3.1 HX measurement

A sensitive but difficult density-dependent H–D exchange measurement, developed by Linderstrøm-Lang and co-workers (Linderstrøm-Lang & Schellman, Reference Linderstrøm-Lang, Schellman, Boyer, Lardy and Myrback1959; Hvidt & Nielsen, Reference Hvidt and Nielsen1966) in their groundbreaking HX studies, was soon displaced by H–T exchange measured by gel filtration methods (Englander, Reference Englander1963), which has in turn given way to extensively used 2D NMR (Wagner & Wüthrich, Reference Wagner and Wüthrich1982; Wand & Englander, Reference Wand and Englander1996), making it easily possible to obtain residue-resolved HX rate data. More recently a proteolytic fragmentation method (Englander et al. Reference Englander, Rogero and Englander1985) together with analysis by mass spectrometry (Zhang & Smith, Reference Zhang and Smith1993; Eyles & Kaltashov, Reference Eyles and Kaltashov2004) makes it possible to obtain segment-resolved HX information for proteins that are too large for NMR and even to move toward amino-acid resolution in favorable cases (Englander et al. Reference Englander, Del Mar, Li, Englander, Kim, Stranz, Hamuro and Woods2003; Englander, Reference Englander2006).

3.2 HX chemistry

The factors that affect the rate of exchange between amide and solvent hydrogens at the primary chemical level are pH, temperature, inductive and steric effects of nearest-neighbor side-chains, and kinetic, equilibrium, and solvent isotope effects. These various factors have been accurately calibrated in small structureless amide models (Molday et al. Reference Molday, Englander and Kallen1972; Bai et al. Reference Bai, Milne, Mayne and Englander1993; Connelly et al. Reference Connelly, Bai, Jeng, Mayne and Englander1993). From these calibrations, the second-order HX rate constant that these factors produce under any given conditions, known as the intrinsic rate constant (k _int), can be computed, and the expected chemical HX rate (k _ch) can be obtained as k _int multiplied by the catalyst concentration [k _ch=k _int (cat)]. The calculation is conveniently accessible at HX2.Med.UPenn.Edu/download.html and elsewhere. Because amides have higher basicity than hydroxide ion, effective catalysts are limited to hydroxide ion itself in the normal pH range, and hydroxide to amide collision must occur hundreds of times on average before a successful proton transfer event (Englander & Kallenbach, Reference Englander and Kallenbach1983). Specific acid catalysis by hydronium ion becomes important at pH 3 and below.

The HX rates of amide hydrogens are remarkably well placed for protein studies. At pH 7 and 0°C, an average HX rate for unprotected amides is about 1 s⁻¹. In structured proteins rates can be greatly slowed and are spread over many orders of magnitude. The rate increases by a factor of 10 per pH unit and per ~22°C in temperature, which makes possible the experimental adjustment of HX rates over a range eight orders of magnitude wide between pH 4, 0°C and pH 10, 40°C. HX lifetimes between milliseconds and months can be conveniently measured. Accordingly, the entire range of information-rich protein HX behavior can be moved into the laboratory time window.

3.3 HX analysis

Protecting protein structure, almost always involving an H-bonding interaction, makes HX slower than the baseline chemical rate. Over the years many workers have considered modes by which HX catalyst might reach and remove exchangeable hydrogens. It now appears, as inferred by Linderstrøm-Lang, that hydrogens protected by H-bonded structure can exchange only when their protecting H-bond is transiently broken and they are brought into contact with external solvent, which requires some significant structural distortion or ‘opening’ reaction, as in Eq. (1). At steady state, the continuing HX rate is then given by Eq. (2), which can be reduced as shown when structure is stable (k _cl≫k _op).

(1)

(2)

When a hydrogen bond transiently separates and the hydrogen is made accessible to attack by exchange catalyst, a kinetic competition ensues between k _cl and k _ch. If reclosing is faster than exchange (k _cl>k _ch), then opening and reclosing will occur repeatedly before a successful HX event. The measured exchange rate will then be given by k _ch multiplied down by the fraction of time that the hydrogen is accessible, essentially the pre-equilibrium opening constant, K _op, as in Eq. (3). This is known as the EX2 regime (bimolecular exchange). In this case, measured k _ex together with the predictable value of k _int [k _ch=k _int (cat)] leads to the equilibrium constant for the opening reaction and its free energy. Alternatively, if k _ch>k _cl, for example at increased catalyst concentration (high pH) or decreased structural stability (e.g. mild denaturant), then exchange will occur upon each opening. Measured HX rate then rises to an upper limit equal to the structural opening rate [Eq. (4)], the so-called EX1 limit (monomolecular exchange).

(3)

(4)

These equations were first given by Kai U. Linderstrøm-Lang (Reference Linderstrøm-Lang and Neuberger1958) (Hvidt & Nielsen, Reference Hvidt and Nielsen1966; Englander & Kallenbach, Reference Englander and Kallenbach1983). The more complex non-steady state solutions required by some HX experiments were given by Hvidt and Schellman (Hvidt, Reference Hvidt1964; Krishna et al. Reference Krishna, Hoang, Lin and Englander2004a).

3.4 HX structural physics

The exchange of structurally protected hydrogens proceeds through ‘open’ HX competent states that exist only a fraction of the time [Eq. (1)]. The structural information available depends on the kind of opening that dominates exchange. We distinguish cooperative segmental unfolding reactions and more local distortional fluctuations. Cooperative unfolding reactions have a recognizable signature. They cause multiple neighboring hydrogens to exchange with very similar ΔG _ex [EX2 exchange, Eq. (3)] and k _op [EX1 exchange, Eq. (4)], and they have a sizeable dependence on destabilants that promote cooperative unfoldings (denaturant, temperature, pH, pressure). In contrast local structural fluctuations are marked by disparate HX rates for neighboring residues and near-zero sensitivity to destabilants.

3.5 Summary

Exchangable amide hydrogens provide universal probes for protein structure and for some of its dynamic and thermodynamic properties at amino-acid resolution. The chemistry of the HX process, the measurement of protein HX, and its analysis in terms of structural dynamics are well understood. In structured proteins, opening reactions that determine HX behavior range from local fluctuations that break as little as one protecting H-bond at a time, through larger partial unfolding reactions, up through whole molecule global unfolding. The measurement of HX behavior and its analysis in these terms can provide profound insight into protein structure, dynamics, design, and function as well as the protein folding process.

4.1 Foldons in kinetic folding

4.1.2 Structure of a kinetic folding intermediate

The most detailed HX pulse-labeling results have been obtained for the particularly favorable case of a Cyt c intermediate that can be made to accumulate to a very high level (85% of the population) (Krishna et al. Reference Krishna, Lin, Mayne and Walter Englander2003a). Figure 2a shows results obtained when the intensity of the labeling pulse was varied over a 300-fold range (50 ms pulse between pH 7·5 and pH 10). This range accesses both the EX2 regime at lower pH which measures structural stability [Eq. (3); labeling rises with pH], and the EX1 regime at higher pH which provides rate information [Eq. (4); labeling becomes independent of pH], although a more complex analysis is required in this non-steady-state situation (Krishna et al. Reference Krishna, Lin, Mayne and Walter Englander2003a, Reference Krishna, Hoang, Lin and Englander2004a). The results specify the structure of the trapped intermediate (Fig. 2a) and its biophysical properties (Fig. 2b).

Fig. 2.

HX pulse-labeling results for the blocked initial intermediate in Cyt c kinetic folding. (a) The degree of labeling imposed at each measurable amide during the pulse (colored curves), analyzed by 2D NMR of the refolded native protein, can be compared with the black dashed curve expected for the case of no protection, scaled to 0·85, the fraction of the population in the intermediate state at the time of the HX pulse. The horizontal offset in the EX2 region relates to the stability against labeling. The plateau at higher pH (EX1 region) indicates the limiting k _op rate. (b) Parameters of the trapped N/C bi-helical intermediate.

Major protection is found for all of the amides that are H-bonded in the N and C helices of the native protein (blue in Figs 1, 2a), indicating that the entire length of both segments is protected. Stopped-flow circular dichroism shows the formation of an equivalent amount of helix confirming that the two terminal segments exist as helices in the intermediate. Little other H-bonded structure is found. Some core hydrophobic residues of the 60s helix (Met65, Leu68) have small protection (K _op~1) suggesting burial but not helix formation. Some minimal protection is seen for His33 and Thr78 which form main chain to side-chain bends in the native protein and retain some protection even in the unfolded protein.

The site-resolved stability for both helices is maximal at the position where they dock in the native protein (Fig. 2b), indicating their native-like configuration (see also Colon et al. Reference Colon, Elove, Wakem, Sherman and Roder1996). They exhibit close to the same stability (~1·4 kcal mol⁻¹ at 0·23 m GdmCl, 10°C) and the same unfolding (~10 s⁻¹) and refolding (~100 s⁻¹) rates, confirming their cooperative single foldon nature. As might be expected, there is a fraying-like gradient in rates and stability toward the helix termini (Fig. 2b). The distribution of stability mirrors but is much greater than the value expected for isolated helices (AGADIR-predicted stability +3 to 4 kcal mol⁻¹) consistent with mutual stabilization.

The closing rate calculated from the HX data is the same as the rate measured by stopped-flow fluorescence for 2-state Cyt c folding (in absence of the later blocking barrier), indicating the on-pathway nature of the bihelical intermediate. All of the molecular population folds through this same homogeneously structured form (85% trapped at the time of the pulse with the other 15% having already moved through and reached N).

In short, the kinetically populated folding intermediate resembles in detail a partially constructed native protein. The unstructured regions of the partially folded intermediate undoubtedly represent a broad dynamic ensemble as emphasized by theoretical studies but the same extensive native-like elements are importantly present in all of the molecules. The HX pulse-labeling experiment has now been repeated for transiently blocked intermediates in many proteins. A consistent observation is that structured regions resemble structure within the native protein. The same is true for partially structured proteins more generally, for example for equilibrium molten globules (Baum et al. Reference Baum, Dobson, Evans and Hanley1989; Jeng et al. Reference Jeng, Englander, Elöve, Wand and Roder1990).

4.2 Foldons at equilibrium

4.2.1 The native state HX experiment

The HX pulse-labeling experiment is limited to the study of well populated kinetic intermediates. Most folding intermediates occur after the intrinsic initial rate-limiting step and are invisible to all kinetically based observations. A more powerful method known as native state hydrogen exchange (NHX) can make it possible to study several, perhaps all, of the intermediates that together construct a folding pathway, whether they accumulate to a high level in kinetic folding or not.

The NHX experiment depends on a fundamental concept that has received little attention before (Englander & Kallenbach, Reference Englander and Kallenbach1983). It is true, as in Anfinsen's thermodynamic hypothesis, that proteins are driven to their final native conformation because that is their lowest free-energy state. However, thermodynamic principle also requires that native proteins must continue to populate all of their higher free-energy forms, each according to its Boltzmann factor, and over time the population must cycle through all of the high-energy manifold. Thus protein molecules naturally unfold and refold even under native conditions, repeatedly revisiting the same intermediate forms that carried them down to their native state initially (Bai & Englander, Reference Bai and Englander1996; Englander et al. Reference Englander, Mayne, Bai and Sosnick1997).

Unfortunately, this behavior is normally invisible. The high-energy forms are only infinitesimally populated and the usual methodologies are swamped by signals from the overwhelmingly populated native state. The opposite is true for HX. Measured HX rates receive no contribution from hydrogens protected in the native state but are wholly determined by the transiently populated higher energy forms. Therefore the continual unfolding and refolding behavior of proteins, and parts of proteins, is in principle accessible to HX measurement under native conditions.

The equilibrium version of the NHX experiment can be understood by analogy to the common protein melting experiment. Figure 3a illustrates the standard 2-state denaturant melting curve and its analysis by the usual linear extrapolation method (Pace, Reference Pace1975). The calculated dependence of ΔG°_unf on denaturant is characterized by a large m value (m=∂(ΔG°)/(∂[Den]), which proportions to the size of the unfolding structure (Myers et al. Reference Myers, Pace and Scholtz1995). The usual extrapolation implies that proteins unfold reversibly, albeit invisibly, even at zero denaturant. The value of ΔG°_unf at low denaturant, found by long extrapolation in Fig. 3a, can be measured directly by the NHX experiment. This is true because the opening reaction in Eq. (1) that governs the slowest exchanging amide hydrogens in many proteins is often the transient global unfolding reaction itself (Huyghues-Despointes et al. Reference Huyghues-Despointes, Pace, Englander and Scholtz2001).

Fig. 3.

Native state hydrogen exchange. (a) Illustration of the 2-state denaturant melting curve and its analysis by the usual linear extrapolation method (Pace, Reference Pace1975), showing the sharp dependence of global stability on denaturant concentration even far below the visible melting transition where NHX is measured. (b, c) The analogous measurement by NHX of transient unfolding reactions of the blue and green Cyt c foldons at low denaturant concentration. These large unfolding reactions, initially hidden by local fluctuational HX pathways (m~0), are promoted and revealed by their sharp dependence on denaturant concentration. Residues exposed to HX in each unfolding reaction join the HX isotherm and thus identify the unfolding segments. Each HX isotherm, summarized in panel (d), shows the denaturant-dependent free-energy level (relative to N) for the Cyt c partially unfolded form that first exposes each foldon unit to exchange (color coding connects to Fig. 1). Line thickening shows where HX was actually measured. The overall foldon composition of each partially unfolded form was measured in stability labeling experiments (Section 5, Fig. 5). The infrared foldon was not measured at these conditions (pDr 7, 30°C).

Figure 3b shows the HX behavior of all of the amide hydrogens in the N- and C-terminal helices of Cyt c, plotted as ΔG _HX [from Eq. (3)] against denaturant concentration far below the melting transition (C _mid=2·75 m GdmCl). At low denaturant, many well protected hydrogens normally exchange by way of local fluctuations. These opening reactions are very small as shown by their near-zero m value and the fact that immediately neighboring residues can exchange with very different rates. As denaturant is increased, the large global unfolding, with large m value, is sharply promoted, just as in Fig. 3a, and soon comes to be the dominant exposure pathway. One then sees a merging of the separate local fluctuational HX curves for different amino acids into a common HX isotherm. The HX isotherm in Fig. 3b is generated by the reversible global unfolding of Cyt c under native conditions and can reveal its parameters [e.g. Eq. (3)]. Also the residue-resolved HX data identify the amino-acid amides that are exposed in this last unfolding step. They are all of the residues in the N- and C-terminal helices.

In summary, the NHX experiment is able to directly measure the global unfolding reaction as it occurs under fully native conditions. The same N/C foldon unit found by HX pulse labeling to fold first is found by NHX to unfold last. A similar strategy can reveal structural units that engage in lower free energy more probable cooperative unfolding reactions.

4.3 Limitations in foldon detection

Cooperative subglobal unfolding reactions might have been found as long ago as the original HX studies pursued by Linderstrøm-Lang and co-workers in the 1950s but they escaped detection for 40 years. A major problem has been that the exchange of many hydrogens is often dominated by local fluctuational openings (Fig. 3b, c) which hide the possible participation of these residues in larger unfoldings. The NHX strategy selectively promotes the larger unfoldings so that they come to dominate the measured exchange of the hydrogens that they expose and can then be detected, identified, and characterized.

Amides that continue to exchange preferentially by way of local fluctuations, often toward the ends of secondary structural elements, cannot be assigned to their correct foldon. The same is true for residue NMR cross-peaks that escape detection. The general tendency will be to incorrectly limit foldon extent to the most protected, most easily measured residues. A rigorous definition of the foldon construction of any protein would require a complete accounting of all of its residues. In most cases this is unlikely to be accomplished. Accordingly it seems likely that foldons entrain more complete secondary structural segments than is definitively observed. It is hard to picture how a major mid-region of well structured helices or β-strands could concertedly unfold without also entraining their more distal residues in the same unfolding.

Another limit occurs at the other extreme. If a protein is not sufficiently stable, some subglobal units may independently unfold only at a free-energy level that is higher than the U state. In this case HX of the hydrogens that could reveal foldon behavior will be dominated instead by the global unfolding reaction. The protein then appears to be more 2-state cooperative than is the case. The problem is exacerbated by the fact that subglobal unfoldings tend to occur at surprisingly high ΔG _HX values so that high global stability, perhaps 9 kcal mol⁻¹ or more, is desirable for a successful analysis (although see Korzhnev et al. Reference Korzhnev, Religa, Lundstrom, Fersht and Kay2007).

Even when the presence of large unfolding reactions can be demonstrated, the separation of different foldons may not be obvious because foldon hydrogens tend to exhibit a spread of ΔG _HX values, on the order of 1 kcal mol⁻¹. If the spread between foldons is not greater than the spread within, their discrimination will be difficult. The spread can be due to fraying mechanisms as seen definitively for the Cyt c N/C intermediate by HX pulse labeling (Fig. 2b). Further, in incompletely unfolded forms HX may be partially blocked and slower than has been calibrated for freely exposed small molecule models (Maity et al. Reference Maity, Lim, Rumbley and Englander2003), contributing an artifactual spread to the calculated ΔG _HX values.

Finally, the presence of non-native interactions in unfolded forms can confuse foldon identification. In any incompletely native form, some native interactions are absent and energy- minimizing non-native interactions may be present. This has been seen directly (see Feng et al. Reference Feng, Zhou and Bai2005a).

Attempts have been made to create structure-based algorithms that might find protein foldons by computation (Panchenko et al. Reference Panchenko, Luthey schulten and Wolynes1996; Fischer & Marqusee, Reference Fischer and Marqusee2000; Weinkam et al. Reference Weinkam, Zong and Wolynes2005; Hilser et al. Reference Hilser, Garcia-Moreno, Oas, Kapp and Whitten2006). These important efforts need to be pursued.

4.4 Foldons in many proteins

In spite of the severe limitations just noted, concerted subglobal unfolding reactions have been detected in many proteins. Native state HX experiments have found foldon units in RNase H (Chamberlain et al. Reference Chamberlain, Handel and Marqusee1996), barnase (Vu et al. Reference Vu, Feng and Bai2004), T4 lysozyme (Cellitti et al. Reference Cellitti, Bernstein and Marqusee2007; Kato et al. Reference Kato, Vu, Feng, Zhou and Bai2007), PDZ-3 domain (Feng et al. Reference Feng, Vu and Bai2005b), focal adhesion target domain (Zhou et al. Reference Zhou, Feng and Bai2006), OspA (Yan et al. Reference Yan, Kennedy and Koide2002) and Cyt b ₅₆₂ (Fuentes & Wand, Reference Fuentes and Wand1998a, Reference Fuentes and Wandb; Chu et al. Reference Chu, Pei, Takei and Bai2002; Takei et al. Reference Takei, Pei, Vu and Bai2002). HX pulse-labeling studies of kinetic folding intermediates in many proteins have similarly found specific native-like partially folded forms.

Foldons have been shown in the triosephosphate isomerase dimer by a SH reactivity method that is analogous to the NHX method (Silverman & Harbury, Reference Silverman and Harbury2002a). Kay and co-workers have found unfolding units in three small proteins (Fyn SH3, Abp1p, and FF domains) by an NMR relaxation dispersion method (Korzhnev et al. Reference Korzhnev, Salvatella, Vendruscolo, Nardo, Davidson, Dobson and Kay2004, Reference Korzhnev, Neudecker, Zarrine-Afsar, Davidson and Kay2006, Reference Korzhnev, Religa, Lundstrom, Fersht and Kay2007). The manipulation of ambient conditions and protein engineering have been able to produce molten globules (Ptitsyn, Reference Ptitsyn1995; Raschke & Marqusee, Reference Raschke and Marqusee1997) and autonomous folding units (Oas & Kim, Reference Oas and Kim1988; Dabora et al. Reference Dabora, Pelton and Marqusee1996; Feng et al. Reference Feng, Zhou and Bai2005a) where again one finds that native-like elements are preserved (Baum et al. Reference Baum, Dobson, Evans and Hanley1989; Jeng et al. Reference Jeng, Englander, Elöve, Wand and Roder1990). Wolynes and co-workers developed a theoretical analysis that found foldon units in Cyt c very similar to those found by HX methods (Pletneva et al. Reference Pletneva, Gray and Winkler2005; Weinkam et al. Reference Weinkam, Zong and Wolynes2005).

4.5 Summary

Structural elements that engage in subglobal cooperative unfolding and refolding reactions have now been demonstrated in many proteins by many methods. It appears that proteins may generally be considered to be composed of foldon units.

5.1 The stability labeling experiment

Stability labeling experiments interrogate the condition (folded vs. unfolded) of any given foldon within the various PUFs by selectively perturbing its stability, for example by a specific mutation. The effect of the mutation on the targeted foldon itself and on the other foldons is then measured by the equilibrium NHX experiment. If foldons unfold independently as in Fig. 4a, a destabilizing mutation within one, for example within the yellow foldon, will promote yellow foldon unfolding but it will have no effect on the unfolding equilibrium of the others. If unfolding occurs dependently, e.g. in a sequential unfolding manner as in Fig. 4b, then a destabilizing mutation within the yellow foldon will equally promote the unfolding of all higher lying PUFs. They contain the yellow unfolding and will be destabilized by the same mutation. The lower-lying PUFs will not sense the presence of the mutation because the altered yellow foldon remains folded when they unfold. Partial effects can be interpreted in terms of mutual (de)stabilization rather than obligatory inclusion. The various possible interaction alternatives have been formalized (Krishna et al. Reference Krishna, Maity, Rumbley and Englander2007).

5.2 Stability labeling results

Figure 5a illustrates the results of a stability labeling experiment in which the red foldon in Cyt c was selectively perturbed by reducing the heme iron. This change stabilizes the heme iron bond to its Met80-S ligand in the red loop by 3·2 kcal mol⁻¹, measured independently. NHX results show that the stability of the red loop against unfolding is increased by the same amount (Xu et al. Reference Xu, Mayne and Englander1998; Maity et al. Reference Maity, Maity and Englander2004). This is expected because the red loop unfolding breaks the Fe–S ligation. The higher-lying unfolding reactions are stabilized equally as expected for sequential unfolding but not for independent unfolding or for non-foldon models. A quantitative exception occurs for the final global blue unfolding which is stabilized by an additional 1·9 kcal mol⁻¹. This occurs because heme iron reduction imposes also a second stabilizing effect. It removes the destabilizing +1 charge on the buried oxidized heme iron. Only the last unfolding step (blue unfolding) senses this additional stabilization, evidently because it finally exposes the heme iron to solvent. (The infrared foldon was not measured in this experiment.)

Fig. 5.

Stability labeling experiments to determine partially unfolded forms composition. The modifications indicated directly alter the stability of individual foldons. The measured effect on the stability of the altered foldon (in boldface) and on the other foldons answer the question marks in Figure 4. The red and infrared foldons can unfold separately, in either order (c).

In confirmation, another stability labeling experiment studied a Glu66Ala variant (Maity et al. Reference Maity, Maity, Krishna, Mayne and Englander2005). This surface mutation does not perturb the native structure but it does remove a stabilizing salt link between the green helix and the red loop. Results show that the red loop and all higher-lying unfolding reactions, including in this case the blue unfolding, are equally destabilized by 0·8 kcal mol⁻¹. Thus the red foldon is unfolded in all of the higher-lying PUFs, as for sequential unfolding (Fig. 4b).

Another experiment (Fig. 5b) studied a destabilizing surface mutation within the yellow foldon, Glu62Gly, which removes the Glu62 to Lys60 salt link (Maity et al. Reference Maity, Maity and Englander2004; Krishna et al. Reference Krishna, Maity, Rumbley, Lin and Englander2006). The yellow foldon itself and all higher-lying unfolding reactions are destabilized equally, by about 0·9 kcal mol⁻¹, but the lower-lying red and infrared foldons are unaffected. Thus the yellow foldon is unfolded in all of the higher-lying PUFs but not in the lower ones, as for sequential unfolding (Fig. 4b).

When a destabilizing mutation, Thr47Gly, was placed in the infrared foldon, the infrared foldon itself and all but one of the higher-lying foldons were destabilized equally, by ~0·9 kcal mol⁻¹ (Fig. 5c). Again as for sequential unfolding, the infrared foldon is unfolded in most of the higher-lying PUFs. The one exception, the red foldon, was destabilized only partially, by 0·4 kcal mol⁻¹. The analogous effect occurs in the other direction. When the red foldon was selectively stabilized, the infrared loop was stabilized partially (Krishna et al. Reference Krishna, Maity, Rumbley, Lin and Englander2006). These results show that the red and infrared loops can unfold separately but they are mutually stabilizing as might be expected from their large interaction surface. When one is unfolded, this promotes but does not require unfolding of the other. Thus the states iRYGB, IrYGB, and irYGB all occur.

5.3 The identity of Cyt c PUFs

These results remove the question marks noted before and specify the foldon composition of the dominant Cyt c PUFs as follows, written in the order of increased unfolding: IRYGB(native state), (iR or Ir)YGB, irYGB, iryGB, irygB, irygb(unfolded state). All other high-energy states must also exist but they must be less populated or accessed more slowly than the HX time scale.

6.1 Evidence from stability labeling

The stability labeling experiments described previously show that the foldon composition of the dominant partially unfolded states are just the ones suggested in reaction Scheme 1. In spite of the dictum that one cannot derive a kinetic mechanism from equilibrium data (Clarke & Fersht, Reference Clarke and Fersht1996), these equilibrium-derived PUFs look remarkably like a sequence of kinetic pathway intermediates in which each PUF is produced, one from the other, by the unfolding or refolding of one additional foldon. Additional evidence supports this same reaction sequence, as follows.

6.2 Pathway order by kinetic NHX

A variant of the equilibrium NHX experiment known as kinetic NHX can determine the order of the reversible unfolding reactions as they proceed from the native state (Hoang et al. Reference Hoang, Bédard, Krishna, Lin and Englander2002). The experiment exploits EX1 HX behavior at increasing pH [Eq. (4)]. Results show that the red foldon unfolds first, followed in order by the yellow, then the green, and finally the blue foldon. Later results indicated that the infrared loop tends to unfold even before the red loop although they are able to unfold in either order, completing the foldon inventory (Krishna et al. Reference Krishna, Hoang, Lin and Englander2004a, Reference Krishna, Maity, Rumbley, Lin and Englander2006).

This is just the time sequence for unfolding expected from Scheme 1.

6.3 Red foldon unfolds first

In some cases it has been possible to directly compare HX results with data from standard kinetic folding and unfolding experiments. The global Cyt c unfolding rate measured by stopped-flow as a function of high denaturant concentration can be extrapolated to zero denaturant. The rate obtained (10 s⁻¹) is equal to the rate for red foldon unfolding measured at zero denaturant by the kinetic NHX experiment (Hoang et al. Reference Hoang, Bédard, Krishna, Lin and Englander2002). Apparently both are rate-limited by the same early unfolding barrier, consistent with Scheme 1. At zero denaturant the other foldons unfold much more slowly, whereas they are all rate-limited by an early unfolding barrier at high denaturant. This behavior is the kinetic expression of the equilibrium free-energy ladder in Fig. 3d and the structurally determined sequential unfolding/refolding process. (The infrared foldon was not separately measured in these experiments.)

6.4 Blue foldon folds first

The HX pulse-labeling experiment described before identifies the blue N/C bi-helical foldon as the first to form during whole molecule kinetic folding (Fig. 2a). In the kinetically populated intermediate only the blue foldon is formed; the others join later. In agreement the equilibrium NHX experiment identifies the blue foldon as the last to unfold (at low denaturant; Fig. 3b). The other foldons are seen to unfold earlier at lower free energy, leaving the blue foldon to mark the final step to the globally unfolded state, as expected for Scheme 1.

Further information confirms the on-pathway nature of the blue foldon. The N/C intermediate forms in 3-state folding with the same rate (ΔG ^‡), temperature dependence (ΔH ^‡), and structural (m ^‡) parameters as is seen for the rate-limiting step in 2-state folding (stopped-flow) (Sosnick et al. Reference Sosnick, Mayne and Englander1996). The barrier that determines the 2-state folding rate is obviously on-pathway, and it is the first pathway step, otherwise folding would not be 2-state. Therefore the N/C intermediate that it directly leads to in both 2-state and 3-state folding must be the first on-pathway intermediate in both cases, as in Scheme 1. Similar logic affirms the on-pathway nature of the red foldon unfolding just discussed.

6.5 Green foldon folds next

The blue N/C bi-helical intermediate accumulates in 3-state Cyt c folding because it encounters a large barrier due to the misligation of a peripheral histidine to the heme iron. Both equilibrium and kinetic NHX experiments place the folding of the green foldon next. This sequence explains why the histidine misligation barrier blocks folding after the N/C bi-helix is formed. The peripheral histidine that is responsible for the heme misligation barrier is in the green loop (Fig. 1). In the initial globally unfolded state at neutral pH, the histidine is already misligated, holding the green loop on the wrong side of the heme. When folding is initiated, the N/C bi-helix forms normally but subsequent folding is blocked because the next foldon in line is the green unit. It cannot move into place until the misligation is released in a slow time-requiring error-repair process.

6.6 Pathway branching

Further experiments have shown that the Cyt c folding/unfolding pathway is not perfectly captured by Scheme 1 as initially conjectured. Low pH experiments designed to study the exchange of hydrogens that were otherwise too fast to measure show that the large bottom Ω-loop, initially thought to be part of the yellow foldon, is a separately cooperative least stable unit, now called the infrared foldon (Krishna et al. Reference Krishna, Lin, Rumbley and Englander2003b). Stability labeling experiments performed as a function of decreasing pH or mutation show that the infrared and red foldons can unfold in either order. Either one can unfold first and the other then joins (Krishna et al. Reference Krishna, Maity, Rumbley, Lin and Englander2006). Similarly, the two green segments initially thought to represent a single foldon can unfold separately (at low pH) and their unfolding order is optional (Krishna et al. Reference Krishna, Maity, Rumbley and Englander2007). Either the green loop or the green helix can unfold first, and is then joined by the other.

These results add some minimal branching to the linear sequence as in reaction Scheme 2. The Cyt c pathway that emerges, when read in either direction, exhibits four obligate steps and two optional branch points.

Scheme 2

6.7 Summary

Detailed structural, thermodynamic, and kinetic information for Cyt c has been obtained from HX pulse labeling, kinetic and equilibrium NHX, stability labeling, stopped-flow folding and unfolding, equilibrium melting, and misligation barrier insertion experiments. All results consistently support a defined pathway that builds the final native protein by putting native-like foldon units into place in a stepwise manner. Some parallelism in the form of optional branching can occur, but in a way that is strictly limited by the cooperative foldon principle which specifies a limited number of folding units, and by the sequential stabilization principle which specifies the order of folding and unfolding events as described below.

7.1 The first pathway step

Why does the N-terminal to C-terminal bi-helical PUF form first? Basic polymer principles dictate that closure of the whole molecule loop by N-terminal to C-terminal docking is the least likely event from both kinetic and equilibrium points of view (Ozkan et al. Reference Ozkan, Wu, Chodera and Dill2007). Nevertheless N/C closure occurs as an initial step in kinetic folding, and the reverse is the final step in unfolding. Apparently the protein is designed to make the N/C bi-helix the most stable foldon unit and the first to fold. A similar result was found in HX labeling studies of apomyoglobin (Hughson et al. Reference Hughson, Wright and Baldwin1990; Jennings & Wright, Reference Jennings and Wright1993; Nishimura et al. Reference Nishimura, Dyson and Wright2006). An initial intermediate forms with the native-like N-terminal helix (helix A) and a C-terminal helical pair (helices G and H) docked against each other approximately as in the native protein.

A literature survey provoked by these results (Krishna & Englander, Reference Krishna and Englander2005) found that almost half of known proteins have their N-terminal and C-terminal elements docked together. Many appear to involve their terminal elements in a first folding step as indicated by ϕ-analysis and ψ-analysis. No folding model predicts this most common folding mode. Evidently evolutionary biology has overruled polymer physics, perhaps due to some selected advantage for early N/C closure or perhaps due to the history of protein evolutionary development which, one might speculate, may be reprised by the folding pathways of contemporary proteins.

7.2 Pathway sequence follows the native structure

Subsequent steps (Scheme 2) follow a more understandable pattern (Rumbley et al. Reference Rumbley, Hoang, Mayne and Englander2001). The pathway order of foldon formation appears to be dictated by the native pattern. Where structure already in place is able to guide the formation of only one particular foldon, that step is found. Where prior structure can stabilize either of two incoming foldons, optional branching is seen.

In native Cyt c the N/C bi-helical unit contacts only the green helix and loop (Fig. 1). If folding proceeds in the native context, the initially formed blue unit can guide and stabilize only the two green segments. In fact, both green foldon segments are seen to fold next. They can form in either order (Scheme 2), just as suggested by native Cyt c structure, but both must be in place in order to support the next pathway step which brings the two sequentially distant yellow segments together into a minimal β-sheet. The two yellow segments are appended to two ends of the green segments. In turn, the pre-formed BGYri matrix is necessary to support the final steps, formation of the least stable, mutually supportive red and infrared loops. As might be expected from the native structure, experiment suggests that they can form in either order (Scheme 2).

We refer to this systematic behavior as sequential stabilization and take it as further evidence that the pathway progressively builds the native protein one step at a time in the native context.

7.3 Templating in biochemistry

The templating behavior seen here in terms of a protein folding pathway can be understood as a unimolecular version of familiar observations in bimolecular interactions. For example, intrinsically disordered peptides and proteins are induced to form complementary structure when they encounter their natural partners (Dyson & Wright, Reference Dyson and Wright2002). Segments isolated from the interaction region of binding proteins, although unstructured in solution, adopt the appropriate docking structure when they encounter their natural target protein (Sugase et al. Reference Sugase, Dyson and Wright2007). In domain swapping, segments of one protein are induced to conform with the complementary structure of a sister protein (Schlunegger et al. Reference Schlunegger, Bennett and Eisenberg1997). Many proteins can be induced to join pre-formed amyloids by adopting closely complementary structures. Complementary nucleic acid strands are mutually stabilizing (Watson & Crick, Reference Watson and Crick1953).

Biology is rooted in binding processes that depend on the interaction of small and large molecules with complementary protein structures. The so-called sequential stabilization process simply reframes in these terms the intramolecular foldon-dependent interactions that determine the protein folding process.

7.4 Summary

The foldon principle together with the phenomenon of complementary structure stabilization accounts for the stepwise nature and the experimentally observed sequence of steps in the Cyt c folding pathway. How the first pathway step is predetermined remains to be explained (Plaxo et al. Reference Plaxo, Simons and Baker1998; Fersht & Daggett, Reference Fersht and Daggett2007). Sosnick has suggested that the initial search for the nucleating transition state may similarly be directed by the sequential stabilization principle (Krantz et al. Reference Krantz, Dothager and Sosnick2004; Sosnick et al. Reference Sosnick, Krantz, Dothager and Baxa2006).

9.1 Foldon structure

One wants to understand the structural determinants of foldon units. The well documented foldons in Cyt c closely mimic entire native-like secondary structural elements or pairs thereof. This might be expected. When regular secondary structures are stable in isolation, they are seen to unfold and refold in a cooperative way. When they are integrated into larger protein molecules, the cooperative property may be modified but it is unlikely to be lost. The concerted unfolding of a major region of well structured helices or β-strands seems likely to entrain the entire structured element and terminate only at more flexible end residues.

The cooperativity relationship captured in the Zimm–Bragg (Zimm & Bragg, Reference Zimm and Bragg1959) and Lifson–Roig (Lifson & Roig, Reference Lifson and Roig1961) formulations applies most obviously to helices. Some known foldons do encompass entire helical lengths (Bai et al. Reference Bai, Sosnick, Mayne and Englander1995b; Fuentes & Wand, Reference Fuentes and Wand1998a; Krishna et al. Reference Krishna, Lin, Mayne and Walter Englander2003a; Feng et al. Reference Feng, Zhou and Bai2005a) but others may not (Chamberlain et al. Reference Chamberlain, Handel and Marqusee1996). Moreover, entire Ω-loops act as concerted unfolding units (Hoang et al. Reference Hoang, Bédard, Krishna, Lin and Englander2002; Krishna et al. Reference Krishna, Lin, Rumbley and Englander2003b), unsurprisingly so, because they are internally packed self-contained structures (Leszczynski & Rose, Reference Leszczynski and Rose1986). β-structures tend to break up into smaller separately cooperative units (Chamberlain et al. Reference Chamberlain, Handel and Marqusee1996; Yan et al. Reference Yan, Kennedy and Koide2002, Reference Yan, Gawlak, Smith, Silver, Koide and Koide2004; Bédard et al. Reference Bédard, Mayne, Peterson, Wand and Englander2008).

The component foldon units of PUFs need not precisely mimic the native structure. In unfolded forms, some of the interactions that delimit structural elements in the native protein are absent and other non-native energy-minimizing interactions may be present. Accordingly, one often finds evidence in partially folded intermediates for non-native interactions in addition to strikingly native-like conformation (Radford et al. Reference Radford, Dobson and Evans1992; Capaldi et al. Reference Capaldi, Kleanthous and Radford2002; Krishna et al. Reference Krishna, Lin and Englander2004b; Feng et al. Reference Feng, Zhou and Bai2005a; Bollen et al. Reference Bollen, Kamphuis and van Mierlo2006; Neudecker et al. Reference Neudecker, Zarrine-Afsar, Davidson and Kay2007). Most noteworthy, Bai and colleagues solved the NMR solution structures of two apoCyt b ₅₆₂ PUFs (Feng et al. Reference Feng, Takei, Lipsitz, Tjandra and Bai2003a, Reference Feng, Takei, Lipsitz, Tjandra and Bai2004, Reference Feng, Zhou and Bai2005a). They are largely identical to the two partly unfolded forms found previously by NHX (Fuentes & Wand, Reference Fuentes and Wand1998a, Reference Fuentes and Wandb; Chu et al. Reference Chu, Pei, Takei and Bai2002; Takei et al. Reference Takei, Pei, Vu and Bai2002) but distinct non-native interactions are also present, evidently because they help to energy minimize the PUFs.

In summary, foldon units tend to mimic the cooperative secondary structural units of the native protein from which they derive, or groupings thereof, but they may also incorporate energy-minimizing non-native interactions. Non-native interactions formed during kinetic folding may or may not act to impose large rate-limiting kinetic barriers, depending on the repair-reorganization rate.

9.2 The multi-state nature of protein molecules

The discovery of PUFs modifies the conviction, ingrained in protein chemical thinking by a half century of protein melting experiments (Fig. 3a), that protein molecules are rigorously 2-state objects. A more insightful view of the multi-state nature of protein molecules is illustrated in Fig. 3d. The figure shows the free-energy level relative to the native state of each Cyt c PUF as a function of increasing denaturant concentration (Bai & Englander, Reference Bai and Englander1996).

The native and fully unfolded states are the lowest free energy most populated forms only in the melting transition region. Equilibrium unfolding, measured in this region, will tend to appear 2-state with only the native and fully unfolded states significantly populated (although see Mayne & Englander, Reference Mayne and Englander2000). Under native conditions individual PUFs may be more stable than the unfolded state, as in Fig. 3d. Here multi-state unfolding and refolding can be observed and dissected by NHX and related experiments.

We find that fully and partially unfolded proteins under folding conditions reach the native state by stepping down the ladder of intervening states. This can be directly observed by NHX methods when the intervening PUFs are at lower free energy than the U state. One can imagine that a refolding protein may well experience the same pathway progression, driven by the same structural determinants, even when intermediate PUFs are at higher free energy than U. This track, although uphill initially, provides an easy solution to the Levinthal paradox and may be pertinent to the search for transition states in apparent 2-state folding (Krantz et al. Reference Krantz, Dothager and Sosnick2004; Sosnick et al. Reference Sosnick, Krantz, Dothager and Baxa2006).

One can also imagine that a jump from native into denaturing conditions may cause the protein to descend the now inverted ladder (Fig. 3d) to the lowest free-energy unfolded state.

9.3 The folding energy landscape

Results for many proteins now indicate that a small number of distinct native-like PUFs occupy the dominant local minima in the high free-energy folding landscape under native conditions. These PUFs are thermodynamically favored due to the intrinsically cooperative nature of foldon units and their stabilizing inter-foldon interactions. When foldons are stable relative to U, partially formed cooperative foldons are at higher free energy, essentially by definition.

The cooperative nature of PUFs also determines the stepwise progressive nature of the folding process. The PUFs that are observed by HX dominate the HX measurement precisely because they are the major intermediates visited by the continual unfolding and refolding behavior of the protein. All other possible forms implied in energy landscape diagrams must also exist but it appears that they are less represented or are kinetically isolated and accessed more slowly than the HX time scale. A corollary is that these other forms cannot carry significant flux in the folding/unfolding pathway.

Specifically structured foldons and PUFs have not appeared prominently in theoretical investigations of the landscape, perhaps because the calculations have so far not captured the full importance of local cooperativity effects which depend on multi-body interactions and local geometric considerations.

9.4 Foldons and function

In respect to protein function, it is interesting that the more stable protein foldons seem to provide a supporting scaffold while less stable regions, including loops and turns, often account for functional behaviors. This distribution of responsibility is generally obvious but the biophysical and functional ramifications of this distribution have not been much studied.

In the best worked-out case of Cyt c, the least stable red and infrared foldons correlate with known physical and functional attributes. Physical correlates include the observations that the lowest lying infrared segment is the most dynamic as seen by MD simulations (Garcia & Hummer, Reference Garcia and Hummer1999), NMR relaxation (Fetrow & Baxter, Reference Fetrow and Baxter1999), and susceptibility to proteolysis (Wang & Kallenbach, Reference Wang and Kallenbach1998; Spolaore et al. Reference Spolaore, Bermejo, Zambonin and Fontana2001). Functionally, the lowest lying infrared loop unfolds as a first step in Cyt c-mediated apoptosis and necrosis, and it is seen to unfold when Cyt c binds to lipid membranes (Jemmerson et al. Reference Jemmerson, Liu, Hausauer, Lam, Mondino and Nelson1999). Decrease in stability of the infrared foldon correlates with decreased Cyt c expression (Fetrow et al. Reference Fetrow, Dreher, Wiland, Schaak and Boose1998). It is the least conserved segment in evolution, being deleted as a unit in some species (Pettigrew & Moore, Reference Pettigrew and Moore1987).

Both the equilibrium and the rate of a Cyt c structural transition have been found to be controlled by the properties of the two lowest-lying foldons. In the Cyt c akaline transition, the residue that ligands the heme iron changes by one position, from Met80 to Lys79 (and minimally also Lys73). These residues are all in the red loop foldon. The equilibrium stability of native Cyt c against the transition is quantitatively equal to the equilibrium stability of the red foldon against unfolding over a wide stability range, which can be manipulated by mutations and by denaturant addition (Maity et al. Reference Maity, Rumbley and Englander2006). When Cyt c is jumped to high pH, the transition to the alkaline form is kinetically bi-exponential (Kihara et al. Reference Kihara, Saigo, Nakatani, Hiromi, Ikeda-Saito and Iizuka1976). In the first phase, the deprotonation of an as yet unidentified buried group is rate-limited by the reversible unfolding of the infrared foldon, which allows access by OH^– ion (or buffer base). The slower phase in which the Met80 ligand is replaced by the neighboring Lys79 is ultimately rate-limited by the unfolding of the red foldon (Hoang et al. Reference Hoang, Maity, Krishna, Lin and Englander2003). These observations indicate that, rather than simply sliding over one residue, the transition waits for the unfolding of the entire red foldon, then refolds in either the old or the new position (Hoang et al. Reference Hoang, Maity, Krishna, Lin and Englander2003; Maity et al. Reference Maity, Rumbley and Englander2006).

A dysfunctionality found for many proteins, their ability to be drawn into growing amyloid fibrils, undoubtedly requires the spontaneous unfolding of parts of the protein, like the reversible foldon unfolding behavior described above. For example, the tendency of transthyretin to form amyloid is known to be controlled by the stability of the tetramer against dissociation and transient unfolding (Kelly et al. Reference Kelly, Colon, Lai, Lashuel, McCulloch, McCutchen, Miroy and Peterson1997). The next step, recruitment into an amyloid fibril, involves an encounter with the growing end of a compatible amyloid fibril by the partially unfolded protein and its adoption of complementary beta structure driven by a templating mechanism. This intermolecular step mimics the intramolecular sequential stabilization process, which guides the analogous recruitment of foldons into the growing protein during kinetic folding.

9.5 Summary

In addition to the protein folding process, the structure and behavior of foldon units and the PUFs that they construct have significance for protein behavior and properties more broadly including stability, cooperativity, dynamics, design, function, and malfunction.

10.1 Two fundamentally different views

The integrated foldon construction of proteins together with the sequential stabilization principle can be expected to produce well defined folding pathways. All of the protein molecules in a given population should fold identically, through the same set of predetermined intermediates, although with optional branching when pre-existing structure is able to template the formation of more than one foldon unit.

Theoretical and experimental results have often been interpreted very differently (Wallace & Matthews, Reference Wallace and Matthews2002). Computer simulations find many alternative pathways in which proteins are constructed one amino acid at a time in no particular order (Plotkin & Onuchic, Reference Plotkin and Onuchic2002a, Reference Plotkin and Onuchicb). Experimental results show that different population fractions can accumulate different kinetic intermediates and fold to the native state at different rates. These results have been interpreted in terms of independent unrelated pathway schemes that emulate the theoretically derived multi-track view, although with many fewer tracks.

This uncertainty concerns the most fundamental conceptualization of the folding process. Do proteins fold by the stepwise incorporation of foldon units, predetermined by native-like structure and interactions, or do different population fractions fold through unrelated intermediates in independent pathways? These clearly opposed interpretations of clearly correct experimental observations can be reconciled by the realization that refolding proteins tend to make errors in a probabilistic way. Different population fractions may experience blocking errors at different points in the pathway, and therefore populate different intermediates and fold at different rates. This behavior mimics independent unrelated pathways even though all of the molecules may use the same native-like foldons and fold through the same PUFs templated by the same native-like interactions.

We first consider whether an optional error hypothesis can account for known examples of heterogeneous folding kinetics. It can. We then consider structural information that can distinguish the two different folding models.

10.2 The independent unrelated pathways (IUP) model

Heterogeneous folding, seen by theory and experiment, is commonly taken to indicate that different population fractions fold by way of different intermediates in different pathways. Intermediates in the different tracks are not considered to be built from common native-like units. We call this view the IUP model to emphasize that intermediate structures in one track have no particular relationship to those in another.

IUP models drawn to fit heterogeneous kinetic folding results are of the form in Scheme 3, with the added possibility of cross-pathway interchanges. The reaction scheme is written to symbolize that different population fractions show different behaviors and different rates because they flow through different intermediates, or none at all, in different tracks through the energy landscape. The experimental observation of additional folding phases is explained by the ad hoc postulation of additional pathways or intermediates. An inherent assumption is that the specified intermediates (I_i) will accumulate and produce 3-state kinetic folding.

Scheme 3

10.3 The predetermined pathway – optional error (PPOE) model

In contrast, a quantity of structural information detailed before indicates that all of a protein population folds through a pathway that is predetermined by cooperative native-like foldon units and their native-like interactions. In order to explain heterogeneous folding, it is necessary to consider in addition an optional error hypothesis based on probabilistic misfolding, which leads to a PPOE model. The PPOE model assumes that all of a protein population does fold through the same productive on-pathway intermediates but that any one may be taken off the productive pathway by the addition of an optional structure-based error. For example Scheme 4 shows a simplified PPOE reaction scheme in a double T configuration (see Krishna & Englander, Reference Krishna and Englander2007 for a more general version).

Scheme 4

Misfolding errors and the barriers that they impose are probabilistic, not intrinsically coded into the pathway. Therefore they may affect only some fraction of a refolding population. Scheme 4 sets the probability of committing a corrupting error at any pathway point as the I_i to I_i^X rate constant divided by the sum of all rate constants away from I_i. If the return error-repair step is slow, the misfold will act as an inserted kinetic barrier causing the accumulation of I_i^X and slowed folding in that particular population fraction.

Suppose that an optional barrier is encountered with probability between zero and unity. When the error probability is zero, 2-state folding will be seen as often occurs for small proteins. When the probability is high at some pathway point, 3-state folding will predominate. Any other combination will lead to heterogeneous folding with different population fractions blocking at different steps, or none at all, populating different partially corrupted intermediates, and reaching N at different rates. This behavior will give the appearance of multiple independent 2-state and 3-state pathways even though all of the protein population folds through the same productive intermediates in a single predetermined pathway (Sosnick et al. Reference Sosnick, Mayne, Hiller and Englander1994; Sosnick et al. Reference Sosnick, Mayne and Englander1996; Englander et al. Reference Englander, Sosnick, Mayne, Shtilerman, Qi and Bai1998b; Krishna et al. Reference Krishna, Lin and Englander2004b; Krishna & Englander, Reference Krishna and Englander2007).

10.4 Tests of the models

Heterogeneous folding has been observed in a number of well-studied proteins including Cyt c, α-tryptophan synthase, hen egg lysozyme, and staphylococcal nuclease. The kinetic data can be successfully fit by multi-track IUP models, essentially by definition. Can the same results be explained by the PPOE model?

10.4.3 Hen egg-white lysozyme

Radford et al. (Reference Radford, Dobson and Evans1992) used HX pulse labeling to show that a populated intermediate in lysozyme folding is heterogeneous and interpreted this result in terms of multiple parallel pathways. In extensive experiments with lysozyme, Kiefhaber and co-workers discerned multiple kinetic folding and unfolding phases, and intermediate populations, and their dependence on denaturant concentration under a variety of conditions (Kiefhaber, Reference Kiefhaber1995; Kiefhaber et al. Reference Kiefhaber, Bachmann, Wildegger and Wagner1997; Wildegger & Kiefhaber, Reference Wildegger and Kiefhaber1997; Bieri et al. Reference Bieri, Wildegger, Bachmann, Wagner and Kiefhaber1999; Bieri & Kiefhaber, Reference Bieri and Kiefhaber2001). Given the IUP assumption and other constraints, the lysozyme data were thought to require at least two independent pathways, framed as a triangular model (Wildegger & Kiefhaber, Reference Wildegger and Kiefhaber1997). The observation of additional kinetic phases in the presence of elevated salt or pH was explained by additional intermediates and pathways (Bieri et al. Reference Bieri, Wildegger, Bachmann, Wagner and Kiefhaber1999; Bieri & Kiefhaber, Reference Bieri and Kiefhaber2001).

We tested the ability of the PPOE model to explain the extensive kinetic results for lysozyme (Krishna & Englander, Reference Krishna and Englander2007). Figure 6 shows an example. Kiefhaber et al. (Reference Kiefhaber, Bachmann, Wildegger and Wagner1997) measured the three kinetic phases and the time-dependent populations indicated in Fig. 6(a, b) by direct and interrupted kinetic folding and unfolding experiments (stopped-flow fluorescence). An IUP model minimally requires the two independent pathways in Fig. 6c, with eight fitting constants, each with an associated m value (in parentheses). The best global fit is shown.

Fig. 6.

Kinetic folding and unfolding results for hen egg lysozyme. Kiefhaber and co-workers measured the three kinetic phases and the time-dependent populations by standard stopped-flow fluorescence methods. The data shown are globally fit by a two-pathway IUP model [extended triangular model; panels (a)–(c)] and by a PPOE model [single T model; panels (d)–(f)]. Best-fit rate constants are shown, with m values in parentheses (boldface indicates well fixed parameters). Other datasets under other conditions with additional kinetic phases were equally well fit by both models but usually with fewer fitting constants for the PPOE model.

The minimal single-T PPOE model matches all of the qualitative restrictions inferred by the Kiefhaber group to be required by their experimental results and it fits the data quantitatively (Fig. 6d–f). The PPOE data fit is at least as good as for the IUP model previously invoked (χ² shown) and it requires fewer fitting constants (6 vs. 8, plus m values for each). Similar results were found for folding at other solution conditions with additional kinetic phases where again the PPOE model was able to fit the data with equivalent χ² and equal or fewer fitting constants (Krishna & Englander, Reference Krishna and Englander2007).

10.5 IUP or PPOE

Proteins may fold in a 2-state or a 3-state way or in a mixed heterogeneous way with 2-state and different 3-state fractions. The IUP and PPOE models are both framed to account for these complexities. Both models can provide a good fit to any kinetic folding data (Krishna & Englander, Reference Krishna and Englander2007), yet they represent fundamentally different physical mechanisms. It is essential to distinguish the correct model. The previous exercise shows that this distinction cannot be made on the basis of kinetic fitting alone.

The IUP model explains folding complexity in terms of different population fractions folding by way of wholly different intermediates and pathways, as in Scheme 3, often represented as different tracks in the energy landscape. Formal IUP reaction schemes assume that intermediates that accumulate in 3-state pathways do so simply because they are stable. In 2-state pathways written as U directly to N, the implicit assumption is that intermediates are absent or unstable.

Known information contradicts these assumptions. Stable on-pathway intermediates are not intrinsically slow. As we have seen, they can often be demonstrated and characterized even when folding is kinetically 2-state (NHX, SH reactivity analysis, relaxation dispersion). This can be expected. In order to add additional native-like structure to a native-like intermediate, only a small-scale guided search (sequential stabilization) is required. A small guided search to add additional complementary structure is likely to be much faster than the initial whole molecule unguided search necessary to find a nucleating structure that starts the productive pathway. Thus kinetic folding should be intrinsically 2-state.

Nevertheless, 3-state folding is common. On-pathway intermediates are seen to block and go forward far more slowly than they are formed (AGH in apoMb, N/C intermediate in Cyt c, A/D bi-helix plus β-strand in RNase H). In order to accumulate and cause 3-state folding, intermediates must be stable (relative to U) as assumed in IUP models, but they must also encounter a barrier that is larger than all prior barriers. In the PPOE model, it is the additional presence of an inserted error-repair barrier that distinguishes 3-state from apparent 2-state folding and not simply the presence of a stable intermediate.

In agreement, intermediates that accumulate in 3-state folding are often seen to harbor misfolding errors, including Cyt c (Elöve et al. Reference Elöve, Bhuyan and Roder1994; Sosnick et al. Reference Sosnick, Mayne, Hiller and Englander1994), apoMb (Nishimura et al. Reference Nishimura, Dyson and Wright2006), Im7 (Capaldi et al. Reference Capaldi, Kleanthous and Radford2002), and α-Trp synthase (Wu & Matthews, Reference Wu and Matthews2003). This observation provides a nececessary but not a sufficient proof for the blocking role of misfolding because non-native energy-minimizing interactions are likely to be present in any incompletely native state. In the case of Cyt c, it has been possible to compare the populated N/C bi-helical intermediate seen in 3-state folding with a kinetically invisible non-populating intermediate seen by NHX. They are identical (Figs 2, 3b) except for the known histidine to heme misligation error. In Cyt c it is the misligation error that accounts for 3-state folding. In the absence of errors folding is 2-state. The same is true for other well known errors (proline misisomerization, aggregation, etc.).

Folding errors are known to be ubiquitous, both in vitro where they obstruct laboratory and industrial protein production (Chi et al. Reference Chi, Krishnan, Randolph and Carpenter2003) and in vivo where they may result in the loss of more than 30% of synthesized polypeptides (Yewdell, Reference Yewdell2005) and account for a significant fraction of human pathologies. Well-known misfolding errors that can transiently block folding include prolyl and non-prolyl peptide bond misisomerization, transient aggregation, non-native hydrophobic clusters, disulfide shuffling, heme misligation, topological misarrangement, and non-native domain docking modes. These errors are optional, not intrinsic to the folding process. They can often be made to appear or not depending on ambient conditions. For example, proline misisomerization barriers depend on the length of time the protein is held unfolded before initiating refolding. Aggregation-dependent barriers can depend on concentration, temperature, and pH. Optional errors will variably affect different population fractions, leading to heterogeneous folding. Intermediates that populate in 3-state folding are often seen to be native-like, especially by HX pulse labeling (e.g. Fig. 2). It is unlikely that they are produced by, rather than rendered kinetically visible by, these non-specific optionally inserted barriers.

The PPOE model formalizes all of these observations in terms of productive, intrinsically fast intermediates in a stepwise pathway that is common to the entire refolding population. In heterogeneous folding it is the optional misfolding barriers that vary and not the pathway or its predetermined on-pathway intermediates.

10.6 Comparison with theoretical results

Theory-based IUP models generally visualize many independent pathways, commonly represented as multiple tracks that descend through a funnel-shaped energy landscape. As noted before, the experimental support for this view is questionable. We suspect that theory-based results do not find concerted foldons and their sequential stabilization behavior because the pairwise potential functions and model geometries commonly used do not adequately capture the fundamental cooperativity of protein structures on which foldon structures and PUF to foldon interactions are based (Chan et al. Reference Chan, Shimizu and Kaya2004, although see Weinkam et al. Reference Weinkam, Zong and Wolynes2005).

In any case, the conflict between the PPOE model and simulation results seems to be more apparent than real. The multi-track behavior commonly observed by theory focuses a microscopic view that seems more pertinent to the initial unguided whole molecule search step. Experiment is only able to detect macroscopic folding pathway behavior. At this level, detailed structural information supports a much more determinate pathway.

10.7 Summary

IUP models, motivated by kinetic rather than structural information, account for heterogeneous folding by the ad hoc postulation of multiple independent pathways. However, the properties of pathway intermediates implicit in the IUP model – their unrelatedness and their intrinsically slow folding – are contradicted by experiment. Detailed results now available for the structure of folding intermediates and the pathways that they construct show protein folding to be a much more determinate process directed at each step by the same principles and interactions that determine the final native state. The PPOE model is a formal statement of this information. It is able to quantitatively fit observed kinetic folding behavior at least as well as IUP models. It is not inconsistent with the concept of a funneled energy landscape, even though this abstraction is often drawn to represent IUP-like behavior with multiple independent folding tracks.