increasing the thermal stability of an oligomeric protein, beta-glucuronidase

13
Increasing the Thermal Stability of an Oligomeric Protein, Beta-glucuronidase Humberto Flores and Andrew D. Ellington* Department of Chemistry and Biochemistry, Institute for Cellular and Molecular Biology ICMB a4800/MBB 3.424, University of Texas at Austin 26th and Speedway, Austin TX 78712, USA The reporter enzyme beta-glucuronidase was mutagenized and evolved for thermostability. After four cycles of screening the best variant was more active than the wild-type enzyme, and retained function at 70 C, whereas the wild-type enzyme lost function at 65 C. Variants derived from sequential mutagenesis were shuffled together, and re-screened for thermostability. The best variants retained activities at even higher tem- peratures (80 C), but had specific activities that were now less than that of the wild-type enzyme. The mutations clustered near the tetramer inter- face of the enzyme, and many of the evolved variants showed much greater resistance to quaternary structure disruption at high tempera- tures, which is also a characteristic of naturally thermostable enzymes. Together, these results suggest a pathway for the evolution of thermo- stability in which enzymes initially become stable at high temperatures without loss of activity at low temperatures, while further evolution leads to enzymes that have kinetic parameters that are optimized for high temperatures. # 2002 Academic Press Keywords: beta-glucuronidase; directed evolution; thermostability, DNA shuffling; random mutagenesis *Corresponding author Introduction Proteins from thermophilic organisms have pro- ven to be extremely useful for high temperature applications. There appear to be multiple strategies by which a protein can become thermostable (for a review, see Vieille & Zeikus 1 ). Comparative sequence analyses of the genomes of thermophilic and mesophilic organisms have revealed that ther- mophilic enzymes show marked preferences for some amino acid residues. 2 The preference is most obvious when only surface amino acid residues are analyzed. 3 In addition, comparative structural ana- lyses of thermophilic and mesophilic proteins have revealed that in some instances the surface loops of thermophilic proteins are shorter that in their mesophilic homologues (for a review, see Wintrode & Arnold 4 ). Disulfide bonds, salt bridges or metal- binding sites are also adaptations that are fre- quently found in thermophilic proteins. 1,5 Finally, the oligomerization state of thermophilic proteins seems to be greater than that of mesophilic proteins. 6,7 For example, Shima et al. 6 showed that the quaternary state of formyltransferase from Methanopyrus kandleri is important for thermo- stability, while Thoma et al. 7 showed that the ther- mostability of the Thermotoga maritime phosphoribosylanthranilate isomerase derives from interactions between monomeric subunits. Protein engineering has been used to increase the thermostability of proteins. As with natural proteins, the introduction of disulfide bonds or metal-binding sites, or changes that lower the entropy of unfolded states have been shown to improve stability. By a combination of rational design and the introduction of residues found in natural thermostable variants, the moderately stable thermolysin-like protease from Bacillus stear- othermophilus was able to function at temperatures up to 100 C, while its activity at lower tempera- tures remained unchanged. 8 Similarly, comparative sequence analysis followed by the rational design of a ‘‘consensus’’ phytase from Aspergillus niger yielded a variant that had increased thermostabil- ity and no change in activity at low temperatures. 9 While rational design has proven successful, directed evolution has also been used to increase protein thermostability (for reviews, see Wintrode & Arnold; 4 Arnold et al. 10 ). Directed evolution is E-mail address of the corresponding author: [email protected] Abbreviations used: GUS, beta-glucuronidase; IPTG, isopropylthio-beta-D-galactoside; X-Glu, 5-bromo-4- chloro-3-indolyl-b-D-glucuronide; pNPG, p-nitrophenyl- beta-D-glucuronide. doi:10.1006/jmbi.2001.5223 available online at http://www.idealibrary.com on J. Mol. Biol. (2002) 315, 325–337 0022-2836/02/030325–13 $35.00/0 # 2002 Academic Press

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Page 1: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

doi:10.1006/jmbi.2001.5223 available online at http://www.idealibrary.com on J. Mol. Biol. (2002) 315, 325±337

Increasing the Thermal Stability of an OligomericProtein, Beta-glucuronidase

Humberto Flores and Andrew D. Ellington*

Department of Chemistry andBiochemistry, Institute forCellular and Molecular BiologyICMB a4800/MBB 3.424,University of Texas at Austin26th and Speedway, AustinTX 78712, USA

E-mail address of the [email protected]

Abbreviations used: GUS, beta-glisopropylthio-beta-D-galactoside; X-chloro-3-indolyl-b-D-glucuronide; pNbeta-D-glucuronide.

0022-2836/02/030325±13 $35.00/0

The reporter enzyme beta-glucuronidase was mutagenized and evolvedfor thermostability. After four cycles of screening the best variant wasmore active than the wild-type enzyme, and retained function at 70 �C,whereas the wild-type enzyme lost function at 65 �C. Variants derivedfrom sequential mutagenesis were shuf¯ed together, and re-screened forthermostability. The best variants retained activities at even higher tem-peratures (80 �C), but had speci®c activities that were now less than thatof the wild-type enzyme. The mutations clustered near the tetramer inter-face of the enzyme, and many of the evolved variants showed muchgreater resistance to quaternary structure disruption at high tempera-tures, which is also a characteristic of naturally thermostable enzymes.Together, these results suggest a pathway for the evolution of thermo-stability in which enzymes initially become stable at high temperatureswithout loss of activity at low temperatures, while further evolutionleads to enzymes that have kinetic parameters that are optimized forhigh temperatures.

# 2002 Academic Press

Keywords: beta-glucuronidase; directed evolution; thermostability,DNA shuf¯ing; random mutagenesis

*Corresponding author

Introduction

Proteins from thermophilic organisms have pro-ven to be extremely useful for high temperatureapplications. There appear to be multiple strategiesby which a protein can become thermostable (for areview, see Vieille & Zeikus1). Comparativesequence analyses of the genomes of thermophilicand mesophilic organisms have revealed that ther-mophilic enzymes show marked preferences forsome amino acid residues.2 The preference is mostobvious when only surface amino acid residues areanalyzed.3 In addition, comparative structural ana-lyses of thermophilic and mesophilic proteins haverevealed that in some instances the surface loops ofthermophilic proteins are shorter that in theirmesophilic homologues (for a review, see Wintrode& Arnold4). Disul®de bonds, salt bridges or metal-binding sites are also adaptations that are fre-quently found in thermophilic proteins.1,5 Finally,the oligomerization state of thermophilic proteins

ing author:

ucuronidase; IPTG,Glu, 5-bromo-4-

PG, p-nitrophenyl-

seems to be greater than that of mesophilicproteins.6,7 For example, Shima et al.6 showed thatthe quaternary state of formyltransferase fromMethanopyrus kandleri is important for thermo-stability, while Thoma et al.7 showed that the ther-mostability of the Thermotoga maritimephosphoribosylanthranilate isomerase derives frominteractions between monomeric subunits.

Protein engineering has been used to increasethe thermostability of proteins. As with naturalproteins, the introduction of disul®de bonds ormetal-binding sites, or changes that lower theentropy of unfolded states have been shown toimprove stability. By a combination of rationaldesign and the introduction of residues found innatural thermostable variants, the moderatelystable thermolysin-like protease from Bacillus stear-othermophilus was able to function at temperaturesup to 100 �C, while its activity at lower tempera-tures remained unchanged.8 Similarly, comparativesequence analysis followed by the rational designof a ``consensus'' phytase from Aspergillus nigeryielded a variant that had increased thermostabil-ity and no change in activity at low temperatures.9

While rational design has proven successful,directed evolution has also been used to increaseprotein thermostability (for reviews, see Wintrode& Arnold;4 Arnold et al.10). Directed evolution is

# 2002 Academic Press

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326 Increasing Thermostability of an Oligomeric Protein

especially powerful because knowledge of thethree-dimensional structure of a protein is notrequired to undertake engineering efforts. TheBacillus subtilis p-nitrobenzyl esterase has beenevolved for thermostability, and the best mutantshowed higher activity than the wild-type enzymeat a variety of temperatures, including very hightemperatures where the wild-type enzyme wasinactive.11 B. subtilis subtilisin E has similarly beenevolved, and the best variant was again more ther-mostable without loss of activity at lowtemperatures.12 Finally, a psychrophilic protease,subtilisin S41, was evolved for thermostability, andthe best variant was more stable and active at alltemperatures tested.13 In each of these instances,the screen was for residual activity at low tempera-ture after exposure to high temperature and theevolved variants showed enhanced thermostabil-ity.

There have also been examples of selections car-ried out at high temperatures. The kanamycinnucleotidyltransferase from Staphylococcus aureuswas mutated by DNA shuf¯ing, and thermostablevariants were selected following transformation ofT. thermophilus. After three rounds of shuf¯ing thebest mutant protein remained active after a tenminute incubation at 70 �C, but was completelyinactivated at 75 �C.14 As another example, achimeric 3-isopropylmalate dehydrogenase waschemically mutated and active variants wereselected in T. thermophilus at high temperature. Thebest variant showed slightly improved thermo-stability.15

Overall, these results reveal that proteins can beengineered to have broad thermal activitypro®les.13 This is surprising, since natural thermo-philic proteins tend to not have broad thermal pro-®les. While thermophilic proteins and mesophilicproteins tend to have speci®c activities that aresimilar at their respective physiological tempera-tures, thermophilic proteins generally have loweractivities at mesophilic or lower temperatures,while mesophilic proteins generally have loweractivities at thermophilic or higher temperatures(for a review, see Jaenicke & Bohm16), althoughthere are some counterexamples.12,17 For example,T. maritimaL-isoaspartyl methyltransferase17 and Thermoactino-myces vulgaris thermitase,12 retain high activityrates even at low temperatures.

One possible reconciliation of the results ofdirected and natural evolutionary experiments isthat proteins that have been evolved in the labora-tory have tended to be monomeric, while manynatural thermophilic proteins have been found tobe oligomeric (for a review, see Vieille & Zeikus1).For example, Pyrococcus woesei triosephosphate iso-merase is a tetramer, while its mesophilic homol-ogues are dimers.18 Similarly, T. maritima lactatedehydrogenase is an octamer, while a mesophilichomologoue is a tetramer.19 Another possiblereconciliation of directed and natural evolution isthat directed evolution has not yet optimized pro-

teins for thermostability, and that proteins withbroad thermal optima are intermediates on a path-way towards true thermophily. Indeed, these twohypotheses may impinge on one another, and thepathways by which monomers and oligomersattain thermophily may be different. In thisrespect, it should be noted that the two counterex-amples alluded to above that have broad thermalpro®les are both monomers.

In order to better understand the pathways bywhich monomeric and oligomeric enzymes maybecome thermostable, and to discern whetherenzymes which resemble natural thermophiles canbe generated by directed evolution, we have usedthe homotetrameric protein b-glucuronidase (GUS)from the mesophile Escherichia coli as a model sys-tem. While the three-dimensional structure of theprotein is not known, the structure of the humanhomotetramer homologue has been solved,20 andthe E. coli sequence (46 % identical) can be super-imposed on the solved structure.21 Each monomeris arranged into three structural domains: a highlydistorted barrel-like structure with a jelly roll motifand two b-hairpin insertions (domain I); an immu-noglobulin-like constant domain (domain II); and aC-terminal TIM-barrel fold containing the activesite and the tetramer interface (domain III;Figure 1).

We screened for GUS variants that had residualactivity after exposure to high temperatures. Whileit proved possible to identify proteins with broadthermal pro®les, as had previously been the casefor monomeric enzymes, extreme thermostability(activity at 80 �C) was unattainable without loss ofactivity. The extremely thermostable enzymes did,however, show greatly improved tetramerizationparameters. It is possible that the evolution ofhighly thermostable oligomeric enzymes must pro-ceed either via neutral or even deleterious variants.

Results and Discussion

Screening for thermostablebeta-glucuronidase variants

The screen for thermostable variants of beta-glucuronidase was similar to screens that have pre-viously been used to direct the evolution of otherenzymes.11,12,22 ± 24 The genes of variants that werereproducibly thermostable were mixed, furthermutagenized (via mutagenic PCR), and subjectedto additional rounds of screening at progressivelyhigher temperatures. In order to better mimic natu-ral evolutionary processes and to identify the rela-tive independence and interdependence ofdifferent amino acid substitutions that arose,recombination (i.e., DNA shuf¯ing) was notinitially used between rounds of screening.

In each round of screening between 3000 and16,000 individual enzyme variants were examined.The number of reproducibly active enzyme var-iants in each round ranged from one to ®ve(Figure 2). Following round 4 it proved dif®cult to

Page 3: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

Figure 1. Structural model of E. coli GUS. Domain I, ajelly roll motif and two b-hairpin insertions, is shown ingreen; domain II, an immunoglobulin-like constantdomain, is shown in pink; and domain III, a C-terminalTIM-barrel fold containing the active site and the tetra-mer interface, is shown in purple. The catalytic residuesare shown in black and represented as balls-and-sticks.

Figure 2. Evolution of thermostability. Along the top,the number of colonies screened in each round and thescreening conditions are indicated. Below, the names ofindividual variants derived from each round are shown,and the sequence relationships between these variantsare indicated by arrows (see also Figure 3). In round 5,variants were independently mutagenized and screenedtwice. The ®rst screen was carried out starting from allvariants recovered from round 4, while the secondscreen started from only variant IV-5.

Figure 3. Sequence relationships between thermo-stable variants. The evolutionary relationships indicatedin Figure 2 are shown in greater detail. Hypothesizedparental and derived variants are connected by lines.Each box contains the new amino acid substitutions thatare found in a variant relative to its hypothesizedparent.

Increasing Thermostability of an Oligomeric Protein 327

recover enzyme variants that had high activityin vitro at temperatures in excess of 70 �C (seebelow). Therefore, the most thermostable andactive variant from this round (IV-5) was againmutagenized and screened for thermostability.

After each round of screening all reproduciblythermostable enzyme variants were sequenced(Table 1A). The number of sequence changes (bothcoding and non-coding) increased as a function ofthe round and the screening temperature. Unsur-prisingly, many of the sequence substitutions fromthe ®rst two rounds carried forward into laterrounds. For example, the D185N substitution thatarose in the ®rst round of screening did not revertthroughout the course of the directed evolutionexperiment. Similarly, the F51Y, G368C, N369S,Y517F, K567R and G601D substitutions that arosein the second round of screening were alsoretained throughout the remainder of the exper-iment. However, from the third round onward,several different evolutionary paths were followed(Figure 3). Enzyme variant III-1 gave rise to IV-4,which in turn gave rise to V-4. Enzyme variant III-2 gave rise to all other thermostable enzymes,including IV-2 which in turn gave rise to V-2. Ofcourse, since enzyme variant IV-5 was separatelymutagenized it could only give rise to V-1 and itsdescendents.

It is interesting to note that some amino acidsubstitutions that were not ®xed in early roundsstill arose independently in subsequent rounds. Forexample, the C197S substitution in enzyme variantII-1 is independently derived in variant IV-1; theA64V substitution in enzyme variant III-1 is inde-pendently derived in variant IV-1; and the serinesubstitution at position 550 appears to have arisenindependently several times during rounds 4 and5. These enzyme variants may also have arisen asa result of recombination between templates

during error-prone PCR,25,26 but we believe this isless likely because nearby silent changes were notcoordinately transferred between templates. More-over, some positions can adopt different thermo-stabilizing amino acid residues. For example, the

Page 4: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

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328 Increasing Thermostability of an Oligomeric Protein

Page 5: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

Increasing Thermostability of an Oligomeric Protein 329

methionine residue at position 516 could be substi-tuted with either an isoleucine or a valine residue.The fact that these enzyme variants arose in inde-pendent lineages at different times suggests thatthey may be thermostabilizing in many geneticbackgrounds (Figure 3 and Table 1A).

Thermostabilities of evolved variants

Results from ®lter screens and solution re-screens indicated that the enzyme variants becameprogressively more resistant to thermal denatura-tion in each round. In order to judge whether ornot the largely qualitative ®lter and solutionscreens were in fact generating substantive differ-ences in enzyme thermostability, the best enzymesfrom the ®nal rounds of directed evolution werepuri®ed and assayed. Two different measures ofthermostability were assessed: thermotoleranceand thermal preference. Thermotolerances ofenzymes were measured by ®rst heating enzymesto a given temperature for ten minutes, thenmeasuring their remaining activities at room tem-perature (Figure 4(a)). The thermal preferences ofenzymes were measured by ®rst heating theenzymes to a given temperature for ®ve minutes,then measuring their activities at that temperature(Figure 4(b)). In general, the thermal tolerances ofenzymes were mirrored by their thermal prefer-ences; enzymes that showed greater ability to resisthigh temperatures were also more active at thosetemperatures.

During the re-screening assays that followedeach round the thermotolerances of any variantsthat were carried into additional rounds (e.g. I-2,II-3, etc.) were compared to those of the wild-typeenzyme at a variety of temperatures, including

Figure 4. Speci®c activities of thermostable variants. (a) Acminute) following heating to the indicated tempearture for teminute) of enzyme variants at a given temperature, following

ambient and screening temperatures. There wasnever any loss of activity relative to the wild-typeenzyme. Enzymes IV-3, IV-4, and IV-5 from round4 showed substantially more activity than enzymesIV-1 and IV-2 in the initial re-screens, and werepuri®ed. While all three enzymes showed greaterthermal tolerance than the wild-type, only enzymeIV-5 retained wild-type activity following exposureto high temperatures (Figure 4(a)). Indeed, whilethe wild-type enzyme showed little or no activityabove 65 to 70 �C, enzyme IV-5 was more active atthese temperatures than the wild-type enzyme wasat lower temperatures (Figure 4(b)). Enzyme IV-5also had a broader thermal preference than thewild-type when assayed at higher temperatures(Figure 4(b)). These results are reminescent of thoseobtained by Frances Arnold and her co-workers11

who demonstrated that B. subtilis p-nitrobenzylesterase could be evolved for thermostability. Theoptimal temperature of the esterase was increasedby 10 deg. C and the variant showed greaterspeci®c activities at a variety of temperatures thandid the wild-type enzyme. Similarly, B. subtilis sub-tilisin E was evolved for thermostability withoutloss of activity at lower temperatures. The optimaltemperature was increased by 16 deg. C and theactivity at 37 �C was 15 times that of the wild-type.12

Interestingly, all of the variants from round 5and beyond, including the immediate descendentsof enzyme IV-5, had much lower activities thaneither the wild-type or IV-5 at most temperatures(see Figure 4(b), for examples). Nonetheless, theround 5 variants showed greater residual activitiesthan enzyme IV-5 at the highest temperaturesassayed (Figure 4(a)). For example, while enzymeIV-5 was the most active variant after exposure to

tivity remaining at 25 �C (in pmol of pNPG hydrolyzed/n minutes. (b) Activities (in pmol of pNPG hydrolyzed/pre-heating to that temperature for ®ve minutes.

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330 Increasing Thermostability of an Oligomeric Protein

70 �C, its activity dropped dramatically afterexposure to 75 �C, while all of the round 5 variantsretained some residual activity at 75 �C and even80 �C. Thus, it seems likely that the screen workedexactly as it was designed to, identifying thosecolonies with residual activity, however small, fol-lowing exposure to high temperatures. Again, therelative residual activities of enzymes were mir-rored by their activities when assayed at a giventemperature (compare Figure 4(a) and (b)). Forexample, enzyme VI-1 generally had lowerresidual activity following incubation at a giventemperature than did enzyme VI-2 and also exhib-ited lower activity when assayed at a giventemperature.

When enzyme activities following exposure tothe highest temperatures are examined, the evol-utionary trends become even more clear. All of theenzymes from the latter rounds held more of theirinitial activities at progressively higher tempera-tures, irrespective of whether they were initiallylow activity variants, such as VI-1, or higheractivity variants, such as VI-2. In particular, at80 �C enzymes from the ®nal rounds show muchgreater residual activity than variants from earlierrounds (Figure 4(a)), and the thermal pro®les ofthe enzyme variants become much broader and¯atter.

DNA shuffling to furtherimprove thermostability

While beta-glucuronidases that were functionalat high temperatures were isolated, it appeared asthough improvements in thermostability came at acost: the loss of enzyme speci®c activity. It is poss-ible that there exist pathways for increasing thethermostability of beta-glucuronidase that do notinvolve loss of activity. However, the fact that twoseparate screens that started from the most broadlyactive enzyme, IV-5, did not yield enzymes withhigh speci®city activities at high temperaturessuggests two additional hypotheses: ®rst, it is poss-ible that there is no pathway between mesophilicand thermophilic enzymes that does not involve aloss of speci®c activity; or second, the enzymesthat arose during the initial rounds of our screenhad accumulated multiple mutations that made itdif®cult or impossible to attain high speci®c activi-ties at higher temperatures.

To determine whether enzymes from round 4contained mutations that somehow suppressed thefurther evolution of thermostability, enzyme var-iants from different rounds (II-1, II-2, IV-1, V-2, V-4, VI-1 and VI-2) were mixed and individualmutations were recombined by DNA shuf¯ing.27

These enzyme variants were chosen because theyspanned almost all of the sequence substitutionsthat had arisen during the course of the selection;enzyme variant IV-5 was left out of the mixture inorder to avoid over-representation in subsequentrounds. The shuf¯ed enzyme variants were againscreened for activity following exposure to extre-

mely high temperature (90 �C, 15 minutes), andfour shuf¯ed variants were chosen from amongst26,000 colonies for further characterization. One ofthese, S-2, exhibited high residual activity. In fact,S-2 had greater residual speci®c activity afterexposure to temperatures above 75 �C than did thevariant that had previously proven most resilient,enzyme IV-5 (Figure 4(a)). The speci®c activity ofenzyme S-2 at high temperatures was also higherthan that of all other enzyme variants from rounds5 and 6 (Figure 4(b)). Enzyme S-2 continued thetrend exhibited by enzymes from earlier rounds ofscreening, in that it was much more thermostablethan most of the parental enzymes, and almost asthermostable as the best parent, VI-1. Nonetheless,enzyme S-2 was not the most thermostableshuf¯ed variant. Variant S-3 retained more of itsinitial activity than did variant S-2 as temperatureis increased. Overall, DNA shuf¯ing appeared toperfectly meld two pre-existing phenotypes: thehigh speci®c activity of enzyme IV-5 and the highthermostability of enzyme VI-1.

Unsurprisingly, many of the sequence substi-tutions that were ®xed in the parental enzymevariants reappeared in the shuf¯ed variants(Table 1B). For example, the sequence substitutionsF51Y, A64V, F517Y, F525Y, K567R, Q585H, andG601D were all largely ®xed by the fourth roundof screening, and all appeared in the shuf¯edvariants, despite the fact that variants II-1 and II-2were present in the mixture used for shuf¯ing anddid not contain these sequence changes. Other sub-stitutions that were ®xed in the ®fth round ofscreening, such as S550N, or that were present inthe lineage that descended from V-1, such asS559G and F582Y, also appeared in the shuf¯edvariants.

The reappearance of sequence substitutions fromearlier rounds was expected, but what was surpris-ing was that other substitutions were quickly ®xedduring shuf¯ing or could be readily dispensedwith. For example, M516I appeared in only oneenzyme variant, in the ®fth round of screening, yetwas found in all four of the shuf¯ed variants. Con-versely, N27Y and I349Y appeared in several ear-lier enzyme variants, yet were found in only one ofthe four shuf¯ed variants. These sequence substi-tutions may be neutral or deleterious mutationsthat have been backcrossed out by the wild-typesequence, as has been observed in previous DNAshuf¯ing experiments.28 ± 30 The behavior of thesequence substitutions G368C and N369S wasunique, as these were ®xed in the early rounds ofscreening, yet were found in only two out of thefour shuf¯ed variants. Interestingly, the two var-iants that did not have these joint amino acid sub-stitutions instead had the adjacent substitutionG364C. It is possible that these substitutions inter-fere with one another, and hence negatively covaryin the shuf¯ed variants.

Page 7: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

Figure 5. Quaternary structures of GUS protein var-iants. GUS variants in loading buffer were heated at agiven temperature for 5 min and then developed on apolyacrylamide gel containing 0.1 % SDS. Lane 1, wild-type; 2, IV-3; 3, IV-4; 4, IV-5; 5, V-2; 6, V-4; 7, V-1; 8, VI-1, 9, VI-2; 10, S-1; 11, S-2; 12, S-3; 13, S-4. Molecularmass standards (left) are bovine serum albumin, 66 kDa;phosphorylase b, 97.4 kDa; Myosin, 222, kDa.

Increasing Thermostability of an Oligomeric Protein 331

Enzyme kinetics

While the measured activities of GUS improvedat higher temperatures, it was unclear how thedetailed kinetic properties of the enzyme variantsmay have changed. Therefore, initial velocities ofseveral of the most thermostable variants weredetermined at ambient temperature as a functionof substrate concentration, and simple Michaelis-Menten constants were derived (Table 2). EnzymesIV-5 and, to some extent, enzyme S-2 had kineticparameters similar to that of the wild-type, but allof the other enzyme variants showed some dimin-ution of activity. Increases and decreases in themeasured Km values were observed but neverexceeded twofold. Catalytic rates (kcat) of theenzyme variants all decreased, but were neverdiminished by more than fourfold. The catalyticef®ciency, kcat/Km decreased in all variants exceptIV-5.

The kinetic parameters of enzyme IV-5 were con-sistent with those previously observed in otherdirected evolution experiments, where wild-typekinetic parameters were frequently maintained oreven enhanced as thermostabilities were increased.However, in all other instances improvements inthermostability seemed to require a tradeoff in kin-etic competency. Indeed, the enzyme variantswhich had the greatest residual activities andbroadest thermal preferences, such as VI-1 andS-3, had some of the greatest decreases in kcat

or increases in Km, and hence the worst catalyticef®ciencies.

Quaternary structural changes

Inasmuch as GUS is one of the ®rst oligomericenzymes to be evolved for thermostability, it wasessential to determine whether oligomer stabilitysomehow played a role in improved thermostabil-ity. Slightly denaturing gel electrophoresis (SDS-PAGE, with 0.5 % SDS in the loading buffer and0.1 % in the gel) as a function of temperature wasused to probe the stability of the GUS tetramer(Figure 5). At ambient temperatures, the wild-typeenzyme was roughly evenly divided betweenmonomeric and tetrameric forms, but as the tem-perature was increased to 50 �C it quickly became

Table 2. Kinetic parameters of thermostable variants

Km (mM)

WT 102.4 � 10.0IV-5 105.2 � 13.2V-4 167.7 � 15.3V-1 74.4 � 5.5VI-1 135.4 � 9.3VI-2 132.0 � 17.4S-1 129.4 � 10.4S-2 89.2 � 5.5S-3 116.4 � 5.8S-4 129.6 � 8.9

Error estimates are standard deviations and were calculated based

completely monomeric. In contrast, all of theevolved enzyme variants had much greater qua-ternary structural stability at high temperatures.The least stable variant amongst those assayed wasIV-4, which showed some tendency towardsmonomerization even at ambient temperatures,and was completely monomeric at 55 �C. In con-trast, several of the variants with the greatestmeasured thermostabilities also show the greatesttendency towards tetramerization, even at hightemperatures. For example, enzyme IV-5 and sev-eral enzymes from the ®fth round of screeningretained some quaternary structure even at 60 �C.It is likely that these were native tetramers, sincethe loading buffer contained b-mercaptoethanoland would have suppressed the accumulation ofdisul®de-bonded aggregates. In fact, the enzymevariants retained at least some activity at tempera-tures even higher than the temperatures at whichquaternary structures appeared to be lost. Thisapparent discrepancy between solution and gel-based assays was likely due to the fact that theSDS in the gel assisted in the dissolution of qua-ternary structures.

Kcat (sÿ1) Kcat/Km (sÿ1 mMÿ1)

878 � 31 8.6887 � 40 8.4453 � 17 2.7346 � 8 4.6232 � 6 1.7444 � 22 3.4327 � 10 2.5619 � 13 6.9263 � 5 2.3351 � 8 2.7

on the results of three independent trials.

Page 8: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

332 Increasing Thermostability of an Oligomeric Protein

The shuf¯ed variants were particularly interest-ing, as several showed even more substantial ten-dencies to remain tetramers at high temperatures.For example, S1, S3, and S4 retained at least someoligomeric structure at 65 �C, while none of theparental enzymes did (Figure 5). The fact that thequaternary structure of enzyme variant S2appeared to be less stable than that of the othershuf¯ed variants was interesting, since S2 wasroughly as thermostable as the other shuf¯ed var-iants (Figure 4). At 70 �C all enzyme variants weremonomeric (data not shown).

The improved tetramerization of GUS variantscan be readily explained based on the sequencesubstitutions that were ®xed. While the structureof the E. coli GUS has not been solved, it is highlyhomologous to human GUS (46 % sequenceidentity)20 and to E. coli beta-galactosidase (24 %sequence identity),20 for which X-ray crystal struc-tures are known. A structural model for E. coli

Figure 6. Mapping thermostable variants onto themodeled GUS structure. (a) Tertiary structural model ofthe GUS tetramer, via the Swiss-Model server. Each sub-unit is shown in a different color. Amino acid residuesthat were changed as a result of selection are shown asballs. Red balls represent residues that were conservedafter shuf¯ing, while yellow balls represent residuesthat were lost after shuf¯ing. (b) Expanded view of asingle subunit. Domain I is green, domain II is pink anddomain III is purple, as in Figure 1. The catalytic resi-dues are shown in black and represented as balls andsticks. The site of the insertion on loop relative to thehuman enzyme is indicated by an arrow.

GUS is shown in Figure 6. This model was derivedusing the Swiss-Model server,31,32 using humanGUS and E. coli beta-galactosidase as templates.The model contains only residues 1-592 of E. coliGUS; the last 11 amino acid residues could not bemapped onto the structure. The structure has threedomains. The ®rst domain is a highly distortedbarrel-like structure with a jelly roll motif and twob-hairpin insertions (residues 1-179), the seconddomain is an immunoglobulin-like constantdomain (residues 180-287), and the last, C-terminaldomain is a TIM-barrel (residues 288-592). TheTIM-barrel domain contains the catalytic residues(Glu413, Glu504 and Tyr468) and also residues thatlie at the tetramer interface.20,33 The active site resi-dues are found near the carboxy termini of domainIII, as has been observed in other enzymes with aTIM-barrel fold20 and are localized within a largecleft that occurs at the interface of two monomers.

Following the initial six rounds of screeningthere were eight amino acid substitutions indomain I, six in domain II, and 18 in the large(�300 residue) domain III (Table 3). After shuf-¯ing, 11 of these substitutions were lost, 20 were

Table 3. Structural map of amino acid substitutions

Localization Domain

Asn27Tyr Surface ILeu39Ile Surface IArg43Gln Interface IAla44Glu Interface IPhe51Tyr Buried IAsp59Glya Surface IAla64Val Surface IGlu115Asp Surface IGln158Leu Surface IAsp185Asn Surface IIGln195His Surface IICys197Ser Surface IIAsp203Gly Surface IIThr226Asn Surface IILys286Glu Surface IILys304Arg Buried IIIIle349Phe Buried IIIGly364Cys Surface IIIGly368Cys Surface IIIAsn369Ser Surface IIILys370Glu Surface IIIThr480Ala Interface IIIMet516Ile Interface IIITyr517Phe Interface IIITyr525Phe Interface IIIMet532Thr Interface IIIAsn550Ser Buried IIIGly559Ser Interface IIIAsn566Ser Interface IIILys567Arg Interface IIIPhe582Tyr Interface IIIGln585His Interface IIIGly601Asp ND III

Suggested assignments are based on the structural modelshown in Figure 6. Bolded residues are amino acid substitu-tions that were conserved following DNA shuf¯ing.

ND, No structural assignment could be determined.a Indicates a new amino acid substitution acquired after

DNA shuf¯ing.

Page 9: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

Figure 7. Models for the evolution of thermostability.(a) Characteristic pathways for the evolution of thermo-stability, I. During directed evolution, thermotoleranceand speci®c activity may be increased at each cycle.Symbols: &, thermotolerance; *, speci®c activity. Inthis graph, units on the Y axis are abitrary. (b) Charac-teristic pathways for the evolution of thermostability, II.Alternatively, thermotolerance may initially beincreased, but the overall speci®c activity of variantsremains low. As additional mutations accumulate,speci®c activity gradually increases. Representations areas in (a). (c) Characteristic phenotypes from directedevolution. As a result of the evolutionary pathwaydescribed in (a), variant enzymes may become quiteactive over a broad thermal spectra. (d) Characteristicphenotypes from natural selection. As a result of theevolutionary pathway described in (b), the thermal pro-®les of mesophilic (ms) enzymes may separate fromthose of thermophilic (th) enzymes. It is also possiblethat this is the behavior that is observed during the lat-ter stages of evolution of the GUS variants described inthis paper.

Increasing Thermostability of an Oligomeric Protein 333

conserved and one was introduced (Asp59Gly).Domains I and II lost eight amino acid substi-tutions, while domain III lost only three. Thesequence substitutions that were ®xed duringdirected evolution and shuf¯ing were not near thecatalytic residues (Figure 6(b)), but many of themwere on or adjacent to monomer-monomer ordimer-dimer interfaces (Figure 6(a) and Table 3).The fact that the active site and the tetramer inter-faces were adjacent to one another may alsoexplain why there was an inverse relationshipbetween thermostability and activity; mutationsthat stabilized the interface may have also alteredthe structure of the active site.

In addition, previous studies had found that thethermostability of some enzymes could beimproved by the stabilization of large loopstructures.34,35 Based on homology modelling asdescribed above, E. coli GUS has a large loop com-prising residues 360-371, whereas the human pro-tein has only three amino acid residues in a similarloop (Figure 6(b)). It is interesting to note thatduring the initial screens this large loop accumu-lated four amino acid substitutions (Gly364Cys,Gly368Cys, Asn369Ser and Lys370Glu). All ofthese substitutions were introduced into the shuf-¯ing experiment except for K370E, and all wereretained following shuf¯ing. These results con®rmthe importance of loop residues for thermostability.Indeed, of all the amino acid substitutions thatwere conserved following shuf¯ing, only four are``buried'' in the protein interior.

Pathways for the evolution of thermostability

Directed evolution experiments such as thosedescribed here are consistent with several pre-viously proposed models for the evolution of ther-mostability (Figure 7). In one model, both theresistance to thermal denaturation (thermotoler-ance) and speci®c activities at higher temperaturesincrease gradually, moving by degrees from amesophilic preference to a thermophilic preference(Figure 7(a)).12 Alternatively, proteins may initiallybecome more resistant to denaturation, and onlylater recover speci®c activity at high temperatures(Figure 7(b)).11 Our results with enzyme IV-5 aremost consistent with the ®rst model (Figure 7(a)),in that IV-5 shows both resistance to denaturationand high speci®c activity at high temperatures(Figure 4(a) and (b)). However, while variantsshow greater resistance to denaturation in laterrounds of screening, their speci®c activities atincreasing temperatures do not correspondinglyincrease (Figure 4), as in the second model(Figure 7(b)).

These two models are not inconsistent with oneanother, and may merely represent different stagesduring the evolution of thermophilic proteins frommesophilic proteins. Initially, evolved proteins mayshow improved thermotolerance, the same or bet-ter speci®c activity than the wild-type or parentalprotein at low temperature, and enhanced speci®c

activities at high temperatures (Figure 7(c)). Ulti-mately, proteins from thermophiles have speci®cactivities and thermal activity pro®les similar totheir mesophilic counterparts, but both of thesecharacteristics are shifted to higher temperatures(Figure 7(d)),36 a behavior that has been called the``corresponding state'' by Jaenicke.37 However, it isassumed that the corresponding state at high tem-peratures comes at the expense of enzyme activityat lower temperatures. In this combined model,thermostable enzyme variants that initially assumebroad thermotolerance and thermal activity pro-®les can be thought of as intermediates on the wayto enzyme variants that are more fully optimizedfor function at high temperatures, and that assumemore narrow thermal activity pro®les at those tem-peratures.

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334 Increasing Thermostability of an Oligomeric Protein

We and others have observed many features ofthe proposed combined model for the evolution ofthermal stability. The speci®c activity of variant S-2at its optimal temperature, 55 �C, is similar to thatof the mesophilic, wild-type parental enzyme atphysiological temperatures (Figure 8), as thoughthese enzymes indeed have corresponding states.More importantly, a trade-off between speci®cactivities at high and low temperatures seems toexist. Point mutations led to improved speci®cactivities at higher temperatures, but as screeningcontinued and DNA shuf¯ing was introduced novariant was recovered that had a speci®c activityat ambient temperatures that was similar to that ofthe wild-type protein. Our results are similar tothose obtained during the directed evolution ofthermostable variants of b-glucosidase A from Pae-nibacillus polymyxa.38 In that report, random muta-genesis was also used to generate variants, and thelibraries were also screened for residual activityfollowing exposure to high temperatures. Someevolved glucosidase variants actually showed bet-ter catalytic parameters than the wild-type enzyme.However, when the amino acid substitutionsfound in discrete variants were combined, theoverall thermal resistance of the protein wasincreased, but only at the expense of glucosidasespeci®c activity.

There are two provisos to the proposed com-bined model when applied to the natural evolution

Figure 8. Activities of GUS variants at optimal tem-peratures. The activity of the wild-type enzyme isshown at 40 �C, close to physiological temperature, eventhough the activity of the wild-type enzyme was higherat higher temperatures. For the variants, their optimaltemperatures were assumed to be where their highestactivities were found. For IV-5 this was the activity at65 �C; V-4 at 55 �C; S-1 at 60 �C; S-2 at 55 �C and S-4 at60 �C.

of thermostability. First, the initial assumption of abroad thermotolerance may have few naturalcounterparts and instead may merely be a result ofthe screening conditions used in directed evolutionexperiments. That is, while natural proteins pre-sumably evolve at a given temperature, thedirected evolution of thermostability frequentlyinvolves exposure at high temperature and screen-ing at ambient temperatures, for purely practicalreasons (see, for example, the protocols in Giver;11

Zhao;12 Miyazaki;13 Song23). Thus, the broad ther-motolerances characteristic of arti®cially evolvedproteins may merely be a result of the fact that youget what you screen for: proteins that must notdenature at high temperatures, and yet must stillshow activity at ambient temperatures. This provi-so is credible, but arti®cially thermostable proteinsare typically not only thermotolerant or resistant tohigh temperatures, but are actually active at hightemperatures, as we have previously noted (seeFigure 4) and as others have also observed.11 ± 13

Second, the apparent inability of directed evol-ution to yield GUS or glucosidase variants that areboth highly active and highly thermostable var-iants at ®rst glance appears to contrast with pre-viously reported results for the directed evolutionof other proteins, such as p-nitrobenzyl esterase,11

subtilisin E12 and subtilisin S41.13 The apparentdifference in results might be due to the fact thatboth GUS and the glucosidase were oligomericproteins, while these other proteins were mono-mers. Thus, it may be that monomeric and oligo-meric proteins follow quite distinct mechanisticand phenotypic pathways during the evolution ofthermostability. However, we instead believe thatprevious studies in which proteins evolved broadthermal optima may have stopped before the limitsof thermostability were reached. Mutant IV-5initially behaves like other proteins that have beenevolved for thermostaiblity, in that at temperaturesabove ambient the activity is greatly increased, butat a ``critical temperature'' (in this case 70 �C) thespeci®c activity quickly drops, and further screen-ing does not yield substantial improvements inthermostability or activity. Similarly, the evolvedmonomeric proteins B. subtilis p-nitrobenzylesterase11 and B. subtilis subtilisin E12 also hadbroad thermostabilities, but their activities quicklydropped at 60 �C and 76 �C, respectively. Thus,many monomeric and oligomeric proteins mayhave limits to the thermostabilities that can initiallybe achieved by screening for thermotolerance(although these limits will likely differ for eachprotein). Additional improvements in thermostabil-ity may only be garnered by extensive mutationthat re-optimizes the catalyst to function solely athigh temperautres and by screening for function atthe desired temperature. Consistent with thishypothesis, it is interesting to note that when thepsychrophilic protease subtilisin S41 variant 3-2G7was evolved for ®ve additional rounds, there waslittle additional improvement in thermostability,39

Page 11: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

Increasing Thermostability of an Oligomeric Protein 335

and there was actually a slight decrease in thespeci®c activity of the evolved variant.

While these hypotheses are interesting it is stilldif®cult to draw general conclusions from the lim-ited number of studies that have so far been car-ried out. The suggestion by Zhao & Arnold12 that asmall number of mutations can yield thermophilicenzymes may have limited import, because theevolved mesophilic enzyme subtilisin E and itsnatural thermophilic counterpart thermitase wereboth somewhat different from most thermophilicproteins in that they had broad thermal activitypro®les. Moreover, these proteases were also extra-cellular rather than intracellular, and extracellularenzymes are in general more stable to environmen-tal perturbations, including temperature.40 Thus,subtilisin E might in some ways be considered tohave been ``pre-evolved'' to become a thermitase-like enzyme. Conversely, our suggestion thatbroad thermotolerance is an intermediate stageduring the evolution of thermophily may be oflimited import because the active site of GUS isadjacent to its oligomerization domain, and thismay enforce a perceived trade-off between broadthermotolerance and catalytic activity that wouldnot be relevant to other enzymes. On the otherhand, results with GUS may be especially perti-nent, since about 10 % of all three dimensionalstructures known are TIM-barrels.41,42

Irrespective of whether arti®cially thermostableproteins follow evolutionary pathways similar tothose of naturally thermostable proteins, themethods that we and others have developed haveimportant implications for biotechnology. Byaccumulating a relatively small number ofmutations both the thermostability and the activityof a protein can be greatly increased.11,12,15,24

Further increases in thermostability are possible,and even though the variants lose some activity asthey adopt an even broader thermal pro®le, theynonetheless retain wild-type levels of activity attheir optimal temperatures (Figure 8) and substan-tial activities at even higher temperatures(Figure 4(b)). Ultimately, by allowing proteins toaccumulate large numbers of mutations that re®netheir activities at high temperatures it may bepossible to move into new thermal regimes and tocreate extremely hyperthermophilic proteins forindustry.

Materials and Methods

Library construction

The gene encoding E. coli GUS was mutated by error-prone PCR,43 using the oligonucleotides pet 50(50-AGATCTCGATCCCGCGAAATTAATACGA-30) andpet 30 (50-CGGGCTTTGTTAGCAGCCGGATCTC-30. ThePCR product was digested with XbaI and HindIII restric-tion enzymes (NEB, Berverly, MA) and the isolated frag-ment was cloned into the vector pET28a(�) (Novagen,Madison, WI).

Enzyme variants identi®ed in a given round of screen-ing were pooled and used as templates for the gener-

ation of further mutants by mutagenic PCR. In laterrounds, DNA shuf¯ing was carried out to recombineindividual sequence changes.27 PCR products weredigested with DNase I (0.01 units) (Epicentre technol-ogies, Madison, WI) for ten minutes at ambient tempera-ture. The cleavage reaction was loaded onto a 2 %agarose gel and fragments between 50 bp and 300 bpwere gel-puri®ed (Qiagen, Valencia, CA). Approximately1 mg of puri®ed DNA fragments were used for genereassembly without primers, and one-tenth of the ampli-®ed products were used as templates for a PCR ampli®-cation with primers. The ®nal PCR product was digestedwith XbaI/HindIII and cloned into pET28a(�).

Screening for thermostability

The screen for thermostability was modi®ed from ascreen described by Matsumura et al.21 for the identi®-cation of GUS variants that were resistant to inactivationby glutaraldehyde. The enzyme library was transformedinto E. coli strain DH5�Lac (DE3) cells44 that carried anadditional plasmid, pLysS, that reduced the toxicity ofT7 RNA polymerase expression.45 and plated on LBplates containing 34 mg/ml chloramphenicol and 25 mg/ml kanamycin. After 16 hours of growth at 37 �C, colo-nies were absorbed onto a nitrocellulose ®lter and trans-ferred colony-side-up to LB kan/chl plates containing0.5 mM IPTG. The colonies were re-grew and GUSexpression was allowed to proceed at 37 �C for 12 hours.Cells were disrupted with chloroform gas for 15 minutesby placing the plate containing the ®lter face down overa glass dish containing chloroform. The nitrocellulose®lter was transferred to ®lter paper #3 (Whatman, Maid-stone, England) that had been wetted with GUS buffer(50 mM sodium phosphate, pH 7; 1 mM EDTA; 5 mM2-mercaptoethanol). The ®lter paper was transferred to alarge disposable polystyrene weigh dish (Fisher Scienti-®c, Pittsburgh, PA) and ¯oated on a water bath at theappropriate temperature (65-90 �C) for 5-15 minutes. Theweigh dish was then transferred to room temperaturefor ®ve minutes, and incubated with GUS buffer contain-ing 40 mg/ml X-Glu (5-bromo-4-chloro-3-indolyl-b-D-glu-curonide; Gold Biotechnology, St. Louis, MO). Thereaction proceeded for ten minutes and the ®lter wasthen dried. Colonies with higher GUS activity were typi-cally more blue. To re-check phenotype, 1.5 ml of LBwas inoculated with a variant, cultures were grown toan A600 � 0.6, and the expression of GUS was inducedby adding 0.5 mM IPTG. After three hours, 40 ml ofinduced culture was heated for ten minutes at the tem-perature used for screening and residual activity wasdetermined using pNPG (p-nitrophenyl-b-D-glucuronide)as a substrate. Only enzyme variants that were consist-ently more thermostable than parental enzymes werecarried into the next round of mutagenesis. Plasmidscontaining variants were puri®ed, mixed, and used astemplates for error-prone PCR.43

Protein purification

Plasmids bearing mutant genes were cleaved withNdeI and HindIII, and the fragments were cloned intopTE28a such that the protein was fused to the aminoterminal histidine tag. The expression constructs weretransformed into E. coli strain DH5�Lac (DE3) cells car-rying the plasmid pLysS. Transformants were grown in350 ml of LB kan/chl at 37 �C to mid-log phase(A600 � 0.6), IPTG was added to induce protein

Page 12: Increasing the thermal stability of an oligomeric protein, beta-glucuronidase

336 Increasing Thermostability of an Oligomeric Protein

expression, and the cells were allowed to grow for anadditional three hours. The induced cells were collectedby centrifugation and lysed by adding 5 ml of B-PER(Pierce, Rockford IL) containing 1 unit DNase I, 5 mMMgCl2 and 0.5 M NaCl2. The lysates were centrifuged at1000 rpm for 30 minutes and passed over an af®nitynickel chelate column. The columns were washed with10 column volumes of wash buffer (50 mM phosphate(pH 7), 0.5 M NaCl2, 60 mM imidazole) and the proteinswere eluted with 0.5 M imidazole in phosphate buffer(50 mM phosphate (pH 7), 0.5 M NaCl2). The eluted pro-teins were dialyzed against GUS buffer and concen-trations were determined via Bradford protein assay(Bio-Rad, Hercules CA). The homogeneity of proteinsamples was determined by SDS-PAGE.

Assays for residual activity

Residual activities were determined after incubatingisolated enzymes at a variety of temperatures. Some0.5 pmol of GUS protein in 20 ml of GUS buffer wasincubated for ten minutes at a given temperature. Theprotein was cooled on ice and residual activity wasmeasured at 23 �C in 1 ml of GUS buffer containing300 mM pNPG. The reaction was followed at 405 nm.Data shown are the average of three independentmeasurements.

Assays at high temperature

Activities were determined at a variety of tempera-tures. 0.25 pmol of GUS protein in 48 ml of GUS bufferwas pre-incubated for ®ve minutes at a given tempera-ture and 400 mM pNPG pre-incubated at the sametemperature was added. The reaction was allowed todevelop for one minute and was stopped by adding50 ml of 5 N NaOH and cooling on ice. The ®nal absor-bance was measured at 405 nm. The data shown are theaverage of three independent measurements.

Kinetic parameters

Kinetic parameters (Km and Kcat) were determineddirectly via curve-®tting routines on Kaleidagraph soft-ware (Adelbeck Software, Reading, PA). The substrate(pNPG) and enzyme concentrations used for the deter-mination of the kinetic parameters were 10-500 mM and0.5 nM respectively. Reactions were carried out for twominutes at 23 �C. Initial velocities were determined usinga Shimadzu UV-1601 spectrophotometer (ShimadzuScienti®c Instruments, Columbia, MD) at 405 nm.

Quaternary structure determinations

SDS-PAGE was used to ascertain the oligomerizationstate of GUS. A 1 mg sample of GUS protein in 10 ml ofloading buffer (50 mM Tris-HCl (pH 6.8), 0.5 % SDS,10 % glycerol, 28 mM b-mercaptoethanol, 0.05 % bromo-phenol blue) was heated for ®ve minutes at a giventemperature. Samples were developed on a SDS-8 %polyacrylamide gel and protein was visualized viaCoomassie Blue staining.

Acknowledgements

H.F. thanks the Instituto de Biotecnologia/UNAM forassistance with his postdoctoral fellowship. This researchwas supported by a grant from the Of®ce of NavalResearch, and by a MURI award from the ArmyResearch Of®ce.

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Edited by P. E. Wright

(Received 8 August 2001; received in revised form 31 October 2001; accepted 1 November 2001)