Advances in Biological Solid-State NMR: Proteins and Membrane-Active Peptides

by Frances Separovic (Editor), Akira Naito (Editor)

Overview

The complexity and heterogeneity of biological systems has posed an immense challenge in recent years. An increasingly important tool for obtaining molecular and atomic scale information on a range of large biological molecules and cellular components is solid-state NMR. This technique can address fascinating problems in structural biology, including the arrangement of supramolecular complexes and fibril formation in relation to molecular folding, misfolding and aggregation.

Advances in Biological Solid-State NMR brings the reader up to date with chapters from international leaders of this growing field, covering the most recent developments in the methodology and applications of solid-state NMR to studies of membrane interactions and molecular motions. A much needed discussion of membrane systems is detailed alongside important developments in in situ analysis.

Topics include applications to biological membranes, membrane active peptides, membrane proteins, protein assemblies and in-cell NMR. This exposition of an invaluable technique will interest those working in a range of related spectroscopic and biological fields. A basic introduction invites those interested to familiarise themselves with the basic mathematical and conceptual foundations of solid-state NMR. A thorough and comprehensive discussion of this promising technique follows, which is essential reading for those working or studying at postgraduate level in this exciting field.

Product Details

ISBN-13:	9781849739108
Publisher:	RSC
Publication date:	03/06/2014
Series:	New Developments in NMR , #3
Pages:	630
Product dimensions:	6.40(w) x 9.30(h) x 1.50(d)

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Advances in Biological Solid-State NMR

Proteins and Membrane-Active Peptides

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By Frances Separovic, Akira Naito

The Royal Society of Chemistry

Copyright © 2014 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-84973-910-8

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CHAPTER 1

Introduction to Biological Solid-State NMR

M. WEINGARTH AND M. BALDUS *

Bijvoet Center for Biomolecular Research, Faculty of Science, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands

* Email: [e-mail]

1.1 Preface

Solid-state nuclear magnetic resonance has emerged as an established spectroscopic technique to provide atomic-scale information in complex biological systems. Recent years, with the appearance of the first de novo structures of membrane proteins and solid-state NMR spectroscopists unraveling the details of native cellular components at atomic resolution, indeed seem to mark a watershed moment for solid-state NMR becoming a leading technique to study highly disordered or heterogeneous biological systems.

These stunning advances, however, are hardwon. What catches one's eye, especially for eyes used to the spectral resolution of liquid-state NMR, is the broadness of non-modulated solid-state NMR signals. For liquid-state spectroscopists, such data may appear as a featureless blob, from which structural parameters are hardly deducible, let alone at atomic resolution (Figure 1.1). The broadness of the signals, which easily exceeds dozens of kHz or even several MHz, results from the presence of anisotropic interactions in solid-state NMR spectra, and a large part of solid-state NMR methodology refers to the manipulation of the Hamiltonian to dissect the anisotropic interactions or to suppress their influence on NMR spectra in a controlled manner.

1.2 Interactions in Biological Solid-State NMR

Interactions which affect the spin system and its associated Hamiltonian can be classified as external and internal (eqn 1.1). The external Hamiltonian is directly under the control of the NMR operator and consists of the Zeeman interaction and the rf (radio-frequency) fields, while the internal Hamiltonian includes the interaction of the spins with the local electronic environment (chemical shift), with each other (dipolar and scalar couplings) and with electric field gradients (quadrupolar coupling). The internal interactions may be modulated by the spectroscopist by means of rf pulses or magic angle spinning.

Htotal = Hexternal + Hinternal (1.1)

1.2.1 General and Rotational Properties of NMR Interactions

Before we summarize the most relevant interactions in biological solid-state NMR, we will briefly discuss their general appearance and properties. Whether external or internal interactions, their Hamiltonians can be depicted as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)

with I and S as row and column vectors, respectively, and à as a second-rank Cartesian tensor as a means to represent the anisotropy of an interaction, corresponding to a 3×3 square matrix. In this equation, I is a spin operator, while the other vector S represents either a second spin (dipolar or scalar coupling), or a magnetic (chemical shift) or an electric field (quadrupolar coupling). Subjected to rapid isotropic molecular motion, à is averaged to its trace, which is the sum of the diagonal elements:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.3)

Besides the Cartesian representation, irreducible spherical tensor operators are a particularly appropriate basis to describe transformations in solid-state NMR:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 1.4

In this representation, it is easily visible that any NMR interaction can be broken down into a spatial part, represented by spherical tensor A, and a spin part, represented by spherical tensor operators T. Indices k indicate the rank of a tensor, which has 2m+1 orders (which are irreducible spherical tensors). Component A00 is the isotropic, A1-m is the antisymmetric and A2-m is the anisotropic part of an interaction. Since the antisymmetric part can usually be ignored, and since the static magnetic field B0 is usually orders of magnitude larger than the internal interactions (with the exception of certain quadrupolar interactions), the summation can be reduced in the so-called secular approximation to:

H = A00T00+A20T20 (1.5)

neglecting all terms that vanish over time and retaining only those that commute with B0. Rotations of spherical tensors are carried out by Wigner rotation matrices D of the same rank, with the Euler angles α, β and γ(eqn 1.6). Details of all these operations can be found in standard references.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.6)

NMR interactions have their simplest form in their principal axis system (PAS), in which all off-diagonal elements are zero. Yet, NMR signals are detected in the laboratory frame, into which the interactions thus have to be transformed to analyze their effect on the spectrum. Transformations between different frames obey the following relation, which is called the addition theorem of Wigner rotation matrices:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.7)

According to these rules, NMR interactions can be transformed from one frame into another. Typically, in solid-state NMR, transformations include a transformation from the PAS to a molecular frame, which is fixed to the molecular structure and in which all NMR interactions share a common orientation, followed by a transformation to a rotor frame to take into account the powder averaging, and finally into the laboratory frame (Figure 1.2).

1.2.2 Chemical Shift Anisotropy

Nuclei possessing a spin I have an associated nuclear magnetic dipole moment μ = γhI, with γ as the gyromagnetic ratio. For an isolated spin-½ nucleus, subjected to a static magnetic field B0 along the z-axis, this gives rise to energy levels separated by ΔE=-γhB0 =hω0 with ω0 denoting the Larmor frequency. The resonance frequencies observed in NMR spectra, however, usually slightly differ from the Larmor frequency. This difference is called the chemical shift, which is caused by variations in the electron distribution around nuclei. The electron distribution around a given nucleus is rarely spherically symmetric, and the resulting anisotropic local field is termed the chemical shift anisotropy (CSA; see Figure 1.3). The CSA may be described as a Cartesian second-rank tensor, the trace of which is the isotropic chemical shift:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.8)

The chemical shift tensor can be characterized (note that there are different nomenclature conventions; here we use the Haeberlen convention with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] by its reduced anisotropy σ and anisotropy Δσ = 3σ/2, which reflect the deviation from cubic symmetry, and its asymmetry η, which reflects the deviation from axial symmetry (Figure 1.3):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.9)

For an axially symmetric CSA tensor, with θ defining the direction of B0 in the PAS of the CSA tensor, the resonance frequency can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.10)

The non-zero elements of the irreducible spherical tensor operators in the PAS of the chemical shift are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.11)

1.2.3 Dipolar Coupling

The local magnetic moments [??] of spins do not only interact with B0 but also with each other. For example, in the context of the dipolar coupling, the magnetic moments interact directly through space. The interaction energy between two magnetic moments [??] with a distance r12 (assuming that both dipoles have the same orientation to r12; see Figure 1.4) is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.12)

which after replacement of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and reformulation in polar coordinates yields the dipolar Hamiltonian with the so-called dipolar alphabet:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.13)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.14)

The terms C–F contain single-quantum I[+ or -]1I2z and double- quantum operators I[+ or -]1I[+ or -]2 and can therefore be safely neglected in the secular approximation. Note that if γ1 ≠ γ2 the B term is also non-secular and can be omitted, which is the reason for the different expression for heteronuclear HIS and homonuclear HII dipolar Hamiltonians (eqn 1.15). Theta (θ) is defined by the direction of the internuclear vector in a coordinate system in which the B0 field is in the direction of the z-axis.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.15)

with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as the dipolar coupling constant. The dipolar coupling tensor is axially symmetric and traceless; hence APAS20 is its only PAS component in the secular approximation.

1.2.4 Scalar Coupling

Scalar couplings are indirect interactions mediated through electrons, which usually act via covalent bonds. The term "scalar" already indicates this interaction to be usually rotational-invariant, i.e. isotropic with the scalar coupling tensor Jjj reduced to its trace. Scalar couplings are often small in comparison to other interactions in solid-state NMR and may be obscured by a broad powder pattern. However, they can of course be exploited in the solid state, too, especially in combination with magic angle spinning. The homo- and heteronuclear scalar coupling interactions are respectively described by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.16)

1.2.5 Quadrupolar Coupling

Nuclei possessing a spin I > ½ have an electric quadrupole moment arising from a non-spherical distribution of the electric charge around the nucleus. This moment interacts with the electric field gradient, which arises by virtue of the distribution of other nuclei and electrons in the vicinity of the nucleus. Since quadrupolar nuclei are, except for deuterium, non-standard nuclei for biological solid-state NMR, we will not dwell further on this NMR interaction and refer the interested reader elsewhere.

1.2.6 Magic Angle Spinning

Solid-state NMR experiments of biological samples are usually subjected to magic angle spinning (MAS), which is a technique to average the spatial part of second-rank interactions by making the interactions time-dependent. MAS can greatly enhance spectral resolution and sensitivity. It implies spinning a rotor containing the sample at a certain angle with respect to the static B0 field (Figure 1.5), at which the spatial anisotropic part of the interactions, describable as second-rank tensors like the dipolar coupling or the CSA, are averaged out. The orientation dependence of these interactions is proportional to 3(cos2θ -1)/2, which is the second Legendre polynomial P2(cos θ). This expression becomes zero at θ = 54.74° which is, therefore, also called the magic angle θm (Figure 1.5). For axial symmetric tensors, it can be shown that MAS yields the average orientation function:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.17)

For asymmetric CSA tensors, one obtains a term depending on the orientation of all three principal axes to the spinning axis. Since this term is also multiplied by P2(cos θ) due to MAS, both axial symmetric and asymmetric CSA tensors are averaged out by fast spinning. If the MAS frequency is smaller than the magnitude of the CSA, a spinning sideband pattern is observed in the NMR spectrum, which at higher spinning frequencies collapses into one resolved peak (Figure 1.5).

For an interaction that commutes with itself over time (referred to as inhomogeneous by Maricq and Waugh), MAS achieves complete averaging. This is, however, not the case for time-dependent homogeneous interactions (which do not commute with themselves over time), like strong homonuclear dipolar proton couplings. We will refer to a hand-waving explanation to illustrate the latter. As discussed above (see Section 1.2.3), unlike HISD, HIID exhibits a secular B-term which contains zero-quantum operators inducing flip-flop transitions among spins I at a ratio proportional to the strengths of HIID. This means that the spin states and thus the local dipolar fields are not constant over time (they are mixed by the B-term), while MAS only works efficiently if the interaction is static for at least one rotor period. It is important to keep in mind that the presence of one homogeneous interaction suffices to render all internal interactions homogeneous and thus difficult to be spun out completely. The reason for this behaviour is that NMR interactions are entangled with the homonuclear couplings in higher order cross-terms (see below and elsewhere for further reading). Interestingly, the efficiency of flip-flop transitions decreases with increasing chemical shift differences, i.e. with increasing B0, reducing the homogenous character of interactions like dipolar proton–proton couplings. These dependencies become, for example, apparent using average Hamiltonian or Floquet theory.

Note that MAS is limited to second-rank tensors, which does not suffice to suppress interactions like quadrupolar couplings, which in addition to a P2(cos θ) orientation dependence also exhibit a P4(cos θ) dependence. An elegant means to suppress these interactions further is the double rotation (DOR) technique, which requires spinning the sample at two angles simultaneously.

1.3 Cross Polarization

Cross polarization (CP) is a method to enhance the sensitivity of heteronuclear NMR experiments, in which polarization is transferred from the abundant proton bath across the heteronuclear dipolar couplings to the heteronuclei. The technique, analogously to the INEPT experiment in solution, exploits the much higher equilibrium Boltzmann polarization of the protons.

Cross polarization requires simultaneous rf irradiation of the protons (I) and the heteronuclei (S), spin-locking both species. The irradiation has to fulfill the Hartmann–Hahn matching condition ωS1 = ωI1 in the static case, and ωS1 = ωI1 [+ or -]nωrot for spinning samples (with n = 1,2).

(Continues...)

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Table of Contents

Introduction to Biological Solid-State NMR;
Combining NMR Spectroscopic Measurements and Molecular Dynamics Simulations to Determine the Orientation of Amphipathic Peptides in Lipid Bilayers;
13C−13C Distance Measurements by Polarisation Transfer Matrix Analysis of 13C Spin Diffusion in Uniformly 13C-Labeled Molecular Complex under Magic Angle Spinning;
Demonstration of the Equivalence of Solid-state NMR Orientational Constraints from Magnetic and Rotational Alignment of the Coat Protein in a Filamentous Bacteriophage;
Membrane Protein Interactions;
Magnetic liposomes and bicelles: new tools for membrane-peptides structural studies;
Membranes and Their Lipids: A Molecular Insight into Their Organization and Function;
Structural studies of small bioactive compounds interacting with membranes and proteins;
Lipopolysaccharide Induces Raft Domain Expansion in a Cholesterol-Containing Membrane;
Deuterium NMR of mixed lipid membranes;
Membrane Interactions of Amphiphilic Peptides with Antimicrobial Potential: A Solid-State NMR Study;
Investigations of the structure, topology and dynamics of membrane-associated polypeptides by solid-state NMR spectroscopy;
NMR of Lipids and Lipid/Peptide Mixtures;
NMR investigations of the structure and dynamics of antimicrobial peptides: The peptaibol alamethicin;
Solid-state NMR studies of antimicrobial peptide interactions with specific lipid environments;
Dynamic Structure Analysis of Peptides in Membranes by Solid-State NMR;
Structural Dynamics of Retinal in Rhodopsin Activation Viewed by Solid-State 2H NMR Spectroscopy;
Helical Membrane Protein Structure: Strategy for Success;
Chemistry and Structure via Solid-State NMR;
Photoactivated Structural Changes in Photoreceptor Membrane Proteins as Revealed by in situ Photoirradiation Solid-State NMR Spectroscopy;
A Promising Prognosis for Solid-State NMR of Functional Membrane Protein Complexes;
Structural Topologies of Phosphorylated and Non-phosphorylated Oligomeric Phospholamban in Lipid Membranes by Hybrid NMR Approach;
Structural Insights from solid-state NMR into the Function of the Bacteriorhodopsin Photoreceptor Protein;
2H solid-state NMR study of peptide-membrane interactions in intact bacteria;
Magic Angle Spinning NMR Spectroscopy for Resolving Structure and Mechanisms of Function of Membrane Protein Assemblies Involved in Photosynthetic Energy Conversio;
Large protein complexes revealed by solution state NMR: G Proteins and G Protein-activated inwardly rectifying potassium ion channel (GIRK);
NMR studies of small molecules interacting with amyloidogenic proteins;
Solid-State NMR Studies of β-Amyloid Fibrils and Related Assemblies;
Subject Index