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A New Intrinsic Thermal Parameter for Enzymes Reveals True Temperature Optima

2004; Elsevier BV; Volume: 279; Issue: 20 Linguagem: Inglês

10.1074/jbc.m309143200

1083-351X

Michelle E. Peterson, Robert Eisenthal, Michael J. Danson, A. Spence, Roy M. Daniel,

thermodynamics and calorimetric analyses

Two established thermal properties of enzymes are the Arrhenius activation energy and thermal stability. Arising from anomalies found in the variation of enzyme activity with temperature, a comparison has been made of experimental data for the activity and stability properties of five different enzymes with theoretical models. The results provide evidence for a new and fundamental third thermal parameter of enzymes, Teq, arising from a subsecond timescale-reversible temperature-dependent equilibrium between the active enzyme and an inactive (or less active) form. Thus, at temperatures above its optimum, the decrease in enzyme activity arising from the temperature-dependent shift in this equilibrium is up to two orders of magnitude greater than what occurs through thermal denaturation. This parameter has important implications for our understanding of the connection between catalytic activity and thermostability and of the effect of temperature on enzyme reactions within the cell. Unlike the Arrhenius activation energy, which is unaffected by the source ("evolved") temperature of the enzyme, and enzyme stability, which is not necessarily related to activity, Teq is central to the physiological adaptation of an enzyme to its environmental temperature and links the molecular, physiological, and environmental aspects of the adaptation of life to temperature in a way that has not been described previously. We may therefore expect the effect of evolution on Teq with respect to enzyme temperature/activity effects to be more important than on thermal stability. Teq is also an important parameter to consider when engineering enzymes to modify their thermal properties by both rational design and by directed enzyme evolution. Two established thermal properties of enzymes are the Arrhenius activation energy and thermal stability. Arising from anomalies found in the variation of enzyme activity with temperature, a comparison has been made of experimental data for the activity and stability properties of five different enzymes with theoretical models. The results provide evidence for a new and fundamental third thermal parameter of enzymes, Teq, arising from a subsecond timescale-reversible temperature-dependent equilibrium between the active enzyme and an inactive (or less active) form. Thus, at temperatures above its optimum, the decrease in enzyme activity arising from the temperature-dependent shift in this equilibrium is up to two orders of magnitude greater than what occurs through thermal denaturation. This parameter has important implications for our understanding of the connection between catalytic activity and thermostability and of the effect of temperature on enzyme reactions within the cell. Unlike the Arrhenius activation energy, which is unaffected by the source ("evolved") temperature of the enzyme, and enzyme stability, which is not necessarily related to activity, Teq is central to the physiological adaptation of an enzyme to its environmental temperature and links the molecular, physiological, and environmental aspects of the adaptation of life to temperature in a way that has not been described previously. We may therefore expect the effect of evolution on Teq with respect to enzyme temperature/activity effects to be more important than on thermal stability. Teq is also an important parameter to consider when engineering enzymes to modify their thermal properties by both rational design and by directed enzyme evolution. A graph of the rate of product generation against temperature is sometimes presented to show the "temperature optimum" (Topt) of an enzyme; however, it is a misconception that this optimum is an intrinsic enzyme property. The descending limb of this plot arises mostly from the denaturation of the enzyme and, because denaturation is both time- and temperature-dependent, shorter assays give a higher Topt. In this classical description, the variation in enzyme activity with temperature can be described as follows, Vmax=kcat⋅[E0]⋅e−kinact⋅t(Eq. 1) where Vmax = maximum velocity of the enzyme, kcat = the catalytic constant of the enzyme, [E0] = total concentration of enzyme, kinact = thermal inactivation rate constant, and t = assay duration. Both rate constants, kcat and kinact, are dependent on temperature. This gives rise to temperature/activity graphs as shown in Fig. 1A where it can be seen that the apparent Topt decreases with increasing time during the assay, but at zero time (i.e. under initial rate conditions) no temperature optimum exists (1Daniel R.M. Danson M.J. Eisenthal R. Trends Biochem. Sci. 2001; 26: 223-225Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar). In the Classical Model the temperature-dependent behavior of the enzyme arises from the activation energy of the reaction and the thermal stability of the enzyme. Arising from anomalies found in the variation of enzyme activity with temperature (2Thomas T.M. Scopes R.K. Biochem. J. 1998; 330: 1087-1095Crossref PubMed Scopus (73) Google Scholar, 3Gerike U. Russell N.J. Danson M.J. Hough D.W. Eur. J. Biochem. 1997; 248: 49-57Crossref PubMed Scopus (72) Google Scholar, 4Buchanan C.L. Connaris H. Hough D.W. Reeve C.D. Danson M.J. Biochem. J. 1999; 343: 563-570Crossref PubMed Scopus (102) Google Scholar, 5Arnott M.A. Michael R.A. Thompson C.R. Hough D.W. Danson M.J. J. Mol. Biol. 2000; 304: 655-666Crossref Scopus (63) Google Scholar, 6Medina D.C. Hanna E. MacRae I.J. Fisher A.J. Segel I.H. Arch. Biochem. Biophys. 2001; 393: 51-60Crossref PubMed Scopus (5) Google Scholar), a proposal (1Daniel R.M. Danson M.J. Eisenthal R. Trends Biochem. Sci. 2001; 26: 223-225Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar) has been made for a third temperature-dependent property of enzymes involving the reversible equilibrium between active and inactive forms of an enzyme and implying a "true" temperature optimum. In this model (the Equilibrium Model), the active form of the enzyme (Eact) is in reversible equilibrium with an inactive form (Einact), and it is the inactive form that undergoes irreversible thermal inactivation to the thermally denatured state (X), Eact⇄Einact→X as this reaction shows. In this situation, the concentration of the active enzyme at any time point is defined by (Eact)=(E0)−(X)1+Keq(Eq. 2) where Keq is the equilibrium constant between active and inactive forms of the enzyme (Keq = (Einact)/(Eact)). Thus Keq becomes a new temperature-dependent property of an enzyme in addition to kcat and kinact, and its variation with temperature is given by ln(Keq)=ΔHeqR(1Teq−1T)(Eq. 3) where ΔHeq is the enthalpic change associated with the conversion of an active to an inactive enzyme, and Teq is the temperature at the midpoint of transition between the two forms. That is, Teq is the temperature at which Keq = 1 and ΔGeq = 0, therefore, Teq = ΔHeq/ΔSeq. (We previously (1Daniel R.M. Danson M.J. Eisenthal R. Trends Biochem. Sci. 2001; 26: 223-225Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar) used the term Tm to designate this temperature but now prefer the term Teq, as it is the temperature at which the concentrations of Einact and Eact are equal.) In this Equilibrium Model the temperature-dependent behavior of an enzyme can be explained only by the inclusion of an additional intrinsic thermal parameter, Teq. The effect of incorporating the parameters Keq and Teq into the simulations (see Fig. 1B) yields major differences from the Classical Model shown in Fig. 1A showing an initial rate temperature optimum that is obviously independent of assay duration and enabling an experimental distinction between the two models. To compare the experimental data with the models, five enzymes from a variety of sources were assayed for activity at different temperatures, using continuous assays to allow the simultaneous measurement of activity and thermal stability in the same cuvette and, therefore, under identical conditions. These measurements allow the generation of a unique temperature profile for each enzyme. Most of this work has been carried out on monomeric enzymes to avoid the potentially complicating effects of subunit dissociation. The data presented support the Equilibrium Model hypothesis involving Keq as an intrinsic temperature-dependent property of enzymes. The consequence is that in such cases Teq must now be considered as a new thermal parameter that is a characteristic of any particular enzyme and that gives rise to a true temperature optimum. Enzymes and Reagents—Alkaline phosphatase from calf intestinal mucosa was purchased from Roche Applied Science. Adenosine deaminase from bovine spleen, aryl-acylamidase from Pseudomonas fluorescens, and β-lactamase from Bacillus cereus were purchased from Sigma. Acid phosphatase from wheat germ was purchased from Serva Electrophoresis GmbH (Heidelberg, Germany). Reagents for the analysis of the activity of these enzymes were purchased from Sigma, Merck, and Oxoid Ltd. (Basingstoke, UK). All other chemicals used were of analytical grade. Buffers were adjusted to the appropriate pH value at the assay temperature using a combination electrode calibrated at this temperature. Enzyme Assays—All enzymic activities were measured using continuous assays on a Thermospectronic™ helios γ-spectrophotometer equipped with a Thermospectronic™ single cell peltier effect cuvette holder. This system was networked to a computer installed with Vision32™ (Version 1.25, Unicam Ltd.) software including the Vision Enhanced Rate Programme capable of recording absorbance changes over time intervals of down to 0.125 s. Substrate concentrations were maintained at ∼10 times Km to minimize the effects of any possible increases in Km with temperature. Where these concentrations could not be maintained (e.g. because of substrate solubility), tests were conducted to confirm that there was no decrease in rate over the assay period because of substrate depletion. No evidence was found for either substrate or product inhibition under the experimental conditions described. Adenosine deaminase (EC 3.5.4.4, adenosine aminohydrolyase) activity was measured by following the decrease in absorbance at 265 nm (Δϵ265 = 8.1 mm–1·cm–1) resulting from the deamination of adenosine to inosine (7Pfrogner N. Arch. Biochem. Biophys. 1967; 119: 141-146Crossref PubMed Scopus (25) Google Scholar). Reaction mixtures (1 ml) contained 0.1 m sodium phosphate, pH 7.4, 0.12 mm adenosine, and 0.003 units of enzyme. One unit is defined as the amount of enzyme that hydrolyzes 1 μmole/min adenosine to inosine at 30 °C. Acid phosphatase (EC 3.1.3.2, orthophosphoric-monoester phosphohydrolase (acid optimum)) activity was measured using p-nitrophenyl phosphate (pNPP) 1The abbreviations used are: pNPP, p-nitrophenyl phosphate; pNAA, p-nitroacetanilide. as substrate (8Hollander V.P. Boyer P.D. The Enzymes. 4. Academic Press, New York1971: 449-498Google Scholar). Reaction mixtures (1 ml) contained 0.1 m sodium acetate, pH 5.0, 10 mm pNPP, and 0.024 units of enzyme. The release of p-nitrophenol was monitored at 410 nm (Δϵ410 = 3.4 mm–1·cm–1). One unit is defined as the amount of enzyme that hydrolyzes 1 μmole/min pNPP to p-nitrophenol at 37 °C. Alkaline phosphatase (EC 3.1.3.1, orthophosphoric-monoester phosphohydrolase (alkaline optimum)) activity was measured using pNPP as substrate (9Fernley H.N. Boyer P.D. The Enzymes. 4. Academic Press, New York1971: 417-447Google Scholar). Reaction mixtures (1 ml) contained 0.1 m diethanolamine/HCl, pH 8.5, 0.5 mm MgCl2, 10 mm pNPP, and 0.02 units of enzyme. The release of p-nitrophenol was monitored at 405 nm (Δϵ405 = 18.3 mm–1·cm–1). One unit is defined as the amount of enzyme that hydrolyzes 1 μmole/min pNPP to p-nitrophenol at 37 °C. Aryl-acylamidase (EC 3.5.1.13, aryl-acylamide amidohydrolyase) activity was measured by following the increase in absorbance at 382 nm (Δϵ382 = 18.4 mm–1·cm–1) corresponding to the release of p-nitroaniline from the p-nitroacetanilide (pNAA) substrate (10Hammond P.M. Price C.P. Scawen M.D. Eur. J. Biochem. 1983; 132: 651-655Crossref PubMed Scopus (40) Google Scholar). Reaction mixtures contained 0.1 m Tris/HCl, pH 8.6, 0.75 mm pNAA, and 0.018 units of enzyme. One unit is defined as the amount of enzyme required to catalyze the hydrolysis of 1 μmole/min pNAA at 37 °C. β-lactamase (EC 3.5.2.6, β-lactamhydrolase) activity was measured by following the increase in absorbance at 485 nm (Δϵ485 = 20.5 mm–1·cm–1) associated with the hydrolysis of the β-lactam ring of nitrocefin (11O'Callaghan C.H. Morris A. Kirby S.M. Shingler A.H. Antimicrob. Agents Chemother. 1972; 1: 283-288Crossref PubMed Scopus (1482) Google Scholar). Reaction mixtures contained 0.05 m sodium phosphate, pH 7.0, 0.1 mm nitrocefin, and 0.003 units of enzyme. One unit is defined as that which will hydrolyze the β-lactam ring of 1 μmole of cephalosporin/min at 25 °C. Data Collection—For each enzyme, progress curves (absorbance versus time) at a variety of temperatures were collected, and the time interval was set so that an absorbance reading was collected every second. Assay reactions were initiated by the addition of microliter amounts of enzyme that had no significant effect on the temperature. Three progress curves were collected at each temperature, each for a 5-min period. Where the slope for these triplicates deviated by more than 10%, the reactions were repeated. Temperature was recorded using a Cole-Palmer Digi-Sense® thermocouple thermometer accurate to ±0.1% of the reading and calibrated using a Cole-Parmer NIST-traceable high resolution glass thermometer. The temperature probe was placed inside the cuvette adjacent to the light path during temperature equilibration prior to the initiation of the reaction and again immediately after completion of each enzyme reaction. Measurements of temperature were also taken at the top and bottom of the cuvette to check for temperature gradients. Where the temperature measured before and after the reaction differed by more than 0.1 °C, the reaction was repeated. Data Analysis—For each enzyme, the catalytic rates (expressed as μm·s–1) were calculated at 1 s time intervals along the three progress curves at each temperature. The averages of each time point value were used to generate three-dimensional plots of rate (v) versus temperature (T in Kelvin) versus time (t in seconds) (SigmaPlot® 2001 for Windows, Version 7.101, SPSS). Data were smoothed using a Loess transformation, a curve-fitting technique based on local regression that applies a tricube weight function to elicit trends from noisy data (12Cleveland W.S. Visualizing Data. Hobart Press, New Jersey1993Google Scholar). The first data point was obtained at ∼2 s because of the lag between the addition of enzyme to the reaction mixture and the start of data collection. The data for zero time were obtained during the smoothing process, which extrapolates back to zero using the trend elicited from the data. The data for each enzyme were analyzed to provide values of ΔGcat‡ (the activation energy of the catalytic reaction), ΔGinact‡ (the activation energy of the thermal inactivation process), ΔHeq (the enthalpy change for the transition between active and inactive forms of the enzyme), and Teq (the temperature for the midpoint of this transition). Initial estimates of these parameters were calculated from two-dimensional analyses. Firstly, for the data at t = 0 (where there is no thermal inactivation), Eyring plots of ln(v/T) versus 1/T give values of ΔHcat‡ and ΔScat‡ (from the slope and intercept, respectively) from which ΔGcat‡ can thus be calculated at any temperature of the assay. Secondly, at each assay temperature, plots of ln(v) versus time were used to calculate rate constants (kinact) for the thermal inactivation process; Eyring plots of these data (ln(kinact/T) versus 1/T) similarly give values of ΔHinact‡ and ΔSinact‡, and hence, of ΔGinact‡. Values of Keq were calculated from an Arrhenius plot (ln(v) versus 1/T) for the data at t = 0. That is, according to the Equilibrium Model (1Daniel R.M. Danson M.J. Eisenthal R. Trends Biochem. Sci. 2001; 26: 223-225Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar), in the absence of any thermal inactivation the deviation from linearity in the Arrhenius plot is attributed to a shifting of the equilibrium from active to inactive forms. A comparison of the observed values with those from the extrapolated linear portion can thus be used to calculate the value of Keq at any temperature. Using Equation 3, values of ΔHeq and Teq were subsequently determined from a plot of ln(Keq) versus 1/T. Using these estimates of the thermodynamic parameters, the complete data set for each enzyme (rate versus time versus temperature) was fitted to the Equilibrium Model equations to derive the values given in Table I. The fits were performed using Scientist software (Micromath), employing a non-linear least squares minimization of the numerically integrated rate equations utilizing Powell's algorithm.Table ISummary of experimentally determined thermodynamic parametersEnzymeOriginGrowth temp.ToptTeqΔGcat‡ΔGinact‡ΔHeq°C°C°CkJ·mol-1kJ·mol-1kJ·mol-1Aryl-acylamidaseP. fluorescens2541443793165β-lactamaseB. cereus3053753891103Acid phosphatasewheat germ15-25aSpring germination temperatures.646531138183Adenosine deaminasebovine spleen39597326100146Alkaline phosphatasebovine intestine39637018108220a Spring germination temperatures. Open table in a new tab Protein Determination—Protein concentrations were determined from A280 measurements or by the colorimetric methods of Bradford and biuret (13Scopes R.K. Cantor C.R. Protein Purification: Principles and Practice. Springer-Verlag, San Diego1994: 44-50Crossref Google Scholar). The overall dependence of velocity on temperature with time can be described in our model by the relationship, (Eq. 4) where kB is Boltzmann's constant and h is Planck's constant. A comparison of the simulated plots for the Classical and Equilibrium Models (Fig. 1, A and B) with the experimentally determined three-dimensional plots of rate versus time versus temperature (Figs. 1C and 2, A–D) shows that all the enzymes studied conform to the Equilibrium Model, i.e. they display clear temperature optima at time 0 when there can be no loss of activity because of thermal inactivation. Analysis of the data gives values for ΔGcat‡, ΔGinact‡, ΔHeq, and Teq for each enzyme (Table I) assuming that the data can be described by the Equilibrium Model. Taking adenosine deaminase as the example, these parameters were used to simulate the three-dimensional plot (Fig. 1D), and a comparison with the plot of the experimental data (Fig. 1C) shows excellent agreement. Similarly good agreement has been obtained with the four other enzymes (data not shown). Setting t = 0 in Equation 4 and differentiating with respect to T gives, (Eq. 5) and when dVmax/dT is set to zero (i.e. at the maximum of the rate/temperature profile in the observed range of T) T = Topt.It can be demonstrated that for the range of parameter values typically shown for enzymes, 1Teq−1Topt≈−RΔHeqln(ΔHeq−ΔGcat‡ΔG‡cat)(Eq. 6) and further manipulation provides the relationship Topt≈Teq(1−αTeq)(Eq. 7) where α≈RΔHeqln(ΔHeq−ΔGcat‡ΔGcat‡) and α is small (such that αTeq ≪ 1). Thus in general, for enzymes whose thermal activity-dependence follows the Equilibrium Model, Topt will be close in value to Teq and always smaller (by the term αTeq2). Across the range of values of ΔGcat‡ and ΔHeq encountered in this study, Topt and Teq follow an essentially linear relationship. A plot of relative activity at zero time versus temperature (Fig. 3) illustrates that all five enzymes display a true temperature optima of catalytic activity as defined by the Equilibrium Model and that the values of Topt are essentially in accordance with the determined values of Teq (Table I). For β-lactamase and adenosine deaminase, the difference between Topt and Teq is greater than for the other enzymes, and both enzymes have relatively low ΔHeq values, which will have a major influence on this difference (Equation 7). It should be stressed that ΔGinact‡ is not a factor in the position of the peaks illustrated in Fig. 3 as the curves are determined at time zero where there is no thermal inactivation process. As also noted by Thomas and Scopes (2Thomas T.M. Scopes R.K. Biochem. J. 1998; 330: 1087-1095Crossref PubMed Scopus (73) Google Scholar), in all cases reported here the Topt is ∼20–40 °C above the optimum growth temperature/body temperature of the source organisms. Although the application of the Equilibrium Model has the potential to be complicated by temperature-induced subunit dissociation in the case of oligomeric enzymes, we find no evidence to suggest that this treatment is restricted to monomeric enzymes. The data for the dimeric alkaline phosphatase adhere equally well to the Equilibrium Model as do the other, monomeric, enzymes investigated here. The results and their analysis indicate that the experimental velocity data as a function of temperature can be described by the Equilibrium Model, suggesting Keq as an intrinsic temperature-dependent property of enzymes and supporting the hypothesis that these enzymes possess a third thermal parameter (Teq) alongside the Arrhenius activation energy and the activation energy for thermal stability. Currently, we have no evidence bearing on the molecular basis of the equilibrium between Eact and Einact, although it is clearly a fast process relative to thermal denaturation. All the variation of activity with temperature at zero time (Figs. 2 and 3) occurs as a result of changes in the Eact/Einact equilibrium and is thus attained over timescales shorter than the mixing process, for example, <1 s, whereas the measured rate of irreversible thermal inactivation (conversion from Einact to denatured state) is at least two orders of magnitude slower over the same temperature range. For example, in the case of arylacylamidase (Fig. 2A), at 51 °C the activity at time zero is ∼40% lower than at the "optimum" temperature (46 °C), whereas the activity/timeline at this temperature shows that it takes ∼60 s for 40% denaturation to occur. As the native/denatured transition is generally a two-state process for single-domain proteins (14Creighton T.E. Proteins. W. H. Freeman, New York1993: 287-325Google Scholar), Einact is unlikely to be significantly unfolded. A reversible conformational change is most likely, and we speculate that the differing effects of temperature on the various weak interactions stabilizing the protein structure offer an opportunity for a shift of structure with changing temperature leading to a change in activity. The existence of conformational substates in equilibrium over sub-second timescales is widely accepted (15Brooks C.L. Karplus M. Pettitt B.M. Adv. Chem. Phys. 1988; 71: 1-259Google Scholar, 16Svensson A.-K. O'Neill Jr., J.C. Matthews C.R. J. Mol. Biol. 2003; 326: 569-583Crossref PubMed Scopus (18) Google Scholar), and it has been suggested recently that adaptation to thermal stability may involve a change in the scale of fluctuations around the average state (17Wintrode P.L. Zhang D. Vaidehi N. Arnold F.H. Goddard III, W.A. J. Mol. Biol. 2003; 327: 745-757Crossref PubMed Scopus (90) Google Scholar). Teq is important in describing the effect of temperature on enzymes and in particular on the role of temperature as a selection pressure on enzyme structure and function. There is no evidence connecting the Arrhenius activation energy of an enzyme to its thermal environment, and although there is a strong correlation between thermal stability and the environmental temperature of the source organism, it is known that enzyme thermal stability also reflects resistance to other cellular conditions such as the action of proteases (18Daniel R.M. Dines M. Petach H.H. Biochem. J. 1996; 317: 1-11Crossref PubMed Scopus (235) Google Scholar). Teq is central to the physiological adaptation of an enzyme to its environmental temperature and links the molecular, physiological, and environmental aspects of the adaptation of life to temperature in a way that has not been possible previously. We predict that Teq will be a better expression of the effect of environmental temperature on the evolution of the enzyme than thermal stability. Thus we might expect differences in the overall shapes of the curves such as those shown in Fig. 2 to describe the fit of an enzyme to its thermal environment, especially at the high temperature part of the graph, because the shape of the low temperature part of the graph will be determined largely by the Arrhenius activation energy. Teq thus provides an important new parameter for matching the properties of an enzyme to its cellular and environmental function. In terms of protein engineering, Teq provides an additional parameter that determines the thermoactivity of an enzyme and therefore must be considered when designing enzymes for particular functions. Much of the enzyme engineering is directed at stabilizing enzymes against denaturation. The results here suggest that engineering to manipulate the Eact/Einact equilibrium (i.e. Teq) may be equally productive and that Teq must also be shifted to higher temperatures to obtain the expected catalytic benefits of enhanced enzyme thermostability. It will be important to distinguish between mutations that affect stability from those that affect Teq. We thank C. Collet for some of the preliminary work on β-lactamase and C. Cary and C. Monk for assistance in collecting some of the data presented in this paper.