Effect of slow conformational exchange on 2D NOTEY spectra

JOURNAL

OF MAGNETIC

RESONANCE

94, 387-393 ( 1991)

NOTES Effect of Slow Conformational Exchange on 2D NOESY Spectra BOYOUNG CHOE, GARY W . COOK, AND N. R~MA KRISHNA* ComprehensiveCancer Center and the Departments of Physics and Biochemistry, University of Alabama at Birmingham, University Station, Birmingham, Alabama 35294 Received January 24, 1991; revised March 12, 1991

The application of the 2D NOESY technique for the assignment of resonancesand for conformational studies of biologically significant m o lecules is well established( I ) . This technique identifies all nuclear spins experiencing a magnetization exchange through dipolar cross relaxation or chemical and conformational exchange (2). Sequence-specificassignment of resonancesis facilitated by the identification of dipolar cross-relaxation connectivity networks between proximal protons in the 2D NOESY spectra of proteins and nucleic acids ( 1). Cross peaks induced by conformational exchangebetween different forms of proteins (3) and DNA oligomers (4) have been used to extend the assignmentsfrom one form to another. In the phase-sensitive2D NOESY spectra of large m o lecules for which wo7, > 5 1’2/2, the exchangecross peaks have the same sign (positive) as the dipolar relaxation cross peaks and hence could be difficult to identify without an a priori knowledge of the system under investigation. However, this lim itation is lifted in the 2D ROESY experiment since the conformational exchangecross peaks and the dipolar cross peaks have opposite signs (5). W h ile comparing the baseto sugar H2’, H2” regions (which also contain crosspeaks between the thymine methyl group and its own H6 base proton) in the proton 600 MHz 2D NOESY spectraof the DNA duplex [ d( 5 ‘CGCGCGCGTCC3 ’). d( 5 ‘GGACGCGCGCG3’)] obtained at 296 K (not shown) and 3 15 K (Fig. 1A), we noted the appearanceof some intense additional NOESY cross peaks at the higher temperature. These are indicated by arrows in F ig. 1A. Similar additional NOESY cross peaks were also observed in the base to sugar H 1’proton region, which also contains the CH5 to CH6 NOESY cross peaks. These peaks are totally absent in the spectra obtained at a m b ient temperature (296 K). A closer examination also revealed the appearanceof new cross peaks near the diagonal in the NOESY spectra at the higher temperatures (not shown). A 2D ROESY experiment identified these peaks as arising due to an exchangebetweendistinct conformations. The 2D ROESY spectrum in F ig. 1B clearly shows that the thymine CHs group giving rise to a resonanceon the high-field side is experiencing a conformational exchangeto two other forms which are themselvesnot directly exchangecoupled under the experimental conditions chosen. The observation of these exchangecross peaks led us to suspectthat the new peaks we observedin the higher-temperature NOESY spectra (indicated by arrows in F ig. 1A) m ight be the * To whom correspondenceshould be addressed. 387

QO22-2364J91$3.00 Copyright 0 1991 by Academic Pres, Inc. All rights ofreproduction in any form reserved.

388

NOTES

.

1.6

1.6

1.8

I

2.0

I 7.0

I

1

1.4

7.6

Chemical Shift

@pm)

2.2 2.2

2.0 Chemical Shift

1.8

1.6

@pm)

FIG. 1. The 600 MHz phase-sensitive (TPPI (27)) 2D NOESY and ROESY spectra of the duplex d[ 5’CGCGCGCGTCC3’]~ d[ 5’GGACGCGCGCG3’] (pH 5’,4Msodium chloride, 20% methanol, 50 mA4 phosphate buffer, 3 15 K). (A) Two-dimensional NOESY spectrum obtained with a mixing time of 600 ms. A long mixing time was used to build up the exchange-mediated NOESY peaks. The cross peaks enclosed by squares represent the thymine base CHs to H6 NOESY peaks from three distinct conformations under which the duplex exists. The cross peaks indicated by arrows represent the conformationalexchange-mediated NOESY cross peaks that connect the normal cross peaks in squares. (B) Two-dimensional ROESY spectrum showing the conformational exchange of the high-field thymine CHs resonance from one form of DNA to two other forms. The solid contours represent the positive levels, while the dashed contours represent the negative levels. A spin-lock pulse duration of 200 ms was used for the experiment.

result of a transfer of NOE due to conformational exchange. These peaks connect the normal NOESY peaks arising from within each conformation (enclosed in squares in Fig. IA). Similar cross peaks can also be observed in heteronuclear correlated exchange experiments in the presence of conformational exchange slow on the chemical-shift scale (6, 7). From these peaks, the rate constants for exchange could be determined (6, 7). The principal focus of this Note is to point out the complications in the extraction of NOESY information even in the simplest of cases in the presence of slow conformational exchange. To explain these new peaks, we have considered a simplified model consisting of a two-spin- 1 system undergoing a conformational exchange between two sites which are equally populated. The spin system is labeled AX and A’X ‘, respectively, in these two sites. At each site, the two spins are assumed to relax by identical dipolar relaxation rates, a situation appropriate for cytosine H5-H6 and thymine CH3-H6 protons during the exchange of a DNA duplex between two distinct conformational forms of similar size. The Solomon equation for cross relaxation (8) modified to include an exchange term (9) can be written for the magnetization of spin A as -dM,/dt

= (p + k)(M,

- MAO) + a(Mx - AI,,) - k(M,, - MAO),

[II

where MA, MA, etc. refer to the magnetizations, MA,,, MAVo,etc. refer to their thermal equilibrium values, and k is the rate constant for exchange between the two confor-

389

NOTES

mations. Similar equations can be set up for the magnetizations of the remaining spins. The terms p and u defining the dipolar relaxation rates are given by p= w,+2w,+w~

[21

and u= iv,-- wt.

131

IV,, IV,, and W0 are double-, single-, and zero-quantum transition rates defined in standard texts ( 10). By deriving the general solutions for the set of equations [l] and adapting them to the 2D NOESY experiment, one can arrive at the following expressions for the intensities of diagonal (AA) and cross (AA’, AX, AX ‘) peaks defined in Fig. 2 as Z(AA) = C( 1 + exp(-2kr,))(

1 + exp(2ar,))exp(-(p

+ g)r,)

Z(AA’) = C( 1 - exp(-2kr,))(

1 + exp(2aT,))exp( -(p + 6)~~)

Z(AX) = C( 1 + exp(-2kT,))(

1 - exp(L?aT,))exp(-(p

+

u)T,)

Z(AX’) = C( 1 - exp(-2k?,))(l

- exp(&rr,))exp(-(p

+

u)T,).

141

In the above equations, C is a constant of proportionality. The Z( AA’) cross peak is the direct result of a conformational exchange, and Z( AX) is the NOESY cross peak while Z( A X ‘) is an exchange-mediated NOESY cross peak. The behavior of Z( AA), Z( AA’), Z( AX), and Z( AX ‘) as a function of m ixing time T, for short correlation time ( OPT, < 1) and long correlation time (L&)7,> 5 ‘I2 / 2 ) situations is shown in Figs.

x’

x

A’

A

f1

FIG. 2. Definition of peaks Z( AA), Z( AA’), Z( AX), and Z( AX ‘) in the 2D NOESY spectrum of a twospin system undergoing conformational exchange between two forms. AX and A’X ‘. I( AX) is the normal NOESY cross peak while Z( AX ‘) is the exchange-mediated NOESY cross peak. Z( AA’) is the exchange cross peak.

390

NOTES

3 and 4 for different conformational exchange rates. In the NOESY spectrum shown in Fig. 1A, the cross peaks indicated by arrows represent the Z(AX ‘) peaks, while the peaks enclosed in squares represent the Z( AX) peaks. From a description of the effects presented in Figs. 1-4, several comments are in order. These are discussed below. The basis for the appearance of the conformationd-exchange-mediated NOESY cross peaks of the type Z( A X ‘) is similar to that for the appearance of spindiffbsionmediated (through an intermediate proton) cross peaks between two distant protons (distance greater than 4.5 8) in the NOESY spectra of large molecules obtained with long mixing times ( Z Z-13). Analogous effects can also be expected in one-dimensional =o.o13

k =0.0013

k

k = 0.0013

k=O.o13

k =0.13

k=0.13

FIG. 3. LkpendenceofthepeakintensitiesZ(AA),Z(AA’). Z(AX),andZ(AX’)onthemixingtime(r, in seconds) for the short correlation time limit of a two-proton system with dipolar relaxation. A distance of 2.45 A, a rotational correlation time of lo-” s, and an operating kequency of 600 MHz have been assumed. The behavior of the peaks is shown for three ditferent exchange rates (k/ ] c ] = 0.1, 1, and 10, where k is the exchange rate and ] u 1 is the magnitude of the cross-relaxation rate defined in Eq. [ 31). The proportionality constant C in Eq. 14 ] was assumed to be unity in computing the intensities.

391

NOTES

k= 0.0236

k=

0.236

k=

2.36

AA

1.1 AP:

1.0 0.5

=m

=tn k=

0.0236

k = 0.236

k = 2.36

I2 r---w 0.8

AX a4 0.0P

0.4

AX’

FIG. 4. Same as in Fig. 3 except that the rotational correlation time is 10e9 s. Situations corresponding to three different exchange rates (k/ 1(r 1 = 0.1, 1, and 10) are shown.

transient NOE experiments ( 14- 16 ) . Hence recording NOESY spectra with relatively small m ixing times can m inimize artifacts associated with conformational exchange. However, unlike spin di5ussion, which comes into play in the NOESY spectra only for large molecules for which wo7, > 5 ‘12/2, conformational exchange can influence the NOESY spectra of small molecules as well (Fig. 3). A variety of methodologies for quantitative structural interpretation now exist that attempt to overcome lim itations associated with the two-spin approximation and to incorporate corrections associatedwith long m ixing times and spin diffusion ( I 7-21) . Some of these methodologies attempt to fit the NOESY cross-peak growth curves for several m ixing times ( I 7-20). From the set of Eqs. [ 4 1, it is clear that in the presence of conformational exchange, the time-dependent evolution of cross peaks of the type I( AX) which carry the true dipolar cross-relaxation information (hence distance information) is influenced by terms containing conformational exchange. Hence, when-

392

NOTES

ever significant conformational exchange (under slow exchange on the chemical-shift scale) is indicated, it will be necessary to consider explicitly any possible correction due to conformational exchange in fitting the NOESY growth curves. It is clear from Eq. [ 41 that the exchange rate constant k can be easily estimated from the ratio of Z( AA) to Z( AA’) or Z( AX) to Z(AX ‘) for the special case considered here (i.e., equal populations and identical relaxation rates at both sites). As expected, the initial slopes for Z( AA’) and Z( AX) give the exchange and dipolar cross-relaxation rates, respectively, while the initial slope for Z(AX ‘) is zero. It is easily shown that, even when the populations at both the sites are not equal, the rate constants can still be extracted if the dipolar relaxation rates at both sites are equal. If the extraction of exchange rate constants is the primary purpose, the use of 13C-13Cexchange (22) or ‘H- 13Cheteronuclear correlated exchange spectroscopic methods (6, 7) offers an attractive alternative. Since the value of the cross-relaxation rate 0 has a strong dependence upon the internuclear distance for each proton pair in a given conformation, and the exchange rate constant k is independent of the distance, the relative influence of conformational exchange on the NOESY cross peaks within each molecule also varies. If the two spins have different relaxation rates at the two sites (due to variations in distances, correlation times, or additional relaxation pathways including dipolar interaction with other spins), the relative influence of the conformational exchange may also be affected. As was the case with the DNA oligomer used in our study, it is not uncommon to see significant exchange-mediated NOESY cross peaks for only some of the protons undergoing conformational exchange. The general phenomenon that we have described here in 2D NOESY experiments is directly related to the one-dimensional transferred NOE effects under slow exchange conditions described in the literature to determine the conformation of a ligand bound to an enzyme (23-26). In fact, many of the effects described here have been implicitly understood within the framework of 1D transferred NOE experiments. Here we have used, for mathematical simplicity, a rather simplified model, in which the populations as well as the relaxation rates at the two sites are identical, to describe the effects observed in the DNA studies. This work can be extended in a straightforward manner to the case where the populations and correlation times of the exchanging systems are different, such as in the exchange of a ligand between free and enzyme-bound states under slow exchange conditions (W. Lee and N. R. Krishna, submitted). ACKNOWLEDGMENTS The NMR experiments were performed on a Bruker AM-600 spectrometer at the NMR Core Facility of the Comprehensive Cancer Center. Support of this work by Grants DMB-8705496 from the NSF and CA13 148 from the NC1 is gratefidly acknowledged. REFERENCES 1. K. WOTHRICH, “NMR of Proteins and Nucleic Acids,” Wiley, New York, 1986. 2. R. R. ERNST, G. BODENHAUSEN,AND A. WOKAUN, “Principles of Nuclear Magnetic Resonance in One and Two Dimensions,” Chap. 9, Clarendon Press, Oxford, 1987. 3. J. BOYD, G. R. MOORE, AND G. WILLIAMS, J. Magn. Resun. 58,5 I1 ( 1984). 4. J. FEIGON, A. H.-J. WANG, G. A., VAN DER MAREL, J. H. VAN BOOM, AND A. RICH, Nucleic Acids Rex 12, 1243 (1984).

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