Proc. Natl. Acad. Sci. USA Vol. 92, pp. 8926-8929, September 1995 Biochemistry

Negative activation enthalpies in the kinetics of protein folding (barnase/chymotrypsin inhibitor 2/transition state/hydrophobic effect)

MIKAEL OLIVEBERG, YEE-Joo TAN, AND AiAN R. FERSHT* Cambridge Center for Protein Engineering, Hills Road, Cambridge CB2 2QH, United Kingdom Contributed by Alan R. Fersht, June 12, 1995

ABSTRACT Although the rates of chemical reactions where kB is the Boltzmann constant, h is the Planck constant, become faster with increasing temperature, the converse may K is the transmission coefficient, AGt is the free energy of be observed with protein-folding reactions. The rate constant activation, ASt is the eniropy of activation, and Ait is the for folding initially increases with temperature, goes through enthalpy of activation. (kBTK/h).e0Qs$/R) corresponds to the a maximum, and then decreases. The activation enthalpy is Arrhenius preexponential factor A. AGt, Alt, and TASt are thus highly temperature dependent because of a large change the quasithermodynamic quantities of the equilibrium between in specific heat (ACp). Such a ACp term is usually presumed the ground state and the activated complex (Ai = EA- RT). to be a consequence of a large decrease in exposure of Whereas ASt can be either positive or negative, Alt is always hydrophobic surfaces to water as the reaction proceeds from positive for an elementary reaction step because energy is the denatured state to the transition state for folding: the required to create the partly broken bonds of the activated hydrophobic side chains are surrounded by "icebergs" of complex. As with the Arrhenius expression, it follows from Eq. water that melt with increasing temperature, thus making a 1 that the rate constantbecomes faster at higher temperatures. large contribution to the Cp of the denatured state and a Since Eq. 1 is deriVed for elementary reaction steps, it cannot smaller one to the more compact transition state. The rate be applied directly to more complex protein-folding reactions; could also be affected by temperature-induced changes in the the rate of crossover of high-dimensional protein transition conformational population of the ground state: the heat states may well be different from that of smaller molecules and, required for the progressive melting of residual structure in hence, it is not possible to obtain an absolute value for the free the denatured state will contribute to ACp. By examining two energy of activation. However, it may still be possible to proteins with different refolding mechanisms, we are able to interpret changes in AGt as well as the value of Alt, since these these two processes; barley chymotrypsin inhib- are directly linked to changes in the quasithermodynamic find both of equilibrium between the ground state and the transition state itor 2, which refolds from a highly unfolded state, fits well to in the protein-folding reaction (3). a hydrophobic interaction model with a constant ACp of In this report, we show that the protein-folding process, activation, whereas barnase, which refolds from a more which represents a high-dimensional reaction between amino structured denatured state, deviates from this ideal behavior. acid residues and solvent molecules, displays, under some conditions, a negative activation enthalpy: the refolding rate In 1889, Arrhenius demonstrated that chemical reaction rates constant becomes smaller with increasing temperatures (cf. are determined by an activation energy (EA) and that the refs. 4-7). The behavior appears to be associated with tran- temperature dependence of the reaction rate can be expressed sient disruption of water molecules which are coordinated by analogy with the van't Hoff equation-i.e., the temperature around the denatured protein, and it has implications for the dependence of the reaction rate follows that expected for an interpretation of Arrhenius plots of any protein reaction equilibrium constant between the ground state and the tran- involving large-scale conformational changes in aqueous so- sition barrier (1). Since, in the Arrhenius theory, the rate lution. constant (k) is determined by the ratio of the activation energy to the temperature, and by the frequency of collisions that EXPERIMENTAL PROCEDURES produce the reaction (A), the reaction rate becomes faster at higher temperatures (k = AeEA/RT, where R is the gas constant Chymotrypsin inhibitor 2 (CI2) from barley was expressed and and T is thermodynamic temperature). Most chemical reac- purified as described (8), as was barnase (9). The folding tions obey the Arrhenius equation and show linear plots of ln experiments were performed with a stopped-flow apparatus k versus 1/T. In enzymatic reactions, however, kinks and from Applied Photophysics, equipped with a mercury preci- curvature in these so-called Arrhenius plots are used as sion thermometer and connected to an external thermostat indicators of changes in the reaction mechanism-i.e., changes bath: 16 ,uM protein was denatured in 32 mM HCI (pH 1.5) and of EA with temperature. Forty-six years later, Eyring (2) mixed 1:1 with a Mes refolding buffer (7 mM acid form and 93 presented the transition-state theory whose central idea is also mM sodium salt) to a final pH of 6.3. The refolding reaction based on a quasithermodynamic equilibrium between the was monitored by fluorescence, using a 315-nm cut-off filter ground state and the activated complex (Kt): the reaction rate with excitation at 280 nm. The rate constants were obtained by at any given temperature depends only on the concentration of nonlinear regression analysis using the software package the activated complex and the rate of crossover ofthis activated KALEIDAGRAPH (Adelbeck Software, Reading, PA). complex, RESULTS AND DISCUSSION k = (kBTK/h)-Kt = (kBTK/h)e-(AG*/R) The two small proteins barnase and CI2 fold by different = (kBTK/h).e(AS/R)e-(AHI/R), [1] kinetics at 25°C. Barnase has been demonstrated to fold via multistep kinetics, with the process observed during the mil- The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in Abbreviation: CI2, chymotrypsin inhibitor 2. accordance with 18 U.S.C. §1734 solely to indicate this fact. *To whom reprint requests should be addressed. 8926 Downloaded by guest on September 26, 2021 Biochemistry: Oliveberg et al. Proc. Natl. Acad. Sci. USA 92 (1995) 8927

lisecond time range being dominated by the conversion of a -0.50 folding intermediate to the native state (10). C12, on the other hand, folds and unfolds by simple two-state kinetics (8). Both proteins consist of single polypeptide chains with no crosslinks, and all their peptidyl-prolyl bonds are in the thermodynami- cally favored trans conformation. Between 70% and 80% of the molecules fold in a single rapid phase from the denatured conformation that has all trans peptidyl-prolyl bonds. The slow minor phases, resulting from the isomerization of cis peptidyl- prolyl bonds, are not analyzed here. The temperature dependence of the refolding rate constant (kobs) is shown in Fig. 1 for C12 and in Fig. 2 for barnase. The plots of ln(kobs/I) against 1IT display strong curvatures. With C12, which refolds from the fully unfolded state, the refolding rate constant is related to the temperature dependence of the activation energy, AGt-D (8). In this case, a simple explanation for the curvature of ln(kobs/T) is provided by comparison with the thermodynamics for cold unfolding. Here, the protein stability does not decrease monotonically with temperature as predicted from the van't Hoff equation but shows typically a maximum around physiological temperatures and decreases at higher and lower temperatures (11) (Fig. 3). The effect is thought to be due to differences in the hydration shell between the native and denatured protein conformations, which is manifested as a change in heat capacity ACN-D upon unfold- ing: the denatured protein has a more extensive hydration shell due to its larger surface area and exposure of hydrophobic residues, and the heat capacity is related to the heat required to melt the hydration shell (12). ACN-D gives rise to a temperature dependence of the unfolding enthalpy (AJHND) and the unfolding entropy (ASN-D), Reaction coordinate ACDCNT= (AHN-D) -T 8(ASN-D) [2] FIG. 1. (Upper) Temperature dependence of the refolding rate constant for C12, shown as an Eyring plot-i.e., ln(kf/7) against 1/T. The slope of such a plot is AHt-D. The plot illustrates the nonlinearity which, in turn, causes a curvature in temperature dependence induced by changes in heat capacity between the ground state and the of the free energy of unfolding [AGN-D(T)] according to transition barrier. k has units of s-1. The solid curve is the theoretical plot of E .1 fitted to Eq. 3 with AHt-D(2980C) = 7 + 0.2 kcal/mol AGN-D() = MHN-D(T' - TASND(T) = AHND(Tm) and ACt% = -307 ± 6 cal/mol/K (1 cal = 4.18 J). CI2 displays D two-state kinetics where the denatured state (D) and the native state + ACN (T - Tm)- T[ASND(Tm) + AC ln(T/Tm)], [3] (N) interconvert over a common transition barrier (t), D z± t 2± N. The ground state for the refolding reaction is D and the refolding rate where Tm is the reference temperature at which AHN-D(Tm) is constant (kf) is determined by the difference in free energy between determined, in this case the midpoint for the thermal unfolding D and t; the temperature dependence of kf is determined by the transition. A graphical representation of AGN-D(7j is given in accompanying change in enthalpy (AH-D, Eq. 1). Between 50°C and Fig. 3. 250C (0.0031 < 1/T < 0.00335), the plot of ln kf/T against 1/T shows If we assume, analogously, that the high-energy protein a negative slope-i.e., the refolding rate constant increases with conformation that constitutes the transition state temperature. This corresponds to a positive activation enthalpy (t) between (AH4-D > 0) in accordance with most other chemical reactions. the denatured and the native state affects the water shell of the Around 50°C (1/1T 0.0031), kf displays a maximum value of 115 s-1. ground state, it follows that the free energy of activation At this temperature AH-D - 0, and the refolding reaction shows only (AG*-D) is associated with a change in heat capacity according small changes with temperature. Above 50°C (1/1T < 0.0031), the to Eq. 3 (cf. refs. 4 and 7). As shown in Fig. 3, this will lead to gradient of the Eyring plot becomes positive-i.e., the refolding rate a minimum in AG-D(T)/RT. At the temperature where constant decreases with increasing temperature (AH-D < 0). The AG-D(T)/RT is minimal, the refolding rate constant (i.e., complex temperature dependence of the protein-folding process is k/i) reaches a maximal value (Eq. 1), and below and above this caused by a difference in heat capacity between the denatured ground the rate constant decreases. The kinetics state (D) and the activation barrier (t) which results in a temperature temperature pre- dependence of AJ-D (Eq. 2). (Lower) Free-energy diagrams at 25°C dicted by this straightforward assumption is in precise agree- and at the midpoint for the thermal unfolding transition at 88°C. Since ment with experimental observations of the refolding rate the observed rate constant is always the sum of the forward and the constants of C12 (Fig. 1). The parameters obtained from the reverse rate constants (in this case kobs = kD-N + ku), the contribution fit of Eqs. 1 and 2 in Fig. 1 are AHt-D(2980C) = 7 + 0.2 from the unfolding rate constant to kobs becomes predominant at kcal/mol and AC*-D - -307 ± 6 cal/mol/K. temperatures above 88°C where ku > kD-N- we have used barnase to how in Second, exemplify changes the ground state for the refolding reaction is the thermally the ground state of the refolding reaction cause deviations unfolded state (D) (8) (Fig. 2). The change of denatured state from the simple kinetic behavior of CI2 and how these in the preequilibrium has pronounced effects on the kinetics, secondary effects can be distinguished from the temperature since the observed refolding rate constant (kf°bs) is determined dependence of the activation energy (Figs. 1 and 2). In contrast not only by the activation barrier (AG*-I() a kf) but also by to C12, barnase refolds from a compact denatured state at the relative occupancy of I (C). In a three-state model [D a room temperature (Fig. 2). At higher temperatures, however, I . (4) 2 N], this compact conformation (I) becomes destabilized relative to more unfolded denatured conformations, so that above 45°C k4bs = C/kf + ku, [4] Downloaded by guest on September 26, 2021 8928 Biochemistry: Oliveberg et al. Proc. Natl. Acad. Sci. USA 92 (1995)

-2.0 40 AG*-D/RT 30 -3.0 20 t fkmaxI 4.0 _ 10 - AGND/RT 00 ~~~~~~obs 0 o ln(kf IT)

0 t ; I\

-5.0 0 00° -10 Tm T.codT I"%II -6.0 InI1U 0.0029 0.003 i 0.0032 0.0033X 0.0034 0.0035 0.0036 -100 -50 0 50 100 150 11/T T (K) FIG. 3. Temperature dependence of the equilibrium constant of unfolding (AGN-D/RT) and the quasithermodynamic equilibrium constant between the denatured state and the transition state (AGt-D/RT) of C12, illustrating the relation between cold-unfolding phenomena and negative activation enthalpies in protein folding. The t kD curvature of the plots is due to changes in heat capacity between the t~~~~kD conformations in the folding pathway. AGN-D/RT is derived from thermal unfolding data (unpublished work) and Eq. 3. C12 shows a maximum stability around 0WC, its melting temperature is around 88°C N DDI (Tm), and the cold-denaturation process is predicted to take place at NI -50°C (Tc01d). The free-energy difference between the denatured N ground state and the activation barrier (AGf-D) is derived from the obs obs obs refolding kinetics and Eqs. 1 and 3. Although the absolute value of kf =C-kf+ku; kfo0C.kf; k-f =kf; AGt-D cannot be strictly determined by Eq. 1, its variation with C.kf kD-N = ku kf = kD-N kf >ku temperature corresponds directly to the temperature dependence of the refolding kinetics. The refolding rate constant shows a maximum Reaction coordinate value at 50°C, where the transition barrier is lowest, and it decreases at higher or lower temperatures. FIG. 2. Eyring plot of the observed refolding rate constant for barnase. The plot illustrates nonlinearity induced by a combination of state and the changes in the preequilibrium and heat-capacity changes between the difference between the compact denatured preequilibrium and the transition state. k has units of s-1. The solid transition barrier (kf), and its curvature reflects the difference curve is the fit of Eq. 1 and Eq. 3 to the data at low temperatures with in heat capacity of these two conformations (AHt-I(2980C) = AHf-I(2980C) = 4 kcal/mol and AC*-' = -300 cal/mol/K. Barnase 4 kcal/mol and AC - -300 cal/mol/K). At temperatures shows deviations from two-state kinetics: at 25°C, the protein refolds above 33°C, it is apparent that the observed rate constant from a compact denatured species (I) which is 2-3 kcal more stable becomes progressively slower than kf (Fig. 2). This deviation than the thermally unfolded state (D). The preequilibrium (D a± I), reflects the disappearance of I in the preequilibrium = which is fast and takes place in the dead time of the stopped-flow (kfbs instrument, changes with temperature: below 33°C (1T > 0.00326), C-kf -- 0 as [I] -> 0). Our results show that curved Arrhenius and I is the ground state for the refolding reaction, whereas above 50°C plots (apparent) (1/T < 0.0031) D is the ground state. The observed refolding rate negative activation enthalpies can be due to heat-capacity constant (kobs) is determined by both the free-energy difference changes in the activated complex, temperature-induced between I and the transition barrier (t) (i.e., kf) and the occupancy of changes of the ground state, or a combination of both. In I in the preequilibrium (C) (Eq. 4). Below 33°C (1/T > 0.00326), where addition, nonlinearity can be caused by a change of rate- C 1, k bsequals kf, and the curvature of the plot reflects the change limiting step-i.e., a temperature-induced change of activation in heat capacity between I and the transition barrier (t). The solid line kinks or curvatures in the Arrhenius shows kf extrapolated from T < 33°C into higher temperatures (Eqs. barrier. Accordingly, plot cannot to without 1 and 3). In the D 2. I transition region (T > 330C), kobs becomes be related directly the reaction mechanism progressively slower than kf as the ground state for the refolding some knowledge about the preequilibrium and the transition

reaction shifts from I to D and C -* 0 (Eq. 4). The midpoint for the state. In particular, changes in heat capacity must be taken into D T± I transition occurs around 45°C (1T > 0.00314), where kf account when evaluating protein reactions involving large- corresponds to the rate constant expected for the free-energy differ- scale conformational changes in aqueous solution. This may ence between D and t (kD-N, dotted line). kD-N is calculated from the have implications for enzyme catalysis and electron-transfer unfolding rate constant and the free energy of unfolding. Since kfbs is reactions in which the rate-limiting step involves conforma- always the sum of the forward and the reverse rate constants (kfbs = C-kf + ku), the contribution from the unfolding rate constant becomes tional switches of the structure. predominant at temperatures above 55°C where ku > C-kf. The lower panels show free-energy diagrams at 25°C where I is the most stable 1. Arrhenius, S. (1889) Z. Phys. Chem. 4, 226-248. species in the preequilibrium, at the midpoint for the thermal unfold- 2. Eyring, H. (1935) Chem. Rev. 17, 65-77. ing transition of I (45°C), and at the midpoint for the thermal unfolding 3. Fersht, A. R., Matouschek, A. & Serrano, L. (1992) J. Mol. Biol. transition of N (55°C). 224, 771-782. 4. Hagerman, P. J. & Baldwin, R. L. (1976) Biochemistry 15, 1462- 1473. where C = [I]/([I] + [D]) and ku is the unfolding rate constant. An for the of 5. Pohl, F. M. (1976) FEBS Lett. 65, 293-296. expression temperature dependence ln(kf°bs/T) 6. Segawa, S.-I. & Suguhara, M. (1984) Biopolymers 23, 2473-2488. against 1/T is fitted to the experimental data obtained at T < 7. Chen, B., Baase, W. A. & Schellman, J. A. (1989) Biochemistry 330C (Eqs. 1 and 3; cf. Fig. 1). Below 33°C, I is the predominant 26, 691-699. species in the preequilibrium. The fitted function is used to 8. Jackson, S. E. & Fersht, A. R. (1991) Biochemistry 30, 10428- represent the rate constant expected from the free-energy 10435. Downloaded by guest on September 26, 2021 Biochemistry: Oliveberg et al. Proc. Natl. Acad. Sci. USA 92 (1995) 8929

9. Serrano, L. & Fersht, A. R. (1989) Nature (London) 342, 296- 11. Privalov, P. L., Griko, Y. V., Venyaminov, S. Y. & Kutyshenko, 299. V. P. (1986) J. Mol. Biol. 190, 487-498. 10. Matouschek, A., Kellis, J. T., Jr., Serrano, L., Bycroft, M. & 12. Privalov, P. L. & Makhatadze, G. I. (1990) J. Mol. Biol. 213, Fersht, A. R. (1990) Nature (London) 346, 440-445. 385-391. Downloaded by guest on September 26, 2021