TROSY, transverse relaxation-optimized spectroscopycomplexity of the NMR spectra, both of which increase with increasing molecular size [16-19]. The use of TROSY [20] together with

TROSY, transverse relaxation-optimized spectroscopy

Konstantin Pervushin

Laboratorium für Physikalische Chemie, Swiss Federal Institute of Technology, ETH- Hönggerberg,

CH-8093 Zürich, Switzerland.

Konstantin Pervushin: [email protected]

EMBO Practical Course, Heidelberg September 10-17, 2003

TROSY scope The general problem posed in 3D structure determination of biomolecules by NMR involves the

collection of a sufficiently dense set of experimental restraints to define the structure. Experimental

restraints can be derived from interproton NOEs [1-3], residual dipole-dipole couplings and CSA

interactions [4-9], scalar J couplings [1, 10], J couplings across hydrogen bonds [11, 12] and auto- and

cross-correlated relaxation rates [13, 14]. Currently available computer-based 3D structure

reconstruction methods require that a large number of experimental restraints are assigned to particular

atoms in the protein’s chemical structure at the outset of structure determination [15]. In large proteins

this assignment problem is aggravated by fast transverse relaxation of the spins of interest and the

complexity of the NMR spectra, both of which increase with increasing molecular size [16-19]. The use

of TROSY [20] together with uniform deuteration [21-24] reduces the transverse relaxation rates of 1HN, 15N and 13Caromatic spins. TROSY triple resonance 3-D and 4-D NMR experiments were developed

[25-28] enabling successful assignment of the backbone resonances in large biomolecules.

1

Oligomeric proteinsLarge single chain proteinsβ-barrel membrane proteins Polytopic  α-helical membrane proteins 

Nucleic acids and small proteins

Protein/protein and 

Large supramolecular complexes

protein/nucleic acid interactions 200 kDa

100 kDa

50 kDa

800 kDa

(fine detailes of 3D structures, dynamics)

(bb and sc assignment, 3D folds, dynamics)

(chem. shift mapping, surface mapping,

(detection of individual resonances)

drug discovery)

The estimated range of molecular weights of biological systems the most effectively studied by TROSY NMR

Biological molecules studied by TROSY

- With the use of TROSY the backbone 1HN, 15N, 13Cα and side-chain 13Cβ resonances were

assigned in 81.4 kDa E. coli malate synthase G (MSG), a 723-residue monomeric enzyme, and an

isoaspartyl linkage in the protein sequence was identified [29].

- TROSY was successfully used to establish the backbone 1HN, 15N, 13Cα and side-chain 13Cβ

resonance assignment of a uniformly 2H,15N,13C labeled homooctameric S. aureus 7,8-dihydroneopterin

aldolase [30] with molecular weight of 110 kDa.

- The 44 kDa 30% randomly deuterated and uniformly 13C,15N-labeled water soluble trimeric

enzyme B. subtilis Chorismate Mutase was used to develop a set of TROSY-type experiments for

backbone assignment of large nonedeuterated or only partially deuterated proteins [31-33].

- The use of TROSY-based NMR experiments with the E. coli integral membrane proteins OmpX

and OmpA in mixed micelles with the detergent 1,2- dicaproyl-glycero-3-phosphocholine (DHPC) [34].

For OmpX, complete sequence-specific NMR assignments have been obtained for the polypeptide

backbone. The 13C chemical shifts and nuclear Overhauser effect data then resulted in the identification

of the regular secondary structure elements of OmpX/DHPC in solution, and in the collection of an

input of conformational constraints for the computation of the global fold of the protein [34]. For

OmpA, the NMR assignments are so far limited to about 80% of the polypeptide chain [35, 36],

indicating different dynamic properties of the reconstituted OmpA β-barrel from those of OmpX.

2

Intermolecular nuclear Overhauser effects (NOEs) between the integral outer membrane protein OmpX

from E. coli and DHPC provided a detailed description of protein-detergent interactions [37].

- The global fold of E. coli PagP, a bacterial outer membrane enzyme which transfers a palmitate

chain from a phospholipid to lipid A, was determined in both dodecylphosphocholine (DPC) and n-

octyl-beta-D-glucoside (OG) detergent micelles using TROSY [38]. PagP consists of an eight-stranded

anti-parallel β-barrel preceded by an amphipathic α-helix. The β-barrel is well defined, whereas NMR

relaxation measurements reveal considerable mobility in the loops connecting individual β-strands.

- A model of a E. coli diacylglycerol kinase (DAGK), an α-helical polytopic membrane protein that

spans the lipid bilayer three times and which is active in some micellar systems, was built based on the

use of TROSY among other solution NMR techniques [39-41]. It was established that DAGK is

homotrimeric in decyl maltoside (DM) micelles and mixed micelles. The aggregate detergent-protein

molecular mass of DAGK in both octyl glucoside and DM micelles was determined to be in the range of

100-110 kDa.

- Some of the backbone resonances were assigned in a paradigm of all polytopic transmembrane

proteins - bacteriorhodopsin [42].

- On the surface of the NMR structure of the 23 kDa two-domain periplasmic chaperone FimC

from E. coli the contact sites with the 28 kDa mannose-binding type-1 pilus subunit FimH were

identified by 15N and 1H NMR chemical shift mapping, using TROSY [43].

- NOE steady-state cross-relaxation combined with TROSY allowed identification of the binding

surface of protein A with the Fc portion of immunoglobulin G [44].

- The interaction between the lectin chaperone calreticulin (CRT) assisting the folding and quality

control of newly synthesized glycoproteins in the endoplasmic reticulum (ER) and the thiol- disulfide

oxidoreductase (ERp57) promoting the formation of disulfide bonds in glycoproteins was studied by

TROSY [45].

- Transverse relaxation-optimized spectroscopy provided data on the thermodynamics and kinetics

of the complex formation and on the structure of this 66.5 kDa complex. Chemical shift mapping

showed that interactions with ERp57 occur exclusively through amino acid residues in the polypeptide

segment 225-251 of CRT(189-288), which forms the tip of the hairpin structure of this domain [45].

- Compared with conventional NMR correlation spectroscopy [46], [15N,1H]-TROSY [20, 47]

yielded about 70% and 30% reduction of the 15N and 1H line widths, respectively, in the signals of the

guanosine 15N1–1H and thymidine 15N3–

1H imino groups in 15N-labeled DNA [12]. The reduced TROSY

line widths then allowed the direct observation of scalar couplings across hydrogen bonds involved in

base pairing either by direct measurement in resolved multiplet fine structures [12, 48] or in more

complex coherence transfer experiments [11, 12, 48-52].

3

- In conjunction with quantum-chemical calculations [49, 53], precise measurements of scalar

couplings across hydrogen bonds can be expected to provide novel insights into the nature of hydrogen

bonds in macromolecules.

- TROSY was used to extend applicability of the conventional 15N and 13C relaxation

measurements [54] for studies of intramolecular dynamics in large nucleic acids [55] and proteins [56].

Extremely large (in NMR scale) protein complexes

The cross relaxation-enhanced polarization transfer (CRINEPT) technique in combination with

TROSY optimized for large systems promises yet another several fold increase in the molecular size

limit for NMR studies [57, 58]. These techniques prevent deterioration of the NMR spectra by the rapid

transverse relaxation of the magnetization to which large, slowly tumbling molecules are otherwise

subject. With the experimental conditions used, the line widths of the TROSY-components of the 1H-

and 15N- signals were of the order of 60 Hz at 400 kDa, whereas, for structures of size 800 kDa, the line

widths were about 75 Hz for 15N and 110 Hz for 1H [58]. The uniformly 2H,15N- labelled 72 kDa

homoheptameric co-chaperonin GroES, either free in solution or in 800 kDa complex with the

homotetradecameric chaperonin GroEL or with the 400 kDa single-ring GroEL variant SR1 were

successfully studied in solution [59]. Most amino acids of GroES showed the same resonances whether

free in solution or in complex with chaperonin; however, residues 17-32 showed large chemical shift

changes on binding. This established the utility of these techniques for solution NMR studies that

should permit the exploration of structure, dynamics and interactions in large macromolecular

complexes [59].

4

ppm

7.87.98.08.18.2 ppm

124.5

125.0

125.5

126.0

126.5

8.0 2(1H) [ppm]8.2

COSY no dec.

7.707.757.807.857.907.958.008.058.108.158.20 ppm124.5125.0125.5126.0126.5 ppm

126 1(15N) [ppm] 8.0 2(1H) [ppm]8.2

125

126

1(15N)[ppm]

124

1

2

4

3S

SI

I

S34 S12 I13 I24

αα

ω ω

ω

ω

αβ

βα

ββ

Energy level diagram of a two spin 1/2 system IS showing the identification of components of the 2D multiplet with

off-diagonal density matrix elements expressed via single transition basis operators, I13, I24, S12 and S34, connecting

eigenstates j and k of the static Hamiltonian superoperator. The diagram is not drawn to scale. 2D cross-peak from the

[15N,1H]-HSQC spectrum of a backbone amide moiety of u- [15N,2H]-Aldolase, 110 kDa at 20oC measured without 1H and 15N decoupling.

TROSY techniques

1. Coherent evolution: coherence/polarization transfer by unitary rotations and design of NMR

experiments.

2. Stochastic processes: spin relaxation in a multispin system.

3. A combination of both: polarization transfer by relaxation.

5

1. Coherent evolution: coherence/polarization transfer by unitary rotations and design of NMR

experiment.

Set of basis operators for a two spin ½ system.

The vector Basis forms an orthonormal, zero-trace, and by multiplication with i the skew-Hermitian

(see some useful explanations in Appendix) (or antihermitian, A† = -A, where † means adjoint or hermitian

conjugation or A† = Conjugate//Transpose//A operation) basis set for Lie Algebra su(4) special unitary

group for a 4 energy-level problem.

Each individual spin operator can be represented by a 4x4 matrix:

6

This basis set ensures that each of the individual exponentials of the form ebi is unitary.

This would not be the case if, for instance, irreducible spherical tensor or single-element

polarization/step operators were chosen as a basis, in which case bindings between the coefficients in

the exponentials are needed to ensure unitarity of the full propagator [60].)

7

However the irreducible spherical tensor T2,0 forms a unitary propagator. It corresponds to the

dipolar hamiltonian, HD = aD Sqrt[6] T2,0.

8

The single-element polarization/step operators:

The multiple quantum operators:

Design of the optimum coherent experiment

9

The conversion of one state to another can be associated with a transfer efficiency. Consider,e.g. [61],

the transfer from a quantum-mechanical state represented by an operator B to a state represented by an

operator A by a unitary transformation U (ignoring dissipative processes)

where Q is a residual operator. The higher the coefficient

the more efficient is the transfer process and thereby the experiment. Determination of amax for a given

coherence or polarization transfer process falls in the field of spin-dynamics bounds. So far, three types

of such bounds have been described for a given transfer B→A.

where ΛX is a vector with the eigenvalues of the Hermitian operator X arranged in descending order

while ΣX is a vector with the singular values of the matrix representation of the operator X also arranged

in descending order. The singular values defined as positive of a matrix M are the nonzero elements of a

diagonal matrix Σ that arise by diagonalization of M by unitary matrices T and V according to M=TΣV†.

Arbitrary matrices can be decomposed in this way and for Hermitian matrices it holds that T = V.

Singular value decomposition is an important element of many numerical matrix algorithms. The basic

idea is to write any matrix m in the form u* mD v, where m is a diagonal matrix, D u and v are row

orthonormal matrices, and u is the Hermitian transpose of u. The function SingularValues[m]

returns a list containing the matrix

*

u, the list of diagonal elements of m , and the matrix D v. The diagonal

elements of m are known as the singular values of the matrix D m. One interpretation of the singular

values is as follows. If you take a unit sphere in n-dimensional space, and multiply each vector in it by

an män matrix m, you will get an ellipsoid in m-dimensional space. The singular values give the lengths

of the principal axes of the ellipsoid. If the matrix m is singular in some way, this will be reflected in the

shape of the ellipsoid. In fact, the ratio of the largest singular value of a matrix to the smallest one gives

a condition number of the matrix, which determines, for example, the accuracy of numerical matrix

inverses. Very small singular values are usually numerically meaningless. SingularValues removes

any singular values that are smaller than a certain tolerance multiplied by the largest singular value. The

10

Hermitian bound applies for Hermitian operators A and B and there is a guarantee that the maximum

efficiency can be achieved by a unitary transformation.

(1) Select the desired polarization transfer pathway.

For the single quantum TROSY in hermitian operators it is:

Sx[2] + 2Sx[2]**Sz[3] → Sx[3] + 2Sx[3]**Sz[2]

In raiselowering (nonhermitian) operators:

S+[2] + 2S+[2]**Sz[3] → S-[3] + 2S-[3]**S-[2]

(note, that only the “minus” operators are directly detectable [62])

(2) Determine amax.

The hermitian bound:

The hermitian bound:

11

Hence, we obtain aherm = aSVD = 1.

(3) Use the energy level diagram to search for appropriate selective rotations.

Double Quantum rotations with the phases x and y.

αα

βα αβ

ββ

αα

βα αβ

ββ

For a selective Double Quantum (DQ) x phase π pulse ( πx

sel) the effective hamiltonian takes the form

with the spin functions ordered |αα>, |βα>, |αβ>, |ββ> in the Hilvert space. It follows that the rotation

in Fig must be of an angle π in order to achieve the maximum possible coherence transfer efficiency.

Explicitly, the rotation is

It corresponds to a π rotation operating selectively on the double quantum transition of the two spins

and can indeed be realized experimentally provided there resolved scalar (J) or dipolar coupling

between them.

12

By constructing the corresponding propagators one can verify achieved hermitian and SVD

bounds:

The symbol i indicates a π/2 phase shift of the detected operator.

For a selective Double Quantum (DQ) y phase π pulse ( πysel) the effective hamiltonian takes the form

with the spin functions ordered |αα>, |βα>, |αβ>, |ββ> in the Hilvert space.

Explicitly, the rotation is

13

Zero Quantum rotations with the phases x and y.

αα

βα αβ

ββ

αα

βα αβ

ββ

For a selective Zero Quantum (ZQ) x phase π pulse ( πx

sel) the effective hamiltonian takes the form

or

representing a planar mixing sequence which earlier has been proposed for the accomplishment of

the coherence order selective anti-phase transfer [63].

For a selective Zero Quantum (ZQ) y phase π pulse ( πy

sel) the effective hamiltonian takes the form

14

or

(4) Find out whether the experiment can be realized in a nonselective manner.

We start with the notion that operators Sx[2]**Sx[3] and Sy[2]**Sy[3] commute as well as the

Sx[2]**Sy[3] and Sy[2]**Sx[3] operators.

and

In general,

The propagator

may straightforwardly be converted into a practical pulse sequence using relations of the type

15

transforming the transverse bilinear rotations into mixtures of linear and longitudinal bilinear rotations

which can be realized by rf irradiation and evolution under heteronuclear JIS coupling, respectively. The

latter is typically accomplished by free precession under the unperturbed Hamiltonian

which additionally shows dependence on the isotropic chemical shifts for the two spin species.

Undesired influence from the chemical shifts may by standard means be eliminated by p-pulse

refocusing, i.e.,

resulting in

The practical pulse sequence propagator is (t = 1/(4 JIS)

where the final z rotation is irrelevant in the practical implementation [64].

t2t1

y

15N

1H-y

-y

y

y

The ZQ propagator

represents an original pulse sequence proposed by Pervushin et al. [20] and subsequently called the

SingleTrasition-to-Single Transition Polarization Transfer element (ST2-PT) [47].

16

t2t1

y

15N

1Hy

y

A practical implementation of the TROSY experiment based on the ST2-PT element.

Relevant polarization transfer pasways can be represented by the diagram

When both pathways indicated are retained, two diagonally shifted signals represent two out of the four 15N–1H multiplet components in the resulting [15N, 1H]-correlation spectrum. The undesired polarization

17

transfer pathway,12 → 13, is suppressed either by 2-step cycling of the phases ψ1 and ψ5 or by

application of PFGs during t1 and at time point d. The remaining anti-echo polarization transfer

pathway, 34 → 24, connects a single transition of spin S with a single transition of spin I, and in

alternate scans with inversion of the rf-phases ψ2 and ψ4, the corresponding echo transfer, 12 → 13, is

recorded. In the experiments of Fig. 2 we used both the 1H and 15N steady-state magnetizations. The

product operator analysis accounts for this by the following density matrix at time b in the experimental

scheme

The constant factors u and v reflect the relative magnitudes of the steady-state 1H and 15N

magnetizations, respectively, which are determined by the gyromagnetic ratios, the spin–lattice

relaxation rates and the delay between individual data recordings. Since the S34 operators are transferred

to observable magnetization, both the 1H and 15N steady-state magnetizations add up to the signal

obtained with the pulse sequence, which is proportional to (u-v)/2.

Zero quantum TROSY experiment [65]

(1) The desired polarization transfer pathways are

2S+[2]**S-[3] → S-[3] + 2S-[3]**S-[2] (ZQ)

2S+[2]**S+[3] → S-[3] + 2S-[3]**S-[2] (DQ)

(2) The SVD bound is:

amax

SVD = 1.

(3) The energy level diagram to search for appropriate selective rotations.

18

αα

βα αβ

ββ

αα

βα αβ

ββ

For a selective αα−αβ x phase π pulse ( πx

sel) the effective hamiltonian takes the form

with the spin functions ordered |αα>, |βα>, |αβ>, |ββ> in the Hilvert space. The effective

hamiltonian is

(4) Implementation of the effective hamiltonian.

For the transfer process in question we first eliminate the ‘‘selective element’’ represented by the

polarization operators out of the rotations

Since involved operators commute, one obtains

The first z-rotation is immaterial, resulting in the ZQ-TROSY experimental scheme:

19

t2t1

y

15N

1Hy -y

A practical implementation of the TROSY experiment based on the ZQ element.

Relevant polarization transfer pasways can be represented by the diagram

ZQ-TROSY is effectively used in the context of 3D 15N-resolved NOESY in order to suppress

strong diagonal peaks.

20

21

2. Stochastic processes: spin relaxation in a multispin system

Transverse relaxation in coupled spin systems

We consider a system of two scalar coupled spins ½, I and S, with a scalar coupling constant JIS,

which is located in a protein molecule. T2 relaxation of this spin system is dominated by the DD

coupling of I and S and by CSA of each individual spin, since the stereochemistry of the polypeptide

chain restricts additional interactions of I and S to weak scalar and DD couplings with a small number

of remote protons, Ik. The relaxation rates of the individual multiplet components of spins I and S in a

single quantum spectrum may then be widely different due to the effect of interference between IS

dipolar coupling and anisotropic chemical shift on transverse relaxation [66-68]. Shimizy [69]

suggested to use the DD/CSA interference effect for determination of absolute sign of the coupling

constants by measuring the saturation or the width of each component of a NMR spectrum that gives

multiplet lines through spin-spin couplings. Detailed descriptions of the interference effects on

transverse relaxation in coupled spin systems are available [67, 70-74].

The simplest functional form of the transverse relaxation equations can be obtained by using

single-transition and zero- and double-quantum basis operators [2, 65, 67, 75]. In the slow-tumbling

limit for an isolated IS spin system in the absence of rf pulses and rf field inhomogeneities only terms in

J(0) need to be retained resulting in an uncoupled system of differential equations with the diagonal

form of the first-order relaxation matrix.

where J(ω) represents the spectral density functions at the frequencies indicated:

22

ωS and ωI are the Larmor frequencies of the spins S and I,

h is the Plank constant divided by 2π, rIS the distance between S and I, B0 the polarizing magnetic field,

and ∆σS and ∆σI are the differences between the axial and the perpendicular principal components of

the axially symmetric chemical shift tensors of spins S and I, respectively. Ckl = 0.5(3cos2Θkl-1) and Θkl

the angle between the unique tensor axes of the interactions k and l. The single-transition basis operators

To quantitatively evaluate the transverse relaxation optimization effect and contributions from

other mechanisms of relaxation we consider a specific example where I and S are identified as the 1HN

and 15N spins in a 15N–1H moiety. The internuclear distances and CSA tensors in various model

compounds including amide moieties in short peptides were extensively studied by solid state NMR, so

that we use the data obtained there: the internuclear distance r(15N−1HN) = 1.04 Å for the peptide

backbone amide moieties [76]; ∆σ(1HN) = σzz – (σxx + σyy)/2 = 15 ppm, is axially symmetric with the

angle between the zz axis and the 15N−1HN bond = 10o [77, 78]; ∆σ(15N) = σzz – (σxx + σyy)/2 = -155

ppm, is axially symmetric with the angle between zz axis and 15N− 1HN bond = 15o [79].

0

50

100

200

1000500 1500B0 (1H) [MHz]

(1HN)

[Hz]

(2)

(1)

(3)

10000

50

100

200

500 1500B0 (1H) [MHz]

(15N)

[Hz]

(2)

(1)

(3)

R M(1) 20 ns (~50 kDa)(2) 60 ns (~150 kDa)(3) 320 ns (~800 kDa)

23

The above parameters of the protein backbone amide moiety along with DD contributions from

remote protons are used to calculate dependence of the TROSY 1HN and 15N line width on the

polarizing magnetic field strength expressed in the frequency units for three hypothetical proteins with

molecular weights in the range 50 to 800 kDa. Figure 3 shows that at 1H frequencies in the range of 900

to 1100 MHz significant attenuation of transverse relaxation can be achieved simultaneously for the

TROSY component of the 1HN and 15N multiplets observed for the 15N–1H moieties. For a comparison,

predicted 1HN and 15N line width for the conventional [15N,1H]-HSQC experiment is plotted showing

that the conventional scheme is not applicable for proteins with molecular weights above 150 kDa.

The relevant relaxation rates of 15N-1HN coupled and heteronuclear decoupled resonances were

determined experimentally [80]. A comparison of decay rates for the two 15N-{1HN} doublet

components shows average ratios of 4.8 and 3.5 at 800- and 600-MHz 1H frequency, respectively, in the

perdeuterated proteins, For the protonated proteins these ratios are 3.2 (800 MHz) and 2.4 (600 MHz).

Relative to the regular HSQC experiment, the enhancement in TROSY 15N resolution is 2.6

(perdeuterated; 800 MHz), 2.0 (perdeuterated; 600 MHz), 2.1 (protonated; 800 MHz), and 1.7

(protonated; 600 MHz). For the 1HN dimension, the upheld 1HN-{15N} component on average relaxes

slower than the downfield 1HN-{15N} component by a factor of 1.8 (perdeuterated; 800 MHz) and 1.6

(perdeuterated; 600 MHz). The reported data correspond well with the rates expected on the basis of the

theoretical calculations [26].

24

Appendix

25

26

REFERENCES

27

1. Wuthrich, K., NMR of Proteins and Nucleic Acids. 1986, New York: Wiley. 2. Ernst, R.R., G. Bodenhausen, and A. Wokaun, The Principles of Nuclear Magnetic Resonance in

One and Two Dimensions. 1987, Oxford: Clarendon. 3. Clore, G.M. and A.M. Gronenborn, Science, 1991. 252(5011): p. 1390-9. 4. Ernst, M. and R.R. Ernst, Journal of Magnetic Resonance Series A, 1994. 110(2): p. 202-213. 5. Tolman, J.R., et al., Proceedings of the National Academy of Sciences of the United States of

America, 1995. 92(20): p. 9279-9283. 6. Tjandra, N. and A. Bax, Science, 1997. 278(5340): p. 1111-1114. 7. Tjandra, N., et al., Nat. Struct. Biol., 1997. 4(9): p. 732-8. 8. Choy, W.Y., et al., Journal of Biomolecular Nmr, 2001. 21(1): p. 31-40. 9. Wu, Z.R., N. Tjandra, and A. Bax, Journal of the American Chemical Society, 2001. 123(15): p.

3617-3618. 10. Bax, A., Current Opinion in Structural Biology, 1994. 4(5): p. 738-744. 11. Dingley, A.J. and S. Grzesiek, Journal of the American Chemical Society, 1998. 120(33): p.

8293-8297. 12. Pervushin, K., et al., Proceedings of the National Academy of Sciences of the United States of

America, 1998. 95(24): p. 14147-14151. 13. Tjandra, N., et al., Nat Struct Biol, 1997. 4(6): p. 443-9. 14. Reif, B., M. Hennig, and C. Griesinger, Science, 1997. 276(5316): p. 1230-1233. 15. Clore, G.M. and C.D. Schwieters, Current Opinion in Structural Biology, 2002. 12(2): p. 146-

153. 16. Wagner, G., Journal of Biomolecular Nmr, 1993. 3(4): p. 375-385. 17. Kay, L.E. and K.H. Gardner, Current Opinion in Structural Biology, 1997. 7(5): p. 722-731. 18. Clore, G.M. and A.M. Gronenborn, Nat Struct Biol, 1997. 4 Suppl: p. 849-853. 19. Clore, G.M. and A.M. Gronenborn, Curr Opin Chem Biol, 1998. 2(5): p. 564-70. 20. Pervushin, K., et al., Proceedings of the National Academy of Sciences of the United States of

America, 1997. 94(23): p. 12366-12371. 21. LeMaster, D.M., Methods in Enzymology, 1989. 177: p. 23-43. 22. LeMaster, D.M., Annual Review of Biophysics and Biophysical Chemistry, 1990. 19: p. 243-

266. 23. LeMaster, D.M., Quarterly Reviews of Biophysics, 1990. 23(2): p. 133-174. 24. Venters, R.A., et al., Journal of Molecular Biology, 1996. 264(5): p. 1101-1116. 25. Salzmann, M., et al., Journal of the American Chemical Society, 1999. 121(4): p. 844-848. 26. Salzmann, M., et al., Proceedings of the National Academy of Sciences of the United States of

America, 1998. 95(23): p. 13585-13590. 27. Yang, D.W. and L.E. Kay, Journal of the American Chemical Society, 1999. 121(11): p. 2571-

2575. 28. Konrat, R., D.W. Yang, and L.E. Kay, Journal of Biomolecular Nmr, 1999. 15(4): p. 309-313. 29. Tugarinov, V., et al., Journal of the American Chemical Society, 2002. 124(34): p. 10025-

10035. 30. Salzmann, M., et al., J. Am. Chem. Soc., 2000. 122(31): p. 7543-7548. 31. Eletsky, A., A. Kienhofer, and K. Pervushin, Journal of Biomolecular Nmr, 2001. 20(2): p. 177-

180. 32. Eletsky, A., et al., Journal of Biomolecular Nmr, 2002. 24(1): p. 31-39. 33. Hu, K.F., A. Eletsky, and K. Pervushin, Journal of Biomolecular Nmr, 2003. 26(1): p. 69-77. 34. Fernandez, C., et al., Febs Letters, 2001. 504(3): p. 173-178. 35. Arora, A., et al., Nature Structural Biology, 2001. 8(4): p. 334-338. 36. Pervushin, K., D. Braun, and K. Wuthrich, J. Biomol. NMR, 2000. 17: p. 195-202. 37. Fernandez, C., et al., Proceedings of the National Academy of Sciences of the United States of

America, 2002. 99(21): p. 13533-13537. 38. Hwang, P.M., et al., Proc. Natl. Acad. Sci. USA., 2002. 99(21): p. 13560-13565.

28

39. Sanders, C.R., et al., Biophysical Journal, 1998. 74(2): p. A130-A130. 40. Sanders, C.R. and K. Oxenoid, Biophysical Journal, 2002. 82(1): p. 1721. 41. Vinogradova, O., et al., Biophysical Journal, 1997. 72(6): p. 2688-2701. 42. Schubert, M., et al., Chembiochem, 2002. 3(10): p. 1019-1023. 43. Pellecchia, M., et al., Nature Structural Biology, 1999. 6(4): p. 336-339. 44. Takahashi, H., et al., Nature Structural Biology, 2000. 7(3): p. 220-223. 45. Frickel, E.M., et al., Proceedings of the National Academy of Sciences of the United States of

America, 2002. 99(4): p. 1954-1959. 46. Cavanagh, J., et al., Protein NMR Spectroscopy: Principles and Practice. 1996, New York:

Academic Press. 47. Pervushin, K., G. Wider, and K. Wuthrich, Journal of Biomolecular Nmr, 1998. 12(2): p. 345-

348. 48. Pervushin, K., et al., Journal of Biomolecular Nmr, 2000. 16(1): p. 39-46. 49. Dingley, A.J., et al., Journal of the American Chemical Society, 1999. 121(25): p. 6019-6027. 50. Majumdar, A., et al., Journal of Biomolecular Nmr, 1999. 15(3): p. 207-211. 51. Majumdar, A., A. Kettani, and E. Skripkin, Journal of Biomolecular Nmr, 1999. 14(1): p. 67-70. 52. Wohnert, J., et al., Nucleic Acids Research, 1999. 27(15): p. 3104-3110. 53. Scheurer, C. and R. Bruschweiler, Journal of the American Chemical Society, 1999. 121(37): p.

8661-8662. 54. Wagner, G., Current Opinion in Structural Biology, 1993. 3(5): p. 748-754. 55. Boisbouvier, J., et al., Journal of Biomolecular Nmr, 1999. 14(3): p. 241-252. 56. Loria, J.P., M. Rance, and A.G. Palmer, Journal of Biomolecular Nmr, 1999. 15(2): p. 151-155. 57. Riek, R., et al., Proceedings of the National Academy of Sciences of the United States of

America, 1999. 96(9): p. 4918-4923. 58. Riek, R., et al., Journal of the American Chemical Society, 2002. 124(41): p. 12144-12153. 59. Fiaux, J., et al., Nature, 2002. 418(6894): p. 207-211. 60. Untidt, T.S. and N.C. Nielsen, Journal of Chemical Physics, 2000. 113(19): p. 8464-8471. 61. Nielsen, N.C., H. Thogersen, and O.W. Sorensen, Journal of Chemical Physics, 1996. 105(10):

p. 3962-3968. 62. Levitt, M.H., Journal of Magnetic Resonance, 1997. 126(2): p. 164-182. 63. Sattler, M., et al., Journal of Biomolecular Nmr, 1995. 6(1): p. 11-22. 64. Yang, D.W. and L.E. Kay, Journal of Biomolecular Nmr, 1999. 13(1): p. 3-10. 65. Pervushin, K., et al., Proceedings of the National Academy of Sciences of the United States of

America, 1999. 96(17): p. 9607-9612. 66. Gueron, M., J.L. Leroy, and J. Griffey, J. Am. Chem. Soc., 1983. 105(25): p. 7262-7266. 67. Goldman, M., Journal Magnetic Resonance, 1984. 60: p. 437-452. 68. Farrar, T.C. and T.C. Stringfellow, eds. Encyclopedia of NMR: Relaxation of Transverse

Magnetization for Coupled Spins. Encyclopedia of NMR, ed. D.M. Grant and R.K. Harris. Vol. 6. 1996, Wiley: New York. 4101-4107.

69. Shimizy, H., Journal of Chemical Physics, 1964. 40(11): p. 3357-3364. 70. Blicharski, J.S., Physics Letters, 1967. 24(11): p. 608-610. 71. Blicharski, J.S., Acta Physica Polonica, 1972. 41: p. 223-236. 72. Vold, R.R. and R.L. Vold, Journal of Chemical Physics, 1975. 64(1): p. 320-332. 73. Vold, R.R. and R.L. Vold, Progress in NMR Spectroscopy, 1978. 12: p. 79-133. 74. Mayne, C.L. and S.A. Smith, eds. Encyclopedia of NMR: Relaxation Processes in Coupled-Spin

Systems. Encyclopedia of NMR, ed. D.M. Grant and R.K. Harris. Vol. 6. 1996, wiley: New York. 4053-4071.

75. Sorensen, O.W., et al., Progress in Nuclear Magnetic Resonance Spectroscopy, 1983. 16: p. 163-192.

76. Roberts, J.E., et al., Journal of the American Chemical Society, 1987. 109(14): p. 4163-4169. 77. Gerald, R., et al., Journal of the American Chemical Society, 1993. 115(2): p. 777-782.

29

78. Ramamoorthy, A., C.H. Wu, and S.J. Opella, Journal of the American Chemical Society, 1997. 119(43): p. 10479-10486.

79. Wu, C.H., et al., Journal of the American Chemical Society, 1995. 117(22): p. 6148-6149. 80. Kontaxis, G., G.M. Clore, and A. Bax, Journal of Magnetic Resonance, 2000. 143(1): p. 184-

196.

30