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Enzyme and Microbial Technology 42 (2008) 278–283

Esterase activity of bovine serum albumin up to 160 ◦C:A new benchmark for biocatalysis

Jesus Cordova a, Jessica D. Ryan b, Boonchai B. Boonyaratanakornkit b, Douglas S. Clark b,∗a Departamento de Ingenierıa Quımica-CUCEI, Universidad de Guadalajara, Jalisco 44480, Mexico

b Department of Chemical Engineering, University of California, Berkeley, CA 94720-1462, USA

Received 30 August 2007; received in revised form 8 October 2007; accepted 9 October 2007

bstract

Albumins are highly conserved proteins that carry out a multitude of physiological functions and exhibit a broad range of catalytic activities.oreover, amino acid sequence comparisons of the albumin multigene family indicate that albumins diverged from a common ancestor. Here we

eport that bovine serum albumin (BSA) can catalyze ester hydrolysis at high temperatures (as high as 160 ◦C) well beyond the temperature limitseported for enzymatic catalysis, including for enzymes from known hyperthermophiles. Furthermore, BSA exhibited a ∼133-fold increase in itsurnover number (kcat) toward p-nitrophenyl palmitate from 70 to 150 ◦C. When BSA was incubated for 1 h at 150 ◦C in the presence of 25 mMDS, it retained complete esterase activity, indicating that a catalytically competent orientation of amino acid residues exists in the denaturedr partially unfolded protein. However, esterase activity diminished to ∼50% upon disruption of the protein’s disulfide bridges and disappeared

ompletely when BSA was digested by proteases. These results point to a new standard of robustness for biocatalytic activity at high temperatures.atalytic activity and promiscuity at very high temperatures could have been advantageous to enzymes in primitive organisms evolving in hotnvironments, making BSA an intriguing model for early enzymes.

2007 Elsevier Inc. All rights reserved.

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eywords: Promiscuity; Ester hydrolysis; Hyperthermophilic enzyme activity;

. Introduction

Specificity is often considered to be a distinctive feature ofiocatalytic activity. In recent years, however, it has becomelear that some enzymes have additional functions outside ofheir primary catalytic reactivities. Some enzymes ‘moonlight’,erving non-catalytic regulatory functions, while others are cat-lytically promiscuous, having the ability to catalyze secondaryeactions on multiple substrates within the same active site [1,2].rom an evolutionary perspective, such promiscuous activityinefficient and rudimentary as it may be) could have providedncestral cells with an adaptive advantage, enabling survival androviding a foundation for further evolution [3]. Furthermore,he relatively small number of enzyme superfamilies suggests

hat evolution has solved myriad cellular requirements withimited enzymatic resources [4,3]. These observations providetrong support for the central role of divergent evolution in

∗ Corresponding author. Tel.: +1 510 642 2408; fax: +1 510 643 1228.E-mail address: clark@cchem.berkeley.edu (D.S. Clark).

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141-0229/$ – see front matter © 2007 Elsevier Inc. All rights reserved.oi:10.1016/j.enzmictec.2007.10.007

al stability; Detergent effects

iology, whereby catalytic promiscuity may be considered asstarting point for enzyme evolution [5].

Serum albumin is the most abundant protein in the sera of ver-ebrates and has been one of the most extensively studied of allroteins [6]. The primary structures of several species of albuminre known, and mammalian types show amino acid sequencedentities of about 70–80%. In particular, human serum albu-

in (HSA) and bovine serum albumin (BSA) share a sequenceomology of 76% [7]. In addition to its regulatory role ofaintaining blood osmolarity, serum albumin also serves as a

ransport protein for fatty acids and can bind a diverse range ofetabolites and xenobiotics [6,8,9]. In HSA, for example, five

rincipal binding sites for medium- or long-chain fatty acidsave been located [8].

A remarkable functional property of albumins is theirromiscuous catalytic activity toward a broad range of organicolecules, including esters, amides, phosphates and benzisox-

zoles [10–12]. In particular, the hydrolysis of p-nitrophenolsters by HSA was first reported in 1951 [13]. This “esterase-ike” activity has been localized to the sub-domain IIIA ofSA [14,15]. HSA is characterized by a heart shape and is

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omposed of three structurally similar domains (designated–III), each of which is stabilized by an unusually large numberf internal disulfide bonds (17 in total). Each domain consistsf two sub-domains (A and B) that share common structurallements [9,8]. Site-directed mutagenesis studies have shownhat Arg-410 and Tyr-411 are essential for the esterase activityf HSA, and a reaction mechanism similar to that of proteasesas been proposed [15,16]. A covalent intermediate is formedn the active site, and throughout the catalytic reaction, Arg-410emains hydrogen-bonded to Asn-391, suggesting the presencef a catalytic triad [17].

In the present work, we report ester hydrolysis by BSAt extraordinarily high temperatures beyond those previouslyeported for biological reactions. When considered in connec-ion with the catalytic promiscuity of albumins, this extremeeactivity points to a model whereby high thermostability andromiscuous activity may have been synergistic properties ofncestral enzymes in primitive organisms evolving in high-emperature environments.

. Material and methods

.1. Chemicals

All the reagents, substrates and BSA (fatty acid-free, fraction V) were pur-hased from Sigma (St. Louis, MO, USA).

.2. Measurement of protein concentration

The protein concentration was measured using the Bradford Bio-Rad (Her-ules, California) protein microassay [18].

.3. Determination of esterase activity

The hydrolysis of p-nitrophenyl acyl esters catalyzed by BSA was followedpectrophotometrically by monitoring the formation of p-nitrophenol (pNP) at10 nm (AVIV Model 14DS UV–vis spectrophotometer). Typical assays wereerformed as follows: 900 �l of 50 mM Pipes buffer pH 7, containing 1 MaCl and 50 �l of 0.1 mM BSA, were mixed together in a 1 ml-cuvette andre-heated in a water bath at the assay temperature. For reaction temperatures90 ◦C, the mixtures were pre-heated to 90 ◦C before the addition of 50 �l ofmM p-nitrophenyl acyl ester dissolved in isopropanol. This reaction mixtureas immediately placed in the spectrophotometer set at the assay temperature.he background substrate hydrolysis was accounted for with blanks containinguffer instead of BSA for all conditions tested. All experiments were performedn duplicate or in triplicate, and the values in the figures and tables represent the

eans ± the standard deviation. Extinction coefficients for pNP at 410 nm wereetermined for each assay temperature. The calculated coefficients increased lin-arly from 10.04 × 103 M−1 cm−1 at 60 ◦C to 11.01 × 103 M−1 cm−1 at 160 ◦C.ne unit (U) was defined as the release of 1 �mol of p-nitrophenol per minute.

.4. BSA specificity

The BSA specificity was determined by assaying the activity of BSA towards-nitrophenyl (pNP-) acyl esters having different chain lengths (C2 = acetate,3 = propionate, C4 = butyrate, C6 = caproate, C8 = caprylate, C10 = caprate,12 = laurate, C14 = myristate and C16 = palmitate). Assays times were eitheror 15 min depending on the substrate.

.5. Effect of SDS on esterase activity

The effect of SDS on BSA esterase activity was studied using two con-entrations of pNP-myristate (50 and 500 �M) at 95 ◦C with NaCl excluded

tr

l Technology 42 (2008) 278–283 279

rom the buffer solution. The assay buffer contained varying amounts of SDSanging from 0 to 25 mM for solutions containing 50 �M substrate, and 0 to5 mM for solutions containing 500 �M substrate. Tweens (polyoxyethyleneetergents) and Tritons were avoided because their solutions became cloudy atigh temperatures and interfered with the esterase activity assay.

.6. Effect of incubation temperature on esterase activity

The effect of temperature on BSA activity was studied using pNP-palmitates a substrate. For kinetic studies, the BSA concentration was decreased as thencubation temperature increased in order to increase the time over which thenitial rate could be measured (from 10 �M for 70 ◦C to 0.25 �M for 150 ◦Cr 160 ◦C). At temperatures >95 ◦C, the reaction system was pressurized to0 psi using argon to prevent boiling of the reaction mixture. After placinghe cuvette in the spectrophotometer, the reaction mixture reached a set-pointemperature of 160 ◦C in 4 min. Consequently, for all assays above 95 ◦C, the ratef substrate hydrolysis was measured after 5 min of incubation at the set-pointemperature. Spontaneous substrate hydrolysis was not observed at temperaturesess than 150 ◦C, and only a slight background hydrolysis rate was observed andubtracted from assay data at 160 ◦C. The contribution of BSA aggregation at50 ◦C to the optical density at 410 nm was negligible (<1%) compared to thatf pNP release.

.7. Effect of the substrate concentration on esterase kinetics

The effect of the substrate concentration (pNP-palmitate) on BSA esterasectivity was examined at 70 and 150 ◦C in the absence of SDS. Kinetic param-ters were determined from Lineweaver-Burk plots.

.8. BSA digestion

BSA (0.4 mM) was dissolved in 100 mM Tris–HCl, pH 8.2, containing 8 Mrea. The BSA disulfide bonds were reduced by adding dithiothreitol to a finaloncentration of 7 mM and incubating at 60 ◦C for 60 min. Free sulfhydrylroups were then blocked by adding iodoacetamide to a final concentration of5 mM followed by incubation at 25 ◦C for 15 min in the dark. The sample wasiluted eightfold with 100 mM Tris–HCl, pH 8, containing 1.2 mM CaCl2, giv-ng a final urea concentration of 1 M, and the unfolded protein was then digestedy adding proteases (trypsin, chymotrypsin, or subtilisin A) in a molar ratio toSA of 1:50. The digest solutions were then incubated for 36 h at 37 ◦C. Resid-al activities were assayed for each digestion step at 95 and 150 ◦C. Controlsacked the addition of proteases, but were incubated for 36 h at 37 ◦C.

.9. BSA stability experiments

BSA solutions (100 �M) containing either 25 mM or no SDS were incubatedt 150 ◦C for 1 h. Following the incubation, protein samples were centrifugedt 20,800 × g for 10 min and the residual esterase activity of 50 �l of the super-atant was assayed at 95 ◦C using pNP-myristate as the substrate. NaCl wasxcluded from the buffer solution and SDS (3 mM) was added instead.

.10. Hydrolysis of other esters

The hydrolysis of other esters was measured according to previously pub-ished methods. The experiments were performed at 90 ◦C and the substratesnd methods used were the following: 4-methylumbelliferyl-butyrate and 4-ethylumbelliferyl-oleate by fluorescence [19], Tween 20 and Tween 80 by

pectrophotometry [20], palmitin, tripalmitin and triolein by a colorimetric assay21], tricaprylin and tributirin by titrimetry [22].

. Results

BSA has been shown to exhibit optimal esterase activityoward p-nitrophenyl esters at pH 9.5 [16,17]. However, we car-ied out assays at pH 7.0 because the ester substrates had greater

280 J. Cordova et al. / Enzyme and Microbial Technology 42 (2008) 278–283

Fig. 1. BSA specificity towards p-nitrophenyl acyl esters of different chainlengths (C2 = acetate, C3 = propionate, C4 = butyrate, C6 = caproate,CCs

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rresponding kinetic parameters (Table 1) were estimated usingLineweaver–Burk plots shown in Fig. 4. BSA catalyzed thehydrolysis of pNP-palmitate at 70 and 150 ◦C (without SDS)with catalytic efficiencies (kcat/KM) of 1.03 and 22.2 mM−1 s−1,

8 = caprylate, C10 = caprate, C12 = laurate, C14 = myristate and16 = palmitate). Assays were performed at 95 ◦C. The error bars represent the

tandard deviation (n = 3).

hermal stability over a broader temperature range at neutral pH.he addition of NaCl (1 M) further increased the stability of theubstrates, but had no effect on BSA esterase activity at highemperatures (data not shown).

.1. BSA specificity

BSA specificity at 95 ◦C towards p-nitrophenyl (pNP-) acylsters with different chain lengths is shown in Fig. 1. Theydrophobicity of the substrate side-chain influenced the reac-ion rate, which was highest for pNP-esters with an acyl moietyf 6–12 carbon atoms. Despite the preference of BSA for shorter-hain esters such as pNP-caprylate (C8), pNP-myristate (C14)nd pNP-palmitate (C16) were used in further temperature stud-es because of their superior thermal stability.

.2. Effect of SDS on esterase activity

The effect of SDS on BSA esterase activity was measuredt 95 ◦C for solutions containing two different pNP-myristateoncentrations. For solutions containing 50 �M substrate, theptimal SDS concentration was 2.8 mM, and increasing the SDSoncentration to 22 mM led to complete inhibition of activ-ty. Solutions containing 500 �M substrate displayed a similarrend, with optimal activity exhibited in 5.6 mM SDS and nearomplete inhibition observed in 65 mM SDS (Fig. 2).

.3. Effect of temperature and SDS on esterase activity

The hydrolytic activity of BSA towards pNP-palmitate50 �M) was measured at temperatures ranging from 60 to60 ◦C. Fig. 3 shows activity data for assays containing eithero SDS or 2.8 mM SDS. The esterase activity of BSA was

early undetectable at incubation temperatures below 80 ◦C inhe absence of SDS, while esterase activity increased when SDS2.8 mM) was added, resulting in quantifiable pNP-palmitateydrolysis at temperatures as low as 60 ◦C. In the absence of

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s a substrate at two concentrations: 50 �M (�) and 500 �M (©). Assays wereerformed at 95 ◦C. The error bars represent the standard deviation (n = 3), butre not shown when they are smaller than the symbols.

DS, esterase activity increased with temperature, reaching aaximum at 150 ◦C. The surfactant had an inhibitory effect at

emperatures above 100 ◦C, as shown in Fig. 3, and was notdded at temperatures above 140 ◦C. Remarkably, the hydrol-sis rate increased 290-fold from 70 to 150 ◦C (from 1.28 to71 U/g BSA). At 160 ◦C, a slight decrease in esterase activityas observed. Temperatures higher than 160 ◦C could not be

nvestigated because of equipment limitations. The hydrolyticctivity of BSA towards pNP-myristate was also measured andsimilar temperature dependence on activity was observed (dataot shown).

.4. Effect of substrate concentration on esterase activity

The Michaelis–Menten equation can be used to describe theate of BSA-mediated pNP-palmitate hydrolysis, and the cor-

ig. 3. Specific esterase activity of BSA toward p-nitrophenyl-palmitate as aunction of temperature, with (©) or without (�) SDS (2.8 mM). The error barsepresent mean deviations (n = 2).

J. Cordova et al. / Enzyme and Microbial Technology 42 (2008) 278–283 281

Table 1Kinetic parameters for BSA-catalyzed hydrolysis of pNP-palmitate

Temperature (◦C) kcat (10−3 s−1) KM (�M) kcat/KM (mM s)−1

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Table 2Residual esterase activity of BSA following potentially denaturing treatments

Treatment Residual esterase activity (%)a

Assay at 95 ◦C Assay at 150 ◦C

Controlb 100 100In 8 M urea 90.4 ± 1.9 105 ± 8.1Disulfide bridges reduced 35.9 ± 1.8 59.3 ± 7.7

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espectively. From 70 to 150 ◦C, the turnover number (kcat)ncreased 133-fold (from 3.18 × 10−3 to 424 × 10−3 s−1), whilehe Michaelis constant (KM) increased only sixfold (from 3.10 to9.1 �M). It is interesting to note that for reactions at both 70 and50 ◦C, the data points corresponding to the highest substrateoncentrations fall slightly below the linear-fit lines, suggestinghe possibility of substrate activation or cooperativity at highubstrate concentrations.

.5. BSA digestion by proteases

BSA was digested by three proteases (trypsin, chymotrypsin,

nd subtilisin A), and residual esterase activities were assayedt 95 and 150 ◦C. BSA digestion by these proteases was con-rmed with SDS-polyacrylamide gel electrophoresis; that is, no

ntact BSA was observed on the gel following digestion with

ig. 4. Lineweaver–Burk representations of assays performed at 70 and 150 ◦C.he assays were performed at 70 ◦C (�) and 150 ◦C (©). The error bars represent

he standard deviation (n = 3), but are not shown when they are smaller than theymbols.

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a Residual esterase activities towards pNP-palmitate were assayed at 95 and50 ◦C.b Untreated BSA. Values are the means ± standard deviations (n = 3).

ach protease, and only relatively small (<∼20 kDa) peptideragments were evident. Furthermore, the proteolytic diges-ion completely eliminated BSA esterase activity at both assayemperatures (data not shown). The protein digestion protocolequired denaturation by urea (8 M) and reduction of the disul-de bridges using dithiothreitol and iodoacetamide. AlthoughM urea typically denatures proteins [23], BSA esterase activ-

ty was retained (Table 2). However, disruption of the disulfideridges induced a loss in esterase activity of 64 and 41% at 95nd 150 ◦C, respectively.

.6. BSA stability at 150 ◦C

BSA stability at 150 ◦C was investigated by incubating therotein for 1 h with and without 25 mM SDS. In the absence ofDS, aggregation occurred after thermal treatment (followed at50 nm; data not shown) and the esterase activity diminishedy 64% (Table 3). Under these conditions, the loss of esterasectivity was directly related to the aggregation as evidenced byhe inactivity of the aggregated protein (isolated by centrifuga-ion for 10 min at 20,800 × g). On the other hand, the presencef SDS effectively prevented aggregation and, consequently,sterase activity was completely retained after the heat treatmentTable 3).

BSA aggregation at high temperatures in the absence of SDSas dependent on the protein concentration (data not shown).or studies of esterase activity as a function of incubation tem-erature, a BSA concentration of 0.25 �M was used at 150 ◦C,hereas in stability experiments, the BSA concentration was00 �M. The contribution of possible BSA aggregation to the

ctivity assays at 150 ◦C was insignificant, as control experi-ents indicated that aggregation under the assay conditions had

n insignificant (<1%) effect on the absorbance change at 410 nmssociated with pNP-palmitate hydrolysis.

able 3ffect of SDS (25 mM) on the thermostability of BSAa

dditive Protein (g/l) Esterase activity (U/l)b

Before After Before After

o SDS 2.94 ± 0.01 1.64 ± 0.04 70.2 ± 4.0 25.6 ± 2.4DS 2.88 ± 0.06 2.92 ± 0.01 72.3 ± 0.7 75.1 ± 1.1

a Protein concentration and esterase activity were assayed before and aftereat-treatment (150 ◦C, 1 h).b Esterase activity was assayed at 95 ◦C towards pNP-myristate. Values are

he means ± standard deviations (n = 3).

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.7. Hydrolysis of other esters

Serum albumins have been shown to exhibit esterase activityowards several esters [10]. We observed hydrolytic activity ofSA at 90 ◦C towards 4-methylumbelliferyl esters (-butyratend -oleate), Tweens (20 and 80), and a mono-acyl glycerolpalmitin); however, triglycerides were not hydrolyzed (resultsot shown). These results reveal that BSA possesses esterasectivity but not true lipase activity.

. Discussion

BSA exhibits catalytic activity up to at least 160 ◦C, whichs well beyond the highest temperature at which an enzymeas previously been shown to retain activity. For example,he proteasome from the hyperthermophile Methanocaldococ-us jannaschii displayed hydrolytic activity up to 130 ◦C,hich is one of the highest temperatures reported for the

unction of any enzyme [24]. Furthermore, the catalytic effi-iencies obtained in the present work (1.03 and 22.2 mM−1 s−1

or pNP-palmitate at 70 and 150 ◦C, respectively) areigher than those reported previously for several albumin-atalyzed reactions, including the HSA-catalyzed hydrolysisf pNP-laurate at 25 ◦C (kcat/KM = 0.0257 mM−1 s−1) [16], theabbit-SA-catalyzed hydrolysis of carbamate carbaryl at 37 ◦C

kcat/KM = 3.0 × 10−4 mM−1 s−1) [25], and the BSA-catalyzedsomerization of 1,2-benzisoxazole at 25 ◦C in acetonitrilekcat/KM = 0.00877 mM−1 s−1) [11]. Not only are the catalyticfficiency and turnover number (kcat) measured at 150 ◦Celatively high compared to measurements made for other BSA-atalyzed reactions at lower temperatures, but they are also highelative to promiscuous activities of other enzymes [5,1,26].urthermore, the Michaelis constants (KM) at 70 and 150 ◦C3.10 and 19.1 �M, respectively) are small compared to thoseor many enzymatic reactions. In all, these results illustrate thatSA functions relatively well as a biocatalyst at extraordinarilyigh temperatures.

The esterase activity of BSA at 95 ◦C was higher toward pNP-aprylate than any of the other pNP-esters (Fig. 1). This findinggrees with the results at 35 ◦C of Østdal and Andersen [27],ndicating that the pNP-esterase specificity of BSA is indepen-ent of temperature over this range. By comparison, Sakurai etl. found that the catalytic activity of HSA at 25 ◦C was moreronounced for short-chain substrates and maximum for pNP-ropionate [16]. In general, it is assumed that HSA has a greaterffinity for small, negatively charged hydrophobic molecules9,16].

At 95 ◦C, SDS had either a positive or negative effect onsterase activity, depending on the surfactant and substrate con-entrations (Fig. 2). The activation by SDS at relatively lowoncentrations may result from a lubrication effect, leading tomore flexible protein, whereas inhibition at higher concen-

rations may be due to denaturation [28] and/or competitive

nhibition of BSA by SDS. Tween 20 and fatty acids were alsohown to inhibit BSA-catalyzed hydrolysis of pNP-myristate27]. Similar inhibitory effects of detergents have been reportedor lipases [29].

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l Technology 42 (2008) 278–283

The esterase activity of the BSA solution containing 25 mMDS was unaffected after incubation at 150 ◦C for 1 h, but sam-les lacking SDS lost significant esterase activity. The protectiveffect of SDS may result from the amphiphilic nature of thenionic surfactant. SDS may help preserve the protein structurey bridging nonpolar residues and positively charged residuesocated on different loops within the protein [29]. Furthermore,DS reduces BSA aggregation by increasing electrostatic repul-ion between protein molecules [28], and has previously beenhown to improve BSA thermal stability over a range of assayemperatures [28,30].

Assuming that BSA is at least partially denatured at 150 ◦C,ubstrate binding to a functional active site is still possible inhe partly unfolded protein. Thus, the amino-acid side chainsnvolved in substrate binding and catalysis maintain an orienta-ion (or orientations) suitable to carry out ester hydrolysis. Themino acid residues involved directly in the catalytic site of HSAR-410 and Y-411) are adjacent [15] (the corresponding residuesf BSA are R-409 and Y-410). In the crystal structure of the pro-ein, the distance between the hydroxyl group of Y-411 and theerminal nitrogen atom of the guanido group of R-410 is only.7 A [9]. Proper positioning of these residues for catalysis ispparently preserved in thermally denatured conformations ofSA as well.

The catalytic activity of denatured BSA was also evident fol-owing treatment with urea. Although BSA is denatured at 8 Mrea [23], its esterase activity was completely retained (Table 2).owever, disruption of disulfide bonds reduced esterase activ-

ty by 44–64%, indicating that disulfide bridges help to maintainhe catalytically competent conformation(s). The large numberf disulfide bridges in BSA (17) may also contribute to the pro-ein’s high thermal stability and help prevent complete unfoldingt very high temperatures. In this connection, Matsushita et al.eparately expressed the three domains of HSA, and concludedhat interdomain interaction is crucial for full esterase activity31]. Furthermore, loss of activity upon proteolytic digestion ofSA (Table 2) indicated that esterase activity requires the intactolypeptide.

The wide range of reactions catalyzed by BSA, together withts natural abundance and relatively high catalytic efficiencyt extreme temperatures, make BSA an appealing candidateor biocatalytic applications, including bioprocesses in non-queous solvents. For example, Liu and Lemma-Gray utilizedSA to catalyze the isomerization of 1,2-benzisoxazole in purecetonitrile [11]. Another possible application is in detoxifi-ation processes at low substrate concentrations. A promisingxample along these lines was demonstrated by Sogorb et al.,ho exploited the esterase activity of Rabbit-SA to hydrolyze

arbamate carbaryl, eliminating the toxicity of this pesticide25].

Finally, our results with BSA have bearing on the evolution-ry hypothesis that promiscuous enzymes may have maximizedhe catalytic versatility of ancestral cells with small gene con-

ents and limited enzyme resources [3,32]. The promiscuousctivity of albumins and their apparent divergence from a com-on ancestor support the hypothesis that ancestral albumins

r similar proteins may have performed catalytic functions in

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rimitive life forms at high temperatures. Hyperthermophilicrganisms, in their possible role as the earliest ancestors ofife [33], would certainly have benefitted from the synergyf promiscuity and catalysis at high temperatures. Such aombination may have been a vital factor in meeting theiochemical and survival requirements of hyperthermophilicncestral cells. The extent to which albumin-like proteinsay have facilitated high-temperature survival and adapta-

ion remains unresolved; however, their functional versatilitynd robustness does warrant consideration of albumins as aossible model for the early-stage development of primordialnzymes.

cknowledgments

Jesus Cordova acknowledges the fellowships received fromC-MEXUS-Conacyt and from AMC-FUMEC. This work was

upported by the National Science Foundation.

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