Protein dynamics

Physica A 201 (1993) 332-345 North-Holland SDI: 037%4371(93)E0267-I

Protein dynamics Fritz Paraka3b and Hans Frauenfelderc’d “Institut fiir Molekulare Biophysik, FB 21 Universitiit Mainr J. Welderweg 26, 55099 Mainz, Germany bFakultiit fiir Physik E17, T.U. Miinchen, 85748 Garching, Germany ‘National Laboratory of Los Alamos, Los Alamos, NM, USA ‘University of Illinois, Urbana, IL, USA

Protein dynamics reveals the complexity of these biomolecules. The structural fluctuations and relaxations are determined by a rugged energy landscape where the vallies, the conformational substates, are arranged in a hierarchy of tiers. Several experimental techniques have been used to study the different aspects of protein dynamics. We discuss X-ray structure determinations and pressure tuned hole burning experiments to study structural distributions. Equilibrium fluctuations have been studied by Mijssbauer spectroscopy, Rayleigh scattering of Mijssbauer radiation and incoherent neutron scattering. Most results on structural relaxations have been obtained from the CO rebinding kinetics in CO ligated myoglobin after flash-photolysis. In addition some MGssbauer investigations of structural relaxation are discussed.

1. Proteins as complex systems

Physicists used to be proud that they were only looking at simple systems and they left the real systems to the chemists and the engineers. During the past few decades, however, a shift has occured and physicists have begun to realize that there can be beauty in complex systems. Glasses, spin-glasses, and other disordered systems have become fashionable and the field of complexity has acquired respectability. Nature is full of complex systems; the brain is a prime example. It will, however, be a long time before a “physics of the brain” with predictive power, can be created and we have to be more modest. We can therefore ask: what is the simplest complex system that shows true complexity, but is accessible at present to our tools and techniques? We will try to show here that biomolecules, in particular proteins, can be systems of interest to physicists. Proteins are the machines of life; they perform essentially all work in living They are formed from 20 building blocks, the amino acids. systems”. Following commands from DNA, of the order of 100 amino acids are linked xl For an introduction to proteins see R.E. Dickerson and I. Geis [l] and L. Stryer [2]. 037%4371/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

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together to form a long polypeptide chain. The chain folds into the working system, an approximately globular nearly closed packed structure. The chemical bonds along the primary chain are strong and cannot be broken by thermal fluctuations. Weak forces like hydrogen bridges, hydrophobic interactions, van der Waals forces and electrostatic forces stabilize the three-dimensional structure. These weak bonds can break and reform and permit extensive motions. Without these motions, proteins could not function. Consequently the study of motions is crucial. Basic concepts for an understanding of the dynamic behaviour of proteins emerged from the study of the rebinding kinetics of CO in myoglobin, Mb, after flash photolysis of CO-ligated myoglobin, MbCO [3], MbCOkMb+CO.

(1)

The rebinding kinetics have been studied in a temperature regime from 40 K to room temperature. While at room temperature rebinding kinetics followed the expected exponential time course, the rebinding data below about 160 K showed extreme exponential behaviour. The survival probability N(t), i.e. the fraction of proteins that had not rebound a ligand at the time t after the photodissociation, had to be described by a power law, N(t) = N(0) (1 + Id)-“. At low temperatures, the photodissociated CO molecule remains in a cavity inside the protein and rebinds from there. If rebinding were to occur over a barrier of unique height H, N(t) would be exponential in time, N(t) = exp(-kt), with k given by an Arrhenius equation k(H, T) = A exp(-HIRT). The experimentally observed nonexponential time dependence can be explained by assuming that the barrier does not have a unique height, but the different protein molecules have different barrier heights, with g(H) dH denoting the probability of finding a barrier between H and H + dH. The survival probability then becomes N(t) = j g(H) exp[-k(H)

t] dH .

(2)

Here one characteristic signal of a complex system appears, a distribution. Properties in complex systems, in particular in proteins, cannot be described by unique values, but must be characterized in terms of distributions. The description of the rebinding kinetics in terms of a temperature-independent activation enthalpy distribution g(H) works well up to a temperature of about 160 K. The crucial question then arises: what gives rise to g(H)? The interpretation introduced in about 1975 [3] is again based on complexity: a protein folds relatively rapidly and therefore cannot find the state of lowest

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conformational

Fig. 1. Scheme of the conformational

space, one-dimensional

coordinate

cut. G is the Gibbs free energy.

energy. In each individual folding event, a somewhat different structure will be reached. If the Gibbs energy of the protein is plotted as a function of a conformational coordinate, a rugged energy landscape, sketched in fig. 1, will result. Of course fig. 1 gives only a one-dimensional cross section through a high-dimensional energy landscape, but the essential idea is clear: the ground state of a protein is highly degenerate. Proteins share this property with other complex systems such as glasses and spin glasses, but the consequences of this property are particularly clear in proteins. Each valley in the energy landscape corresponds to a conformational substate (CS). Why do proteins exhibit rugged energy landscapes? The answer most likely lies in the combination of two crucial properties of complex systems, disorder (or aperiodicity) and frustration. Proteins clearly are aperiodic. Equally clear they are frustrated: sidechains from different amino acids try to occupy the same space upon folding. The nonexponential time dependence of CO rebinding after photodissociation is only one manifestation of the existence of conformational substates. Their existence has been verified by a number of other experiments such as X-ray structure analysis [4-61, Mossbauer spectroscopy [7-121, and specific heat measurement [13,14]. These and related experiments have led to a number of concepts which probably hold not only for myoglobin, but may be generally true for all proteins. A protein like Mb can exist in a number of conformations or states. Myoglobin exists in two stable states, the ligated (r) conformation MbCO, and the unligated (t) conformation Mb. In Mb, the sixth coordination is free. The structures of the two states differ; in MbCO, the iron is in the heme plane and the heme is essentially planar. In Mb, the heme is domed and the iron has moved out of the heme plane. As mentioned above, protein molecules in a given conformation do not all have exactly the same structure, but differ somewhat. In analogy to magnetic substates, the different structures are interpreted and called conformational substates.

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These preliminary remarks and analogies to atomic, condensed matter, nuclear, and particle physics suggest that the first goal of the experimental exploration and the theoretical interpretation of protein dynamics should concentrate on the energy landscape. Once general features of the energy landscape are known, additional aspects such as structural distributions, equilibrium fluctuations, and structural relaxations can be explored. Of course, in reality all these features are studied simultaneously.

2. The energy landscape of proteins In fig. 1 we have sketched a rugged energy landscape. The study of such landscapes in proteins is still at a very early stage, comparable to atomic physics at Balmer’s time. Only in one protein, Mb, have the extensive investigations been performed. These studies imply that the arrangement of substates is not as simple as indicated in fig. 1 [15]. Substates are arranged in a hierarchy of at least four tiers [16]. The arrangement is shown schematically in fig. 2. The barriers between substates in tier 0 (CS 0) are considerably higher than those in tier 1 and so on. It turns out that there are only a few substates in tier 0 and they are different enough so that their structure, dynamic and kinetic properties, and their relative energies, entropies, and volumes can be determined. They can therefore be characterized individually and they can be called taxonomic substates. Substates of the lower tiers are more numerous, can no longer be characterized individually and their properties must be described by distributions; they can be called statistical substates. At very low

MbCO

Tier

0

Tier

1

.. Tler

n

i

‘;

..

. . _.

CSO

Taxonomic

CSl

Statistical

.. .. . .. ;: .

.‘:

; : ; ‘, .a..

,+,

; ‘, . .

.

: ..

: .. CSn . l

Fig. 2. Hierarchy of conformational substates in proteins. CO ligated myoglobin, MbCO, has a well-defined conformation with a high number of conformational substates at different tiers.

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temperatures, a given protein will be frozen into a particular substate. As the temperature increases, equilibrium fluctuations will set in and the protein will move among the substates of the lower tier, say CS,. No transitions among the higher substates occur. As the temperature is increased further, transitions among the higher CS will also occur. The protein motions become progressively more ergodic. Finally, above about 200 K transitions among the taxonomic substates will set in and the protein will fluctuate wildly. This overview shows that there are considerable similarities between the energy landscape in proteins and in other “simple” complex systems such as glasses. It also shows that the exploration of the energy landscape is only at a beginning and much work will be required before a more complete picture will be available.

3. Structural distributions The energy landscape alone does not tell us about the structural properties of a given substate. Structural information is needed, however, to understand the function of proteins. Taxonomic substates can be studied by standard techniques. Statistical substates, however, require a different approach. Their structural distributions are revealed themselves in the Debye-Waller factor of X-ray structure analysis, in NMR structure determination and in hole burning experiments. Figs. 3 and 4 show the results of X-ray structure analysis. In fig. 3 the mean square displacement, (x2), obtained from the Debye-Waller factor

0.3

2 0.2 t-T 5 0.1

0 0

120

80

40

Residue

160

Number

Fig. 3. Mean square displacements, (x2), of the residues of Mb averaged over atoms N-C-C as function of the residue number determined by X-ray structure circles T = 300 K [6], full circles T = 40 K (Aumann, Hartmann, Nienhaus, Parak,

the backboneanalysis; open unpublished).

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r

-

x

x

e o,a~

txx 0

60

180

120

f I 240

o ooooo

zj I 300

T(K)

Fig. 4. Mean square displacements, (x’) , in Mb determined by different techniques as function of the temperature T. Circles: Mossbauer effect on the iron; full circles: Mb deoxy crystals; open circles: freeze dried Mb; full square: RSMR measurements at Bragg reflections of a single crystal; open squares: average values of all non-hydrogen atoms determined by X-ray structure analysis; crosses: incoherent neutron scattering, average over all H-atoms which cannot be replaced by soaking in D,O [21].

during the structural refinement procedure is shown for measurements at room temperature and at 40 K. The displacements are averaged over the backbone atoms -N-C-Cof each residue and plotted as a function of the residue number. In fig. 4 we give the mean square displacement, (x2), averaged over all non-hydrogen atoms of myoglobin as a function of temperature (open squares). Several features are immediately obvious: the structural distributions vary along the chain as discussed in [4]. The distributions are large at the loops and smaller along the helical parts of the molecules. They depend on temperature. This observation proves that the molecules are not statically frozen in the statistical substates but fluctuate among them. Low-temperature data and the extrapolation to T = 0 K show, however, that there exists a zero-point distribution which cannot be explained by zero-point vibrations. This is one of the facts that makes proteins similar to glasses. Recently, a pressure tuned hole burning experiment has been performed [17] using protoporphyrin IX as chromatophore. This chromophore was investigated in two different environments. First it was dissolved in a mixture of dimethylformamide and glycerol. In the second sample the heme group of myoglobin was replaced by protoporphyrin IX. After burning a hole into the inhomogeneously broadened line around 16 000 cm-’ the shift of this hole was measured as a function of the applied pressure. Fig. 5 shows the results obtained in the glass forming liquid and in the protein. Protoporphyrin IX

338

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H. Frauenfelder

,.I.IIII,.I,II.I..,,,,,,,,15800

16000

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-80 16200

15600

15800 i7

16000

16200

(cm-‘)

Fig. 5. Frequency shift of a hole per pressure as function of the hole burning frequency. (a) Protoporphyrin IX dissolved in dimethylformamid and (b) apomyoglobin reconstituted with protoporphyrin IX [17].

embedded in the glass forming liquid yields the well-known results for organic glasses: one well-defined vacuum frequency (v,,, = 15 880 cm-‘) and one welldefined slope which yields the compressibility (K = 0.1 GPa-‘). The chromatophores are sensitive to the environment within a sphere with a radius of about 30 A. The result indicates that on the average the inhomogenities around each chromatophore are the same. Protoporphyrin IX incorporated into apomyoglobin behaves very different. In addition to the vacuum frequency found in the simple glass sample we obtained another one at vvac= 16 080 cm-‘. The compressibilities vary in the range from K = 0.12 to 0.30 GPa-‘. Although these experiments again indicate a glass-like behaviour there is one central difference: within their range of sensitivity, the chromatophores “see” on the average different inhomogenities. This result can only be understood assuming that myoglobin molecules in different conformational substates stabilize different tautomers of protoporphyrin IX. The model leads to a correlation between absorption frequencies and specific protein structures.

4. Equilibrium fluctuations In X-ray structure analysis all molecules of the crystal contribute to each Bragg reflection. Therefore, the measured mean square displacements represent an ensemble average. The (x2)-values reveal dynamic processes only via their temperature dependence. In order to study equilibrium fluctuations we need time sensitive experimental methods. Time and energy are conjugated quantities. Therefore, the energy resolution of a spectroscopic method determines its time sensitivity. In iron-containing proteins one can study the structural fluctuations at the position of the iron by using Mossbauer spec-

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troscopy. The energy resolution of about lo-’ eV corresponds to a sensitivity for motions on a time scale faster than 1OOns. Incoherent neutron scattering yields information on protein dynamics on a time scale of 100~s. In the neutron experiments one averages over the motions of all hydrogen atoms of the molecule. Fig. 6 shows the Mossbauer spectrum of crystals of deoxymyoglobin measured at 80 K and at room temperature. The 80 K spectrum can be fitted by two Lorentzians with an area proportional to exp(-k2(X2)) with k = 27rlh and A = 0.86 A for “Fe. The same fit is not sufficient for the room temperature spectrum. A broad line has to be added indicating a quasielastic process. Fig. 4 gives the mean square displacements, (x2), of the iron in myoglobin obtained from the area of the Lorentzians as a function of temperature. Measurements on deoxymyoglobin crystals and on freeze dried myoglobin are compared. At low temperatures the (x2)-values can be fitted phenomelogically by a Debye law. At about 200 K in both samples the mean square displacements increase dramatically indicating the availability of new channels of motions. Intuitively one may identify the onset of the increase with a glass transition at T, = 200 K. This glass-like transition occurs also in the dry protein although with a smaller magnitude. The glass-like transition is an inherent property of the protein. The hydration water makes the motions easier but the protein is not simply a label for a glass transition within the crystal water or the solvent. Rayleigh scattering of Mossbauer radiation (RSMR) is another method to

I

I

I

-5

0

5

Velocity

1

(mm/s)

Fig. 6. Miissbauer spectra of deoxymyoglobin crystals at T = 80 K and T = 245 K. The transmission of the spectra is drawn in different scales. The solid lines give at least squares fit with two Lorentzians. In the high temperature spectrum the same parameters were used as in the 80K spectrum. The discrepancy to the experimental data is clearly seen at 245 K.

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investigate dynamics with the energy resolution and the time sensitivity of Mossbauer spectroscopy. In these experiments the 14.4 KeV radiation of a 57Fe transition is scattered by all electrons within the sample. The scattered radiation is analyzed by a Mossbauer absorber. Only quanta that have been scattered without an energy transfer can be absorbed by a Mossbauer effect in this analyzer [18]. Consequently, one is able to separate elastic and inelastic scattering. This method has been applied to analyze the Bragg peaked inelastic scattering in a myoglobin crystal [19]. The existence of inelastic scattered radiation peaked in the vicinity of the Bragg reflections indicates the presence of long-range correlated motions within the protein crystal with a phonon wavelength larger than the unit cell dimensions. We call these motions lattice vibrations. A large contribution comes from intermolecular motions. Note that the mean square displacement determined by RSMR averages over all atoms within the molecule. In fig. 4 an (x*)-value is shown, determined by RSMR from Bragg reflections in the resolution range between 15 and 3.6 A [19,20]. It is close to the linear extrapolation of the low temperature (x*)-values determined by Mdssbauer absorption spectroscopy at the position of the iron. Consequently, one has to assume that below Tg the main contributions to the mean square displacement come from lattice vibrations while above Tg intramolecular motions dominate. Incoherent neutron scattering allows to determine energy transfers up to 10 meV [21,22]. In freeze dried myoglobin hydrated with D,O (h = 0.38 g D,O/g Mb) below 200 K elastic and inelastic scattering can be well separated. Quasielastic scattering becomes important at higher temperatures (compare fig. 7). From these measurements average mean square displacements have been calculated for all hydrogen atoms in myoglobin that cannot be exchanged by soaking the proteins in D,O. The results are again shown in fig. 4. The phenomological behaviour is similar to that found by Mdssbauer spectroscopy. Even the glass transition occurs in the same temperature region. In the low temperature regime the mean square displacements of the protons are clearly larger than the lattice vibrations determined by Mossbauer spectroscopy. Probably this comes from an additional contribution of harmonic intramolecular proton motions. There exist a number of models in order to describe the intramolecular dynamics of proteins above T,. Quasielastic lines in the Mossbauer spectra and the neutron scattering experiments indicate that some type of diffusional motion is present. Therefore some models are based on the diffusion within water. Some water molecules cluster together by hydrogen bridges and perform vibration during the time r,,. During the time TV some molecules perform free diffusion (compare for instance [23]). Sitting on a specific atom within the protein, for instance the iron, one can apply this picture. During the

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I

0 250 K a 300K

I

I

4 ElmeV

0

I

8

J

Fig. 7. Dynamical structure factor S(Q, E) at Q = 1.5 A-’ resealed by the Bose factor to a common temperature of 180 K [22]. Q corresponds to k and E to o of eq. (3).

time T,, a molecule performs vibrations within a certain conformational substate. With respect to the iron the molecule goes into a transition state for the time r1 where it performs diffusional type motions till it is trapped again in another conformational substate. Mossbauer experiments have been analyzed with the Brownian oscillator model. In order to limit the diffusion in space, the Langevin equation was modified by introducing a harmonic back-driving force

WI. Mossbauer and neutron scattering experiments can also be described using the model of jump diffusion. Here the time r1 is neglected and the jump rate is determined only by r,, where the molecule rests in one conformational substate. A distribution of T,, according to Davidson-Cole [25] is assumed. This model yields the scattering law

S(k, 0) = -

Im(1 + io7JP 7To

,

where hw is the energy transfer and TVis the maximum value of T,,. In the case of neutron scattering this equation describes the experimental data over a wide range of energy transfers. The corresponding processes are attributed to a-relaxations. The experimentally obtained S(k, o) curve shows a biphasic behaviour. The deviations of the experimental values from eq. (3) are attributed to /?-relaxations [21]. The Davidson-Cole distribution of T,, is also

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used to interpret Mijssbauer experiments. Astonishingly iron dissolved in glycerol behaves very similarly to iron in myoglobin. The interpretation of the glycerol data is given in [26]. First results of the application of the DavidsonCole model to myoglobin are shown in [27]. Neutron scattering experiments on myoglobin as well as Mossbauer experiments in glycerol can be understood by using the mode-coupling theory [22,28]. Nevertheless, we are still far away from an unique physical picture of protein specific dynamics. It should be mentioned that in all models where a vibration in a certain cage is assumed the square root of the (x*)-values determined from X-ray structure analysis can be used to estimate the dimension of this cage with respect to each individual atom.

5. Structural relaxation Information on protein motions comes from two types of experiments, protein quakes [15] and pressure or temperature jump studies [29]. The first type can be explained with the example of myoglobin. The liganded and the deoxy form of Mb have a somewhat different structure. After photodissociation, the protein consequently must change its structure and this rearrangement will move from the heme outward like a quake. The protein quake can change the properties of some spectroscopic markers [30] and it can also increase the height of the barrier for rebinding at the heme iron [31]. Both of these effects have been observed [30,32,33]. A closer look at these relaxation effects reveals more similarities between proteins and glasses: the time dependence of the relaxation phenomena is given by stretched exponentials,

4(t) = exp[-WI , with /3 s 1. The temperature dependence of the rate coefficient not given by an Arrhenius relation, but by a Ferry law, k(T)

=

A exp[ - (EIRT)2]

.

k

in eq. (4) is

(5)

These two relations again show that proteins are complex systems and that their study can yield insight into the physics of complex systems. One remarkable effect is seen if rebinding after photodissociation at low temperatures is investigated after illumination: extended illumination slows ligand binding [30,34]. A light-induced shift of the rebinding barrier is also found by Mossbauer spectroscopy [35]. The result of the Mossbauer experi-

F. Parak, H. Frauenfelder

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" 10-l

" 100

" 101

" 102 Time

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" 103

" 10'

" 105

" 108

IO'

(s)

Fig. 8. Rebinding kinetics of CO after flash-photolysis of MbCO. N(t) is the fraction of molecules that had not rebound CO after the time t. Circles: optical experiments in the Soret region at T = 40 K taken from [37]; squares: Miissbauer experiments at T = 37.5 K; line: interpolation of the Miissbauer data to T = 40 K [35].

ment is shown in fig. 8. The faster curve is taken from ref. [3] and represents rebinding without extended illumination. The slower curve was taken by Mossbauer spectroscopy after illuminating the sample for 24 h. The dramatic effect of the illumination is clearly visible. Finally we would like to mention a new method to study structural relaxations in myoglobin [36]. The Fe(II1) of metmyoglobin dissolved in a water-glycerol solution is reduced by irradiation with X-rays. The resultant Fe(I1) complex is in the low spin state. If the reduction is performed at 80 K most of the molecules stay in the conformation of metmyoglobin. Raising the temperature allows the molecules to relax to the equilibrium deoxymyoglobin state, with Fe(I1) high spin. Following the relaxation kinetics at different temperatures one can determine the barrier height distributions between the intermediate Fe(I1) low spin myoglobin and the equilibrium Fe(I1) high spin myoglobin. First results indicate that the relaxation process is nonexponential in time. It cannot be described by a temperature independent barrier height distribution.

Acknowledgements

Support from the Deutsche Forschungsgemeinschaft Chemie is gratefully acknowledged.

and the Fonds

der

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K. Korszun, S. Khlaid, C. Alter, J. Sorge and E. Gabbidon, Biochemistry 26 (1987) 4785. [35] H. Winkler, M. Franke, A.X. Trautwein and F. Parak, Hyperfine Interactions 58 (1990) 2405. [36] V.E. Prusakov, R.A. Stukan and F. Parak, Chemitsch. Fisika 9 (1990) 44 [Russian]. [37] A. Ansari, J. Beret&en, D. Braunstein, B.R. Cowen, H. Frauenfelder, M.K. Hong, I.E.T. Iben, J.B. Johnson, P. Ormos, T.B. Sauke, R. Scholl, A. Schulte, P.J. Steinbach, J. Vittitow and R.D. Young, Biophys. Chem. 26 (1987) 337.