[16]Observation of internal motility of proteins by nuclear magnetic resonance in solution

[16]

NMR

OF PROTEIN

MOTILITY

IN SOLUTION

307

leads to fluctuations larger than would be permitted in a rigid polypeptide matrix. For motions on a longer time scale, our understanding is more limited. When the motion of interest can be described in terms of a reaction path (e.g., hinge-bending, local-activated event), methods exist for determining the nature and rate of the process. However, for the motions that are slow as a result of their complexity and involve large-scale structural changes, extensions of the approaches described in this review are required. Harmonic and simplified model dynamics, as well as reaction-path calculations, can provide information on slower processes, such as opening fluctuations and helix-coil transitions, but a detailed treatment of protein folding is beyond the reach of present methods. It is to be hoped the required methodological developments and the experiments to test the results will not be too long in forthcoming.

[16] O b s e r v a t i o n o f I n t e r n a l M o t i l i t y o f P r o t e i n s b y N u c l e a r M a g n e t i c R e s o n a n c e in S o l u t i o n

By GERHARD WAGNER and KURT WUTHRICH Protein conformations are the result of a multitude of weak, nonbonding interactions between different atoms of the polypeptide chain and between the polypeptide and the surrounding medium. The latter may be, for example, an aqueous solvent, an ordered lipid lattice in biological membranes, or the crystal lattice in the single crystals used for X-ray studies. Specific interactions with substrates and effector molecules may also influence the protein conformation. Since the contribution of each individual nonbonding interaction to the free energy which stabilizes the conformation is typically of the same order of magnitude as the thermal energy at temperatures near 300 K, these "secondary bonds" are constantly being broken and reformed. Two consequences of the resulting dynamic nature of the spatial molecular structures are that protein conformations can readily adapt to changes of the environment and that the spatial structures of protein molecules in thermodynamic equilibrium fluctuate about a structure of minimum free energy. Detailed descriptions of the conformational transitions that occur when the environment is varied have been presented for several proteins for which both the initial and final states could be studied by single-crystal METHODS IN ENZYMOLOGY, VOL. 131

Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.

308

S T R U C T U R ADYNAMICS L AND MOBILITY OF PROTEINS

[161

X-ray methods.1 With the use of nuclear magnetic resonance (NMR) such studies can be further extended to proteins in noncrystalline environments, which may be more closely related to the physiological milieu. 23 NMR data will in general bear on both static and dynamic aspects of the protein conformations and the method offers a wide spectrum of possible applications. The following discussion, however, is limited to the use of NMR for investigations of intramolecular rate processes ("internal motility") in proteins which are in thermodynamic equilibrium. Prominent NMR manifestations of internal protein motility are found in the spin relaxation, 4-1° in flipping motions of the aromatic side chains, 7,J°,lJ-~5 and in the exchange of labile protons with the solv e n t . 7,1°,16-25 NMR studies of these processes at variable temperature and pressure result in a detailed, quantitative characterization, which includes activation enthalpies, activation entropies, and activation v o l u m e s . 14,23.25 For each of these different NMR measurements the information content is R. Huber, Trends Biochem. Sci. 4, 227 (1979). 2 K. Wiithrich, G. Wider, G. Wagner, and W. Braun, J. Mol. Biol. 155, 311 (1982). 3 W. Braun, G. Wider, K. H. Lee, and K. WiJthrich, J. Mol. Biol. 169, 921 (1983). 4 A. Allerhand, D. Doddrell, and R. Komoroski, J. Chem. Phys. 55, 189 (1971). 5 D. Doddrell, V. Glushko, and A. Alterhand, J. Chem. Phys. 56, 3683 (1972). 6 D. E. Woessner and B. S. Snowden, Adv. Mol. Relaxation Processes 3, 181 (1972). 7 K. Wi~thrich, " N M R in Biological Research: Peptides and Proteins." Elsevier, Amsterdam, 1976. 8 R. Richarz, K. Nagayama, and K. W~ithrich, Biochemistry 19, 5189 (1980). 9 A. A. Ribeiro, R. King, C. Restivo, and O. Jardetzky, J. Am. Chem. Soc. 102, 4040 (1980). 10 O. Jardetzky and G. C. K. Roberts, "NMR in Molecular Biology." Academic Press, New York, 1981. " K. Wiithrich and G. Wagner, FEBS Lett. 50, 265 (1975). 12 I. D. Campbell, C. M. Dobson, and R. J. P. Williams, Proc. R. Soc. London Ser. B 189, 503 (1975). J3 I. D. Campbell, C. M. Dobson, G. R. Moore, S. J. Perkins, and R. J. P. Williams, FEBS Lett. 70, 96 (1976). 14 G. Wagner, A. DeMarco, and K. W/ithrich, Biophys. Struct. Mech. 2, 139 (1976). 15 K. Wfithrich and G. Wagner, Trends Biochem. Sci. 3, 227 (1979). 16 j. D. Glickson, C. C. McDonald, and W. D. Phillips, Biochem. Biophys. Res. Commun. 35, 492 (1969). 17 S. Karplus, G. H. Snyder, and B. D. Sykes, Biochemistry 14, 3612 (1973). ~8 A. Masson and K. Wiithrich, FEBS Lett. 31, 114 (1973). 19 B. D. Hilton and C. K. Woodward, Biochemistry 18, 5834 (1979). 20 R. Richarz, P. Sehr, G. Wagner, and K. WiJthrich, J. Mol. Biol. 130, 19 (1979). 2~ G. Wagner and K. Wiithrich, J. Mol. Biol. 130, 31 (1979). 22 G. Wagner and K. Wtithrich, J. Mol. Biol. 134, 75 (1979). 23 C. K. Woodward and B. D. Hilton, Biophys. J. 32, 561 (1980). 24 G. Wagner and K. Wfithrich, J. Mol. Biol. 160, 343 (1982). 25 G. Wagner, Q. Rev. Biophys. 16, I (1983).

[16]

NMR

O F P R O T E I N M O T I L I T Y IN S O L U T I O N

309

dramatically increased when sequence-specific resonance assignments have been established. With the presently available experimental techniques it is then possible to map the local motility across the entire protein structure and thus to investigate concerted motions which would involve larger areas of the molecular structure. This chapter describes primarily how such a result can be obtained. NMR Time Scales NMR experiments provide three separate "time windows" for observation of kinetic processes. Thus motional processes in proteins with widely different time constants, r, can be observed: slow processes with r >~ 10 min, events with medium time constants, r ~ 1-10 -s sec, and fast processes with r ~< 10 -9 sec. For slow processes where the state of the system does not change significantly during the time needed for recording a one-dimensional (1D) or two-dimensional (2D) NMR spectrum, the time course of the reaction can be monitored by comparison of different, consecutively recorded NMR spectra. This requires that spectral parameters change as a consequence of the kinetic process. One particular application is the measurement of hydrogen-deuterium exchange rates. Processes on a medium time scale can be observed when a nucleus undergoes an exchange between two sites, A and B, with the resonance frequencies VA and VB, respectively. The rate of exchange, re, can be determined by line shape analysis if it is in the range of the difference of the resonance frequencies, Av = [VA -- VB[. The expected line shapes are shown in Fig. 1. There are two kinetic limits. If the exchange rate is much slower than Au, two separate resonances are observed at VAand VB. If the exchange rate ve is much faster than hv, one averaged resonance is observed at (VA + UB)/2. Between these extreme situations the exchange broadens the resonances and then the exchange rate can be determined from line shape analysis. In the limit of slow exchange, the exchange rate v~ is simply related to the line broadening, By, of the resonances at /2A and b' a : ve = 27rSv

(1)

In the limit of fast exchange the exchange rate, v~, can be obtained from the line broadening, 8u, of the averaged resonance at (VA + Va)/2: /"e ~--

"n'(Av) 2/48v

(2)

Between these limits, in the range of intermediate exchange, the exchange rates have to be determined by comparison of the line shapes with com-

310

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

[16]

v~ v

4.10 6

4.101

__

_

2"if'

__

4 . 1 0 -1

I

!! I

'

4.10-"

FIG. 1. Line shapes for a spin jumping between two equally populated states A (UA) and B (vB) for varying values of the quotient of the relative chemical shift in Hz IrA - vBI, and the exchange frequency, ve.

puter simulated spectra. 10,13,14As long as the exchange is sufficiently slow so that two lines can be observed, saturation transfer techniques can also be used to determine two-site exchange rates. 26-28 With this method the resonance of one of the exchanging protons is saturated by selective radio frequency irradiation. This saturation is transferred to the other, corresponding resonance position by the exchange process. Measurement of the amount of saturation transfer allows determination of the exchange r a t e s . 26-28

Similar exchange effects are manifested in the averaging of spin-spin coupling constants. If the torsion angle between two coupled spins jumps between two orientations with the respective coupling constants JA and JB, an average coupling constant will be observed if the jump rate b' e >~> ]JA JB[- If ve ~ ]JA -- JB[ both coupling constants will be manifested in the spectrum. 10,29 - -

26 S. Fors6n and R. A. Hoffman, J. Chem. Phys. 39, 2892 (1963). z7 I. D. Campbell, C. M. Dobson, R. G. Ratcliffe, and R. G. P. Williams, J. Magn. Reson. 29, 397 (1978). 28 j. j. Led and H. Gesmar, J. Magn. Reson. 49, 444 (1982). 29 K. Nagayama and K. Wiithrich, Eur. J. Biochem. 114, 369 (1981).

[16]

N M R OF PROTEIN MOTILITY IN SOLUTION

311

Fast internal motions that occur on the time scale of the NMR frequencies can be studied with relaxation time measurements. In globular proteins in solution the relaxation times for spin 1/2 nuclei are mainly determined by the modulation of the dipole-dipole interactions between different nuclei by motional processes. The dominant contribution to these motional processes comes from the overall rotational diffusion of the globular protein (the correlation time for the overall rotation of a protein of ~6000 Da is ~3 × 10 -9 sec). If there are internal motions with similar or faster rates, these can be manifested in the relaxation times of the respective nuclei. The data can be obtained either from measurements of spin-lattice relaxation times, TI, spin-spin relaxation times, T2, or cross-relaxation rates in nuclear Overhauser enhancements. 4-1°

Exchange of Labile Protons A characteristic feature of a globular protein structure is the network of intramolecular hydrogen bonds. The difference in Gibbs free energy of intramolecular hydrogen bonds relative to intermolecular hydrogen bonds with the solvent is of the order of only a few kcal/mol. Thus opening and reforming of these bonds have to be expected to be main features of internal motions in proteins. As a consequence of the opening of hydrogen bonds, contact between internal amide protons and the solvent may occur. If the protein is transferred from a protonated to a deuterated solvent, such internal amide protons will exchange against deuterium and their IH NMR signals will disappear. 3°,3~ The amide protons of the peptide bond provide the most complete set of probes to study hydrogen exchange in proteins. Nevertheless, other labile protons have been used, such as the NH2 groups of asparagine or the indole NH of tryptophan. 32'33 In principle the NH2 groups of glutamine and the labile protons of arginine or lysine side chains can also be studied when located in the interior of proteins. 3L32 All other labile protons, in particular those of hydroxyl or carboxyl groups, are expected to exchange too rapidly to be studied by N M R . 31'32 In 1D NMR spectra the intensities of the absorption lines are directly proportional to the ~H concentration at the respective peptide groups. This has commonly been used to measure exchange rates of well separated resonances. As an example, Fig. 2 shows the low field spectrum of a 30 A. Hvidt and S. O. Nielsen, Adv. Protein Chem. 21, 287 (1966). 31 S. W. Englander, S. W. Downer, and H. Teitelbaum, Annu. Rev. Biochem. 41,903 (1972). 32 K. Wiathrich and G. Wagner, J. Mol. Biol. 130, 1 (1979). 33 I. D. Campbell, C. M. Dobson, and R. J. P. Williams, Proc. R. Soc. London Ser. B 189, 485 (1975).

312

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

25 23 24

.92

!,

,, ,~,.,

2.03

,

.,/,.'Iv I

,

cxch.

11

Z9

m

1.18

2.85

[16]

,Ill I

'

,,

1

PPM

FIG. 2. Region from 6.0 to 11.0 ppm of the 1H NMR spectra of a snail trypsin inhibitor at 36 ° and p2H 5.0 recorded at different times after dissolving the protein in 2H20. The resonances of the labile protons observed in the top spectrum are numbered in the order of the chemical shifts. The time which has elapsed between the sample preparation and the recording o f the spectra is indicated on the left-hand side. 35

snail trypsin inhibitor, recorded at different times after the protein was dissolved in 2H20. The signals of labile protons which are numbered in the first spectrum disappear with time, and exchange rates can be calculated from a plot of the peak intensities vs time. 35In two-dimensional correlated (COSY) spectra the relative intensity of each cross peak is determined by the degree of protonation of the peptide group. Therefore the time dependence of the intensity of each individual cross peak can be used for determining exchange rates. This has been done for the basic pancreatic trypsin inhibitor (BPTI),24,25 a s is demonstrated in Figs. 3 and 4. With this technique a complete survey of ~H-2H exchange rates has been obtained. These data are shown in Fig. 5, which is a plot of the logarithm of the exchange rates vs the amino acid sequence. Exchange rates faster than 10 -1 min -1 cannot be measured by this method. 24In Fig. 5 this is indicated 34 R. E. Wedin, M. Delepierre, C. M. Dobson, and F. M. Poulsen, Biochemistry 21, 1098 (1982). 35 G. Wagner, K. Wtithrich, and H. Tschesche, Eur. J. Biochem. 89, 367 (1978).

[16]

N M R OF PROTEIN MOTILITY IN SOLUTION

*

/ ~

0

-4

'~

..... O

'O

313

I180 N24

~Y23

K41 O e " Ir 7 ( ~

F33 O31~

~L

0

R20

5

N44

~F22

0

1720 _rain

83040 rain

0Y21

~ _

74 0

0

v-

Oo $ o 0%0

~+

YlO

0 ,----

660 min

,

39840min

G28-

/

G56

R53 b152 +

o

G36

B

O

•

i

0

,L 4 ,

0

0 0

- -240 - - J rain ----

0+_

T32 i

i

-I~

i

I ]

4 wI

O3 ~. :

!~+:

Ila _10min

10

o 9

@:c38

5

oo $ LF880~,in

C30

~

:,I, 0

(ppm)

8

10

u2 (ppm)

L6

1[ (ppm) IdI

0 @ °+;+ /

0 9

8

7

~2 (r,pm)

FIG, 3. Absolute value 500 MHz ~H COSY spectra of 0.02 M solutions of BPTI in zH~O recorded at different times after dissolving the protein. The solutions were freshly prepared at 24 + and then kept at 36 ° to allow exchange of protein amide protons with 2H of the solvent. At the times indicated in the figure, a particular solution was cooled to 24 ° and a spectrum was recorded in 12 hr. Only the region of the NH-C"H cross peaks is shown lot = 3.6-6.0 ppm, co2 = 6.6-10.8 ppm). The peaks that disappeared in the course of the experiment are identified in the last spectrum, where they can be observed readily. Thus this figure affords a qualitative survey of the exchange rates (for quantitative data, see Fig. 4). The peaks that did not disappear within 80,000 rain are identified in the last spectrum. 24

with an upward arrow. These rapidly exchanging amide protons correspond essentially to the protein surface, as can be seen from inspection of the solvent accessible surface area of the individual amide groups calculated from the X-ray structure 24,36,37 (Fig. 5). All exchange rates slower 36 B. Lee and F. M. Richards, J. Mol. Biol, 55, 379 (1971). 37 C. Chothia and J. Janin, Nature (London) 256, 705 (1975).

314

STRUCTURAL

--('~2 = 8.23 EPm

DYNAMICS

8.42 p_pm

AND MOBILITY

[16]

OF PROTEINS

7 5 6 p_pm

6.94 p_pm

C5

L29 IA27

I18

Iro28

RS3

",",' I

.......~ . . . . . .

83040

m m

39840

rnm

15000

mln

........ J''~,'.,'. . .

5880

mm

.......... ",',. . . .

1720 mm

,,, . . . . . . .

'',',,,"

,if ~.'',l'~, v

......... ':":', -

i

,

~

......

......

660

rain

240

mln

10 min

(ppm)

FIG. 4. Vertical cross-sections of the spectra shown in Fig. 3 taken at 4 different positions along the tozaxis. At the top of the figure, those residues are identified for which oJ2coincides with to2 of the cross-section. The cross-peaks of the residues indicated in parentheses are located so close to the cross-sections that tails of the peaks are observed in these presentations. 24

than 10 -~ min -1 must correspond to amide groups that are shielded from solvent contact and therefore provide information on internal motions in the protein conformation. A meaningful interpretation of the exchange rates can be based on the following scheme of the exchange mechanisms25,30,31: kl C(IH)

.

k " O(IH) ~ k_, q-l_,o

k,

O(-'H) .

" C(2H)

(3)

kt

Closed states C(~H) are in equilibrium with open states O(~H). Exchange is possible only from the open states O ( ] H ) and leads, in the presence of 2HzO, to deuteration of the peptide site. The experimentally observable overall exchange rate, km, is approximately 3°,3j

klk3 km -

k2 + k3

(4)

There are two limiting kinetic situations. If k 3 ~ k2 (EXI process) each opening of the "closed state," C, leads to an isotope exchange and we

[16]

N M R OF PROTEIN MOTILITY IN SOLUTION

315

k(min-1)36° i 10-4 i

T

i

10-6 ! i

accessible surface area

6; 4 ÷;

~S

A

I I

oH-bonds

i

i

1

O IIIIInl

II

II

P residue

number

i

1()

20

lid

I

P

30

1 0

40

IIIIIII

!

J

¢ 50

FIG. 5. Amide proton exchange data for BPTI at p2H 3.5 and 36° and selected features of the crystal structure of BPTI. The horizontal scale represents the amino acid sequence of BPTI. The graph at the top is a logarithmic representation of the individual exchange rates, km, at 36°. Arrows pointing upward indicate that the exchange was too fast to be measured with the COSY experiments. Arrows pointing downward indicate that the exchange was too slow to be measured quantitatively within the maximum exchange time. In the lower part of the figure the static accessible surface area is plotted for the backbone peptide nitrogens, and the intramolecular hydrogen bonds in the crystal structure are indicated by filled vertical bars (intramolecular H-bonds with main chain carbonyls) or open bars (H-bonds to side chains or internal water molecules). Residues which are part of regular c~ or/3 secondary structure are joined by horizontal bars. 24.25

have km = kl

(5)

In this case the exchange rate gives directly the opening rate of the protein fluctuation. The pH and temperature dependences of the protein fluctuations are directly obtained from km. If two amide protons are adjacent in the three-dimensional structure of the protein and opening exposes both labile protons simultaneously, both protons should exchange in a correlated way. 38 If k3 ~ k2 (EX2process) only a small portion of all openings 38 G. Wagner, Biochem. Biophys. Res. Commun. 97, 614 (1980).

316

S T R U C T U R ADYNAMICS L AND MOBILITY OF PROTEINS

[16]

leads to exchange of internal protons and

km= (kl/k2)k3

(6)

In this case no correlated exchange would be expected for neighboring protons, 39 and the parameters of the proton fluctuations are masked by the intrinsic exchange rates, k3. If k3 is known, then the equilibrium constant k~/kz can be determined. The pH and temperature dependence of km contains contributions of k~, k2, and k3. k3 is directly proportional to the hydroxyl or hydronium ion concentration in the base or acid catalyzed regime, respectively, k3 has been measured experimentally with small model peptides. 3°'31'39 A plot of log k3 vs pErt is V shaped, it decreases with slope - 1 below p2H 3, and increases with slope + 1 above p2H 3. For EX2 exchange in a protein a plot of log km v s p2H should show the same V shape, which would, however, be shifted to slower rates by log (k2/k2). Two criteria can be used for distinguishing experimentally between EX~ and EX2 processes, the p2H dependence of the exchange rates 3°'31 and measurements of nuclear Overhauser effects (NOE). 39 The appearance of a V-shaped curve for the pH dependence of the exchange rates indicates an EX2 process. This criterion is, however, not a firm proof since k~ may sometimes have a similar pH dependence as k3. Another method for distinguishing between EX~ and EX2 processes analyzes the NOE between adjacent labile protons, i.e., the transfer of saturation from one labile proton to an adjacent one via dipole-dipole interaction. 39This is demonstrated in Fig. 6. If two neighboring protons exchange in a correlated way (EX0 the apparent NOE between the two protons should be the same in the fully protonated protein and in the case when the two peptide sites are half exchanged, since either both sites are protonated or both are deuterated in each individual molecule. In the uncorrelated case (EX2) the NOE between the two labile protons should decrease in the partially deuterated protein, since mixed pairs of protonated and deuterated peptide sites appear for which no IH-~H NOE can be obtained. With this method the exchange of labile protons has been analyzed in BPTI. 4° It was found that under most experimental conditions the exchange follows an EXE mechanism. However, correlated exchange (EXI mechanism) for some labile protons of the central/3-sheet is observed over a small range of temperature and pH (T > 50 °, pH -7-10), a fact that could not be derived from the pH dependence of the exchange rates alone. 39 R. S. Molday, S. W. Englander, and R. G. Kallen, Biochemistry 11, 150 (1972). 4o H. Roder, Ph.D. thesis No. 6932, ETH Ziirich, 1981.

[16]

317

N M R OF PROTEIN MOTILITY IN SOLUTION

F22

I

N-H;-.....o=c C~

Q31

N24

I

!l

t=O

C=

I

I

C=O ..........H--N

I

BI

A f

F22

Q31

N24

i!

t=60min

i

B ~o

~

a

"~

6

PPM

FIG. 6. (A) 360 MHz NOE differences spectrum of a 20 mM solution of BPTI in ~H20 at p2H 4.6, 24°. Lower trace: reference spectrum; upper trace: NOE difference spectrum. (B) Same experiment but prior to the measurement the sample was kept at 60°, pZH 8.0 for 1 hr to partially exchange the amide protons. Left-hand side: schematic representation of two adjacent hydrogen bonds connecting opposite strands of an antiparallel/3-sheet. The two amide protons HA and Ha are separated by approximately 2.6 ~,. The relative magnetization transfer is the same in the fresh solution and in the partially exchanged sample (-12%). This indicates correlated exchange at these conditions? 8

Aromatic Ring Flips and Other Rotational Motions of Amino Acid Side Chains

The rotational mobility of phenylalanine or tyrosine side chains in the anisotropic environment of the protein interior is manifested by the symmetry of the spin systems. A rotating tyrosine ring has a symmetric twoline spectrum of AA'BB' symmetry, while a rigid side chain will generally show an unsymmetric four-line spectrum. H-j5 The transition from slow to fast rotation can be observed by variation of the temperature. This is demonstrated in Fig. 7 for the aromatic side chains of BPTI. ~4,~5 The

318

[16]

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

Experiment

Phe 45 RATE(s-1) ~ 4

Tyr 35 !/

RATE (,4)

,8

j

PPM FIG. 7. Temperature dependence of the aromatic resonances in the 360 MHz ~H NMR spectrum of BPTI. For Tyr-35 and Phe-45, the spectra are simulated individually and the flip rates at different temperatures obtained from the best fit with the experimental data are indicated. In the experimental spectrum at 4° the resonances of four protons of Phe-45 (©) and two protons of Tyr-35 (&) are readily recognized, whereas the other lines are masked by resonances of the other aromatics in the protein. Most of the resonance lines of Phe-45 and Tyr-35 are also resolved in the spectra at higher temperatures and the transition from slow to rapid ring flipping is readily apparent. 15

averaged resonances of the chemically equivalent ring protons are almost exactly in the middle of the resonance positions of the corresponding lines at low temperature. This is evidence that the averaging is only between two states, i.e., between two orientations of the ring corresponding to two indistinguishable energy minima. This means that the time spent in equilibrium orientation is long relative to the time used for the flip motion. Thus, ring flips are rare events compared with the lifetime of a particular ring orientation of minimum energy. The frequencies of the 180° flips (i.e., a two site exchange) can be determined quantitatively by line shape analysis. ~°-~5 Saturation transfer techniques 26-z8 have also been used as an al-

[16]

N M R OF PROTEIN MOTILITY IN SOLUTION

319

i

12

~JH~H#Z 10 (Hz) 8 6 4 2 I

I

I

I

I

I

2

4

6

8

10

12

~JHc~H[~ (Hz) FIG. 8. Correlation diagram for the vicinal coupling constants JHaHB2and JH,HO3 in amino acid residues. The solid curve represents the correlation between the two vicinal protonproton coupling constants in the molecular fragment C~H-C#H2 for a rigid molecule. The broken line represents the correlation for a flexible molecule, where it was assumed that the time dependent variations o f x 1 extended over a range of X0~ -+ 30 ° and that within this range each value of X~ was equally populated. (Obviously, for different types of fluctuations, e.g., for a harmonic fluctuation about X0~, the dotted curve would correspond to a situation where considerably larger amplitudes than +_30° might occur.) The diagram contains data for BPT1 in 2H20 solution at p2H 7.0 and 68 °. Since the measured coupling constants had not been assigned stereospecifically, all the data were arbitrarily plotted in the upper left triangle of the correlation diagram. Data points located on the two curves or in the narrow band between the curves are indicated by the filled circles, the other ones by the position of the amino acid in the sequence. 29

ternative method for measuring flip rates of some aromatic side chains of cytochrome c. 13 In amino acids with a/3-methylene group and hence two correlated vicinal coupling constants, 3JH~H~2and 3JH~H~3, studies of the correlation between the two coupling constants (Fig. 8) provide a basis for qualitative distinction between different limiting dynamic situations. 29 In the correlation diagram of Fig. 8 data points located on the curves or in the narrow band between the solid and the dotted curve are compatible with a situation where the amino acid residues are locked in unique positions X~, with the internal mobility about X1 restricted to rapid fluctuations about this position. On the other hand, correlation points located within the area bounded by the peripheral branches of the dotted curve may indicate rapid averaging between two or several distinct values of X1 (e.g., the classical gauche, gauche and trans conformers about single bonds between tetrahedral carbon atoms). However, correlation points in the central area of Fig. 8 can also result for immobilized side chains if the two C~ methylene protons have identical chemical shifts. Therefore, in order to

320

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

[16]

obtain unambiguous evidence for a mobile side chain, the data on the correlation of the spin-spin couplings must be complemented with additional experiments. Figure 8 shows data obtained for BPTI, where nearly all amino acid side chains in the interior of the protein were found to be locked into unique spatial orientations, with the mobility restricted to rapid rotational fluctuations about a unique value for the dihedral angle XI. The most fruitful application of the correlation diagram of Fig. 8 appears to be for studies of surface residues in globular proteins, where this technique can provide an unambiguous identification of immobilized side chains. Measurements of the spin-spin coupling c o n s t a n t s 3J~/3 can be obtained with phase sensitive COSY experiments recorded with high digital resolution in 602,41 or by 2D J-resolved spectroscopy. 29 Spin Relaxation Measurements For spin 1/2 nuclei the relaxation is usually dominated by internuclear interactions, so that the measured relaxation times must be correlated with both the internuclear distances and the effective correlation time for the modulation of the interactions. For studies of protein motility it is preferable to select, therefore, molecular fragments in which two or several nuclei are located at fixed relative distances by the covalent bonds. Carbon atoms which are covalently linked with hydrogen atoms are particularly suitable, since the ~3C relaxation is usually largely dominated by IH-13C dipole-dipole coupling. ~3C relaxation parameters then vary with the correlation function and hence with the overall rotational mobility of the observed J3C-1H g r o u p s . 4,7 Figure 9 shows a measurement of the longitudinal relaxation times, TI, for the methyl carbons in BPTI. 8 Even when TI measurements are obtained at different frequencies and complemented by studies of nuclear Overhauser enhancements and transverse relaxation times, T2, the experimental relaxation parameters are usually not sufficient to characterize a unique type of motion for the observed group of atoms. A model which is compatible with the presently available relaxation data for the methyl carbons in BPTI is presented in Fig. 10. 8 In addition to the overall rotational tumbling of the protein and rotation of the methyl groups about the bond through which they are linked with the protein, the model invokes a "wobbling motion" of the methyl rotation axis. A sample of parameters obtained for the motility of the methyl groups is given in the legend to Fig. 10. The alanine methyls are of special interest, since their wobbling manifests flexibility of the polypeptide back4~ D. Marion and K. Wiithrich, Biochem. Biophys. Res. Commun. 113, 967 (1983).

[16]

NMR

O F P R O T E I N M O T I L I T Y 1N S O L U T I O N

321

(t) s r

P

Jl 0n m !'

q~lkh,d c gre

b

a

[msec] 6OO 46O

~

240

~ J ~ ~ ~ . ~ ~

180 140

~

IO0

'

~

~

~

70 33 2o

~

~

~

11

20 ppm 10 FIG. 9. Measurement of 13C relaxation times T 1. High field region from 5 to 25 ppm of partially relaxed proton noise-decoupled ~3C NMR spectra at 25.1 MHz of a 0.025 M solution of BPTI in 2H20 , pZH 4.2, T = 40°. The spectra were obtained with a (180°-r-90 °acquire-t) pulse sequence, with t = 1.6 sec. The delay times r are indicated on the right. The letters in the top trace indicate individual assignments of the methyl carbon lines. (a, b) lle188 and lie-198; (c) Met-52e; (d) lle-19y; (e) Ala-48/3; (f) lle-18y; (g) Ala-25/3; (h, i) Ala-16fl, Ala-40fl; (j) Ala-58fl; (k) Ala-27/3; (m) Thr-1 ly; (n) Thr-54y; (o) Thr-32y; (q) Leu-68; (l, p, r, s, t) Leu-6~, Leu-298, Leu-29~, Val-34y, Val-34y:

bone. Other models have also been proposed which would be compatible with the presently available data o n B P T I . 9J° In contrast to measurements of carbon longitudinal relaxation times, longitudinal 1H relaxation times are less suitable for studies of dynamic phenomena since they are usually dominated by dipole-dipole interaction to more than one other nucleus. This is not the case when one measures individual cross-relaxation rates, o-u, between pairs of nuclei via N O E . 42'43 The cross-relaxation rate, o-u, between spins i and j with resonance frequencies oJi and coj is determined by the intramolecular distance, 42 G. Wagner and K. W0thrich, J. Magn. Reson. 33, 675 (1979). 43 A. A. Bothner-By and J. N. Noggle, J. Am. Chem. Soc. 101, 5152 (1979).

322

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

/s

[16]

DF

~

R

FIG. 10. "Wobbling in a cone" model used for the interpretation of ~3C relaxation data in BPTI. The relaxation of spin I (~3C) by dipole-dipole coupling with spin S (---~H) is considered. The two spins are located in a spherical particle which undergoes isotropic rotational motions with the diffusion constant DR. The vector r which connects the two spins is attached at a fixed angle 0o to an axis about which it rotates with a diffusion constant Dr. This rotation axis is further allowed to wobble with a diffusion constant Dw inside a cone defined by the half-angle 0ma,. From an analysis of the methyl carbon relaxation parameters (Fig. 9) the following parameters for the molecular mobility of BPTI resulted from this analysis: for the overall rotational motions, ~'R = 4 X 10 -9 sec; for the librational "wobbling" of the backbone carbons of alanine in a cone with Omax= 20°, rw = 1 X 10 9 sec; for the librational motions of individual aliphatic side chains in cones with Oma~varying between 30 and 60 °, rw = 4 x 10 to to 3 x I0 9 sec; for methyl rotation about the C-C bond, rF ~< 1 × 10 u sec.8

rij, b e t w e e n t h e t w o s p i n s a n d t h e r o t a t i o n a l c o r r e l a t i o n t i m e , 7c, f o r r o t a t i o n a l t u m b l i n g o f t h e i n t e r n u c l e a r v e c t o r r~j:

O'ij =

10r 6.

1 + (09i + 60i)2r~ -

I + (w~Z

°~i)'~-c'" 2

(7)

T h e c r o s s r e l a x a t i o n r a t e , o-ii , c a n b e d e t e r m i n e d e x p e r i m e n t a l l y f r o m t h e initial b u i l d - u p o f t h e N O E s . 42,43 F o r n u c l e i at a w e l l - d e f i n e d d i s t a n c e , s u c h

[16]

N M R OF PROTEIN MOTILITY IN SOLUTION

323

as two methylene protons or two protons of an aromatic side chain, the value of o-ij can be used to determine the rotational correlation time, Zc.44 If ~'c is considerably shorter than the correlation time for the overall rotation of the protein, an internal motion is indicated. This has been analyzed in some detail for the tryptophan side chains in l y s o z y m e . 44,45

Activation Enthalpies, Activation Entropies, and Activation Volumes from NMR Studies at Variable Temperature and Pressure Whenever rates can be determined quantitatively, a further characterization of internal motions can be obtained by variation of temperature and pressure. According to Eyring's theory for rate processes 46 the rate k is given by k=--h--exp-

--

~-/ =

exp-

\-~-~-+

R-T

~-!

(8)

From a plot of I n k vs 1/T or vs P the activation enthalpy, AH*, the activation entropy, AS*, or the activation volume, AV*, respectively, can be determined. Eyring's theory allows a straightforward evaluation of the data. It has been pointed out, however, that it neglects frictional effects in kinetic processes and may thus lead to irrelevant values for the energy parameters of the activated state. 25,47-49 Kramers 5° has formulated an alternative theory for rate processes which would allow a better evaluation of kinetic data, provided that some information about local frictional coefficients or local viscosities, ~, respectively, are available. In the latter theory we have

(AE* PAV* AS*) RT + R----T-- R

k = f(~) exp - \

(9)

where f('o) is proportional to ~ or ~- ~in the limits of low and high viscosity, respectively. Since the viscosity, ~, may also vary with temperature

44 E. T. Olejniczak, F. M. Poulsen, and C. M. Dobson, J. Am. Chem. Soc. 103, 6574 (1981). 45 C. M. Dobson, E. T. Olejniczak, F. M. Poulsen, and R. G. Ratcliffe, J. Magn. Reson. 48, 97 (1982). 46 H. Eyring, J. Chem. Phys. 3, 107 (1935). 47 D. Beece, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, L. Reinisch, A. H. Reynolds, L. B. Sorensen, and K. T. Yue, Biochemistry 19, 5147 (1981). 48 j. A. McCammon and M. Karplus, Biopolymers 19, 1375 (1980). 49 M. Karplus and J. A. McCammon, FEBS Lett. 131, 34 (1981). ~0 H. A. Kramers, Physica 7, 285 (1940).

324

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

[16]

or pressure, the values of AH*, AS*, or AV* determined with Eyring's theory may be biased by the variation of 9 with temperature and pressure, respectively. Assuming that the internal viscosity in proteins behaves similarly to that of normal, liquid hydrocarbons 25,49 we have

0 In 9]

~ 800 K

0 - - f f " ~ / p = 1 bar

(lo)

and

0 In "0]

a p /T=25° --~ 8 × 10 -4 bar -1

(11)

This corresponds to apparent activation enthalpies and activation volumes of 1.6 kcal/mol and 21 cm3/mol, respectively. Activation enthalpies that have been determined on the basis of Eyring's theory for flips of aromatic side chains ~4 or for the exchange of labile protons are much larger than 1.6 kcal/mol. It appears therefore for these particular processes that Eyring's theory gives quite relevant energy parameters. Some activation volumes for internal motions in proteins that have been determined on the basis of Eyring's theory are not much larger than 21 cm3/mol and have therefore to be interpreted with caution, z5,5~

Sequence-Specific Resonance Assignments NMR spectra contain a large number of resolved signals which can be used to study motional effects. The value of these studies depends crucially on the assignment of the resonances to individual atoms of the protein, since this allows a location of the various internal motions in the protein. In the last few years assignment techniques have become available where resonances are identified sequentially along the polypeptide backbone. These techniques are strongly facilitated by the use of twodimensional NMR. At present nearly complete assignments of the proton NMR spectra are available for a number of small proteins. When assignments of the proton NMR spectrum are available, the resonances of protonated carbons can be assigned by heteronuclear spin decoupling in 1D experiments, 52 or by 2D heteronuclear correlated spectroscopy. 53

51 G. Wagner, FEBS Lett. 112, 280 (1980). 52 R. Richarz and K. Wiithrich, Biochemistry 17, 2263 (1978). 53 T.-M. Chau and J. L. Markley, J. Am. Chem. Soc. 104, 4010 (1982).

N M R OF PROTEIN MOTILITY IN SOLUTION

[16]

I

t

325 I

km

(10-2min-l'

f

sl

/

23-20-33 ~ - 22 21

km =

kl

k3

9

28 36

18

I

50

I

100

1sok3(rnin_ 1)

FIG. 11. Plot of the exchange rates, kin, of the individual amide protons of BPTI vs their intrinsic exchange rates, k3, at 68°, p2H 3.5. The data points are identified with the number in the amino acid sequence. Location in the/3-sheet, the C-terminal a-helix, and the N-terminal 3~0-helix is indicated by © and A, respectively. In the domain of EX_, exchange, amide protons that get solvent contact only by the same fluctuation should appear on a straight line. Groups of protons in the same secondary structure, for which such a correlation seems to be possible, are connected in the figure. -'5

326

STRUCTURAL DYNAMICS AND MOBILITY OF PROTEINS

[16]

Concerted Motions The sequence-specific resonance assignments are particularly useful for amide exchange studies, since amide protons represent a large number of internal NMR probes for the mapping of internal motions. 25 In the regime of EX2 exchange some information can be obtained about concerted motions by comparison of the exchange rates of individual amide protons. For this comparison we plot the exchange rates, km, vs the respective intrinsic exchange rates, k3, for all internal amide protons (see Fig. 11 for BPTI). Since we have EX2 exchange, the exchange rates of all amide protons that exchange due to the same internal motion should appear on a straight line, and the slope of this line would be the equilibrium constant, kl/kz, of the respective opening reaction [Eq. (6)]. Figure 11 shows that the exchange in the N-terminal 310-helix could be explained by a single fluctuation. In the C-terminal a-helix at least three different fluctuations have to be assumed. In the central/3-sheet nine protons show a certain correlation with a correlation coefficient of 0.9 (Phe-22, Tyr-23, Arg-20, Tyr-21, Phe-33, Ile-18, Leu-29, Gln-31, and Asn-24). Additional fluctuations have to be assumed for the peripheral parts of the B-sheet (Tyr-35, Phe-45, Ala-16), and for the/3-turn. 25 Similar to the mapping of internal motility from amide proton exchange studies, different maps are obtained from evaluation of the flip frequencies for individually assigned aromatic r i n g s 22 o r the relaxation parameters of individually assigned carbon atoms. 8 Obviously, one then has the possibility of comparing the motility maps obtained from the different experiments. In the case of BPTI such comparisons have resulted in the proposal of a "hydrophobic domain architecture ''22,54 to explain the apparent occurrence of different types of concerted internal fluctuations. Acknowledgments Financial support by the Swiss National Science Foundation (project 3.284-0.82) is gratefully acknowledged.

54 K. Wfithrich, G. Wagner, R. Richarz, and W. Braun, Biophys. J. 32, 549 (1980).