Change in Heat Capacity for Enzyme Catalysis DeterminesTemperature Dependence of Enzyme Catalyzed RatesJoanne K. Hobbs,† Wanting Jiao,‡ Ashley D. Easter,† Emily J. Parker,‡ Louis A. Schipper,§

and Vickery L. Arcus*,†

†Department of Biological Sciences, Faculty of Science and Engineering, University of Waikato, Hamilton 3240, New Zealand‡Biomolecular Interaction Centre and Department of Chemistry, University of Canterbury, Christchurch 8041, New Zealand§Department of Earth and Ocean Sciences, Faculty of Science and Engineering, University of Waikato, Hamilton 3240, New Zealand

*S Supporting Information

ABSTRACT: The increase in enzymatic rates with temperature up to an optimumtemperature (Topt) is widely attributed to classical Arrhenius behavior, with the decrease inenzymatic rates above Topt ascribed to protein denaturation and/or aggregation. This accountpersists despite many investigators noting that denaturation is insufficient to explain thedecline in enzymatic rates above Topt. Here we show that it is the change in heat capacityassociated with enzyme catalysis (ΔC‡

p) and its effect on the temperature dependence ofΔG‡ that determines the temperature dependence of enzyme activity. Through mutagenesis,we demonstrate that the Topt of an enzyme is correlated with ΔC‡

p and that changes to ΔC‡p

are sufficient to change Topt without affecting the catalytic rate. Furthermore, using X-raycrystallography and molecular dynamics simulations we reveal the molecular detailsunderpinning these changes in ΔC‡

p. The influence of ΔC‡p on enzymatic rates has

implications for the temperature dependence of biological rates from enzymes to ecosystems.

The relationship between temperature and the rate of achemical reaction is most simply described by the 19th

century Arrhenius equation: k = A e−EA/RT, where k is the rateconstant, A is a pre-exponential factor, EA is the activationenergy for the reaction, R is the universal gas constant, and T isthe temperature. Early in the 20th century, Eyring and Polanyideveloped Transition State Theory, expanding the Arrheniusequation and expressing k in terms of Boltzmann and Planck’sconstants (kB, h), the transmission coefficient (κ, for simplicityassumed to be 1 here), and the difference in Gibbs free energybetween the ground state and the transition state (ΔG‡, eqs 1and 2). In turn, ΔC‡

p (the difference in heat capacity betweenthe ground state and the transition state at constant pressure)quantifies the temperature dependence of ΔG‡ and thus,describes the temperature dependence of the reaction rateaccording to eq 3:

= −Δ ‡k

k Th

e G RTB /(1)

= − Δ ‡⎛⎝⎜

⎞⎠⎟k

k Th

GRT

ln( ) ln[ ]B

(2)

= −Δ + Δ −

+Δ + Δ

‡ ‡

‡ ‡

⎛⎝⎜

⎞⎠⎟k

k Th

H C T T

RT

S C T T

R

ln( ) ln[ ( )]

[ ln( / )]

T p

T p

B 0

0

0

0

(3)

where T0 is a reference temperature, and ΔH‡T0and ΔS‡T0

arethe difference in enthalpy and entropy between the groundstate and the transition state, respectively, at T0.

1 If ΔG‡ issimply linearly dependent on temperature according to ΔG‡ =ΔH‡ − TΔS‡, then ΔC‡

p = 0 and eq 3 collapses to an Arrheniusfunction. However, if ΔH‡ and ΔS‡ are temperature dependent,then ΔC‡

p ≠ 0, and the relationship between rate andtemperature will show curvature in an ln(k) versus T plot(Figure 1a).Negative curvature is well documented for the temperature

dependence of enzymatic rates, giving rise to temperatureoptima (Topt) for enzymes.

2,3 Previously, this negative curvaturehas been attributed to Arrhenius-like behavior for temperaturesbelow Topt, combined with enzyme denaturation and/oraggregation for temperatures >Topt. A similar model incorpo-rating protein denaturation is also used to explain thetemperature dependence of microorganism growth rates.4,5

Explanations based on denaturation are inadequate as severalstudies have noted that denaturation alone is insufficient toexplain the decrease in enzyme rates above Topt.

2,6,7

Furthermore, an enigmatic characteristic of psychrophilicenzymes is their loss of activity at temperatures well belowtheir denaturation temperature.3 Recently, an alternative modelhas been proposed which postulates (ad hoc) an inactive, foldedintermediate, in rapid equilibrium with the active enzyme to

Received: July 5, 2013Accepted: September 9, 2013

Letters

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© XXXX American Chemical Society A dx.doi.org/10.1021/cb4005029 | ACS Chem. Biol. XXXX, XXX, XXX−XXX

account for the negative curvature of the temperaturedependence of enzyme rates.2

Curvature is a natural consequence of eq 3 (Figure 1a), andhere, we show that the temperature dependence of enzymaticrates is attributable to negative values of ΔC‡

p for enzymecatalysis. ΔC‡

p is a critical parameter in statistical thermody-namics that has not previously been considered for enzymecatalysis. We have measured ΔC‡

p for a number of enzymes,and we find that eq 3 can fully account for the observeddownward curvature in enzymatic rates above Topt independentof denaturation. Furthermore, we present a physical explanationfor the magnitude and sign of ΔC‡

p and show that Topt andΔC‡

p are correlated, as theory predicts.We initially investigated the temperature−rate relationship

for enzymes using the well-studied enzyme barnase (ribonu-clease; E.C. 3.1.27.3), and its stabilized double mutant A43C/S80C, whose Michaelis−Menten kinetics and unfolding rateswith temperature have been well documented1,8,9 (Figure 1b).The curvature seen in an ln(kcat) versus T plot for wildtypebarnase could be rationalized as a combination of Arrhenius-like behavior at temperatures below 312 K (Topt) anddenaturation above 312 K (the temperature midpoint ofthermal unfolding, Tm, for barnase is 326 K).8 However, thiscannot account for the curvature of A43C/S80C, whichcontains a stabilizing disulfide bond and has an increased Tm(331 K).8 Although this mutant has been stabilized, thecurvature in ln(kcat) versus temperature remains, and there is noincrease in Topt (Figure 1b). The failure of the textbook model(Arrhenius + denaturation) to explain the Topt of A43C/S80Ccan be simply resolved by considering a negative value for ΔC‡

pfor catalysis. Fitting eq 3 to the temperature−rate data forwildtype barnase and A43C/S80C gives similar, large andnegative ΔC‡

p values of −4.6 ± 0.8 and −5.3 ± 0.4 kJ mol−1

K−1, respectively (Figure 1b). Although ΔC‡p has not

previously been considered with respect to enzyme catalysis,these values are commensurate with those previouslydetermined for an enzyme binding to a transition stateanalogue at equilibrium.10 We note that these large, negativevalues for ΔC‡

p pertain to the reaction system as a whole, which

includes both the reactants and the enzyme. One would notexpect to see such large values for simple organic reactionsalone.We used a second enzyme, MalL (α-glucosidase; E.C.

3.2.1.10), to test the generality of our description and probe therelationship between ΔC‡

p and Topt. By screening a library of268 single amino acid substitution mutants of MalL, weidentified four point mutations that conferred increases in Topt:V200A, V200S, V200T, and G202P. The temperature−ratedata for these enzymes were fitted to eq 3 to determine ΔC‡

p(Figure 2a). In each case, the enzymatic rates at eachtemperature tested were determined using the first 10 s ofrate data to ensure that they were not confounded bydenaturation. The mutants V200T and V200A showed modestincreases in Topt compared with wildtype MalL (ΔTopt = 2.3and 5.7 K, respectively). These mutations also resulted inmodest increases in ΔC‡

p (ΔΔC‡p = 0.7 and 1.2 kJ mol−1 K−1,

respectively). In the case of V200A, significant changes wereobserved in both the enzyme’s affinity for the substrate (KM)and its turnover rate (kcat; Figure 2b). The mutants V200S andG202P exhibited greater increases in Topt when compared withwildtype MalL (ΔTopt = 9.3 and 7.5 K, respectively), whichwere accompanied by large increases in ΔC‡

p (ΔΔC‡p = 5.7

and 5.9 kJ mol−1 K−1, respectively). These changes had noeffect on the Michaelis−Menten kinetics for V200S; however,the G202P mutation resulted in significant impairment of kcat(Figure 2b).The MalL mutants suggest a correlation between ΔC‡

p andTopt, and this is supported by theory. Provided ΔC‡

p ≠ 0, Topt isdefined by eq 3 when δk/δT = 0 and hence

−Δ =Δ +

−‡

‡

CH RT

T TpT opt

opt 0

0

(4)

Thus, changing ΔC‡p is sufficient to change Topt without

compromising Michaelis−Menten parameters (i.e., no changein ΔH‡ and hence no impact on ΔG‡). This is clearly the casefor wildtype MalL, V200T, and V200S, whose kcat values arenearly identical at 313 K but where the temperature

Figure 1. Effect of ΔC‡p on the temperature dependence of reaction rates. (a) Schematic representation of the relationship between temperature and

rate as modeled by eq 3 when different values of ΔC‡p are applied. (b) Fit of eq 3 to temperature-rate data for barnase (black ●) and A43C/S80C

(orange ●). Data shown are the initial rate of enzyme activity at different temperatures as a function of the enzyme concentration (kcat) and themean of at least two replicates. Error bars, where visible, represent the SD; ΔC‡

p values are in kJ mol−1 K−1 (±SE). Topt is defined as the highesttemperature at which the maximum rate of activity was observed.

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dependence of the catalyzed rate differs (Figure 2a). Wecombined data for MalL and barnase mutants with dataobtained for variants of a third enzyme, LeuB,11 and found thatthe correlation predicted by eq 4 holds for all three enzymesover a wide temperature range (Figure 3). This emphasizes thatchanges in Topt (without affecting enzyme kinetics) are possiblevia changes to ΔC‡

p. This finding has important implications

for biotechnology, where manipulation of an enzyme’s Toptwithout compromising catalytic kinetics is an ongoingchallenge.If ΔC‡

p ≠ 0, eq 3 provides further constraints on thethermodynamics of enzyme catalysis by fixing ΔH‡ at the Toptfor an enzyme. At Topt, ΔH‡ = −RTopt provided ΔC‡

p ≠ 0. Thisimplies that the enthalpic contributions to enzyme catalysis arevery similar for all enzymes (provided enzyme kinetics aremeasured at the Topt for the enzyme). Fixing ΔH‡ at Topt alsoimplies a central role of ΔS‡ in determining enzyme rates as thisis the only parameter that can vary at Topt. This is illustratedhere for MalL where an increase in rate is the result of anincrease in ΔS‡ near the active site upon the mutation V200A,although this is accompanied by a weaker KM for catalysis andthus a comparatively poorer kcat/KM value overall (Figure 2b).The V200S and G202P mutants exhibit large increases in

ΔC‡p and Topt compared with wildtype MalL. What underlies

these increases in ΔC‡p? The greatest contribution to the heat

capacity of a folded protein is the number of availablevibrational and rotational modes associated with covalentbonds (i.e., protein dynamics). These modes contribute anestimated 85% of the Cp term for globular proteins.12,13 Thehydration term is thought to contribute the remaining ∼15% tothe Cp for globular proteins. In contrast, the hydration termcontributes up to 40% of the Cp for unfolded proteins, and thischange in hydration is the dominant factor affecting ΔCp forprotein folding.1 If large numbers of vibrational and rotationalmodes are available to a protein, this will give rise to a highvalue for Cp, whereas a reduction in these modes will lead to alower value of Cp for the same protein. To effect a change in Cpfor an enzyme-catalyzed reaction, either there needs to be achange to the number of conformational modes available to thereactants (i.e., free enzyme + enzyme−substrate complex) or achange to these modes at the transition state (i.e., enzyme−transition state complex).We determined high-resolution crystal structures for wild-

type MalL, V200S, and G202P (Supplementary Table 1) andcombined these with molecular dynamics (MD) simulations tocompare the conformational dynamics of these enzymes. Thestructures of the three proteins are very similar, with root-mean-square deviations (rmsd) between wildtype MalL andV200S of 0.18 Å, and between wildtype MalL and G202P of0.20 Å. In contrast, the dynamics simulations of the apo-enzymes show marked differences, and the number ofconformational states available to the V200S mutant issubstantially reduced when compared with wildtype MalL(Figure 4a,b). This, combined with the lack of change in kcat(Figure 2b), indicates that the basis for the change in ΔC‡

p forV200S is the rigidification of the ground state (E + S ⇌ ES)without an impact on the transition state and thus no impact onthe rate (Figure 4b). The crystal structure of V200S also showsthat the mutation introduces two new hydrogen bonds thatform part of a network of short- and long-range interactions(Supplementary Figure 1). This network of interactions in theapoenzyme provides an explanation for the reduced number ofavailable conformational states. In contrast, the G202Pmutation has not affected the conformational dynamics forthe apoenzyme when compared with the wildtype (Figure 4b,c)but has compromised the transition state as evidenced by itsimpaired kcat (Figure 2b). In this case, the increase in ΔC‡

p hasbeen achieved by increasing the flexibility of the transition state,but this has come at the cost of kcat (i.e., the increased flexibilityof the transition state has caused an increase in ΔG‡ for the

Figure 2. Effect of mutation on the Topt, ΔC‡p, and Michaelis−Menten

parameters of the α-glucosidase MalL. (a) Fit of eq 3 to temperature−rate data for wildtype MalL and its mutants. Data shown are the initialrate of enzyme activity at different temperatures as a function of theenzyme concentration (kcat) and the mean of three replicates. Errorbars, where visible, represent the SD. ΔC‡

p values are in kJ mol−1 K−1

(±SE). Arrows indicate the Topt for each enzyme, which is defined asin Figure 1. (b) Michaelis−Menten parameters for MalL and itsmutants determined at 318 K (±SE of fitting).

Figure 3. Relationship between Topt and ΔC‡p for enzymes. The

relationship between Topt and ΔC‡p for an enzyme as described by eq

4 is shown using data for variants of barnase, MalL, and LeuB(Supplementary Table 3). When combining ΔC‡

p values for differentenzymes, it is necessary to change the units to J g−1 K−1 by dividing bythe enzymeMr (the number of vibrational modes contributing to ΔC‡

pfor proteins has been shown previously to be linearly correlated withMr).

29 The curve represents the fit of eq 4 to the data when T0 = 306K. Error bars, where visible, represent the SE in ΔC‡

p/Mr.

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reaction and therefore a reduction in the enzyme-catalyzedrate). These MD simulations clearly illustrate the twomechanisms through which the ΔC‡

p of an enzyme-catalyzedreaction, and therefore the Topt, can change.The Topt−ΔC‡

p correlation provides an explanation for therigidity of thermophilic enzymes.14 To increase Topt withoutcompromising rate requires increases in the ΔC‡

p for catalysisand thus increases in enzyme rigidity (irrespective of therequirements for stability at high temperatures). It also providesan explanation for the anomalous temperature dependence ofreaction rates for psychrophilic enzymes.3 The Topt−ΔC‡

prelationship implies that increased flexibility in the groundstate is required to achieve lower ΔC‡

p values and hence lowerTopt values. Further, eq 3 implies that increases in ΔS‡ arerequired to enhance rates at low temperatures given that ΔH‡ isfixed and linearly dependent on Topt. Intriguingly, therelationship between ΔC‡

p and the temperature dependenceof catalyzed rates may also suggest a role for ΔC‡

p in allosteryand oligomerization, and this warrants further investigation.Our results point toward changes in protein dynamics as the

source of the changes to ΔC‡p for enzyme catalysis; however,

the role of water and desolvation of the active site should alsobe considered. The significant difference in ΔC‡

p for V200Scompared with V200T, and the lack of difference in their kcatvalues at 313 K, suggests that the dominant contributor to ΔC‡

pis conformational dynamics, and the contribution of water issmall. However, we do not discount the role of water, and thisis the subject of ongoing experiments in our laboratory.Understanding precisely how enzymes work has been the

subject of renewed debate recently, in particular the role ofprotein dynamics in catalysis.15,16 Arguments have beenpresented based on statistical thermodynamics,17 MD,15

transition state barrier crossing,18 and Marcus theory andpreorganization,16 among others. The size and magnitude ofΔC‡

p for enzyme catalysis is consistent with each of these

descriptions. In terms of statistical thermodynamics, a largenegative ΔC‡

p is the result of the very tight binding of thetransition state and the reduction in the number of conforma-tional states available to the system at the transition statecompared with the ground state. In terms of transition statebarrier crossing, a large negative ΔC‡

p is the result of theinstantaneous reduction in the vibrational and rotational modesof the enzyme at the transition state barrier. We anticipate thatmeasuring ΔC‡

p for a wide range of enzymes and their mutants,combined with sophisticated simulations, will provide exper-imental access to the nature of the transition state for enzymecatalysis.Enzymes are a fundamental component of biological systems

and the drivers of cellular metabolism. As such, we speculatethat curvature in the temperature dependence of enzymaticrates will make a significant contribution to the temperaturedependence of metabolic processes inside cells. In general,enzyme Topt values are well correlated with the optimumgrowth temperature of the parent organism.11 Thus, we wouldexpect to see an observed ΔC‡

p signature (ΔC‡p,obs) in the

temperature dependence of microorganism growth rates evenbefore the effects of the complex regulatory responsesassociated with temperature are considered. Indeed, negativecurvature in microorganism growth rates has long beenknown.5 As with enzymes, the curvature in microorganismgrowth rates is usually attributed to denaturation above Topt.

4,5

We note here that eq 3 models the temperature dependence ofgrowth rates for diverse microorganisms with R2 valuesconsistently >0.9 (Supplementary Table 2 and SupplementaryFigure 2), including the curvature below Topt (a particularfailure of the growth rate models that invoke denaturation19).The derived ΔC‡

p,obs values are also consistent with thosemeasured for enzyme catalysis (Figure 3) and much greater(and therefore more influential) than the ΔC‡

p associated with

Figure 4. Dynamics simulations for wildtype MalL, V200S, and G202P. Depictions of the 3D structure of MalL summarizing its MD trajectories,colored blue through red for the most rigid to the most dynamic regions (from the trajectory) with accompanying increases in tube width. A graph ofCp versus reaction coordinate is shown below each structure. The locations of the V200S and G202P mutations are indicated by spheres. (a) MDtrajectories for wildtype MalL. (b) Trajectories for V200S showing a significant reduction in the dynamics for the loops surrounding the active site.This has lowered the Cp for the ground state (E + S ⇌ ES). A slight increase in flexibility is also observed for the helix consisting of residues 259−275, which is not seen in the other two systems. (c) Trajectories for G202P showing no change in the dynamics of the free enzyme and implying thatΔC‡

p has been reduced by increasing the Cp for the enzyme−transition state complex (E−TS) without affecting Cp for the ground state.

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denaturation and incorporated into the Ratkowsky growth ratemodel.4

In conclusion, we have demonstrated that the ΔC‡p

associated with enzyme catalysis explains the temperaturedependence of enzymatic rates and that there is a clearmolecular mechanism underpinning enzymatic ΔC‡

p. Theinfluence of ΔC‡

p on allostery, oligomerization, and biologicalrates at the whole cell level requires further investigation.Nevertheless, it is likely that enzymatic ΔC‡

p values contributeto the temperature dependence of biological rates at largerscales.

■ METHODSMutagenesis, Protein Expression, and Protein Purification.

Mutagenesis was performed using the Quikchange Site-DirectedMutagenesis kit and either the barnase expression constructpMT100220 or malL from Bacillus subtilis 168 in pPROEX HTb astemplate. Barnase and A43C/S80C were expressed and purified asdescribed elsewhere.20 MalL and its mutants were expressed at 18 °Covernight and purified as previously described,21 with furtherpurification by size-exclusion chromatography.Enzyme Assays. The activities of barnase and MalL enzymes on a

fluorogenic nucleotide substrate and p-nitrophenol-α-D-glucopyrano-side, respectively, were determined as previously described.21,22

Temperature profiles were determined by measuring activity at 2−3°C intervals using substrate at either 2 × KM (barnase) or 10 × KM(MalL). Barnase and A43C/S80C data were corrected for Vmax basedon KM determinations at two temperatures. Fits to eq 3 wereperformed in GraphPad Prism 6.0 with the reference temperature setto Topt − 4.Crystallization and Structure Determination. Crystallization of

MalL proteins was performed using the hanging drop method at 18°C. Crystals of wildtype MalL were obtained in 100 mM Bis-Tris pH6.5, 200 mM LiSO4, and 20% (w/v) PEG 3350. V200S and G202Pwere crystallized in 100 mM Tris pH 7.5 containing 22% and 24% (w/v) PEG 4000, respectively. Data collection was performed on flash-cooled crystals at the Australian synchrotron. The crystallizationcondition plus 15% glycerol was used as cryoprotectant. All data wereindexed and integrated with MOSFLM23 and scaled using Aimless.24

The wildtype structure was solved by molecular replacement usingPhaser25 and the structure of MalL from B. cereus (1UOK) as thesearch model. This was followed by iterative cycles of manual modelbuilding with Coot,26 and further refinement using Refmac.27 Thestructures of V200S and G202P were determined using the sameprotocol but using the structure of wildtype MalL as the search model.MD Simulations. MD simulations using the crystal structure of

wildtype MalL were conducted with NAMD28 running on theBlueFern supercomputer at the University of Canterbury. Crystallo-graphic water and ligands were deleted, and missing residues were builtin with Coot26 in accordance with the electron density map so that thedynamic properties of the disordered loops could be examined. ForV200S and G202P, starting structures were generated by in silicomutation of the wildtype structure. Starting structures were solvatedwith explicit TIP3 water molecules in a box in VMD and ionized byadding Na+ and Cl− ions to balance the net charge. Ions were addedwith a minimum distance of 5 Å from the molecule and each other.MD simulations were conducted with the CHARMM22 all-hydrogenparameter file for proteins at 322.15 K and 1 atm. The cutoff distancefor van der Waals interactions was set to 12 Å. In each simulation, thesystem was first minimized for 5000 steps followed by 270 ns ofdynamics simulations conducted with 2 fs time steps. The trajectorywas written out at 100 ps time intervals, and a total of 2700 frameswere obtained from each simulation.

■ ASSOCIATED CONTENT*S Supporting InformationData collection and refinement statistics for MalL enzymes;ΔC‡

p values for microorganism growth rates; details of enzymes

datasets included in Figure 3; key differences between thecrystal structures of wildtype MalL, V200S, and G202P;ΔC‡

p,obs values for the temperature dependence of micro-organism growth rates.. This material is available free of chargevia the Internet at http://pubs.acs.org.

Accession CodesThe refined crystal structures for wildtype MalL, V200S, andG202P have been deposited in the Protein Data Bank underaccession numbers 4M56, 4MAZ, and 4MB1, respectively.

■ AUTHOR INFORMATIONCorresponding Author*(V.L.A.) E-mail: varcus@waikato.ac.nz. Tel: +64 7 838 4679.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe would like to thank N. Pace (Texas A&M University) forproviding the plasmid pMT1002 and J. Steemson for X-ray datacollection for wildtype MalL. We thank V. Schramm, J. Clarke,M. Steyn-Ross, and A. Steyn-Ross for valuable discussions andcritical reading of the manuscript. This work was supported bya research grant from the Marsden Fund of New Zealand. X-raydiffraction data were collected at the Australian synchrotron,and we thank the NZ Synchrotron Group for funding.

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