Subdomain competition, cooperativity and topological frustration in the folding of CheY

Abstract

The folding of multidomain proteins often proceeds in a hierarchical fashion with individual domains folding independent of each other. A large single domain protein, however, can consist of multiple modules whose folding may be autonomous or interdependent in ways that are unclear. We use coarse-grained simulations to explore the folding landscape of the two-subdomain bacterial response regulator CheY. Thermodynamic and kinetic characterization shows the landscape to be highly analogous to the four-state landscape reported for another two-subdomain protein, T4 lysozyme. An on-pathway intermediate structured in the more stable, nucleating subdomain was observed as well as transient states frustrated in off-pathway contacts prematurely structured in the weaker subdomain. Local unfolding, or backtracking, was observed in the frustrated state before the native conformation could be reached. Nonproductive frustration was attributable to competition for van der Waals contacts between the two subdomains. In the accompanying paper stopped-flow kinetic measurements support an off-pathway burst-phase intermediate, seemingly consistent with our prediction of early frustration in the folding landscape of CheY. Comparison of the folding mechanisms for CheY, T4 lysozyme and interleukin-1β leads us to postulate that subdomain competition is a general feature of large single domain proteins with multiple folding modules.

Introduction

The mechanism by which a protein adopts its unique native fold remains a fundamental question in biology. Knowledge of the factors controlling how a polypeptide sequence dictates its own structure is not only necessary for efforts in structure prediction and protein design but will further our understanding of the thermodynamics governing protein stability and conformational dynamics. Failure of a protein to reach the native state can be deleterious. Partially unfolded or misfolded intermediates can lead to protein self-association and the formation of pathogenic oligomers and aggregates.¹ A protein need not always fold to a well-structured, highly ordered native state, however. It has recently been discovered that large protein segments lacking a well-structured fold can also be functional. Intrinsically unstructured proteins contain highly conserved disordered regions that can be involved in target binding and recognition.² In many disordered segments target binding can then induce a population shift to a well-structured fold. A fundamental step in understanding the conformational landscape of proteins as it relates to folding, aggregation and functional dynamics is the characterization of folding pathways and the nature of intermediates populated en route from the unfolded ensemble to the native state.

A number of experimental techniques have proven valuable for elucidating folding pathways. Phi-value analysis of mutations can determine which regions of a protein are natively structured in the folding transition state.³ Nuclear magnetic resonance (NMR) and pulse-labeling hydrogen exchange have been used to monitor the development of site-specific structure in early kinetic intermediates during folding reactions.^4–6 Rare thermodynamic intermediates have been probed using native state hydrogen exchange (NSHX), which reports on the structure of high-energy, partially unfolded conformations in equilibrium with the native state.^7,8 Recently these techniques have been increasingly applied to large single domain proteins with complex folding mechanisms.^9–13

The folding of multidomain proteins typically proceeds in a hierarchical fashion with individual domains folding independent of each other,¹⁴ which is important for evolutionary domain shuffling.¹⁵ A large single domain protein, however, can consist of multiple modules whose folding may be autonomous or interdependent in ways we are only beginning to understand.¹⁶ The 164-residue T4 lysozyme (T4L), for instance, consists of an α-helical C-terminal subdomain and a predominantly β-sheet N-terminal subdomain. NSHX has identified an on-pathway “hidden” intermediate structured in the C-terminus but unstructured in the N-terminus, the formation of which is the rate-limiting step in folding as illustrated by the cartoon in Fig. 1A.^10–13,17 Isolated as fragments the C-terminus folds in absence of its partner subdomain whereas the N-terminus does not.^11,18 The C-terminal subdomain thus serves as the folding nucleus in T4L with the N-terminus rapidly folding once it has formed.

Fig. 1.

(a) Generic reaction diagram for four-state folding in proteins with competing subdomains. In T4 lysozyme, hydrogen exchange studies have identified a thermodynamic on-pathway intermediate with fully structured C-terminus but unstructured N-terminus and an early off-pathway kinetic intermediate partially structured in both terminii.¹⁰,¹³ (b) Topology of βα-repeat protein CheY with N-terminal (yellow) and C-terminal (blue) folding subdomains. (c) Three possible classifications for a folding intermediate: obligate on-pathway intermediate, misfolded off-pathway ‘trap’, or on-pathway intermediate in which the rate of direct transfer from U to N is nonnegligible.

Interestingly, pulse-labeling hydrogen exchange identified a second intermediate prior to the rate-limiting step in T4L folding. This kinetic intermediate formed rapidly (within the temporal resolution of the mixing device) and was partially structured in both subdomains.^4,10 Since the N-terminus is unstructured in the on-pathway intermediate, the early intermediate must undergo an N-terminal unfolding event in order to proceed to the native state. Such transient formation of structure that must be undone prior to productive progression of folding to the native state constitutes off-pathway frustration, or “backtracking”, in the landscape.

Another multi-subdomain protein whose folding has been studied is 129-residue bacterial chemotactic response regulator CheY. A member of the second most common flavodoxin fold family, CheY consists of five β α-repeats arranged in a central parallel β-sheet surrounded by α-helices (Fig. 1B). Phi-value analysis has identified two folding subdomains in CheY: an N-terminal subdomain that is highly structured in the folding transition state and a C-terminal subdomain that is unstructured in the transition state.¹⁹ It has been observed that van der Waals contacts are weaker in the C-subdomain than the N-subdomain.^19,20 Helix 4 lacks a strong N-capping residue and there is a cavity lined by several alanines between this helix and the rest of the protein, which gives rise to flexibility at the α₄β₅ surface of the protein. Cavity-filling mutants have demonstrated that this flexibility is important for function;^21,22 upon phosphorylation of the loop connecting strand 3 and helix 3 the α₄β₅ surface undergoes a conformational rearrangement and binds downstream target FliM to modulate flagellar motility.^23–25 The folding mechanism that has emerged for CheY is that the formation of the stable N-terminus is rate-limiting and serves to nucleate the weaker C-terminus.

In the present work we use molecular simulation to explore the landscape of subdomain folding in CheY. Our thermodynamic and kinetic characterization shows the landscape to be highly analogous to the four-state landscape of T4L and establishes a molecular basis for the four-state folding mechanism. Namely, the four-state-like landscape is a consequence of frustration caused by the competition for van der Waals contacts between the N- and C-terminal subdomains.

Our simulations employed the coarse-grained model developed by Karanicolas and Brooks for folding simulations.²⁶ The protein is represented as a string of C_α beads that interact via a Gō-like potential in which only residue pairs that are in contact in the native state experience a pairwise attractive force. Gō models have been successful in reproducing the qualitative nature of folding transition states and intermediates for a range of proteins.^27–32 This success is a consequence of protein folding landscapes being largely determined by the topology of the native state and having evolved to be dominated by native interactions.³³ Non-native interactions, which can cause energetic frustration in the folding landscape, are generally responsible for minimal perturbations in the structure of transition states.²⁸ Gō-like landscapes ignore non-native interactions and lack energetic frustration but may still contain frustration of another variety, which arises when native interactions form in the incorrect order. This type of frustration is dictated by the specific fold geometry and has been termed topological frustration.^34,35 The authors note that frustration is a term used in physics in many different contexts; in this manuscript the term shall be reserved solely for signifying topological frustration in folding. Our present studies focus on topological frustration in the folding of CheY’s N-and C-terminal subdomains.

Results and Discussion

The sequence of events in CheY folding was mapped out by examining the dependence of the free energy on several structural properties. For such equilibrium thermodynamic calculations, multicanonical umbrella sampling was used to ensure the entire accessible landscape was sampled, including unfolded, native and high energy intermediate species. The authors note that more exact methods exist for characterizing the folding transition state ensemble;^36–40 the goal of the present work was not to rigorously determine the structure of the transition state but rather to elucidate the folding mechanism of CheY by determining the most probable relative order of structure formation events. Multicanonical equilibrium simulations have proven useful in the study of complex folding behavior when multiple reaction coordinates are necessary to describe the essential features of folding mechanisms.^28,41 To lend support to the mechanism established by our equilibrium simulations of the thermodynamic landscape, 100 independent, unbiased kinetic folding runs were also performed starting from a random coil unfolded structure under conditions promoting the native state. The relative sequence of folding events observed in the ensemble kinetic simulations was in good agreement with the most probable pathway revealed from thermodynamic landscape calculations.

N-terminal nucleation

The free energy landscape was characterized at the folding transition temperature so that both the native and unfolded basins could be clearly defined. The fraction of native contacts formed, denoted Q, is a useful progress variable for monitoring the formation of secondary and tertiary structure.^41–43 The free energy was computed as a function of the fraction of native contacts formed in the N- and C-terminal subdomains at the transition temperature (Fig. 2). The resulting Gō landscape agrees with experimental observations that the N-terminus is partially structured in the folding transition state whereas the C-terminus is not.¹⁹ The C-subdomain does not access its folded basin until the N-subdomain has folded and relies on contacts at the interface between the two subdomains for its stability, corroborating that the N-terminus serves as the folding nucleus. Additionally, the C-subdomain exhibited dynamic instability as evidenced by the large width of its native basin, visiting both structured and largely unstructured states within the native basin. C-terminal instability is not surprising given its deficiency in van der Waals contacts. Our Gō model assigned an average of 1.61 and 1.26 native contacts per residue in the N- and C-subdomains, respectively.

Fig. 2.

Thermodynamic characterization of the N-terminally nucleated folding landscape for CheY. The free energy is shown as a function of the fraction of native contacts formed within the N-terminal subdomain (Q_N-terminal) and the fraction of native contacts formed within the C-terminal subdomain (Q_C-terminal). Contours are drawn every kcal/mol; values exceeding 10 kcal/mol and regions not sampled are shown in yellow. This energy scale is used throughout the text. The free energy is computed at the folding transition temperature, here and throughout the text, such that the folded and unfolded states are equally populated.

Additional insight into the sequence of folding events can be gained by looking at the formation of three topologically equivalent β α β motifs in CheY, which are centered at helices 1, 3 and 4. The three triads have 1.33, 1.07, and 0.83 contacts per residue and fold in order of decreasing contact density: 75% of contacts were satisfied for β₁α₁β_2, β₃α₃β₄, and β₄α₄β₅ as early as Q_Total = 0.4, 0.5, and 0.6, respectively (Fig. 3). The β₄α₄β₅ region had the lowest contact density in the protein and the widest native basin, revealing that C-terminal instability originates in this functionally crucial segment that has been shown experimentally to be flexible in the inactive, unphosphorylated state.^21,22 Fig. 3 also shows that elongation of the central β-sheet proceeds N-terminal to C-terminal. Further decomposition of the energy landscape shows that strands 1, 2 and 3 come together at approximately the same time in a concerted fashion, followed later by the addition of strand 4 and then finally strand 5 (see Fig. S1 in Supplementary Data).

Fig. 3.

Sequential assembly of three topologically equivalent triad segments within CheY. The free energy is shown as a function of the fraction of native contacts formed in the entire protein and within the regions spanning strands 1 and 2 and helix 1 (a), strands 3 and 4 and helix 3 (b), and strands 4 and 5 and helix 4 (c). Significant frustration is seen for the helix 3 triad, as evidenced by the high energy barrier bisecting the upper half of the pathway from U to N at Q_Total = 0.37 (b).

Quasistable folding intermediate

Projections of the folding landscape onto the structural progress coordinate radius of gyration, R_g, reveal the presence of a quasistable intermediate. Fig. 4 shows a shallow minimum at R_g = 22 Å, Q_Total = 0.5 of depth ΔF = 0.8 ± 0.1 kcal/mol that corresponds to a structured N-terminus and unstructured C-terminus. Further analysis of the intermediate demonstrates that the interfaces between strands 3 and 4 and helices 2 and 3 are also formed (Fig. S2). The folding intermediate is thus structured in the region from strand 1 to strand 4 and shall henceforth be denoted N_heptad. Kinetic folding trajectories also confirm that the thermodynamic basin in Fig. 4A is N_heptad. To provide cross-validation between the multicanonical equilibrium simulations and ensemble kinetic simulations subsets of conformations sampled during kinetic folding simulations were extracted corresponding to four regions of interest in the thermodynamic landscape and the probability of formation was computed for various structural elements (Table 1). The third column of Table 1 confirms that the basin in question is structured from strand 1 to strand 4 in kinetic trajectories.

Fig. 4.

Characterization of a quasistable intermediate. The free energy is shown as a function of radius of gyration and the fraction of native contacts formed in the entire protein (a) and within the N- (b) and C-terminal (c) subdomains. The shallow basin at R_g = 22 Å, Q_Total = 0.5 corresponds to an intermediate with a structured N-terminus and unstructured C-terminus.

Table 1.

Probabilities for formation of structural elements within subsets of conformations sampled during kinetic folding simulations

Structural element	(Rg = 19 Å, QTotal = 0.37)a	(Rg = 21 Å, QTotal = 0.5)	(QTotal = 0.3, Qβ3α3β4 = 0.6)	(QTotal = 0.25, Qβ4α4β5 = 0.55)
α1	0.78	0.77	0.69	0.72
α2	0.61	0.80	0.60	0.58
α3	0.72	0.80	0.81	0.69
α4	0.63	0.59	0.59	0.84
α5	0.52	0.44	0.42	0.44
β1–β2 b	0.32	0.71	0.02	0.06
β1–β3	0.09	0.74	0.00	0.01
β3–β4	0.21	0.67	0.57	0.03
β4–β5	0.03	0.01	0.00	0.29
α1–rest	0.40	0.36	0.06	0.09
α2–rest	0.19	0.75	0.35	0.06
α3–rest	0.28	0.59	0.49	0.15
α4–rest	0.13	0.12	0.11	0.21
α5–rest	0.30	0.05	0.04	0.06
α1–α5	0.45	0.03	0.02	0.04
α2–α3	0.20	0.76	0.52	0.03
α3–α4	0.02	0.01	0.01	0.00
β1α1β2	0.53	0.71	0.33	0.37
β3α3β4	0.43	0.73	0.67	0.30
β4α4β5	0.27	0.26	0.25	0.51
<Rg> (Å)	19.1	21.4	26.5	28.9

^aThe average fraction of native contacts formed for various structural elements was computed for conformations in kinetic simulations with 18 Å < R_g < 20 Å and 0.29 < Q_Total < 0.42= 0.37, and similarly for the regions of conformational space specified in columns 3–5.

^bDashes are used to denote native contacts between two elements of secondary structure: e.g., between strands 1 and 2 (β₁–β₂) or between helix 1 and the rest of the protein (α₁–rest).

Incidentally, the structure of the folding transition state can be estimated from the second column of Table 1, which corresponds to the region in the vicinity of (R_g = 19 Å, Q_Total = 0.37) in Fig 4A. The data in Table 1 corroborate that structure in the transition state is concentrated in the N-terminal subdomain; this is in qualitative agreement with experimental phi-values for CheY. If we compute the average phi-values reported by Lopez-Hernandez et al. for each element of secondary structure in CheY we have <φ_β1> = 0.61, <φ_β2> strand 2 = 0.82, <φ_β3> strand 3 = 0.35, <φ_β4> strand 4 = 0.03, <φ_β5> strand 5 = –0.03, <φ_α1> helix 1 = –0.11, <φ_α2> helix 2 = 0.26, <φ_α3> helix 3 = –0.05, <φ_α4> helix 4 = –0.10 and <φ_α5> = 0.09.¹⁹ Hence it is evident that the transition state is partially structured in strands 1, 2 and 3 and helix 2 (the N-terminal subdomain) and unstructured in the C-terminal subdomain.

It is possible for trajectories to cross from U directly to N without getting stuck, even if only transiently, in the quasistable basin at R_g = 22 Å. Kinetic folding simulations corroborate that it is not necessary to populate a persistent N_heptad intermediate in passing from U to N (Fig. 5). Of the 100 independent kinetic runs performed, roughly half the trajectories passed directly form U to N and half proceeded via an N_heptad intermediate that persisted long enough to be observable. N_heptad can thus be regarded as a non-obligate, on-pathway intermediate.

Fig. 5.

Kinetic characterization of a non-obligate intermediate. The fraction of native contacts formed in the N- (red) and C-termini (green) is shown for two representative folding trajectories (a and b). Kinetic folding trajectories were equally likely to proceed through a long-lived intermediate (b) or to fold directly from U to N (a). The kinetic intermediate is N_heptad, as confirmed by the trajectory’s time courses for contacts formed between strands 3 and 4 (blue), helices 2 and 3 (pink), and helix 5 and the rest of the protein (cyan). For clarity, kinetic traces are shown as the moving average of 50 successive snapshots.

To determine the minimal folding fragment of CheY, unbiased single simulation folding runs were performed on seven N-terminal fragments of increasing length: β₁α₁β₂, β₁α₁β₂α₂, … , (βα)₄β₅; which we denote N₃, N₄, … , N₉. The simulations were ten times longer than the average time required for the full-length protein to fold, yet only fragments N_7, N₈ and N₉ folded to a stable structure. This result is consistent with in vitro and in silico fragment studies on other proteins such as barnase and chymotrypsin inhibitor 2 that underscore the highly cooperative nature of folding.^44–46 Also of note is that fragments N₈ and N₉ folded to a stable N_heptad structure but their respective C-terminal α₄ and α₄β₅ regions were disordered. N_heptad is therefore analogous to the nearly self-sufficient C-terminal subdomain of T4L.^11,18 C-terminal stability in T4L is not surprising given its N- and C-terminal subdomains have 1.3 and 1.9 native contacts per residue, respectively (as assigned by our Gō model to 2LZM.pdb). By comparison, CheY’s N_heptad and β₄α₄β₅α₅ regions have 1.7 and 1.1 native contacts per residue, respectively. For both proteins, the more stable subdomain serves as the nucleus around which the weaker terminus folds.

In the accompanying paper⁴⁷ circular dichroism, intrinsic fluorescence and NMR spectroscopy were used to perform a global analysis of the overall folding mechanism for CheY. Inclusion of an off-pathway intermediate was needed to best explain the kinetic data. Testing an additional on-pathway intermediate was not possible with the model as it would lead to overparameterization of the system; thus it is unclear whether N_heptad should be truly regarded as an intermediate. In light of the marginal stability of the on-pathway N_heptad intermediate we have observed it could indeed alternatively be considered as part of a broad transition state ensemble.

In the case of CheY structural homolog apoflavodoxin, it has been remarked by Sancho and coworkers that the on-pathway folding intermediate is “useless but probably harmless.”⁴⁸ Variants of apoflavodoxin have been observed to fit either the four-state linear mechanism of Fig. 1A or a three-state triangular mechanism (Fig. 1C), underscoring the precarious nature of intermediates in the flavodoxin fold family.^48,49 The rate of transfer from I^on to N in the triangular mechanism of Anabaena apoflavodoxin was found to be sufficiently slow that I^on could essentially be regarded as an off-pathway intermediate. Incidentally, our Gō-like equilibrium landscape for CheY appears two-state when folding is monitored in one dimension along a single progress coordinate. No discernable intermediate is evident when the free energy is expressed as a one-dimensional function of the fraction of total native contacts formed nor from the temperature dependence of the heat capacity (Fig. S3). A growing line of evidence suggests that even in small proteins with apparent two-state folding, intermediates can be found once more precise experimental techniques are employed.^50,51 Our observation of a triangular mechanism with an on-pathway, metastable intermediate lying in close proximity to the direct path from U to N offers one scenario in which an intermediate can be found in apparent two-state folding.

Topological frustration

Frustration in the form of structurally localized off-pathway contacts is evident in the early stages of β₃α₃β₄ folding, with the triad forming immediately from U but then backtracking while the N-terminal subdomain folds before proceeding on to the native state (Fig. 3B). Further decomposition of the landscape shows that backtracking during the formation of the N-terminal subdomain also occurs at the interface between helices 2 and 3 (Fig. 6B). Roughly one fourth of the kinetic simulations exhibited early frustration at the subdomain interface involving strands 3 and 4 and helices 2 and 3 (Fig. 7).

Fig. 6.

Frustration involving the C-terminus. The free energy is shown as a function of the fraction of native contacts formed in the N-terminus and between strands 3 and 4 (a), helices 2 and 3 (b), strands 4 and 5 (c), and helices 3 and 4 (d). N-terminal folding is seen to accompany an initial unfolding of contacts involving the C-terminus, as evidenced by the high energy barrier bisecting the path to N at Q_N-terminal = 0.4.

Fig. 7.

Example of a frustrated kinetic trajectory. The fraction of native contacts formed in the N- (red) and C-termini (green) and their interface is shown for a representative folding trajectory exhibiting frustration. The frustration is attributable to interfacial contacts not involving helix 5, as confirmed by the trajectory’s time courses for contacts formed between strands 3 and 4 (blue), helices 2 and 3 (pink), and helix 5 and the rest of the protein (cyan). On average, one out of every four folding simulations exhibited such frustration.

A small degree of frustration is also present within the C-terminal subdomain. Strands 4 and 5 and helices 3 and 4 transiently come together prior to N-terminal folding (compare Figs. 3C, 6C and 6D), but these species were not observable in the kinetic simulations. Fig. 8 shows that only interfacial frustration had a discernable influence on the overall ensemble-averaged kinetic time course, which we attribute to the greater density of contacts at the interface than within the C-subdomain. The negative slopes in the time courses at Q_Total = 0.4 indicate local unfolding of interfacial contacts while N-terminal folding is still in progress. Note that the small negative slopes at Q_Total = 0.6 correspond to a slight loosening of the structure prior to final maturation and are not to be confused with the more dominant early frustration. Subtle loosening of structure is often observed late in the folding of α-helices during the maturation of tertiary structure in our Gō model and has also been reported elsewhere.²⁷

Fig. 8.

Influence of frustration on kinetics. The fraction of native contacts formed at each time point was computed for 100 independent folding simulations and ensemble-averaged. The mean fraction of contacts formed is shown as a function of the fraction of native contacts formed in the entire protein for contacts between strands 3 and 4 (red), helices 2 and 3 (green), strands 4 and 5 (blue), and helices 3 and 4 (pink). The large negative slopes at Q_Total = 0.4 indicate local unfolding, or backtracking, of interfacial contacts not involving helix 5.

The cause of early frustration becomes more apparent in Fig. 9. An anticorrelation is initially observed between subdomain folding and interface formation. The initial burst in N-terminal folding at Q_Total = 0.4 coincides with backtracking of interfacial contacts. The N-subdomain, with its greater density of native contacts, is outcompeting the α₂β₃α₃β₄ region for contacts and causing its local unfolding. Similarly, the main phase of C-terminal folding at Q_Total = 0.6 is accompanied by a slight loosening of interfacial as well as N-terminal contacts prior to their final maturation. Hence, it is evident that topological frustration is the consequence of competition for N-terminal, C-terminal and interfacial native contacts.

Fig. 9.

Competition for interactions in kinetic simulations. The mean fraction of contacts formed is shown as a function of the fraction of native contacts formed in the entire protein for contacts in the N- (red) and C-termini (green) and their interface excepting helix 5 (blue). Note that the largest burst of N-terminal folding coincides with a decrease in interfacial contacts at Q_Total = 0.4; additionally, the main phase of C-terminal contact formation at Q_Total = 0.6 is accompanied by a small loss of N-terminal and interfacial contacts prior to their final maturation.

The reader may desire a better physical explanation for C-terminal frustration. The anticorrelation between subdomain and interfacial folding seen in Fig. 9 suggests that the act of contact formation in the N-subdomain exerts a kind of pulling force on the α₂β₃α₃β₄ interface, dislodging interfacial contacts in favor of the stronger N-terminal contacts. The inability of interfacial/C-terminal contacts to form at Q_N-terminal = 0.4 (Fig. 6) suggests that their formation is sterically precluded by the transition state structural ensemble for N-terminal folding, which is essentially an expanded version of the native N-subdomain (Q_N-terminal = 0.4, R_g = 18.8 Å). Loosening of preformed structure must therefore occur in order to access the folding transition state.

Topological frustration has recently been observed in interleukin-1β, a slow folder with low contact order.³⁴ Interleukin-1β consists of three four-stranded β-trefoils, denoted N-terminal, central and C-terminal, that have 0.70, 0.89 and 0.73 native contacts per residue, respectively (as assigned by our Gō model to 6I1B.pdb). Gō-like simulations by Onuchic and colleagues show the central trefoil, with the most contacts, folds first and nucleates the N- and C-termini. Analogous to our results for CheY, backtracking was observed in the C-terminal trefoil during the main folding phase of the central trefoil. During the final stages of folding, a slight loosening was also observed in central contacts during the folding of the N- and C-termini, akin to what we have observed in CheY at Q_Total = 0.6.

Two previous studies have reported backtracking in helices 4 and 5 of CheY. A Gō model study performed by Clementi et al. characterized an on-pathway intermediate and an earlier misfolded intermediate by generating contact probability maps for their corresponding structural ensembles.²⁷ This study employed a simple Gō model in which all native contacts are assigned equal interaction strengths. It should be noted that in the present work the weighting of contact strengths in our flavored Gō model was rather uniform throughout CheY so our results can readily be compared to this earlier study. One notable difference between the two models, however, is that we do not employ a dihedral potential to bias torsional degrees of freedom to the native state. Clementi et al. observed an on-pathway intermediate unstructured in helices 4 and 5 but structured in helices 1, 2 and 3, which is consistent with our observation of N_heptad. Additionally, they observed an earlier misfolded intermediate that was structured in all five helices. Earlier experimental work by Lopez-Hernandez et al. demonstrated that helix propensity-enhancing mutants in CheY lead to a decrease in the rate of folding and also suggested that helices 3, 4 and 5 undergo a transition from structured to unstructured during folding.⁵²

The structure of the folding transition state observed in the present work can be estimated from the second column of Table 1. If we compare the transition state to N_heptad (third column of Table 1), we indeed see backtracking in helices 4 and 5. Helices 4 and 5 have 0.63 and 0.52 probability of forming in the transition state, which is then reduced to 0.59 and 0.44, respectively, in the N_heptad intermediate. Kinetic backtracking in helices 4 and 5 is better illustrated when the mean fraction of contacts formed for all five helices is shown as a function of native contacts formed in the entire protein (Fig. S4). As hinted above, this subtle loosening of secondary structure late in folding is likely required for the maturation of tertiary structure and is not to be confused with the more dominant early frustration we have observed at the interface between the N- and C-terminal subdomains that is the focus of the present work. Experimental phi-value analysis using the method recently proposed by Weikl and Dill⁵³ of decomposing helical phi-values into secondary and tertiary structure components could potentially shed additional light on the role of intrahelical versus interhelical frustration in CheY.

In the accompanying paper⁴⁷ stopped-flow kinetic measurements support an off-pathway burst-phase intermediate formed within the dead time of the apparatus. The authors would like to point out that our Gō-like simulation results are not at odds with this and other reported experimental observations and, more importantly, provide a testable prediction. Perhaps pulse-labeling and native state hydrogen exchange studies such as those performed on T4L will be able to answer whether there is indeed an off-pathway burst-phase intermediate in CheY due to competition arising from the C-terminal subdomain.

Conclusion

We used a Gō-like coarse-grained model to explore the landscape of subdomain folding in β α-repeat protein CheY. The sequence of folding events we have observed can be summarized as follows. Strands 1, 2 and 3 of the central β-sheet align simultaneously and cooperatively. Formation of the N-terminal subdomain is followed by the formation of the β₃α₃β₄ triad, which is then subsequently reinforced by formation of the helix 2-helix 3 interface. Next the β₄α4β₅ triad forms and is then reinforced by formation of the helix 3-helix 4 interface and the packing of helix 5 onto the N- and C-subdomains. The α₂β₃α₃β4 tetrad causes frustration by transiently coming together prior to formation of the N-subdomain.

While direct paths are populated from U to N in a two-state-like fashion, monitoring the folding progress along multiple structural reaction coordinates enabled the detection of transient intermediate states. Analogous to the four-state folding mechanism in T4L, an on-pathway intermediate structured in the more stable subdomain was observed as well as states frustrated in off-pathway contacts prematurely structured in the weaker subdomain. These metastable intermediates were shown to be a consequence of competition for native contacts between the N- and C-subdomains. Functional requirements for flexibility, and hence a lower density of native contacts, in CheY’s C-terminus thus have a dramatic effect on the folding mechanism. Subdomain competition for interactions is evident in CheY, T4L and interleukin-1β, and we postulate this to be a general feature of large single domain proteins with multiple folding modules.

Materials and Methods

Coarse-grained model

We employed the coarse-grained model developed by Karanicolas and Brooks for folding simulations.²⁶ The protein backbone is represented as a string of beads connected by virtual bonds. Each bead represents a single amino acid and is located at the α-carbon position. Bond lengths are kept fixed, bond angles are subject to a harmonic restraint and dihedral angles are subject to potentials representing sequence-dependent flexibility and conformational preferences in Ramachandran space. Nonbonded interactions are represented using a Gō model in which only residues that are in contact in the native state (taken to be crystal structure 3CHY.pdb) interact favorably. Backbone hydrogen bonds and sidechain pairs with nonhydrogen atoms separated by less than 4.5 Å interact via a pairwise potential that consists of an energy well and a small desolvation barrier. The interaction energies of sidechain native contacts are scaled according to their abundance in the Protein Data Bank as reported by Miyazawa and Jernigan.⁵⁴ Residues not in contact in the native state interact via a repulsive volume exclusion term. We refer the reader to Karanicolas and Brooks²⁶ for a complete description of the model potential and its parameters.

Simulation details

Molecular dynamics simulations were performed in Cartesian space using CHARMM⁵⁵ within the gorex.pl module of the MMTSB Tool Set.⁵⁶ Langevin dynamics with a 1.36 ps^–1 friction coefficient was used to maintain thermal equilibrium and the time step was set at 22 fs. For kinetic folding simulations 100 independent runs were each performed for 2×10⁸ dynamics steps at 0.87 T_f, where T_f is the folding transition temperature defined by the maximum in the heat capacity curve, C_v(T). The authors note that absolute timescales can not be obtained due to the coarse-grained nature of the Gō model and the lack of explicit solvent molecules. Unfolded starting structures for the folding runs were generated by equilibration at 1.5 T_f for 10⁷ dynamics steps starting from randomly assigned initial velocities. Conformational snapshots were recorded every 10⁵ dynamics steps. The fraction of native contacts formed, Q, was used to monitor folding progress. Each contact was considered formed if its residue pair was within a cutoff distance chosen such that the given contact is satisfied 85% of the time in native state simulations at 0.83 T_f.

Thermodynamic characterization

To characterize the entire accessible free energy landscape a two-dimensional extension of replica-exchange molecular dynamics⁵⁷ was performed. Each replica was assigned one of four temperatures (0.87, 0.97, 1.08 or 1.20 T_f) and one of seven harmonic biasing restraints on the radius of gyration, R_g, for a total of 28 replicas. To ensure overlap between the R_g distributions harmonic potentials were used with minima at 1.0, 1.1. 1.2, 1.3, 1.5, 1.7 and 2.0 $R_{\text{g}}^0$, where $R_{\text{g}}^0$ is the radius of gyration of the native state, with force constants 0.5, 5.0, 5.0, 5.0, 4.0, 0.8 and 0.5 kcal/mol-Ų, respectively. Stiff restraints were required at intermediate radii to sample the high energy transition region between the unfolded and native states. Conformational exchanges between temperature windows and restraints were attempted every 40,000 dynamics steps and the snapshots were recorded. The exchange frequency remained between ~10% and 40% throughout the 6×10⁸-step simulation. Finally, conformations were combined from all 28 replicas for a total of 4.2×10⁵ structures and the multidimensional weighted histogram analysis method^58,59 was used to obtain the unbiased free energy at T_f projected along various progress coordinates. To ensure convergence of the results the above procedure was carried out twice.

Supplementary Material

01. Supplementary Material.

Figures S1 to S4