Spectral Diffusion Experiment with a Denatured Protein

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Spectral Diffusion Experiment with a Denatured Protein
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  Spectral Diffusion Experiment with a Denatured Protein Vladimir V. Ponkratov and Josef Friedrich* Physik-Department and Lehrstuhl fu¨r Physik Weihenstephan, Technische Uni V  ersita¨t Mu¨nchen, D-85350 Freising, Germany Dejan Markovic † and Hugo Scheer  Department Biologie I  s  Bereich Botanik, Menzinger Strausse 67, D-80638 Mu¨nchen, Germany Jane M. Vanderkooi  Department of Biochemistry and Biophysics, Uni V  ersity of Pennsyl V  ania, Philadelphia, Pennsyl V  ania 19104 Recei V  ed: July 3, 2003; In Final Form: October 20, 2003 Spectral diffusion broadening of cytochrome  c  carrying the free-base analogue of heme is investigated in itsunfolded state and compared with the corresponding broadening in the native state. Spectral diffusion ismuch larger in the unfolded state, in comparison to the native state. Interestingly, the time law that governsspectral diffusion changes as the aging time increases, from a power-law behavior in the native state to anapparent logarithmic behavior in the unfolded state. 1. Introduction Proteins do show features of randomness. On nanoscopicscales and below, there is a distribution of structures and, as aconsequence, there is a distribution of energies, barriers, foldingrates, folding trajectories, etc. 1,2 Accordingly, on the proper timescales, a single protein may be considered as an “individual”that is well-distinguished from another protein of the samespecies, e.g., by a different energy of the native state, a differentthermal stability, a different folding rate, etc. This situation isdescribed in a most transparent fashion within the concept of an energy landscape. 3,4 Within such a framework, it is clearthat the native state, for example, consists of many structuralsubstates in all of which the protein is, at least in principle,functioning. Apart from the ensemble of native states, a proteinhas a much larger ensemble of denatured states. Within thisensemble, there are characteristic sets of substates e.g., the so-called molten globule. 5 Although the molten globule belongsto the ensemble of denatured states, its substates are, in regardto their structural features, similar to those of the native state. 6,7 Another characteristic set of states within the ensemble of denatured states is the random coil. The associated substatesare structurally very dissimilar from the native state and,accordingly, comprise a much larger region in structural phasespace. 8 An immediate consequence of this distribution of structuresis structural dynamics. At sufficiently high temperature, this ismost obvious: The protein can cross structural barriers bythermal activation, 9,10 including a transfer from the ensembleof native states to the ensemble of denatured states. 11,12 Evenat extremely low temperatures, structural dynamics are notforbidden and do occur, for instance, through tunneling betweenclosely related structures. 13 Activated processes also may occur,as long as  V   /  k  B T  , which is the ratio of the structural barrier  V  to the thermal energy  k  B T  , is in an appropriate range. 14,15 Atlow temperatures, this motion in structural phase space can beprecisely measured with spectral diffusion experiments. 16 Inthese experiments, the line width of an optical transition of amarker molecule is measured as a function of time. Wheneverthe protein undergoes a structural change, the frequency of themarker molecule changes. The frequency changes due tostructural relaxation are small; therefore, the associated spectral jumps can only be observed if the monitoring lines aresufficiently sharp. In this respect, hole-burning techniques offerseveral advantages. On one hand, the lines are very narrow,with a width that is similar to the homogeneous line width. Onthe other hand, holes may live almost forever, which allowseven the very slow dynamics, which occur on the scale of daysor longer, to be investigated. As a consequence, structural jumpscan be observed as long as they produce frequency jumps onthe order of the homogeneous line width. Typically, at 4 K, therespective frequency scale is on the order of a gigahertz. In anensemble experiment, these frequency jumps manifest them-selves as a broadening of the burnt-in hole. This broadening isdependent on the temperature of the sample. The homogeneousline width is strongly temperature dependent; 17,18 therefore, thecontribution to the hole from spectral diffusion can be measuredmost precisely at liquid helium temperatures. 19 Broadening of a spectral hole due to spectral diffusion processes reflects thedynamics of structural fluctuation and relaxation processes thatoccur in disordered systems such as glasses, polymers, and alsoproteins. These systems are characterized by a broad distributionof rates. 20 This distribution of rates reflects features of the energylandscape and the associated structural phase space, which isthe objective of our present investigation.Spectral diffusion was srcinally discovered in glasses. 21 Indeed, glasses are also characterized by an energy landscape,however, obviously by one that differs significantly from thatof proteins. The protein landscape has the shape of a narrow * Author to whom correspondence should be addressed. E-mail:J.Friedrich@lrz.tu-muenchen.de. † Current address: University of Nish, Faculty of Technology, 16000Leskovac, Serbia (Yugoslavia). 1109  J. Phys. Chem. B  2004,  108,  1109 - 111410.1021/jp0359135 CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 12/23/2003  funnel, where the average gradient toward the native state issteep, which is a necessary requirement for a high driving forcetoward the native state. 5 A narrow funnel structure of the free-energy landscape implies a limited region in structural phasespace where the protein can move around. In contrast, a glassdoes not have a distinguished set of states that is similar to thatof a protein and, accordingly, has no pronounced funnelstructure. As a consequence, the area in structural phase spacespanned by the accessible states is much larger, as is reflectedin a significantly stronger spectral diffusion broadening as wellas in a different time dependence. 22,34 In this paper, it is our goal to (i) investigate the spectraldiffusion dynamics of a protein, namely cytochrome  c  carryingthe free base analogue of heme, in its unfolded state and (ii)compare the results with the corresponding behavior of the sameprotein in its native state. We have investigated the spectraldiffusion dynamics in the native state previously under differentexperimental conditions. 28,33 In the unfolded state, the proteinattains most probably a random coil structure. Consequently,the number of accessible structural states is larger than that inthe native state. This structural heterogeneity should be reflectedin spectral diffusion broadening. Whether this is true or not isone goal of the present investigation. A second goal is todetermine whether the time law of the structural dynamicschanges in the random coil structure, as compared to the nativestructure. In most cases, it has been found that structuraldynamics in the native state are governed by a power law. 23 Incontrast, the corresponding dynamics in glasses follow alogarithmic time law. 21 We consider the time laws that governspectral diffusion to be interesting features, because they mayshed light on the dynamics at higher temperatures, 9 where thebiologically important processes occur. 2. Experimental SectionMaterials.  Horse heart cytochrome  c  (Fe - Cc) was fromSigma, and cytochrome  c  carrying the free base analogue of heme (H 2 - Cc) was prepared as described previously by theextraction of iron from the chromophore. 24 Guanidiniumhydrochloride (Gua, from Sigma) and urea (Schwarz-Mann)were of ultrapure grade; all other chemicals and solvents werereagent grade. Sample Preparation and Stock Solutions.  For the unfoldingexperiments, Fe - Cc was dissolved in potassium phosphatebuffer (50 mM, pH 7.3) and H 2 - Cc was dissolved in  tris -HClbuffer (10 mM, pH 8.3) at an optical density of 0.6 in a 1 cmcuvette at 280 nm. These solutions were prepared fresh everyday. Gua was dissolved in a 2:1 (v/v) mixture of glycerol andpotassium phosphate buffer (50 mM, pH 7.3, for Fe - Cc) or a1:1 (v/v) mixture of glycerol and  tris -HCl (10 mM, pH 8.3, forH 2 - Cc). For the spectral diffusion experiments, 6 M Gua wasdissolved in a 2:1 (v/v) mixture of glycerol and potassiumphosphate buffer. H 2 - Cc was added to this solution, resultingin a final concentration of  ∼ 10 mg/mL. To avoid protonation,the pH was adjusted to  ∼ 7 via the addition of KOH (1 M).This mixture was sealed in a homemade cuvette with a pathlength of 6 mm. The optical density in the spectral range wherethe hole-burning experiments were performed (615 nm) was0.3 at liquid helium temperature. Unfolding Experiments.  Unfolding of H 2 - Cc was inducedby treatment with increasing concentrations of Gua. 25,26 Justbefore the measurements, appropriate aliquots of the respectiveprotein stock solution s the Gua solution and a Gua - freeglycerol/buffer solution s were mixed. The circular dichroism(CD) spectra (using Jobin-Yvon circular dichrograph V) wererecorded immediately after mixing in a range of 208 - 250 nmusing a 1-mm cuvette. From each spectrum, the CD signal( ∆  A 248  -  ∆  A 224 ) was extracted. 27 In Figure 1, this quantity isplotted on a relative scale against the Gua concentration. Asimilar series of experiments was conducted with urea as thedenaturant, using a maximum concentration of 10 M. Spectral Diffusion Experiment.  The spectral diffusionexperiments were performed at a temperature of 4.2 K. Thesealed sample was cooled to 4.2 K within 20 min. Hole burningwas performed with a dye ring laser (Coherent, model CW 899-21) pumped at 532 nm by a frequency-doubled neodymium:vanadate laser (Verdi). The width of the laser line was < 1 MHz.Power levels for burning were 30 - 60  µ W/cm 2 . To avoidreburning, the reading signal was reduced by more than 3 ordersof magnitude. The holes were monitored in the transmissionmode and processed by a computer. In our experiment, we varytwo time parameters: the aging time ( t  a ) and the waiting time( t  w ). The aging time is defined as the width of the time windowbetween cooling and hole burning, and the waiting time isdefined as the width of the time window between hole burningand hole reading. Several holes were burned at different agingtimes varying from  t  a  )  1 to  t  a  )  192 h. The hole broadeningwas measured over a period of approximately two weeks. Thetime resolution of the experiment, as defined by the time neededto burn and read a hole, was a couple of minutes. Data Evaluation.  The quantitative evaluation of a spectraldiffusion experiment relies on a certain assumption about theshape of the spectral diffusion kernel, that a portion of the lineshape that causes the time evolution of the hole within theexperimental time window is set by the waiting time  t  w . Wehave been analyzing spectral diffusion in proteins within theframework of a conformational diffusion model, which impliesa Gaussian line shape of the respective kernel. To evaluate allthe experiments with the same procedure, we fitted Voigtiansto the measured hole shapes and extracted the associatedGaussian kernel. The Lorentzian component of this Voigtiancan be considered to be an empirical fit to the hole when it ismeasured for the first time at the beginning of the each waiting Figure 1.  Circular dichroism (CD) signal  ∆  A  at 224 nm (in arbitraryunits), as a function of concentration of the denaturing agent, guani-dinium hydrochloride (Gua). Data are normalized to the CD signal atzero concentration of Gua. The respective data for H 2 - Cc (Figure 1a)are compared with those for Fe - Cc (Figure 1b). The respectivestructures of the two chromophores are shown in the insets. The fulllines are guides to the eye. 1110  J. Phys. Chem. B, Vol. 108, No. 3, 2004  Ponkratov et al.  time experiment. In all cases, the hole immediately after burningwas well fit by a Lorentzian. Note that spectral diffusionprocesses may occur on time scales that range from nanosecondsto practically infinity. Our experimental time window covers just a small range, extending from minutes to several days.Hence, the initial shape of the hole may already contain aspectral diffusion kernel, which, however, does not influenceour evaluation procedure, because it is incorporated into theinitial hole shape that is deconvoluted from the experimentallymeasured dependence on  t  w . For clarity, we mention that, forall the holes in a given  t  w  experiment, the initial empiricalLorentzian line shape was kept constant.We call the standard deviation  σ   of the Gaussian kernel thespectral diffusion width. This is the quantity in which we areinterested. We stress that the Gaussian line shape assumptionmight not reflect the proper physics for the unfolded protein.In the unfolded state, the chromophore may become exposedto the solvent; hence, glasslike excitations (two-level systems,TLS), might contribute to spectral diffusion and change thefeatures of the respective line shape. However, we did notchange the evaluation procedure, so data are treated in the samefashion. This is mandatory for comparative experiments. Notethat, within the restrictions of our evaluation procedure, the fitsto the data are unique within the error margins. For  t  w  valueslarger than  ∼ 10 3 min, the error bars barely exceed the size of the data point symbol in the graphs. At shorter times, they arelarger, because the time-dependent component that we extractfrom the line shape becomes smaller.In regard to the inhomogeneously broadened spectrum of theunfolded protein, we decomposed it into a minimum numberof Gaussians. It is clear that such a procedure carries somearbitrariness; however, it should be good enough for anestimation of the inhomogeneous bandwidths involved. The lineshape of the native protein, too, is a superposition of severalcomponents that we associate with the tautomeric states of theinner-ring protons. However, the features of the central com-ponent are sufficiently well-separated from the others, so thatits Gaussian shape could be independently fitted. 33 3. Results Cytochrome  c  is largely  R  -helical; hence, the far-UV CDsignal is expected to decay as the protein unfolds. Theexperiments show that a concentration of the denaturing agentas high as 4 M is needed for complete unfolding of Fe - Cc andeven 6 M for H 2 - Cc. Both H 2 - Cc and the unmodified protein(Fe - Cc) show a sigmoidal decrease of the CD signal as theconcentration increases, reaching the same final plateau nearzero CD at Gua concentrations of   > 5 M (see Figure 1).However, for H 2 - Cc, a 50% decrease in the CD signal isalready attained at a concentration of 2.4 M, as compared to2.8 M for Fe - Cc. The cooperativity of the denaturing transition,as reflected in the slope of the CD signal in the transition region,is much lower for H 2 - Cc than for Fe - Cc. The major differencebetween the two samples is the presence and absence, respec-tively, of the central Fe atom (see structure insets in Figure 1);therefore, it seems that coordination of the latter with the proteinincreases stability and cooperativity, most likely by decreasingsample heterogeneity. A similar behavior has been found formyoglobin, where a variety of chromophores can be inserted.These results will be published elsewhere. Apart from theunfolding experiments with Gua, we also performed controlexperiments with urea. Unfolding with this reagent was nevercomplete, not even at the highest accessible concentrations ( ∼ 10M). Therefore, the spectral diffusion experiment was done withGua. Also, the low-temperature spectra in the unfolded statewere somewhat different: The peak at 16 400 cm - 1 (Figure 2a)was absent in the urea-denatured sample. From a comparisonof the spectra in the two different denaturing agents, it seemedthat the dominant transition in the denatured state is around16 250 cm - 1 . Accordingly, we conducted our spectral diffusionexperiments in a narrow range around this frequency.Figure 2 shows the inhomogeneous spectra of H 2 - Cc in theunfolded state (Figure 2a) and in the native state (Figure 2b). 28 We observe a series of interesting features. Compared to thenative state, the spectrum becomes more complex. First, a bandat around 15 700 cm - 1 grows; this band is only weakly indicatedin the native state. We observed that the intensity of this bandincreases as time increases at room temperature and that it growsmuch faster in the unfolded state than in the folded state. Onthe basis of this observation and on the red shift of the band,we assign it to the formation of an aggregated species. Second,the band at ∼ 16 250 cm - 1 strongly changes shape and becomesmuch broader. Already in the native state, this band is composedof at least three subbands, which may srcinate from thetautomeric states of the inner-ring protons of the free baseporphyrin. Obviously, these states shift and broaden as theprotein becomes unfolded. The spectral diffusion experimentswere performed in a narrow frequency range of   ∼ 50 cm - 1 around the positions marked in Figure 2 with an arrow.Figure 3 shows the spectral diffusion behavior of the unfoldedprotein, which is compared to the respective behavior of theprotein in the native state in Figure 4. 28 Two distinct featurescatch the eye. First, broadening in the unfolded protein (6 MGua) is significantly larger (approximately twice as large as thatin the native state). Second, in both states, spectral diffusionbroadening is subject to aging. Aging is manifested by theslowing of spectral diffusion. In the native state, aging doesnot change the time law of this broadening process in asignificant fashion. At all aging times (up to 120 h) at whichwe performed experiments, spectral diffusion is governed by a Figure 2.  Inhomogeneous long-wavelength absorption for H 2 - Cc (a)in the chemically unfolded state (6 M Gua) and (b) in the native state.The spectrum of the denatured protein clearly is composed of severalcomponents that belong to different substates, such as, for example,conformers. The arrow indicates the spectral region where hole burningwas performed. Spectral Diffusion with a Denatured Protein  J. Phys. Chem. B, Vol. 108, No. 3, 2004  1111  power law. 28 The respective exponent is 0.29  (  0.03. In theunfolded state, however, the spectral diffusion behavior changessignificantly as the aging time  t  a  progresses. At short agingtimes, the time law is still well-described by a power law, similarto that of the native state. The corresponding exponent is 0.26 (  0.01. As the aging time increases, spectral diffusion broad-ening slows dramatically for long waiting times. We compareaging times of 91 h for the unfolded protein with 72 and 120 hfor the folded protein. 28 The experiments with the unfoldedprotein at  t  a ) 192 h demonstrate that an additional increase inthe aging time does not further change the peculiar deviationfrom the power law. The 192 h data almost fall on top of the91 h data, as is very clearly seen in the linear - logarithmicrepresentation in Figure 3b. Within the 3 orders of magnitudeof our experimental time window, the time evolution can bewell fit by assuming log  t  w  behavior. Because we cannot offeran interpretation of this behavior, we consider the logarithmicfit curve to be a guide for the eye, rather than a definitivestatement. However, the main result s that the time evolutionchanges with aging time in the unfolded protein s is definitive. 4. DiscussionAspects of Spectral Diffusion Physics.  Spectral diffusiondynamics are quite intimately associated with structural disorder.Structural disorder, on the other hand, results in an energylandscape that is characterized by structural traps with a broaddistribution of barriers separating these traps. The dynamics of a system in a rough energy landscape may be characterized bytwo types of processes, namely, fluctuations that are associatedwith a local equilibrium and aging processes. The latter aretypical nonequilibrium processes and are a characteristic featureof deeply frozen structurally disordered materials. Agingprocesses are indicative of the fact that the system underinvestigation has become trapped for some time in a local energyminimum during cooling from which it may eventually getexpelled, just to become trapped again in another localminimum. 29 They are a consequence of the fact that the systemmoves toward its global energy minimum. At sufficiently lowtemperatures, these processes become extremely slow. If theresidence time in a local structural trap is long enough, a localthermodynamic equilibrium may be established between struc-tural states accessible at the experimental bath temperature.Accordingly, the relaxation processes connected with sampleaging are accompanied by structural fluctuation processes. In aseries of spectral diffusion experiments with various deeplyfrozen proteins, we have investigated the related structuraldynamics. 28,30 The main outcome of these experiments can besummarized: Structural dynamics at low temperatures are soslow that one can safely characterize proteins as nonergodicsystems. The spectral diffusion width is governed by a powerlaw in time whose exponent varies in a narrow range of  ∼ 0.25.This behavior is contrary to that of glasses, where the spectraldiffusion width is governed by logarithmic time laws. In allcases where proteins could be compared with glasses, thespectral diffusion width was significantly smaller for pro-teins. 22 It is a major goal of any model of spectral diffusion to relatethe spectral diffusion width to the characteristic features of theenergy landscape. In glasses, for example, this landscape isrepresented by almost-degenerate, localized two-level systems(the TLSs) that represent the two lowest states in a double wellpotential. The spectral diffusion width is proportional to thenumber of TLSs that have changed their state during a certainwaiting time  t  w . This is directly related to the change of conformational entropy ( ∆ S  ), which the system experiencesduring  t  w . Along these lines of reasoning, one can say that themeasured width is related to the area in structural phase spacethat the system has explored during  t  w .In proteins, spectral diffusion dynamics have been directlyconnected with conformational diffusion in phase space, which Figure 3.  Time evolution of the line width of spectral holes burned atvarious aging times ( t  a ). The behavior of the unfolded free-basechromoprotein (H 2 - Cc, 6 M Gua) is shown: Figure 3a shows a log - log plot, whereas Figure 3b shows the same data in a linear - logarithmicrepresentation. This representation clearly demonstrates the strikingchange in the time evolution of the spectral holes as  t  a  increases. Figure 4.  Comparative data of the spectral diffusion width, as afunction of the waiting time  t  w  of the native free base chromoprotein(H 2 - Cc) 28 (a) in a log - log representation and (b) in a linear - logarithmic representation. Note that (i) the spectral diffusion width( σ  ) is significantly smaller than that of the unfolded protein (see Figure3), and (ii) the power-law behavior of the time evolution does notchange as the aging times  t  a  increase. The power-law exponent is R) 0.29  (  0.03. 1112  J. Phys. Chem. B, Vol. 108, No. 3, 2004  Ponkratov et al.  is a very different approach, in comparison to the glass case. 30 Hence, in this case, the relation between the explored area instructural phase space and the line width is even more obviousbecause the width scales directly with the mean square displace-ment  〈  x 2 〉  in conformation space. If one assumes that confor-mational dynamics are governed by a random walk along a one-dimensional (1D) trajectory in conformation space, the spectraldiffusion width scales with the end-to-end distance, which itself scales with  t  w1/4 , in agreement with the experiments. 31 Thestructure of a protein is well-defined but not as well as thestructure of a crystal. Low temperature  〈  x 2 〉  values, for instance,are much larger than those in crystals. 32 Hence, on length scalesat or below ∼ 0.1 Å, the average structure is much less defined.Consequently, structural fluctuation and relaxation processes dooccur and can be monitored via spectral diffusion experiments.However, because of the narrow funnel structure of the energylandscape of the native protein, the processes must be muchmore restricted, in comparison to systems without such a funnelstructure. Spectral Diffusion and Protein Unfolding.  The results inFigure 3 definitely show that the protein in the unfolded stateis subject to significantly enhanced spectral diffusion dynamics.We stress that, in cytochrome  c , the chromophore is covalentlybound to the polypeptide chain, unlike, for instance, that inmyoglobin. Therefore, unfolding does not mean that thechromophore just diffuses into the solvent environment. Anenhancement of the spectral diffusion dynamics may have tworeasons: (i) enhanced structural dynamics, because the acces-sible phase space has been increased (as previously discussed),and/or (ii) an enhanced coupling of the chromophore to thesolvent environment. After unfolding, the concentration of thedenaturing agent is high, and, hence, we cannot definitivelyexclude the possibility that the chromophore solvent couplingmay be influenced. However, for the following reasons, we donot consider such a possibility as the main factor for thetremendous increase in spectral diffusion broadening. First,because the chromophore is still covalently bound to thepolypeptide chain, its nearby solvent environment is stillsignificantly determined by the amino acid residues. Second, adoubling of the chromophore solvent interaction due to thepresence of Gua seems to be, by far, too large, considering thefact that the solvent shift does not change at all in the unfoldedstate (see Figure 2). On the other hand, the inhomogeneous linewidth changes strongly, which is consistent with the assumptionof a larger phase space. Along these lines of reasoning, weattribute at least a major portion of the enhanced spectraldiffusion broadening to the breaking up of the native structureand the concomitant transition from a folded protein to a randomcoil. In the random coil state, structural dynamics are much lessrestricted; the accessible structural phase space is larger, andthis is obviously reflected in the enhanced spectral diffusionbroadening. Time Evolution of the Hole Width.  An interesting observa-tion is the fact that the dependence of the hole width on waitingtime  t  w  changes in a qualitative fashion as the aging time  t  a increases. As stressed previously, the time evolution of the holewidth in native proteins is governed by a power law in time,according to various experiments that have been performed todate. The srcin of this power law can be seen in an anomalousstructural diffusion process in conformation space. Quite incontrast to the protein case, spectral diffusion in randomsolvents, similar to glasses or polymers, is governed bylogarithmic time laws. The srcin of the logarithmic behaviormay be, as in glasses, the occurrence of TLS whose relaxationrates are distributed over many orders of magnitude, becauseof the random structure of the material.What we observe here is really very surprising. The first dataset of our spectral diffusion experiments at a short aging time t  a  is well-described by a power law in  t  w . The exponent is notvery different from that which is observed in the native state(see Figure 3a), irrespective of the fact that the magnitude of the broadening is tremendously increased. Although the powerlaw is retained in the native state data as the sample ages, itchanges gradually to a different behavior in the unfolded state.We stress that we can only speculate on the underlying reasonsfor this behavior. It seems that irregular behavior is observed,in comparison to that of the native state, which is responsiblefor this observation. This irregular behavior could lead to a timedependence of the power law exponent  R  , in the sense that itslows as a function of time so that the slope becomes smalleras time increases. In regard to the physics behind such behavior,it would mean that the dispersion of fluctuation rates involvedwould grow with time. Another possibility could srcinate inthe TLS of the host glass. Because protein unfolding exposesthe chromophore to the solvent, these TLSs might becomeimportant as the relaxation of the polypeptide chains slows asthe aging time  t  a  increases.Currently, we cannot really solve the puzzle as to whatgoverns the breakdown of the power-law behavior. Moreexperiments are required to reach more-definitive conclusions. 5. Conclusions We investigated spectral diffusion in a protein in thechemically unfolded state and compared it with results fromearlier experiments on the same protein in the native state.Unfolding increases the inhomogeneous broadening tremen-dously, and it also increases spectral diffusion. We related thisobservation to an increase in the accessible structural phasespace in the unfolded state. A most interesting observation isthe fact that the qualitative behavior of the time evolution of the hole width changes in the unfolded state from a power lawat short aging times to a significantly slower time dependence.We have discussed possible reasons; however, for an unambigu-ous interpretation, more experiments are needed. Acknowledgment.  The authors gratefully acknowledgesupport from the DFG (SFB 533, A1, and B5) and from theFonds der Chemischen Industrie. D.M. was supported byDAAD. References and Notes (1) Frauenfelder, H.; Parak, F.; Young, R.  Annu. Re V  . Biophys. Biophys.Chem.  1988 ,  17  , 451.(2) Dill, K. A.; Chan, H. S.  Nat. Struct. Biol.  1997 ,  4 , 10.(3) Frauenfelder, H.; Sligar, S. G.; Wolynes, P. G.  Science  1991 ,  254 ,1598.(4) Frauenfelder, H.; Leeson, D. T.  Nat. Struct. Biol.  1998 ,  5 , 757.(5) Wolynes, P. G.; Onuchic, J. N.; Thirumalai, D.  Science  1995 ,  267  ,1619.(6) Silva, J. L.; Fognel, D.; Royer, C. A.  Trends Biochem. Sci.  2002 , 26  , 612.(7) Nash, D. P.; Jonas, J.  Biochemistry  1997 ,  36  , 14375.(8) Dobson, C. M.; Sali, A.; Karplus, M.  Angew. Chem.  1998 ,  110 ,908.(9) Shibata, Y.; Kurita, A.; Kushida, T.  Biochemistry  1999 ,  38  , 1789.(10) Lim, M.; Jackson, T. A.; Anfinrud, P. A.  Proc. Natl. Acad. Sci.U.S.A.  1993 ,  90 , 8302.(11) Lesch, H.; Stadlbauer H.; Friedrich, J.; Vanderkooi, J. M.  Biophys. J.  2002 ,  82 , 1644.(12) Privalov, P.  Ad  V  . Protein Chem.  1979 ,  33 , 167.(13) Fritsch, K. D.; Friedrich, J.  Physica D  1997 ,  107  , 218.(14) Ko¨hler W.; Friedrich, J.; Scheer, H.  Phys. Re V  . A  1988 ,  37  , 660. Spectral Diffusion with a Denatured Protein  J. Phys. Chem. B, Vol. 108, No. 3, 2004  1113
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