FEBS Letters 587 (2013) 2738–2743

journal homepage: www.FEBSLetters .org

Review

Temperature and the catalytic activity of enzymes: A freshunderstanding

0014-5793/$36.00 � 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.febslet.2013.06.027

⇑ Corresponding author.E-mail address: m.j.danson@bath.ac.uk (M.J. Danson).

Roy M. Daniel a, Michael J. Danson b,⇑a Thermophile Research Unit, Department of Biological Sciences, University of Waikato, Hamilton, New Zealandb Centre for Extremophile Research, Department of Biology & Biochemistry, University of Bath, Bath BA2 7AY, UK

a r t i c l e i n f o

Article history:Received 4 June 2013Revised 18 June 2013Accepted 19 June 2013Available online 27 June 2013

Edited by Athel Cornish-Bowden

Keywords:EnzymeTemperatureCatalytic activityEquilibrium Model

a b s t r a c t

The discovery of an additional step in the progression of an enzyme from the active to inactive stateunder the influence of temperature has led to a better match with experimental data for all enzymesthat follow Michaelis–Menten kinetics, and to an increased understanding of the process. The newmodel of the process, the Equilibrium Model, describes an additional mechanism by which temper-ature affects the activity of enzymes, with implications for ecological, metabolic, structural, andapplied studies of enzymes.� 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

1. Introduction

Leonor Michaelis and Maud Menten are often regarded as thefounders of modern quantitative enzymology. In their studies oninvertase [1], they recognised the necessity of assaying the enzymeunder defined and controlled conditions, principally with respectto the pH of the reaction, and the need to measure initial rates,thereby avoiding various complicating factors including the knowninhibition of the enzyme by the product of the reaction. Their datathen fitted what we now know as the Michaelis–Menten equation,the fundamental equation of enzyme kinetics:

V ¼ Vmax½S�KM þ ½S�

ð1Þ

Clearly, in addition to a defined pH, kinetic measurements are madewith a constant amount of enzyme in the assay, and at a constanttemperature that does not result in loss of catalytic activity duringthe time course of the assay. The choice of assay temperature is ex-tremely important since the way enzymes respond to temperatureis fundamental to many areas of biology. Thus, it is this aspect, theeffect of temperature on enzyme catalytic activity, that we wish toexplore in the current paper, and provide new insights that are ofboth theoretical and practical importance.

Where the effect of temperature on enzyme activity has beenconsidered, textbooks have said that higher temperatures increaseenzyme activity to a certain point, after which the enzyme dena-tures, losing its activity irreversibly (e.g., [2–4]). In this model,the change in enzyme activity with increasing temperature is sim-ply the combined result of the effect of temperature increasing kcat

and kinact on a simple two step conversion (i.e., Eact ? X), then thetime-dependent loss of activity, expressed as Vmax, is described bythe following equation:

Vmax ¼ kcat � ½E0� � e�kinact �t ð2Þ

where Vmax = maximum velocity of enzyme; kcat = enzyme’s cata-lytic constant; [E0] = total concentration of enzyme; kinact = thermalinactivation rate constant; t = assay duration.

The variation of the two rate constants in Eq. (2) with temper-ature is given by:

kcat ¼kBT

he�

DGzcat

RT

� �ð3Þ

and

kinact ¼kBT

he�

DGzinactRT

� �ð4Þ

where kB = Boltzmann’s constant; R = Gas constant; T = absolutetemperature; h = Planck’s constant; DGzcat ¼ activation energy ofthe catalysed reaction; DGzinact ¼ activation energy of the thermalinactivation process.

050

100

150

200

290300

310320

330340

0.0

0.5

1.0

1.5

2.0

2.5

Rat

e(µ

M/s

)

Temperature(K)

Time(s)

Fig. 1. The Classical theory of the effect of temperature on enzyme activity. Thetemperature dependence of enzyme activity with time. The data were simulatedusing Eqs. (2)–(4), with the parameter values: DGzcat ¼ 75 kJ mol�1 andDGzinact ¼ 95 kJ mol�1. Note that the apparent temperature optimum decreases withincreasing length of the assay. Reproduced with permission from [24].

050

100

150

200

280300

320340

360

0.00

0.05

0.10

0.15

0.20

0.25

Rat

e(µM

/s)

Temperature(K) Time(s)

Fig. 2. The Equilibrium Model for the effect of temperature on enzyme activity. Thetemperature dependence of enzyme activity with time. The data were simulatedusing Eqs. (3)–(6), with the parameter values: DGzcat ¼ 75 kJ mol�1

; DGzinact ¼95 kJ mol�1

; DHeq ¼ kJ mol�1 and Teq = 320 K. Reproduced with permission from[24].

R.M. Daniel, M.J. Danson / FEBS Letters 587 (2013) 2738–2743 2739

Using these equations, and inserting plausible values for DGzcat

and DGzinact, a plot of activity against temperature and time canbe constructed (Fig. 1). At zero time there is no denaturation, de-fined here as the time-dependent, irreversible loss of activity,and initial rates will therefore rise continuously with temperature;the expected reaction progress with time at various temperaturescan be seen later in Fig. 5C. However, despite this model beingcommonly used to describe the effect of temperature on enzymeactivity, it is now clear that no enzymes actually exhibit thisbehaviour; careful measurements show that initial rates declineat high temperatures independent of irreversible inactivation. Are-examination of the effect of temperature on enzyme catalyticactivity has therefore led to the proposal of a new model [5,6],the Equilibrium Model, described below.

2. The Equilibrium Model

The new model for the temperature-dependent behaviour ofenzymes, the Equilibrium Model, introduces an intermediate inac-tive (but not denatured) form of the enzyme that is in rapid equi-librium with the active form, and it is the inactive form thatundergoes irreversible thermal inactivation to the denatured (irre-versibly inactive) state (X):

Eact �Keq

Einact !kinact X

where Eact is the active form of the enzyme, which is in equilibriumwith the inactive form, Einact. Keq is the equilibrium constantdescribing the ratio of Einact/Eact; kinact is the rate constant for theEinact to X reaction; and X is the irreversibly-inactivated form ofthe enzyme. Within this model, there is no implication that the con-version of Einact to X occurs in a single step, or that X is a single spe-cies, only that they can be considered as such since all speciesbeyond Einact are irreversibly inactivated.

Using the Equilibrium Model, the variation of enzyme activitywith temperature can be expressed by:

Vmax ¼kcatE0e�

kinactKeq t1þKeq

1þ Keqð5Þ

where

Keq ¼ eDHeq

R1

Teq�1

T

� �ð6Þ

Teq is the temperature at which the Eact/Einact equilibrium is at itsmid-point (Keq = 1, DGeq = 0, and therefore Teq = DHeq/DSeq), whereDHeq is the change in enthalpy for the Eact/Einact transition. In thiscase, a plot of rate vs temperature vs time (Fig. 2) does have an opti-mum for initial rates (i.e., at zero time) because the Eact/Einact equil-ibration is rapid. This is known from the experimental observationthat enzyme initial rates do in fact decline at high temperatures (seeFig. 6 for an example), and at all temperatures the Eact/Einact equili-bration is faster than the time needed to start the reaction in a stir-red spectrophotometer cuvette (of the order of 1–3 s), and the lineof product vs time extrapolates back to zero [7–10].

So far, all enzymes we have studied that obey Michaelis–Men-ten kinetics follow this Model [7–9], irrespective of mechanismor structure (e.g., Table 1), and all have a temperature optimumfor initial rates, as expected from the Model. Nevertheless, manyenzymes do not follow ideal kinetics, when the enzyme is sub-strate or product inhibited for example, and the Model must be re-garded as describing an ideal, and a degree of departure may occurafter significant reaction progress, as is the case for all models ofenzyme behaviour.

3. Mechanism of the Equilibrium Model

The discovery of a new and apparently universal mechanism bywhich enzymes lose activity as the temperature rises is of consid-erable interest in itself, and has a number of interesting implica-tions. Although the Equilibrium Model does not of itself offer anexplanation of the molecular basis of the Eact/Einact transition, thisinterconversion can be clearly differentiated from denaturation.Compared with denaturation, it operates over much shorter time-scales [6,7,9,11,12], structural changes are imperceptible [9], andthe associated DHeq is an order of magnitude smaller than DHunfold

[9,13–15]. Moreover, changes of Teq can be independent of changesin stability [9]. Thus, the evidence indicates that the Eact/Einact tran-sition involves only a small conformational change and there is

Table 1Thermodynamic parameters for eight enzymes fitted to the Equilibrium Model.

Organism Enzyme Tgrowth

(�C)DGzcat ðkJ mol�1Þ DGzinact ðkJ mol�1Þ DHeq

(kJ mol�1)Teq

(�C)Number ofsubunits

Relativemolecularmass

Reaction class andEC number

Thermus sp. RT41a Alkalinephosphatase

75 72 99 305 90 2 97000 HydrolaseEC 3.1.3.1

Caldocellulosiruptorsacchrolyticus

b-Glucosidase 70 88 103 149 74 1 54000 HydrolaseEC 3.2.1.21

Thermoplasmaacidophilum

Citrate synthase 60 77 103 164 88 2 86000 TransferaseEC 2.3.3.1

Bos taurus Glutamatedehydrogenase

39 63 93 264 53 6 330000 OxidoreductaseEC 1.4.1.2

Bos taurus c-Glutamyltransferase

39 63 98 109 52 2 88000 TransferaseEC 2.3.2.2

Sus scrofa Fumarase 39 60 92 378 59 4 194000 LyaseEC 4.2.1.2

Wheat germ Acidphosphatase

20 79 95 142 64 1 55000 HydrolaseEC 3.1.3.2

Moritella profunda Dihydrofolatereductase

2 67 93 104 55 1 18000 OxidoreductaseEC 1.5.1.3

The parameters of all enzymes were derived by fitting assay data to the Equilibrium Model (http://hdl.handle.net/10289/3791) and thus relate to active enzymes in thepresence of substrate and cofactor [8,9]. The exceptions are the growth temperature optima (Tgrowth) of the source organism, which are cited from various sources.

Fig. 3. The effect of temperature on initial rates for two enzymes with different DHeq values, showing the effect of DHeq on the temperature sensitivity of the Eact/Einact

equilibrium. The lines represent the initial (zero time) activity of two enzymes at various temperatures based on their Equilibrium Model parameters derived fromexperimental data: Pseudomonas dulcis b-glucosidase (----) (DHeq = 100 kJ/mol) and Escherichia coli malate dehydrogenase (–) (DHeq = 619 kJ/mol). On each curve, at a varietyof temperatures, the proportion of the enzyme in the Einact form is given as a per cent value. The Teq value for each enzyme is also given. Reproduced with permission from [5].

2740 R.M. Daniel, M.J. Danson / FEBS Letters 587 (2013) 2738–2743

additional evidence that the mechanism is located at the activesite. That is, Teq and DHeq are substrate dependent, in that theyvary in the same enzyme if different substrates are used, Km

changes often coincide with the Eact/Einact transition, and pointmutations at the active site can change Teq and DHeq without sig-nificant changes in DGzinact [9,16]. The active-site localisation ofthe transition is not unexpected, given that conformational flexibil-ity is often inherent in an enzymes catalytic mechanism, and thusthe active site might be one of the most susceptible parts of an en-zyme to temperature-induced conformational changes.

While there are a number of possible molecular bases for theEinact/Eact interconversion, the effect of temperature on chargedamino acids is a likely factor in the observed effects [3,17].The pKa values of amino acid side-chains are temperature sensi-tive. In particular, basic residues such as histidine and lysine,which are common components of active sites and their sur-roundings, and the N-terminal amino group, exhibit relativelylarge changes in charge with temperature, with shifts of up to

a pH unit with a 30 �C temperature change. Since the ionisableresidues of amino acid side chains interact with the charges onadjacent ionised residues, and with neighbouring peptide di-poles, polar residues and bound water, temperature changeshave the potential to change the charge and charge distributionat the active site. Many enzyme mechanisms have a close depen-dence on the charge of specific catalytic residues. On this basisalone, a temperature-driven pKa shift can have a significant di-rect effect on catalysis in many, if not all, enzymes. Equallyimportant, changes in pKa can cause conformational changes.For example, if a conformation at or near the active site is re-tained by an ionic bond (e.g., Asp-Lys) then, if the pKa of Lysis shifted down by a temperature increase, its positive chargewill decrease and the ionic bond weakened, potentially leadingto a conformational change. The overall effect of charge changeson enzyme activity are evidenced by their pH dependence,where large changes in enzyme activity can be caused bychanges of less than a single pH unit of the solvent.

Fig. 4. A plot showing the effect of the Equilibrium Model parameters on thetemperature-dependent activity of enzymes. The value of DGzinact determines thetime-dependent loss of activity at any temperature due to thermal denaturation.When measuring initial (zero time) rates, the rapid reduction in activity at hightemperatures arises from the conversion of Eact to Einact and is governed by Teq andDHeq. At any point along the time axis, the activity of the enzyme is thusdetermined by all three thermodynamic parameters. Reproduced from withpermission [5].

0 200 400

0

50

100

150

200

Pro

duct

(µ

M)

Tim

0 200 400 600 800 1000

Time (s)

0

5

10

15

20

25

30

Pro

duct

(µM

)

a

c

Fig. 5. The effect of Teq on time courses of product concentration simulated at various temModel (Teq = 350 K); (B) Equilibrium Model (Teq = 300 K), using DGzcat ¼ 75 kJ mol�1

DGzcat ¼ 75 kJ mol�1 and DGzinact ¼ 95 kJ mol�1. Reproduced with permission from [24].

R.M. Daniel, M.J. Danson / FEBS Letters 587 (2013) 2738–2743 2741

For most enzymes, the Eact/Einact transition described by theEquilibrium Model has an DHeq in the range 100–300 kJ/mol[8,9], so that a 10–20 �C decrease in temperature below that atwhich 50% of the enzyme is in the inactive form will lead to a shiftin the Eact/Einact transition to a point where 90% of the enzyme is inthe inactive form (Fig. 3). This is not inconsistent with the changesat an active site that might arise from a change in pKa over thistemperature change [3,17].

4. Implications of the Equilibrium Model

Measurement of the Equilibrium Model parameters (see: http://hdl.handle.net/10289/3791) has provided a fuller and more accu-rate explanation of the effect of temperature on enzymes, and en-abled the identification of a number of potential implications of theModel.

First, correlation analysis of the key parameters of the Equilib-

rium Model DGzcat; DGzinact; DHeq; and Teq

� �of enzymes from

organisms with growth temperatures ranging from 2 to 75 �Cshows that Teq correlates with much greater significance to theoptimal growth temperature of the source organism than doesthe DGzinact [8], indicating an evolutionary significance for the Equi-librium Model parameters. Additionally, DHeq can be considered asa quantitative measure of the temperature range over which an

600 800 1000

e (s)

Time (s)

0 200 400 600 800 10000

100

200

300

400

500

600

Pro

duct

(µ

M)

b

peratures. 310 K (blue); 320 K (green); 330 K (purple); 340 K (red). (A) Equilibrium; DGzinact ¼ 95 kJ mol�1 and DHzeq ¼ 95 kJ mol�1, and (C) Classical Model, using

Fig. 6. Bioreactor progress curves for the alkaline phosphatase-catalysed hydrolysis of p-nitrophenyl as a function of temperature. Reproduced from [5] with permission.

2742 R.M. Daniel, M.J. Danson / FEBS Letters 587 (2013) 2738–2743

enzyme is most active. A large DHeq leads to an enzyme with asharp and relatively narrow temperature optimum, whereas asmall DHeq results in an enzyme with a broad temperature opti-mum, so that activity is relatively less sensitive to changes in tem-perature (Fig. 3). Therefore, if a particular enzyme has a high DHeq,for example, then a shift in temperature away from Teq is muchmore likely to lead to a significant change in enzyme activity. Ofthe enzymes for which we have DHeq values, about 50% have DHeq

values of less than 150 kJ/mol (i.e., fairly broad temperature opti-ma), and about 15% have values greater than 400 kJ/mol (relativelynarrow temperature optima) [8,9]. This effect may imply a moresophisticated and selective control of metabolism by temperaturethan currently envisaged. However, given that the Model is basedon Vmax data, the extent to which the model applies under physio-logical conditions may depend upon the degree to which enzymesare substrate-saturated, since the degree to which the Model ap-plies under conditions where substrate is not saturating has notbeen investigated. The extent of substrate saturation in vivo isuncertain and, although it has been argued that substrate concen-trations in vivo should be close to half-saturation [18,19], examplesof saturation are known [20].

A second implication concerns the stability of enzymes and at-tempts to manipulate this. Although enzymes are only marginallystable at the growth temperature of the source, we know they canbe stable and functional at very high temperatures [21], and thatthe addition of a single productive stabilising interaction cangreatly increase the half-life [22]. With this in mind, and giventhe considerable importance of stable enzymes in biotechnologyand the substantial efforts in this field (published and unpub-lished), the attempts to increase the useful temperature of enzymeactivity by directed mutagenesis have been, with some notableexceptions, disappointing. Activity at high temperature dependson Teq and DHeq as well as on stability (Fig. 4), offering an explana-tion for the difficulty of engineering enzymes to act at higher tem-peratures. That is, most directed mutagenesis has focussed on

enhancing DGzinact, but it is clear from Fig. 4 that, while enhancingDGzinact may reduce the loss of activity with time, unless Teq and/or DHeq are also changed this may have little effect on activity ata higher temperature. This may explain why attempts to improveDGzinact by directed mutagenesis has been significantly less success-ful in improving activity at high temperatures than directed evolu-tion of enzymes since these may also lead to productive changes inTeq and/or DHeq (see [23] for a general discussion of engineeringstrategies).

A third consequence arises when the questions of activity andstability are combined. As pointed out by Eisenthal et al. [24], pre-dictions of the effect of time and temperature on the output of en-zyme reactors are different depending on whether the ‘‘Classical’’or Equilibrium Model is used (Fig. 5). When using an enzyme ina batch reactor for a biocatalytic conversion, intuition would pre-dict that the higher the operating temperature, the faster the cata-lysed reaction, but also the less stable the enzyme. In fact,experimental data show this is only generally true if Teq exceedsthe working temperature of the reactor. If Teq is less than the work-ing temperature, the reverse is true (compare Fig. 5A and B). Typ-ical time courses of product formation at various temperaturespredicted by the Classical Model (which will never show the effectseen in Fig. 5A) are shown in Fig. 5C for comparison. Experimentaldata for an enzyme reactor in which alkaline phosphatase(Teq = 319 K) catalyses the hydrolysis of p-nitrophenyl [25] confirmthe predictions of the Model, showing that when the reactor work-ing temperature is below Teq then as the temperature rises so doesthe initial rate (Fig. 6); however, when it is above Teq, as the tem-perature rises the initial rate declines.

5. Concluding remarks

In this paper, we have summarised a new model, the Equilib-rium Model, that gives a more complete understanding of the ef-fect of temperature on an enzyme’s catalytic activity. Given the

R.M. Daniel, M.J. Danson / FEBS Letters 587 (2013) 2738–2743 2743

excellent fit to all enzymes so far tested, the evidence that theModel accurately describes the effect of temperature on enzymesis convincing. The importance of this increased understanding ofthe effect of temperature on enzyme activity is evident from itsoccurrence in all enzymes that follow Michaelis–Menten kinetics,irrespective of structure and mechanism. In addition to the impli-cations described above, the Model describes a second way inwhich temperature affects enzyme activity, probably via the activesite, and has implications for structural, metabolic, ecological andapplied studies of enzymes.

Acknowledgements

This work was supported by a grant from the Royal Society ofNew Zealand Marsden Fund (UOW0501). M.J.D. gratefullyacknowledges financial support from the UK Biotechnology andBiological Sciences Research Council, The Royal Society, and theUS Air Force Office of Scientific Research. Professor Robert Eisen-thal (1936–2007) was one of the key architects of the EquilibriumModel and contributed to all the work described here.

References

[1] Michaelis, L. and Menten, M.L. (1913) Kinetik der Invertinwirkung. Biochem.Zeitschrift 49, 333–369.

[2] Copeland, R.A. (2000) Enzymes: A Practical Introduction to Structure,Mechanism and Data Analysis, Wiley-VCH, New York.

[3] Dixon, M. and Webb, E.C. (1979) Enzymes, Longman Group Ltd., London.[4] Devlin, T.M. (2011) Textbook of Biochemistry with Clinical Correlations, John

Wiley & Sons, Inc., USA.[5] Daniel, R.M. and Danson, M.J. (2010) A new understanding of how

temperature affects the catalytic activity of enzymes. Trends Biochem. Sci.35, 584–591.

[6] Daniel, R.M., Danson, M.J. and Eisenthal, R. (2001) The temperature optima ofenzymes: a new perspective on an old phenomenon. Trends Biochem. Sci. 26,223–225.

[7] Peterson, M.E., Eisenthal, R., Danson, M.J., Spence, A. and Daniel, R.M. (2004) Anew intrinsic thermal parameter for enzymes reveals true temperatureoptima. J. Biol. Chem. 279, 20717–20722.

[8] Lee, C.K., Daniel, R.M., Shepherd, C., Saul, D., Cary, S.C., Danson, M.J., Eisenthal,R. and Peterson, M.E. (2007) Eurythermalism and the temperature dependenceof enzyme activity. FASEB J. 21, 1934–1941.

[9] Daniel, R.M., Peterson, M.P., Danson, M.J., Price, N.C., Kelly, S.M., Monk, C.R.,Weinberg, C.S., Oudshoorn, M.L. and Lee, C.K. (2010) The molecular basis of theeffect of temperature on enzyme activity. Biochem. J. 425, 353–360.

[10] Peterson, M.E., Daniel, R.M., Danson, M.J. and Eisenthal, R. (2007) Thedependence of enzyme activity on temperature: determination andvalidation of parameters. Biochem. J. 402, 331–337.

[11] Fulton, K.F., Devlin, G.L., Jodun, R.A., Silvestri, L., Bottomley, S.P., Fersht, A.R.and Buckle, A.M. (2005) PFD: a database for the investigation of proteinfolding kinetics and stability. Nucleic Acids Res. 33, D279–D283.

[12] Tsou, C.L. (1995) Inactivation precedes overall molecular conformationchanges during enzyme denaturation. Biochim. Biophys. Acta 1253, 151–162.

[13] Arroyo-Reyna, A., Tello-Solis, S.R. and Rojo-Dominguez, A. (2004) Stabilityparameters for one-step mechanism of irreversible protein denaturation: amethod based on nonlinear regression of calorimetric peaks with nonzeroDCp. Anal. Biochem. 328, 123–130.

[14] Creighton, T.E. (1993) Proteins, W.H. Freeman, New York.[15] Privalov, P.L. and Khechinashvili, N.N. (1974) A thermodynamic approach to

the problem of stabilization of globular protein structure: a calorimetric study.J. Mol. Biol. 86, 665–684.

[16] Nunn, C. E. M. (2010) Ph.D. thesis. University of Bath, UK.[17] Danson, M.J., Hough, D.W., Russell, R.J.M., Taylor, G.L. and Pearl, L. (1996)

Enzyme thermostability and thermoactivity. Protein Eng. 9, 629–630.[18] Fersht, A.R. (1974) Catalysis, binding and enzyme–substrate complementarity.

Proc. R. Soc. Lond. B 187, 397–407.[19] Cornish-Bowden, A. (1976) The effect of natural selection on enzyme catalysis.

J. Mol. Biol. 101, 1–9.[20] Bennett, B.D., Kimball, E.H., Gao, M., Osterhout, R., Van Dien, S.J. and

Rabinowitz, J.D. (2009) Absolute metabolite concentrations and impliedenzyme active site occupancy in Escherichia coli. Nat. Chem. Biol. 5, 593–599.

[21] Piller, K., Daniel, R.M. and Petach, H. (1996) Properties and stabilisation of anextracellular a-glucosidase from the extremely thermophilic archaebacteriaThermococcus strain AN1: enzyme activity at 130 �C. Biochim. Biophys. Acta1292, 197–205.

[22] Perutz, M.F. and Raidt, H. (1975) Stereochemical basis of heat stability inbacterial ferredoxins and in haemoglobin. Nature 255, 256–259.

[23] Kazlauskas, R.J. and Bornscheuer, U.T. (2009) Finding better proteinengineering strategies. Nat. Chem. Biol. 5, 526–529.

[24] Eisenthal, R., Peterson, M.E., Daniel, R.M. and Danson, M.J. (2006) The thermalbehaviour of enzyme activity: implications for biotechnology. TrendsBiotechnol. 24, 289–292.

[25] Oudshoorn, M. (2008) M.Sc. thesis. University of Waikato, New Zealand.