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Application of Physical Organic Chemistry to Engineered Mutants Of Proc. Natl. Acad. Sci. USA Vol. 90, pp. 7814-7818, August 1993 Biochemnstry Application of physical organic chemistry to engineered mutants of proteins: Hammond postulate behavior in the transition state of protein folding (protein engineering/linear free-energy relationships/barne) ANDREAS MATOUSCHEK*t AND ALAN R. FERSHT*t *Cambridge Centre for Protein Engineering, University Chemical Laboratory, Lensfield Road, Cambridge, CB2 lEW, United Kingdom; and tMedical Research Council Centre, Hills Road, Cambridge, CB2 2QH, United Kingdom Contributed by Alan R. Fersht, May 26, 1993 ABSTRACT Transition states in protein folding may be m are very informative per se. Proteins are denatured by analyzed by linear free-energy reationships (LFERs) analo- solvents such as urea and guanidinium chloride solutions gous to the Br0nsted equation for changes in reactivity with because all parts ofproteins, but especially hydrophobic side changes in structure. There is an additional source of LFERs chains, are more soluble in denaturant solutions than in in protein folding: the perturbation ofthe equilibrium and rate water. m_F and mu_F are proportional to the change in constants by denaturants. These LFERs give a measure of the exposure ofamino acids as the structure ofthe folded protein position of the transition state along the reaction coordinate. changes to that of the transition or unfolded state. The The transition state for folding/unfolding of barnase has been average fractional increase in exposure to solvent of the analyzed by both types of LFERs: changing the structure by protein in the transition state relative to that on complete protein engineering and perturbation by denaturants. The unfolding is given by m>F/mU_F (12). The ratio m*.F/mU_F is combination has allowed the direct monitoring of Hammond thus an index of the position of the transition state on the postulate behavior of the transition state on the reaction reaction coordinate. Eqs. 1 and 2 may be combined to give pathway. Movement of the transition state has been found and a(AGtF)/a(AGu_F) = mt.F/mU_F, so that the quantity mt.F/ analyzed to give further details ofthe order ofevents in protein mUF corresponds also to a Br0nsted ( value. folding. The position of the transition state on the reaction coor- dinate can thus be determined by using the slopes of unfold- Structure-activity studies are fundamental to the methods of ing kinetics and equilibrium denaturation. The sensitivity of physical organic chemistry. Some ofthe basic concepts have the rate and equilibrium constants to the concentration of been found to be applicable to the study of proteins whose denaturants provides additional probes of the position of the structures have been subtly altered by site-directed muta- transition state on the reaction pathway. We now analyze the genesis, both for the analysis of catalysis (1-6) and for transition state for the unfolding of the small ribonuclease mapping the pathway of protein unfolding and folding at the barnase, which has been subject to considerable earlier level of individual atomic interactions (7-11). In physical studies (7, 10). organic chemistry, structure-activity relationships are often analyzed by linear free-energy relationships (LFERs) such as MATERIALS AND METHODS the Br0nsted equation for changes in reactivity with changes in structure. That is, a rate constant k responds to changes in All the mutations discussed here have been described before an associated equilibrium constant K according to a log k/a (9) or will be discussed elsewhere. The proteins were ex- log K = X. An analogous equation may be applied to the pressed and purified and their free energies ofunfolding were analysis of transition states and intermediates in protein determined by urea denaturation as published (9). The rate folding where the structure of the protein is altered by constants of protein unfolding were measured as described site-directed mutagenesis. There is an additional way of (7, 10). constructing LFERs to study the rates of protein unfolding and folding: the rates and equilibria of unfolding may be RESULTS perturbed by the addition of denaturants. Both the equilib- rium and activation free energies ofunfolding have generally The rate constants of unfolding of barnase and its mutants been found to be linearly related to the concentration of were generally measured at six equally spaced urea concen- denaturant (urea or guanidinium chloride) (12, 13): trations from 6.0 to 8.5 M. Fig. 1 shows plots oflog ku against [urea] for wild-type barnase and all the Ile -) Val mutations AGU-F = AGUH20 - mu.F[denaturant] [1] in the main hydrophobic core. All plots seem perfectly linear. However, just as classical LFERs can deviate from linearity AGtF = AGH - MtF[denaturant], [2] when plotted over a very wide range of changes in activity, the relationship between log ku and [urea] for barnase devi- where AGU-F is the difference in free energy between folded ates from linearity when the rate constants are analyzed over and unfolded protein at a given denaturant concentration, a very wide range of urea concentrations. The data are fully AG*.F is the difference in free energy between the transition described by state and the folded protein at a given denaturant concen- tration, AGWH, and AGH20are the values in water, and mu_F log ku = log kiH20 + mk.[urea] - 0.014[urea]2, [3] and m.F are constants for a particular protein. The quantities so that mt-F = 2.303RT(mk,, - 0.014[urea]). We therefore The publication costs of this article were defrayed in part by page charge choose a fixed concentration of urea for the determination of payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact. Abbreviation: LFER, linear free-energy relationship. 7814 Downloaded by guest on October 2, 2021 Biochemistry: Matouschek and Fersht Proc. Natl. Acad. Sci. USA 90 (1993) 7815 1.5 protein engineering procedure. (i) In simple physical organic chemistry, one looks systematically at the effects of substit- 1.0 | uents on different parts of the reactant. The division and attribution of the effects are usually clear. In protein folding 0.5 and enzyme catalysis, the changes are distributed widely [ over the macromolecule and have to be grouped by experi- ment and analysis. (ii) The reactions in classical physical -0) 0.0 F o organic chemistry generally involve covalent bond changes 0 that are subject to quantum theory. In particular, electron -0.5 1 transfer reactions in biological systems can be analyzed by simple equations, such as the Marcus relationship (14). The -1.0 changes in proteins that we have examined involve nonco- I valent interactions which may be analyzed by classical sta- -1.51' tistical mechanics. (iii) Reaction coordinate diagrams for 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 protein folding must contain a large number ofintermediates, both sequential and in parallel, that differ only slightly in [urea] (M) energy. There is a linear dependence of mtF/mu_F on AAG>F for FIG. 1. Plots of log kI,, versus [urea] for wild-type barnase and all specific sets of mutations (Fig. 2 a and b). As the value of Ile -. Val mutants in the main hydrophobic core. AAGt_F increases (i.e., the energy difference between the m>_F. Here, the value is 7.25 M, which is the middle of the transition state and the ground state increases), the value of concentration range generally used. The slopes m.F are mtF/mUF also increases; i.e., the position of the transition found to vary significantly with mutation. state on the reaction coordinate moves away from the ground The change in free energy of activation, AAGtF, on state. This is the experimental observation of the Hammond mutation is defined by postulate (15). Hammond formulated the following postulate in order to describe the experimentally observed correlations AAGt.F = -RTln(k1/ku), [4] between changes in equilibrium and rate constants upon modification ofthe reagent: "If two states, as for example, a where ku is the first-order rate constant for the unfolding of transition state and an unstable intermediate, occur consec- a mutant and k. is that for wild-type barnase. utively during a reaction process and have nearly the same The values of m .F, mU-F, mt.F/mU_F, and AAG>F for 7.25 energy content, their interconversion will involve only a M urea are listed in Table 1. The values in water should not small reorganization of the molecular structure" (15). The be used for the following analysis because errors in the closer the two states are in energy, the more their structures experimental determination of m-F and AAGtF will be resemble each other. Mutations in the main hydrophobic core statistically correlated: errors leading to lower values ofmt-F and in the major a-helix show clear correlations ofthe energy will automatically yield lower extrapolated values of AAGtF difference between transition state and folded state with the and vice versa. At 7.25 M urea, the errors in the two position on the reaction coordinate of the two states relative parameters will not be significantly correlated. to each other. Fig. 2a shows a plot of m-F/mU_F against AAG*F for all The mutations of barnase can be separated into three mutations in the main hydrophobic core of barnase, with the groups, those in the main hydrophobic core, those in the values of AAG>F and m-F at 7.25 M. The plots show that major a-helix, and those affecting neither hydrophobic cores mt4p/mU_F is correlated with AAGt.F (correlation coefficient nor helices. Hammond-type behavior is exhibited clearly by r = 0.70, number of points n = 20) with the intercept on the mutations in the major a-helix (Fig.
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