrelated genomic and folding thermodynamicproperties with a selection of ten amino acidproperties related to hydrophobicity. The twoamino acid properties showing the strongestcorrelations, however, also take into account othertypes of interactions, besides the hydrophobiceffect. We therefore sometimes refer to the set often properties by the term “interactivity” to stressthat the hydrophobic effect plays a central role, butnot the only one. Amino acid properties are stronglycorrelated both with genomic properties and withexperimental and calculated thermodynamicproperties, thus supporting the correlationsdiscovered through our computational approach.

Previously, Gu et al.12 and D’Onofrio et al.13

considered the relationship between protein

Genomic Determinants of Protein Folding 1453

hydrophobicity, a proteomic property, and theGCC content of the corresponding gene, a genomicproperty (variation in GCC content is much largerbetween genomes than within a genome). Sincethese two studies produced contradicting results,we reconsidered this issue here, using severalhydrophobicity scales. Our main conclusion is thatthere is a positive correlation between proteinhydrophobicity (in a general sense) on one side,and GCC content and genome size on the other.

Figure 1. Average normalized energy gap versusaverage free energy per residue. Each point represents aprokaryotic species.

Results

Fold recognition

For 94% of the data set (908 proteins out of 965)one homologous protein was recognized as the bestscoring model, even when sequence identitybetween target and template was as low as 15%.The remaining 6% of proteins were discarded fromthe analysis. For these proteins, at least onehomologous model obtained an effective energyvery close to the one of the best scoring model, sothat the normalized energy gap a was extremelysmall. The discarded proteins mostly belonged toone offive families (AckA; Ddl, Dyr, Efts and RnpA)and to organisms characterized by a small value ofthe normalized energy gap a. Therefore, theirinclusion in the statistics would have made theaverage normalized energy gap for these specieseven smaller, thus strengthening the observedcorrelations.

Our alignments compared favorably with thosestored in the PFAM database of aligned proteinfamilies,14 in the sense that the sequence identitiescorrelated very strongly with those obtained fromthe PFAM alignments and in several cases evensurpassed these.

Correlations of protein thermodynamicparameters

We have characterized protein folding thermo-dynamics through two variables: the unfolding freeenergy per residue, measuring stability with respectto the unfolded state, and the normalized energygap a, measuring stability with respect to misfoldedstates.

These two quantities are negatively correlated(RZK0.40, student-t K3.7, 71 degrees of freedom,P!5!10K4; Figure 1). A similar correlation wasfound in an analysis of a large database of non-redundant protein structures.15

Protein thermodynamics correlates withhydrophobicity

The correlation between unfolding free energyand the normalized energy gap was furtherexamined by considering a key property of aprotein sequence, the mean hydrophobicity. Morehydrophobic proteins tend to have larger unfolding

free energy (they are more stable with respect tounfolding), but also have a smaller energy gap(many alternative states have low effective freeenergy). A maximally hydrophobic protein wouldbehave like a homopolymer, with a vanishing freeenergy gap, and without a unique native state.Although hydrophobicity plays a central role in

the protein folding literature, there is no agreementon how to measure it. Hundreds of empiricalhydropathy scales have been proposed. We used aselection of eight hydropathy scales from theliterature plus two amino acid properties recentlystudied by one of us and co-workers,16 denoted byIH and CH, which correlate strongly with otherhydropathy scales. For each organism, we havecalculated the mean hydrophobicity of its proteins,using all ten scales, and correlated these withthermodynamic and genomic properties.For each hydropathy scale, the average hydro-

phobicity is positively correlated with the averageof the calculated unfolding free energy per residue,and negatively correlated with the predictednormalized energy gap (Table 1). Correlationsvary in extent, but not in sign, depending on thescale chosen. We found the weakest correlationfor the Kyte & Doolittle (KD) scale (correlationcoefficients RZ0.22,K0.37, respectively). This is notunexpected, given that KD is a hydropathy scalemainly used for identification of transmembranehelices that attributes small or even negative valuesto aromatic residues, which interact very strongly.The KD scale also correlates least strongly withgenomic properties (see below). The strongestcorrelations with protein folding thermodynamicproperties were found for the novel scales IH(RZ0.83, K0.68, respectively) and CH (RZ0.83,K0.72, respectively). In addition, this result is notunexpected, since the IH scale was derived from theenergy function that we used for computationalestimates, and the CH scale correlates very strongly

Table 1. Correlation coefficients of different hydrophobicity scales with genomic and proteomic properties

CH IH G98 FP AV MP WW R88 L76 KD

a K0.72 K0.68 K0.61 K0.52 K0.58 K0.45 K0.46 K0.39 K0.35 K0.37F/N 0.83 0.83 0.54 0.57 0.58 0.67 0.49 0.32 0.35 0.22GC12 K0.72 K0.59 K0.48 K0.42 K0.40 K0.32 K0.34 K0.32 K0.26 K0.14GC3 K0.56 K0.43 K0.39 K0.35 K0.30 K0.20 K0.25 K0.21 K0.20 K0.06Size K0.61 K0.55 K0.48 K0.42 K0.41 K0.38 K0.35 K0.27 K0.23 K0.16PC-1 K0.90 K0.83 K0.69 K0.67 K0.66 K0.61 K0.57 K0.47 K0.43 K0.33

With 73 organisms, a 0.05 significance level is achieved for jRjO0.20 and a 0.01 significance level for jRjO0.27. The variables consideredare: (1) normalized energy gap, a; (2) unfolding free energy per residue, F/N; GCC content at first and second (3) and third (4) codonposition; (5) genome size; (6) principal component coefficient, PC-1. Hydropathy scales are ranked according to the value of PC-1. Noticethat the scales that correlate more strongly with thermodynamic properties also tend to correlate more strongly with genomicproperties. The hydropathy scales considered are: (1) CH, Connectivity scale (U. Bastolla et al., unpublished results), (2) IH, Interactionscale (U. Bastolla et al., unpublished results), (3) G98, hydrophobic-polar classification;12 (4) FP, Fauchere & Pliska transfer freeenergies;68 (5) AV, average hydrophobicity scale;72 (6) MP, Manavalan, & Ponnuswamy;70 (7) WW,71 (8) R88, transfer free energiescalculated by Roseman;69 (9) L76, Levitt;66 (10) KD, Kyte & Doolittle.67


with it. More surprisingly, these two scales alsoshow the strongest correlations with genomicproperties like genome size and composition(see below).

For three out of ten scales (KD, R88, L76), thecorrelations were not significant unless the proper-ties of each protein were normalized with respect tothe representative sequence of each protein family.This normalization reduces the effect of proteintopology and chain length relative to the effect ofsequence changes.

The average thermodynamic parameters versusaverage hydrophobicities measured with IH para-meters are plotted in Figure 2. Each point representsone organism. Besides prokaryotic species, we alsoshow proteins from chloroplast and eukaryoticnuclear genomes. They show a similar pattern asproteins from prokaryotic genomes, except thatthe proteins from metazoans (Homo sapiens and

Figure 2. Average thermodynamic properties of pro-teins of different organisms as a function of the IHinteractivity of their sequences. The symbols fitted by thecontinuous line (decreasing with hydrophobicity) rep-resent the normalized energy gap, and the symbols fittedby the broken line (increasing with hydrophobicity)represent the unfolding free energy per residue. Thecorrelation coefficient is RZ0.83 between interactivityand calculated unfolding free energy and RZK0.68between interactivity and normalized energy gap.

Caenorabditis elegans) appear to be more stable thanexpected on the basis of the general trend. This isprobably an effect of the fact that the templates forstructural modeling were in this case mostly humanproteins, which increases the predicted stability.

Protein thermodynamics correlates withgenome size

Genome size was found to be strongly correlatedwith the average protein thermodynamic para-meters. It correlated positively with the normalizedenergy gap with correlation coefficient RZ0.65,P!10K6 (Figure 3) and negatively with the calcu-lated unfolding free energy per residue, RZK0.49,P!10K5. These correlations can be understoodthrough the negative correlation between genomesize and mean hydrophobicity (see below). Proteinsin smaller genomes, like those of intracellularbacteria, tend to be more hydrophobic and hencetend to have larger unfolding free energy (they aremore stable with respect to the unfolded state) andsmaller normalized energy gap (they are less stablewith respect to misfolded states). The lattercondition is expected to cause less efficient folding.

Results look qualitatively similar for each of the21 protein families which were included in the

Figure 3. Average of the normalized energy gap versusgenome size.


calculation of species averages. A different patternwas observed for the chaperone DnaK, which wasnot used for species averages. No correlationbetween thermodynamic and genomic propertieswas found for this protein. As mentioned above,chaperones buffer the effects of detrimentalmutations, and they appear to be important forthe maintenance of fitness in intracellular bacteria.The aberrant pattern for DnaK therefore reinforcesthe proposed scenario of folding problems forproteins from small bacterial genomes.

Compositional bias

In the analysis of GCC composition of genes,third codon positions and first plus second codonpositions were considered separately. The thirdcodon position is almost neutral with respect toselection at the protein level, although it can besubject to selection for optimal codon usage.16 Thisposition is thought to reflect mostly mutationalforces, at least in prokaryotic genomes.17,18 Asoriginally noticed by Sueoka,19 the GCC compo-sition of a gene strongly influences the amino acidcomposition of its coded protein. Bernardi &Bernardi were the first to notice that the GC contentat first and second position, GC12, is stronglycorrelated with the one at third position, GC3,

20

and both are correlated with the genomic GCCcontent.

The GCC content at third position, GC3, variedbroadly from 0.09 to 0.95 in the species examined. Incontrast, the GCC content and first plus secondcodon positions, GC12, only varied from 0.27 to 0.59,due to selection at the protein level. In our data set,the correlation coefficient between GC12 and GC3 isRZ0.87 (Figure 4), and both values are stronglycorrelated with the genomic GC content (correlationcoefficient RZ0.98 for GC3 and RZ0.93 for GC12).Similar results were reported by several authors,but we show the plot in Figure 4 in order to

Figure 4. GCC content at first and second (vertical)versus third (horizontal axis) codon position. The corre-lation coefficient is RZ0.87.

highlight that the GC12 versus GC3 curve is concavedownwards. This means that bacteria with low GC3

have a lower GC12 than would be expected fromextrapolation of the pattern of bacteria with highGC3. All of the former have obligatory intracellularlifestyles.Intracellular bacteria are characterized by a

strong compositional bias towards nucleotides Aand T and by reduced genomes. This association isquantitative. The GCC content correlates withgenome size, as previously observed by Moran.21

For the genomes considered here, the correlationcoefficient is RZ0.65, tZ7.3, P!10K6 (Figure 5).Genome size and GCC content appear to beuncorrelated in Archaea and thermophilicEubacteria, while they are significantly correlatedboth in free-living bacteria (RZ0.52, P!10K3) and,more strongly, in intracellular bacteria (RZ0.72,P!10K4).Consistently with the correlation between

genome size and composition, the GC3 was foundto be negatively correlated with the predictedfolding free energy per residue (RZK0.52,tZK5.15, P!10K5) and positively correlatedwith the normalized energy gap (RZ0.42, tZ3.9,P!10K3). For GC12, these correlations were evenstronger. RZK0.77 (tZK6.4, P!10K6) and RZ0.58(tZ6.1, P!10K6), respectively. This is explained bythe fact that first and particularly second codonposition affect the encoded amino acid much morethan the third codon position, whose changes areoften synonymous.

Genomic properties and hydrophobicity

We have reconsidered the relationship betweenprotein hydrophobicity and the GCC content of thecorresponding gene. Previous results were contra-dictory. Gu et al., using a simple classification ofamino acid residues in three classes from hydro-phobic to polar, showed that the GCC content of a

Figure 5. Genome size versus genomic GCC content.Intracellular bacteria cluster in the lower left corner of thisplot.

Figure 6. Mean protein hydrophobicity measured withthe scale CH versus genome size. Each point represents aprokaryotic species.


gene is negatively correlated with the hydrophobiccontent of the corresponding protein.12 In theirstudy, the G98 classification of amino acid residueswas used and each protein family was examinedseparately. D’Onofrio et al.13 came to the oppositeconclusion using the KD hydropathy scale andaveraging over sequences that corresponded todifferent protein families. Here, we correlatedaverage hydrophobicities with three genomicproperties: GC12, GC3 and genome size; weconsidered ten different hydrophobicity scales,and we averaged hydrophobicities of proteins ofthe same organism in two different ways.

In the first calculation, we averaged hydro-phobicities without normalizing them. This isanalogous to the procedure followed by D’Onofrioet al.13 We found significant (P!0.05) negativecorrelations between GC12 and hydrophobicity forsix hydrophobicity scales (CH, IH, WW, MP, FP,AV), non-significant negative correlation for threescales (R88, L76, G98) and a weak but significantpositive correlation for the scale KD. The latter wasused by D’Onofrio et al.,13 whose results are herequalitatively reproduced. The GC3 showed signifi-cant negative correlations only for three scales(CH, IH, WW) and significant positive correlationsfor the scale KD, while the genome size showedsignificant negative correlations for four scales(CH, IH, WW, MP) and no case of significantpositive correlations.

In the second calculation, hydrophobicities werenormalized before averaging, as explained inMaterials and Methods. By doing so, the between-genome differences due to variation in the foldcomposition are strongly reduced. This calculationis thus analogous to the work of Gu et al.,12 whoconsidered each protein family separately. Almostall hydrophobicity scales yielded highly significant(P!0.01) negative correlation with the GC12, asignificant but weaker correlation (P!0.05) withthe GC3, and a correlation of intermediate value(P!0.01) with the genome size. The only exceptionswere the L76 scale, which showed correlations onlyat the 5 % level, and the KD scale, which showednon-significant (but still negative) correlations. Thestrongest correlations were observed for the scalesCH (RZK0.72,K0.56 andK0.61 for GC12, GC3 andgenome size, respectively), IH (RZK0.59, K0.43and K0.55), G98 (RZK0.48, K0.39 andK0.48) andFP (RZK0.42, K0.35 and K0.42). It is interestingthat almost the same ranking is observed for thecorrelation between hydrophobicity and thermo-dynamic properties: the hydrophobicity scales thatcorrelate strongest with GCC content are also thosewhich correlate strongest with protein thermo-dynamic parameters.

The relationship between genome size andhydrophobicity, calculated using the novel scaleCH, is shown in Figure 6.

Results concerning normalized protein propertiesare summarized in Table 1. We conclude thatprotein hydrophobicity, as measured by nine ofthe ten scales considered, is negatively correlated

with both GCC content and genome size, but formost scales correlations are only significant whenprotein properties are normalized in order to reducetheir dependence on family-specific properties likelength and topology. The KD scale is the only onethat does not show significant correlations with anygenomic property even after averaging. The use ofthis scale, and the fact that proteins with differentlength and topology were averaged together,explains the apparent contradiction between ourresults and the results obtained by D’Onofrio et al.13

Sequence similarity

Sequence similarity between the protein exam-ined and the protein used as structural templateinfluenced positively the estimated protein stab-ility: it correlated positively with the energy gap(RZ0.55) and also, although not significantly, withthe unfolding free energy. Therefore, the reportednegative correlation between energy gap andunfolding free energy would become stronger ifwe correct for this artifact.

We observed a positive correlation betweengenome size and sequence similarity with the beststructural model. This is due to the fact that proteinsare mostly crystallized from a few model organ-isms, which happen to be free-living bacteria withlarge genomes. Very few proteins from pathogenicbacteria have been crystallized, and none fromendosymbionts. In this case, the extent of thecorrelation between genome size and energy gapwould be lower after correcting for sequencesimilarity. This artifact, however, does not affectthe hydrophobicity, which does not depend ontemplate structure, and only slightly affects theunfolding free energy. As explored hereafter, theextent of the artifact can be significantly reducedthrough principal component analysis (PCA).

Figure 7. First and second principal components.


Principal component analysis

The properties that we have described so farprovide a coherent quantitative characterization ofthe intracellular lifestyle. Intracellular bacteria arecharacterized by reduced genome size, AT richgenes, and hydrophobic (interactive) proteins withlarge unfolding free energy but a low normalizedenergy gap. These properties were studied togetherthrough PCA (see Table 2). The first principalcomponent obtained distinguished very effectivelybetween intracellular and free-living bacteria.Interesting outliers included Yersinia pestis andMycobacterium leprae, which are pathogens of recentorigin that still retain moderately large genomesand a high GCC content, and Fusobacteriumnucleatum, a bacterium that lives in dental plaqueand has a very strong compositional bias towardsACT. The first PC correlated strongly with genomicproperties (genome size, RZ0.81; GC3, RZ0.77;GC12, RZ0.88) and with proteomic properties(unfolding free energy, RZK0.75; normalizedenergy gap, RZ0.81; hydrophobicity or inter-activity, correlation ranging from RZK0.33 for theKD scale to RZK0.90 for the CH scale) Itscorrelation with the sequence similarity withthe representative sequence was much weaker(RZ0.39). The first principal component explained58 percent of the total variance.

By contrast, the second component correlatedstrongest with sequence similarity (RZ0.85), thenwith the effective free energy (RZ0.47) and thenormalized energy gap (RZ0.42), and did notsignificantly correlate with the remaining variables.Its value can therefore be interpreted as the excessof calculated stability, both for the free energy andfor the normalized energy gap, attributed toproteins with high similarity to the best model.The second component explained only 17% of thetotal variance, and it was particularly large in theclade of enterobacteria, since many of the proteinscrystallized are derived from E. coli (see Figure 7).Note that the endosymbiotic species B. aphidicolaand Wigglesworthia, which are closely related toE. coli, also have large value of the second principalcomponent. The stability of their proteins istherefore overestimated, and nevertheless they

Table 2. Matrix of correlation coefficients

a F/N Hydro

F/N K0.41Hydro K0.72 0.83Size 0.65 K0.49 K0.61GC12 0.58 K0.60 K0.72GC3 0.42 K0.47 K0.56Seq.id. 0.55 0.05 K0.35PC-1 0.81 K0.75 K0.90PC-2 0.42 0.47 0.06

The columns and rows represent three protein related quantities: nhydrophobicity (CH scale); three genomic quantities: genome size,content at third codon position (GC3); percent identity with the seq(PC-2) principal component of the correlation matrix. With 73 organisignificance level for jRjO0.27.

present the smallest predicted values of thenormalized energy gap.

Discussion

We have shown that the computational thermo-dynamic properties of orthologous prokaryoticproteins, sharing the same structure, function andevolutionary origin, but encoded in differentorganisms, are quantitatively correlated with twotraits of the genomes in which they evolved:genome size and the GCC content of its genes.

Computational approach

In this study, we calculated folding thermo-dynamic properties using an effective free energyfunction and a fold recognition algorithm. Thevalidity of our computational approach is demon-strated by a strong correlation between calculatedand experimental unfolding free energies for proteinsfoldingwith two-states thermodynamics (correlationcoefficientRZ0.95;U.B., unpublished results) and fora database of more than thousand mutants (corre-lation coefficient RZ0.65; U.B., unpublished results).The validity of the energy function is also supportedby its success as a scoring function in our foldrecognitionalgorithm.The structure of a homologous

size GC12 GC3 Seq.id.

0.650.61 0.890.33 0.27 0.180.81 0.88 0.77 0.390.07 K0.16 K0.21 0.85

ormalized energy gap a, folding free energy per residue F/N,GCC content at first and second codon position (GC12), GCCuence of the representative protein, and first (PC-1) and secondsms, a 0.05 significance level is achieved for jRjO0.20 and a 0.01


protein always appeared in the top three scores andgot highest scores in 94% of the cases, despite we didnot score sequence similarity. A result that furthersupports our computational analysis is the existenceof correlations between hydrophobicity and genomicproperties. These correlations do not rely on ourmethod for predicting folding thermodynamicproperties and thus constitute an independent lineof evidence for a correlation between genomic andproteomic properties.

As mentioned above, the similarity between thesequence of the target protein and the sequence of thebest structural template can influence the estimatedthermodynamic parameters. However, PCA showedthat the excess of stability attributed to proteins thatare very similar to their structural template onlycontributes to the second principal component. Sinceprincipal components are orthogonal, interpretationof the second component as the unwanted influenceof sequence similarity on estimated stability impliesthat the first component is largely free from this effect.The first component can thus safely be interpreted asa quantitative characterization of the intracellularlifestyle. Proteins from endosymbiotic enterobacteriapresent properties typical of intracellular organisms(largeunfolding free energy, small normalizedenergygap) despite their high similarity with templateproteins from E. coli.

The notion that hydrophobicity is one of themain forces in protein folding is a long-standingconcept22 and has been subject to intense exper-imental study.23 Mutational studies have pointedat the importance of hydrogen bonds for providingstability against unfolding, comparable to that of thehydrophobic effect.24 In this study, we did notexplicitly consider hydrogen-bonding. However,since orthologous proteins share very similar andoften identical secondary structure, differences instability between them rarely arise from differencesin the network of hydrogen bonds of their main-chains. Hydrogen bonds involving side-chains areimplicitly taken into account by our energy function.Electrostatic interactions are another essential sourceof stability for folded proteins that our energyfunction takes into account implicitly. Togetherwith other factors, they are thought to be crucial forthe thermostability of proteins in thermophilicorganisms.25–27 Interactions of aromatic ringsbetween themselves28,29 andwithpositively chargedresidues30–32 have also been proposed as an import-ant source of thermostability and can be effectivelyreproduced through our energy function.

Despite the importance of these energy terms,hydrophobicity provides the largest contribution toour calculated unfolding free energy and it providesa simple key for the interpretation of our results.Among the hydropathy scales used here, the largestexplanatory power for both genomic and proteomicproperties was displayed by the scales CH and IH.The IH scale was derived from our interactionmatrix, thus it is not a surprise that it correlatesvery strongly with computational estimates ofthermodynamic properties, but it is surprising

that this scale is also the second in the rank of thecorrelations with genomic properties. The CH scale,derived from the connectivity properties of aminoacid residues in solved crystal structures(U. Bastolla et al. unpublished results), correlatesstrongest both with genomic and with thermo-dynamic properties. Since this scale was obtainedindependently of the effective energy function, itgives strong independent support to the corre-lations highlighted here.

The KD scale shows the weakest correlation bothwith genomic and with thermodynamic properties.This scale attributes small or negative hydrophobi-city to aromatic amino acid residues (Phe, Trp, Tyr),which have some of the largest hydrophobicityvalues in other empirical scales. They have alsovery high values in the novel IH and CH scales,since they tend to form rather strong inter-residueinteractions and they tend to be very connected.Enhanced aromatic interactions have been found inproteins of thermophilic organisms.29 For thesereasons, the aromatic content is expected to corre-late strongly with folding thermodynamic proper-ties. Failure to attribute large values to hydrophobicamino acid residues explains the weak correlationbetween the KD scale and thermodynamic proper-ties. It also explains the weak correlation betweenthe KD scale and the ACT content, which isstrongly correlated with the aromatic content(PheZTTY, TyrZTAY, WZTGG).

Unfolding versus misfolding

In this study, we observed that the unfolding freeenergy per residue and the normalized energy gap,a computational measure of folding efficiency, arenegatively correlated. This implies that orthologousproteins that are more stable with respect tounfolding are less stable with respect to misfolding.We consider this an instance of frustration in proteinsequence space: natural selection for both thermo-dynamic properties acts in opposite directions, thusit cannot optimize both at the same time and has totrade-off between them.

At first sight this result seems counterintuitive,but it can easily be understood considering theeffect of hydrophobicity. Mean protein hydropho-bicity correlates positively with the calculatedunfolding free energy and negatively with thenormalized energy gap. The latter correlation isexpected, since a highly hydrophobic sequence willhave several compact conformations with effectiveenergies comparable to the native state. The limit ofa maximally hydrophobic sequence corresponds toa homopolymer, in which the normalized energygap shrinks to zero. No folding is expected in thislimit, also according to theory and simulation oflattice polymers.33,34 All the hydrophobicity scalesthat we considered are correlated with calculatedthermodynamic properties. For some scale thesecorrelations are so strong that they fully explain thenegative correlation between unfolding free energyand normalized energy gap.

† There are several reasons for this interpretation: First,selection for codon usage is only important for highlyexpressed proteins and large effective populations.Recent studies found extremely weak indications ofselection for codon usage in genes of B. aphidicola.54,73

Second, a recent study has attributed the differences incodon usage between bacterial species to genomicmutational bias.18 Third, the effect of codon usage on theGC3 is very reduced when averaging over all possiblecodons. Fourth, the strong correlation between the basecomposition at third codon positions and at first plussecond codon positions17,20 is hard to explain by selection,because selection at third positions acts on codon usagewhile at the other positions it acts on amino acid usage.This correlation is most simply explained by thehypothesis that base composition reflects the mutationalbias. Last, the GCC content at third codon positionscorrelates strongly with the GCC content at pseudogenesand intergenic spacers.


The role of the hydrophobic effect on the stabilityof the native state is demonstrated by severalexperimental studies.23 It has been recognizedonly more recently that hydrophobicity also affectsthe stability of misfolded states.

Intermediate states of protein folding can becharacterized as metastable, partially folded states.They may occur in the pathway between theunfolded and the native state (for instance, inter-mediate states where one domain is folded andanother one is not yet) or off-pathway, in which casethey act as kinetic traps that slow down the foldingprocess. Folding intermediates are not an intrinsiccharacteristic of a protein. Several experiments haveshown that mutations, as well as physico-chemicalchanges in the solvent, like pH and temperaturechanges, can stabilize or destabilize folding inter-mediates. Often, mutations stabilizing foldingintermediates also result in more hydrophobicsequences.35 Uversky,36 analyzing a large sampleof proteins with and without intermediate states,demonstrated that the existence of folding inter-mediates is strongly dependent on the content ofhydrophobic and charged amino acid residues inthe protein sequence. Intermediate states wereonly found in proteins with relatively high hydro-phobicity and low net charge.

The role of hydrophobicity in folding kinetics hasrecently been a subject of intense study. It has beenshown that non-native hydrophobic interactionsthat stabilize on-pathway intermediate states orfolding transition states can speed up the foldingrate considerably.37–40 This appears to be in quali-tative agreement with a simple theoretical modelthat demonstrates that a little increase in non-nativeinteractions can accelerate protein folding.41

However, a too large extent of non-native inter-actions will increase the ruggedness of the free-energy landscape, with the consequence of slowingdown folding and kinetically trapping the proteinin off-pathway conformations.41–43 In naturalproteins this extreme behavior is not observed,although off-pathway intermediates have beencharacterized for several proteins.44–48

Intermediate states may induce irreversibleaggregation, often mediated by hydrophobic inter-actions or by the formation of an amyloid betastructure.49,50 Molecular chaperones assist foldingin vivo by sequestrating proteins in misfolded andintermediate states, thus preventing aggregationand speeding up the folding process.51 Therefore,very hydrophobic globular proteins are expected toexperience problems of slow folding and aggrega-tion. Our results concerning the small value of thenormalized energy gap for very hydrophobicproteins strongly support this view. Consistentwith this is the observation of very high expressionof chaperones in insect endosymbionts,9,10 whoseproteins are characterized by very hydrophobicproteins with a very low normalized energy gap.

It is well known that natural proteins aremarginally stable, i.e. their unfolding free energyis of the order of kBT. Two explanations have been

proposed for this common feature. The first onestates that marginal stability is functionallyimportant because proteins need flexibility inorder to function. The other point of view assertsthat marginal stability is an unavoidable conse-quence of molecular evolution, with the selectiveadvantage of improved stability being balanced bythe mutational pressure.52 Our result does notdirectly apply to this debate, but it may suggestanother factor of the observed marginal stability:since we have shown that an improved stabilityagainst unfolding is often attained at the expense ofstability against misfolding, not only the mutationalpressure, but also negative selection againstmisfolding and potential aggregation problemsmight prevent protein sequences from reachingvery large unfolding free energies.

Genomic versus proteomic properties

The main result of this paper is that the normal-ized energy gap of homologous prokaryoticproteins is positively correlated with the genomesize and the GCC composition of the corres-ponding genes, whereas the unfolding free energyper residue is negatively correlated with bothgenomic properties. The present analysis confirmsour previous finding that the normalized energygap tends to be lower for proteins encoded inobligatory intracellular bacteria, whose proteins aretherefore expected to fold less efficiently thanproteins encoded in their free-living relatives.8

There are two complementary explanations of therelationship between protein thermodynamics andgenomic properties, based on mutational bias andon natural selection, respectively.

Mutational bias

Following Muto & Osawa,18 we interpret the GCC content at third codon positions as an indicator ofthe genomic mutational bias rather than of codonusage bias†. Due to the structure of the genetic code,a mutational bias towards ACT at the DNA level


translates into a mutational bias toward morehydrophobic residues at the protein level. Thisassociation is confirmed by the correlation betweenthe hydrophobicity of the translated protein and theACT content at first and second codon position.This is strong for several hydropathy scales andsignificant for all those we tested, with the onlyexception of the KD scale that attributes negative orlow hydrophobicity to aromatic residues.

Selection strength

For reduced genomes, genome size may beregarded as a quantitative characterization of theextent or age of the intracellular lifestyle of themicrobial organism. Bacteria that became intra-cellular recently, as was probably the case forY. pestis and M. leprae, have a larger genome thanbacteria that became obligatory intracellular muchlonger ago. The intracellular lifestyle implies areduced effective population size due to bottlenecksthat occur during transmission to new hosts.Therefore, the efficacy of selection is expected tobe reduced,2,3 particularly in asexual populationslacking effective recombination. The observedcorrelation between genome size and normalizedenergy gap is consistent with a weaker purifyingselection in intracellular bacteria. This interpret-ation is also consistent with a computational studyof the stability of the 16 S rRNA of aphid endo-symbionts5 and with the extremely high expressionlevel of chaperones observed in these bacteria.9,10

These two interpretations are not mutuallyexclusive. We believe that both of them have to beinvoked to explain the observed patterns. In fact,the influence of mutational bias on protein compo-sition ultimately depends on natural selection.

It has been observed in several studies that theamino acid usage is strongly influenced by genomicGCC content,19,20,50 and this, in the case ofendosymbionts of the genus Buchnera, has beenmainly attributed to mutational bias.54,55 Therelationship between mutational bias and aminoacid composition is best expressed in the scatterplot of GC12 versus GC3,

20 Figure 4. The linearcorrelation is quite strong, RZ0.87. Through GC12,the GC3 also influences hydrophobicity (the corre-lation coefficient goes from RZK0.20 to K0.56 fornine out of ten hydropathy scales).

Since hydrophobicity is expected to influenceprotein folding thermodynamics, as our calcu-lations indicate, one wonders about the selectiveeffect of these global changes in proteomic proper-ties. Lobry,53 from comparative analysis of bacterialgenomes, has suggested the existence of a selectivepressure towards “optimal” amino acid frequen-cies. This selective pressure is visible in Figure 4, inthe fact that the variance of the GC12 is muchnarrower than the variance of the GC3. Never-theless, purifying selection is not strong enough toremove the influence of the mutational bias onamino acid frequencies. We believe that the balance

between unfolding free energy and the normalizedenergy gap that we have described before plays acrucial role in this respect. Proteins more hydro-phobic than average will have larger unfolding freeenergy but a smaller normalized energy gap. Formoderate hydrophobicity, this displacement isprobably almost selectively neutral, since it isadvantageous for one property but not for theother one.

We expect that very hydrophobic proteinsequences bear a selective disadvantage. This isindicated in our calculation by the small value of thenormalized energy gap in hydrophobic proteins.Experimentally, very hydrophobic sequences aremore likely to have folding intermediate states andare more prone to aggregation. The high expressionlevel of chaperonins in intracellular organisms alsosuggests the existence of potential folding problemsfor proteins of these organisms. Therefore, oneshould expect that the GC12 versus GC3 curve isconcave upwards for small GC3, due to selectionagainst highly hydrophobic sequences. Figure 4,however, indicates the contrary: the GC12 ofproteins of organisms with low GC3 is even smallerthan one would expect from extrapolation ofproteins with high and moderate GC3. We considerthis fact a strong indication that selection efficacy isreduced in organisms with low GC3, as it isexpected, since these organisms are mostly obligatepathogens or endosymbionts characterized byreduced population size.

We stress that the interpretation discussed abovedoes not involve a monotonic accumulation ofdeleterious mutations that unavoidably leads toextinction, which would be in disagreement withthe fact that endosymbionts survived for severalhundred millions years in their respective hosts.Protein thermodynamics results from a balancebetween selection, where unfolding free energy andnormalized energy gap pull in opposite directions,and mutation. The less stable the protein, the lesslikely it is that mutations will have a detrimentaleffect on its stability. Thus, a reduction in selectivestrength may be compatible with stationary (on theaverage) values of the folding parameters, even if ata reduced level of stability. This view is shared witha recent population genetic model of compensatorynearly neutral mutations,56 and it will be the subjectof a future investigation.

It has recently been reported that the rates ofin vitro refolding of orthologous proteins inprokaryotes and eukaryotes correlate with theirdifferential rates of biosynthesis (U. Bastolla & O.Demetrius, unpublished results). In this experi-mental work, the authors concluded that fasterfolding in prokaryotes, in which chain elongationis faster, minimizes the occurrence of unfoldednascent proteins. In endosymbiotic bacteria proteinsynthesis is thought to be slower than in free-livingbacteria. An indication of this is the weak codonusage bias towards more frequent tRNA species inendosymbiotic bacteria.54 Another indication forthis is their very slow growth rate. This suggests an


alternative explanation for our observation ofreduced protein folding efficiency in intracellularbacteria: it is possible that it is due to weakerselection on folding efficiency when the proteinchain is translated very slowly. In order to contrastthis possible interpretation, we have examinedeukaryotic proteins, which are also synthesizedslower than proteins of free-living bacteria, and wehave noticed that their normalized energy gap islarger than that of intracellular bacterial proteins.Therefore, the interpretation that relates the lowfolding efficiency of proteins of intracellularbacteria to their slow biosynthesis rate does notappear to be supported by the data.

† The Institute for Genomic Research, url: http://www.tigr.org/TIGRFAMs/index.shtml

Conclusion

In summary, both mutational pressure andvariable selective strength appear responsible forthe systematic differences between orthologousproteins of different bacteria, sharing the samestructure and function but having different thermo-dynamic properties. A mutational bias towardsACTat the DNA level translates into a bias towardsmore hydrophobic proteins, which are character-ized by larger unfolding free energies but lowerstability against misfolding. Probably these twoopposite effects almost balance for moderatelyhydrophobic proteins, so that purifying selectioncannot avoid the influence of the mutational bias onthe amino acid frequencies. We expect, however,that a too large hydrophobicity has a negative effecton protein folding efficiency and on fitness,particularly due to the increased risk of proteinaggregation. This expectation is confirmed by thevery low value of the normalized energy gap. Incontrast, the influence of the mutational bias on theprotein composition, as indicated by the slope of theGC12 versus GC3 curve, is even larger for large biasthan for moderate bias, as if natural selection wereless able to counteract the effect of mutational bias.The most plausible explanation seems that theefficacy of purifying selection is reduced in theorganisms characterized by a strong AT bias. Theseorganisms are mostly intracellular bacteria, theyhave a small effective population size and theirgenomes do not recombine. They are also charac-terized by a very reduced genome size, which canbe regarded as another quantitative characteriz-ation of the extent of their intracellular lifestyle.

It remains to be explained why intracellularlifestyle and low GCC content always tend to gotogether. The influence that mutational bias andreduced selection exert on protein thermodynamicsis probably part of the answer.

Our results are also relevant for the studies ofprotein folding. They confirm the importance of thenormalized energy gap, a crucial parameter in thestatistical mechanical models of protein folding.Through natural selection, naturally occurringproteins are different from random heteropolymers,for which the normalized energy gap vanishes, but

species in which selection is weaker have proteinsthat seem to dangerously approach randomheteropolymers. Thus this computational approachprovides a bridge between population genetics andmolecular evolution on the one hand and thestatistical mechanics of biological macromoleculeson the other.

Materials and Methods

Protein families

We selected a total of 21 families of small homologousproteins for which at least one structure is known, andwhich are also present in the reduced genomes ofobligatory intracellular bacteria. They are listed inTable 3. In addition, we studied the Chaperone DnaK,which was not used to calculate average properties, sinceits function in assisting protein folding sets it apart fromthe other 21 families (see below).For each protein family we included sequences from

the PFAM database,14 complemented with sequencesfrom the TIGRFAM database of homologous families ofcompleted prokaryotic genomes†. Only the best match tothe family from each organism was considered. In case ofalmost equivalent matches, we chose the sequence thatprovided the largest value of the energy gap.

Prokaryotic species

The following 73 prokaryotic species were studied.Archaea: Aeropyrum pernix, Archaeoglobus fulgidus,Methanobacterium thermoautotrophicum, Methanococcusjannaschii, Pyrococcus furiosus. Thermophylic bacteria:Aquifex aeolicus, Bacillus stearothermophilus, Thermotogamaritima, Thermus aquaticus, Thermoanaerobacter tengcon-gensis. Free-living bacteria: Agrobacterium tumefaciens,Bacillus anthracis, B. subtilis, B. halodurans, Brucella meli-tensis, Caulobacter crescentus, Chlorobium tepidum, Clostri-dium acetobutylicum, C. perfringens, Corynebacteriumglutamicum, Deinococcus radiodurans, Escherichia coli K12,E. coli O157, Enterococcus faecalis, Fusobacterium nucleatum,Haemophilus influenzae, Lactococcus lactis, Listeria innocua,L. monocytogenes, Mycobacterium tuberculosis, Neisseriameningitidis, Nostoc sp., Pasteurella multocida, Pseudomonasaeruginosa, P. putida, P. syringae, Ralstonia solanacearum,Rhizobium loti, R. meliloti, Salmonella typhimurium,Shewanella oneidensis, Shigella flexneri, Staphylococcusaureus, Streptomyces coelicolor, Synechocystis sp., Vibriocholerae, Xylella fastidiosa, Xanthomonac axonopodis,Zymomonas mobilis. Obligatory endosymbionts and para-sites: Borrelia burgdorferi, Campylobacter jejuni, Chlamydiapneumoniae, C. muridarum, C. trachomatis, Coxiella burnettii,Helicobacter pylori, Mycoplasma capricolum, M. genitalium,M. pneumoniae, Mycobacterium leprae, Treponema pallidum,Ureaplasma parvum, Yersinia pestis, Wigglesworthiaglossinidia, Wolbachia sp., Buchnera aphidicola from theaphid hosts Baizongia pistacea, Schizaphis graminum andAcyrthosiphon pisum. We note that several of the free-living bacteria are opportunistic parasites.In addition, homologous proteins from five algal

chloroplasts (Cyanidium caldarium, Guillardia theta,Euglena gracilis, Porphyra purpurea) and from six

http://www.cab.inta.es/~CAFASP


Table 3. Protein families studied, PFAM code and representative proteins in the PDB

Protein Gene PFAM Representative structures Length

Acetate kinase(dom.2)

ackA PF00871 1g99 (ACKA_METTE) 241

ATP synthase 3 AtpC PF00401 1aqt (ATPE_ECOLI) 138Chaperone proteindnaK

dnaK PF00012 1dkz(DNAK_ECOLI) 603

D-ala D-ala ligase Ddl PF07478 1iov (DDLB_ECOLI), 1e4eB (VANA_ENTFC), 1ehiA (DDL-LEUME) 305–377PF01820

Citrate synthase gltA PF00285 1k3p (CYSY_ECOLI), 1a59 (CISY_ABDS2), 1iom (Q72J03), 1aj8(CISY_PYRFU), 1o7! (CISY_SULSO), 6csc (CISY_CHICK), 1cts(CISY_PIG)

371–433

3-Dehydroquinase Aroq PF001220 1d0iE (AROQ_STRCO), 2dhqA (AROD_MYCTU) 146–156Dihydrofolatereductase

folA PF00186 1ra9 (DYR ECOLI), 3dfr (DYR_LACCA), 1df7 (DYR_MYCTU), 1d1g(DYR_THEMA), 1vdr (DYR_HALVO), 1dyr (DYR_PNECA), 1drf(DYR_HUMAN), 8dfr (DYR_CHICK)

159–206

DUTPase dut PF00692 1euw (DUT_ECOLI) 151Elongation factor TS efts PF00889 1efuB (EFTS_ECOLI), 1tfe (EFTS_THETH) 142–207Flavodoxin flav PF00258 1ag9 (FLAV_ECOLI), 1f4p (FLAV_DESVH), 1czn (FLAV_SYNP7),

1rcf (FLAV_ANASP), 5nul (FLAV_CLOBE), 1fue (FLAV_HELPJ)138–175

Peptide deformylase def PF01327 1g2a (DEF_ECOLI) 168Peptidyl-tRNAhydrolase

pth PF01195 2pth (PTH_ECOLI) 194

Phosphocarrierprotein H

PtsH PF00381 1opd (PTHP_ECOLI), 2hpr (PTHP_BACSU), 1ptf (PTHP_STRFE),1pch (PTHP_MYCCA)

85–88

Phosphopantetheineadenyltransferase

coad PF01467 1b6tA (COAD_ECOLI) 159

50 S ribosomalprotein L14

rl14 PF00238 1whi (RL14_BACST), 1jj2J (RL14_HALMA) 122–132

Ribosomalmethyltransferase J

ftsJ PF01728 1ej0 (RRMJ_ECOLI) 180

RNase H rnhA PF00075 2rn2 (RNH_ECOLI), 1ril (RNH_THETH) 155–166RNase P RnpA PF00825 1a6f (RNPA_BACSU), 1d6t (RNPA_STAAW) 116–117Thioredoxin I trxA PF00085 2trx (THIO_ECOLI), 1thx (THI2_ANASP), 1fb6 (THIM_SPIOL),

1dby (THIM_CHLRE), 1ep7 (THIH_CHLRE), 1erv (THIO_HUMAN)105–140

Thioredoxin trxB PF00070 1trb (TRXB_ECOLI), 1fl2 (AHPF_ECOLI), 1vdc (TRB1_ARATH) 320–330Triosephosphateisomerase

Tpi PF00121 1tre (TPIS_ECOLI), 1aw2 (TPIS_VIBMA), 2btm (TPIS_BACST), 1b9b(TPIS_THEMA), 1hg3 (TPIS_PYRWO), 1ydv (TPIS_PLAFA), 1tpf(TPIS_TRYBB), 1tcd (TPIS_TRYCR), 1amk (TPIS_LEIME), 7tim(TPIS_YEAST), 1hti (TPIS_HUMAN), 1tph (TPIS_CHICK)

225–255

Triptophan synthasea chain

TrpA PF00290 1qopA (TRPA_SALTY), 1geq (TRPA_PYRFU) 248–268


eukaryotic nuclear genomes (Saccharomyces cerevisiae,Arabidopsis thaliana, Chlamydomonas reinhardtii, Spinaciaoleracea, Homo sapiens, Caenorhabditis elegans) have alsobeen examined when available.

Protein model and effective free energy

The protein model that we adopt is described in detailin the paper by Bastolla et al.57 Briefly, protein structuresare represented as contact matrices such that Cij equalsone if residues at i and j are in contact and zero otherwise.Given a sequence SZ{S1,.,SN} and its contact matrix C,the configurational free energy, including the entropy ofthe solvent, but not chain entropy, is assumed to have theform of the sum of contact interactions,EðC;SÞ=kBTZ

PCijUðSi; SjÞ, where U(a; b) is the 20!20

interaction matrix in the work done by Bava et al.58

The calculated unfolding free energy of theprotein folded in the native configuration Cnat, withrespect to the unfolded state, is estimated asDGðCnat;SÞZkBTZKEðCnat;SÞ=kBTCNs, where N ischain length and s is a term representing the configura-tional entropy per residue minus the stabilization due tothe hydrogen bonding network of secondary structure.A fit of the above equation to the unfolding free energiesof 44 globular proteins with two-states folding thermo-dynamics and no disulphide bonds from the database

Protherm58 suggests that s is almost constant for differentprotein topologies and indicates that DG(Cnat,S) isstrongly correlated with the experimental free energy,with correlation coefficient RZ0.95. The correlation is stillrather strong (RZ0.85) if the two quantities are dividedby chain length (UB, unpublished data). Therefore we usethe quantity DG(Cnat;S)ZNkBT as an estimate of theunfolding free energy per residue.

Fold recognition

For most of the sequences studied the native structurewas not known, but the structure of one or moreorthologous proteins were available in the Protein DataBank (PDB). Alignments were generated by threadingsequences on the more than 6000 structures present in thelast release of the PDBselect90 database.59 The bestcandidate native structure was identified by minimizingthe sum of the effective energy plus a gap penalty term.Alternative low energy structures were then used tocalculate the energy gap. We applied two differentalignment strategies, which gave the same qualitativeresults.

Fixed sequence-structure alignment

For each protein family, we chose a representative


sequence of known structure and aligned all othersequences to it. For each sequence, we then forcedstructures in the PDB to follow the same pattern ofalignment with predetermined gaps, which were notpenalized. In nearly all cases, the representative structurewas correctly identified as the native state. In a few cases,manual improvement of the alignments was necessary toobtain this result.

Optimized sequence-structure alignment

In this approach, for each possible sequence structurealignment the placement of gaps was optimized byminimizing the effective free energy function plus a gappenalty term, using the program Protfinder†. In mostcases, the structure of one of the orthologous proteins wasrecognized as the best model. The few sequences forwhich this did not happen were discarded. These weremostly sequences with many gaps in the alignmentwith structures of homologous proteins and sequencesbelonging to genomes characterized by low energy gapsin encoded proteins. Despite the fact that our alignmentscore is not based on sequence identity, the alignmentsthat we obtained were often coincident, and sometimesbetter than the ones obtained by sequence basedmethods.Because the method does not require manual inspectionof the alignments, it could be applied to a larger numberof proteins. We report here only results obtained throughthis method. The fixed alignment method gave qualitat-ively identical results, which were partially reported inthe work done by van Ham.8

We discarded proteins for which a gap in the alignmentobtained by the fold recognition algorithm was largerthan 15% of the sequence. Such gaps correspond toinsertion or deletion of long loops, terminal regions oreven entire domains. We also discarded proteins forwhich the fold recognition algorithm provided a struc-tural model not derived from a homologous protein.

Normalized energy gap

Statistical mechanical studies of protein folding haveshown that fast folding and thermodynamic stability ofthe native state require that the free energy landscape ofthe protein chain is smooth.59–64 We use the normalizedenergy gap a64 as a quantitative measure of the smooth-ness of the free energy landscape. A large value of aimplies that all low energy structures are very similar tothe native one. This is a measure of the stability withrespect to misfolded states. If a is very small, limitedthermodynamic stability of the native state, limitedstability against mutations, slow folding, misfolding andaggregation problems are expected. As a measure ofstructural similarity we use the overlap q(C;C 0), whichcounts the number of common contacts between twostructuresC andC 0, normalized so that q(C;C 0) equals oneif and only if C and C 0 share all of their contacts. The freeenergy landscape is said to be smooth if configurationsvery different from the native one, Cnat, all have highenergy. This is a prerequisite for stability and fast folding.The normalized energy gap a is defined through the set ofinequalities:

EðC;SÞKEðCnat;SÞ

jEðCnat;SÞjRaðSÞð1KqðC;CnatÞÞ (1)

† http://www.cab.inta.es/~CAFASP

where C is any alternative configuration. A large value ofa is also a prerequisite for successful fold recognition.

Sequence similarity

The estimates of thermodynamic parameters depend inpart on the protein giving the best structural match in thefold recognition. They are inadequately estimated if aconsiderable fraction of the sequence cannot be aligned tothe model structure. We therefore discarded all proteinsfor which less than 85% of the sequence could be aligned.Sequence similarity with the best structural model alsohas a strong effect. Since the difference between thestructures of two homologous proteins increases withtheir sequence dissimilarity,65 the less similar thesequences, the worse the structural model will be. Thisis an unavoidable problem. However, despite the fact thatour results are not fully reliable for every individualprotein, we expect that the correlations that they allow todiscover remain valid when experimentally measuredquantities are used instead of our computationalestimates.

Interactivity and hydrophobicity

We have correlated genomic and folding thermo-dynamic properties with the mean values of ten aminoacid properties h(a); aZ1,.,20. All of the studiedproperties are related to hydrophobicity. Eight of themrepresent empirical or computational hydrophobicityscales, the last two are related to the typical interactionstrength and the typical connectivity of each amino acidtype. These last two scales yield the strongest correlationsboth with folding thermodynamics and with genomicproperties. We refer to these ten properties collectivelywith the term interactivity, because they try to measurehow strongly the amino acid residues in the proteinsequence interact with each other.The properties that we considered are: (1) the L76

hydropathy scale derived by Levitt in 1976 usingexperimental data and theoretical calculations;66 (2) theKD hydropathy scale, derived by KD in 1982 to identifytrans-membrane helices using diverse experimentaldata;67 (3) the FP hydropathy scale derived by Fauchere& Pliska in 1983 from the experimental measurement ofoctanol/water partition coefficients;68 (4) the R88hydropathy scale derived by Roseman in 1988 based onthe transfer of solutes from water to alkane solvents;69 (5)the MP hydropathy scale, derived by Manavalan &Ponnuswamy in 1978 from statistical properties ofglobular proteins;70 (6) the augmented Whilmey Whitehydropathy scaleWW, derived by Jayasinghe et al. in 2001to improve recognition of transmembrane helices;71 (7)the AV hydropathy scale derived by Palliser & Parry in2001 by averaging 127 normalized hydropathy scalespublished in the literature;72 (8) the G98 classification ofamino acid residues into polar, hydrophobic and amphi-philic classes, adopted by Gu et al.12 to investigate therelationship between the hydrophobicity of a protein andthe nucleotide composition of the corresponding gene;(9) the interaction scale IH obtained from the maineigenvector of the interaction matrixU(a;b) used here. It isknown in fact that the main eigenvector of contactinteraction matricies is strongly related to hydro-phobicity.74 (10) Last, the connectivity scale CH, thatmaximizes the correlation with the principal eigenvectorsof protein contact matrices for a non-redundant set ofPDB structures (U. Bastolla et al., unpublished results).All these scales are positively correlated with each



other, with correlation coefficients ranging from aminimum of 0.68 between the KD and L76 scales to amaximum of 0.95 between IH and CH scales.For each protein, we calculated the mean interactivity

as HðSÞZP

hðSiÞ=N and correlate it to genomic andthermodynamic properties.

Averages

The effective free energy per residue in our modeldepends strongly on the number of contacts per residueNc/N and on chain length, two structural properties thatare almost constant in proteins of the same family. Prior toaveraging the properties of proteins belonging to differentfamilies and contained in the same genome, properties ofindividual proteins were normalized by dividing them bythe corresponding properties of the protein representativeof the family. This allowed to underline the effects ofsequence evolution with respect to the effects of proteintopology. The representative protein was chosen as thesequence with largest normalized energy gap. Otherchoices (for instance proteins from model organisms)yielded the same qualitative results. The normalizedproperties of the proteins of the same organismwere thenaveraged. Only organisms for which we found at leastfive suitable proteins were considered in the study.For each organism, we calculated the average of the

following normalized protein properties: (1) unfoldingfree energy per residue; (2) normalized energy gap; (3)mean interactivity (in this case we added an offset so thatall mean interactivities result positive, as explainedbelow); (4 and 5) GCC content of the correspondinggene, distinguishing between first and second codonposition on one hand and third on the other hand; (6)sequence similarity with the representative structure.The normalization was to be performed with caution in

the case of interactivity, since some hydropathy scalesdesigned to identify transmembrane helices attribute zeromean hydrophobicity to globular proteins. In this case,different proteins within the same family may haveinteractivities with different sign, and the normalizationmay completely obscure the results. To overcome thisproblem, we add a constant offset to all hydrophobicityscales and rescale them in such a way that thehydrophobicity is positive for all proteins in our set. Wechoose the offset and the scale factor so that the average ofthe mean hydrophobicity and the mean hydrophobicitysquared over all proteins in our set are the same for all ofthe scales considered.

Principal component analysis

PCA selects the combinations of variables explainingmost of the variance in multivariate data sets. For eachorganism, we considered seven variables: the variables(1–6) listed above plus genome size. The use of PCAallowed to reduce the unwanted effect of sequencesimilarity on our results.

Acknowledgements

U.B. thanks Javier Tamames for introducing himto this subject. During this work, U.B., E.V. andR.C.H.J.vH. have been supported through grantsfrom INTA (Spain). U.B. has been partly supported

through the I3P Network on Bioinformatics of theCSIC (Spain), financed by the European SocialFund. A.M. has been supported through grantBMC2003-00305 from Ministerio de Ciencia yTecnologia (MiCyt), Spain.

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Edited by J. Thornton

(Received 4 May 2004; received in revised form 24 August 2004; accepted 27 August 2004)

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