Hydrogen exchange kinetics of proteins in denaturants: a generalized two-process model†1

Article No. jmbi.1998.2484 available online at http://www.idealibrary.com on

J. Mol. Biol. (1999) 286, 607±616

Hydrogen Exchange Kinetics of Proteins in Denaturants: A Generalized Two-Process Model{ Hong Qian1* and Sunney I. Chan2 1

Department of Applied Mathematics, University of Washington, Seattle WA 98195 USA 2

Noyes Laboratory of Chemical Physics, 127-72, California Institute of Technology Pasadena CA 91125, USA

The recent progress in measurements on the amide hydrogen exchange (HX) in proteins under varying denaturing conditions, both at equilibrium and in transient relaxation, necessitates the development of a unifying theory which quantitatively relates the HX rates to the conformational energetics of the proteins. We present here a comprehensive kinetic model for the site-speci®c HX of proteins under varying solvent denaturing conditions based on the two-state protein folding model. The generalized two-process model considers both conformational ¯uctuations and residual protections, respectively, within the folded and unfolded states of a protein, as well as a global kinetic folding-unfolding transition between the two states. The global transition can be either rapid or slow, depending on the solvent condition for the protein. This novel model is applicable to the traditional equilibrium HX measurements in both EX2 and EX1 regimes, and also the recently introduced transient pulse-labeling HX experiments. A set of simple analytical equations is provided for quantitative interpretation of experimental data. The model emphasizes the use of full time-course of bi-exponential HX kinetics, rather than ®tting time-course data to single rate constants, to obtain quantitative information about ¯uctuating conformers within the folded and unfolded states of proteins. This HX kinetic model naturally unfolds into a simple two-state and two-stage kinetic interpretation for protein folding. It suggests that the various observed intermediates of a protein can be interpreted as dominant isomers of either the folded or the unfolded state under different solvent conditions. This simple, minimalist's view of protein folding is consistent with various recent experimental observations on folding kinetics by HX. # 1999 Academic Press

*Corresponding author

Keywords: protein folding; intermediates; local ¯uctuations; moltenglobule; pulse-labeling

Introduction Due to the highly cooperative nature of protein structures, the simplest model for protein folding in aqueous solution considers only two states: a folded state in which a polypeptide ¯uctuates among an ensemble of highly ordered structures, and an unfolded state in which the polypeptide adopts a large number of random conformations. {Dedicated to Dr Andrew Morton, who tragically passed away on July 17, 1998, for the living memory of many long discussions on hydrogen exchange kinetics and protein folding intermediates. Abbreviations used: HX, hydrogen exchange; CD, circular dichroism. Email address of the corresponding author: [email protected] 0022-2836/99/070607±10 $30.00/0

This two-state model hypothesizes that the conformational transitions within each state are fast, but the transitions between the two states are relatively slow (Creighton, 1988; Zwanzig, 1997). In the language of energy landscape, the latter is equivalent to asserting that conformers within each state are separated by relatively low energy barriers, while the one separating the two sets of states is substantial in height. In other words, the two molecular populations are well separated both structurally and energetically. Contrary to the crystallographic view of proteins, however, the highly ordered structures still have signi®cant conformational ¯exibility. Under or near the ``native'' condition, a protein ¯uctuates among a wide spectrum of conformations, ranging from small local ¯uctuations to major conformational changes, even all the way to the globally unfolded forms. The # 1999 Academic Press

608 likelihood for these events to occur is, of course, directly related to their relative free energy. The two-state model is applicable to a wide range of experimental measurements (Schellman, 1987; Qian & Chan, 1996; Qian, 1997). The meaning of two-state model is perhaps most clearly demonstrated when a protein is subjected to solvent containing increasing amounts of denaturant. The twostate model predicts that under all denaturant concentrations, there is a coexistence between an identi®able folded state and an identi®able unfolded state of the protein, with the population of the latter increasing at the expense of the former with increasing concentration of denaturant. However, the distributions of structures (conformations) within each of the two states must also change with the solvent condition, which appear as the two non-¯at baselines in the experimental measurements of equilibrium denaturation of proteins (Schellman, 1987). In aqueous solution, a protein can exchange its peptide amide protons with solvent, in principle, from both states, either through ¯uctuations within the folded state or through global unfolding, respectively. This view of protein hydrogen exchange (HX) has been known as the two-process model (Woodward & Hilton, 1980). Under the usual native conditions, the rate of returning to the folded conformation from unfolding excursions, as well as the ¯uctuation within the folded state, are fast with respect to the intrinsic rate of HX (Bai et al., 1993); hence both of these HX processes of a native protein can be described by the EX2 mechanism (Hvidt & Nielsen, 1966; Woodward et al., 1982) wherein the HX rates can be expressed directly in terms of the equilibrium energetics for the rapid global transition and the local ¯uctuations (Englander & Kallenbach, 1983). In 1994, the two-process model was modi®ed to describe the HX of proteins in the presence of mild denaturant concentrations (e.g. between 0 and 0.7 M GdnHCl, Bai et al., 1994; Qian et al., 1994). The revised model explains experimental observations and validates the EX2 mechanism for HX under these solvent conditions (Mayo & Baldwin, 1993; Bai et al., 1994). However, more recent experimental measurements undertaken in the presence of stronger denaturant (4.5 M or higher GdnHCl) indicate that the kinetics of global folding are no longer fast with respect to the intrinsic HX rate. Accordingly, the two-process model needs to be further extended to encompass the full range of HX kinetics (most notably EX1) engendered over the broader range of denaturant concentration. (Pedersen et al., 1993; Kiefhaber & Baldwin, 1995, 1996; Loh et al., 1996; Parker et al, 1998). Following Professor Baldwin and his colleagues, we will call the augmented model the generalized two-process model. As we shall show, the generalized two-process model also provides a quantitative framework for interpreting HX measurements in the transient kinetic folding experiments by the pulse-labeling technique (Udgaonkar & Baldwin, 1988; Roder et al., 1988; Matouschek et al., 1989).

Hydrogen Exchange of Proteins

According to the thermodynamic theory of protein denaturation, the unfolded state is preferentially stabilized in the presence of denaturant (Schellman, 1987). Therefore, the rate constant for global folding transition decreases with increasing denaturant concentration. Measurements on the folding kinetics of various proteins also indicate that denaturant increases the global unfolding rate constant (Beasty et al., 1986; Matouschek et al., 1989; Chen et al., 1992; Huang & Oas, 1995b). Furthermore, recent experimental evidence suggests that the ¯uctuations within the folded state also depend on the denaturant concentration (Bai et al., 1995; Chamberlain et al., 1996; Qian, 1997). Therefore, HX kinetics in a strongly denaturing solvent needs to be interpreted in terms of the generalized two-process model in order to account for the following features: (i) Denaturant changes the equilibrium distribution among the ¯uctuating conformers within the folded state. Speci®cally, both the mean structure and ¯uctuation of the folded state can change with the solvent condition. This gives rise to a different ``mean'' structure for folded state under different solvent conditions (Dill & Shortle, 1991). Note however these conformers are often still in rapid equilibria (EX2) under the strong denaturant condition though this needs not to be the case in principle. Global unfolding measurements such as circular dichroism (CD) are usually insensitive to such redistribution except a minor baseline effect (Qian et al., 1994; Sosnick et al., 1996; Qian, 1997). (ii) The non-EX2 mechanism for HX from the globally unfolded state has to be included in the model. This observation as well as (i) above are supported by the recent experiments on RNase A (Kiefhaber et al., 1995; Kiefhaber & Baldwin, 1995). (iii) There is also a change in the equilibrium distribution among the unfolded polypeptide conformations upon changing solvent condition. Kinetic experiments on T4 lysozyme and RNase A have shown that, in water, there exist transient unfolded conformations with signi®cant protection against HX (Udgaonkar & Baldwin, 1990; Lu & Dahlquist, 1992). Hence it is natural to postulate that the unfolded state includes, in addition to the expected ensemble of ¯uctuating random conformations, conformers which are molten-globule-like, with amide protons protected against HX with solvent. Note that these molten globules could even dominate the ensemble in the absence of denaturant, though the unfolded ensemble itself would just be a minor population overall at equilibrium in aqueous solution. Accordingly, such molten globules would only be detected kinetically in the early stage of refolding. Figure 1 schematically illustrates the relative energetics of folded and unfolded states under native and denaturing solvent conditions. The above three generalizations re¯ect the three major developments in the HX measurements of proteins in the past decade: the pulse-labeling refolding kinetics (Udgaonkar & Baldwin, 1988; Roder et al., 1988), the denaturant-dependent equilibrium HX (Kim & Woodward, 1993; Mayo &

609

Hydrogen Exchange of Proteins

Figure 1. Schematic diagram showing the different two-state energy functions under different solvent conditions. The left and right energy wells represent the unfolded and folded states, respectively. The top energy landscape depicts the situation for denaturing conditions while the bottom one corresponds to native solvent conditions. Thus, the mean structures of both folded and unfolded states (the minima of the wells), as well as the position of the transition state, can change with the solvent condition, as indicated by the !jj . Furthermore, the ¯uctuations within each well (the shape of the wells) can also change with solvent condition. This diagram emphasizes the continuous polymer nature of protein ¯uctuations: both the F and U states are ensembles of conformations which change with solvent conditions. For more discussion on energy landscape, see Doyle et al. (1997).

Baldwin, 1993; Bai et al., 1995), and the HX of unfolding kinetics (Kiefhaber et al., 1995; Kiefhaber & Baldwin, 1995). Many of these experiments have led to the hypothesis of some type of intermediate conformations between the idealized folded and unfolded conformations, which are de®ned under different solvent conditions. On the other hand, several recent HX kinetic experiments on protein folding have argued that the global kinetics of proteins are highly cooperative with single transitionstate (cf Jackson & Fersht, 1991; Huang & Oas, 1995a,b; Yi & Baker, 1996). The generalized twoprocess model provides a cogent and quantitative model for all of these experimental observations.

HX in Denaturant: From EX2 to EX1 The full time-course of a HX kinetics contains more information than just a single rate constant. With the increasing complexity of local and global protein ¯uctuations/transitions with mixed fast and slow processes, it is no longer adequate to con-

Figure 2. Expected ``apparent free energy'' derived from HX, de®ned as
Ghx ˆ ÿ RT ln[k1/(kx ÿ k1)], as a function of the denaturant concentration [D]. Here kop ˆ 0:001emop ‰DŠ=RT ; kx ˆ 1:0, and the global unfolding free energy
Gg ˆ ÿ RTln(kop/kcl) ˆ 8.5 ÿ 3.5[D] as shown by the continuous line. These values are taken from Loh et al. (1996) for RNase A. The numbers in the ®gure are the values for mop. With increasing denaturant concentration, the EX2 is no longer valid. After switching away from EX2, the kinetics is dominated by kop and mop. Eventually, when kop4kx, the k1/(kx ÿ k1) again becomes kop/kcl and
Ghx again agrees with
Gg.

sider only the limiting cases of EX1 and EX2. The treatment of the full kinetics for a simple openclose site was elegantly presented more than 30 years ago (Hvidt, 1964) when the pH-dependent HX of lysozyme was ®rst observed. That study led to the conception of EX1 and EX2 (Hvidt & Nielsen, 1966). In Appendix I, we have collected some essentials of the full kinetics for HX reaction (the Linderstrom-Lang scheme): kop

kx

HX incompetent „ HX competent ÿ! exchanged kcl

…1† A common feature of all the three major developments in protein HX in recent years is the use of denaturant of varying concentrations. Even though the refolding (unfolding) kinetics is observed entirely in aqueous (denaturing) solution, initially, the protein is in an equilibrium state in denaturant (water). In order to quantitatively address these recent HX measurements, we now incorporate a simple denaturant dependence into the rate constants kop and kcl (Beasty et al., 1986; Matouschek et al., 1989; Chen et al., 1992; Huang & Oas, 1995b): 0 mop ‰DŠ=RT e ; kop ˆ kop

kcl ˆ kcl0 eÿmcl ‰DŠ=RT

…2†

where both mop and mcl 5 0 and mop ‡ mcl ˆ mg is the equilibrium m-value (Qian et al., 1994). Hence, with increasing denaturant concentration, kcl decreases and the HX mechanism switches away from EX2. Figure 2 gives such an example. It illus-

610

Hydrogen Exchange of Proteins

Table 1. Limiting behaviors for HX kinetics kcl\kop 4kx 5kx

4kx

5kx

kop kx kop ‡kcl

k1 ˆ   k1 ˆ kx 1 ÿ kkopcl ;

;

k2 ˆ kop ‡ kcl

k2 ˆ kop

k1 ˆ kop, k2 ˆ kx

Limiting cases for HX Kinetics. Note that in general two phases are present in a full HX kinetics: k1 and k2 for the smaller and larger rate constants, respectively. One of the kinetic rate constants is unimolecular, while the other is bimolecular. The upper row is the traditional EX2 limit, and the lower-right is the traditional EX1 limit.

trates that under mild denaturing condition when EX2 is valid, the
Ghx ˆ ÿ RT ln[k1/(kx ÿ k1)] agrees with
Gg ˆ ÿ RT ln(kop/kcl), where k1 is the observed HX rate constant (see Appendix I for more details). However, with increasing denaturant concentration, the EX2 is no longer valid. The characteristic HX behavior beyond the EX2 regime is also depicted in Figure 2. Since kop increases with denaturant concentration, [D], ultimately kop will be greater than kx. When this happens, the observed HX rate constant approaches to that of kx (see Table 1). Hence, there are three regions in the denaturation: the EX2 region when kcl >kx, the EX1 region when both kcl and kop < kx, and ®nally the region where kcl < kx < kop. It is interesting to note that in the third region, again k1/(kx ÿ k1) ˆ kop/kcl. As shown in the Figure 2, for larger mop (>1.5), the second region disappears; while for small mop, the third region appears only at extremely high denaturant concentrations. These subtle behaviors have not been observed yet experimentally.

HX According to the Generalized Two-process Model The kinetic scheme for the generalized two-process model can be written as: F

kxf

kgu

kxu

ÿ F „ U ÿ! U  kgf

…3†

where F denotes the folded state which consists of ¯uctuating conformers N and N0 , and U denotes the unfolded state which consists of ¯uctuating conformers D and D0 : Klf

F : N „ N0;

Klu

U : D „ D0

…30 †

These ¯uctuations have rapid equilibria with local equilibrium constants Klf and Klu, respectively. We use the 0 to denote the novel states in our model. Hence our notations are that N0 and N represent the local HX competent and incompetent conformers within the folded state, respectively. Similarly, D and D0 represent the local HX competent and incompetent conformers within the unfolded state, respectively. All the states N, N0 , D, and D0 are locally de®ned with respect to a single amide proton in a protein. For example, N0 could be a

¯uctuating a-helix; D0 might have residual protections. It is important to note that the local HX competence (the Ks) are de®ned only locally, i.e. sitespeci®c, with reference to individual amide protons (Qian et al., 1994). Hence, there are different Klf and Klu for each amide. These parameters contain valuable information about local energetics within the folded and unfolded states of a protein (Qian, 1997). The HX rate constants from folded and unfolded states, therefore, are: kxf ˆ

Klf kx ; 1 ‡ Klf

kxu ˆ

kx 1 ‡ Klu

…4†

We adopt the convention of using upper case Ks for equilibrium constants and lower case ks for rate constants. The scheme in equations (3) and (30 ) is the kinetic counterpart of the four-state equilibrium model we proposed earlier (Qian & Chan, 1996). Conceptually, the two-process model emphasizes the two routes for HX of each amide protons in a protein: a local ¯uctuation within the folded state and a global unfolding. The former process is unique for each individual amide, while the latter is common for all amides and can also be observed by measurements like CD, as required by a cooperative two-state transition. If both processes are fast with respect to intrinsic HX, then the HX is described completely by EX2 and quite simple. On the other hand, if both processes were slow, then the exchange would occur by a complete EX1 mechanism with k1 ˆ kgu ‡ klo, where klo is the opening rate constant for local ¯uctuations. However, all the experimental measurements to date corroborate that the local ¯uctuations show only EX2 type of HX. Hence, the generalized two-process model assumes that conformational ¯uctuation within the folded and unfolded states are in rapid equilibrium, as shown in equation (30 ) (Loh et al., 1996). Quantitatively, the kinetics of HX based on the mechanism given in equations (3) and (30 ) are described by two exponentials with the general form (Appendix II): ‰fraction of proteins exchangedŠ ˆ ‰F Š ‡ ‰U  Š ˆ 1 ÿ A1 eÿk1 t ÿ A2 eÿk2 t ;

A1 ‡ A2 ˆ 1

…5†

The rate constants The two rate constants for this problem can be obtained (Appendix II): 1 k1;2 ˆ …kgu ‡ kgf ‡ kxf ‡ kxu † 2 q  …kgu ‡ kgf ‡ kxu ÿ kxf †2 ÿ 4kgu …kxu ÿ kxf † …6† Note that there are four ks on the right-hand-side of equation (6). Two of them, kgu and kgf, can be obtained from global unfolding kinetic measure-

611

Hydrogen Exchange of Proteins

ments, such as by stop-¯ow CD in terms of the equilibrium constant Kg ˆ kgu/kgf and the relaxation rate constant kgu ‡ kgf. The remaining rate constants kxf and kxu can thus be determined from HX kinetic measurements on k1 and k2. Hence, knowing the global unfolding kinetics, in principle one can determine the parameters for local ¯uctuation, Klf and Klu, from HX measurement through equation (4), irrespective of the HX mechanism. For most situations which include EX1 and EX2, equation (6) can be approximated by kgu …kxu ÿ kxf † kxu ‡ kxf ‡ kgu ‡ kgf

k1 ˆ kxf ‡

k2 ˆ kxu ‡ kgu ‡ kgf …7†

where k1 < kxu < k2. In the EX2 limit, kgf4kxu and kgu4kxf. We therefore have: k1 Kg …1 ‡ Klf † ‡ Klf …1 ‡ Klu †  kx …1 ‡ Kg †…1 ‡ Klf †…1 ‡ Klu † and

k2  kgf ‡ kgu

…8†

Klf …1 ‡ Klu † ‡ …1 ‡ Klf †Kg k1 …9† ˆ eÿ
Ghx =RT ˆ kx ÿ k1 1 ‡ Klu ‡ Kg Klu …1 ‡ Klf † When Klu ˆ 0, this is exactly the equation (6) of Qian et al. (1994). In the case of the mixed EX1/EX2 under the unfolding condition, kgf5kgu5kxu ˆ kx and kxf5kx, we have: Klf kx 1 ‡ Klf

and

k2  kx …10†

which is exactly the equation (5) of Loh et al. (1996). Similarly, for the case of the mixed EX1/EX2 under the refolding condition, kxf 5kgf5kxu and kgu 0, and we have: k1  kxf

and

k2  kxu

…11†

These are the equations used by Lu & Dahlquist (1992). The amplitudes In a full kinetic analysis, the kinetic amplitudes are as informative as kinetic rate constants. The corresponding amplitudes for the two kinetic phases are: A1 ˆ

k2 ÿ …fD …0† ‡ fN 0 …0††kx ; k2 ÿ k1

A2 ˆ

…fD …0† ‡ fN 0 …0††kx ÿ k1 ; k2 ÿ k1

A1 ‡ A2 ˆ 1

We now can see that the amplitude of the fast kinetic phase (A2) depends on the type of HX experiment one carries out: if one is performing a really fast kinetic measurement as in a transient unfolding, then fD(0)  fD0 (0)  fN0 (0)  0; if the measurement for the fast transient is slow, then fD(0)  fD0 (0)  0 but fN0 (0) ˆ Kl/(1 ‡ Kl ) where the folded states are equilibrated. On the other hand, if one measures equilibrium HX, then: fN 0 …0† ˆ

kgf klf  kgf ‡ kgu 1 ‡ klf

…14†

fD …0† ˆ

kgu 1  kgf ‡ kgu 1 ‡ klu

…15†

and

and hence:

k1  kgu ‡ kxf ˆ kgu ‡

is the fraction of the protein initially in the open conformation within the folded state. For the unfolding kinetics at mixed EX1/EX2 limit (Kiefhaber et al., 1995), we have:   Klf A2  fD …0† ‡ fN 0 …0† ÿ …13† 1 ‡ Klf

…12†

where fD(0) is the fraction of protein initially in the open conformation of the unfolded state, and fN0 (0)

With decreasing dead-time in the kinetic measurement, the amplitude of fast kinetic phase, the initial drop, decreases (Kiefhaber et al., 1995).

Using HX to Estimate Energetics Within the Folded State According to the two-process model, the amide with the slowest exchange rate may re¯ect the global unfolding process of a protein (Figure 3). Hence, it has been suggested that HX measurements can be used as an alternative method to obtain the free energy of global unfolding (Kim & Woodward, 1993; Bai et al., 1994). The argument, however, is based on the validity of EX2 mechanism for HX. As we have shown, when HX is in EX1, the HX rate constants no longer provide information on the equilibrium of the unfolding process. Rather, the information concerning the equilibrium is contained in the amplitudes of the kinetic phases of HX, i.e. occupancy (Udgaonkar & Baldwin, 1990). Therefore, it becomes desirable to analyze HX kinetics by the full kinetic equation without involving any a priori assumption about EX1 or EX2. For HX in a complete EX2 regime, the rate constants are directly related to free energies. According to the two-process model, the
Ghx of an individual amide proton equals
Gg if there is neither local ¯uctuation in the folded state nor residual protection in the unfolded state (Klf ˆ Klu ˆ 0). The local ¯uctuation causes
Ghx <
Gg while residual protection causes
Ghx >
Gg. Hence an observation of
Ghx being greater than
Gg is an indication for the presence of some process(es) which is no longer fast enough with respect to kx, and the conformational ¯uctu-

612

Hydrogen Exchange of Proteins

and CD. We emphasize that since state N0 (D0 ) is in rapid equilibrium with N (D), one no longer can assert whether it is on or off the unfolding (folding) pathway (Clarke & Fersht, 1996). The novel, rich information in these HX measurements, however, is about the equilibrium energetics within the folded state (Klf) and unfolded state (Klu) under various solvent conditions. Such information can be obtained when combining the HX with CD measurements. For example, useful information about the energetics of the folded state have been obtained in cytochrome c and RNase H (Bai et al., 1995; Chamberlain et al., 1996) where EX2 is still the valid HX mechanism. The present analysis provides a quantitative framework for extending their approach to HX in a non-EX2 regime; it obviates the usual restriction on the experiments. The analytical equations given above can be easily incorporated into least-square ®tting procedures for data analysis. Such a computer program has been developed. (For more information, see http:// www.amath.washington.edu/  qian/hxsim.gif.) Experimental measurements on Klf and Klu as functions of denaturant concentration and temperature will greatly enhance our ability of computing energetics of proteins (Qian, 1997).

A Two-state Two-stage Model for the Protein Folding Kinetics Figure 3. The ``apparent free energy'' derived from HX as predicted by the generalized two-process model. The global unfolding free energies are as same as in Figure 2 (the continuous lines), and mop ˆ 0.5. The numbers in the Figure are parameter values for local energetics (Klf, Klu). In (a) we show that local ¯uctuations always lower the apparent free energy
Ghx. In (b) we show that when there is a signi®cant protection in the unfolded state (Klu40), it is possible for
Ghx to be greater than
Gg (the continuous line). The initial region of each curve re¯ects the local ¯uctuations within the folded state. Each curve then merges into the global transition with slope mg (EX2). If there is a residual protection within the unfolded state, then the curve is displaced upward. Finally, each HX switches from EX2 to EX1 at high denaturant concentration with slope mop.

ation of proteins could not be considered as rapid equilibrium with respect to HX. In RNase A, this has been the case for proline-isomerization (Bai et al., 1994) and also the case at high pH. (Kiefhaber & Baldwin, 1995). One corollary derived from the present model, which assumes rapid equilibria among local conformational ¯uctuations in the folded state and residual protections in the unfolded state, is that the current HX measurements provide no kinetic information about the protein folding other than the global folding kinetics, which could be measured by other methods such as ¯uorescence

Two-state kinetics is usually understood as having only a single step. However, the protein folding and unfolding kinetic measurements all invoke the changing of solvent conditions as the initiation of the relaxation kinetics. Since both the folded and unfolded states of a protein are ensembles of conformations of a polypeptide, it is important to realize that both states themselves could have signi®cant structural changes associated with the changing solvent condition: the ``baselines'' in the traditional spectroscopic measurements (Figure 1). This is in sharp contrast to the simple kinetics of bond breaking/making reactions in traditional chemistry (Doyle et al., 1997). The very initial events after changing the solvent condition are fast (non-activated) energy downhill processes within the folded and unfolded states. If the transition state moves, then there is also a small fraction of unfolded protein directly becoming folded through a downhill process. These energy downhill processes are non-exponential and very fast, which are then followed by the thermally activated two-state transition. Therefore, protein folding kinetics involves two stages, which we refer to as the fast downhill process and the relatively slower, cooperative, activation process. The latter one is consistent with the equilibrium two-state transition and the kgf and kgu we de®ned above. The fast process is an unique feature for conformational transition of polymers, which does not have a counterpart in chemical kinetics of small molecules. This process exhibits two

613

Hydrogen Exchange of Proteins

major parallel components: the majority of the unfolded polypeptides initially in denaturant, when suddenly exposed to aqueous solvent which is considered to be a less good solvent, collapse into a molten globular-like form. A much smaller fraction, however, because of their initial conformation at the time of changing solvent, will collapse into the folded state. These collapses are the redistribution of the conformation within the unfolded and folded states due to the changing solvent since Klu and Klf are usually denaturant dependent (Bai et al., 1995; Chamberlain et al., 1996; Qian, 1997). They are fast, without signi®cant activation barrier. Scuh a process (also known as the burst phase) has been recently observed in fast kinetic studies of folding of cytochrome c (Hagen et al., 1996; Sosnick et al., 1996; and see Eaton et al., 1996 for a recent review on fast folding kinetics). Sosnick et al. also observed the correlation between the CD change in this fast process and the equilibrium baseline, as expected from the present model (also see Qian, 1997). It is interesting to note that even the uncharged homopolymer experience multiple-stage collapse due to changing solvent (Yu et al., 1992). The partition of the two parallel components in the fast process depends on the movement of the transition state (ensemble) upon the solvent change (Doyle et al, 1997). If there is a large movement of the transition state toward the unfolded state, then there could be a signi®cant fraction of the protein molecules collapse into the folded state, a scenario which has been discussed by the statistical mechanic theory of protein folding (the so called type 0 scenario, see Bryngelson et al., 1995). The two-stage kinetic model enables us to interprete the various molten globular intermediates as dominant isomers of either folded or unfolded state under different solvent conditions. Their existence is inevitably transient in kinetics. Interpreting the molten globular intermediates as the unfolded state of protein under native condition is not new (Dill & Shortle, 1991). There is a growing body of experimental evidence that shows that the unfolded states of proteins in aqueous solution are compact and have loose structures. Some of these molten globules, e.g. a-lactalbumin, have signi®cant native-like secondary structures and contacts (Peng & Kim, 1994; Peng et al., 1995). The secondary structures are more likely to be a-helices than the b-sheets (Wu et al., 1995), which is expected since the helical interactions are more local than those in the sheets. In other molten globules, e.g. staphylococcal nuclease, even a single residue mutation can affect their ``structures'', stabilities, and dynamics (Flanagan et al., 1993, Alexandrescu et al., 1994). We realize that it is a highly contentious issue whether most molten globules are intermediates on the folding pathways of proteins or simply minor equilibrium species of their folded and/or unfolded states. The above discussion though naturally derived from our analysis, is nevertheless

based on a rather biased view on this matter. With most studies in the past decade suggesting molten globules as kinetic intermediates, we feel this alternative point of view is justi®ed. Furthermore, the equilibrium point of view has the advantage of being closer to a minimalist's model which is also a natural extension of the traditional two-state hypothesis. The debate aside, however, the quantitative model presented here provides a powerful approach to experimentally obtain detailed energetics of proteins within their native states. The generalized two-process model for protein hydrogen exchange and the two-state/two-stage folding kinetics are completely in accord with each other, and should be considered as different perspectives of a same model. It is clearly a simpli®ed model, but its strength lies in its conceptual simplicity and its consistency with most current experimental observations on protein folding and unfolding kinetics from stop-¯ow, pulse-labeling, and continuous-¯ow studies (Kiefhaber et al., 1995; Sosnick et al., 1996; Hagen et al., 1996).

Acknowledgments We thank W. A. Baase, Y. Bai, D. Baker, R.L. Baldwin, D. Barrick, J. U. Bowie, H. S. Chan, K. A. Dill, D. Eisenberg, S. W. Englander, N. R. Kallenbach, S. N. Loh, S. L. Mayo, J. N. Onuchic, Z. Y. Peng, C. A. Rohl, D. Shortle, A. Y. Su, M. VaÂsquez, P. G. Wolynes, C. K. Woodward, and R. Zwanzig for many helpful and stimulating discussions on HX and protein folding kinetics in the past several years. H.Q. thanks Professor John Schellman, who ®rst worked out the material in the Appendix I more than 30 years ago (Hvidt, 1964), for introducing him to the thermodynamics and kinetics of protein folding.

Reference Alexandrescu, A. T., Abeygunawardana, C. & Shortle, D. (1994). Structure and dynamics of a denatured 131-residue fragment of staphylococcal nuclease: a heteronuclear NMR study. Biochemistry, 33, 10631072. Bai, Y., Milne, J. S., Mayne, L. & Englander, S. W. (1993). Primary structure effects on peptide group hydrogen exchange. Proteins: Struct. Funct. Genet. 17, 75-83. Bai, Y., Milne, J. S., Mayne, L. & Englander, S. W. (1994). Protein stability parameters measured by hydrogen exchange. Proteins: Struct. Funct. Genet. 20, 4-14. Bai, Y., Sosnick, T. R., Mayne, L. & Englander, S. W. (1995). Protein folding intermediates: native-state hydrogen exchange. Science, 269, 192-197. Beasty, A. M., Hurle, M. R., Manz, J. T., Stackhouse, T., Onuffer, J. J. & Matthews, C. R. (1986). Effects of the phenylalanine-22 ! leucine, glutamic acid49 ! methionine, glycine-234 ! aspartic acid, and glycine-234 ! lysine mutations on the folding and stability of the a subunit of tryptophan synthase from Escherichia coli. Biochemistry, 25, 2965-2974.

614 Bryngelson, J. D., Onuchic, J. N., Socci, N. D. & Wolynes, P. G. (1995). Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins Struct. Funct. Genet. 21, 167-195. Chamberlain, A. K., Handel, T. M. & Marqusee, S. (1996). Detection of rare partially folded molecules in equilibrium with native conformation of RNase H. Nature Struct. Biol. 3, 782-787. Chen, B. L., Baase, W. A., Nicholson, H. & Schellman, J. A. (1992). Folding kinetics of T4 lysozyme and nine mutants at 12  C. Biochemistry, 31, 1464-1476. Clarke, J. & Fersht, A. R. (1996). An evaluation of the use of hydrogen exchange at equilibrium to probe intermediates on the protein folding pathway. Folding Design, 1, 243-254. Creighton, T. E. (1988). Toward a better understanding of protein folding pathways. Proc. Natl Acad. Sci. USA, 85, 5082-5086. Dill, K. A. & Shortle, D. (1991). Denatured states of proteins. Annu. Rev. Biochem. 60, 795-825. Doyle, R., Simon, K. T., Qian, H. & Baker, D. (1997). Local interactions and the optimization of protein folding. Proteins: Struct. Funct. Genet. 29, 282-291. Eaton, W. A., Thompson, P. A., Chan, C. K., Hagen, S. J. & Hofrichter, J. (1996). Fast events in protein folding. Structure, 4, 1133-1139. Englander, S. W. & Kallenbach, N. R. (1983). Hydrogen exchange and structural dynamics of protein and nucleic acids. Quart. Rev. Biophys. 16, 521-655. Flanagan, J. M., Kataoka, M., Fujisawa, T. & Engelman, D. M. (1993). Mutations can cause large changes in the conformation of a denatured protein. Biochemistry, 32, 10359-10370. Hagen, S. J., Hofrichter, J., Szabo, A. & Eaton, W. A. (1996). Diffusion-limited contact formation in unfolded cytochrome c-estimating the maximum rate of protein-folding. Proc. Natl Acad. Sci. USA, 93, 11615-11617. Huang, G. S. & Oas, T. G. (1995a). Structure and stability of monomeric l repressor: NMR evidence for two-state transition folding. Biochemistry, 34, 38843892. Huang, G. S. & Oas, T. G. (1995b). Submillisecond folding of monomeric l repressor. Proc. Natl Acad. Sci. USA, 92, 6878-6882. Hvidt, A. (1964). A discussion of the pH dependence of the hydrogen-deuterium exchange of proteins. Compt. Rend. Trav. Lab. Carlsberg, 34, 299-317. Hvidt, A. & Nielsen, S. O. (1966). Hydrogen exchange in proteins. Advan. Protein. Chem. 21, 287-386. Jackson, S. E. & Fersht, A. R. (1991). Folding of chymotrypsin inhibitor 2. 1: evidence for a two-state transition. Biochemistry, 30, 10428-10435. Kiefhaber, T. & Baldwin, R. L. (1995). Kinetics of hydrogen bond breakage in the process of unfolding of ribonuclease A measured by pulsed hydrogen exchange. Proc. Natl Acad. Sci. USA, 92, 2657-2661. Kiefhaber, T. & Baldwin, R. L. (1996). Hydrogen exchange and the unfolding pathway of ribonuclease A. Biophys. Chem. 59, 351-356. Kiefhaber, T., Labhardt, A. M. & Baldwin, R. L. (1995). Direct NMR evidence for an intermediate preceding the rate-limiting step in the unfolding of ribonuclease A. Nature, 375, 513-515. Kim, K. S. & Woodward, C. K. (1993). Protein internal ¯exibility and global stability: effect of urea on hydrogen exchange rates of bovine pancreatic trypsin inhibitor. Biochemistry, 32, 9609-9613.

Hydrogen Exchange of Proteins Loh, S. N., Rohl, C. A., Kiefhaber, T. & Baldwin, R. L. (1996). A general two-process model describes the hydrogen exchange behavior of RNase A in unfolding conditions. Proc. Natl Acad. Sci. USA, 93, 19821987. Lu, J. & Dahlquist, F. W. (1992). Detection and characterization of an early folding intermediate of T4 lysozyme using pulsed hydrogen exchange and two-dimensional NMR. Biochemistry, 31, 4749-4756. Matouschek, A., Kellis, J. T., Serrano, L. & Fersht, A. R. (1989). Mapping the transition state and pathway of protein folding by protein engineering. Nature, 340, 122-126. Mayo, S. L. & Baldwin, R. L. (1993). Guanidinium chloride induction of partial unfolding in amide proton exchange in RNase A. Science, 262, 873-876. Parker, M. J., Dempsey, C. E., Hosszu, L. L. P., Waltho, J. P. & Clarke, A. R. (1998). Topology, sequence evolution and folding dynamics of an immunoglobulin domain. Nature Struct. Biol. 5, 194-198. Pedersen, T. G., Thomsen, N. K., Andersen, K. V., Madsen, J. C. & Poulsen, F. M. (1993). Determination of the rate constants k1 and k2 of the Linderstrom-Lang model for protein amide hydrogen exchange: a study of the individual amides in hen egg-white lysozyme. J. Mol. Biol. 230, 651-660. Peng, Z. Y. & Kim, P. S. (1994). A protein dissection study of a molten globule. Biochemistry, 33, 21362141. Peng, Z. Y., Wu, L. C. & Kim, P. S. (1995). Local structural preferences in the a-lactalbumin molten globule. Biochemistry, 34, 3248-3252. Qian, H. (1997). Thermodynamic hierarchy and local energetics of folded proteins. J. Mol. Biol. 267, 198206. Qian, H. & Chan, S. I. (1996). Interaction between a helical residue and tertiary structures: helix propensities in small peptides and in native proteins. J. Mol. Biol. 261, 279-288. Qian, H., Mayo, S. L. & Morton, A. (1994). Protein hydrogen exchange: quantitative analysis by a twoprocess model. Biochemistry, 33, 8167-8171. Roder, H., Elove, G. A. & Englander, S. W. (1988). Structural characterization of folding intermediates in cytochrome c by H-exchange labeling and proton NMR. Nature, 335, 700-704. Schellman, J. A. (1987). The thermodynamic stability of proteins. Annu. Rev. Biophys. Biophys. Chem. 16, 115137. Sosnick, T. R., Mayne, L. & Englander, S. W. (1996). Molecular collapse: the rate-limiting step in twostate cytochrome c folding. Proteins: Struct. Funct. Genet. 24, 413-426. Udgaonkar, J. B. & Baldwin, R. L. (1988). NMR evidence for an early framework intermediate on the folding pathway of ribonuclease A. Nature, 335, 694-699. Udgaonkar, J. B. & Baldwin, R. L. (1990). Early folding intermediate of ribonuclease A. Proc. Natl Acad. Sci. USA, 87, 8197-8201. Woodward, C. K. & Hilton, B. D. (1980). Hydrogen isotope exchange kinetics of single protons in bovine pancreatic trypsin inhibitor. Biophys. J. 32, 561-575. Woodward, C. K., Simon, I. & TuÈchsen, E. (1982). Hydrogen exchange and the dynamic structure of proteins. Mol. Cell. Biochem. 48, 135-160. Wu, L. C., Peng, Z. Y. & Kim, P. S. (1995). Bipartite structure of the a-lactalbumin molten globule. Nature Struct. Biol. 2, 281-285.

615

Hydrogen Exchange of Proteins Yi, Q. & Baker, D. (1996). Direct evidence for a 2-state protein unfolding transition from hydrogen-deuterium exchange, mass-spectrometry, and NMR. Protein Sci. 5, 1060-1066. Yu, J., Wang, Z. & Chu, B. (1992). Kinetic study of coilto-globule transition. Macromolecules, 25, 1618-1620. Zwanzig, R. (1997). Two-state models of protein folding kinetics. Proc. Natl Acad. Sci. USA, 94, 148-150.

Appendix I: The Full Kinetic Treatment of HX (Hvidt, 1964) The rate constants The full HX kinetics (equation (1)) usually exhibits two kinetic phases with rate constants: q kop ‡ kcl ‡ kx  …kop ‡ kcl ‡ kx †2 ÿ 4kop kx k1;2 ˆ 2 …AI1† When kopkx5(kop ‡ kcl ‡ kx)2 which corresponds to most experimental situations which include EX1 and EX2, this formula can be approximated by k1 ˆ

kop kx kx ‡ kop ‡ kcl

k2 ˆ kx ‡ kop ‡ kcl

…AI2†

where k1 < kx < k2. The only situation where this approximation fails is when kop and kx are on the same order, while they are not much less than kcl. Under the native condition, equation (AI2) is valid since kcl4kop. In fact, it can be further simpli®ed to k1 ˆ [kop/(kcl ‡ kx)]kx and k2 ˆ kcl ‡ kx irrespective of the magnitude of kx. This is neither EX1 nor EX2 scenario. If in addition we also have kcl4kx, then we have the well known EX2 limit: k1 ˆ

kop kx kcl

…AI3†

Note that kop > kx is not required for native protein HX by the EX2 mechanism. If a protein is under a very strong denaturing condition (kop4kcl) and furthermore kop4kx, then k1 ˆ kx(1 ÿ kcl/kop) and k2 ˆ kop. Note this is not the usual EX1 limit. In fact, under this condition k1/(kx ÿ k1) ˆ kop/kcl, as in EX2! If, however, kx4kop4kcl, which is the case of most denaturing conditions, k1 ˆ kop and k2 ˆ kx. This is the limiting case of EX1. Table 1 gives a list for HX rates in the various limiting cases.

The amplitudes There is additional information in the full kinetics of HX other than the single, smaller rate constant k1 (Pedersen et al., 1993). Usually the larger rate constant k2 is too fast to be observed. However, the amplitude of the fast phase shows up in

the HX kinetics as an initial drop. The magnitude of this drop provides us with further quantitative information about the protein folding/unfolding process. The amplitude of the fast kinetic phase in HX is related to the initial distribution between the open and closed states. This initial distribution re¯ects the type of experiments one does. For example, for an equilibrium measurement, the open and closed state are exactly at their equilibrium ratio. In a transient relaxation experiment, the initial distribution might be mostly in the closed state. This difference will lead to different amplitudes. The amplitudes associated with the fast (k2) and slow (k1) phases are: A2 ˆ

kx f o ÿ k1 ; k2 ÿ k1

A1 ˆ

k2 ÿ kx f o ; k2 ÿ k1

A1 ‡ A2 ˆ 1 …AI4†

where fo is the fraction of open state at the initial time of HX. The rapid equilibrium: EX2 When both kop and kcl4kx, the HX is slow. In this scenario, the chemical reaction is always in equilibrium and one should not expect to obtain any more information about the reaction except the equilibrium constant (kop/kcl). This statement is justi®ed, since in EX2 limit the k1 is on the order of kx or less, but k2 are on the order of kop ‡ kcl, and the amplitude of the fast kinetic phase is: A2 ˆ

kx f o ÿ k1 kx f o ÿ k1  1 k2 ÿ k 1 k2

…AI5†

In other words, the HX kinetics by EX2 mechanism gives only a single exponential with rate constant [kop/(kcl ‡ kop)]kx. The HX kinetics in EX1 Different from EX2, the full HX kinetic behavior in EX1 depends on the initial condition fo. It is intuitive that the fast phase has rate constant k2 ˆ kx and A2  fo. Hence the initial drop in EX1 measurements re¯ects the fraction of molecules in the open state at time zero.

Reference Hvidt, A. (1964). A discussion of the pH dependence of the hydrogen-deuterium exchange of proteins. Compt. Rend. Trav. Lab. Carlsberg, 34, 299-317. Pedersen, T. G., Thomsen, N. K., Andersen, K. V., Madsen, J. C. & Poulsen, F. M. (1993). Determination of the rate constants k1 and k2 of the Linderstrom-Lang model for protein amide hydrogen exchange: a study of the individual amides in hen egg-white lysozyme. J. Mol. Biol. 230, 651-660.

616

Hydrogen Exchange of Proteins

Appendix II: The Full Kinetic Treatment for the HX of Generalized Two-Process Model The kinetics for equations (3) and (30 ) can be written in terms of the following three differential equations: d‰FŠ ˆ ÿ…kgu ‡ kxf †‰FŠ ‡ kgf ‰UŠ dt

…AII1†

d‰UŠ ˆ kgu ‰FŠ ÿ …kgf ‡ kxu †‰UŠ dt

…AII2†

d…jF Š ‡ ‰U  Š† ˆ kxf ‰FŠ ‡ kxu ‰UŠ dt

…AII3†

The ®rst two equations can be analytically solved to yield two rate constants (eigenvalues): 1 k1;2 ˆ …kgu ‡ kgf ‡ kxf ‡ kxu † 2 q  …kgu ‡ kgf ‡ kxf ‡ kxu †2ÿ 4…kgu kxu ‡ kgf kxf ‡ kxf kxu †

Mathematically, the kinetics described by equations (AII1)-(AII3) can also be re-cast in the simplest form of HX described by equation (1) (the Linderstrom-Lang scheme) if we de®ne: kop ˆ

Klf kgf Klf …kxu ÿ kxf † kgu ‡ ‡ 1 ÿ Klf Klu 1 ‡ Klu 1 ‡ Klf

…AII6†

kcl ˆ

kgf Klu …kxf ÿ kxu † Klu kgu ‡ ‡ 1 ‡ Klu 1 ‡ Klf 1 ÿ Klf Klu

…AII7†

They are reduced to kgu and kgf if there are local ¯uctuations in neither folded nor unfolded states, i.e. Klf ˆ Klu ˆ 0 (Englander & Kallenbach, 1983). Finally, with the algebraic transformation: [C] ˆ [N0 ] ‡ [D], [O] ˆ [N] ‡ [D0 ], and [O*] ˆ [F*] ‡ [U*], the differential equations (AII1)-(AII3) become the familiar form: d‰CŠ ˆ ÿkop ‰CŠ ‡ kcl ‰OŠ dt d‰OŠ ˆ kop ‰CŠ ÿ …kcl ‡ kx †‰OŠ dt d‰O Š ˆ kx ‰OŠ dt

1 ˆ …kgu ‡ kgf ‡ kxf ‡ kxu † 2 q …AII4†  …kgu ‡ kgf ‡ kxu ÿ kxf †2 ÿ 4kgu …kxu ÿ kxf †

Substituting equations (AII6) and (AII7) into equation (AI1) also yields equation (AII4).

The fraction of protons having been exchanged at time t, be it in the folded or the unfolded state, is:

Reference





‰fraction of proteins exchangedŠ ˆ ‰F Š ‡ ‰U Š ˆ 1 ÿ A1 eÿk1 t ÿ A2 eÿk2 t ;

A1 ‡ A2 ˆ 1

…AII5†

Englander, S. W. & Kallenbach, N. R. (1983). Hydrogen exchange and structural dynamics of protein and nucleic acids. Quart. Rev. Biophys. 16, 521-655.

Edited by P. E. Wright (Received 27 July 1998; received in revised form 8 December 1998; accepted 9 December 1998)