A Thermodynamic Molecular Switch in Biological Systems: Ribonuclease S؅ Fragment Complementation Reactions

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provided by Elsevier - Publisher Connector 416 Biophysical Journal Volume 78 January 2000 416–429

Paul W. Chun Department of Biochemistry and Molecular Biology, University of Florida College of Medicine, Gainesville, Florida 32610-0245 USA

ABSTRACT It is well known that essentially all biological systems function over a very narrow temperature range. Most typical macromolecular interactions show ⌬H°(T) positive (unfavorable) and a positive ⌬S°(T) (favorable) at low temperature, because of a positive (⌬Cp°/T). Because ⌬G°(T) for biological systems shows a complicated behavior, wherein ⌬G°(T) changes from positive to negative, then reaches a negative value of maximum magnitude (favorable), and finally becomes positive as temperature increases, it is clear that a deeper-lying thermodynamic explanation is required. This communication demonstrates that the critical factor is a temperature-dependent ⌬Cp°(T) (heat capacity change) of reaction that is positive at low temperature but switches to a negative value at a temperature well below the ambient range. Thus the thermodynamic molecular switch determines the behavior patterns of the Gibbs free energy change and hence a change in the equilibrium ⌬ ⌬ ⌬ ⌬ constant, Keq, and/or spontaneity. The subsequent, mathematically predictable changes in H°(T), S°(T), W°(T), and G°(T) give rise to the classically observed behavior patterns in biological reactivity, as may be seen in ribonuclease SЈ fragment complementation reactions.

INTRODUCTION Shortly after T. H. Benzinger published a paper in 1971 It has been well established in pure and applied chemistry titled “Thermodynamics, Chemical Reactions and Molecu- of simple molecules that reaction energies at room temper- lar Biology,” the question arose whether thermochemical ature can be understood in terms of two contributions, one descriptions of biochemical systems in the literature were related to energy differences at 0 K (the innate inherent inadequate or wrong or both. bond energy) and the other associated with integrals of heat After years of detailed study on interacting protein sys- capacity data over a range of temperatures (the thermal tems and their thermodynamic parameters, it is possible to agitation energy). The necessity of a comparable separation formulate a viewpoint of thermodynamic reactions that is of energy terms for biological reactions, however, has not both adequate and consistent when applied to biological been obvious to most workers in structural and molecular systems, and which considers the innate thermodynamic biology. The innate thermodynamic quantities (Gibbs, quantities in structural biology. 1878; Planck, 1927; Moelwyn-Hughes, 1957; Lewis and As made apparent in Benzinger’s pioneering studies, in Randall, 1961), particularly the innate temperature-invariant any chemical reaction involving small molecules, differ- enthalpy, represent differences in chemical bonding energy ences in heat capacities between products and reactants of products minus reactants and thus control the heat of could be considered negligible, and consequently, the heat reaction. of reaction consists primarily of the contribution from the In biological systems, which function over a very narrow chemical bonding term and, therefore, is a close approxi- temperature range, the standard Gibbs free energy change, mation of the chemical bond energy. Thus many scientists ⌬GЊ are comfortable thinking about reaction enthalpy in terms of , shows a complicated behavior, changing from positive “bonds formed minus bonds broken,” that is, based upon the to negative, then reaching a negative (and thus favorable) difference in bond energies between products and reactants. minimum, before finally becoming positive as temperature In the case of biological interactions, Benzinger observed increases. that the difference between the heat capacities of products It is reasonable to search for an underlying thermody- and reactants may be substantial enough to totally obscure namic explanation for the greater complexity known to any difference between the chemical bonding term and the occur in typical biological systems. This communication heat capacity integral. Thus the heat of reaction as tradi- proposes that the critical factor driving this process is a tionally defined cannot be used to accurately represent the temperature-dependent heat capacity change of reaction, chemical forces associated with these systems. which is positive at low temperature but switches to a negative value at a temperature well below the ambient range. This thermodynamic molecular switch determines Received for publication 15 July 1999 and in final form 27 August 1999. the behavior patterns of the Gibbs free energy change, and Address reprint requests to Dr. Paul W. Chun, Department of Biochemistry hence a change in the equilibrium constant, K , and/or and Molecular Biology, University of Florida College of Medicine, P.O. eq Box 100245, Gainesville, FL 32610-0245. Tel.: 352-392-3356; Fax: 352- spontaneity. The subsequent, mathematically predictable 392-2953; E-mail: [email protected]. changes in ⌬HЊ, ⌬SЊ, ⌬WЊ, and ⌬GЊ that arise as a result of © 2000 by the Biophysical Society this thermodynamic molecular switch are demonstrated in 0006-3495/00/01/416/14 $2.00 RNase SЈ fragment complementation reactions. Thermodynamic Molecular Switch in RNase SЈ 417

THE INNATE THERMODYNAMIC QUANTITIES practical reasons, for instance, the relationship between ⌬ H°reaction and the temperature coefficient of the equilibrium The Gibbs free energy, or more correctly, the change in ϭϪ⌬ Њ constant, Keq, dln Keq/d(1/T) H (T)/R. Kirchhoff’s partial molar free energy for the components in a reaction law (Moelwyn-Hughes, 1957; Lewis and Randall, 1961) mixture, undoubtedly does provide the correct thermody- ⌬ Њ ϭ⌬ Њ ϩ͐298 ⌬ states that H298 H (T0) 0 Cp dT, where this last namic criterion of equilibrium. Furthermore, it is often term represents the thermal agitation energy (heat capacity desirable to relate the drive toward equilibrium to a struc- ⌬ Њ integrals), while the constant term H (T0) represents the tural aspect of a system, that is, to understand the underlying enthalpy of reaction at 0 K. For small molecules, reaction ⌬GЊ factors that contribute to the change in as a function of enthalpies are often obtained around room temperature, and temperature for a specific reaction. the heat of reaction is estimated in terms of the innate ⌬GЊ Certain components of the total change in may be temperature-invariant enthalpy (inherent chemical bond en- described as “innate,” that is, the quantity ⌬GЊ has an ⌬ Њ ergy), H (T0). (The innate temperature-invariant enthalpy, extrapolated value even at absolute zero temperature. There ⌬ ⌬ H(T0) (or in some texts, H0), is an equivalent terminol- are also components that change with temperature. We note, ogy for this quantity in the inherent 0 K enthalpy (innate T ϭ T⌬SЊϭ for example, that at 0K, 0. Accordingly, thermodynamic quantity). It represents the chemical bond ⌬GЊϭ⌬HЊϪT⌬SЊ because (Gibbs, 1978; Planck, 1927; energy difference corrected to 0 K.) Moelwyn-Hughes, 1957; Lewis and Randall, 1961), it is T. L. Cottrell (1958) pointed out 40 years ago that ⌬HЊ ⌬HЊ ϭ⌬GЊ ⌬HЊ T ϭ 298 found that at absolute zero K, 0 0 ( ( 0) and ⌬HЊ(T ) differ only by ϳ1% in small molecules, but in ⌬GЊ T 0 ( 0) in some texts). The residual values of these quan- 1971 T. H. Benzinger made the crucial observation that this tities (note that entropy is excluded) are the same at absolute difference is large in biological macromolecules because of zero of the temperature scale and may be said to describe the large magnitude of the heat capacity integrals (thermal the innate thermodynamic stability of the system. agitation energy). In other words, for small molecules, For a chemical reaction, the difference in these quantities ⌬HЊ Ϫ⌬HЊ(T ) is a correction of only a few percent, ⌬HЊ ϭ⌬GЊ 298 0 between reactants and products, that is, 0 0, rep- whereas for biological macromolecules, the heat capacity resents the differences in the innate thermodynamic stability integrals can be large, from 10% to 90% of the total heat of between reactants and products, or the change in stability reaction. At present the scientific literature provides no between reactants and products as the reaction occurs. “silver bullet,” that is, no highly accurate method for eval- ⌬ Њ Ϫ⌬ Њ uating H298 H (T0) in large biological macromole- THE GIAUQUE FUNCTION AND PLANCK- cules; however, Chun’s work (1988, 1994, 1995, 1996b, BENZINGER THERMAL WORK FUNCTION 1997a, 1998) has extensively addressed the problem. One form of the free energy function, the Giauque function (Giauque, 1930a,b; Giauque and Blue, 1930; Giauque and METHODS AND COMPUTATIONAL ЊϪ Њ ϭ Kemp, 1938; Giauque and Meads, 1941), (G0 H0 )/T PROCEDURES Ϫ⌿Њ ⌿Њ ϭ Ϫ Њ /T, where G°T H0, has been extensively used in chemistry and physics. An equivalent formulation has To analyze the thermodynamic processes operating in a recently found application in the biochemical literature as particular biological system, it is necessary to extrapolate the Planck-Benzinger thermal work function (Chun, 1988, the thermodynamic parameters over a much broader tem- 1994, 1996b, 1997a, 1998), where the application to a given perature range. The enthalpy, entropy, and heat capacity situation is quite different. Here the Planck-Benzinger ther- terms are evaluated as partial derivatives of the Gibbs free ⌬ Њ ϭ⌬ Њ Ϫ⌬ Њ energy function defined by Helmholtz-Kelvin’s expression mal work function, W (T) H (T0) G (T), represents the strictly thermal components of any intra- or inter- (Moelywn-Hughes, 1957; Lewis and Randall, 1961): molecular bonding term, that is, energy other than the Ѩ⌬G͑T͒/ѨT ϭ Ϫ⌬S͑T͒, ͕Ѩ⌬G͑T͒/T͖/ѨT ϭ Ϫ⌬H͑T͒/T2 inherent difference in the 0 K portion of the interaction energy. The latter is the only energy term in constant Ѩ⌬H͑T͒/ѨT ϭ ⌬Cp͑T͒, Ѩ⌬S͑T͒/ѨT ϭ ⌬Cp͑T͒/T pressure processes at absolute zero Kelvin. Thus ⌬WЊ(T) expresses completely the thermal energy difference of the In continuing studies on dozens of interacting protein process involved. Application of the thermal work function systems, it has been shown in our laboratory that the third- permits the separation of 0 K energy differences and energy order polynomial function provides a good fit in the tem- differences associated with heat capacity integrals for a perature range accessible in biochemical systems (Chun, fuller understanding of reaction energies. 1988, 1994, 1997a, 1998). In fact, it is shown to be correct in the low-temperature limit. The rationale for selecting the linear and nonlinear third-order (T3 model) polynomial Measuring enthalpy values functions for ⌬GЊ(T) ϭ ␣ ϩ ␤T2 ϩ ␥T3 (macromolecular Enthalpies of reaction are frequently measured at or near interactions) and ⌬H(T) ϭ ␣ ϩ ␤T3e␥T (macromolecular room temperature (298 K) for a variety of theoretical and unfolding) is found in the fundamentals of relevant quantum

Biophysical Journal 78(1) 416–429 418 Chun

theory (Planck, 1927; Moelywn-Hughes, 1957). At low temperatures, the specific heat of a simple solid becomes ϭ ␲4 ␷ 3 CV (12 /5)(N0K)(kT/h m) . With a proper substitution ␪ ϭ ␷ ϭ ϭ ␲4 ␪ 3 of h m/k and R N0k, Cv (12 R/5)(T/ ) (Moe- lywn-Hughes, 1957; Lewis and Randall, 1961). Clearly, the ␷ energy and specific heat are universal functions of (kT/h m) ␪ or (T/ ). Here k is the Boltzmann constant, CV is the specific ␷ heat at constant volume, and m is the maximum frequency of vibration of an atom in a solid state, as in Planck’s theory (Planck, 1927).

Determination of the Gibbs free energy change as a function of temperature Ϫ1 1. The binding constants, KB (M ), as a function of temperature, were evaluated from the calorimetric titration of the S-protein of RNase S with various substitutions at 13 Met -S-peptide, as reported by Naghibi et al. (1995). FIGURE 1 Thermodynamic plots of the standard Gibbs free energy We converted these binding constants into the Gibbs free change of the fragment complementation reaction of a ribonuclease SЈ energy change as a function of temperature. system as a function of temperature in the temperature range of 273–313 K, 2. The Gibbs free energy data for the fragment complemen- at pH 7.0 in 0.3 M NaCl based on data reported by Hearn et al. (1971). The experimental data for equilibrium and calorimetric measurements were tation reactions of S-peptide with S-protein and of evaluated with the general linear model procedure of statistical analysis of 13 Met(O2) -S-peptide with S-protein were also extracted the IMSL subroutine. The solid line represents fitted data. F ϭ 0.001; thus from figures 4 and 5, respectively, of Hearn et al. (1971). the goodness of fit of the experimental data was 99.9% or better in each 3. The data for the Gibbs free energy change of thermal case. The expansion coefficients ␣, ␤, and ␥ for 20S-RNase SЈ and 13S-RNase SЈ were (Chun, 1997a) as follows: unfolding of four mutants were extracted from figures 3 Ј ⌬ Њ 20-S[I], formation of 20S-RNase S : and 4 of Connelly et al. (1991), using the expression Gd ␣ ϭ 34.05 Ϯ 1.30 kcal molϪ1; ␤ ϭϪ1.856 ϫ 10Ϫ3 kcal molϪ1 KϪ2; ϭ ⌬ Ϫ⌬ ⌬ Ϫ6 Ϫ1 Ϫ3 2 (mutant) { G°d(WT) G°d}, where G°d(WT)asa ␥ ϭ 4.5447 ϫ 10 kcal mol K ; R ϭ 0.9995; SD ϭ 0.01342; function of temperature was evaluated from figure 2 of PR Ͼ F ϭ 0.0001. Connelly et al. (1991). 13-S[II], formation of 13S-RNase SЈ: ␣ ϭ 19.49 Ϯ 1.08 kcal molϪ1; ␤ ϭϪ1.2034 ϫ 10Ϫ3 kcal molϪ1 KϪ2; ␥ ϭ 3.0989 ϫ 10Ϫ6 kcal molϪ1 KϪ3; R2 ϭ 0.990; SD ϭ 0.02436; PR Ͼ Computational procedure for macromolecular F ϭ 0.0002. interactions (The practical use of Benzinger’s method (1971) requires parameters. ⌬HЊ(T), ⌬CpЊ(T), T⌬SЊ(T), and ⌬WЊ(T) are “the experimental determination of the all-important zero- defined as follows: point enthalpy and free entropy terms” pointed out by ⌬HЊ͑T͒ ϭ ␣ Ϫ ␤T2 Ϫ 2␥T3 (2) Rhodes (1991). As noted by Rhodes, Benzinger was pessi- mistic about the prospects for practical use of his method, ⌬CpЊ͑T͒ ϭ Ϫ2␤T Ϫ 6␥T2 (3) due to the difficulty of obtaining the required (temperature- invariant) quantities. Our solutions to this difficulty are T⌬SЊ͑T͒ ϭ Ϫ2␤T2 Ϫ 3␥T3 (4) addressed in the present series of papers (Chun, 1988, 1994, ⌬WЊ͑T͒ ϭ Ϫ␤T2 Ϫ ␥T3 (5) 1995, 1996a,b, 1998).) The approach that we follow re-

quires exact determination of Keq for the relevant biological To extrapolate down to 0 K, it is necessary to consider processes as a function of absolute temperature. Of critical normal solution states of macromolecules. Here the 0 K ⌬ importance, however, is the calculation of Cp°reaction as a limit would presumably refer to the glassy condition (Chun, function of temperature as shown in Eq. 3. In this treatment, 1996a), that is, a condition with all thermal agitation frozen the Gibbs free energy data, as shown in Figs. 1 and 2, A–D, out, but retaining the general physical chemical properties were fitted to a three-term linear polynomial function in the of solution—since a pure crystalline form of macromole- 273–320 K temperature range, the range in which experi- cules is rarely encountered in practice. (Why is Helmholtz- ments have been conducted: Kelvin’s expression considered to be a continuous function? Our evaluation of the innate temperature-invariant enthalpy ⌬GЊ͑T͒ ϭ ␣ ϩ ␤T2 ϩ ␥T3 (1) for hydrogen-bonded water in equilibrium with non-hydro- Once evaluated as shown in Figs. 1 and 2, A–D, the gen-bonded water molecules is based on Helmholtz free coefficients ␣, ␤, and ␥ were fitted to other thermodynamic energy data reported by Nemethy and Scheraga [1962]. The

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FIGURE 2 Thermodynamic plot of the nonstandard Gibbs free energy change of the fragment complementation reaction of the S-protein of RNase SЈ with various substitutions at Met13 S-peptide as a function of temperature, based on data reported by Naghibi et al. (1995) and by Varadarajan et al. (1992) in the temperature range of 288–303 K in 50 mM sodium acetate with 100 mM NaCl, pH 6.0. The experimental data for differential scanning calorimetry were evaluated with the general linear model procedure of statistical analysis of the IMSL subroutine. The solid line represents fitted data. F ϭ 0.001; thus the goodness of fit of the experimental data was 99.9% or better in each case. The expansion coefficients ␣, ␤, and ␥ for various substitutions at Met13 as a function of temperature (Chun, 1997a) were as follows. (A) M13A RNase SЈ: ␣ ϭ 25.05 Ϯ 0.36 kcal molϪ1; ␤ ϭϪ1.358 ϫ 10Ϫ3 kcal molϪ1 KϪ2; ␥ ϭ 3.384 ϫ 10Ϫ6 kcal molϪ1 KϪ3; R2 ϭ 0.9998; SD ϭ 4.122 ϫ 10Ϫ4;PRϾ F ϭ 0.001. (B) M13F RNase SЈ: ␣ ϭ 85.68 Ϯ 1.43 kcal molϪ1; ␤ ϭϪ3.587 ϫ 10Ϫ3 kcal molϪ1 KϪ2; ␥ ϭ 3.384 ϫ 10Ϫ6 kcal molϪ1 KϪ3; R2 ϭ 0.0934; SD ϭ 0.0143; PR Ͼ F ϭ 0.0. (C) M13␣-NBA RNase SЈ: ␣ ϭ 22.32 Ϯ 0.78 kcal molϪ1; ␤ ϭϪ1.269 ϫ 10Ϫ3 kcal molϪ1 KϪ2; ␥ ϭ 3.111 ϫ 10Ϫ6 kcal molϪ1 KϪ3; R2 ϭ 0.9994; SD ϭ 5.494 ϫ 10Ϫ4;PRϾ F ϭ 0.001. (D) M13Norleucine RNase SЈ: ␣ ϭϪ33.52 Ϯ 0.78 kcal molϪ1; ␤ ϭ 6.997 ϫ 10Ϫ4 kcal molϪ1 KϪ2; ␥ ϭϪ1.403 ϫ 10Ϫ6 kcal molϪ1 KϪ3; R2 ϭ 0.9999; SD ϭ 1.6319 ϫ 10Ϫ5;PRϾ F ϭ 0.001. entropy of the system appears to remain independent of the transformation between water monomer and n-mer at temperature, suggesting that there is no significant temper- zero Kelvin. As with most small molecules, the thermal ature-dependent difference in the degree of orientation be- agitation energy is minimal. ⌬W(T) ϭ T⌬S(T), ⌬H(T) ϭ ⌬ tween unbound and hydrogen-bound water molecules in H(T0) over the entire temperature range from0Ktothe equilibrium in the system. A similar conclusion could be temperature of interest. ⌬S(T) obtained from Helmholtz free reached based on the dielectric relaxation of water as a energy data and ⌬S(T) from dielectric relaxation data re- function of temperature as reported by Collie et al. [1948]. main constant and have values of 17.44 cal molϪ1 degϪ1 This implies that there is a nonzero entropy difference for and 4.98 cal molϪ1 degϪ1, respectively. These values are

Biophysical Journal 78(1) 416–429 420 Chun independent of temperature, and can be extrapolated to 0 K experimental conditions. This IMSL program was incorpo- [unpublished results] [Chun, 1996a]. There may be a small rated into software for the computer-aided analysis of bio- ⌬ Њ ⌬ Њ finite S (T0)or S0 of formation. For these dilute systems chemical processes, and each data point was evaluated with of macromolecules, the ⌬CpЊ/T is largely controlled by the extrapolation of F-statistics with an IBM personal computer solvent water. As already noted, the assumed reference (Chun, 1991; Barr et al., 1985), as shown in Figs. 3, A and condition is glassy ice at 0K, which probably does have a B,4,A–C, and 5, A–C. ⌬ Њ ⌬ Њ small S0. In the case of G (T) of formation, phase tran- A built-in restriction in the extrapolation procedure is that sition is indeed important. When dealing with ⌬GЊ(T)of the values for ⌬HЊ(T) and ⌬GЊ(T) determined from the reaction, no phase transition is taking place. In this case, all polynomial functions intersect at zero Kelvin with zero thermodynamic functions are continuous.) slope on a thermodynamic plot, thus obeying Planck’s def- Values of these thermodynamic parameters were regen- inition of the Nernst heat theorem (Moelwyn-Hughes, 1957; erated from the fitted coefficients of ␣, ␤, and ␥, using the Lewis and Randall, 1961). By our definition, the value of ⌬ Њ International Mathematical Subroutine Library (IMSL) soft- H (T0) will be positive. Other polynomial functions failed ware for linear and nonlinear polynomial regression analy- to meet all three restrictions of ⌬HЊ(T) and ⌬GЊ(T) inter- ⌬ Њ sis. Each equation was interactively executed in steps of one secting at zero Kelvin with zero slope, and H (T0) being K, and the values were plotted and overlaid for each set of positive and thus were discarded.

FIGURE 3 Thermodynamic plots of the fragment complementation reaction of 20-S [I] RNase SЈ (A) and of 13-S [II] RNase SЈ (B) as a function of temperature at pH 7.0 in 0.3 M NaCl. Each data point between 0 and 360 K was evaluated with extrapolation of F-statistics. Data points below 273 K were extrapolated from the experimental data. (Reprinted from Chun, P.W., 1997a, J. Phys. Chem. 101B: 7835. ©1997, American Chemical Society.) (C and D) A close-up view of a portion of 20-S [I] RNase SЈ (C) and of 13-S [II] RNase SЈ (D) over the temperature range of0Kto360K,with the magnitude Ϫ Ϫ1 Ϫ1 ⌬ Њ ͗ ͘ϭ of the y-axis reduced to 1.0 to 1.0 kcal mol K . Thermodynamic molecular switch occurs when Cp (T)at TCp 135 K changes sign from positive ͗ ͘ϭ ⌬ Њ ⌬ Њ to negative at Ts 270 K. Cp (T) and S (T) reach a maximum at 65 K and 135 K, respectively.

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It is clear that a temperature-dependent model simpler than the third-order Gibbs polynomial model (T3 model) cannot be used at low temperature and has been found to be unacceptable at room temperature; therefore it would be reasonable to apply a more complex model in the interven- ing temperature region only if the facts demand a more complex fit. In fact, the facts do not require a different function; the model as described has been found to have both strong correlative power and very good predictive power. The fitted thermal data (⌬GЊ(T), ⌬HЊ(T), ⌬WЊ(T), T⌬SЊ(T), and ⌬CpЊ(T)) are reasonable not only over the measured experimental range (near room temperature) but in the low-temperature limit. The fitting curves do nothing strange in the experimentally inaccessible region, but rather smoothly approach the low-temperature limit. The thermal dependency presented here is the best (and essentially the only) approach known.

Computational procedure for protein unfolding It has been known for some time that the folded states of many proteins are only marginally stable under the best of conditions. The delicate balance between folded and unfolded forms may be disrupted by such environmental changes as an increase in temperature, variation of pH, and addition of denaturants or Hofmeister anions. In the case of protein unfolding or DNA unwinding, however, the nonlinear (T3) model for ⌬H͑T͒ ϭ ␣ ϩ ␤T 3e␥T (6) must be applied (Chun, 1994, 1997b, 1998, 1999). In this treatment, the Gibbs free energy data, as shown in Fig. 6, were fitted to a three-term nonlinear enthalpy polynomial function in the 295–330 K temperature range, the range in which experiments have been conducted. Once evaluated as shown in Fig. 6, the coefficients ␣, ␤, and ␥ were fitted to other thermodynamic parameters. ⌬H(T), ⌬G(T), ⌬Cp(T), T⌬S(T), and ⌬W(T) are defined as follows: ⌬G͑T͒ ϭ ␣ Ϫ ␤Te␥T͑␥T Ϫ 1͒/␥2 (7)

⌬Cp͑T͒ ϭ ␤T 2e␥T͑␥T ϩ 3͒ (8)

T⌬S͑T͒ ϭ ␤Te␥T͓T 2 ϩ ͑␥T Ϫ 1͒/␥2͔ (9)

⌬W͑T͒ ϭ Ϫ␤Te␥T͑␥T Ϫ 1͒/␥2 (10) FIGURE 4 Thermodynamic plots of the fragment complementation reaction of S-protein of RNase SЈ with various substitutions at Met13 of Values of these thermodynamic parameters were regen- S-peptide as a function of temperature in 50 mM sodium acetate with 100 erated from the fitted coefficients ␣, ␤, and ␥, using the mM NaCl, pH 6.0. Each data point between 0 and 380 K was evaluated with extrapolation of F-statistics. (A) M13A RNase SЈ.(B) M13F RNase general nonlinear model procedure of IMSL’s statistical SЈ.(C) M13␣-NBA RNase SЈ. subroutines as shown in Fig. 7, A–D. Each data point between 0 and 350 K was evaluated with extrapolation of F-statistics (Chun, 1991; Barr et al., 1985). F ϭ 0.001; thus the goodness of fit of experimental data was 99.8% or better in each case.

Biophysical Journal 78(1) 416–429 422 Chun

FIGURE 6 Thermodynamic plots of the Gibbs free energy change of the mutant form of phage T4 lysozyme as a function of temperature in the

temperature range of 298–328 K, at pH 2.5 in 20 mM KH2PO4 containing 25 mM KCl and 0.5 mM dithiothreitol, based on data reported by Connelly et al. (1991). The experimental data for differential scanning calorimetric measurements were evaluated with the nonlinear model data reported by Connelly et al. (1991). The experimental data for differential scanning calorimetric measurements were evaluated with the nonlinear model procedure of statistical analysis of the IMSL subroutine (Chun, 1991; Barr et al., 1985). The solid line represents fitted data F ϭ 0.01; thus the goodness of fit of the experimental data was 98.8% or better in each case. ⌬H(T) ϭ ␣ ϩ ␤T3e␥T. The expansion coefficients ␣, ␤, and ␥ for wild-type T157, T157R, T157A, and T157N were as follows: WTT157: ␣ ϭ 15.09 Ϯ 0.35 kcal molϪ1; ␤ ϭ 1.44 ϫ 10Ϫ9 kcal molϪ1 KϪ3; ␥ ϭ 2.37 ϫ 10Ϫ2 kcal molϪ1 KϪ1. T157R: ␣ ϭ 15.12 Ϯ 0.65 kcal molϪ1; ␤ ϭ 1.06 ϫ 10Ϫ9 kcal molϪ1 KϪ3; ␥ ϭ 2.37 ϫ 10Ϫ2 kcal molϪ1 KϪ1. T157A: ␣ ϭ 14.48 Ϯ 0.34 kcal molϪ1; ␤ ϭ 1.38 ϫ 10Ϫ9 kcal molϪ1 KϪ3; ␥ ϭ 2.35 ϫ 10Ϫ2 kcal molϪ1 KϪ1. T157N: ␣ ϭ 14.49 Ϯ 0.24 kcal molϪ1; ␤ ϭ 1.33 ϫ 10Ϫ9 kcal molϪ1 KϪ3; ␥ ϭ 2.41 ϫ 10Ϫ2 kcal molϪ1 KϪ1. WT157: R2 ϭ 0.998; chisig ϭ 0.0057; PR Ͼ F ϭ 0.01 T157R: R2 ϭ 0.998; chisig ϭ 0.0189; PR Ͼ F ϭ 0.01 T157A: R2 ϭ 0.999; chisig ϭ 0.0055; PR Ͼ F ϭ 0.01 T157N: R2 ϭ 0.999; chisig ϭ 0.0057; PR Ͼ F ϭ 0.01.

RESULTS AND DISCUSSION Gibbs free energy change as a function of temperature Plots of the Gibbs free energy change as a function of temperature of ribunuclease SЈ and S-peptides–S-protein interaction shown in Figs. 1 and 2, A–C are typical of biological reactions in that they show a Gibbs free energy

͗ ͘ ⌬ Њ ⌬ Њ TCp changes sign from positive to negative, while S (T)orT S (T) ͗ ͘ changes from positive to negative at Ts , as shown in Tables 2 and 4. (A) FIGURE 5 A close-up view of a portion of the fragment complementa- M13A RNase SЈ: Both ⌬CpЊ(T) and ⌬SЊ(T)orT⌬SЊ(T) reach a maximum tion reaction of S-protein of RNase SЈ with substitutions at Met13 of at 65 K and 135 K, respectively. (B) M13F RNase SЈ: Both ⌬CpЊ(T) and S-peptide, over the temperature range of0Kto360K,with the magnitude ⌬SЊ(T)orT⌬SЊ(T) reach a maximum at 65 K and 135 K, respectively. (C) of the y-axis reduced to 0.5 to Ϫ0.5 (except for B, where it is 5 to Ϫ5) kcal M13␣-NBA RNase SЈ: Both ⌬CpЊ(T) and ⌬SЊ(T)orT⌬SЊ(T) reach a molϪ1 KϪ1. Thermodynamic molecular switch occurs when ⌬CpЊ(T)at maximum at 70 K and 135 K, respectively.

Biophysical Journal 78(1) 416–429 Thermodynamic Molecular Switch in RNase SЈ 423

FIGURE 7 Thermodynamic plot of the reversible unfolding of wild-type T4 phage lysozyme in which the threonine residue at position has been replaced ⌬ ϭ⌬ ϩ͐T ⌬ ϭ ϩ ϭ by four different residues. The experimental conditions were identical to those in Fig. 6. (A) T157: H(T) H(T0) 0 Cp(T)dT 15.09 149.93 Ϫ1 ⌬ ϭ⌬ ϩ͐T ⌬ ϭ ϩ ϭ Ϫ1 ⌬ ϭ⌬ ϩ͐T ⌬ ϭ 165.02 kcal mol .(B) T157R: H(T) H(T0) 0 Cp(T)dT 15.12 162.13 177.25 kcal mol .(C) T157A: H(T) H(T0) 0 Cp(T)dT ϩ ϭ Ϫ1 ⌬ ϭ⌬ ϩ͐T ⌬ ϭ ϩ ϭ Ϫ1 14.48 147.76 162.24 kcal mol .(D) T157N: H(T) H(T0) 0 Cp(T)dT 14.49 151.78 166.27 kcal mol .

change minimum at the point of equilibrium in the system at shown as a function of temperature. The innate temperature- ͗ ͘ ⌬ Њ ϭ ⌬ Њ Ts , the stable temperature at which T S (T) 0. This is invariant enthalpy, H (T0), may be evaluated at four points ͗ ͘ ͗ ͘ ͗ ͘ not the case, however, for the S-protein–S-peptide reaction on these curves: Th , Ts , Tm , and zero Kelvin (Chun, in which norleucine has been substituted for Met13 (shown 1994, 1995, 1996a,b, 1997a, 1998) (see Table 1). in Fig. 2 D). The fitted coefficients of ␣, ␤, and ␥ were A plot of the Gibbs polynomial function, ⌬GЊ(T) ϭ ␣ ϩ Ϫ Ϫ found to be Ϫ33.52 Ϯ 0.78 kcal mol 1, 6.997 ϫ 10 4 kcal ␤T2 ϩ ␥T 3, as a function of temperature exhibits an initial Ϫ1 Ϫ2 Ϫ ϫ Ϫ6 Ϫ1 Ϫ3 ⌬ Њ ͗ ͘ mol K , and 1.403 10 kcal mol K , respec- value of zero for G (T)at Th and a negative value of ͗ ͘ ͗ ͘ ͗ ͘ ⌬ Њ ͗ ͘ ⌬ Њ tively. No values for Th , Ts ,or Tm could determined. In maximum magnitude for G (T)at Ts , and the G (T) ͗ ͘ ͗ ͘ this case, it is inferred that no fragment complementation value again reaches zero at Tm . Here Ts is the stable ⌬ Њ ϭ ͗ ͘ reaction takes place, that is, the S-peptide does not realign temperature at which T S (T) 0, Tm is the melting Ј ͗ ͘ with the ribonuclease S system to form the native structure, temperature, and Th is the harmonious temperature at ⌬ Њ ⌬ Њ ⌬ Њ although it may bind elsewhere as part of a transfer reaction. which G (T) is zero, Cp(T) approaches zero, and T S (T) reaches a positive maximum. Values of the innate temperature-invariant enthalpy at ͗T ͘, ͗T ͘, ͗T ͘ are compared Analysis of the Planck-Benzinger thermal h s m with those at zero K as shown in Figs. 3, A and B, and work function 4, A–C (see Table 1). Thermodynamic plots of ribonuclease SЈ fragment comple- ⌬ Њ ϭ⌬ Њ ⌬ Њ ϭ ͗ ͘ mentation reactions (Figs. 3, A and B, and 4, A–C) are 1. H (T0) W (Th), G (T) 0at Th .

Biophysical Journal 78(1) 416–429 424 Chun

⌬ ͗ ͘ ͗ ͘ ͗ ͘ TABLE 1 Comparison of H(T0)at Th , Ts , Tm and zero K for the S-protein–S-peptide interaction with various substitutions of Met13 ⌬ Њ H (T0)at ⌬ Њ ͗ ͘ ⌬ Њ ͗ ͘ ͗ ͘ ⌬ Њ ͗ ͘ H (T0)at Th H (T0)at Ts Tm H (T0)at0K Ts Ϫ1 Ϫ1 Ϫ1 Ϫ1 ͗ ͘ ͗ ͐͘⌬Њ Substitution (kcal mol ) (kcal mol ) (kcal mol ) (kcal mol ) Th (K) Tm Cp dT M13A RNase SЈ 25.67 Ϯ 0.63 24.46 Ϯ 0.39 24.21 Ϯ 0.57 25.05 Ϯ 0.57 185 270 340 Ϫ85.00 M13F RNase SЈ 85.69 Ϯ 0.35 85.39 Ϯ 0.13 85.39 Ϯ 0.38 85.55 Ϯ 0.38 225 280 325 Ϫ105.83 M13␣-NBA RNase SЈ 22.32 Ϯ 0.19 22.33 Ϯ 2.32 22.01 Ϯ 0.57 23.06 Ϯ 0.57 186 270 350 Ϫ82.03 M13 norleucine RNase SЈ ———Ϫ33.52 ——— — Ϯ 0.13 20S RNase SЈ 20-S[I] 34.05 Ϯ 1.30 34.05 Ϯ 0.54 34.02 Ϯ 0.36 34.05 Ϯ 1.30 180 273 345 Ϫ118.25 13S RNase SЈ 13-S[II] 19.49 Ϯ 1.00 19.49 Ϯ 0.42 19.01 Ϯ 0.13 19.49 Ϯ 1.10 160 265 345 Ϫ88.62 Compiled using the general linear model procedure of statistical analysis of IMSL subroutine. F ϭ 0.001; thus the goodness of fit of the experimental data ͗ ͘ was 99.8% or better in each use. Observed values for Tm are consistent with experimental values. (Reprinted from P. W. Chun, 1997a, J. Phys. Chem. 101B:7835. ©1997, American Chemical Society.)

⌬ Њ ϭ⌬Њ ϩ⌬Њ ⌬ Њ ϭ Ϫ1 2. H (T0) W (Ts)max G (Ts)min, H (TS) kcal mol , respectively. The innate temperature-invariant ⌬ Њ ͗ ͘ G (TS)min at Ts . enthalpy for 20S[I] is nearly the same as those for RNase A ⌬ Њ ϭ⌬ Њ ⌬ Њ ϭ ͗ ͘ 3. H (T0) W (Tm), G (T) 0at Tm , and one can in 20% or 30% glycerol (Chun, 1996a), which are 37 and 33 define the heat of reaction as ⌬HЊ(T) ϭ⌬HЊ(T ) ϩ͐T Ϫ1 0 T0 kcal mol , respectively. This we infer to involve the ⌬C° T T ⌬ Њ p( )d . dimeric form of both RNase A and 20-S[I]. The H (T0) ⌬ Њ Ϫ1 4. H (T0) is evaluated at zero K. value for 13-S[II] is ϳ19 kcal mol , which we infer to The values of ⌬WЊ(T) and ⌬GЊ(T) exhibit a positive involve the monomeric form. Our results are consistent with maximum and negative value of maximum magnitude (neg- findings reported by Crestfield et al. (1962). ⌬ Њ Ј ͗ ͘ Each of three H (T0) values of M13F RNase S comple- ative minimum), respectively, at Ts ; therefore, the innate ⌬ Њ ϭ⌬ Њ ϩ mentation reactions are three to four times greater than temperature-invariant enthalpy, H (T0) W (Ts)max ⌬ Њ ͗ ͘ those of M13A or M13 ␣-NBA, as shown in Table 1. This G (Ts)min at Ts . The innate temperature-invariant enthalpy at the melting temperature is, by the integrated Kirch- suggests that with substitution of phenylalanine-13 strong ⌬ Њ ϭ⌬ Њ ϩ͐T ⌬ Њ site-specific interaction prevails, resulting in dimer or hoff expression, H (T) H (T0) 0 Cp (T)dT, where ⌬HЊ(T) and T⌬SЊ(T) are of the same magnitude, ⌬WЊ(T) ϭ higher aggregates. ⌬ Њ ⌬ Њ Burley and Petsko (1985), in analyzing neighboring aro- H (T0), and G (T) approaches zero. The nature of the biochemical thermodynamic compensation that takes place matic groups in four biphenyl peptides or peptide analogs ͗ ͘ ͗ ͘ between Th and Tm may be characterized by evaluating and 34 proteins, reported that 60% of aromatic side chains ⌬ Њ H (T0) and the heat capacity integrals, as shown in Figs. 3, in proteins are involved in aromatic pairs, 80% of which A and B, and 4 A–C, and Table 1. form networks of three or more interacting aromatic side We found values for the innate temperature-invariant chains. In phenyl ring centroids, the dihydral angles ap- ⌬ Њ enthalpy, H (T0), for the fragment complementation reac- proached 90°. tion of 20S-RNase SЈ and 13S-RNase SЈ in conformational A possible model for the fragment complementation re- transition at neutral pH to be 34.05 Ϯ 1.30 and 19.49 Ϯ 1.10 action of S-peptide with S-protein if phenylalanine were to

TABLE 2 Thermodynamic molecular switch in ⌬Cp°(T) and ⌬S°(T) Fragment-complementation Thermodynamic Molecular switch at Effect on sign of reaction quantities temperature, Kelvin ⌬GЊ(T)or⌬HЊ(T) Ј⌬Њ ϭ ͗ ͘ ϩ 3 Ϫ 20S RNase S Cp (T) 0at TCp 135 ( ) ( ) ⌬ Њ ϭ ͗ ͘ ϩ 3 Ϫ S (T) 0at Ts 270 ( ) ( ) Ј⌬Њ ϭ ͗ ͘ ϩ 3 Ϫ 13S RNase S Cp (T) 0at TCp 133 ( ) ( ) ⌬ Њ ϭ ͗ ͘ ϩ 3 Ϫ S (T) 0at Ts 265 ( ) ( ) Ј⌬Њ ϭ ͗ ͘ ϩ 3 Ϫ M13F RNase S Cp (T) 0at TCp 135 ( ) ( ) ⌬ Њ ϭ ͗ ͘ ϩ 3 Ϫ S (T) 0at Ts 280 ( ) ( ) Ј⌬Њ ϭ ͗ ͘ ϩ 3 Ϫ M13A-RNase S Cp (T) 0at TCp 130 ( ) ( ) ⌬ Њ ϭ ͗ ͘ ϩ 3 Ϫ S (T) 0at Ts 275 ( ) ( ) ␣ Ј⌬Њ ϭ ͗ ͘ ϩ 3 Ϫ M13 NBA-RNase S Cp (T) 0at TCp 135 ( ) ( ) ⌬ Њ ϭ ͗ ͘ ϩ 3 Ϫ S (T) 0at Ts 270 ( ) ( ) Ј⌬Њ ϭ ͗ ͘ Norleucine 13-RNase S Cp (T) 0at TCp —— ⌬ Њ ϭ ͗ ͘ S (T) 0at Ts ——

Biophysical Journal 78(1) 416–429 Thermodynamic Molecular Switch in RNase SЈ 425 be substituted for Met13 incorporates feasible strong, site- All chemical reactions can be characterized by four dif- specific Phe-Phe interaction (Phe8 3 Phe120 and Phe13 3 ferent thermodynamic behavior patterns, in the simplest Phe8 3 Phe120), giving rise to the large innate temperature- case where the sign of ⌬CpЊ(T) is fixed. These may be invariant enthalpy (Chun, 1997a). charted as in Table 3. In biological systems, ⌬HЊ(T) and ⌬SЊ(T) are positive at low temperature. As the reaction temperature increases, Thermodynamic molecular switch in both ⌬HЊ(T) and ⌬SЊ(T) become negative; that is scheme 4 biological systems of Table 3 goes to scheme 1: ⌬HЊ(ϩ), ⌬SЊ(ϩ) 3 ⌬HЊ(Ϫ), ⌬HЊ(T) and ⌬SЊ(T) are simple fundamental thermodynamic ⌬SЊ(Ϫ). In this thermodynamic switch unique to and char- functions. In each case the respective value at a given acteristic of biological systems, ⌬CpЊ(T) changes from pos- ͗ ͘ temperature is determined in a straightforward way, using itive to negative at TCp , the temperature at which the following expression: ⌬CpЊ(T) ϭ 0, where ⌬SЊ(T) is at a positive maximum close ͗ ͘ to TCp . As seen in Table 4, the negative Gibbs free energy T ͗ ͘ Ј Ј minimum at Ts of 20S-RNase S and 13S-RNase S falls ͓⌬HЊ Ϫ ⌬HЊ͑T ͔͒ ϭ ͵ ⌬CpЊ͑T͒, Ј T 0 at 270 and 265 K, respectively. For M13A-RNase S and ␣ Ј ⌬ Њ ͗ ͘ 0 M13 -NBA-RNase S values for G (T)at Ts are 275 Ј ⌬ Њ and 270 K. In M13F-RNase S , the value of G (Ts)min at T ͗ ͘ ⌬ Њ ⌬ Њ Ts is highest, 280 K. The sign of S (T)orT S (T) whereas ⌬SЊ ϭ ͵ ͑⌬CpЊ/T͒dT T ͗ ͘ changes from positive to negative at Ts , as shown in Table 4: 0 ⌬GЊ͑T͒͑ϩ͒ 3 ⌬GЊ͑T ͒ ͑Ϫ͒ 3 ⌬GЊ͑T͒͑ϩ͒ ⌬ Њ s min Note that the value of the enthalpy change at 0 K, H (T0), ⌬ Њ͑ϩ͒ 3 ⌬ Њ͑Ϫ͒ ⌬ Њ ϭ ͗ ͘ is important, but distinct and separate from the thermal S S , where S 0at TS agitation term. Many authors have entirely ignored this ͗ ͘ ⌬ Њ when dealing with biological systems. At temperature TS , a simple algebraic sum of W (Ts) ⌬ Њ ⌬ Њ ⌬ Њ ϭ In contrast, the Gibbs free energy function is a composite and H (TS) yields the value of H (T0), i.e., H (T0) ⌬ Њ ϩ⌬ Њ quantity, defined as a trade-off of ⌬HЊ(T) and ⌬SЊ(T) terms: W (TS)max H (TS) (see Figs. 3, A and B,4A, and 5 C). ͗ ͘ ⌬ Њ ϭ At Ts there exists an optimal balance of H (TS) ⌬ Њ͑ ͒ ϭ ⌬ Њ͑ ͒ Ϫ ⌬ Њ͑ ͒ ⌬ Њ ⌬ Њ G T H T T S T G (TS)min and T S (T), so there will be a minimum negative Gibbs free energy change and the maximum work can T T be accomplished. ⌬GЊ͑T͒ ϭ ⌬HЊ͑T ͒ ϩ ͵ ⌬CpЊdT Ϫ T͵ ͑⌬CpЊ/T͒dT 0 In 13S-RNase SЈ and 20S-RNase SЈ, ⌬CpЊ(T) reaches a 0 0 maximum at 65 K, while the sign changes from positive to negative at ͗T ͘ϭ135 K, ⌬CpЊ(T) ϭ 0. ⌬CpЊ(T)(ϩ) 3 In consequence ⌬GЊ(T) displays an interesting variety of Cp ⌬CpЊ(T)(Ϫ)at͗T ͘. ⌬SЊ(T)orT⌬SЊ(T) in both cases is at behavior patterns as the temperature changes. ⌬GЊ can Cp a maximum at 130 K. In the mutants M13A-RNase SЈ, change sign (K from Ͻ1toϾ1 or vice versa) only if ⌬HЊ eq M13F-RNase SЈ, and M13␣-NBA-RNase SЈ, ⌬CpЊ(T) and ⌬SЊ remain of the same sign. That is to say, reaches a maximum at 65 K, 65 K, and 70 K, respectively, 1. If ⌬HЊ is (ϩ) and ⌬SЊ is (ϩ) then ⌬GЊ goes from (ϩ), while ⌬SЊ(T)orT⌬SЊ(T) for all three is at a maximum at which is unfavorable, to (Ϫ), which is favorable (from 135 K. Ͻ Ͼ Keq 1toKeq 1). This communication demonstrates that the critical factor 2. If ⌬HЊ is (Ϫ) and ⌬SЊ is (Ϫ) then ⌬GЊ goes from (Ϫ), is a temperature-dependent heat of reaction, ⌬CpЊ(T), which which is favorable, to (ϩ), which is unfavorable (from is positive at low temperature but switches to a negative Ͼ Ͻ ͗ ͘ ⌬ Њ ϭ Keq 1toKeq 1). value at TCp , the temperature at which Cp (T) 0, as

TABLE 3 Thermodynamic behavior patterns of chemical reactions Standard Gibbs free energy change ⌬GЊ(T) Thermodynamic Low High Sign Characteristic quantities temperature temperature changes chemical reactions ⌬ Њ Ϫ ⌬ Њ Ϫ Ϫ ϩ ϩ 4 1. H ( ), S ( )() favorable ( ) unfavorable Yes NH3 HCl -- NH4Cl ⌬ Њ Ϫ ⌬ Њ ϩ Ϫ Ϫ ϩ N 2. H ( ), S ( )() favorable ( ) favorable No I2 Cl2 2ICl ⌬ Њ ϩ ⌬ Њ Ϫ ϩ ϩ N ϩ 3. H ( ), S ( )() unfavorable ( ) unfavorable No 2HCl H2 Cl2 ⌬ Њ ϩ ⌬ Њ ϩ ϩ Ϫ N ϩ 4. H ( ), S ( )() unfavorable ( ) favorable Yes PCl5 PCl3 Cl2

Biophysical Journal 78(1) 416–429 426 Chun

TABLE 4 Thermodynamic molecular switch in Gibbs free energy change Molecular switch Fragment-complementation Thermodynamic at temperature, Effect on sign of reaction quantities Kelvin ⌬GЊ(T)or⌬HЊ(T) Ј⌬Њ ͗ ͘ ϩ 3 Ϫ 20S-RNase S G (T)at Th 183 ( ) ( ) ⌬ Њ ͗ ͘ G (T)at Ts 270 Negative minimum ⌬ Њ ͗ ͘ Ϫ 3 ϩ G (T)at Tm 345 ( ) ( ) ⌬HЊ(T) 258 (ϩ) 3 (Ϫ) Ј⌬Њ ͗ ͘ ϩ 3 Ϫ 13S-RNase S G (T)at Th 165 ( ) ( ) ⌬ Њ ͗ ͘ G (T)at Ts 265 Negative minimum ⌬ Њ ͗ ͘ Ϫ 3 ϩ G (T)at Tm 343 ( ) ( ) ⌬HЊ(T) 248 (ϩ) 3 (Ϫ) Ј⌬Њ ͗ ͘ ϩ 3 Ϫ M13F-RNase S G (T)at Th 225 ( ) ( ) ⌬ Њ ͗ ͘ G (T)at Ts 280 Negative minimum ⌬ Њ ͗ ͘ Ϫ 3 ϩ G (T)at Tm 325 ( ) ( ) ⌬HЊ(T) 275 (ϩ) 3 (Ϫ) Ј⌬Њ ͗ ͘ ϩ 3 Ϫ M13A-RNase S G (T)at Th 183 ( ) ( ) ⌬ Њ ͗ ͘ G (T)at Ts 275 Negative minimum ⌬ Њ ͗ ͘ Ϫ 3 ϩ G (T)at Tm 340 ( ) ( ) ⌬H(T) 255 (ϩ) 3 (Ϫ) ␣ Ј⌬Њ ͗ ͘ ϩ 3 Ϫ M13 NBA RNase S G (T)at Th 178 ( ) ( ) ⌬ Њ ͗ ͘ G (T)at Ts 270 Negative minimum ⌬ Њ ͗ ͘ Ϫ 3 ϩ G (T)at Tm 345 ( ) ( ) ⌬HЊ(T) 255 (ϩ) 3 (Ϫ) M13Norleucine RNase SЈ ——— shown in Figs. 3, C and D, and 5, A–C, and Table 2. Note processes is not a clear and urgent demand of the physical that the switch in the sign of ⌬CpЊ(T) causes the change in universe. In fact, life exists only over a limited temperature ⌬ Њ G (T) and hence a change in the equilibrium constant, Keq, range when the balance of energy and entropy demands is ͗ ͘ and/or spontaneity. favorable. There is a lower cutoff point, Th , where entropy In protein unfolding, such as the unfolding of wild-type is favorable but energy (enthalpy) is unfavorable, and an ͗ ͘ T4 phage lysozyme in which the threonine residue at posi- upper cutoff, Tm , above which energy (enthalpy) is favor- tion 157 has been replaced by four different amino acid able but entropy is unfavorable. Only between these two residues (Fig. 7), the process obviously differs over the full limits where ⌬GЊ(T) ϭ 0 is the net chemical driving force temperature range. In this case, there is a single cut-off (indicated by ⌬GЊ(T)) favorable for such biological pro- ͗ ͘ point, Tm , at which energy is unfavorable but entropy is cesses as protein folding, protein-protein interaction, or favorable and ⌬G ϭ 0, as shown in Fig. 7 (see Table 5). protein self-assembly. Within this temperature range there Note that the thermal agitation energy is 10 times greater will be a point with minimum (negative) free energy ͗ ͘ than the innate temperature-invariant enthalpy. The differ- change, Ts , at which the maximum work can be done. ence in the innate temperature-invariant enthalpy between folded and unfolded forms is small, as little as 2–17 kcal molϪ1 (Chun, 1994, 1998, 1999). There is no trade-off TABLE 5 Comparison of ⌬H(T )at0Kand͗T ͘ for the ⌬ ⌬ 0 m between H(T) and T S(T) in protein unfolding (Chun, unfolding of phage T4 lysozyme in which the threonine 1994, 1997b, 1999), nor is any thermodynamic molecular residue at position 157 has been replaced by seven different switch observed, that is, ⌬H(T), T⌬S(T) and ⌬Cp(T) remain residues ⌬ positive and G(T) changes from positive to negative. ͐⌬Cp(T)dT ⌬ ⌬ ͗ ͘ ⌬ ϵ ⌬ ͗ ͘ H(T0)at0K H(T0)at Tm [ H(Tm) T S(Tm)] Tm (kcal molϪ1) (kcal molϪ1) (kcal molϪ1) (K) ͗ ͘ What is the importance of Ts ? WT(T15) 15.09 Ϯ 0.35 14.93 Ϯ 0.17 146.77 Х 146.99 330 ⌬ Њ ϭ⌬ Њ ⌬ Њ Ϯ Ϯ Х Here the balance of H (TS) G (TS)min and T S (T) T157R 15.12 0.65 15.15 0.34 162.13 162.88 345 demands in the system are favorable. At this temperature, T157A 14.48 Ϯ 0.34 14.43 Ϯ 0.22 147.76 Х 147.50 330 Ϯ Ϯ Х there will be a minimum negative Gibbs free energy change, T157N 14.49 0.24 14.46 0.57 151.78 152.37 330 and the maximum work can be accomplished for biological The experimental data for differential scanning calorimetric measurements in 20 mM KH PO containing 25 mM KCl and 0.5 mM KCl and 0.1 mM processes such as transpiration, digestion, reproduction, or 2 4 ⌬ Њ ϭ dithiothreitol adjusted with HCl to pH 2.5 were evaluated with the non- locomotion, among others. When G (T) 0 for a biolog- linear model procedure of statistical analysis of the IMSL subroutine. ical system (or for that matter, any energy system), such Each data point between 0 and 350 K was evaluated with extrapolation of work is impossible. The possibility of the existence of life F-statistics (Chun, 1991; Barr et al., 1985).

Biophysical Journal 78(1) 416–429 Thermodynamic Molecular Switch in RNase SЈ 427

Њ The critical role of the temperature-dependent Geffective is the thermodynamic potential. What counts are the effective heat capacity change of reaction minimum values at chemical equilibrium obtainable from the partition function, f (Moelwyn-Hughes, 1957). The Gibbs free energy function was The Gibbs free energy function may be expressed as subsequently defined by Giauque (Giauque, 1930a,b; Giauque and Blue, Њ Ϫ 1930; Giauque and Meads, 1941; Giauque and Kemp, 1938) as (GT Њ ϭϪ␺ Њ Ϫ Њ ϭϪ␺ЊϭϪ ͐T Њ Ϫ͐T Њ T T H0)/T /T, then (GT H0) {T 0(Cp /T)dT 0(Cp dT} ⌬GЊ͑T͒ ϭ ⌬HЊ͑T ͒ ϩ ͵ ⌬CpЊdT Ϫ T͵ ͑⌬CpЊ/T͒dT when expressed as the heat capacity term. Values for Ϫ␺° for pure solids 0 are tabulated in the National Bureau of Standards’ Circular 500 (Chase et 0 0 al., 1985) and JANAF thermodynamic tables (Rossini and Wagnman, In consequence ⌬GЊ(T) displays an interesting variety of 1952). For an ideal gas or pure solid, this function would be equivalent to Њ ϭ Њ Ϫ Њ the Planck-Benzinger thermal work function, W (T) H0 G (T) (Ben- behavior patterns as the temperature changes. Most typical Њ Ϫ Њ ϭϪ␺Њ zinger, 1971). The Giauque function, GT H0 , has been sterile so processes of biological molecules or biopolymers, for ex- far in terms of its application to biological systems. In contrast, the ample, protein folding or protein-protein interactions, show equivalent (although independently derived) Planck-Benzinger thermal ⌬HЊ(T) positive (unfavorable) and a positive ⌬SЊ(T) (favor- work function has been quite fruitful. able) at low temperature, due to a positive (⌬CpЊ/T). If In 1971, T. H. Benzinger proposed a thermal work function to take into ⌬CpЊ(T) were positive, and the sign invariant at all temper- account both Boltzmann statistical energy effects and energies of quantum- ⌬ Њ mechanical bonds. While the latter are usually not altered significantly in atures, then this combination would predict that G (T) for micromolecular reactions, it was Benzinger’s conjecture that the large- an association equilibrium process would change from pos- scale and long-range changes of conformation that accompany protein itive to negative as temperature increases. Because ⌬GЊ(T) folding or assembly might generate significant energy differences because for biological systems shows a complicated behavior, of the cumulative alteration of their numerous covalent bond structures. It wherein ⌬GЊ(T) changes from positive to negative, then is probably true that the Giauque function could have been used and would have been appropriate—it simply was not. Rather, Benzinger pursued a reaching a negative (and thus favorable) minimum, before separate path, although one that can be related to the work of Giauque and finally becoming positive as temperature increases, it is other chemists. clear that a deeper thermodynamic explanation is required. Planck’s characteristic function (Planck, 1927) may be expressed as This communication demonstrates that the critical factor ␺ ϭ H/T Ϫ S. A proper substitution of the Kirchhoff equation (Moelwyn- Hughes, 1957; Lewis and Randall, 1961), ⌬HЊ(T) ϭ⌬HЊ(T ) ϩ͐T ⌬CpЊdT is the temperature-dependent ⌬CpЊ(T) (heat capacity 0 0 and ⌬SЊϭ͐T (⌬CpЊ/T)dT, into the above expression will yield change) of reaction, which is positive at low temperature but 0 ͗ ͘ switches to a negative value at TCp , well below the ambi- ⌬ Њ ⌬ Њ͑ ͒ T T G H T0 1 ent range at which ⌬CpЊ(T) ϭ 0. ϭ ϩ ͵ ⌬CpЊdT Ϫ ͫ͵ ͑⌬CpЊ/T͒dTͬ T T T ⌬ Њ͑ ͒͑ϩ͒ 3 ⌬ Њ͑ ͒͑Ϫ͒ ͗ ͘ 0 0 Cp T Cp T at TCp

This thermodynamic switch determines the behavior pat- T T terns of the Gibbs free energy change and hence a change in ⌬GЊ ϭ ⌬HЊ͑T ͒ Ϫ T͵ ͑⌬CpЊ/T͒dT Ϫ ͵ ⌬CpЊdT 0 ͫ ͬ the equilibrium constant, K , and/or spontaneity. The sub- eq 0 0 sequent, mathematically predictable changes in ⌬HЊ(T), ⌬SЊ(T), ⌬WЊ(T), and ⌬GЊ(T) give rise to classically ob- By Benzinger’s definition: ⌬WЊϭ[T ͐T (⌬CpЊ/T)dT Ϫ͐T ⌬CpЊdT] served behavior patterns in biological reactivity that may be 0 0 Ј ⌬ Њ ϭ ⌬ Њ͑ ͒ Ϫ ⌬ Њ seen in the ribonuclease S fragment complementation re- G H T0 W actions. In cases of protein unfolding such as wild-type T4 phage lysozyme in which the threonine residue at position The Planck-Benzinger thermal work function is therefore expressed as 157 has been replaced by four different amino acid residues, ⌬ Њ͑ ͒ ϭ ⌬ Њ͑ ͒ Ϫ ⌬ Њ͑ ͒ no thermodynamic molecular switch is observed. W T H T0 G T The S-peptide–S-protein fragment complementation re- The Planck-Benzinger thermal work function, ⌬WЊ(T), represents the action provides a unique means of delineating the role of strictly thermal components of any intra- or intermolecular bonding term in each amino acid substitution and studying the effects of a system, that is, energy other than the inherent difference of the 0 K substitution on the structure and folding dynamics of pro- portion of the interaction energy term at absolute zero Kelvin. teins. A detailed thermodynamic analysis such as we have described should be an essential component of any future studies involving the site-directed, mutagenic approach to APPENDIX II: MINIMUM REQUIREMENTS FOR the examination of structure-function problems in proteins. CORRECT TREATMENT OF TEMPERATURE DEPENDENCE OF Keq IN BIOLOGICAL SYSTEMS Ѩ Ѩ ϭ ⌬ Њ 2 APPENDIX I: THE GIAUQUE FUNCTION AND THE A simplistic integration of ( ln Keq/ T) ( H /RT ) with the assumption ⌬ ϭ⌬ ϩ⌬ Њ PLANCK-BENZINGER THERMAL that HT° °RefH Cp T has frequently been presented. However, WORK FUNCTION there is absolutely no independent evidence for this “one-adjustable term” assumption in biological systems, that is, that ⌬CpЊ(T) is fixed. The basic It should be noted that the Gibbs free energy for an ideal diatomic molecule equations are correct, but realistically, ⌬CpЊ(T) is an elaborate function of ϭ Њ Ϫ Њ ϭϪ in the standard state is G°effective Gtotal E0 NkT ln f/e, where temperature.

Biophysical Journal 78(1) 416–429 428 Chun

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