In the Classroom
The Effect of Temperature on the Enzyme-Catalyzed Reaction: Insights from Thermodynamics nez-Riveres Juan Carlos Aledo* and Susana Jime Departamento de Biología Molecular y Bioquímica, Facultad de Ciencias, Universidad de M alaga, 29071 M alaga, Spain *
[email protected] Manuel Tena Departamento de Bioquímica y Biología Molecular, Edificio Severo Ochoa, Campus de Rabanales, Universidad de C ordoba, 14071 C ordoba, Spain
Metabolism sustains life, which has evolved the ability to thrive in a broad range of different thermal environments. Many plants, poikilotherm (cold-blooded) animals, and microorganisms can exhibit metabolic activity within a wide interval of temperatures, in some cases covering 40-50 °C (1). Not surprisingly, temperature plays an important role in various aspects of the life history, ecology, and physiology of these organisms (2). Thus, information on how temperature affects metabolic rates has an interest that transcends the academic boundaries of biochemistry. Temperature governs metabolism through its effects on rates of biochemical reactions. More concretely, the rate constant, k, of a reaction is a function of the absolute temperature, T. The form of such a function is phenomenologically described by the Arrhenius equation kðT Þ ¼ Ae - Ea =RT
(1Þ
where A is the pre-exponential factor, R is the gas constant, and Ea is the activation energy (3). The latter can be obtained from the slope in an Arrhenius plot of d ln k (2Þ Ea ¼ - R - 1 dT The temperature coefficient Q10, defined as the ratio of the rates of the reaction at T2 = (T1 þ 10) K and T1 K, is widely used for comparative purposes and, using eq 1, can be expressed as Q10 ¼ eðT2 - T1 ÞEa =RT1 T2
(3Þ
Although the Q10 is widely used to express the temperature dependence of enzyme-catalyzed reactions, some caveats regarding the interpretation of data should be made explicit when teaching the influence of temperature on the enzyme-catalyzed reaction rate. In particular, the risks of using concepts derived from the theory of elementary reactions in the study of multistep reactions should be pointed out. Caveats For an elementary chemical reaction, for example, the monomolecular conversion of the substrate S into the product P, the rate law states that the reaction rate, v(T), is proportional to the concentration of reactant, with the proportionality 296
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constant given by k
s P Sf vðT Þ ¼ kðT Þ½S
(reaction 1Þ (4Þ
If we think of this reaction taking place in aqueous solution, it is reasonable to assume that an increase in 10 °C should not significantly modify the concentration of S. Under these circumstances, it does not matter whether we define the Q10 as a ratio between reaction rates or rate constants because the substrate concentration in numerator and denominator cancel each other. Because activation energies for most elementary reactions have positive values (4), the value of Q10 must be greater than 1, which is interpreted as chemical reaction rates always increase with temperature. However, the situation is different for enzyme-catalyzed reactions. A common practice in enzymology is to use rates as proxy for rate constants. Although this approach can be convenient, it also involves many risks students should be aware of. First, almost all enzymes become denatured if they are exposed to extreme temperatures. Therefore, the recorded rate could be reflecting the effect of temperature on the enzyme stability rather than the target rate constant. Second, because the equilibrium constant can be sensitive to temperature, the pKa's of ionizable residues involved in the catalysis as well as the affinity of the enzyme for activators or inhibitors can also be drastically modified by temperature changes. Nevertheless, let us assume that we are dealing with an enzyme that is not affected by any of the mentioned drawbacks. That is, within the considered temperature range, the enzyme is stable and there are not changes in the pKa's or the binding of any effector. Under such circumstances, is it possible to find anomalous Ea and Q10 values? In other words, is it possible to account for an enzyme working faster at lower temperatures without appealing to thermal denaturation? The answer, as we discuss next, is affirmative. A Simple Model Mechanisms of enzyme-catalyzed reactions taking place within cells are complex because they may include multiple substrates and products, effectors, conformational transitions,
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In the Classroom
and so forth. Nevertheless, as an initial teaching approach, we propose the simplest model of an enzyme-catalyzed reaction, which is a two-step mechanism involving a rapid and reversible reaction that yields the enzyme-substrate complex (ES), followed by a slower and irreversible reaction that transforms the enzyme-bound substrate into free product: k1
E þ S a ES k-1
k2
ES f s EþP
(reaction 2Þ (reaction 3Þ
According to chemical kinetics, when there are several steps, the slow or rate-limiting elementary step (reaction 3 in our model) determines the reaction rate, (5Þ v ¼ kcat ½ES where k2 has been renamed as kcat to stress its relevance. During the course of finding the Q10, one could be tempted to simplify the calculations by assuming that [ES] is not affected by temperature, as we did for [S] in the noncatalyzed reaction. However, herein we must be aware that [ES] is either an equilibrium concentration (according to a rapidequilibrium approach) or alternatively a steady-state concentration (if we deal with the Briggs-Haldane model). In any event, for a given substrate concentration, [ES] will depend on the value of Km, defined as (k-1 þ kcat)/k1 or k-1/k1, if k-1 . kcat, which, in turn, is obviously influenced by temperature. In summary, for an enzyme-catalyzed reaction the Q10 values should be expressed as vðT2 Þ ½kcat ðT2 Þ½½ESðT2 Þ ¼ (6Þ Q10 ¼ vðT1 Þ ½kcat ðT1 Þ½½ESðT1 Þ Nevertheless, most values reported in the literature for enzymatic reactions are calculated as kcat ðT2 Þ Q10 ¼ (7Þ kcat ðT1 Þ by making [ES](T1) = [ES](T2) = [E]0, where [E]0 is the total enzyme concentration. However, that is correct only when the reaction rates are measured at saturating concentrations of substrate. Although this approach may be appropriate, the information conveyed is of limited interest because it only applies to conditions of saturation whereas in vivo most enzymes work at subsaturating concentrations of their substrates. Enzymes Working Faster at Lower Temperatures The question addressed in this section is whether an increase of temperature within the range of enzyme stability can lead to a decreased reaction rate. For initial rates assessed in the absence of product, the proper function to be used is the Michaelis-Menten equation, which is a function of the substrate concentration and the temperature: ½E0 ½S (8Þ vðT , ½SÞ ¼ kcat ðT Þ Km ðT Þ þ ½S At saturating concentrations of substrate (Km , [S]), this equation can be simplified: (9Þ vðT Þ ¼ ½kcat ðT Þ½E0
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As it has been discussed, under such conditions any effect on the reaction rate reflects the effect of temperature on the catalytic constant kcat ðT Þ ¼ A3 e - Ea3 =RT
(10Þ
where A3 and Ea3 are the pre-exponential factor and the activation energy, respectively, of elementary reaction 3. Therefore, Ea3 > 0 and consequently Q10 > 1 and, thus, an increase in temperature is paralleled by an increase in velocity. This affirmation is not a surprise. However, the situation is more complicated and more interesting when the enzyme faces nonsaturating substrate concentrations. Under these circumstances, raising the temperature can lead to a decrease in the reaction rate, even within the temperature range where the native conformation of the enzymatic protein is not affected (5-7). Inspection of eq 8 indicates that such anomalous response would be possible if an increase at higher temperature on enzyme activity (increment in kcat) is outweighed by a decrease at higher temperature on enzyme-substrate affinity (increment in Km). In fact, U-shaped temperature profiles of Km values, delimiting a temperature range for which the enzyme-substrate affinity increases with falling temperature, have been observed experimentally in a variety of enzyme systems (8). The requirements for achieving an anomalous temperature response (Ea < 0 and Q10 < 1) of the enzyme-catalyzed reaction rate can be easily analyzed under the condition [S] , Km, for example, when the Michaelis-Menten equation can be approximated by kcat ðT Þ ½E ½S (11Þ vðT , ½SÞ ¼ Km ðT Þ 0 where the so-called specificity constant, kcat/Km, can be interpreted as the apparent second-order rate constant for the enzymatic reaction (6). A more elaborated interpretation of this ratio between constants can be found in an article by Northrop in this Journal (9). By applying the Arrhenius law, we can consider kcat ðT Þ ¼ Aapp e - Eapp =RT (12Þ kapp ðT Þ ¼ Km ðT Þ where Eapp and Aapp are the apparent activation energy and preexponential factor, respectively. For the sake of simplicity we assume Km to be the equilibrium constant for the dissociation of the complex ES (the inverse of reaction 2). This allows us to use the van't Hoff equation to express its dependence on the temperature Km ðT Þ ¼ eΔH °2 =RT e - ΔS°2 =R
(13Þ
where ΔH°2 and ΔS°2 are the standard enthalpy and entropy changes for the binding of S to the enzyme (reaction 2). Now, substitution of kcat and Km (from eqs 10 and 13) into eq 12, leads to A3 e - Ea3 =RT ¼ Aapp e - Eapp =RT (14Þ eΔH°2 =RT e - ΔS°2 =R After some basic arrangements, eq 14 yields
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ðeΔS°2 =R A3 Þe - Ea3 =RT ¼ Aapp eðΔH °2 - Eapp Þ=RT
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(15Þ
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By equating the corresponding factors and exponentials of eq 15, the following relations are obtained: Aapp ¼ eΔS°2 =R A3
(16Þ
Eapp ¼ ΔH °2 þ Ea3
(17Þ
It should be stressed that Aapp and Eapp only apply to conditions where [S] , Km. Now we are ready to address the question: when will Eapp be negative? To give an answer, we focus our attention on eq 17. Importantly, Ea3 is always positive because reaction 3 is an elementary reaction. On the other hand, the binding of the substrate to the enzyme can be either an endothermic (8, 10) or an exothermic process (10). In the first case, Eapp > 0 because we are adding two positive numbers. However, when the activation energy of the catalytic step (Ea3) is low and the binding of the substrate is strongly exothermic ΔH°2 , 0, then Eapp can be negative, yielding Q10 < 1. Therefore, one would predict low Ea3 and exothermic substrate bindings for enzymes adapted to work at low temperatures. Not surprisingly, the activation energy (Ea3) of poikilotherm enzymatic reactions shows a remarkable positive correlation with the environmental temperature (2, 11). Fishes and Enzymes Fundulus heteroclitus is a species of fish living in the Atlantic coast of North America. This region features one of the steepest thermal gradients in the world (1 °C per degree of latitude). Thus, fish living at the two ends of the species' geographical range experience an ∼15 °C difference in mean annual water temperatures. Interestingly, there is a remarkable north-south cline in the frequencies of allelic variants of the gene coding for the heart-type or B lactate dehydrogenase (LDH-B4, EC 1.1.1.27). Populations inhabiting northern waters are essentially homozygously fixed for the Ldh-Bb allele, whereas populations from the species' southern extreme are fixed for the Ldh-Ba allele. Place and Powers studied the effect of temperature on the kinetic properties of these two allozymes (5, 6) and found that for both allozymes Vm (the maximum velocity at saturating concentrations of substrate; proportional to kcat) increased monotonously with temperature. However, the behavior of Vm/Km (proportional to kcat/Km) was much more useful in explaining the adaptative character of each variant. The LDH-B4b allozyme, whose gene frequency is greatest in the northern colder waters, has a greater Vm/Km at low temperatures than the other enzyme phenotype. At the higher temperatures, the situation is reversed with LDH-B4a having a greater catalytic rate (Figure 1). Nevertheless, the relevant question is, What will happen with the in vivo catalyzed-reaction rate, if temperature drops from 35 to 25 °C? Because the measured intracellular pyruvate and lactate concentrations are generally less than their respective Km values (6), at physiological substrate concentrations the rate will be related to Vm/Km. From the data in Figure 1 it can be observed that the specificity constant of the allozyme LDH-B4b goes up when temperature drops from 35 to 25 °C. Using numerical data given in Table 3 from ref 6, we have calculated a Q10 of 0.70, which is clearly below unity. Therefore, we are led to conclude that the reaction rate should increase because of the decrease in temperature. Concluding Remarks The thermal shifts that organisms experience in nature have pervasive effects on the rates of their enzyme-catalyzed metabolic 298
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Figure 1. Specificity constant as a nonmonotone function of temperature. The data used to draw the plot were taken from ref 6. The pyruvate reduction by LDH at saturating concentrations of NADH was studied. Concretely, the specificity constant for both allozymes, LDH-B4a (open squares) and LDH-B4b (filled diamonds), were determined as a function of temperature.
reactions. Because thermokinetics is a complex subject, a detailed and rigorous exposition is difficult in a teaching context. Usually, the problem is oversimplified by implicitly introducing the assumption that the thermal effect is confined to the catalytic constant. Such an approach is only appropriate when the reaction rate is measured at saturating concentrations of substrate. However, this is far from the normal situation within the cell, where most enzymes work at subsaturating concentrations of their substrates. Thus, we propose for teaching purposes the use of a simple thermokinetic treatment of the Michaelis-Menten model able to account for those enzymes that work faster at lower temperature. Acknowledgment The authors are grateful to Alicia Esteban del Valle and Ana R. Quesada for discussions and suggestions. We thank Athel Cornish-Bowden for sharing his opinion regarding the temperature dependence of the specificity constant. We are indebted to George Somero, who brought to our attention references and data without which this work would have never been completed. This work was supported by grant CGL 2007-65010 from the Spanish Ministerio de Educacion y Ciencias. Literature Cited 1. Siddiqui, K.; Cavicchioli, R. Annu. Rev. Biochem. 2006, 75, 403–433. 2. Somero, G. Comp. Biochem. Physiol. B Biochem. Mol. Biol. 2004, 139, 321–333. 3. Laidler, K. J. J. Chem. Educ. 1984, 61, 494–498. 4. Truhlar, D.; Kohen, A. Proc. Natl. Acad. Sci. U.S.A. 2001, 198, 848–851. 5. Place, A.; Powers, D. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 2354–2358. 6. Place, A.; Powers, D. J. Biol. Chem. 1984, 259, 1309–1318. 7. Borgmann, U.; Moon, T. Can. J. Biochem. 1975, 53, 998–1004. 8. Andjus, R.; Dzakula, Z.; Marjanovic, M.; Zivadinovic, D. J. Theor. Biol. 2002, 217, 33–46. 9. Northrop, D. J. Chem. Educ. 1998, 75, 1153–1157. 10. Copeland, W.; Nealon, D.; Rej, R. Clin. Chem. 1985, 31, 185–190. 11. Johnston, I.; Goldspink, G. Nature 1975, 257, 620–622.
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