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University of Groningen

Exploring protein energy landscapesThorn Leeson, Daniël; Wiersma, D. A.

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Publication date:1997

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'SD ' '(tw)&'(t0w)

SPECTRAL DIFFUSION IN HEME PROTEINS

47

(5.1)

5SPECTRAL DIFFUSION IN HEME PROTEINS

5.1 Introduction

In this chapter, the results of spectral diffusion experiments on Zn-cytochrome cand Zn-myoglobin are presented. Based on these results, a detailed image of the low-energypart of the potential energy surface of these proteins will be constructed. Furthermore, therelation between the low-energy part and the overall energy landscape will be discussed. Aswas recently reported, [Tho97] a full interpretation of the 3PSE-results cannot be givenwithout specifically taking into consideration the spectral hole burning experiments ofFritsch et al. [Fri96] Therefore, these results will be included in the discussion, as well as thehole burning results of Shibata et al. [Shi96]

5.2 Spectral diffusion in Zn-cytochrome c and Zn-myoglobin below 2.0 K

Although most of the work presented here was done on Zn-myoglobin, the firstexperiments were performed on Zn-cytochrome c. The waiting time dependence of the linewidth was studied at 1.8 K. The results are displayed in Fig. 5.1. Plotted is

which is the increase of the line width relative to its value at the shortest waiting time thatwas measured (in this case t = 12 ns). Although the scatter in the data is substantial, it canw

0

be clearly seen that the line broadening is a stepwise function of waiting time. The line widthincreases between 10 ns and 1 µs, after which it remains constant until approximately0.1 ms. At this point, the line width starts to increase again, but appears to level off in thems-region. From this point on, the discussion will focus on the second contribution to the linebroadening, i.e. from 0.1 ms onwards. The line broadening on the faster time scales will be

EXPLORING PROTEIN ENERGY LANDSCAPES

48

Figure 5.1 Dependence of the line width on waiting time for Zn-cytochrome c, recorded at1.8 K, and for Zn-myoglobin, recorded at 1.9 K. (Left hand side) The solid lines through thedata are fits to Eq. 3.15, using the distributions of relaxation rates, given by Eq. 5.2, that aredisplayed on the right hand side. The fit parameters were: Cyt c: T = 63 MHz, A = 10 s ,6.2 -1

R = 10 s , F = 0.25 (fixed parameter), C = 0.23 GHz. Mb: T = 55 MHz, A = 10 s ,03.1 -1 6.4 -1

R = 10 s , F = 0.25 (fixed parameter), C = 0.14 Ghz.01.4 -1

dealt with in chapter 6. The leveling off of the line width in the ms-region will be a frequentlyreappearing motive in the remainder of this chapter. Before further analyzing this result, onecan make a general phase space argument. In terms of the spectral fluctuations, the levelingoff of the line broadening implies that the accessible frequency space of each chromophoreis restricted. It corresponds to the situation where the time scale of the experiment is muchlonger than the time scale at which the chromophores explore this part of their frequencyspace. Because there is a relation between the resonance frequency of the optical centre andthe conformation of the protein, the leveling off implies that the protein is exploring arestricted part of its conformational phase space and is doing so on a sharply defined timescale.

Figure 5.1 also shows the results of an experiment performed under almost identicalconditions on Zn-myoglobin. The chromophore and the solvent are the same for bothsystems. However, for Zn-myoglobin the temperature was slightly higher: 1.9 K. Apart fromthe fact that the overall increase of the line width is smaller, Zn-myoglobin exhibits behavior

P(R)R ' T for A < logR % Cexp&ln (R/R0

2F

2


49

(5.2)

very similar to that of Zn-cytochrome c. The line width initially increases, before reachinga plateau at approximately 1 µs. However, in the case of Zn-myoglobin the plateau reachesmuch further, only at around 1 ms does the line width start to increase again. The questionwhether the second contribution to the line broadening levels off, as it did forZn-cytochrome c, cannot be answered at this point, because the time window of theexperiment does not reach far enough. However, it will be demonstrated below that the linebroadening of Zn-cytochrome c and Zn-myoglobin most likely originate from a similar typeof relaxation mechanism. The comparison between Zn-cytochrome c and Zn-myoglobinprovides additional information, in the sense that the line broadening features observed atlonger waiting times can be safely attributed to protein fluctuations, as opposed to structuralrelaxation of the solvent. Had they been induced by the solvent, identical behavior wouldhave been expected for both proteins. Note that we cannot draw the same conclusion for theshort time scale broadening (see chapter 6).

Because no specific model is available to describe spectral diffusion induced by structuralrelaxation in proteins at cryogenic temperatures, we start off the analysis of the experimentalresults in terms of the sudden-jump model that was introduced in chapter 3. It should beemphasized that this is only a first attempt to analyze the data. By applying the sudden-jumpmodel we inherently assume that, similar to glasses, the relaxation phenomena in proteinsand the corresponding energy surface can be described by the two-level system model, which,although having been proposed in the recent literature, [Sin84, Zol91a, Kur95, Shi96,Rel96a, Rel96b] remains speculative. The solid lines through the data in Fig. 5.1 are fits toEq. 3.15, yielding the rate distributions of fluctuating perturbers that are displayed. Both thedata on Zn-cytochrome c and Zn-myoglobin can be fitted to a distribution of fluctuation ratescomprising two features, namely a hyperbolic function that cuts off around log R = 6.3 toaccount for the short time scale line broadening, and a sharp log-normal distribution [Jan86]to account for the line broadening in the ms-region. The exact fitting function is

Note that the sudden increase and subsequent leveling off of the line broadening ofZn-cytochrome c in the ms-region demands the narrow range of fluctuation rates. The exactwidth of the sharp feature is uncertain due to the scatter in the experimental data.Furthermore, it should be emphasized that the data on Zn-myoglobin, by itself, provideinsufficient evidence to assume that a narrow distribution also applies to this protein. Here,we only wish to demonstrate that the data on Zn-cytochrome c and Zn-myoglobin can beinterpreted within the same framework, and that the data on Zn-myoglobin is at leastconsistent with this picture. Further insight is provided in the next section.


50

Figure 5.2 Waiting time dependence of the line width of Zn-myoglobin between 1.7 and3.4 K. (Left hand side) The solid lines through the data are fits to Eq. 3.15, using thedistributions of fluctuation rates displayed on the right hand side.

5.3 Spectral diffusion in Zn-myoglobin between 1.7 and 3.4 K

To establish whether a narrow distribution of fluctuation rates also applies toZn-myoglobin, we performed a study of the temperature dependence of its spectral diffusionbehavior. The idea behind this experiment is straightforward. The rate of a particularfluctuation should increase with temperature, and therefore, by raising the temperature itshould be possible to shift a narrow feature of the fluctuation rate distribution. If thedistribution is as narrow as was assumed in the previous section, at sufficiently hightemperature, it will have shifted far enough into the direction of higher rates to observe theleveling off of the line broadening, analogous to Zn-cytochrome c. Figure 5.2 shows thewaiting time dependence of the line width of Zn-myoglobin in the region between 1 µs and

R0 ' Aexp(&E/kT)


51

(5.3)

Figure 5.3 Temperature dependence of the fluctuation rate, R , corresponding to the0position of the distribution displayed in Fig. 5.2. The solid line through the data is a fit toEq. 5.3 with A = 2 × 10 and E = 0.20 kJ mol .6 -1

100 ms, for temperatures between 1.7 and 3.4 K. At 1.7 K, no line broadening is observedwithin this time window. However, as was shown above, at 1.9 K there is an increase of theline width in the ms-region. As the temperature is further increased, the line broadening startsoff at a shorter waiting time and at 2.7 K it levels off in the ms-region. This means that theline broadening indeed occurs within a short time interval, but also that the time scale onwhich it occurs shifts with temperature. The solid lines in Fig. 5.2 are fits of the data to Eq.3.15, yielding a narrow distribution of fluctuation rates, as was also required for Zn-cytochrome c. In Fig. 5.3 the fluctuation rate, R , corresponding to the centre of the0distribution displayed in Fig. 5.2, is plotted as a function of temperature. The data fit wellto a simple activation law, i.e.

A fit of the data to Eq. 5.3 yields a barrier height, E, of 0.20 kJ mol , and a preexponential-1

factor, A, of 2×10 . This suggests that the conformational rearrangements that induce the6

spectral diffusion occur via thermally activated barrier crossing. However, the smallpreexponential factor may point to a tunneling contribution to the fluctuation rate.

Now that we have established the main contribution to the spectral diffusion of Zn-cytochrome c and Zn-myoglobin in the ms-region, it seems appropriate to make a firstattempt to interpret this result in less abstract terms. We describe two borderline cases, theessentials of which are represented in Fig. 5.4. The simplest way to explain the linebroadening behavior is by way of a two-state model, where each protein in the ensemble isfluctuating at a particular rate between two conformational states. In other words, the proteinas a whole, or part of it, acts a single two-level system. The fact that only a single two-level


52

Figure 5.4 Two different representations of the potential energy surface of the protein toexplain the observed line broadening behavior. See text for explanation.

system is observed implies that the total number of two-level systems of the protein is small,which can be rationalized in terms of the small dimensions of the system. [Sin84, Zol91a,Kur95, Shi96] Note that in this case the width of the rate distribution is purely an ensembleproperty. A different approach is to abandon the two-level system model and assume apotential with a large number of conformational substates, i.e. a multi-state model. Thispotential is characterized by a distribution of barrier heights between the conformationalsubstates. In order to explain the narrow time window in which the spectral diffusion occurs,this distribution has to be quite narrow. In this case, the width of the rate distribution reflectsthe distribution of energy barriers and preexponential factors within the multi-level potential,and therefore is a property of a single protein. Such a view is in agreement with a hierarchicalorganization of the energy landscape, as was introduced in section 2.3.3, because this modelimplies that the overall distribution of barrier heights comprises a number of discretefeatures, each of which corresponds to a single hierarchical tier. This would imply that themulti-level potential describes a single tier within the structural hierarchy. The remainingsections will yield more insight into the detailed structure of the energy landscape.

5.4 Spectral diffusion in Zn-myoglobin between 3.0 and 23 K

Upon close inspection of Fig. 5.2, we can observe that the line broadening in the ms-region is reactivated at 3.0 K, after having leveled off at 2.7 K. However, the data also showthat the additional line broadening is clearly separated from the broadening induced by thenarrow feature. Therefore, in terms of the sudden-jump model, the additional line broadeningmust originate from a second feature in the distribution of fluctuation rates. More insight intothis behavior is obtained by expanding the temperature range. Figure 5.5 shows the waitingtime dependence of the line width between 10 ns and 100 ms, in the temperature rangebetween 3.0 and 4.7 K. From now on, the narrow feature in the rate distribution, responsible


53

Figure 5.5 Waiting time dependence of the line width of Zn-myoglobin between 3.0 and 4.7K. The solid lines through the data are fits to Eq. 3.15, using the distributions of fluctuationrates that are displayed.

for the line broadening between 1.7 and 3.4 K, is denoted as a. The second feature, that isactivated at 3.0 K, is referred to as b. Essentially, the data between 3.0 and 4.7 K exhibit thesame behavior as those between 1.7 and 3.4 K, namely the activation of a new feature at thelowest temperature, the shifting with temperature of the onset of the line broadeningassociated with this feature, and eventually, the leveling off of the spectral diffusion at the

P(R)R ' T for A < logR % jiTi exp &

ln (R/R0,i

2Fi

2


54

(5.4)

highest temperature. Therefore, we must conclude that, like feature a, feature b is relativelynarrow and shifts as a function of temperature. The fact that feature a cannot be resolvedanymore above 4 K is because it shifts within the range of the continuous broadeningbetween 10 ns and 10 µs. The data in Fig. 5.5 were fitted to Eq. 3.15 with the distributionsthat are displayed. The exact fitting function is:

Some remarks about the fitting of the data are in order. First of all, the log-normal shape forthe narrow features, and the cut off hyperbolic function to account for the short time scalebroadening, are assumptions. Although the data definitely show that the rate distributionmust comprise a number of discrete features, the scatter is too large to accurately determinethe exact shape of the individual features. The data were fitted with a fixed width for the twolog-normal features and a fixed amplitude ratio between the two of 1.55. The choice of theseparameters was based on preliminary fits of the data where all parameters were allowed tovary. All other parameters, most importantly the position of the two log-normal features,were allowed to vary. We emphasize that the data at individual temperatures, althoughalways being consistent, do not allow an unambiguous assignment to the rate distributionsthat are displayed in Fig. 5.5, but that the overall picture arises from careful considerationof the complete temperature range. Note, that although their relative amplitude was fixed,the total amplitude of the two log-normal functions was allowed to vary, and does not changesignificantly as a function of temperature. This confirms that the two sharp features are theonly sources of line broadening in the region between 10 µs and 100 ms.

The waiting time dependence of the line width between 5.6 and 12 K is shown in Fig. 5.6.What becomes immediately apparent, is the remarkable similarity between these data andthose recorded between 3.0 and 4.7 K. The data at 5.6 K supply evidence for a third featurein the rate distribution, denoted as c, as can be concluded from additional line broadening inthe ms-region. The line broadening associated with feature c eventually levels off, at 8.1 K,from which we conclude that feature c also is relatively narrow and shifts as a function oftemperature. The leveling off of the line broadening becomes even more pronounced at 12K. Due to the increase of the fluctuation rate of feature c, a plateau appears between 0.1 and100 ms. The fits of the data to Eq. 3.15 were performed in the same way as for the data ofFig. 5.5. This time the data were fitted to a cut off hyperbolic function, and three log-normalfunctions with a fixed value for their relative amplitudes. However, in Fig. 5.6 we only showthat part of the distribution, and the corresponding fit, that was used for further analysis.

It appears that each subsequent feature contributing to the line broadening has both alarger width and a larger amplitude than the previous one. This means that the line


55

Figure 5.6 Waiting time dependence of the line width of Zn-myoglobin between 5.6 and 12K. The solid lines through the data are fits to Eq. 3.15, using the distributions of fluctuationrates that are displayed.

broadening occurs within a broader time window and has a larger magnitude. The increasein magnitude is approximately 1.5-fold for each subsequent feature. More information isprovided by plotting the temperature dependence of all three features, a, b, and c, as is donein Fig. 5.7. We observe that features b and c follow the same activation law as feature a. Thethermodynamic parameters resulting from fits of the data to Eq. 5.3 are listed in


56

Figure 5.7 Temperature dependence of the fluctuation rates, R , corresponding to the0positions of the distributions a (circles), b (triangles) and c (squares) that were displayed inFigs. 5.2, 5.5 and 5.6. The solid lines are fits to Eq. 5.3.

Table 5.1 Thermodynamic parameters for conformational fluctuations of myoglobin

a b c

E (kJ mol ) 0.20 0.38 0.57-1

A (s ) 2×10 1×10 5×10-1 6 7 6

table 5.1. Each subsequent feature contributing to the line broadening is associated with alarger energy barrier than the previous one. Another interesting observation is the smallpreexponential factor, observed for all three features, which may point towards a tunnelingcontribution to the relaxation rate. In an attempt to detect additional line broadeningcontributions, we extended the temperature range to 23 K, which, due to the fast decay of the3PSE at this temperature (see chapter 6), is approaching the temporal resolution of theexperimental set-up. The results are shown in Fig. 5.8. Although the scatter of the data ismuch worse than at lower temperatures it is still quite clear that, while the data at 17 K stillexhibit a pronounced plateau between 0.1 and 100 ms, the line broadening in this region isreactivated at 23 K. Evidently, at this temperature a fourth feature, feature d, in thedistribution of fluctuation rates starts contributing to the spectral diffusion. We did notperform a complete temperature dependence in this region, and therefore, we cannot statewith certainty that feature d behaves identically as features a, b and c. However, assuming


57

Figure 5.8 Waiting time dependence of the line width of Zn-myoglobin at 17 K (opentriangles) and at 23 K (closed circles).

that it does, it is possible to make a (rough) estimate of the energy barrier corresponding tothis feature by assuming the preexponential of 10 that was found for the other features.7

Doing so, we estimate the barrier to be 3 kJ mol . The most logical explanation of the-1

absence of line broadening in the ms-region between 8 and 17 K is that there is a large gapin the distribution of barrier heights between 0.6 and 3 kJ mol . We postpone further-1

interpretation of this gap, and other aspects of these results, until we have presented somerecent hole burning results. This is done in the section 5.7.

5.5 The importance of heating effects in stimulated photon echo experiments

Very recently, Zilker and Haarer [Zil97] and Neu et al. [Neu97] addressed the problemof possible heating effects in stimulated photon echo experiments. As was mentioned insection 3.3, a stimulated photon echo experiment with waiting times exceeding thefluorescence lifetime requires a bottleneck state to temporarily store the excited statepopulation. In many cases, and also in the experiments presented in this thesis, the lowestlying triplet state of the chromophore serves as the bottleneck state. The intersystem crossingprocess that populates the triplet state results in a release of energy into the focal volume ofthe incident laser beams. As the intersystem crossing yields of Zn-porphyrins are of the orderof 90 %, up to 25 % of the incident laser energy can be transformed into heat during thisprocess, which occurs over the course of the fluorescence lifetime, J . If the heat release isflconsiderably faster than the diffusion of heat out of the focal volume, one can assume thatafter a certain time J the focal volume has been heated up to a temperature T given by thefl 1relation

Q 'm

T1

T0

dTc(T)

M

MtT(r,t)&DL2T(r,t) ' 0

T(t) ' T0 % (T1&T0)1

1% t /Ja& e&t/Jfl


58

(5.5)

(5.6)

(5.7)

where Q is the amount of heat released into the sample, and T is the temperature of the0sample in equilibrium with the helium bath. The amount of laser induced heating dependson the specific heat of the matrix, c(T), the energy carried by the incident laser pulses, thesize of the focal volume, the intersystem crossing efficiency, and the singlet-triplet energysplitting. Neu et al. showed that for a value of T of around 2K, T -T can be as large as 1 K,0 1 0but it should be noted that this is an estimate that critically depends on the experimentalconditions.

Since the heat released by the chromophores inside the focal volume will eventuallydiffuse away, the temperature inside the focal volume becomes a time dependent variable.The time dependence of the temperature inside the focal volume can be obtained by solvingthe heat diffusion equation

for the local temperature T(r, t), where the diffusion constant D = 6 /Dc depends on the heatconductivity, 6, the mass density, D, and the specific heat, c, of the sample. The dominantcontribution to the heat diffusion process is the radial diffusion over the time scale J = a /D,a

2

where a is the spot size of the incident laser beam at the sample. A typical value of J for anaamorphous solid is between 10 and 100 µs. Neu et al. showed that, within certainapproximations, the time dependent temperature inside the focal volume is given by

Eq. 5.7 tells us that during the time it takes for the heat to diffuse out of the focal volume,the temperature is higher than the bath temperature, resulting in an artificially increased linewidth. Zilker and Haarer and Neu et al. pointed out that such an effect may be the cause ofthe plateau between 1 µs and 1 ms observed by Meijers and Wiersma [Mei92] in the waitingtime dependence of Zn-porphin in EtOD glass at 1.5 K (see appendix). Assuming that theexcess heat diffuses on a time scale of the order of 10 µs, one expects an increased line widthup to approximately 1 µs, at which point the heat diffusion process starts to take place, andthe line width is expected to decay towards its value at the bath temperature. If, at constant


59

Figure 5.9 This figure demonstrates how heating effects may lead to a plateau in thewaiting time dependence of the line width. The dashed lines show the logarithmic waitingtime dependence in the absence of heating effects and the additional factor to the line widthdue to the increased temperature as a function of waiting time. The solid line is the sum ofthe two, which is the measured waiting time dependence.

temperature, the line width would be independent of the waiting time, one would observe aconstant line width up to approximately 1 µs which subsequently decreases between 1 µs and0.1 ms. However, if at constant temperature, the line width increases logarithmically withwaiting time, as is often observed for glassy systems, one may observe a plateau in this timewindow. This is illustrated in Fig. 5.9. We wish to emphasize that an estimation of themagnitude of heating effects based on data recorded at constant laser fluence requires an apriori assumption of the waiting time dependence of the line width in the limit of zerofluence. Neu et al. fitted the data of Meijers and Wiersma on Zn-porphin at 1.5 K, and thoseof Zilker and Haarer on Zn-mesotetraphenylporphine in polymethylmethacrylate at 0.75 K,using a model of spectral diffusion in glasses introduced by Silbey et al. [Sil96] We proposea more direct approach by measuring the fluence dependence of the line width at a numberof different waiting times. In this way the effect of sample heating is measured directly, andthe true waiting time dependence, that is the one observed in the limit of zero fluence isobtained, while no a priori assumptions are required.

A preliminary study on the fluence dependence of the spectral diffusion of Zn-porphinin EtOD [Laz97] at 1.8 K seems to confirm the hypothesis of Neu et al. This means that atwaiting times of 10 µs and shorter the echo decay rate is dependent on the laser fluence,while this effect quickly decays around 0.1 ms. A tentative conclusion is that the plateauobserved in the µs-region indeed is a result of excessive sample heating as opposed to a gapin the distribution of two-level system fluctuation rates, as was initially proposed by Meijersand Wiersma. [Mei92]

To be certain that the conclusions that are drawn in this thesis are not affected by anyheating artifacts, we performed a thorough study of the dependence of the line broadening


60

Figure 5.10 Dependence of the line width on the energy in each of the pulses for Zn-myoglobin at 2.0 K at four different waiting times: 12 ns (), 1.0 µs () 0.1 ms (), and 10ms (). The dashed lines mark the average value of the line width for t = 0.1 ms and 10 ms.wThe error in the line width is approximately 0.025 GHz.

in Zn-myoglobin on the applied laser fluence. In this study, performed at 2.0 K, which is veryclose to the lowest temperature studied in this thesis, we varied the energy of each of thelaser pulses from 7 to 70 nJ. For comparison, the experiments on Zn-myoglobin presentedin this thesis were performed using energies of less than 50 nJ per pulse. Note that at 7 nJper pulse the absolute limit of our detection set-up is reached. The results of this experimentare displayed in Fig. 5.10, which shows the 3PSE decay rate at four different waiting timesas a function of the pulse energy used in the experiment. Figure 5.10 shows that, similar towhat has been observed for Zn-porphin in EtOD glass, there appears to be a slightdependence of the decay rate on laser fluence at t = 12 ns and 1 µs, but that such an effectwis not observed for t = 0.1 and 10 ms. It is worthwhile to note that these effects arewapproximately an order of magnitude smaller than what has been observed for Zn-porphinin EtOD glass. The question that naturally arises is to what extent this slight fluencedependence affects the conclusions drawn so far, and those that will be drawn in theremainder of this thesis. The answer is that we can safely conclude that none of theconclusions with respect to the protein energy landscape are in any way affected by heatingeffects, both qualitatively and quantitatively speaking, and that in the worst case some of thedata recorded at the lowest temperatures (< 3 K) may suffer from a mild fluence dependencefor waiting times shorter than 0.1 ms. The explanation is straightforward. The mainconclusion of the previous sections with respect to the spectral diffusion behavior of theprotein is that the distribution of fluctuation rates exhibits a number of discrete features thatshift as a function of temperature. Qualitatively speaking, this conclusion is drawn based on


61

the fact that plateaus observed in the ms-region appear and subsequently disappear as afunction of temperature. Furthermore, the fluctuation rates corresponding to the sharpfeatures, that were used to determine the conformational barrier heights, were all obtainedfrom data in the ms-region. Since Fig. 5.10 clearly shows that this time window is notaffected by the laser fluence, we can safely conclude that heating effects are of negligibleinfluence on the conclusions of this thesis. It should be noted that this conclusion is drawnon the basis of fluence dependent data obtained close to the lowest temperature that wasmeasured. At higher temperatures, any heating effects are expected to become negligiblebecause of the fact that the specific heat strongly increases with temperature, which meansthat the absolute increase in temperature will become smaller. Furthermore, even if theabsolute increase in temperature would remain the same, the relative effect would becomesmaller. Neu et al. showed that even for Zn-porphin in EtOD glass heating effects becomemarginal at around 3 K.

The small dependence of the 3PSE-decay on laser fluence observed in the sub µs-regionmight indicate that the plateau observed between 1 µs and 0.1 ms is less pronounced in thelimit of zero fluence. However, Fig. 5.10 shows that even within this limit, the amount of linebroadening in the region between 12 ns and 1 µs is almost a factor of 4 larger than thebroadening observed in the region between 1 µs and 0.1 ms. Therefore, the data still clearlyshow a crossover to a weaker line broadening regime around 1 µs. This behavior is clearlydifferent from that of Zn-porphin in EtOD glass, where it is observed that the linebroadening becomes close to logarithmic when extrapolated to zero fluence. [Laz97]

At the end of this section, we would like to address the question why heating effects areso much smaller for Zn-myoglobin than for Zn-porphin in EtOD glass. Since theexperimental conditions, such as the focal volume of the incident laser beams can beassumed to be identical, the answer should either be found in the relevant parameters of thematrix, i.e. the specific heat, or those of the chromophore, i.e. the singlet-triplet energysplitting. The fact that, in EtOD glass at 1.8 K, no plateau is observed for Zn-mesoporphyrinIX (see appendix), the chromophore that is also complexed to the protein, suggests that thechromophore rather than the matrix is responsible for the pronounced difference. Since thesinglet-triplet energy splitting is only slightly smaller for Zn-mesoporphyrin IX (3200 cm )-1

[Bec63] than for Zn-porphin (3700 cm ) [Gra71] it is not quite clear what is the cause of-1

the different behavior of the two chromophores. What might play a role is that, for Zn-mesoporphyrin IX, energy may be dumped in the flexible side chains of the porphyrinbackbone.

5.6 The population dimension of the stimulated photon echo

In this section, we present a result that bears no direct relevance to the study of proteinenergy landscapes, but that is important within the general context of line narrowing

Ir(J,tw) 'exp[&4J/T2(tw)]

exp[&4J/T2(t0w)]

exp[&2tw/TB]


62

(5.8)

Figure 5.11 Dependence of the 3PSE-intensity on t at a fixed value of J = 100 ps for Zn-wmyoglobin at 2.0 K. The solid line is the dependence predicted by Eq. 5.8, on the basis of thespectral diffusion behavior at this temperature. The insert shows the result of an identicalexperiment on Zn-cytochrome c at 1.8 K.

experiments in disordered solids. The experiment that is performed is to record the intensityof the 3PSE-signal as a function of the waiting time t , but at a fixed time separation of thewfirst two pulses J. At the shortest waiting time that was measured t = 12 ns, the excited0wstate population has completely decayed into the bottleneck state. Under these conditions,the sudden-jump model predicts that the intensity of the echo signal relative to its value att obeys the relation0w

where I = I(t )/I(t ), and T is the lifetime of the bottleneck state. The first term on the rightr w w B0

hand side of Eq. 5.8 reflects the decay due to spectral diffusion, while the second term is dueto population relaxation of the bottleneck state.

Fig. 5.11 shows the result of this experiment for Zn-myoglobin at 2.0 K for J = 100 ps.The solid line is the decay predicted by Eq. 5.8, on the basis of the expected spectraldiffusion behavior at this temperature and a value of T of 50 ms. The insert in Fig. 5.11Bshows the result of an identical experiment on Zn-cytochrome c at 1.8 K. It is immediatelyobvious from Fig. 5.11 that there is a loss of intensity, occurring in the µs-region, that is notaccounted for by Eq. 5.8. This is particularly interesting because a similar effect, althoughlarger in magnitude, had been observed for chromophore doped glasses by Meijers andWiersma. [Mei94a, Mei94b] We emphasize that the anomalous intensity loss does notdepend on the energy carried by the excitation pulses, and therefore, cannot be attributed toheating effects.


63

At this point, the source of the anomalous relaxation process still remains a source ofdebate. However, the fact that it is also observed for the protein suggests that it may be ageneral phenomenon characteristic to disordered solids, and in fact yields new insight intothe source of this effect. In terms of the frequency grating formalism that was introduced insection 3.2, the intensity loss implies that either the modulation depth of the frequencygrating is reduced independently of the fringe spacing of the grating, or that the grating asa whole shifts away from the spectral region covered by the exciting laser field. The formercould be explained by the occurrence of frequency jumps of the order of the bandwidth ofthe exciting laser field, for instance, due to the coupling to two-level systems in theimmediate vicinity of the chromophore, as suggested by Meijers and Wiersma. [Mei94a,Mei94b] Note, that the effect of frequency jumps of lower amplitude depends on the fringespacing of the frequency grating, and therefore, would also have to be observed in thewaiting time dependence of the echo decay rate, as explained in section 3.3. The problemwith this interpretation is that there is no apparent reason to believe that these processeswould occur on such a specific time scale.

The explanation of the anomalous intensity loss in terms of a shift of the frequencygrating seems much more plausible. There is a fundamental difference with the explanationoffered by Meijers and Wiersma, in the sense that a shift of the frequency grating implies arelaxation process in a well-defined direction rather than a random fluctuation. A relaxationprocess is much more likely to account for the intensity loss because it explains why it occurson a sharply defined time scale. A candidate for a relaxation process is the so-called dynamicStokes shift, that is a structural relaxation of the matrix in response to the optical excitation.Within this context, it is worthwhile to notice that the intensity loss occurs on a time scalean order of magnitude slower in the protein than in a glassy matrix. Figure 5.11 shows thatthe intensity decays between 1 and 10 µs, while in a glassy matrix the intensity loss wouldoccur roughly between 100 ns and 1 µs. Given the lower structural flexibility of the protein,it seems plausible that a structural relaxation occurs on a slower time scale. Further evidencein favor of a frequency shift comes from the fact that, for Zn-porphin in EtOD glass, theeffective accumulation time in an accumulated photon echo experiment (APE) is muchshorter than what would be expected from the lifetime of the bottleneck state. [Mei94a,Mei94b] This can be deduced from the fact that the decay rate of the APE corresponds to a3PSE-decay for t = 1 µs, while the lifetime of the bottleneck state is 100 ms. The APEwsignal is scattered from a frequency grating that accumulates from a train of consecutive lowintensity pulse pairs. Each individual pair creates a grating of very small amplitude, whichadd up to a macroscopic grating if the microscopic grating in the excited state can relax intoa bottleneck state with a lifetime that exceeds the time separation between consecutive pulsepairs. The absolute phase of a frequency grating depends on the phase difference betweenthe excitation pulses, and therefore, for an accumulated grating to build up, this phasedifference needs to be equal for all pulse pairs that contribute to the grating. A frequencyshift will have the same effect as disturbing the phase relationship between the pairs of

'(Tex)&'(T0) ' m4

0

dR [P(R,Tex)&P(R,T0)] [1&exp(&Rtex)]


64

(5.9)

excitation pulses, and therefore, will wipe out the accumulated grating, and in this wayreduce the accumulation time.

5.7 Temperature cycle spectral hole burning experiments

In this section, we review some hole burning experiments from the recent literature thatare of relevance to the work presented in sections 5.2 through 5.4. All of these experimentswere performed on myoglobin complexed to free base protoporphyrin IX.

In a temperature cycle hole burning experiment, the sample is subjected to a cyclictemperature variation during the waiting time between burning and reading a spectral hole.The characteristic variables of such an experiment are the temperature, T , at which the hole0is burned and read, the excursion temperature, T , which is the maximum temperatureexreached during the cycle, and the time, t , during which the sample is at the excursionextemperature. The basic idea behind the experiment is that during the temperature cycle theprotein is able to cross conformational barriers that are not surpassable at T , which causes0the line width to increase relative to its value in the absence of a temperature cycle. Thedependence of the line width on the excursion temperature can yield information on theheight and the distribution of the barriers within the energy surface of the material that isstudied, in a similar way to the waiting time dependent measurements that were presentedin the previous sections. Within the framework of the sudden-jump model, we can expressthe change of the line width, ', as a function of T , in terms of the distribution of fluctuationexrates at T and T respectivelyex 0

An advantage over waiting time dependent measurements at fixed temperatures is that theline width contains no contribution from fast pure dephasing processes at the excursiontemperature. (See Chapter 6) This makes it possible to reach higher temperatures and hence,to measure higher energy barriers than is possible on the basis of 3PSE-experiments.

A. Equilibrium temperature cycle hole burning experiments at 4 K

Shibata et al. [Shi96] performed temperature cycle hole burning experiments with aburning and reading temperature of 4 K, and an excursion temperature that was variedbetween 15 and 70 K. Figure 5.12 shows their results for T = 15-30 K. In addition to aexgradual increase with T , there appears to be a stepwise increase of the line width around 20ex

'(Tex) % 1&exp[&R(Tex) tex]


65

(5.10)

Figure 5.12 Dependence of the line width on the excursion temperature in a temperaturecycle hole burning experiment. The insert is a fit of stepwise increase, from which thecontinuous contribution has been subtracted, to Eq. 5.10. See text for explanation. The datawere obtained from Ref. Shi96.

K. Analogous to what was observed in the 3PSE-experiments, the stepwise increase mustarise from a discrete feature in the distribution of fluctuation rates that shifts as a functionof temperature. If we assume a *-function for the discrete feature, its contribution to thetemperature cycle induced line broadening is proportional to

where R is the fluctuation rate corresponding to the discrete feature. Assuming an activationlaw for the temperature dependence of R, we performed a fit to the data of Fig. 5.12, fromwhich the continuous contribution to the line broadening was subtracted as was done byShibata et al. The fit yields a preexponential factor of 9 × 10 s , and an energy barrier of6 -1

3.7 kJ mol . Note the similarity to the small preexponential factors obtained for features a,-1

b, and c. However, we must emphasize that, since the width of this feature cannot beaccurately determined from these results, these parameters represent lower limits. If its widthis substantially larger than a *-function, both the preexponential factor and the energybarrier are expected to be higher.

It is not completely clear whether the feature that induces the stepwise broadening in thetemperature cycle experiment is the same one or a different one than the feature that inducedthe line broadening in the 3PSE-experiment at 23 K. We are inclined to believe that they aredifferent features because they both are activated at approximately the same temperature,while the temperature cycle experiment is performed on a much longer time scale, five ordersof magnitude larger than the longest waiting time in the 3PSE-experiments. However, thiswould imply that feature d should be observed at a lower temperature in the temperaturecycle experiment, which does not seem to be the case. A possibility is that feature dcorresponds to the gradual increase with T observed in the temperature cycle experiment.ex


66

Figure 5.13 Spectral line shape as a function of the excursion temperature in a temperaturecycle hole burning experiment. Displayed are the line shape of the initially burned hole(dashed line) and the line shapes for T = 56 and 69 K. The data were obtained from Ref.exShi96.

Shibata et al. assigned this gradual increase to coupling to the glassy solvent. We considerthis unlikely since the 3PSE-experiments very clearly show that the heme group of theprotein is not coupled to the long time scale (> µs) dynamics of the glass, and at least up to17 K, the line broadening is exclusively influenced by the protein. A more detailed study ofthe temperature dependence of the spectral diffusion above 17 K will be required to resolvethis matter.

Figure 5.13 shows the line shape of the initially burned hole along with the line shapesfor T = 56 and 69 K. In this region, the line broadening seems to be restricted to the tail ofexthe hole, while the full width at half maximum is hardly affected. However, similar to theprevious contributions, the broadening occurs within a restricted temperature range,consistent with a rather narrow range of activation barriers. By comparing the temperatureat which this contribution is activated to the activation temperature of the previous featureswe estimate the centre of the distribution of barriers to be located around 10 kJ mol , but-1

obviously this is a rather rough estimate. The fact that a change in the line shape is observedrather than an overall broadening of the hole is consistent with the observation of theincreased broadening for each subsequent feature, that was observed in the photon echoexperiments. Apparently, at this point, the frequency shifts induced by crossing of theconformational barrier become so large that the line shape rather than the line width isaffected.

B. Equilibrium and non-equilibrium temperature cycle hole burning at 100 mK.

In these experiments, performed by Fritsch et al., [Fri96] spectral holes were burned ata temperature of 100 mK. Under these conditions, it takes an appreciable time for theensemble of proteins to reach thermal equilibrium. It can be determined from studying the


67

Figure 5.14 Time evolution of spectral holes A (closed circles) and B (open triangles)burned at 100 mK. See text for explanation. The data were obtained from Ref. Fri96.

waiting time dependence of the line width at 100 mK that this takes approximately ten days.[Gaf95a, Tho97] Once equilibrium was established, a spectral hole was burned, referred toas hole A, after which a temperature cycle was applied with T = 4 K. The experiment wasexthen repeated for T = 8 K. The duration of the temperature cycle was approximately 80 min.exA second hole, referred to as hole B, was burned immediately after the temperature cycle.The width of both holes was then monitored as a function of waiting time. The results of thisexperiment for T = 4 K are displayed in Fig. 5.14. Nearly identical results were obtainedexfor T = 8 K. We observe that the broadening of hole A that was induced by the temperatureexcycle is reversed over a period of several hours, but that no complete relaxation towards theinitial l ine width occurs. Approximately one third of the initial broadening is reversed.During this period, hole B behaves as the mirror image of hole A, in the sense that itbroadens by approximately the same amount as hole A narrows. Eventually, line broadeningtakes over again, and the width of both holes seem to asymptotically reach but not to cross.Fritsch et al. [Fri96] analyzed these results in terms of the two-level system model, alongwith results from a similar experiment on the same chromophore directly dissolved into aglassy host. The main conclusion from this analysis is that, contrary to the glass, the two-level system model cannot account for the experimental results. Apparently, a moresophisticated model is required to do justice to the complex features of the protein energylandscape.

5.8 The structure of the energy landscape

The aim of this and the next section is to construct an image of the low-energy part of thepotential energy surface of myoglobin based on the optical line narrowing experimentspresented in sections 5.2 through 5.4, and section 5.7. This analysis will be performed in


68

terms of the concepts used to describe multidimensional potential energy surfaces andprotein energy landscapes introduced in sections 2.1 and 2.2.

The most important conclusion that can be drawn from the complete set of linebroadening experiments, is that the distribution of energy barriers, P(E), between theconformational substates of the protein comprises a number of discrete features. In the recentliterature two opposing views have been expressed to explain this observation. Essentially,these views are extensions of those discussed at the end of section 5.3. Shibata et al. [Kur95,Shi96] suggested that the individual features in P(E) correspond to localized two-levelsystems of the protein. Thorn Leeson and Wiersma [Tho95b] attributed the individualfeatures to transitions between conformational substates within a single tier of ahierarchically organized energy landscape. The latter conclusion was partly based on theincreasing line broadening for each subsequent feature observed in the 3PSE-experiments.The magnitude of the line broadening is related to the amplitude of the correspondingconformational rearrangements, or the increase in phase space volume. Hence, theyconcluded that on short time scales the protein exhibits low-amplitude motions by crossingthe smallest energy barriers, while if either the time window is extended, or the temperatureis increased, higher amplitude motions which require the crossing of larger energy barriersbecome activated.

At this point in the discussion, it becomes necessary to include the results of Fritsch etal., which were presented in section 5.7. They analyzed these results, and the results of acomparative experiment performed on a chromophore doped glass, using the two-levelsystem model. [Fri96] Their main conclusion was that, contrary to the glass, the results ofthe experiments on myoglobin could not be explained in terms of a distribution ofindependent two-level systems. Apparently, a proper interpretation of these results demandsus to consider more global features of the protein energy landscape. From the experimentsof Fritsch et al. we learn that the line broadening induced by a temperature cycle from 100mK to either 4 or 8 K contains a reversible and a non-reversible contribution. Thereversibility must reflect a tendency for some subpopulation of the ensemble of proteins toreturn to the same point in phase space that they occupied when the spectral hole was burned,i.e. before the temperature cycle. This can be explained by assuming a potential well,characterizing a certain conformational substate of the protein, that has a certain roughnesssuperimposed on it, as is displayed in Fig. 5.15. Essentially, this is a funnel-like feature ofthe energy surface as was discussed in section 2.2. The steepness of the well is such that, at100 mK, only the lowest energy state is populated. If the temperature is increased eachprotein starts to access local minima of higher energy, and after a certain time thedistribution of the ensemble of proteins over the local minima satisfies thermal equilibriumconditions. Hence, if the temperature is lowered again to 100 mK the ensemble is in a non-equilibrium state. Reestablishment of thermal equilibrium, i.e. repopulation of the lowestenergy state, will take considerable time because of the roughness of the potential. If one


69

Figure 5.15 Local structure of the conformational substates of the protein based ontemperature cycle hole burning experiments. The closed circles represent the population ofthe local minima at a given time and temperature. Also shown is the expected hole width forhole A and hole B at various instants during the experiment. See text for explanation.

would burn a hole at 100 mK, i.e. hole A, and subsequently apply a temperature cycle, thehole will broaden because the protein can access states of higher energy during the cycle. Ifthere would only be a single conformational substate, this broadening would be completelyreversible since each protein is expected to return to the same point in phase space once thetemperature is lowered again to 100 mK. Since hole B is burned when the sample is in thenon-equilibrium state, right after the temperature cycle, it is expected to broaden by the sameamount, and on the same time scale as hole A narrows. However, the time evolution of thetwo holes is determined by exactly the same process, that is the reestablishment of thermalequilibrium. Their different behavior is merely caused by the fact that they were burned indifferent (non)-equilibrium states. This is also illustrated in Fig. 5.15. However, this pictureis only in qualitative agreement with the experimental results. Fritsch et al. only observed areversibility of the order of 1/3. Apparently, while some subpopulation indeed returns to thesame point, another subpopulation of proteins ends up in a different local minimum after thetemperature cycle. This can be explained by assuming that there is only a small number ofconformational substates, as is sketched in Fig. 5.16. At the excursion temperature, the rateof crossing the barriers between these conformational substates must be much higher thanthe inverse of the duration of the cycle, T , which is approximately 80 minutes, so that afterexthe cycle no memory exists of the initial distribution of the ensemble of proteins over the


70

Figure 5.16 Schematic representation of the energy landscape in the region up to 1 kJ mol-1based on the experimental observations. See text for explanation.

accessible conformational substates. In this case, the probability of ending up in the sameconformational substate as was occupied before the cycle is of the order of 1/N, where N isthe number of states. Note that this probability also depends on the energy splitting betweenthese states. Therefore, the number of conformational substates must be of the order of three.From the 3PSE-experiments we obtained three energy barriers, E , E , and E . Instead ofa b cassigning these to different hierarchical tiers we must carefully consider the possibility thatthese are the barriers between the small number of conformational substates that is requiredby the experiments of Fritsch et al. This implies that features a, b, and c correspond to thesubsequent crossing of barriers E , E , and E , as indicated in Fig. 5.16.a b c

A first test of this hypothesis is the non-reversible contribution to the broadeningobserved in the temperature cycle experiment, which must be consistent with thethermodynamic parameters obtained from the 3PSE-experiments. Qualitatively speaking,in order to contribute to the temperature cycle induced broadening, a structuralrearrangement should occur on a time scale longer than the duration of the cycle, t , atex100 mK, and on a time scale comparable to or shorter than t at the excursion temperature.exFor a quantitative description of the experiment, one may apply Eq. 5.9. A major clue is thatFritsch et al. found the same amount of broadening for T = 4 and 8 K. This observation isexin complete agreement with the results of the 3PSE-experiments, as is illustrated in Fig. 5.17,which shows the temperature cycle induced line broadening predicted on the basis of theparameters from table 5.1, and using Eq. 5.9. For features a, b, and, c the calculated rate ofbarrier crossing is much higher than 1/t , at both 4 and 8 K. Therefore, they contributeexequally to the line broadening at these temperatures. However, the fourth feature does notcontribute at all to the line broadening, since its rate is much smaller than 1/t at eitherextemperature. The absence of spectral diffusion in the ms-region between 8 and 20 Kcorresponds to the absence of spectral diffusion on the time scale of t between 4 and 8 K.exIn terms of the distribution of barrier heights, both of these observations are directly related


71

Figure 5.17 The dependence of the irreversible contribution to the temperature cycleinduced line broadening on the excursion temperature, based on the thermodynamicparameters of table 5.1, and using Eq. 5.9.

to the absence of barriers between 0.6 and 3 kJ mol .-1

There are a number of possible arrangements of conformational substates including threeenergy barriers. For instance, there can be four conformational substates along a singlecoordinate, separated on both sides by barriers much larger than 0.6 kJ mol , as is displayed-1

in Fig. 5.16. Note that in this case there are three possible arrangements of the barriers, onlyone of which is shown. We now denote these conformational substates as CS 1 through CS4. The single coordinate implies that only direct transitions between adjacent conformationalsubstates are possible. For instance, a transition from CS 1 to CS 4 has to occur via CSs 2and 3 and therefore, all three barriers need to be crossed. As a first alternative, there can bethree conformational substates, all of which are mutually connected by a single coordinate,meaning that direct transitions, requiring the crossing of only a single barrier, are possiblebetween all three conformational substates. Note that these are examples of the twoborderline cases of minimal and maximal connectivity between local minima withinsuperbasins, as discussed in section 2.2. As a second alternative we can imagine threeindependent two-level systems, provided that they exhibit a superimposed roughness toaccount for the results of Fritsch et al.

In section 5.4, we already mentioned that an important experimental observation is theincrease in the amount of line broadening for each subsequent feature. For features a, b, andc the amount of spectral diffusion increased by a factor of approximately 1.5 while featured exhibited an amount of spectral diffusion at least 3 times larger than feature c. Althoughthis may be considered as evidence in favor of a hierarchical organization of the energylandscape, [Tho95b] we will now show that this observation can also be understood, evenquantitatively, in terms of the arrangement of Fig. 5.16.

We make three basic assumptions. The first is that all four conformational substates areevenly populated, implying that the conformational substates are degenerate, at leastcompared to the height of the barriers between them. The second assumption is that the

'SD(tw) % ji, j

fij(tw)*i&j*


72

(5.11)

For R « 1/t « 1/R ,R , ' = 1/3*d(162) + 1/3*d(163) + 1/3*d(261) + 1/3*d(263) + 1/3*d(361) +^ c w a b SD1/3*d(362) = 2.67x.

distance between adjacent conformational substates along the conformational coordinate isequal for all adjacent pairs. The third and most important assumption is that the differencein the heme resonance frequency between two conformational substates I and j, )T , isijproportional to the distance between these two states along the coordinate. For example, thefrequency shift that occurs if a protein makes a transition from CS 1 to CS 4 is three timesas large as the shift for going from CS 2 to CS 3. The total amount of line broadening, ' ,SDthat has occurred during t = t and t = t is proportional to the fraction, f , of the total numberw w ij

0

of proteins in the ensemble that have made a transition from CS I to CS j during this intervaltimes the distance, x , between these two states. So, we can writeij

We consider the arrangement of Fig. 5.16 at a given temperature, for which R » R » R ,a b cwhere R is the rate of crossing barrier i. If t is increased until it approaches 1/R , linei w abroadening starts to occur because of transitions between CSs 1 and 2. It is worthwhile tonotice that we are dealing with the crossing of a single barrier, and therefore, the broadeningis properly described by the coupling of the chromophore to a single two-level system. Thismeans that the fitting procedure that was followed for the data of Fig. 5.2 is essentiallycorrect. If t is further increased until R « 1/t « R we are in the situation when the linew b w a ,broadening induced by feature a has leveled off and the line broadened induced by featureb has not yet started, for instance for t = 10 ms at 2.7 K. At this point 1/2 of the populationwthat was initially in CS 1 is now in CS 2, and vice versa, and therefore, ' = 1. This is theSDamount of line broadening induced by feature a. When t approaches 1/R transitionsw bbetween CSs 2 and 3 start to contribute to the line broadening, that is feature b is activated.However, we have to take into account that, at this point, also CSs 1 and 3 becomeconnected. Also the line broadening induced by feature b is properly described by a singletwo-level system (vide infra). Because R » R , 1/t , the line broadening is only affected bya b wthe crossing of the barrier E . However, the dynamic equilibrium between CSs 1 and 2 causesbthe rate of going from CS 3 to CS 2 to be twice as large as the rate of going from CS 2 to CS3. This effect may be the cause of the slightly broader appearance of feature b. For R « 1/tc w« R , R , feature b has also leveled off, and we can calculate the total amount of broadeningb acaused by features a and b to be 2.67. Therefore, the amount of broadening induced by^

feature b is 1.67. Feature c will again be slightly broader because the dynamic equilibriumbetween states 1, 2, and 3 slows down the rate of going from state 3 to 4 as compared to therate of going from state 4 to 3. Along the same lines we calculate that the amount ofbroadening induced by feature c is equal to 2.33. This is in excellent agreement with theexperimental observations. Note, that this only holds for the arrangement shown in Fig. 5.16,and the arrangement with E as the central barrier. For the arrangement with E as the centrala c


73

barrier, features a and b will give the same amount of broadening, while feature c shouldexhibit an approximately four-fold increase. The three-state model can easily be refuted. Inthis case, only crossing the first two barriers induces spectral diffusion. Crossing the thirdbarrier does not add to the line broadening because all conformational substates were alreadyconnected by the first two barriers. Hence, only two features instead of three should beobserved. A third explanation for the increasing magnitude of the line broadening may be acorrelation between the barrier height and the amplitude of the conformationalrearrangement, which in turn is related to the magnitude of the corresponding spectral shift.However, if we assign the individual features to localized two-level systems this still doesnot explain the observed behavior. The coupling between the chromophore and the two-levelsystems is assumed to be dipolar, and therefore the coupling strength goes as 1/r , r being3

the distance between the two-level systems and the chromophore. The two-level systems areassumed to be spatially localized and randomly distributed in space. Consequently, also thecoupling strength between the two-level systems and the chromophore is randomlydistributed. Therefore, even if a correlation between the barrier height and the amplitude ofthe conformational change would exist, it would not necessarily result in a correlationbetween the barrier height and the spectral shift.

One of the main conclusions of this section is that the two-level system model isinsufficient to describe the special features of the protein energy landscape. However, sincewe are using a quantitative description of the line broadening phenomena that is intimatelyrelated to the two-level system model, we need to consider whether such an approach is stillcorrect. We have seen that the line broadening associated with the features a, b, and cessentially corresponds to the barrier crossing between two local minima on the proteinenergy surface. These local minima are part of a complex energy surface, but the energybarriers that separate them from the other parts of the landscape are large enough so that theprotein can assumed to be frozen in this two-level system on the time scale of theexperiment. This is the case for the two states that are connected by barrier E . In the caseaof the crossing of barriers E and E , one of the two local minima that are connected is splitb cinto either two or three conformational substates, but these are in rapid equilibrium ascompared to the time scale on which the highest barrier is crossed, and therefore, a two-statemodel is also valid for feature b and c.

These arguments are related to the kinetic aspect of the line broadening, i.e. the waitingtime dependence of the overall line width. A more complicated issue is whether one expectsa change in the line shape, or temporal decay of the 3PSE, due to the transitions between thefour conformational substates. Such a change is not observed experimentally. For alltemperatures, the shape of the temporal decay of the 3PSE-signal was found to beindependent of the waiting time. However, if each chromophore is effectively coupled to asingle two-level system, the frequency shift induced by the transitions between these twostates would be very narrowly distributed. This would imply that each chromophore mayeither experience an increase or a decrease of its resonance frequency by a sharply defined


74

amount. Shibata et al. [Shi96, Kur95] showed that such a line broadening mechanism maylead to a change in the line shape if the frequency shift is large compared to the initial linewidth. One can give a number of reasons why no change in the line shape was detected in the3PSE-experiments. The first is that the amount of line broadening induced by the sharpfeatures is quite small as compared to the initial line width, typically of the order of 20 %,implying that the change in frequency is in fact small compared to the initial line width. Thesecond reason is that each protein can move around within its local potential, which willbroaden any sharp features in the line broadening profile. The third reason is related to whatwill be discussed in the next section. The essence of this is that there may be very many localminima as sketched in Fig. 5.16, and that each protein resides in a different local minimum.Although we have suggested that a linear correlation exists between the conformationalcoordinate and the resonance frequency of the chromophore, this correlation may be anaverage one, in the sense that the frequency shift induced by a transition between twoconformational substates is different for each local minimum. This would imply that a widedistribution of spectral shifts exists, but that the average shift over all the possible localminima is still linearly correlated to the distance between the states in conformation space.This distribution of frequency shifts may smoothen possible changes in the spectral lineshape.

5.9 The organization of the energy landscape

What we have done so far is to construct a small part of the protein’s potential energysurface. The obvious next step is to find out how the structure of this small part fits withinthe overall organization of the energy landscape. A first question that arises is whether thefour conformational substates are part of an absolute or a local minimum within the energysurface. Simple experimental arguments tell us that we must be dealing with a localminimum. For instance, we can compare the amount of line broadening to the width of theabsorption spectrum. The optical spectrum of Zn-myoglobin is displayed in Fig. 5.18, alongwith a spectrum of Zn-mesoporphyrin IX directly dissolved into a glassy matrix forcomparison. The width of the protein spectrum is approximately 600 cm , which is a-1

measure for the structural indeterminism and hence, the number of conformational substatesor local minima. Since the total amount of broadening induced by the three features, a, b andc is only approximately 0.02 cm , we must conclude that there are a large number of minima-1

left to explore. There is additional experimental evidence, namely the reactivated broadeningat 23 K and the temperature cycle induced broadening observed by Shibata et al., that theseadditional minima are in fact explored. The next level of interpretation of our experimentalresults involves the organization of the protein energy landscape. We recently suggested thatthe stepwise line broadening of Zn-myoglobin provides direct evidence for a hierarchy ofstructural states. [Tho95b] The discussion in section 5.8 has taught us that the situation may


75

Figure 5.18 Optical absorption spectra, recorded at 77 K, of Zn-myoglobin dissolved in3/1 vol. glycerol/water (left hand side), and of Zn-mesoporphyrin IX dissolved in 3/1 vol.glycerol/dimethylformamide (right hand side).

be not as simple as that. Although we concluded that the stepwise broadening is theconsequence of the small number of accessible conformational states, rather than theexistence of a number of hierarchical tiers, this view does not exclude the existence of astructural hierarchy. It appears that the results do support a hierarchical organization, but theargumentation is more complicated than was previously anticipated. The first step in theargumentation is to include the so-called taxonomic substates. [Ans87] It is a well knownfact that myoglobin can exist in three or four discrete, globally different conformationalstates, the evidence for which can be found in multiple stretch frequencies of carbonmonoxide bound to myoglobin, [Mak79] pseudo discrete heme optical absorption spectra,[Tho95a, Gaf95] and x-ray diffraction studies. [Fra79] The discrete bands in the absorptionspectrum of Fig. 5.18 most likely correspond to the different taxonomic substates. Theenergy barriers between the taxonomic substates are of the order of 100 kJ mol . [Joh96]-1

Based on these observations we can construct an energy landscape for the native state ofmyoglobin that looks remarkably similar to the potential sketched in Fig. 5.16, but obviouslyon a much larger scale, both in terms of the energetic and the conformational coordinate, butalso with respect to the difference in the optical frequencies between the conformationalstates. The reason for this is that the energy landscape is organized in such a way that causessimilar structures to be repeatedly observed when the experimental resolution with respectto the energy and length scale of the structural fluctuations is improved. Here, this wasrealized by lowering the temperature, and thus freezing out the large scale fluctuations, andby using a sensitive optical technique to be able to observe the fluctuations on a smallerscale. In order to explain all the experimental observations we adopt the hierarchicalstructure of the energy landscape as proposed by Frauenfelder and coworkers. [Ans85]


76

However, we suggest that the number of conformational states is much smaller than waspreviously anticipated, [Fra91] and that each conformational state on a certain level withinthe hierarchy, starting with the level of the taxonomic states, is split into a small number,typically of the order of three, of conformational substates on the next lower level. Aschematic representation of the corresponding potential surface is sketched in Fig. 5.19. Thenotation used in Fig. 5.19 to characterize the different hierarchical tiers is adopted from Ref.Fra91. CS is defined as the highest level, i.e. that of the taxonomic substates. The lower0tiers are marked as CS , CS and CS . Below, we will go through the experimental evidence1 2 3in favor of the model presented in Fig. 5.19, starting with the lowest tier and subsequentlyascending within the hierarchy.

CS3

The evidence for the existence of conformational substates within this tier mainly comesfrom the line broadening experiments presented in sections 5.2 through 5.4, and section 5.7.The barriers between these substates were obtained from the temperature dependent photonecho experiments, while the assignment to a single hierarchical tier with a small number ofstates was based on the temperature cycle experiments at 100 mK. However, one aspect thatbecomes apparent from looking at Fig. 5.19 still needs to be explained. We suggest that thesame structure that characterizes CS , i.e. the one sketched in Fig. 5.16, is repeated within3each conformational substate of CS . When an experiment is performed below 20 K only2transitions within CS will occur. This means that each protein is frozen within a particular3substate within CS and higher. However, a number of states within the higher tiers is2available and the ensemble of proteins will be distributed over all the accessible states. Note,that some selection is taking place, certainly with respect to the states within CS , because0the experiment is performed within a narrow band of the spectrum. However, a one to onecorrelation between conformation and frequency is not expected, so although we areprobably selecting a large subpopulation within a certain taxonomic substate, a widedistribution of states within the lower tiers is selected. Now, if the conformational substateswithin CS would be characterized by different barriers between them, depending on which3states within CS and CS are occupied, a wide distribution of barriers, centred around some2 1average value, would be measured in the 3PSE-experiment. Instead, we find that thedistribution of energy barriers peaks at three well-defined barriers, i.e. those correspondingto features a, b and c. Therefore, we must conclude that the same barriers between the statesof CS are found independent of the population of the higher tiers. The consequence of this3is that the same experimental features should be observed regardless of the excitationfrequency applied, that is regardless of which conformational substates within CS , CS , and2 1CS are selected. Unfortunately, the experiments could only be performed within the central0band of the absorption spectrum. Photon echoes were measured in the other bands, but


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Figure 5.19 Schematic representation of the energy landscape of myoglobin based on theexperiments presented in this thesis. See text for explanation.

suffered from serious hole burning and fluence dependence, making the collection of highquality data impossible. However, Zollfrank et al. [Zol91a] showed that similar effects inhorseradish peroxidase were independent of the excitation frequency.

CS2

The evidence for the existence of conformational substates within this tier comes fromthe line broadening at 23 K observed in the photon echo experiments, and between 15 and70 K in the temperature cycle hole burning experiments. The assignment of these featuresto a higher tier than those associated with features a, b and c is based on two arguments. Thefirst is the gap in the distribution of barrier heights, P(E), between 0.6 and 3 kJ mol .-1


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According to Fig. 5.19, P(E) should comprise a number of clusters, more or less evenlyspaced on a logarithmic scale, of a small number of discrete features. Each cluster isassociated with a single hierarchical tier, while the discrete features within each clustercorrespond to the barriers between the conformational substates within this tier. We suggestthat the gap between 0.6 and 3 kJ mol is more likely to originate from a transition from one-1

cluster to another than being an additional feature in the cluster corresponding to CS , and3therefore, is due to a transition to a higher hierarchical tier. The second argument thatconfirms this conclusion is that the amount of line broadening induced by feature d is at leastthree times as large as for feature c, while for the other features only an increase ofapproximately 1.5 was observed. This suggests that the structural rearrangements associatedwith feature d correspond to the exploration of larger areas of the conformational phasespace. While the feature observed by Shibata et al. around 20 K probably also belongs toCS , it is not quite clear how the feature they observed around 60 K should be classified. A2problem is that the estimation of the corresponding barrier height is rather inaccurate. Whatis clear however, is that also within CS the number of conformational substates must be2small. This is due to the fact that the line broadening between 20 and 70 K can be assignedto individual features. In section 5.8 we showed that this is due to a small number ofconformational states within one tier, i.e. CS , and this is likely to be the same for CS .3 2

CS1

The experiments in this thesis provide no information on this tier. Evidence is availablefrom CO-rebinding experiments after flash photolysis [Fra91] The information provided byFig. 5.19 is merely an extrapolation based on what is known about the other tiers. However,it has been suggested [Fra91] that for CS the number of conformational substates is large1to the extent that a statistical rather than a taxonomic approach is appropriate for thedescription of this tier. This can be concluded from the fact that the distribution of thebarriers for ligand rebinding for each of the states within CS does not exhibit any discrete0features and appears to be relatively smooth. This observation seems to be in agreement withthe overall appearance of the optical spectrum. At this point, the available experimentalevidence suggests a total number of hierarchical tiers of approximately four. Assuming thateach of these tiers comprises only four conformational substates, we arrive at a total numberof states of 4 = 256. Since the width of the optical spectrum is roughly 600 cm,we must4 -1

conclude that the average distance between two adjacent conformational states in frequencyspace is approximately 2 cm . Considering the fact that the homogeneous line width at low-1

temperature is much smaller than 2 cm this would imply that individual conformational-1

substates at the level of CS are spectrally resolvable. However, the optical spectrum only3supplies direct evidence of the taxonomic nature of CS , while each of the spectral bands0


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Figure 5.20 Optical absorption spectrum of Zn-myoglobin in 3/1 vol. ethylene glycol/water.(solid line) For comparison, the spectrum in 3/1 vol. glycerol/water is also shown. (dashedline)

corresponding to the individual states within CS are smooth and well approximated by0Gaussians. From this we must conclude that the total number of conformational substatesis much larger than 256. Since, the evidence for the taxonomic nature of CS , CS and CS0 2 3is rather convincing the most logical explanation is that the total number of substates withinCS is much larger than for the other tiers. Note, that this argument requires no a priori1assumption about the correlation between conformation and frequency. We can make anestimate of the total number of conformational substates by comparing the spectral diffusioncaused by transitions between adjacent states within the lowest tier, i.e. CS , to the overall3width of the optical spectrum. The increase in the line width induced by feature a is0.003 cm , which is the average difference in frequency between two adjacent states within-1

CS . This implies that the overall spectrum gives room for 600 cm /0.003 cm = 2 × 103-1 -1 5

conformational substates, and yields a total number of the order of 10 states in CS .5 1Therefore, the statistical description of CS seems to be consistent with the appearance of1the optical spectrum.

CS0

As was mentioned above there is a multitude of evidence for the existence of thesesubstates, as well as the fact that they are small in number. In terms of the optical domain,clear evidence is the spectrum of Fig. 5.18. To confirm that the multi-band nature of thespectrum is not due to local effects in the vicinity of the heme group, the spectrum of Zn-myoglobin in ethylene glycol/water is shown in Fig. 5.20. The spectrum in ethylene glycolexhibits the same three distinct bands, however, with a completely different intensity ratio.It seems unlikely that different local conformations, or different tautomeric states of the heme


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Figure 5.21 Topological disconnectivity graph G(M) for the potential energy surface ofmyoglobin constructed on the basis of the results presented in this thesis. The dashed linesindicate a magnification both with respect to the energy and the conformational coordinate.

group [Gaf93] would experience such a dramatic solvent dependence, unless they arestabilized by different global protein conformations. An alternative explanation considersthe different glass transition temperatures of the two solvents. Fluctuations within CS will0freeze out when the glass is formed, and therefore, the amplitude ratio observed in the low-temperature spectrum reflects the population of the taxonomic substates at the glasstransition temperature.

Finally, in Fig. 5.21 we sketch the disconnectivity graph G(M) (see section 2.2) asconstructed on the basis of the analysis of this section and section 5.8. Note that the energiesat which the partitions of the energy surface were obtained were chosen in such a way as tohighlight its most important features.

5.10 Summary and outlook

In the previous sections we have demonstrated how optical line narrowing experimentscan provide a detailed insight into the energy landscape of a protein. The most importantconclusions that can be drawn by both considering the results of photon echo and hole


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burning experiments, are the following:1. The stepwise line broadening observed in 3PSE-experiments between 1.7 and 23 K,

and in temperature cycle hole burning experiments between 15 and 70 K shows that thedistribution of energy barriers between the conformational substates of the protein comprisesa number of discrete features: three features between 0.2 and 0.6 kJ mol and approximately-1

three features between 3 and 10 kJ mol . These results are in agreement with a hierarchical -1

organization of the energy landscape, but in a different way than was previously anticipated.A careful analysis of both photon echo and hole burning results shows that the three featuresobserved between 0.2 and 0.6 kJ mol belong to the same hierarchical tier, rather than to-1

different hierarchical tiers, as was recently proposed. [Tho95b] The transition to the nexthierarchical tier is indicated by the gap in the distribution of energy barriers between 0.6 and3 kJ mol , as is confirmed by a large increase in the amount of line broadening.-1

2. The number of conformational substates in the lower hierarchical tiers appears to bemuch lower than was previously suggested. [Fra91] For the lowest tier we find fourconformational substates, comparable to the number of taxonomic substates. We proposethat each conformational substate in a given hierarchical tier is split into a small number, ofthe order of four, conformational substates on the next lower level. From the increase inbarrier height between the conformational substates in the lowest tier and the next higher tierwe estimate the total numbers of tiers to be four, in excellent agreement with the modelproposed by Frauenfelder and coworkers. [Ans85]

Although the experiments paint a highly detailed picture, our understanding of proteinenergy landscapes is still rudimentary. One of the main problems is that the conformationalcoordinate remains unknown. Although spectral diffusion experiments are an extremelysensitive probe of protein dynamics, they do not provide structural information. Astraightforward but important question that remains unanswered is whether theconformational changes are local or global in character. This question may be addressed bystudying the effect of selective mutations on the dynamic behavior.

Detailed information on the nature of the structural fluctuations is important because itcan yield insight into the question why protein energy landscapes exhibit such a high degreeof organization, as opposed to the energy landscapes of glasses and polymers. At this pointin time, there is still very little known about the possible origin of a hierarchical organizationof the protein energy landscape. A possibility is that different hierarchical levels areassociated with different types of motions, such as complex rearrangements of tertiarystructure, side chain motions, and atomic fluctuations. However, this does not explain someof the special features of the energy landscape, for example the small number ofconformational states in both the highest and lowest hierarchical level. Monte Carlosimulations on the protein, bovine pancreatic trypsin inhibitor, [Nog89, Go89] showed thata hierarchical structure arises from interactions among local parts of the protein, and yieldan energy landscape that, although only covering two hierarchical tiers, is remarkably similarto that drawn in Fig. 5.19. Because the protein structure is a compact, intricate three-


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dimensional arrangement local structural deformations have a much larger range ofinteraction than in glasses. This means that local degrees of freedom may be coupled, suchthat a structural change in one part of the protein may induce structural changes inneighbouring parts, and can even cause a large scale collective rearrangement.

Another question that may arise is whether optical experiments, using the heme groupas a probe, reveal all dynamical processes that occur within the dynamic range that iscovered. Naturally, the heme group is most sensitive to fluctuations occurring within thevicinity of the heme group, but such can also be part of large scale motions. However, awider range of experimental techniques can reveal different aspects of the energy landscape.For instance, recent infrared photon echo experiments on CO bound to myoglobin [Rel96a,Rel96b] showed that fast fluctuations at higher temperature may point towards more glass-like features of the protein energy surface.

Finally, it is important to find out whether the features of the energy landscape arespecific to myoglobin or fit within a more general framework. Obviously, such knowledgecan only be obtained by studying a wider range of systems. The concept of conformationalsubstates certainly seems much more widely applicable, [Ehr92, Den96, Dzu97] while linenarrowing experiments on cytochrome c and horseradish peroxidase indeed show similarbehavior to that of myoglobin. [Tho95a, Zol91a]

Appendix: Spectral diffusion in ethanol glass

The experiments on heme proteins presented in this chapter have been motivated bystudies, using the same methods, on chromophore doped glasses and polymers by Meijersand Wiersma. [Mei92, Mei94a, Mei94b] One of the most striking results from this earlierwork, is the plateau observed in the waiting time dependence of Zn-porphin in EtOD glassat 1.5 K. Zn-porphin has the same chemical structure as Zn-mesoporphyrin IX, howeverwithout any side chains. Meijers and Wiersma observed that the line width as a function oft remains constant in the region between roughly 1 µs and 1 ms, while exhibitingwlogarithmic broadening outside this time window. The interpretation suggested by Meijersand Wiersma is that the distribution of two-level system fluctuation rates is hyperbolic, butexhibits a gap between 1 MHz and 1 KHz. Several alternative explanations for this resulthave been suggested. These include the presence of different types of two-level systems[Jan93], the presence of different coupling mechanisms between the two-level systems andthe chromophores [Zim96], and recently, the existence of heating effects. [Zil97, Neu97]Since in some of this work [Jan93, Sil96] the actual existence of the plateau has been underdebate we, motivated by the improved performance of the experimental set-up, repeated theexperiments of Meijers and Wiersma, and, to obtain more insight into the role of thechromophore, performed a study, under identical experimental conditions, using thechromophore Zn-mesoporphyrin IX, which is the same chromophore that was used in the


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Figure A.1 Spectral diffusion in EtOD glass for Zn-porphin (circles), and Zn-mesoporphyrin IX (triangles) at 1.8 K. The data were averaged from a maximum of five datapoints. The size of each symbol is proportional to the number of data points that wereaveraged. Note how the data for Zn-porphin can be constructed from the data for Zn-mesoporphyrin IX assuming a heating effect as was shown in Fig. 5.9.

work on Zn-myoglobin. The results of this experiment are displayed in Figure A.1. Note thatthe temperature at which the experiment was performed (1.8 K) is slightly higher than in theoriginal experiments of Meijers and Wiersma. The results a

university of groningen exploring protein energy ... · was recently reported, [tho97] a full...

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