Energetics and kinetics of substrate analog-coupledstaphylococcal nuclease folding revealed by astatistical mechanical approachTakuya Mizukamia,1, Shunta Furuzawab,1, Satoru G. Itohc,d,e

, Saho Segawaf, Teikichi Ikurag, Kunio Iharah,Hisashi Okumurac,d,e, Heinrich Rodera,2, and Kosuke Makib,2

aMolecular Therapeutics Program, Fox Chase Cancer Center, Philadelphia, PA 19111; bGraduate School of Science, Nagoya University, 464-8602 Nagoya,Aichi, Japan; cExploratory Research Center on Life and Living Systems, National Institutes of Natural Sciences, 444-8787 Okazaki, Aichi, Japan; dInstitute forMolecular Science, National Institutes of Natural Sciences, 444-8585 Okazaki, Aichi, Japan; eDepartment of Structural Molecular Science, The GraduateUniversity for Advanced Studies, SOKENDAI , 444-8585 Okazaki, Aichi, Japan; fSchool of Science, Nagoya University, 464-8602 Nagoya, Aichi, Japan;gDepartment of Structural Biology, Medical Research Institute, Tokyo Medical and Dental University, Yushima, 113-8510 Bunkyo, Tokyo, Japan; and hCenterfor Gene Research, Nagoya University, 464-8602 Nagoya, Aichi, Japan

Edited by Ken A. Dill, Stony Brook University, Stony Brook, NY, and approved July 1, 2020 (received for review August 18, 2019)

Protein conformational changes associated with ligand binding,especially those involving intrinsically disordered proteins, aremediated by tightly coupled intra- and intermolecular events. Suchreactions are often discussed in terms of two limiting kinetic mech-anisms, conformational selection (CS), where folding precedesbinding, and induced fit (IF), where binding precedes folding. Ithas been shown that coupled folding/binding reactions can pro-ceed along both CS and IF pathways with the flux ratio dependingon conditions such as ligand concentration. However, the struc-tural and energetic basis of such complex reactions remains poorlyunderstood. Therefore, we used experimental, theoretical, andcomputational approaches to explore structural and energetic as-pects of the coupled-folding/binding reaction of staphylococcalnuclease in the presence of the substrate analog adenosine-3′,5′-diphosphate. Optically monitored equilibrium and kinetic data,combined with a statistical mechanical model, gave deeper insightinto the relative importance of specific and Coulombic protein–ligand interactions in governing the reaction mechanism. We alsoinvestigated structural aspects of the reaction at the residue levelusing NMR and all-atom replica-permutation molecular dynamicssimulations. Both approaches yielded clear evidence for accumula-tion of a transient protein–ligand encounter complex early in thereaction under IF-dominant conditions. Quantitative analysis of theequilibrium/kinetic folding revealed that the ligand-dependentCS-to-IF shift resulted from stabilization of the compact transitionstate primarily by weakly ligand-dependent Coulombic interactionswith smaller contributions from specific binding energies. At a moremacroscopic level, the CS-to-IF shift was represented as a displace-ment of the reaction “route” on the free energy surface, which wasconsistent with a flux analysis.

protein folding | protein binding | staphylococcal nuclease |statistical mechanical model | real-time NMR

Many biological processes rely on formation/disassembly ofmolecular complexes of proteins with other macromole-

cules or small-molecule ligands for regulating biological systems,such as signal transduction pathways and enzyme-catalyzed re-actions. Ligand binding is often accompanied by conformationalchanges in one or both binding partners. An extreme example isfound in reactions involving intrinsically disordered proteins(IDPs) that undergo large-scale conformational changes uponrecognition of a target protein during cell signaling (1–3). A fullmechanistic understanding of such systems requires not onlystructural characterization of the ligand-free and -bound formsof the protein but also detailed kinetic and dynamic information.For understanding the kinetic mechanisms of ligand binding

reactions involving conformational changes, it is useful to con-sider two limiting cases (Fig. 1A): 1) conformational selection

(CS), where conformational changes precede the intermolecularbinding step (4, 5), and 2) induced fit (IF), where the second-order binding step precedes and promotes conformationalchanges (6, 7). CS assumes that the ligand binds to a smallfraction of the protein having high ligand-binding affinity to formthe final complex, whereas IF assumes that the ligand initiallybinds to the protein with low affinity, followed by conformationalchanges to form the final complex. These limiting cases are notmutually exclusive, so that the dominant reaction pathway canswitch between CS and IF, depending on conditions such as theligand concentration (8–11).Previous studies have shown that Coulombic interactions are

key in forming protein–ligand complexes through salt bridges andhydrogen bonds at the interface (12–14). Examples range from tightprotein–inhibitor interactions involving little or no conformationalchange, such as that between the Bacillus amyloliquefaciens

Significance

The structural/energetic basis of ligand binding-coupled pro-tein conformational changes remains elusive. There are twolimiting scenarios: conformational selection (CS) and induced-fit (IF). The difference is whether the ligand binds to the pro-tein before (IF) or after (CS) the conformational change. Toelucidate this complex reaction, we developed a statisticalmechanical model considering the physical interactions andapplied it to the staphylococcal nuclease folding coupled withbinding of a small-molecule ligand. Quantitative modelingrevealed that a ligand-dependent CS-to-IF shift resulted fromthe stabilization of the compact transition state by Coulombicinteractions causing a change in the reaction flux ratio. Themodel was supported by experimental/computational evi-dence for transient formation of an encounter complex of theligand with a denatured protein state.

Author contributions: T.M., S.F., and K.M. designed research; T.M., S.F., S.G.I., S.S., T.I., K.I.,H.O., H.R., and K.M. performed research; T.M., S.F., H.R., and K.M. contributed new re-agents/analytic tools; T.M., S.F., S.G.I., H.O., H.R., and K.M. analyzed data; and T.M., S.F.,S.G.I., H.O., H.R., and K.M. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.

Data deposition: NMR resonance assignments for urea-unfolded form SNase have beendeposited in the Biological Magnetic Resonance Data Bank (BMRB entry 50301).1T.M. and S.F. contributed equally to this work.2To whom correspondence may be addressed. Email: roder@fccc.edu or k_maki@synapse.phys.nagoya-u.ac.jp.

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1914349117/-/DCSupplemental.

First published July 31, 2020.

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ribonuclease (barnase) and its intracellular inhibitor, to binding-induced folding of IDPs with high specificity but moderate-to-lowaffinity (15, 16). In addition to Coulombic interactions, specificintermolecular contacts are generally also found at the interface ofIDP complexes with globular domains, as exemplified by the BH3-only protein Puma and the folded BCL-2–like protein MCL-1 (17,18). Therefore, we focused on specific binding and electrostaticinteractions as major factors of ligand binding-coupled reactionsand developed a Hamiltonian to calculate the grand canonicalpartition function with respect to the ligand chemical potential. Thismodel represents a natural progression from the thermodynamic to

the statistical mechanical description of protein–ligand interactionsat a microscopic level. The statistical mechanical analysis allowedus to estimate the relative stability of the species involved in thereaction and the contribution of each interaction as a determinantof the predominant reaction route on the free energy landscape(Fig. 1 A and B).In this study we explored the ligand-coupled folding of

staphylococcal nuclease (SNase) (Fig. 1C), a 149-residue glob-ular protein that has long been used as a model for foldingstudies (19–27). Substrate analogs such as thymidine-3′,5′-diphosphate (pdTp) and adenosine-3′,5′-diphosphate (prAp)significantly stabilize the native complex by bridging the twosubdomains of SNase (Fig. 1C) through specific and Coulombicinteractions (19, 26, 28). We exploited the significant differencein the stability between ligand-free and -bound forms to followthe ligand-coupled folding equilibrium and kinetics of SNaseunder denaturing condition where the free protein is denaturedwhile the prAp-bound form is in the native state. The experi-mental design adopted in the present study was similar to thatused in previous investigations on reduced (ferro) cytochrome c,where the folding was initiated by CO dissociation from thedestabilized CO–protein complex (29). Our choice of SNase as amodel protein for this study was in part motivated by a previousreport that its coupled folding/binding reaction mechanism canbe switched between CS and IF by introducing mutations (26). Avariant destabilizing the β-barrel domain (Fig. 1C) by insertingan Ala between Thr33 and Phe34 exhibits folding behaviorcharacteristic of a CS mechanism in the presence of prAp,whereas a variant lacking the C-terminal 10 residues in theα-helical domain (Fig. 1C) adopts an IF mechanism (26). How-ever, the mechanisms of the prAp binding-coupled folding ofwild-type SNase remained elusive.We investigated the mechanism of prAp binding-coupled

folding of wild-type SNase by means of experimental and com-putational approaches, including equilibrium and kinetic mea-surements utilizing circular dichroism (CD) and fluorescence,NMR spectroscopy, and computer simulations using the all-atomreplica-permutation molecular dynamics (RPMD) method (30,31). RPMD, an extension of replica-exchange (RE) MD simu-lation (32, 33), performs temperature permutation among morethan two replicas using the Suwa-Todo algorithm (34) ratherthan the Metropolis algorithm (35). RPMD has higher samplingefficiency than REMD because of its higher transition ratio fromone temperature to another (36–38).Our quantitative analysis of the kinetics of the coupled

binding/folding reaction vs. prAp concentration gave clearevidence for a ligand-dependent shift of the predominant ki-netic mechanism from CS to IF. While we expect structurallycooperative (two-state) behavior under CS conditions, IFconditions may lead to transient accumulation of an interme-diate state with a (weakly) bound ligand (D-L state in Fig. 1A).To test this hypothesis, we used real-time one-dimensional(1D) and two-dimensional (2D) NMR experiments to mea-sure spectral changes during early stages of the reaction at highprAp concentrations (IF-dominant conditions). As predicted,we were able to directly observe the transient accumulation ofan encounter complex of prAp with a partially structured, buthighly dynamic, form of SNase. Our statistical mechanicalmodel suggests that the shift from CS to IF pathways is drivenby stabilization of the transition state via weakly prAp-dependentCoulombic interactions. The shift in kinetic mechanism is mac-roscopically represented by the displacement of the saddle pointof the reaction “route” on the free energy landscape of theoverall reaction, in agreement with the results obtained by fluxanalysis.

U + L N + L

D-L N-L

KdAP,NKdAP,D

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N

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Free Energy

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H+

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1.0

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140120100806040200Residue number

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0.42 ppm < 0.21 ppm < < 0.42 ppm0 < < 0.21 ppm (white)unassigned in N (gray)

0.4 < probability0.2 < probability < 0.40 < probability< 0.2 (white)

III

III

H1

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A B

C

D

Fig. 1. (A) Unified model of ligand binding-coupled folding via IF and CSpathways (fast association/dissociation limit) and its free energy landscape.(B) Schematic representation of our model. The Hamiltonian with respect tothe substrate (prAp) (green) binding and His protonation (orange) consists ofthe specific binding (upper half) and Coulombic (lower half) interactions.The substrate binding and His protonation states were represented by thecorresponding grand canonical partition function at the constant chemicalpotentials of prAp and proton (pH). The charges arising from the otherfactors were included in the net charge of the SNase molecule. (C) Ribbondiagram of wild-type SNase in a substrate analog (pdTp, green) complexbased on a crystallographic structure (Protein Data Bank ID code 1SNC). TheN-terminal β-barrel and C-terminal α-helical domains are shown on cyan andmagenta background, respectively. The 1H-15N resonance shift on prApbinding the native state (N) is mapped onto the SNase structure: 0 < Δδ < 1SD, 0.21 ppm (white), 1 SD < Δδ < 2 SD (orange), and 2 SD < Δδ (red). Theresidues in gray remained unassigned in N. The residues contacting withpdTp are represented by stick models. The resonance shift at each assignedresidue is shown (Right). (D) A representative structure of SNase in a sub-strate analog (prAp, green) complex obtained by RPMD simulation at 300 K.The residues contacting with prAp at low (<0.2), intermediate (0.2 to 0.4),and high (0.4<) probabilities are shown in white, orange, and red, respec-tively. The corresponding probability of contact at each residue is shown(Right). (C and D) The substrate analog binging site, native secondarystructures, and sequence segments consisting of residues associated prApbinding defined by the NMR measurements in the native state and replica-permutation molecular dynamics simulation at 300 K are shown abovethe panels.

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Results and DiscussionOptimization of Conditions for Ligand-Induced Folding. Because theprAp-bound native state SNase (N-prAp) is significantly morestable than the prAp-free form (N), conditions can be foundwhere the population of N-prAp is much higher than that of N.When monitored by the CD signal at 225 nm (Fig. 2A) andtryptophan fluorescence (SI Appendix, Fig. S1), the urea-unfolding equilibrium of SNase at pH 7.0 and 22 °C showedcooperative unfolding transitions with midpoint concentrations,Cm, of 2.2 M and 3.8 M urea at 0 and 180 μM prAp, respectively(Fig. 2A and SI Appendix, Fig. S1). The difference between thetwo normalized unfolding curves is largest at ∼3 M urea wherethe protein is largely unfolded in the absence of prAp and pre-dominantly folded in the presence of prAp. In an effort to re-produce these results computationally, we performed RPMDsimulations of SNase in the presence and absence of prAp overthe temperature range from 300 K to 500 K as follows. Thesystem contained a single prAp molecule in a cubic unit cell of(62.14 Å)3 corresponding to an effective prAp concentration of∼7 mM. The rmsd of SNase structure in the presence of prApremained unchanged up to 350 K, whereas the correspondingrmsd in the absence of prAp started increasing at ∼320 K

(Fig. 2B), which indicated disruption of the native structure athigher temperature, and thus substantially higher stability, in thepresence of prAp than its absence.The families of optically monitored unfolding transition curves

were well fitted to a two-state model consisting of N (at 0 μMprAp) or N-prAp (at 180 μM prAp) and the unfolded state (U)(Fig. 2A and SI Appendix, Fig. S1). The Gibbs free energy ex-trapolated to 0 M urea (ΔGDN

H2O) and the cooperativity pa-

rameters (mDN) obtained by global fitting of the combined CDand fluorescence data are listed in SI Appendix, Table S1. ThemDN values were almost the same for 0 and 180 μM prAp, in-dicating that the prAp dissociation constant of N (Kd,N) is in-dependent of urea concentration. The urea dependence of thefractional difference between N-prAp and N was maximal at2.9 M urea where the N and N-prAp fractions were 11% and92%, respectively (Fig. 2A and SI Appendix, Fig. S1), and ∼80%of the whole prAp binding-coupled folding reaction could bemonitored. Hereafter, we refer the optimized denaturing con-ditions (2.9 M urea, pH 7.0, 22 °C) as the reference conditions.

Ligand-Induced Conformational Changes. Binding of prAp to SNaseresulted in small, but significant, changes in the CD spectra at0 M urea (by ∼5 × 102 deg·cm2·dmol−1 at 225 nm; Fig. 2A and SIAppendix, Fig. S1), indicative of moderate changes in backboneconformation upon ligand binding under native conditions (19).To characterize these structural changes in more detail, wecompared the 2D NMR (1H-15N heteronuclear single quantumcoherence [HSQC]) spectra of SNase in the presence (1.2 mM)and absence of prAp (SI Appendix, Fig. S1). Major changes inchemical shifts (up to 0.8 ppm) were observed for numerousbackbone resonances in and around the substrate binding sites(Fig. 1C). Consistent with these experimental results, our RPMDsimulations under native conditions (300 K) showed significantligand-induced perturbations in backbone conformation (Fig. 1D)and a concomitant decrease in rmsd relative to the ligand-freeform (Fig. 2B). At 2.9 M urea, all of the spectroscopic prop-erties, including CD (Fig. 2A), fluorescence (SI Appendix, Fig.S1), and HSQC spectra (SI Appendix, Figs. S1 and S3) areconsistent with a largely unfolded conformation in the absenceof ligand and a predominantly folded structure in the presenceof prAp. At 7.5 M urea, the CD and fluorescence spectraremained unchanged upon addition of prAp (SI Appendix, Fig.S1), indicating the affinity for prAp is too low to detect bindingunder strongly denaturing conditions (apparent Kd,D approxi-mately millimolar; discussed below).

Equilibrium and Kinetics of SNase Folding Coupled with prAp Binding.When we monitored the coupled folding/binding equilibrium ofSNase under reference conditions (2.9 M urea, pH 7.0, 22 °C) bymeasuring the changes in ellipticity at 225 nm and Trp fluores-cence as a function of prAp concentration, we observed transi-tions with a midpoint concentration of ∼10 μM prAp (Fig. 2Cand SI Appendix, Fig. S1). The fact that the normalized CD andfluorescence data are superimposable indicates that, in terms ofsecondary and tertiary structure acquisition, the ligand-coupledfolding equilibrium can be described by a cooperative (two-state)mechanism without detectable equilibrium intermediates. How-ever, the heterogeneity of the system consisting of prAp-boundand -free forms at equilibrium makes the coupled folding/bind-ing reaction more complex than a unimolecular folding equilib-rium. Ligand binding to N (N + prAp ⇌ N-prAp) can becharacterized on the basis of the difference in the CD signalbetween these two forms at 0 M urea (Fig. 2A and SI Appendix,Fig. S1). The prAp binding equilibrium under native conditionsshowed a shallow transition at ∼1 μM prAp (Fig. 2C), whichallowed us to decompose the native fraction into N and N-prAppopulations (Fig. 2D). The dominant fraction of N-prAp at >100 μMprAp supports the two-state approximation of the urea-unfolding

A

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500450400350300Temperature (K)

- prAp

+ prAp

D

Fig. 2. (A and B) prAp-induced stabilization of SNase against (A) urea and(B) temperature. (A) Urea-induced equilibrium unfolding transition curveswere measured by CD in the absence and presence of 180 μM prAp at pH 7.0and 22 °C. The CD and normalized data are shown by filled and open sym-bols, respectively. The solid lines show the transition curves obtained byfitting using the two-state model. The green line indicates the difference innative fraction in the absence and presence of 180 μM prAp. (B) Rmsd of anSNase molecule in the absence and presence of a prAp as a function oftemperature calculated by using the replica-permutation molecular dy-namics simulation of the corresponding system. Error bars represents the SDof the rmsd. (C and D) prAp binding-coupled equilibrium folding (at 2.9 Murea) and prAp binding equilibrium of SNase (at 0 M urea) and fractions ofrelevant species as a function of prAp concentration. (C) Changes in ellip-ticity at 225 nm are shown by circles at 0 M and 2.9 M urea at pH 7.0 and22 °C; the corresponding transition curves represent prAp binding to theprAp-free native state (N) and prAp-coupled folding, respectively. Theellipticity values extrapolated to zero time of the folding kinetics and thosefully equilibrated after folding reaction (SI Appendix, Fig. S3) are also shown.(D) Fractions of N/N-prAp (N-prAp: prAp-bound native state), N-prAp, N, andU/D-prAp (U: unfolded state; D-prAp: prAp-bound denatured state) derivedfrom the prAp-coupled equilibrium folding transition curves monitored byellipticity and fluorescence at 374 nm (SI Appendix, Fig. S1G). (C and D) Thesolid lines were obtained by the model analysis. Color codes are explicitlyshown in each panel.

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equilibrium at 180 μM prAp (N-prAp ⇌ U + prAp), given theurea independence of the prAp binding equilibrium as describedabove (SI Appendix, Fig. S1).We then measured the kinetics of SNase folding coupled with

prAp binding at various prAp concentrations under referenceconditions by monitoring Trp fluorescence at 326 nm (Fig. 3A)and the CD signal at 225 nm (SI Appendix, Fig. S3). Single-exponential kinetics was observed under all conditions. A plotof the apparent rate constant, λ, vs. prAp concentration (Fig. 3B)shows that the observed kinetics is independent of the spectro-scopic probe used, indicating that the binding/folding reaction ishighly cooperative. Such two-state behavior is not unexpectedbecause the destabilizing conditions used here (2.9 M urea) arelikely to disfavor accumulation of structural intermediates(19–21, 24).The kinetic behavior we observed (Fig. 3B) suggested that the

reaction at low prAp concentrations (<∼10 μM) was governed byCS rather than IF (4, 8). According to the CS mechanism, onlythe native state can bind the ligand, and the elementary rateconstant of unfolding decreases with increasing ligand concen-tration, due to selective stabilization of N-prAp, while the rate offolding remains unchanged. Thus, at low ligand concentrationswhere the stability of the complex is low the observed rate, λ, ismainly determined by unfolding and decreases as a function ofligand concentration. At high ligand concentrations a pure CSmechanism predicts that λ asymptotically approaches the rate offolding, which is independent of ligand concentration. In con-trast, we observed a significant increase in λ at prAp concen-trations above 100 μM (e.g., approximately twofold faster at∼600 μM than at ∼100 μM prAp; Fig. 3B), which is a clear in-dication that in this regime the reaction is governed by IF ratherthan CS. By quantitative modeling (SI Appendix, SupplementaryResults) we showed that the prAp dependence of λ can be de-scribed in terms of the second-order binding rate for formationof a low-affinity protein–ligand encounter complex (Fig. 1A andSI Appendix, Fig. S4). To test this interpretation further, weanalyzed the prAp dependence of λ assuming several kineticschemes, including CS and IF mechanisms (39). By comparingthe quality of fitting and the behavior predicted by our model(discussed below) and others, we concluded that a shift of thereaction mechanism from CS to IF can indeed account for theexperimental results (SI Appendix, Supplementary Results andFigs. S4 and S5). Similar behavior has also been reported pre-viously for the conformational change and folding of a few otherproteins (8, 40).To gain further structural insight into the coupled folding/

binding reaction and to test our prediction that a protein–ligandencounter complex accumulates transiently under IF conditions(Fig. 1A), we performed real-time 2D NMR experiments undersolution conditions matching those of the fluorescence- and CD-detected kinetic experiments, but higher protein concentration.As a reference for the fully unfolded form, we first recorded a1H-15N HSQC spectrum on a uniformly 15N-labeled sample ofSNase in 2.9 M urea (SI Appendix, Fig. S3). Using standard se-quential assignment procedures (SI Appendix, SupplementaryMaterials and Methods), we were able to resolve and assign 90backbone 1H-15N cross-peaks of the urea-denatured state (Bio-logical Magnetic Resonance Data Bank entry 50301) (41). Wethen recorded a series of fast HSQC spectra (90-s acquisitiontime) as a function of time (120 s to ∼5,000 s) after addition ofexcess ligand (450 μM or 2.6 mM prAp) (Fig. 3C and SI Ap-pendix, Fig. S3). With increasing reaction time the well-dispersedcross-peaks of the native prAp-bound form, N-prAp, appearedand grew in intensity at the expense of the unfolded state. Whenplotting the intensity of resolved peaks vs. time, we observedsingle-exponential behavior with a time constant (366 s at450 μM prAp and 260 s at 2.6 mM prAp) that was identical,within error, for all cross-peaks in both the D-prAp and N-prAp

III

III

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Unfolded statet = 120 s of refolding

9.0 8.5 8.0 7.5

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115

8.10 8.08 8.06 8.04 8.02

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120.6

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7.90 7.88 7.86 7.84 7.82 7.80

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Time (s)

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(ppm

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yt ilibabor P

8.6 8.4 8.2 8.0 7.8 7.6 7.4Unfolded

156237318399480561642723804885966

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E

F

Fig. 3. (A) Kinetic traces of prAp binding-coupled folding monitored by Trpfluorescence at 326 nm at various prAp concentrations under denaturingcondition (2.9 M urea, pH 7.0, 22 °C). The broken and solid lines wereobtained by nonlinear least-squares fitting and by the model analysis, re-spectively. The kinetic traces were appropriately shifted for clarity as indi-cated by circles. Color codes are explicitly shown in the panel. (B) PrApdependence of the apparent rates of the prAp-coupled folding obtained byfitting the ellipticity- and fluorescence-monitored kinetic traces (circles) to asingle-exponential function as well as the rates obtained by 2D (filledsquares) and 1D NMR (open square); the solid lines represent the prAp de-pendence of the elementary rate constants of folding (orange) andunfolding (red) (kDN and kND, respectively) and apparent rate (blue)obtained by the model analysis. (C) Comparison of HSQC spectra betweenthe unfolded state (U) (green) and the first data point of prAp-coupledfolding kinetics at 120 s after the initiation of the reaction (red). Repre-sentative peaks with significant shift (Val23, Val39, and Ile92) are zoomed inthe insets. PrAp dependence of the resonance shift of these residues in thedenatured species at 120 s of the reaction is shown which corresponded tothe binding curve of the transient encounter complex (D-prAp). The blacklines are obtained by nonlinear least-squares global fitting to a bindingfunction. (D) Time-dependent change in 1H resonance in the aromatic side-chain region. A series of the 1H-NMR spectra in the aromatic side chain re-gion especially for histidine He1 is shown as a function of time after theinitiation of the reaction. The side-chain structure of histidine is also shownin the panel. (E) The 1H-15N resonance shift between U and the denaturedspecies at 120 s of the reaction is mapped onto the native structure: 0 < Δδ <1.4 SD, 0.01 ppm (white), 1.4 SD < Δδ < 2 SD (orange), and 2 SD < Δδ (red).The residues in gray remain unassigned in U and D-prAp. The resonance shiftat each assigned residue is shown (Right). (F) A snapshot of the SNasestructure obtained by the RPMD simulation at 500 K. The prAp molecule isshown in green. The residues contacting with prAp at low (<0.2), interme-diate (0.2 to 0.4), and high (0.4<) probabilities are shown in white, orange,and red, respectively. The corresponding probability of contact at each res-idue is shown (Right). (E and F) The substrate analog binging site, nativesecondary structures, and sequence segments consisting of residues associ-ated prAp binding defined by the NMR measurements in the native stateand RPMD simulation at 300 K are shown above the panel.

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states in the presence of prAp (SI Appendix, Fig. S3). This timeconstant also is in close agreement with that observed in opticallymonitored experiments (228 s at 600 μM prAp). Together theseresults provide a stringent test for the structural cooperativity ofthe prAp-induced folding process of SNase.The cross-peaks of the N-prAp state showed no evidence for

time-dependent chemical shift changes, as one would expect forsuch a slow conformational transition, giving rise to extremeslow-exchange conditions on the chemical shift time scale. In thecase of a cooperative folding/binding mechanism we expect theU-state peaks to gradually disappear without any chemical shiftchanges. However, upon closer inspection we noticed that sev-eral of the resonance of the unfolded state underwent small butsignificant changes in chemical shift within the first 120 s afteraddition of excess ligand (450 μM or 2.6 mM prAp) with respectto the unfolded reference spectrum (Figs. 1C and 3C). This re-sult provides clear evidence for rapid (<120 s) formation of anencounter complex of prAp with a highly dynamic form of theprotein (D-prAp). The fact that the spectral changes during earlytimes of the reaction are dominated by chemical shifts ratherthan intensity changes suggests that interconversion between theU- and D-prAp states is fast compared to the frequency differ-ence of a typical resonance in these two states. These early(burst-phase) chemical shift changes were even more pro-nounced in a second series of real-time NMR measurements at aprAp concentration of 2.6 mM, confirming that higher ligandconcentrations cause a shift from CS to IF conditions and favoraccumulation of an encounter complex. Interestingly, the prApdependence of the chemical shifts for some of the most stronglyperturbed residues (Fig. 3 C, Inset) can be fitted to a 1:1 bindingisotherm with an apparent Kd of ∼0.8 mM, suggesting that thedissociation constant of the D-prAp encounter complex is about100-fold higher than that of the native protein–ligand complex(cf. Fig. 2C).At longer times after ligand addition most 1H-15N cross-peaks

of the U state continued to lose intensity without significantchanges in chemical shift and line widths. However, a few cross-peaks, including those assigned to Val23, Val39, and Ile92, un-derwent further shifts in peak position at longer times, along withreduction in the intensity throughout the slow folding/bindingreaction. Apparently, these NH groups are more strongly per-turbed than others by prAp interactions in the encounter com-plex. Chemical shift perturbations are expected to be especiallystrong for side chains involved in coordinating the nucleotideanalog. To test this hypothesis, we recorded a series of 1D 1HNMR spectra as a function of time (120 s to 1,500 s) after ad-dition of 650 μM prAp to urea-denatured SNase in deuteratedbuffer used (10 mM Tris-d11/10 mM CaCl2 in D2O at an un-corrected pH meter reading of 7.0). For most resolved side-chainresonances, including ring protons of Trp140 (resonances be-tween 7.4 and 7.7 ppm in Fig. 3D), we observe only a loss inD-state peaks and concomitant gain in the corresponding reso-nance of the N-prAp state without changes in peak position, asexpected for the slow shift in population from the unfolded tothe native ligand-bound states. In contrast, three resolved reso-nances between 7.8 and 8 ppm (Fig. 3D) assigned to His ringprotons (He1) experience large time-dependent chemical shiftchanges throughout the time course of the folding/binding re-action. This behavior is clearly inconsistent with the cooperative(structurally two-state) model, since the rate-limiting step in theformation of the native complex is far slower (the apparent rate,λ ∼ 10−3 s−1) than the frequency shift of these resonances be-tween U and N-prAp (60 to 90 Hz). Therefore, the reaction mustinvolve additional states that undergo rapid exchange (>100 s−1)with the U- and/or D-prAp state. Although further study isneeded to fully understand the underlying mechanism, the resultsprovide striking evidence for rapid formation of an encounter

complex in which His side chains along with a few backboneNH groups play a key role in binding prAp.

Statistical Mechanical Model. The native state of SNase is signifi-cantly stabilized by prAp binding (N-prAp), which enabled us tofind conditions under which folding is coupled with ligandbinding (Fig. 2 C and D and SI Appendix, Fig. S1). As shown inFig. 1C, N-prAp was stabilized not only by a series of specificprotein–ligand interactions with several residues but also byCoulombic interactions. SNase is a basic protein that attractsnegatively charged nucleic acids to function as a nuclease. Togain insights into the energetic contributions from these twointeractions to prAp binding, we developed a model for repre-senting prAp binding to the relevant species (N, transition state[TS], and D) on the basis of statistical mechanics (see SI Ap-pendix, Supplementary Results for a more detailed description andderivations). The model is an extension of a previous model ofprotonation states for the analysis of pH-induced folding ofapomyoglobin (42).In this model, we assumed a single prAp-binding site with an

intrinsic dissociation constant, Kd,k, in state k (= N, TS, or D)and that prAp has negative charge (ZprAp·e = −2e, where e is aunit charge). We also considered unit charges generated by (de)protonation at the ionizable residues. Four histidine sites (His8,His46, His121, and His124) were assumed to have an intrinsicpKa,k,σ value at the σ-th site (σ = 1 – N; N = 4) in state k becauseof the pKa ∼ pH (7.0) used in this study. The Kd,k and pKa,k,σvalues correspond to the specific binding energy of prAp andproton (at the σ-th site) binding, respectively. The intrinsic val-ues are those for the protein molecule without the net charge.Other basic and acidic side chains were assumed to be fully (de)protonated (SI Appendix, Table S3) due to a pKa far from 7.0. Inaddition, a Ca2+ ion was assumed to remain bound to the SNasemolecule throughout the reaction because the concentrationused in our experiments (10 mM) is far higher than the expecteddissociation constant. In support of this, the Ca2+ is fully boundto Glu43 at 300 and 500 K according to our RPMD simulations(SI Appendix, Fig. S2).The charges arising from the protonated basic and deproto-

nated acidic side chains (at pH 7.0) and the Ca2+ ion resulted inan intrinsic net charge, Zint·e, of +10e (+8e from the SNasemolecule and +2e from the bound Ca2+ ion). All of thesecharges were assumed to be equivalent to each other in terms ofCoulombic interactions and to be uniformly spread over thesurface of a spherical molecule with a charge-averaged apparentradius in state k, rap,k. According to this approximation, theCoulombic potential energy (Vk) for an SNase molecule in statek is essentially represented by a single parameter, rap,k. on thebasis of the Debye–Hückel theory. Thus, the summation of thespecific binding and Coulombic interaction energies well ap-proximates the total Hamiltonian with respect to the prAp/Hisproton binding to an SNase molecule in state k (SI Appendix, Eq.S16 and Supplementary Results). The grand partition function Ξkof the SNase system at the prAp concentration, [prAp], and pH,derived from equilibrium statistical mechanics, is represented asfollows:

Ξk = ∑Xk

exp( − Lk log( Kd,k

[prAp]) − 2.30∑Nσ=1

pk,σ(pH − pKa,k,σ) − βVk(rap,k)),[1]

where Lk is the ligand occupancy at the binding site and pk,σ isthe proton occupancy at the σ-th site of the His residues (equalsto 0 and 1 for the unbound and bound states, correspondingly).β = 1/kBT, with kB and T being the Boltzmann constantand absolute temperature, respectively. The summation ofBoltzmann factors runs over all possible combinations of Lk and

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pk,σ (σ = 1 – N) (Xk) (42). The Gibbs free energy differencebetween states k and l was derived from the ratio of the partitionfunction of the states as

ΔGkl = ΔGrefkl ([prAp] = 0) − RT log(Ξl([prAp])=Ξl(0)

Ξk([prAp])=Ξk(0)), [2]

where R is the gas constant and ΔGrefkl is the contribution to

stability from factors other than prAp, His protonation and thenet charge of SNase, such as hydrophobic effects, and was esti-mated by the urea unfolding under the reference condition (at2.9 M urea and pH 7.0). Ξk (0) is Ξk ([prAp]) at [prAp] → +0(Eq. 1). The activation free energy upon conversion from state kto state l via the TS is also obtained in the same way, and thus thecorresponding elementary rate constant is obtained on the basisof the Arrhenius equation.

Optimization of Physical Parameters.We applied our model (Eqs. 1and 2) to the equilibrium and kinetic behaviors of SNase foldingcoupled with prAp binding obtained above on the basis of anapparent two-state reaction involving N/N-prAp (Nap) andU/D-prAp (Dap) via the transition state, TS/TS-prAp (TSap), as ageneralized version of the CS and IF schemes (SI Appendix,Schemes S3 and S4 and Supplementary Results):

(D-prAp⇌U + prAp) ⇌kDN

kND

(N-prAp⇌N + prAp). [Scheme 1]

In the model calculation, several parameters, including thenative and denatured pKa and rap values as well as the rap valueof the transition state, were constrained to uniquely determinethe remaining ones because the specific binding and Coulombicenergy terms were mutually compatible, as shown by Eq. 1. ThepKa,N values were chosen to reproduce the titration curves ofprotonation of all four His in SNase at ion strengths rangingfrom 10 mM to 1.5 M with carboxy pKa of Asp and Glu fixedto the average values at 1 M salt (i.e., 3.53 and 4.12, respectively)(43, 44). The pKa,D values were adjusted to reproduce the de-crease in the stability of SNase by 1.7 kcal/mol with decreasingthe pH from 9 to 5 (22, 45). The optimized pKa,D values thusobtained (6.47) were consistent with model peptides. The gyrationradii, rap, for N, TS, and U were taken from the literature (22).The gyration radius of the salt-induced molten-globule state ofSNase (22) was used to estimate rap,TS. The Kd, pKa, and rap valueswere considered to be independent of urea concentration.Other physical parameters for Nap, TSap, and Dap were opti-

mized through a manual search to reproduce the kinetic traces(Fig. 3A and SI Appendix, Fig. S3), equilibrium curves of theprAp-coupled folding, and the binding curve of prAp to N(Fig. 2 C and D and SI Appendix, Fig. S1) and to D (the prAp-dependence of the resonance shift of the denatured species at∼120 s of the reaction) (Fig. 3C), according to Scheme 1. Whenwe previously compared the quality of the fitting between themanual search and least-squares fitting using a Monte Carlomethod, we found that both methods led to nearly the samequality of fitting (42). The predicted parameters are listed in SIAppendix, Table S4. Once the prAp dependence of the Nap, TSap,and Dap stabilities was obtained, the Gibbs free energy of theprAp-bound and -free forms of each species was derived fromthe probability distribution of the two forms as a consequence ofequilibrium statistical mechanics. The prAp-dependent equilib-rium and kinetic behavior of the coupled binding/folding reac-tion was fully reproduced by the model analysis (Figs. 2 and 3and SI Appendix, Figs. S1 and S3).

Energetic and Kinetic Mechanisms. Fig. 4A shows the predictedprAp dependence of the Gibbs free energies of Nap, TSap, andDap at representative prAp concentrations (0, 10, and 400 μM).

As the prAp concentration increased, Nap was more stable thanDap at >10 μM prAp (Fig. 2 C and D). Interestingly, TSap, theensemble of TS and TS-prAp, is somewhat stabilized at higherprAp concentrations. Because only TS-prAp, but not TS, isexpected to be stabilized with increasing ligand concentration,this observation supports our conclusion that the IF mechanismis dominant at high prAp concentrations. In contrast, a pure CSmechanism would predict a ligand-free transition state (TS),resulting in prAp-independent stability. This was illustratedmore clearly by the stability of the prAp-bound and -free formsof each species (Fig. 4B). In this reaction, the partitioning be-tween the two pathways was predominantly determined by thestability of the denatured species and the subsequent kinetic

1.77 kcal/mol-0.31 kcal/mol

ElectrostaticSpecific

U TSN

D-prApTS-prApN-prAp

15

10

5

0

-5

GU

k)lo

m/lack(

0

100

2040

6080

k

CS

IF

1.69 kcal/mol2.15 kcal/mol

ElectrostaticSpecific

15

10

5

0

-5

GU

k)lo

m/lac k(

k

%bound

U TS

CS

N

IF

D-prApTS-prApN-prAp100

020

4060

80

10 M prAp

UTS

N

D-prApN-prApTS-prAp

CS

IF

UNTS

D-prApTS-prAp N-prAp

15

10

5

0

-5

ygreneeerF

)lom/la ck(

400 M prAp

IF

10 M prAp 400 M prAp1050Free energy(kcal/mol)

CS

15

10

5

0

-5

ygreneeerF

)lom/lack(

Rel

a tiv

eFl

u x

Fold

ing

Flux

/([U

]+[U

-prA

p]) (

x10-3

s-1)

JUNJIF

JCS

[prAp] ( M) [prAp] ( M)

IFCS

1.0

0.8

0.6

0.4

0.2

0.010

2 4 6 8100

2 4 6 81000

2 4 6 81000010

2 4 6 8100

2 4 6 81000

2 4 6 810000Dapk: TSap Nap

15

10

5

0

-5

GD

k(kca

l/mol

)

400 M prAp

10 M prAp

0 M prAp CS pathway15

10

5

0

-5Free

ener

gy(k

cal/ m

ol)

UCS: TS NIF: D-prApTS-prAp N-prAp

IF pathway for10 M & 400 M

76543210

%bound

A B C D

E

F

Fig. 4. Free energy diagrams and landscapes of prAp binding-coupledfolding of SNase at representative prAp concentrations, obtained by themodel analysis. (A) Free energy diagrams at 0 (red), 10 (blue), and 400 μM(green) prAp. (B) Free energy diagrams of the CS and IF pathways at 10 and400 μM prAp. (C) Folding flux normalized by the concentration of thedenatured species (prAp-bound and -free denatured states). JDN, JCS, and JIFindicate the total flux and the flux via the CS and IF pathways, respectively.(D) Relative flux (normalized by the total flux) via the CS and IF pathways. (E)The free energy profile of the prAp-coupled folding along the CS and IFpathways. The corresponding fluxes (arrows) are drawn along the free en-ergy profile of each pathway. The thickness of the arrows represents the fluxvalues. (F) Free energy landscapes as a function of the fractional prAp-boundform (%bound) at 10 and 400 μM prAp. The macroscopic binding/foldingroute is indicated by the arrow on the free energy landscape. (A and F) Theenergetic contributions of the specific binding and Coulombic interactions tothe stability are shown in pink and light blue, respectively. (E and F) Thestability of each species and the kinetic pathway/reaction route are pro-jected onto the bottom plane by color and arrows, respectively. Color codesof the stability are explicitly shown between E and F.

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barrier. At 10 μM prAp, U and TS were more stable thanD-prAp and TS-prAp, respectively, by ∼2.6 kcal/mol, thus fa-voring the CS pathway (U ⇌ TS ⇌ N ⇌ Nap). However, bothD-prAp and TS-prAp were significantly stabilized at 400 μMprAp, causing a shift to IF (Dap ⇌ TS-prAp ⇌ Nap) as the majorpathway (midpoint concentration ∼190 μM). To further quantifythis shift, we calculated the flux along each pathway, based onthe respective activation free energies (rate constants), whichshowed that 68% of the total flux went along the IF pathway at400 μM prAp (Fig. 4 C and D). Fig. 4E summarized the rela-tionship between the fluxes along the CS and IF pathways, andthe free energies of each species at 10 and 400 μM, demon-strating that the flux is determined by the barrier height of TS-prAp relative to TS.The switch in binding mechanisms can also be represented

from a macroscopic point of view. While the pathway repre-sentation (CS and IF) was used in the above analysis, a moremacroscopic representation gave insight into the averaged be-havior of molecular ensembles, which can be directly related tobulk measurements. In fact, as evidenced by the ligand-dependentNMR resonance shift of the denatured species (Fig. 3C), theconversion from the denatured to the native ligand complex in-volved a preequilibrium between prAp-bound and -free forms.Given the free energies of the prAp-free and -bound species(Gk and Gk-prAp, respectively, for those in state k), the free en-ergy of a mixture, G(x), at an arbitrary ratio x (0 < x < 1) can bewritten as

G(x) = xGk-prAp + (1 − x)Gk + RT(x log x + (1 − x)log(1 − x)).[3]

This represents the free energy landscape of state k as a functionof the fraction of the prAp-bound form normalized by the totalamount of the prAp-bound and -free forms (%bound); the ob-served free energy corresponds to the minimum value at xmin(saddle point) (Eq. 2 and SI Appendix, Eq. S20 and Supplemen-tary Results), where

xmin = exp( −Gk-prAp/RT)(exp( −Gk-prAp/RT) + exp( −Gk=RT))−1.[4]

The %bound value for the transition state (TS and TS-prAp)yields the flux ratio along the IF and CS pathways under pree-quilibrium conditions (rapid binding/dissociation limit) (Eq. 4and SI Appendix, Eq. S32; see SI Appendix, Supplementary Resultsfor derivation of the identity between the relative flux and %bound value at TSap). The free energy profiles showed the mac-roscopic behaviors of the ligand binding-coupled folding (Fig.4F). The %bound values for U and TS increased as the prApconcentration increased from 10 to 400 μM. In particular, theobserved increase in %bound TS (TS-prAp) from 5 to 68% dem-onstrated a ligand-induced CS-to-IF shift. The degree of cou-pling between folding and ligand binding is clearly representedby a thermodynamically meaningful parameter, %bound, andthe free energy profile along each pathway, which provides analternative to detailed energetics for understanding the switch inreaction mechanisms.The Hamiltonian of our model (SI Appendix, Eq. S16 and

Supplementary Results) consisted of two energetic terms, thespecific binding (Esp) and the Coulombic interaction (ECo)terms, whose expectation values provides the contribution to thestability of TSap and Nap. Fig. 4 A and F show Esp and ECo onprAp binding at 10 and 400 μM prAp. For the native species, thetwo terms showed different behaviors: ECo remained essentiallyunchanged whereas Esp increased with increasing prAp concen-tration, leading to a switch of the predominant forces associatedwith prAp binding from Coulombic interactions to specific

binding at a certain prAp concentration. In fact, ECo (<V(rap,N)>)was approximately proportional to <LN> (Eq. 1 and SI Ap-pendix, Eq. S15 and Supplementary Results), resulting in slightprAp dependence at certain prAp concentrations (∼Kd,N–Kd,D).On the other hand, Esp (≈RT log(Kd,k/[prAp]) <Lk>) signifi-cantly increased with increasing the prAp concentration evenwhen the prAp-binding site was fully occupied. Thus, ECo con-tributed to the native stability more significantly due to <LN> ∼1than Esp at 10 μM prAp, which was close to Kd,N (∼19 μM),whereas the contribution from Esp increased at higher prApconcentrations. For TSap, ECo was the major term at 400 μMprAp albeit to a much smaller extent than for Nap becauseKd,TS >> Kd,N; however, it was ECo that induced structural for-mation via the IF pathway.The contributions of Esp and ECo were different between the

native and transition states under the IF-dominant condition asdescribed above; Esp > ECo (2.9 vs. 1.2 kcal/mol) in the nativestate, whereas Esp < ECo (0.0 and 0.9 kcal/mol) in the transitionstate. This estimation was qualitatively supported by the RPMDsimulation in the presence of prAp (∼7 mM). We calculated thenumber of residues contacting with the adenosine and phosphatemoieties (Nad and Nph, respectively) at temperatures rangingfrom 300 K to 500 K (SI Appendix, Fig. S2). Nad > Nph in the nativestate (10.1 vs. 9.6 at 300 K), whereas Nad < Nph in the nonnativestate (6.1 vs. 6.5 at 500 K). This is consistent with the resultsobtained by the model analysis, which assumed that the contactswith adenosine and phosphate moiety were brought about mainly bythe specific binding and Coulombic interactions. This assumptioncan be rationalized based on the structure of the SNase–ligandcomplex (Fig. 1C). The nucleotide base tends to form specificcontacts with hydrophobic residues, including Tyr85, Tyr115, andTyr118, whereas the phosphate groups primarily interacts withcharged residues, including Arg35 and Arg87. This suggested thatthe adenosine and phosphate moieties are associated with SNasemainly through specific binding (Esp) and Coulombic interactions(ECo), respectively.

Structural Insights. Binding of the prAp ligand to native SNase(Fig. 1C) resulted in significant backbone chemical shift perturba-tions for residues in four segments of the sequence (Asp19–Val23,Arg35–Thr41, Arg81–Ala90, and Tyr113–Tyr115), in close agree-ment with the results reported for the pdTp complex of SNase(46–48). Our RPMD simulations at 300 K revealed a strikinglysimilar pattern with the majority of residues with high probabilitiesof prAp contact found in the same four segments (Asp19–Thr22,Arg35–His46, Glu80–Leu89, and Tyr113–Tyr115) (Fig. 1D). Itshould be noted that some of the differences, especially in thePro42–His46 region, are due to missing NMR resonance assign-ments. The segments were distributed around the binding cleft atthe N terminus of β-strand II, the substrate binding loop, the loopbetween β-strands IV and V, and the loop between α-helices H2and H3, respectively, in the tertiary structure.Our observation by real-time 2D NMR that numerous reso-

nances moved away from their initial position in the unfoldedstate during the 120 s dead time of the ligand-induced foldingreaction (Fig. 3 C–E, and SI Appendix, Fig. S3) supported ourprediction that an encounter complex, D-prAp, accumulatesrapidly under IF-dominant conditions and yielded furtherstructural insight. Although the chemical shift changes are muchsmaller than those associated with prAp binding under nativeconditions (compare Fig. 3C with Fig. 1C), the chemical shiftdifferences between the spectra before and 120 s after additionof a small aliquot of prAp are statistically significant (>0.014ppm for Val23 and Ala58 corresponding to two SDs, and >0.01ppm corresponding to 1.4 SDs for 10 other residues). Seven ofthese (Val23, Val39, Glu43, Thr44, Ala90, Tyr91, and Ile92) arelocated in the sequence segments involved in ligand binding tothe native state (Fig. 3E), including the first (Val23), second

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(Arg35–His46), and the C-terminal half of the third segment(Ala90–Ile92), suggesting that native-like interactions with resi-dues in these segments are involved in stabilizing the D-prApencounter complex, albeit with low intrinsic affinity (Kd,D ∼2.7mM). Other residues with >0.01 ppm shifts, including His8(β-strand I), Thr13 (β-strand I), Ala58 (α-helix H1), Val104(α-helix H2), and Ala123 (α-helix H3) (Fig. 3E), are further awayfrom the native binding site, suggesting that the transient inter-action of the ligand with the denatured protein ensemble ishighly dynamic and may involve nonnative interactions. In ad-dition to these perturbations of backbone NH groups, time-resolved 1D NMR experiments showed that the ring protonsof three His residues showed exceptionally large shift changesduring the 120-s dead time (0.025 to 0.03 ppm) and continued toshift at longer times (Fig. 3D). Since none of the four His ofSNase are directly involved in native ligand interactions, thisobservation provides striking evidence for the involvement ofnonnative tertiary protein–ligand interactions in the D-prApencounter complex and further suggests that its conformationis relatively compact.These experimental findings were qualitatively supported by

the RPMD simulation at 500 K. The four segments were stillevident even at 500 K, although the contact probabilities withinthe segments may be overestimated due to the residual fractionwith native-like structures (Fig. 3F). Interestingly, some residueswith moderate contact probability were not implicated in nativeprotein–ligand interactions, in qualitative agreement with theNMR results (Fig. 3E). The combined experimental and com-putational results indicate that the initial encounter of the ligandwith the disordered protein ensemble during early stages of thecoupled binding/folding reaction is mainly governed by native-

like contacts but also involves nonnative interactions with resi-dues throughout the sequence.The stabilization of TS on prAp binding relative to that of

the native species is indicative of the degree of its structureformation around the prAp-binding site, which is analogous tothe ϕ-value analysis in folding studies (49, 50). We used thestability of the prAp-bound and -free forms to define the ϕprAp

value as

ϕprAp = ΔGU-prApTS-prAp − ΔGUTS

ΔGU-prApN-prAp − ΔGUN, [5]

which was normalized by definition, and ϕprAp = 0 and 1 corre-sponded to the absence and full formation of the native-likestructure around the prAp-binding site. The resulting ϕprAp valuewas 0.17, suggesting that the tertiary structure was not yet fullyformed around the binding site (19). In contrast, the overall di-mension (rap,TS) is expected to be compact (∼70% of the totalchange in rap), based on the typical dimension of the salt-inducedmolten globule state (22). This suggests that TSap is a collapsedstate without persistent tertiary structure. Even though it lacksextensive tertiary structure, the prAp-bound TS on the IF path-way is favored at high prAp concentrations (Figs. 3B and 4). Toaddress this question, we estimated the relative development ofthe specific binding and Coulombic energies in TSap by replacingthe free energy in Eq. 5 with the corresponding energetic terms,ϕprAp

sp and ϕprApCo, which were 0.00 and 0.71, respectively. Un-

like the overall ϕprAp, the Coulombic interactions were relativelywell developed in TS compared with the specific binding inter-actions. Thus, a rate-limiting step of the reaction may be recruit-ment of basic residues to form contacts with the phosphate

GU

k (kcal/mol)

%BoundG

(kl/

l)

D19G20

T22V23

D40T41

V39

L38

L37L36R35

Y113V114

Y115Y85

A90 L89

ound

DDDDDD19G20G20G20G20G20G20G20GG20GG2GG20G20202GGG2200

T22T2T2TT2T2TT2TTT22TT2222V23V23VV23V2333VV233V233VV233VV233

D4D4D4D4D4D4D40000D444000DD44DDD4DD4DDDT41T44T4T4TT4T4TTT4

VVV39VVV 99V 999VVVVVVVVVVVVVVVV

LLL388L 8888LLLL 8LLL

L373737777737L 77L L3666R35R35RR3R3R3R3R3RR3R355R35R3R35R35R33R35R353RR3R 55

Y113YY11Y11Y11Y1Y11111Y1Y11Y11YY1Y1Y11YY1Y1Y11Y1YV114V114V114V11V114V11V11411V11414114V1144V114V114V11111V 1VV11VVV 11 44

Y1155555555555555555511555555555585Y85Y85Y85YY8Y8585Y85Y85YY855Y85Y85Y8558555Y855Y858

9000909090900000000000900A9A9A9999999999AAAAA99909090000000000000000000000000000000000000000 899898889L8L8L8L88L8LLL88L888L8L8L8LLL8LL8888888888888888888888LLLLLLLLLLLLLL888888888888899988889999999

D19G20

T22V23

D40T41

V39

L38

L37L36R35

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Y115Y85

A90 L89

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prAp V23A58

I92

V39E43

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GU

k (kcal/mol)

%Bound

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IF pathway[p

rAp]

U

D-prAp

N-prAp

N

Fig. 5. Schematic summarizing the CS-to-IF shift of prAp-coupled folding of SNase. Free energy landscapes of the reaction at 10 and 400 μM prAp are shownalong with the macroscopic binding/folding route and the energetic contributions of the specific binding (pink) and Coulombic (blue) interactions to thestability (Fig. 4). The shape of the landscapes is simplified to explicitly show the saddle point (%bound in TSap). Structural characteristics of prAp-bound forms(D-prAp and N-prAp) are also represented on the basis of the NMR resonance shifts. Residues with the large 1H-15N resonance shift between the prAp-boundand -free forms are explicitly shown with the same color codes as those in Figs. 1 and 3 for N-prAp and D-prAp, respectively.

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groups of prAp, followed by further stabilization of the nativecomplex by specific binding.The prAp-coupled folding described above exhibits striking

contrasts to the spontaneous folding of SNase (19, 24, 25, 27).This protein folds to the native state via a series of intermediatesin a structurally heterogeneous manner. A study of the impact ofpdTp inhibitor on SNase folding showed that the β-barrel do-main forms native-like and compact structures rapidly followedby docking of α-helical domain, especially α-helix H3, to theβ-barrel domain (Fig. 1C), without pdTp stabilizing the transitionstate even at 1 mM pdTp (under IF-dominant conditions in thisstudy) (19). This scenario appears contradictory to the prAp-coupled folding induced by a series of weak contacts with prApover the sequence with ϕprAp

Co ∼0.7. The apparent contradictionmay be reconciled by assuming a switch from spontaneous toligand-induced folding mechanisms, depending on the barrierheight of the rate-limiting step, that is, the spontaneous folding ispreferred when the barrier is sufficiently low even in the absenceof prAp, but folding is coupled with prAp binding when thebarrier is higher in its absence as N is destabilized at higher ureaconcentrations. In support of this idea, in a previous study onurea-induced folding of SNase, the apparent folding rate un-dergoes an abrupt decrease below and sharp increase above themidpoint of the unfolding transition (∼2 M urea) as a function ofurea concentration, along with large amplitude changes, in thepresence of 1 mM pdTp and 10 mM Ca2+ (19). The sharp in-crease in amplitude is especially remarkable, since the amplitudeof the folding phases typically decreases on approaching thetransition region. These observations suggest that the foldingmechanism of SNase may depend on whether it occurs sponta-neously or in the presence of ligand, despite the structural sim-ilarity of the final state.

Conclusions and Further ImplicationsWe developed a statistical mechanical model of the SNase–prApcomplex based on specific and Coulombic interactions and appliedit to the ligand-coupled folding reaction of SNase. The observedligand-induced switch of the kinetic mechanism from CS to IF

was explained on the basis of the prAp dependence of the ap-parent rate and our observation of an encounter complex ofprAp with the denatured state early in the kinetics. The physicalmechanism underlying the CS-to-IF shift was attributed to aslight prAp dependence of Coulombic interactions betweenprAp and TS, which was compact, but without fully developednative-like structure around the prAp-binding site. Energetic,structural, and kinetic aspects of the ligand-coupled folding ofSNase are summarized in Fig. 5.Although SNase is a globular protein differing from IDPs in its

capability of forming specific structure, our model could bevaluable for gaining deeper insight into the energetic and kineticprinciples underlying coupled binding/folding reactions for sys-tems involving IDPs or regions thereof, which play critical rolesin molecular recognition events throughout biology.

Materials and MethodsSNase was expressed and purified as reported previously (20, 51). Fluores-cence, CD, and NMR measurements were performed by using an F-4500spectrofluorometer (Hitachi-Hitech), a Jasco J-600S spectropolarimeter, anda 600-MHz Bruker Avance Neo NMR spectrometer. A stopped-flow deviceconstructed by Unisok Inc. was used in the kinetic CD measurements. RPMDsimulation was performed using the Generalized-Ensemble Molecular Bio-physics program (52). Details of the materials, experimental procedures, andanalysis are provided in SI Appendix, Supplementary Materials and Methods.

Data Availability. NMR resonance assignments for urea-unfolded form SNasehave been deposited in the Biological Magnetic Resonance Data Bank(BMRB entry 50301).

ACKNOWLEDGMENTS. We thank the Center for Gene Research, NagoyaUniversity for performing circular dichroism measurements. We thankDr. Mikio Kataoka for helpful discussion. This study was supported by Grants-in-Aid for Scientific Research (C) from the Japan Society for the Promotionof Science (project numbers 20K06578, 24570181 and 20570153 to K.M.),NIH grant GM116911 to H.R., and NIH Grant CA06927 to the Fox ChaseCancer Center. The Spectroscopy Support Facility at the Fox Chase CancerCenter provided technical support. We used supercomputers at the ResearchCenter for Computational Science, Okazaki Research Facilities, NationalInstitutes of Natural Sciences, Japan.

1. P. E. Wright, H. J. Dyson, Intrinsically unstructured proteins: Re-assessing the proteinstructure-function paradigm. J. Mol. Biol. 293, 321–331 (1999).

2. A. K. Dunker et al., Intrinsically disordered protein. J. Mol. Graph. Model. 19, 26–59(2001).

3. P. E. Wright, H. J. Dyson, Intrinsically disordered proteins in cellular signalling andregulation. Nat. Rev. Mol. Cell Biol. 16, 18–29 (2015).

4. A. D. Vogt, N. Pozzi, Z. Chen, E. Di Cera, Essential role of conformational selection inligand binding. Biophys. Chem. 186, 13–21 (2014).

5. T. R. Weikl, F. Paul, Conformational selection in protein binding and function. ProteinSci. 23, 1508–1518 (2014).

6. D. E. Koshland, Application of a theory of enzyme specificity to protein synthesis.Proc. Natl. Acad. Sci. U.S.A. 44, 98–104 (1958).

7. K. Sugase, H. J. Dyson, P. E. Wright, Mechanism of coupled folding and binding of anintrinsically disordered protein. Nature 447, 1021–1025 (2007).

8. G. G. Hammes, Y. C. Chang, T. G. Oas, Conformational selection or induced fit: A fluxdescription of reaction mechanism. Proc. Natl. Acad. Sci. U.S.A. 106, 13737–13741 (2009).

9. L. Cai, H. X. Zhou, Theory and simulation on the kinetics of protein-ligand bindingcoupled to conformational change. J. Chem. Phys. 134, 105101 (2011).

10. K. G. Daniels et al., Ligand concentration regulates the pathways of coupled proteinfolding and binding. J. Am. Chem. Soc. 136, 822–825 (2014).

11. N. Greives, H. X. Zhou, Both protein dynamics and ligand concentration can shift thebinding mechanism between conformational selection and induced fit. Proc. Natl.Acad. Sci. U.S.A. 111, 10197–10202 (2014).

12. G. Schreiber, G. Haran, H. X. Zhou, Fundamental aspects of protein-protein associa-tion kinetics. Chem. Rev. 109, 839–860 (2009).

13. L. B. Chemes, I. E. Sánchez, G. de Prat-Gay, Kinetic recognition of the retinoblastomatumor suppressor by a specific protein target. J. Mol. Biol. 412, 267–284 (2011).

14. M. Y. Tsai et al., Electrostatics, structure prediction, and the energy landscapes forprotein folding and binding. Protein Sci. 25, 255–269 (2016).

15. G. Schreiber, A. R. Fersht, Energetics of protein-protein interactions: Analysis of thebarnase-barstar interface by single mutations and double mutant cycles. J. Mol. Biol.248, 478–486 (1995).

16. F. Dong, M. Vijayakumar, H. X. Zhou, Comparison of calculation and experimentimplicates significant electrostatic contributions to the binding stability of barnaseand barstar. Biophys. J. 85, 49–60 (2003).

17. J. M. Rogers et al., Interplay between partner and ligand facilitates the folding andbinding of an intrinsically disordered protein. Proc. Natl. Acad. Sci. U.S.A. 111,15420–15425 (2014).

18. M. D. Crabtree, C. A. T. F. Mendonça, Q. R. Bubb, J. Clarke, Folding and bindingpathways of BH3-only proteins are encoded within their intrinsically disordered se-quence, not templated by partner proteins. J. Biol. Chem. 293, 9718–9723 (2018).

19. T. Sugawara, K. Kuwajima, S. Sugai, Folding of staphylococcal nuclease A studied byequilibrium and kinetic circular dichroism spectra. Biochemistry 30, 2698–2706 (1991).

20. T. Ikura, G. P. Tsurupa, K. Kuwajima, Kinetic folding and cis/trans prolyl isomerizationof staphylococcal nuclease. A study by stopped-flow absorption, stopped-flow circulardichroism, and molecular dynamics simulations. Biochemistry 36, 6529–6538 (1997).

21. W. F. Walkenhorst, S. M. Green, H. Roder, Kinetic evidence for folding and unfoldingintermediates in staphylococcal nuclease. Biochemistry 36, 5795–5805 (1997).

22. V. N. Uversky et al., Anion-induced folding of staphylococcal nuclease: Character-ization of multiple equilibrium partially folded intermediates. J. Mol. Biol. 278,879–894 (1998).

23. W. F. Walkenhorst, J. A. Edwards, J. L. Markley, H. Roder, Early formation of a betahairpin during folding of staphylococcal nuclease H124L as detected by pulsed hy-drogen exchange. Protein Sci. 11, 82–91 (2002).

24. K. Maki, H. Cheng, D. A. Dolgikh, M. C. Shastry, H. Roder, Early events during foldingof wild-type staphylococcal nuclease and a single-tryptophan variant studied by ul-trarapid mixing. J. Mol. Biol. 338, 383–400 (2004).

25. K. Maki, H. Cheng, D. A. Dolgikh, H. Roder, Folding kinetics of staphylococcal nucleasestudied by tryptophan engineering and rapid mixing methods. J. Mol. Biol. 368,244–255 (2007).

26. M. Onitsuka, H. Kamikubo, Y. Yamazaki, M. Kataoka, Mechanism of induced folding:Both folding before binding and binding before folding can be realized in staphy-lococcal nuclease mutants. Proteins 72, 837–847 (2008).

27. T. Mizukami, M. Xu, H. Cheng, H. Roder, K. Maki, Nonuniform chain collapse duringearly stages of staphylococcal nuclease folding detected by fluorescence resonanceenergy transfer and ultrarapid mixing methods. Protein Sci. 22, 1336–1348 (2013).

28. P. J. Loll, E. E. Lattman, The crystal structure of the ternary complex of staphylococcalnuclease, Ca2+, and the inhibitor pdTp, refined at 1.65 A. Proteins 5, 183–201 (1989).

29. C. M. Jones et al., Fast events in protein folding initiated by nanosecond laser pho-tolysis. Proc. Natl. Acad. Sci. U.S.A. 90, 11860–11864 (1993).

Mizukami et al. PNAS | August 18, 2020 | vol. 117 | no. 33 | 19961

BIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

Dow

nloa

ded

by g

uest

on

Dec

embe

r 30

, 202

1

30. S. G. Itoh, H. Okumura, Replica-permutation method with the suwa-todo algorithmbeyond the replica-exchange method. J. Chem. Theory Comput. 9, 570–581 (2013).

31. S. G. Itoh, H. Okumura, Hamiltonian replica-permutation method and its applicationsto an alanine dipeptide and amyloid-β(29-42) peptides. J. Comput. Chem. 34,2493–2497 (2013).

32. K. Hukushima, K. Nemoto, Exchange Monte Carlo method and application to spinglass simulations. J. Phys. Soc. Jpn. 65, 1604–1608 (1996).

33. Y. Sugita, Y. Okamoto, Replica-exchange molecular dynamics method for proteinfolding. Chem. Phys. Lett. 314, 141–151 (1999).

34. H. Suwa, S. Todo, Markov chain Monte Carlo method without detailed balance. Phys.Rev. Lett. 105, 120603 (2010).

35. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, Equation ofstate calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953).

36. S. G. Itoh, H. Okumura, Oligomer formation of amyloid-β(29-42) from its monomersusing the Hamiltonian replica-permutation molecular dynamics simulation. J. Phys.Chem. B 120, 6555–6561 (2016).

37. M. Yamauchi, H. Okumura, Development of isothermal-isobaric replica-permutationmethod for molecular dynamics and Monte Carlo simulations and its application toreveal temperature and pressure dependence of folded, misfolded, and unfoldedstates of chignolin. J. Chem. Phys. 147, 184107 (2017).

38. M. Yamauchi, H. Okumura, Replica sub-permutation method for molecular dynamicsand Monte Carlo simulations. J. Comput. Chem. 40, 2694–2711 (2019).

39. F. Paul, T. R. Weikl, How to distinguish conformational selection and induced fit basedon chemical relaxation rates. PLoS Comput. Biol. 12, e1005067 (2016).

40. S. Sen, J. B. Udgaonkar, Binding-induced folding under unfolding conditions:Switching between induced fit and conformational selection mechanisms. J. Biol.Chem. 294, 16942–16952 (2019).

41. T. Mizukami, K. Maki, H. Roder, Urea denatured staphylococcal nuclease BiologicalMagnetic Resonance Data Bank. http://www.bmrb.wisc.edu/data_library/summary/index.php?bmrbId=50301. Deposited 29 May 2020.

42. T. Mizukami, Y. Sakuma, K. Maki, Statistical mechanical model for pH-induced proteinfolding: Application to apomyoglobin. J. Phys. Chem. B 120, 8970–8986 (2016).

43. K. K. Lee, C. A. Fitch, J. T. Lecomte, B. García-Moreno E, Electrostatic effects in highlycharged proteins: Salt sensitivity of pKa values of histidines in staphylococcal nucle-ase. Biochemistry 41, 5656–5667 (2002).

44. C. A. Castañeda et al., Molecular determinants of the pKa values of Asp and Gluresidues in staphylococcal nuclease. Proteins 77, 570–588 (2009).

45. S. T. Whitten, B. García-Moreno E, pH dependence of stability of staphylococcal nu-clease: evidence of substantial electrostatic interactions in the denatured state. Bio-chemistry 39, 14292–14304 (2000).

46. D. A. Torchia, S. W. Sparks, A. Bax, Staphylococcal nuclease: Sequential assignmentsand solution structure. Biochemistry 28, 5509–5524 (1989).

47. D. J. Weber et al., NMR docking of a substrate into the X-ray structure of staphylo-coccal nuclease. Proteins 13, 275–287 (1992).

48. J. Wang et al., Solution structures of staphylococcal nuclease from multidimensional,multinuclear NMR: nuclease-H124L and its ternary complex with Ca2+ and thymidine-3′,5′-bisphosphate. J. Biomol. NMR 10, 143–164 (1997).

49. S. E. Jackson, N. elMasry, A. R. Fersht, Structure of the hydrophobic core in thetransition state for folding of chymotrypsin inhibitor 2: A critical test of the proteinengineering method of analysis. Biochemistry 32, 11270–11278 (1993).

50. L. S. Itzhaki, D. E. Otzen, A. R. Fersht, The structure of the transition state for foldingof chymotrypsin inhibitor 2 analysed by protein engineering methods: Evidence for anucleation-condensation mechanism for protein folding. J. Mol. Biol. 254, 260–288(1995).

51. K. Maki, T. Ikura, T. Hayano, N. Takahashi, K. Kuwajima, Effects of proline mutationson the folding of staphylococcal nuclease. Biochemistry 38, 2213–2223 (1999).

52. H. Okumura, Temperature and pressure denaturation of chignolin: Folding and un-folding simulation by multibaric-multithermal molecular dynamics method. Proteins80, 2397–2416 (2012).

19962 | www.pnas.org/cgi/doi/10.1073/pnas.1914349117 Mizukami et al.

Dow

nloa

ded

by g

uest

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embe

r 30

, 202

1