DOCSLIB.ORG

Ad Bax and Stephan Grzesiek 1 Introduction 1 2 Principles Of

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Ad Bax and Stephan Grzesiek 1 Introduction 1 2 Principles Of positive sign of the ROE effect also allows one immediately ROESY to distinguish cross relaxation from chemical exchange effects, which are always negative. This latter application has proven 6,7 Ad Bax and Stephan Grzesiek critical, for example, in studying hydration of proteins. National Institutes of Health, Bethesda, MD, USA Other important applications lie in the area of macromolec- ular structure determination, where the rotating frame Over- hauser enhancement, owing to its positive sign, tends to be far less susceptible to spin diffusion effects than its longitudi- 1 Introduction 1 nal counterpart.8,9 Although for macromolecules, the inherent 2 Principles of Rotating Frame Overhauser Spectroscopy 1 sensitivity of the ROESY experiment is less than for NOESY, 3 Comparison With Laboratory Frame NOE 2 numerous useful applications to proteins and nucleic acids 4 Experimental Realization 4 have been reported. In addition to the nonselective ROESY 5 Minimization of J Contributions 5 experiment, a number of very interesting selective variants 6 Examples of ROESY Applications 7 have been developed that can selectively probe small sub- 7 Different Areas of Application 7 sets of the Redfield cross-relaxation matrix. These elegant 8 Related Articles 10 ROESY variants are particularly powerful for probing cross 9 References 10 correlation,10– 12 and they have been treated and reviewed in great detail by Bull.13 The discussion below is restricted to the more commonly used nonselective ROESY experiments and their various applications. 1 INTRODUCTION Molecular motion in liquids results in a time dependence 2 PRINCIPLES OF ROTATING FRAME of the dipolar coupling between two spins, which gives OVERHAUSER SPECTROSCOPY rise to transitions between the nuclear spin states. These transitions constitute the basis of the nuclear Overhauser The state of a spin system is most conveniently described by enhancement (NOE) effect, which has long been one of the the density matrix ρˆ. For a system of two spin- 1 nuclei, A and 1 2 NMR cornerstones for the study of molecular structure. As X, ρˆ isasimple4× 4 matrix. Its diagonal elements, ρ11, ρ22, discussed in NOESY, the transition rates are determined by ρ33,andρ44 correspond to the populations of energy levels −6 the square of the dipolar coupling, i.e., by r ,wherer is the 1, ... , 4. An off-diagonal element such as ρ12 represents internuclear distance, by the angular Larmor frequency ω0, the coherence or transition between levels 1 and 2, etc. In and by the decay constant τ c of the autocorrelation function order to describe relaxation phenomena, the Hamiltonian is of the time-dependent dipolar coupling D(t). In conventional ˆ usually split into a spin-dependent part HS and a spin–lattice homonuclear NOE experiments, the change in z magnetization coupling Hˆ . The spin-dependent component Hˆ consists of of a spin B is monitored after the z magnetization of a spin SL S the Zeeman coupling to the main external magnetic field (Hˆ ) A in its immediate vicinity has been perturbed. Provided τ 0 c plus other, much smaller, purely spin-dependent components is known, the rate at which the longitudinal magnetization Hˆ of spin B changes after perturbing the z magnetization of A ( 1) such as chemical shift, J coupling, and coupling of provides a measure of r.Forω τ < 1.12, the z magnetization the spins to radiofrequency (rf) fields. The spin–lattice part 0 c Hˆ of spin B will increase to a value higher than its Boltzmann SL describes the coupling of the spins to the external heat equilibrium value when saturating the resonance of A (positive bath, which is a stochastic process. Transformation into the Hˆ NOE), whereas the opposite holds for ω0τ c > 1.12. For many interaction frame makes the Zeeman term 0 disappear in interesting molecules of intermediate size (500–2000 Da), the explicit form from the Hamiltonian, and hides it as a time product ω0τ c is frequently found to be close to 1, resulting in dependence of the operators and the density matrix. In this very small NOE effects. interaction frame and under a number of approximations, the As outlined above and described in detail elsewhere,1 – 4 the time dependence of the density matrix ρˆ is then described by NOE is a cross-relaxation effect between longitudinal com- ponents of nuclear spin magnetization. In 1983, Bothner-By dρ(t)ˆ =−i[Hˆ , ρˆ] − Rˆρˆ (1) and co-workers developed a different type of NOE experi- dt 1 ment, which measures cross relaxation between magnetiza- tion components that are perpendicular to the static magnetic Rˆ is the Redfield relaxation matrix, which describes the field.5 The original name of this experiment is cross relaxation return to equilibrium of the spin system. The relation appropriate for minimolecules emulated by locked spins, or between its elements and the spectral densities is described CAMELSPIN, but it is more commonly known as ROESY, in detail in Relaxation Theory: Density Matrix Formu- for rotating-frame Overhauser enhancement spectroscopy. As lation. A product R1213ρ13, for example, describes the loss implied in the original acronym of this experiment, the trans- per unit time of the density matrix element ρ12 caused by verse cross relaxation is positive for all values of the rotational the matrix element ρ13. It is important to realize, however, correlation time, i.e., it is the same as that found for small that relaxation is usually a slow process relative to evolution molecules in the NOESY experiment. The original motivation under the static Hamiltonian. Consequently, cross relaxation for this experiment was to study the structure of intermedi- can only occur if the off-diagonal elements ρ12 and ρ13 ate size molecules, which have near-zero longitudinal NOE oscillate at nearly the same frequencies in the laboratory frame, effects. However, as pointed out in the original report,5 the i.e., if the corresponding resonances overlap. In this case, the Encyclopedia of Magnetic Resonance, Online © 2007 John Wiley & Sons, Ltd. This article is © 2007 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Magnetic Resonance in 2007 by John Wiley & Sons, Ltd. DOI: 10.1002/9780470034590.emrstm0473 2 ROESY cross relaxation between the 1–2 and the 1–3 transitions is (a) termed a secular process. If their frequencies are different, 0.65 the exchange of magnetization is a nonsecular process, and can be neglected. ROESY and its selective variants all rely on 0.60 ˆ modifying the spin Hamiltonian H1 in such a manner that cross max 0.55 relaxation can be probed between transitions that would differ in frequency in the absence of radiofrequency irradiation. In ROE 0.50 the standard ROESY experiment, this is accomplished simply by the application of a strong monochromatic rf field, which 0.45 locks all magnetization that is parallel to it and dephases any perpendicular components. Neglecting off-resonance effects, 0.40 the cross-relaxation rate for magnetization components locked along the rf field is therefore identical to the cross relaxation 0.1 1 10 between the transverse magnetization components of two w0tc exactly overlapping resonances (identical spins). 1.0 (b) Following Bothner-By et al.,5 the time dependence of the spin locked magnetization components mA and mB of two homonuclear spins A and B is described by 0.5 AB R dmA(t) =− − / AB R2AmA(t) RABmB(t) (2a) L dt R 0.0 dm (t) B =−R m (t) − R m (t) (2b) dt AB A 2B B where RAB is the cross-relaxation rate of interest, and R2A –0.5 and R2B are the autorelaxation rates, describing the loss of 0.1 1 10 magnetization, which also includes processes other than cross w0tc relaxation between spins A and B. For convenience, we assume below that R2A = R2B = R2, which results in a particularly Figure 1 (a) Maximum obtainable ROE enhancement ROEmax in simple solution of equations (2a) and (2b). If two experiments the isolated two-spin pair approximation, assuming that the spins are relaxed exclusively by homonuclear dipolar interactions. (b) The ratios are done, one with mA(0) = mB(0) = 1 and one with mA(0) of the cross relaxation rates in the laboratory frame, RL , and in the = −mB(0) = 1 (for example, by selectively inverting the AB magnetization of spin B immediately prior to a nonselective rotating frame, RAB, as functions of ω0τ c ◦ 90 x pulse, which is followed by a y-axis spin lock), the time dependence of mA(t)andmB(t) in these two cases is given The maximum Overhauser enhancement obtainable for this by isolated two-spin pair, using the ROE mixing time of equation (4), is shown graphically in Figure 1(a). In practice, the mA(t) = mB(t) = exp[−(R2 + RAB)t](3a)isolated spin pair approximation is usually not valid, and frequently R is much larger than R . In this case, it follows =− = − − 2 AB mA(t) mB(t) exp[ (R2 RAB)t] (3b) from equation (4) that the maximum ROE effect is obtained for The difference between equations (3a) and (3b) represents the ROE, which has a maximum value for t ≈ 1/R2 (8) 1 R + R t = ln 2 AB (4) which means that the highest sensitivity is obtained for a 2R R − R AB 2 AB mixing period on the order of the transverse relaxation time T 2, as measured, for example, by a selective spin echo experiment. In the isolated spin pair approximation, R2 and RAB are given by γ 4h2(µ /4π)2 3 COMPARISON WITH LABORATORY FRAME NOE R = 0 [5J(0) + 9J(ω ) + 6J(2ω )](5) 2 80π 2r6 0 0 In the isolated spin pair approximation and assuming rigid 4 2 2 body motion, comparison of the ROE and NOE results is γ h (µ0/4π) RAB = [4J(0) + 6J(ω0)](6)straightforward.
Load more

Recommended publications
  • "Marius Clore, G: Adventures in Biomolecular NMR" In
    summarize the developments along the way that I have Marius Clore, G: participated in and that have led to these current advances. Adventures in Biomolecular NMR MRC NIMR—FIRST STEPS INTO STRUCTURE DETERMINATION BY NMR (1980–1984) G. Marius Clore When I came to NIMR I was assigned a small office, no larger than about 8 × 8 ft that I shared with Angela Gronen- National Institute of Diabetes and Digestive and Kidney Diseases, born. We quickly decided to team up and work together, as our National Institutes of Health, Bethesda, MD, USA expertise and strengths were clearly very complementary. She had considerably more expertise in wet biochemistry, while I had a greater bent toward instrumentation, technical aspects of NMR, and computation. At that time, Jim Feeney, Gordon Roberts, and Berry Birdsall, located in the same division as us, INTRODUCTION were very interested in the application of transferred satura- tion methods to assign the 1H chemical shifts of small ligands My NMR career started in 1980 when I joined the Division bound to dihydrofolate reductase where exchange between free of Molecular Pharmacology at the Medical Research Council’s and bound states was in slow exchange on the chemical shift National Institute of Medical Research (NIMR) located in Mill time scale. I quickly extended the formalism to deal with such Hill, London. I had been recruited 18 months previously by systems in the context of three-site exchange which provided the director of NIMR, Sir Arnold Burgen, while still a medical the background for our future work on the transferred NOE student at University College Hospital Medical School, on (TRNOE).4,5 the basis of the work I had published on cytochrome oxidase Angela and I had decided to work on the cyclic AMP and other metalloproteins, largely involving low temperature receptor protein (CRP), and having gone to Toulouse to transient kinetics.
    [Show full text]
  • Direct Observation of Dipolar Couplings Between Distant Protons in Weakly Aligned Nucleic Acids
    Direct observation of dipolar couplings between distant protons in weakly aligned nucleic acids Je´ roˆ me Boisbouvier, Frank Delaglio, and Ad Bax† Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520 This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on April 30, 2002. Contributed by Ad Bax, July 23, 2003 Under conditions where macromolecules are aligned very weakly tion range) are self-assembling, highly porous ␣-lamellar bilayers with respect to an external magnetic field, Brownian diffusion no (11, 12) consisting of dimyristoyl phosphatidyl choline and longer averages internuclear dipole–dipole interactions to zero. detergent. When placed in a magnetic field, the bilayers of this The resulting residual dipolar coupling, although typically 3 orders liquid crystalline medium align with their bilayer normal or- of magnitude weaker than in a fully aligned sample, can readily be thogonal to the field. Originally, this medium was developed to measured by solution NMR methods. To date, application of this study, mainly by solid-state NMR technology, the structure and idea has focused primarily on pairs of nuclei separated by one or membrane binding properties of small lipophilic molecules, two covalent bonds, where the internuclear separation is known anchored to the highly ordered bilayers (13, 14). The application and the measured dipolar coupling provides direct information on of the bicelle medium to water-soluble proteins is rather differ- the orientation of the internuclear vector. A method is described ent and takes advantage of the very small deviation from a purely that allows observation of dipolar interactions over much larger random distribution of orientations that is sterically imposed on distances.
    [Show full text]
  • Bax and Grzesiek
    VOLUME 26 NUMBER 4 APRIL 1993 Registered in US.Patent and Trademark Office;Copyright 1993 by the American Chemical Society Methodological Advances in Protein NMR AD BAX*AND STEPHANGRZESIEK* Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892 Receiued August 13, I992 Since the first experimental observation of nuclear peptides. Nearly a decade ago, protein structure magnetic resonance (NMR) in bulk matter more than determination was added to the realm of applications 45 years ago,lI2 its history has been punctuated by a by the introduction of new systematic procedures for series of revolutionary advances that have greatly spectral analysis, primarily developed by Wiithrich and expanded its horizons. Indeed, methodological and co-~orkers.~During the 19809, development of new instrumental developments witnessed over the past two experimental pulse schemes continued to increase the decades have turned NMR into the most diverse power and applicability of 2D NMR to structural spectroscopic tool currently available. Applications characterization of biopolymers. The most important vary from exploration of natural resources3and medical development was undoubtedly the addition of a third imaging to determination of the three-dimensional frequency dimension to the NMR spectra.14J5 The structure of biologically important macromolecules.Pg concept of 3D NMR is so similar to 2D NMR that no The present Account focuses primarily on the meth- new formalism for the description of such experiments odological advances in this latter application, partic- is required. The main problem that had to be solved ularly as they relate to the study of proteins in solution.
    [Show full text]
  • And C R-HR Effective Bond Lengths in a Protein by NMR in a Dilute Liquid
    12334 J. Am. Chem. Soc. 1998, 120, 12334-12341 Determination of Relative N-HN,N-C′,CR-C′, and CR-HR Effective Bond Lengths in a Protein by NMR in a Dilute Liquid Crystalline Phase Marcel Ottiger and Ad Bax* Contribution from the Laboratory of Chemical Physics, National Institute of Diabetes and DigestiVe and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520 ReceiVed July 28, 1998. ReVised Manuscript ReceiVed October 2, 1998 Abstract: Weak alignment of solute macromolecules with the magnetic field can be achieved in a dilute, aqueous liquid crystalline phase of planar phospholipid micelles, consisting of mixtures of dimyristoylphos- phatidylcholine (DMPC) and dihexanoylphosphatidylcholine (DHPC). Alignment of proteins in such a medium is sufficiently weak to retain the simplicity of the isotropic solution NMR spectrum but strong enough to permit accurate measurement of residual one-bond dipolar couplings. Highly accurate one-bond N-HN,CR- HR,CR-C′, and C′-N and two-bond C′-HN dipolar couplings were measured in 13C/15N-enriched ubiquitin. Together with knowledge of the protein’s three-dimensional structure, the dipolar couplings permit calculation of the relative, vibrationally corrected average bond lengths for these interactions. Assuming a C′-N bond length of 1.329 Å (Engh, R. A.; Huber, R. Acta Crystallogr. 1992, A47, 392-400), the relative CR-C′ distance of 1.526 Å is found to be in excellent agreement with results from Engh and Huber (1.525 Å). Using a C′-N bond length of 1.329 Å as a reference, N-HN (1.041 ( 0.006 Å) and CR-HR (1.117 ( 0.007 Å) are considerably longer than equilibrium or average internuclear distances derived from ab initio calculations, electron diffraction, neutron diffraction, or microwave spectroscopy.
    [Show full text]
  • Curriculum Vitae
    Curriculum Vitae Personal Details Full Name Robert Barrington Best Date of Birth 7th October 1976, Cape Town Nationality South African, British Present Position Senior Investigator Laboratory of Chemical Physics National Institutes of Health Bethesda, MD 20892-0520 U. S. A. e-mail [email protected] Tel (W) +1-301-496-5414 Fax (W) +1-301-496-0892 Web NIH Website Google Scholar Professional Experience 11/2016-present Senior Investigator, National Institute of Diabetes and Digestive and Kidney Dis- eases, National Institutes of Health 10/2012-11/2016 Tenure-track investigator, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health 10/2008-9/2012 College Lecturer in Chemistry, Emmanuel College, Cambridge 10/2007-9/2012 Royal Society University Research Fellow, University of Cambridge. 3/2004-9/2007 Post-doctoral research in the Laboratory of Chemical Physics, NIH, Bethesda, MD with William Eaton and Gerhard Hummer. 6/2003-2/2004 Post-doctoral research with Michele Vendruscolo, University of Cambridge. Education 2000-2003 Ph.D. in Chemistry, University of Cambridge (Advisor: Jane Clarke) High Resolution Studies of Protein Folding and Dynamics. 2000 M.Sc. in Chemistry, University of Cape Town (Advisors: Kevin Naidoo, Graham Jackson) Combined NMR and simulation study of carbohydrate linkage dynamics. 1998 B.Sc.(Hons) in Chemistry (First Class), University of Cape Town. 1995-1997 B.Sc. University of Cape Town, Majors in Chemistry, Biochemistry and Mathe- matics with distinction. Professional Associations Editorial Board Member of Biophysical Journal (from Jan 2021) Editorial Board Member of Journal of Biological Chemistry Developer for CHARMM molecular simulation package Member of the American Chemical Society and Biophysical Society Awards 2020 Sackler Award in Biophysics 2012 Royal Society of Chemistry Marlow Award.
    [Show full text]
  • NIDDK Oral History Project Interview with Dr. William Eaton Conducted on January 6, 2020 by Kenneth Durr
    NIDDK Oral History Project Interview with Dr. William Eaton Conducted on January 6, 2020 by Kenneth Durr Kenneth Durr: This is an interview with Dr. William Eaton. Today is January 6th, 2020, and I'm Kenneth Durr. Dr. Eaton, thanks for taking time to talk today. William Eaton: My pleasure. Kenneth Durr: I want to start with some background, and I want to dig into yours just a little bit. You're from Philadelphia, right? William Eaton: Yes. Kenneth Durr: Tell me a little about your family, your upbringing, and what got you toward science. William Eaton: I came from what I call a financially poor, but intellectually rich family. My mother could have been the first woman to ever get an advanced degree in the classics from the University of Pennsylvania. She got a master's degree in Latin in 1927. She motivated all five of us children - I had four siblings - to become good students in school. In spite of their limited financial resources, all five children went to college, three to the University of Pennsylvania and two to Drexel University. I was always a very good student. I give the lion's share of credit to my mother to motivate me to become a good student. Kenneth Durr: Were you one of three who went to University of Pennsylvania? William Eaton: Yes. Kenneth Durr: Okay. William Eaton: I did an undergraduate degree in chemistry. Prepared by National Capitol Contracting 8255 Greensboro Drive, Suite C100 (703) 243-9696 McLean, VA 22102 Kenneth Durr: Why did you choose chemistry? William Eaton: Because my older sister studied chemistry, and I liked chemistry in high school.
    [Show full text]
  • Consistent Blind Protein Structure Generation from NMR Chemical Shift
    Consistent blind protein structure generation SEE COMMENTARY from NMR chemical shift data Yang Shen*, Oliver Lange†, Frank Delaglio*, Paolo Rossi‡, James M. Aramini‡, Gaohua Liu‡, Alexander Eletsky§, Yibing Wu§, Kiran K. Singarapu§, Alexander Lemak¶, Alexandr Ignatchenko¶, Cheryl H. Arrowsmith¶, Thomas Szyperski§, Gaetano T. Montelione‡, David Baker†ʈ, and Ad Bax*ʈ *Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892; †Department of Biochemistry and Howard Hughes Medical Institute, University of Washington, Seattle, WA 98195; ‡Center for Advanced Biotechnology and Medicine, Department of Molecular Biology and Biochemistry, and Northeast Structural Genomics Consortium, Rutgers, The State University of New Jersey, and Robert Wood Johnson Medical School, Piscataway, NJ 08854; §Departments of Chemistry and Structural Biology and Northeast Structural Genomics Consortium, University at Buffalo, State University of New York, Buffalo, NY 14260; and ¶Ontario Cancer Institute, Department of Medical Biophysics, and Northeast Structural Genomics Consortium, University of Toronto, Toronto, ON, Canada M5G IL5 Contributed by Ad Bax, January 10, 2008 (sent for review December 14, 2007) Protein NMR chemical shifts are highly sensitive to local structure. NOE data commonly remains the limiting and most time- A robust protocol is described that exploits this relation for de novo consuming step in the NMR structure determination process. protein structure generation, using as input experimental param- Multiple NMR approaches have been proposed in recent years eters the 13C␣, 13C␤, 13C؅, 15N, 1H␣ and 1HN NMR chemical shifts. that are all aimed at circumventing the need for collection and These shifts are generally available at the early stage of the iterative analysis of NOE data.
    [Show full text]
  • Diffusive and Activated Contributions in Protein Dynamics
    DIFFUSIVE AND ACTIVATED CONTRIBUTIONS IN PROTEIN DYNAMICS by JEREMY COPPERMAN A DISSERTATION Presented to the Department of Physics and the Graduate School of the University of Oregon in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 2016 DISSERTATION APPROVAL PAGE Student: Jeremy Copperman Title: Diffusive and Activated Contributions in Protein Dynamics This dissertation has been accepted and approved in partial fulfillment of the requirements for the Doctor of Philosophy degree in the Department of Physics by: Eric Corwin Chair Marina Guenza Advisor John Toner Core Member James Imamura Core Member William Cresko Institutional Representative and Scott L. Pratt Dean of the Graduate School Original approval signatures are on file with the University of Oregon Graduate School. Degree awarded June 2016 ii c 2016 Jeremy Copperman iii DISSERTATION ABSTRACT Jeremy Copperman Doctor of Philosophy Department of Physics June 2016 Title: Diffusive and Activated Contributions in Protein Dynamics A novel approach is developed to describe the dynamics of proteins, described as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. This is a multi-scale approach, where structural correlations are used as input to an effectively linear description, which can be solved in diffusive modes. The accuracy of the LE4PD is verified by analyzing the predicted dynamics across a set of seven different proteins for which both relaxation data and NMR solution structures are available. The biological function of proteins is encoded in their structure and expressed through the mediation of their dynamics. We present here a study of how local fluctuation relates to binding and function.
    [Show full text]