Florida State University Libraries
Electronic Theses, Treatises and Dissertations The Graduate School
2005 Structure-Function Correlation of the M2 Proton Channel Characterized by Solid-State Nuclear Magnetic Resonance Spectroscopy Jun Hu
Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected]
THE FLORIDA STATE UNIVERSITY
COLLEGE OF ARTS AND SCIENCES
STRUCTURE-FUNCTION CORRELATION OF THE M2 PROTON CHANNEL CHARACTERIZED BY SOLID-STATE NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
By
JUN HU
A Dissertation submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Degree Awarded: Spring Semester, 2005
The members of the Committee approve the dissertation of Jun Hu defended on January 24, 2005.
Timothy A. Cross Professor Directing Dissertation
Peter G. Fajer Outside Committee Member
Michael S. Chapman Committee Member
Naresh Dalal Committee Member
Timothy M. Logan Committee Member
The Office of Graduate Studies has verified and approved the above named committee members.
ii
To my wife, Yan Gu, who makes my life integrate and cheerful, to my parents, Zhaoxin Hu and Qifang Li, for their continuous love and support, and to our expecting son, Joseph G. Hu, whom we have already met twice on the ultrasound screen.
iii
ACKNOWLEDGMENTS
Writing a dissertation is something like drafting a short memoir. The road of science is never even, as we all know. In the years as I was teetering along it, I met so many people giving me warm hands. I want their names to be printed in my dissertation and to be remembered in my science journey. First meeting with Professor Tim Cross was delightful. For an oriental student just stepping on this land and overwhelmed by a whole bunch of words and accents never taught in his English classes, Tim was the first person who I felt was not speaking a foreign language. He has an amazing skill to understand Sino-English. Although at that time I was not completely certain whether I liked his research or not, his knowledge, enthusiasm, shrewdness and humor told me that this was the lab I wanted to join in. His office is always open when he is there. If I want to see him, he always stops any work at hand and talks to me. I do not know how may times I sat in his office with frustration and walked out cheerfully with ideas and hope. I always enjoy those funny stories he told me. He is patient with my naïve ideas. He encourages me to attend many conferences and present my work, while many professors do not do. Now I gradually realize that how important it is to communicate my research with other scientists and conference experience has become a precious wealth to me. His judgment on possibilities, diligence in science, leadership in the lab and coordination of personnel with various expertise have a strong impact on me. I am fortunate in being his student. He is the best mentor of mine. Dr. Riqiang Fu is a brilliant NMR spectroscopist at the National High Magnetic Field Laboratory (NHMFL). I learned much of the fundamental and practical NMR knowledge from him. Whenever I have NMR-related questions and ideas (sometimes very nonsensical and stupid), I go to his office and we talk. He is very patient of explaining every step in the pulse program and encourages me to do NMR experiments independently on spectrometers. I am thankful for his help in these years. I also appreciate Dr. Zhehong Gan for his assistance on the Oxygen-17 project.
iv I thank those colleagues for their help in the lab. Dr. Junfeng Wang introduced this lab to me. We had a very good time when he was here and talked a lot about PISEMA simulation on the phone when he was in Georgia. I learned Insight II from Dr. Sanguk Kim. That leaded my interest to the bio-computation. Dr. Kastuyuki Nishimura and I worked on the M2 project when he was here. We are still very good friends. Dr. Fei Gao taught me how to express the M2 protein, which will certainly help my future career on the biological NMR. Dr. Eduard Chekmenev joined the lab last year. We collaborated on many projects and enjoyed working together. Through the project on the structure determination by PISEMA, Tom Asbury (IMB), Srisairam Achuthan (Department of Mathematics) and I work closely together. Tom is very good at structural modeling and refinement and plays a key role in the M2- TMD structure modeling. Without Sai’s help, I would spend much longer time on Jeff Denny’s dissertation. Prof. Jack Quine (Department of Mathematics) taught me the Euclidean rotation and how to use Maple. Certainly, I will not forget the delicious summer soup in his house and the elegant music performed by Dr. Richard Bertram (Tom’s advisor, IMB & Department of Mathematics) and him. Also, I want to remember those folks here in the big family: Dr. Changlin Tian, Dr. Zhiru Ma, Dr. Farhod Nozirov, Yiming Mo, Conggang Li, Alicia Hopkins, Yuanzi Hua, Jacob Moore, Nguyen Hau, Rick Page, Lee Miller and Mukesh Sharma. I thank Yi Xiong from Prof. Alan Marshall group for her help on the Mass spectroscopy. I wish to thank those staff members: Hank Henricks and Umesh Goli in the BASS lab, Judy McEachern, Karol Bickett and Ashley Blue here at MagLab, for their support. I am also grateful to two secretaries in the chemistry graduate office, Sarah Armour and Ginger Martin, for their assistance on my graduate study. Finally, I would like to thank my committee professors: Prof. Peter G. Fajer, Prof. Michael S. Chapman, Prof. Naresh Dalal and Prof. Timothy M. Logan, for directing my Ph.D. study.
v
TABLE OF CONTENTS
LIST OF TABLES...... ix LIST OF FIGURES ...... x ABSTRACT...... xiv
INTRODUCTION ...... 1 1.1 Membrane Protein Structural Biology...... 1 1.2 Membrane Protein Structures ...... 5 1.2.1 Lipid Bilayers and Membrane Proteins ...... 5 1.2.2 Membrane Proteins versus Soluble Proteins...... 9 1.3 Ion Channels ...... 9 1.3.1 Potassium Channels ...... 10 1.3.2 Proton Channels...... 13 1.4 Solid-state NMR ...... 15 1.4.1 Nuclear Spin Hamiltonian...... 15 1.4.2 Zeeman Hamiltonian and Radio Frequency Hamiltonian ...... 16 1.4.3 Chemical Shift Hamiltonian ...... 16 1.4.4 Dipolar Coupling Hamiltonian ...... 17 1.4.5 J-coupling Hamiltonian...... 17 1.4.6 Quadrupolar Hamiltonian ...... 18 1.4.7 Spin-Rotation Hamiltonian ...... 18 1.4.8 Chemical Shift Tensors and Chemical Shielding Tensors...... 18 1.4.9 Dipolar Coupling Tensors...... 22
WAVES, WHEELS AND HELICES: ORDERLINESS IN PISEMA FUNCTIONS...... 25 2.1 Introduction...... 25 2.2 Torsion Angle ...... 25 2.3 Continuous Frenet Frame and Discrete Frenet Frame ...... 27 2.4 Frames and NMR...... 30 2.4.1 Standard Peptide Plane Geometry ...... 30 2.4.2 Principal Axis Frame and Peptide Plane Frame ...... 31 2.4.3 Helical Axis Frame and Laboratory Frame ...... 32 2.5 PISEMA Powder Spectrum Simulation...... 33 2.6 PISA Wheels...... 36 2.6.1 Transformation from PAF to HAF ...... 36 2.6.2 PISA Wheels...... 42
vi 2.7 PISEMA Waves...... 43 2.7.1 PISEMA Waves...... 44
HISTIDINES: HEART OF THE PROTON CHANNEL FROM THE INFLEUNZA A VIRUS ...... 49 3.1 The M2 Protein and the Influenza A Virus...... 50 3.2 pH Titration of His37 in the M2 TM Domain ...... 53 3.2.1 Sample Preparation ...... 53 3.2.2 Solid-state NMR Experiments ...... 54 3.2.3 Modeling of Multi-step Proton Dissociation of M2-TM Domain Histidines 54 3.2.4 CP Kinetics of His37 15Nδ1 ...... 57 3.2.5 15N CP/MAS NMR Titration of His37 ...... 61 3.2.6 Proton Conduction in the M2 Channel ...... 65
AMANTADINE AND THE M2 PROTON CHANNEL FROM THE INFLUENZA A VIRUS ...... 68 4.1 The Antiviral Drug Amantadine ...... 68 4.2 Amantadine and His37...... 70 4.2.1 Sample Preparation ...... 70 4.2.2 Solid-state NMR Experiments ...... 71 4.2.3 Sharp Signals with Amantadine...... 71 4.2.4 Slow His37 Dynamics with Amantadine...... 72
STRUCTURE OF THE M2 TRANSMEMBRANE DOMAIN WITH AMANTADINE ...... 80 5.1 Structure Determination Using Orientational Restraints ...... 80 5.1.1 Torsion Angle Calculation...... 81 5.1.2 Degeneracy ...... 84 5.1.3 Continuity Rule...... 86 5.1.4 PISEMA Data of M2-TM Domain with Amantadine...... 87 5.1.5 Subunit Structure of M2-TM Domain with Amantadine...... 89 5.1.6 His37 and Trp41 Side Chain Conformations...... 91 5.2 Structure of the M2-TMD with Amantadine ...... 94
CONCLUSIONS, HYPOTHESES AND FURTURE WORKS ..... 98 6.1 Proton Conduction in the M2 Proton Channel...... 98 6.2 Amantadine Binding to the M2 Channel ...... 103 6.3 Solving Ambiguities and (15N, 1H, 15N-1H) 3D NMR Experiments...... 106 6.4 Summary...... 108
vii
APPENDIX A...... 110 A.1 PISEMA Powder Pattern Simulation...... 110 A.2 PISA Wheel Simulation...... 111 A.3 The PISEMA Waves...... 116 A.4 The PISA Helix...... 121 A.5 The Calculation of αB and βB ...... 123 A.6 Calculation of Torsion Angles...... 123 A.7 Spectral Deconvolution...... 125 A.8 15N, 1H, 15N-1H PISA simulation...... 127
APPENDIX B ...... 132 B.1 Fmoc-15N-AA-OH ...... 132 B.2 Fmoc-15N(δ1 or ε2)-(Trt)-His-OH ...... 134 B.3 H13CO-Val-OH ...... 135 B.4 15N-Amantadine ...... 135 B.5 17O Labeled D-Leucine and Fmoc-N-D-Leu-C17O17OH ...... 136 B.6 Cleavage of the M2 TM peptide ...... 137
APPENDIX C ...... 138 Permissions Letter...... 138
BIBLIOGRAPHY...... 142
BIOGRAPHICAL SKETCH...... 160
viii
LIST OF TABLES
1.1 Nobel Prize and membrane proteins...... 4
1.2 The hypothetical proton pathways in membrane proteins ...... 14
2.1 The effect of tilt angle and rotation angle on PISEMA wave functions...... 46
H 15 δ1 3.1 T1ρ and variable-contact-time NMR data of M2-TMP containing N labeled histidine in DMPC/DMPG liposomes at pH 8.8...... 59
3.2 Deconvolution parameters and pH versus Nproton and 4 - Nproton used in the fitting of equations 3.11 and 3.12...... 62
15 δ1 4.1 T1ρ and variable-contact-time NMR data of M2-TMP containing N labeled histidine in DMPC/DMPG liposomes with 10 mM amantadine at pH 8.0 ...... 72
+ released 4.2 [His] /[HisH ] and Nproton of the M2-TM domain with and without 10 mM amantadine...... 79
5.1 The PISEMA data from 15N labeled M2-TM domain in DMPC bilayers with amantadine and the torsion angles calculated from NMR data ...... 91
5.2 The 15N chemical shift principle components and orientations of histidine and tryptophan side chains...... 92
ix
LIST OF FIGURES
1.1 Histogram of the number of MP structures solved per year ...... 2
1.2 A) The structure of a fluid dioleoylphosphocholine bilayer in the liquid-crystalline phase and B) its polarity profile...... 7
1.3 Membrane protein structural motifs and hydrogen bond in different phases ...... 8
1.4 X-ray crystallography structure of truncated KcsA K+ channel in 3.2 Å resolution 11
1.5 Opened and closed states of K+ channels...... 12
1.6 Transfer of protons in a water wire through Grotthus mechanism ...... 13
1.7 The vector relationship between the external magnetic field B0, the induced field Binduced and the effective field Beff that a nuclear spin experiences...... 19
15 1.8 The magnetic field vector B0 and N-H bond vector in the N chemical shift principle axis frame...... 22
1.9 Solid-state 15N NMR spectra at different conditions ...... 24
2.1 Illustration of torsion angle definition ...... 26
2.2 A continuous curve in space and a Frenet frame ...... 27
2.3 The definition of the discrete Frenet frame, the vector components and the exterior angle for a sequence of points...... 28
2.4 The standard peptide plane geometry ...... 31
2.5 The principle axis frame of amide 15N chemical shift and the peptide frame at nitrogen ...... 32
2.6 The helical axis frame and the laboratory frame ...... 33
2.7 Numerical simulation of PISEMA powder patterns ...... 35
2.8 Numerical simulation of the asymmetry factor effect on the PISEMA functions....37
x 2.9 Transformation from PAF to DFF ...... 38
2.10 Discrete Frenet frames at the backbone atoms ...... 40
2.11 PISA wheels...... 43
2.12 PISEMA waves...... 47
2.13 PISA helices...... 48
3.1 The primary sequence of the M2 protein and the life cycle of the influenza A virus ...... 51
3.2 Two hypothetical mechanisms for the M2 conductance...... 52
H 15 δ1 3.3 T1ρ measurement and various-contact-time experiments of N His37 M2-TMP in DMPC/DMPG liposomes at pH 8.8 ...... 58
3.4 The cross-polarization kinetics of 15Nδ1 His37 M2-TMP in DMPC/DMPG liposomes at pH 8.8 ...... 59
3.5 Deconvolution of 15N CP/MAS NMR spectra at pH 6.5 and pH 7.0 ...... 60
3.6 15N CP/MAS NMR spectra of the M2 transmembrane domain in fully hydrated DMPC/DMPG (4:1 molar ratio) liposomes at 4 oC as a function of pH ...... 64
3.7 Analysis of the pH titration data for the His37 labeled M2 TM domain following corrections for cross polarization kinetics and following spectral deconvolution....66
3.8 A model illustrating the opening of the M2 proton channel...... 67
4.1 15N CP/MAS NMR spectra of His37 (15Nδ1 and 15Nε2) M2-TM domain in DMPC/DMPG (4:1 molar ratio) with and without amantadine at different pH values ...... 73
15 15 δ1 4.2 A) T1ρ measurement N CP/MAS NMR spectra of N His37 M2-TMP with 10 mM in DMPC/DMPG liposomes at pH 8.8 and 277K. and B) 15N CP/MAS NMR spectra as a function of various contact time...... 74
H 15 δ1 4.3 A) T1ρ measurement of non-protonated N at 230 ppm and the protonated 15Nδ1–H at 147 ppm with 10 mM amantadine (Figure 4.2A) and B) fitting curves of 15N CP/MAS data extracted from various-contact-time experiment (Figure 4.2B) ...74
4.4 Comparison of PISEMA spectrum 5 15N leucine labeled M2-TM domain in the DMPC lipid bilayers A) in the absence of amantadine and B) in the presence of amantadine ...... 76
xi
4.5 Fitting of [His]/[HisH+] of the M2-TM domain in the presence of 10 mM amantadine versus pH...... 78
5.1 The bond vectors and exterior angles used in the torsion angle calculations ...... 81
15 5.2 Four possible solutions of B0 orientations in the N principle axis frame...... 85
5.3 The Cα chirality ambiguity...... 86
5.4 The oriented sample for PISEMA experiments...... 87
5.5 The comparison between PISEMA spectrum and separated local field spectrum to obtain experimental scaling factor...... 89
5.6 PISEMA data of various 15N site labeled M2-TM domain in DMPC with the amantadine present...... 90
5.7 A) Two PISA wheels in the M2-TM PISEMA spectrum. The spheres represent the PISEMA resonances and B) PISEMA wave simulation of the M2-TM PISEMA data...... 90
5.8 A) Orientations of the N-H vector in the 15N chemical shift principal axis frame and B) the 15N principle axis frame in the histidine and tryptophan molecular frame....93
5.9 PISEMA Spectra of His37 15Nε2 and Trp41 15Nε1 Μ2−ΤΜ domain in DMPC in the presence of amantadine...... 94
5.10 A) The subunit structure of the M2-TMD tetramer with amantadine calculated based on the PISEMA data. B) The comparison between the experimental PISEMA resonances and the calculated PISEMA resonances from the structure of Figure 5.8A...... 96
5.11 The model structure of M2-TMD/amantadine in DMPC bilayers...... 96
6.1 An imidazole-imidazolium complex modeling the histidine lock in the M2 proton channel ...... 100
6.2 The PISEMA spectra of 15N single site labeled M2-TMD in DMPC bilayers at different pH values...... 102
6.3 A) hypothetical amantadine binding model and B) amantadine derivatives ...... 104
6.4 Orientation of 15N chemical shift tensors and amide 1H chemical shift tensors in a peptide plane ...... 107
xii 6.5 Simulated PISA wheels of a) (1H, 15N-1H) correlation, b) (15N, 1H) correlation, c) (15N, 15N-1H) correlation and d) (15N, 1H, 15N-1H) correlation spectra for an ideal α- helix with different tilt angles...... 108
B.1 The flowchart of the synthesis of Fmoc-AA-OH...... 133
B.2 The synthesis of Fmoc-N-His-(Trt)-OH ...... 134
B.3 The synthesis of 15N-amantadine ...... 135
B.4 The mechanism of acid-catalyzed exchange...... 137
xiii
ABSTRACT
Although still in a developing age, solid-state nuclear magnetic resonance (NMR) spectroscopy has been proved to be a powerful tool to study the structure and dynamics of membrane proteins. Here this technique is applied to investigate the channel conductance mechanism and inhibition of the M2 proton channel from the influenza A virus. A four-histidine cluster in the pore of the M2 proton channel has been characterized by cross-polarization magic angle spinning (CP/MAS) NMR experiments over a pH range from 5 to 8.6. Studies were carried out in fully hydrated lipid bilayers with δ1 and ε2 15N labeled imidazole side chains. The first two protons bind to this histidine cluster with high affinity into imidazole-imidazolium dimeric forms with nearly + identical pKas of 8.2 suggesting the possibility of cooperative H binding. The resulting ‘histidine lock’ formed by a pair of imidazole-imidazolium dimers occludes the pore thereby closing the channel. The acid activation of the channel, which has long been associated with a histidine titration, is now associated with the third charge in this cluster that disrupts the ‘histidine lock.’ The H+ selectivity for the channel is explained by either a Grotthüs, water-wire or a histidine shuttle mechanism. Both side chain and backbone NMR data indicate that amantadine, an anti-viral drug, appears to hinder the M2 tetramer dynamics. The structure of the M2 transmembrane helices is determined by a static 2D solid-state NMR technique, polarization inversion of spin exchange at magic angle (PISEMA). Waves, wheels and helical spectral patterns are observed in PISEMA data. Two PISA wheels in the PISEMA spectra demonstrate a helical bend in the transmembrane domain of the M2 protein in the presence of amantadine.
xiv
CHAPTER 1
INTRODUCTION
Membranes and membrane proteins (MPs) play vital roles in cellular functions. Membranes separate cells and intracellular organelles from the surroundings so that many biological reactions and processes occur in relatively isolated media. Membranes are also the carrier where many important biological reactions (e.g. photosynthesis, oxidative phosphorylation and electron transport) take place in MPs. The communication between cells or intracellular organelles and the outside environment ─ the transport of metabolites, macromolecules and ions, for instance ─ is mediated and regulated by MPs.
1.1 Membrane Protein Structural Biology
Perhaps 30% of the proteins coded by the human genome are MPs. To understand the functional activities of MPs, their structures at atomic resolution are important. With the development of automated X-ray crystallography and state-of-the-art solution NMR pulse sequences, the time required for protein structural determination has been significantly shortened for water-soluble proteins. In addition to the traditional structural constraints used in NMR-based structural determination, residual dipolar couplings offer another powerful means to refine and even determine protein structures (for a recent review see (Prestegard et al. 2004). So far, structural genomics has mainly focused on soluble proteins. Despite the importance of MPs in cell function, only a few MP structures are documented in the protein data bank (PDB). Of more than 27,000 protein
1 structures deposited in the PDB (October, 2004), less than 1% are MP structures (http://www.pdb.org). This represents a huge deficit of information about MP structures. MP structure represents a current frontier in structural biology. X-ray crystallography and nuclear magnetic resonance spectroscopy represent two major players in three-dimensional protein structural determination. Although the structural determination of MPs is very challenging and demanding, more and more laboratories have stepped into this fast-growing area. The recent two co-crystal structures of MPs, lactose permease and ammonia transport channel, represent tremendous triumphs in membrane protein structural biology (Abramson et al. 2003; Khademi et al. 2004). According to the statistics from the White group at University of California, Irvine (http://blanco.biomol.uci.edu/Membrane_Proteins_xtal.html), currently there are 158 coordinate files of MPs in the PDB and 86 unique MP structures. Although the number of MP structures per year is increasing after 1992 (Figure 1.1), it is still not comparable with that of soluble protein structures solved each year.
20 18 16 14 Number of 12 membrane 10 protein 8 structures 6 4 2 0 1992 1994 1996 1998 2000 2002 2004 Year
Figure 1.1 Histogram of the number of MP structures solved per year. The number of solved structures for each year was collected from White’s website (http://blanco.biomol.uci.edu/Membrane_Proteins_xtal.html). Note that the number of structures in 2004 represents the current status as of October, 2004.
2 Compared to soluble proteins, MPs require much more time and effort on overexpression, solubilization, purification, refolding and reconstitution. Because the lipid bilayers in which MPs are embedded are so different from the aqueous environment, common approaches used in the crystallization of soluble proteins may not be suitable for the crystallization of MPs. Detergents and organic solvents are often seen in the X-ray crystallographers’ recipes (for a detailed summary on the crystallization conditions for membrane proteins please see http://sb20.lbl.gov/cobessi/membrane_struc.htm and http://www.mpibp-frankfurt.mpg.de /michel/public/memprotstruct.html). There is always a potential that detergents or organic solvents could denature the MP of interest. Thus, functional activity studies ought to be performed in parallel to the structural characterization. Crystallization in lipidc cubic phase, which is detergent-free, opens another promising road for MP structural biology (Chiu et al. 2000; Landau and Rosenbusch 1996; Nollert et al. 1999; Rummel et al. 1998; Shipley 2000). A few MPs have been crystallized successfully using this approach (Belrhali et al. 1999; Katona et al. 2003; Luecke et al. 1999; Pebay-Peyroula et al. 1997). In solution NMR samples, micelles are often used to mimic the lipid bilayers to stabilize the transmembrane domains of MPs (for reviews see (Henry and Sykes 1994; Opella et al. 1994). Besides the potential deleterious effect of detergents (Chou et al. 2002; Krueger-Koplin et al. 2004), slow tumbling of the large micelle-protein complex often results in broad NMR signals due to fast transverse relaxation. Transverse relaxation-optimized spectroscopy (TROSY) ─ which suppresses the fast transverse relaxation and substantially improves spectral resolution and sensitivity ─ is a good NMR technique to deal with super-large proteins or assemblies (Fernandez and Wuthrich 2003). Still, in most cases finding the optimal detergent that produces stable, homogeneous and functionally active samples for NMR studies is time consuming (Krueger-Koplin et al. 2004; Vinogradova et al. 1998). Biological solid-state NMR is a fast developing field (for recent review, see (Luca et al. 2003). In comparison with other spectroscopic means, solid-state NMR has many advantages for studying MPs. First of all, detergent is not required in the MP samples. Thus, searching a suitable detergent that both retain the MP function and satisfy solution NMR experiments is not necessary. For solid-state NMR samples, MPs can be stabilized
3 thermodynamically in their native or near-native environment, i.e. lipid bilayers. In principle, solid-state NMR can be applied to study proteins in cells. Secondly, angular and distance restraints can be obtained quantitatively to provide accurate structural information. Even more than liquid-state NMR, solid-state NMR is a powerful tool for studying protein dynamics. Last, but by no means least, MPs do not need to be crystallized for solid-state NMR experiments, though protein crystals could give rise to high-quality solid-state NMR spectra (Martin and Zilm 2003). Biological solid-state NMR is still in a state of development. With the advent of high field magnets, the major barrier for solid-state NMR now is the relatively scarcity of structural restraints. Three-dimensional structures of membrane proteins help the development of new drugs that target MPs. Approximately, half of all current drug targets in the pharmaceutical industry are MPs (Lundstrom 2004). As in a recent article titled “Long live structure biology” in Nature Structural & Molecular Biology, R. C. Stevens at Scripps Research Institute estimated that “… 50% of the cost of drug discovery would be saved if a target protein structure were used at an early stage to generate leads of high quality” (Stevens 2004). The structural data of MPs would significantly accelerate the drug discovery process. To close this section, here we would like to selectively list a few Nobel Prize laureates for their tremendous contributions to MP structures and functions:
Table 1.1 Nobel Prize and membrane proteins Year Name Category Awarded for Peter Agre Chemistry the discovery of water channels. 2003 Roderick the structural and mechanistic studies of Chemistry MacKinnon ion channels. Paul D. Boyer and their elucidation of the mechanism Chemistry John E. Walker underlying the ATP synthesis. 1997 the first discovery of an ion-transporting Jens C. Skou Chemistry enzyme, Na+, K+-ATPase. Erwin Neher and Physiology for their discoveries concerning the 1991 Bert Sakmann & Medicine function of single ion channels in cells. Johann Deisenhofer, the determination of the 3D structure of a 1988 Robert Huber and Chemistry photosynthetic reaction center. Hartmut Michel
4
1.2 Membrane Protein Structures
1.2.1 Lipid Bilayers and Membrane Proteins
Lipid bilayers are heterogeneous and complex systems that are composite assemblies of amphipathic lipids. This bilayer architecture forms spontaneously in aqueous solution in order to minimize the unfavorable contact between lipid hydrophobic
chains and water. For a lipid bilayer in the liquid crystalline (Lα) phase, the hydrocarbon core is about 30Å thick (Figure 1.2A). Lipid head groups, such as choline, phosphate and glycerol groups, along with water molecules constitute the interfacial region, which is about 15Å thick (Figure 1.2A). Thus, the total length of the interface is approximately equal to the hydrocarbon core. The interfacial region bridges the polar aqueous milieu and the apolar bilayer interior. Many complex electrostatic interactions between lipids and MPs (e.g. lipid headgroup and tryptophan indole ring) take place in this region. The chemical heterogeneity of the interface also explains the electrical polarity gradient in Figure 1.2B. Membrane proteins are unique members of the protein family. So far, only two secondary structural motifs for transmembrane (TM) domains have been observed: α- helical and β-barrel (Figure 1.3A), and α-helical structures seem to be predominant. Unlike soluble proteins, MPs are embedded in the lipid bilayers, which forces a significant limitation on their structural variations. Figure 1.3B lists the energy costs for transferring a peptide bond into different solvent phases (White and Wimley 1999). Clearly, transferring a hydrogen-bonded peptide bond from aqueous phase to an apolar phase dramatically reduces the energy cost. In order to stabilize the polar peptide bonds in the hydrophobic lipid bilayer, the TM segment requires a favorable structural motif such as α-helices and β-barrels to ensure complete hydrogen bonding. How do MP TM helices fold and pack in lipid bilayers? The early belief that MPs are “inside-out proteins” is probably inaccurate (Engelman and Zaccai 1980) because it is found that the TM protein interior is just as hydrophobic as the soluble protein interior
5 (Rees et al. 1989). Low dielectric constant of lipid bilayers requires that the lipid-exposed residues on the surface of MPs should be apolar. Whether the residues in the TM interior are more hydrophobic than those facing the lipid bilayers or not is controversial. Based on the three-dimensional structure of photosynthetic reaction center from Rhodobacter sphaeroides, Rees et al. (1989) calculated the hydorphobicities for the buried, semi- exposed and exposed TM residues and claimed that residues on the surface of MP TM domains have higher average hydrophobicity value than those buried inside the MP. Stevens and Arkin analyzed 62 TM helices from 7 membrane protein structures. They found that hydrophilic vector is a poor indicator of helix orientation and apolar and polar residues do not have any preference for the interior or exterior of the TM domain (Stevens and Arkin 1999). In general, the TM residues are more apolar than those in the extramembrane domains (Spencer and Rees 2002). High hydrophobicity of TM domain has been used as one factor to predict a MP and its TM regions (von Heijne 1992a). Membrane protein transmembrane domain usually has a cylinder-like shape with apolar residues pointing into the hydrophobic bilayer. Polar aromatic residues (not including Phe) such as Trp and Tyr tend to line the interface, which forms an “aromatic belt” (Braun and von Heijne 1999; von Heijne 1999; Yau et al. 1998). In Figure 1.3A, we use the structure of porin as an example and highlight all the aromatic residues to illustrate this phenomenon. Apparently, the aromatic residues are populated at the bilayer interfaces. Although the physics of the aromatic belt is not certain, it is known that those residues contribute to the stabilization of MPs in lipid bilayers. It is related to the rigid and flat rings with π electrons, which could interact with the positive charges on the lipid headgroup via π–cation interactions (Dougherty 1996). In addition, hydrogen bonds between tryptophan Nε1-H and the interfacial groups help align membrane proteins for optimal functional activity (Hu and Cross 1995). Potentially the tyrosine OH group performs a similar function.
6
Figure 1.2. A) The structure of a fluid dioleoylphosphocholine (DOPC) bilayer in the liquid-crystalline phase and B) the polarity profile of DOPC bilayer. The DOPC structure is illustrated by the time-average distributions of the principal structural groups projected onto the bilayer normal. The group charge densities were calculated for each quasi- molecular group using the atomic partial charges defined by Charifson et al. (Charifson et al. 1990) and the group volumes given by Wiener and White (Wiener and White 1992). The figure is reprinted from White and Wimley (1999) with permission.
7
Figure 1.3. Membrane protein structural motifs and hydrogen bonds in different phases. A) Two structural examples of membrane protein transmembrane domains: α- helix and β-barrel. The lipid bilayer is illustrated by dashed lines. The protein on the left is bacteriorhodopsin from halobacterium salinarum at 1.47Å resolution (PDB code: 1MOL). Note the bound lipid molecules are also present in the crystal structure. The β- barrel protein on the right is porin rhodobacter & capsulatus at 1.8Å resolution (PDB code: 2POR). The aromatic residues are highlighted in blue to show the distinctive aromatic belt at the interface. B) The energy costs of partitioning a peptide bond from aqueous phase to less polar phases.
8
1.2.2 Membrane Proteins versus Soluble Proteins
As more and more MP structures are documented in the PDB bank, people start comparing them with the soluble protein (SP) structures focusing on their differences. Whereas MPs share major features with SPs, MPs have their own characteristics. For instance, the hydrophobic effect is no longer a major driving force for the folding of MPs as the environment surrounding the TM region is the apolar hydrocarbon chains instead of water molecules. An early examination of the partial specific volume of bacteriorhodopsin suggests that MPs pack their residues just as tightly as SPs do (Tristram-Nagle et al., 1986), while more recent results indicate that MPs pack actually tighter (Eilers et al., 2000; Eilers et al., 2002). The tight packing of TM helices might contribute to the MP stability and compensate for the lack of a hydrophobic effect. In a low dielectric environment where electrostatic interactions dominate, hydrogen bonds are shorter in TM α-helices than other regions (Kim and Cross 2002). In addition, the TM α- helices appear to be more uniform than the SP ones (Kim and Cross 2002). It has long been recognized that the distribution of MP residues follow a “positive-inside” rule (von Heijne 1999; Wallin and von Heijne 1998), that is, positively charged amino acids such as arginine and lysine tend to distribute more abundantly on the cytoplasmic side than on the periplasmic side (Andersson and von Heijne 1994). This rule has been applied to improve MP topology prediction (von Heijne 1992b).
1.3 Ion Channels
Ion channels are pores. -- Bertil Hille
Before the discovery of ion channels, membranes were thought to be selectively permeable to certain ions (Hille 1992). Obviously, this hypothesis does not hold true, since we know that membranes are almost impermeable to inorganic ions. Years later
9 people realized that ions cross cell membranes facilitated by transporters and ion channels. Ion channels are one kind of MPs with a small cavity through which ions can pass. They provide a medium through which ions are conducted without interacting with the hydrophobic membrane interior. In response to chemical or physical stimuli, many ion channels open and permeate certain ions. It is of essential importance that ion channels can selectively conduct certain type of ions. But not all ion channels are selective. Ion selectivity and channel gating are two main themes in ion channel biology. Here I use the potassium channel as an example to introduce basic features of ion channels.
1.3.1 Potassium Channels
Potassium channels are among the most well-studied ion channels. Prof. Roderick MacKinnon at Rockefeller University won the Novel prize in chemistry in 2003 for his remarkable accomplishment on the functional and structural studies of a series of potassium channels (http://www.nobel.se/). Potassium channels are tetrameric. As shown in Figure 1.4, we can see at a glance that the channel has a pore in the middle with cations in it (Doyle et al. 1998). Although there is a small physical and chemical difference between K+ and Na+, potassium channels select K+ over Na+ by a factor of more than 1000. In addition, such a high selectivity for K+ does not affect the ion conduction rate (108 ions/sec). The potassium selectivity takes place in the selectivity filter, which is located between the central cavity and the extracellular region (Figure 1.4). In the selectivity filter, a threonine hydroxyl oxygen and four backbone carbonyl oxygens (residues VGYG) line the filter and point into the channel, thereby forming four evenly spaced layers for ion binding. The primary sequence of the selectivity filter represents a signature for the potassium channel family and is conserved throughout all potassium channels. The crystal structure of KcsA K+ channels illustrates that the backbone carbonyl oxygens mimic water molecules to solvate potassium ions in the channel (Doyle et al. 1998). In contrast to K+, other ions such as Tl+, Rb+ and Cs+ bind differently in the filter: there are only three predominate binding sites for them (Zhou and MacKinnon 2003). It is postulated that the ionic radius and charge balance in the filter may contribute to the channel selectivity.
10
Figure 1.4. X-ray crystallography structure of truncated KcsA K+ channel in 3.2 Å resolution.
By comparing the crystal structures between closed-state KcsA and opened-state MthK, Jiang et al. proposed that the conformation of outer and pore-lining helices control the gating of the potassium channels (Figure 1.5, Jiang et al., 2002). In the KcsA structure, the inner helices are straight and make a pore that narrows to about 3.5Å in diameter, i.e. it can only accommodate one or two water molecules. In addition, the pore is lined with hydrophobic amino acids. These two structural features impede the ion flow. However, in the structure of MthK, the inner helices are bent and the central cavity is much more spacious and confluent with the cytoplasm, which allows K+ to pass through the channel.
11
Figure 1.5. Opened and closed states of K+ channels. a, MthK (PDB code 1LNQ) and b, KcsA (PDB code 1K4C). Side view (c) and top view (d) of the KcsA (red) and MthK (black) pores are superimposed. Arrows indicate the direction of inner helix expanding from closed (KcsA) state to opened (MthK) state.
12 1.3.2 Proton Channels
Proton channels are special ion channels. Analogous to other ion channels, proton channels selectively conduct protons; the channel structure facilitates attracting protons, but does not tightly bind them; proton channels open and close in response to electrical or chemical stimuli. In biological systems, protons are exchangeable and ubiquitous. It is these unique chemical properties of protons that distinguish proton channels from other ion channels. In a water-filled channel, the transport of protons does not require the net diffusion of protons but can instead take place according to a “Grotthus mechanism”, which involves chemical exchange of hydrogen nuclei among hydrogen-bonded networks (Agmon 1995; Decoursey 2003). Figure 1.6 illustrates the basic concept of this proton transfer mechanism: that is, in the hydrogen-bonded water wire, a proton can “hop” onto the water oxygen at one end of the water wire and transfer of hydrogen bonds allowing the release of a proton at the other end (Figure 1.6A). In order to restore the starting structure to accept another proton, water molecules have to rotate as shown in Figure 1.6B to rearrange the hydrogen-bond assembly. This step is also referred to as “the turning step” (Decoursey 2003). In principle, water molecules can be replaced by suitable protein side chains in a protein interior that are capable of connecting the hydrogen-bond chain. In some membrane proteins like lactose permease, protons pass through the protein on a hydrogen-bonded network intercalated by polar residues and constrained water molecules (Abramson et al. 2003; Lancaster 2003; Stowell et al. 1997).
Figure 1.6. Transfer of protons in a water wire through a Grotthus mechanism.
13 The sole function of proton channels is to allow protons to pass through the channel passively and this proton translocation, usually associated with a pH change, is coupled indirectly to other biological functions. Essentially proton channels provide low- resistance water-filled cavities that facilitate proton transport across the membrane. Polar residues may disrupt the proton conduction pathway and potentially function as channel regulators. Table 1.1 summarizes those hypothetical proton pathways. Clearly, some titratable residues, such as His, Asp and Glu, actively participate in proton translocation, implying their functional roles in proton conduction. At a pH close to their pKa, the residues (e.g. His) are capable of accepting a proton from one side and losing it to the other. The pKa values of free Asp and Glu are low (3.9 and 4.3, respectively). But their pKas inside protein are structure dependent, indicating that protein conformation may control some residues’ proton affinity. H+-ATPase is an excellent example of this principle: the pKa of the key amino acid Asp61 changes with the rotation of the Fo component and consequently controls the direction of proton flow (Fillingame et al. 1992).
Table 1.2. The hypothetical proton pathways in membrane proteins
(This table is adopted from Decoursey, 2002)
14
1.4 Solid-state NMR
Throughout this dissertation, a number of solid-state NMR observables, such as isotropic chemical shifts, anisotropic chemical shifts and dipolar couplings, will be used to explore the structure and function of biological samples. In Chapter 3, 15N isotropic chemical shifts will provide the chemical information on histidine residues in the M2 transmembrane domain (M2-TMD). Relaxation parameters measured in cross polarization kinetic studies monitor the change in dynamics of M2-TMD with and without amantadine. 15N anisotropic chemical shifts and 15N-1H dipolar couplings, measured by PISEMA experiments, will be used to characterize the backbone structure of M2-TMD in the presence of amantadine. In this chapter, basic NMR principles are introduced. More extensive NMR theory can be found in many classic NMR books (Ernst et al. 1987; Levitt 2001; Mehring 1983).
1.4.1 Nuclear Spin Hamiltonian
Any nuclear spin in a condensed substance is not isolated. Unavoidably it will interact with fields generated by other nuclei and electrons having a spin. In principle, the properties of the substance or system should be represented by the total Hamiltonian,
Ĥtotal. Thus, the time-dependent Schrödinger equation can be written as d | Ψ t)( >≅ -i Ĥtotal Ψ t)( > dt total total
where Ψtotal(t) denotes the wave function of the quantum state of the system. In the case of magnetic resonance when only electromagnetic interactions are considered, based on the spin Hamiltonian hypothesis (Levitt 2001) the above equation can be simplified to d | Ψ t)( >≅ -i Ĥspin Ψ t)( > dt spin spin where Ψtotal(t) and Ĥspin represent the state function of the nuclear spin and the nuclear spin Hamiltonian, respectively.
15 It is commonly seen that the total nuclear spin Hamiltonian is expressed by the sum of the external Hamiltonian and the internal Hamiltonian
Ĥspin= Ĥext + Ĥint.
The external Hamiltonian includes the Hamiltonian from the Zeeman interaction (ĤZ ) and the spin radio frequency interaction (Ĥrf). The internal Hamiltonian consists of the chemical shift Hamiltonian (ĤCS), the dipolar coupling Hamiltonian (ĤDC), the quadrupolar coupling Hamiltonian (ĤQC), the J coupling Hamiltonian (ĤJ) and the spin- rotation Hamiltonian (ĤSR). Thereby, the total nuclear spin Hamiltonian can also be written as
Ĥspin= ĤZ + Ĥrf + ĤCS + ĤDC + ĤQC + ĤJ + ĤSR.
1.4.2 Zeeman Hamiltonian and Radio Frequency Hamiltonian
For each spin, the Zeeman interaction is the product of the spin magnetic moment µ and the magnetic field. Consequently, we have
ĤZ = -∑µ B0. (1.1) Similarly, the radio frequency (RF) Hamiltonian can be obtained:
Ĥrf = -B1(t) cos[ωt+φ(t)] ∑γ Ix.
The B1 field usually is many orders of magnitude smaller than the static field B0. The phase and amplitude of the RF irradiation can be modulated. The external Hamiltonian implies that the interaction between the sample and NMR spectrometer is under the control of the NMR spectroscopist. It is the internal Hamiltonian that provides the chemical and physical information on the sample in the NMR probe.
1.4.3 Chemical Shift Hamiltonian
Chemical shift Hamiltonian, sometimes called the nuclear magnetic shielding Hamiltonian, accounts for the interaction of the external magnetic field to the nuclear spin through interactions with electrons. It can be written as
16 ĤCS = ∑γI⋅σ⋅B0. where σ is a rank two tensor. Note that the induced field is σ⋅B0 and the negative sign is canceled by multiplying by another –1 as in equation 1.1. A more detailed description of chemical shift is discussed in section 1.4.8.
1.4.4 Dipolar Coupling Hamiltonian
The direct dipole-dipole interactions between nuclear spins originate from the small magnetic field generated by the nuclear spin magnetic momentum. This interaction is mutual. Dipolar couplings are the communication between a myriad of small spin magnetic fields so that this interaction is through space and exists without any restriction to molecular bonds. The dipolar coupling Hamiltonian is described as
µ0γ γ kj (I j ⋅r jk )(Ik ⋅r jk ) ĤCS = ∑ ( − 3 3)[ 2 − I j ⋅Ik ], 1.4.5 J-coupling Hamiltonian J coupling is also named indirect spin-spin coupling, which is the indirect coupling between two nuclear spins through the bonding electrons. Similar to the chemical shift Hamiltonian, the J-coupling Hamiltonian is given in the form ĤJ = 2.π ∑ I j ⋅ J jk ⋅Ik Again, Jjk is a 3 × 3 matrix called the J-coupling tensor. In solid-state NMR, usually J coupling is ignored as the coupling is very small compared with other couplings. Although it is small, J coupling has been observed in solid-state experiments (Kao and Lii 2002; Massiot et al. 2003). In addition, in high-resolution magic angle spinning experiments, J-decoupling pulse sequences are beneficial to the reduction of signal linewidth (Igumenova and McDermott 2003). 17 1.4.6 Quadrupolar Hamiltonian For nuclear spins I =1/2, the quadrupolar Hamiltonian is zero. In the case of I > 1/2, the nuclear quadrupolar moment interacts with the electric field gradient produced by the electrons. Once again, this interaction is written in the form ĤQC = ∑ Ii ⋅Q ⋅Iii , i with Qi representing the quadrupolar coupling tensor. 1.4.7 Spin-Rotation Hamiltonian Spin rotation Hamiltonian considers the interaction between the nuclear spin and the local magnetic field generated by molecular reorientation. It is given as ĤQC = ∑∑ Ii ⋅Ci, m ⋅Mm , im where M represents the angular momentum of the molecule and C is the spin-rotation tensor. In a solid or anisotropic sample where molecular rotation is restricted, the spin- rotation interaction can be neglected. 1.4.8 Chemical Shift Tensors and Chemical Shielding Tensors There are some contradictory conventions in the definition and symbols of the chemical shift tensors and the chemical shielding tensors. In the literature σ has been used for denoting both chemical shielding and chemical shift. Here, we follow the rules recommended by IUPAC, that is, δ represents the chemical shift and σ is the chemical shielding (RECOMMENDATIONS 1976). Induced by the external magnetic field, directional movement of electrons around a nucleus generates a local magnetic field Binduced, which is also called the shielding -6 field. Although it is about 10 that of B0, Binduced causes a frequency shift of the nuclear spin and distinguishes it from other spin species in the NMR spectrum. This is the so- called chemical shift. Chemical shift reflects the chemical signature of the atom of interest and the chemical environment surrounding it. It is probably the most powerful tool that NMR offers for studying molecules. 18 The effective magnetic field experienced by a nucleus is the sum of B0 and Binduced shown in Figure 1.7 Beff = B0 + Binduced. Figure 1.7. The vector relationship between the external magnetic field B0, the induced field Binduced and the effective field Beff that a nuclear spin experiences. The shielding field depends on the applied magnetic field: Binduced = - σ B0 where σ is a rank 2 3× 3 shielding matrix. This matrix is also named the Cartesian shielding tensor. Since the induced field is extremely small compared to the applied field, a good approximation is that Beff can be calculated by the sum of B0 and the vectorial component of Binduced that is parallel to B0. Therefore, as shown in Figure 1.5, Beff can be written by Beff = B0 + BII. Because 19 B0 ⋅Binduced B0 BII = ( B) induced B0 Binduced B0 B ⋅(σ ⋅B ) B = - 0 0 0 , B0 B0 we have B0 ⋅(σ ⋅B0 ) Beff = 1- B0 . B 2 0 Therefore, the precession frequency of a nucleus is B0 ⋅(σ ⋅B0 ) ϖ = −γ 1- B0 B 2 0 where γ is the gyromagnetic ratio. In practice, the chemical shift usually is measured by taking the ratio of the frequency difference between the sample and a reference frequency so that B0 ⋅[(σ ref −σ )⋅B0 ] ϖ −ϖ B 2 δ = ref = 0 obs ϖ ref B0 ⋅(σ ref ⋅B0 ) 1- 2 B0 B0 B0 ≅ ⋅[(σ ref −σ )⋅ . (1.2) B0 B0 The difference between the sample shielding tensor and the reference shielding tensor (usually it is a scalar multiplied by the identity matrix) leads to another very important 3× 3 Cartesian matrix, chemical shift tensor δ, which is δ = σref −σ. (1.3) Usually the chemical shift matrix is defined by six independent elements: δ xx δ xy δ xz δ = δ yx δ yy δ yz . δ zx δ zy δ zz By proper choice of a certain frame, the above matrix can be transformed into a diagonal matrix such that the off diagonal elements are zero and the entries on the diagonal are 20 designated as δ11, δ22 and δ33 with δ11 ≥ δ22 ≥ δ33, while conventionally chemical shielding elements are specified as σ33 ≥ σ22 ≥ σ11. Now the chemical shift matrix can be represented by δ 33 0 0 δ = 0 δ 0 . (1.4) 22 0 0 δ11 This chemical shift matrix forms an orthogonal frame often called the principal axis frame. In general, the principal axis frame of a nucleus has a fixed orientational relationship with the molecular frame. Consequently, a molecular orientation with respect to the external magnetic field can be deduced by measuring the nuclear anisotropic chemical shift. We will discuss in more detail how peptide plane orientations are obtained from 15N anisotropic chemical shifts in Chapter 5. Finally, from equation 1.2, we arrive at a master equation for calculating the observed anisotropic chemical shift: B0 B0 δ obs = ⋅(δ ⋅ ) . (1.5) B0 B0 The parentheses are retained in order to clarify the dot product sequence when the chemical shift is computed, though in the literature the parentheses are often omitted. Figure 1.7 illustrates the N-H vector of a peptide amide in the 15N principle axis frame. As shown in the figure, if the unit vector of B0 is written by sin(βB )cos(αB ) B = sin( )sin( ) . 0 βB αB cos(βB ) Then using equation 1.5 we can obtain the explicit equation for the observed anisotropic chemical shift as 2 2 2 δ obs = δ 33[sin(βB )cos(αB )] + δ 22[sin(βB )sin(αB )] + δ11cos(βB ) . (1.6) 21 15 Figure 1.8. The magnetic field vector B0 and N-H bond vector in the N chemical shift principal axis frame. The polar angles for B0 are αB and βB, respectively. Similarly, the polar angles for NH are denoted as αNH and βNH. The angle between B0 and N-H is ξ. For single crystal samples in the magnetic field, the molecular orientations are all fixed with respect to the field. In a static solid-state NMR spectrum, a single line will be observed reflecting the uniform orientation of each nucleus. While in a powder sample where the crystallites are randomly oriented with respect to the magnetic field, the solid- state NMR spectrum in most cases is broad as the chemical shift tensors experience all the orientations in space. Each orientation gives rise to an individual frequency. The powder pattern is the superposition of all peaks arising from different orientations (Figure 1.9). This is a typical example of heterogeneous broadening, which is often called chemical shift anisotropy. 1.4.9 Dipolar Coupling Tensors The dipolar coupling tensor D is traceless and axially symmetric. This implies that in high-resolution liquid-state NMR the dipolar coupling is averaged to zero due to 22 the fast molecular tumbling. We use νII to denote the largest element of the dipolar coupling tensor 1 − ν 0 0 2 II 1 D = 0 − ν II 0 ; 2 0 0 ν II the other two elements are ν┴, which is equal to -1/2νII . νII is also equal to the dipolar coupling constant. If the bond length of 15N-1H is regarded as 1.024Ǻ, then the dipolar coupling constant is 10.735 kHz (Wang et al. 2000; Wang et al. 2001). The secular portion of the 15N-1H dipolar splitting is given by 2 ν = νII (3(B0 · NH) -1) 2 = νII (3cos ξ-1). where ξ is the angle between B0 and the N-H vector (Figure 1.8). 23 Figure 1.9. Solid-state 15N NMR spectra for different sample conditions. A) a static 15 powder pattern for a typical amide N. Average values of tensor elements, δ11=202 ppm, δ22 =54 ppm and δ33 = 31 ppm, are used for spectral simulation. B) Isotropic chemical shift of the powder spectrum A, which is 1/3(δ11 + δ22 +δ33 ) = 96 ppm. C) The effect of axial motion on the line-shape of a powder pattern spectrum. 24 CHAPTER 2 WAVES, WHEELS AND HELICES: ORDERLINESS IN PISEMA FUNCTIONS 2.1 Introduction Helices are one of the major structural features in proteins. The propagation of a protein helix can be regarded as an orbit of a set of 4 backbone atoms in the peptide plane upon multiple orientation-preserving Euclidean motions about a helical axis. It is the skew translation of a peptide plane around the helical axis that leads to the periodic pattern of NMR observables. In this chapter, the algorithm to calculate the discrete Euclidean motion for a protein backbone, developed by Denny and Quine, is introduced (Denny et al. 2001; Quine 1999; Quine et al. 1997; Quine and Cross 2000). The chapter begins with the introduction of torsion angles and Frenet frames. Then a few right- handed orthonormal frames related to the backbone structural calculations and the transformation between them are discussed. In the end, PISEMA powder patterns, PISA wheels, PISEMA waves and PISA helices are simulated and analyzed. 2.2 Torsion Angle Torsion or dihedral angles are important parameters in structural biology. It describes a spatial relationship between three vectors. As shown in Figure 2.1, vector a and vector b define one plane and b and c define another. The torsion angle of vector a, b 25 and c around b thereby is calculated as the angle between two plane normals: by the right-handed rule, the second plane normal b× c rotates in counterclockwise direction to superimpose the first plane normal a× b. It is convenient to describe torsion angles in terms of a rotation matrix: a×b b×c R(b,φ) = . (2.1) a×b b×c Clearly, the plane normal vectors need to be normalized. Torsion angles are usually reported in degrees between (-180O, 180O]. Figure 2.1. Illustrative torsion angle definition. The plane normal can be defined by the cross product of two consecutive vectors. The first normal a× b is drawn in red and the second b× c in blue. Assume vector b pointing out of the paper, on the right side, it illustrates that the counterclockwise rotation around b defines the torsion angle. The torsion angle can be written as an argument of a vector (x, y) (except the origin point, (0, 0)): φ = arg(x, y) . (2.2) Then we have: 26 x y cosφ = and sin φ = . x 2 + y2 x 2 + y2 By the torsion angle definition (equation 2.1), we end up with a general formula to compute the torsion angle of three unit vectors u1, u2 and u3: Tor (u1, u2, u3) =arg (-u1 ⋅ u3 + (u1 ⋅ u2)(u2 ⋅ u3), u1 ⋅ (u2 × u3)), (2.3) where Tor stands for the torsion angle function. 2.3 Continuous Frenet Frame and Discrete Frenet Frame A continuous curve in space can be considered as an orbit of a point changing with time. The continuous Frenet frame is often applied to investigate the property of a curve (Figure 2.2). The Frenet frame F at each point on the curve is constructed by three unit vectors: the tangent vector t, the normal vector n and the binormal vector b F = (t, n, b). If the curve is described as a moving vector x(t), those vectors are given by dx/dt dt/dt t = , n = and b = t × n. dx/dt dt/dt By definition F is a right-handed orthonormal frame. The continuous Frenet frame definition is adopted to the discrete Frenet frame. Figure 2.2. A continuous curve in space and a Frenet frame. 27 In order to study the protein backbone structure, Denny and Quine introduced the discrete Frenet frame (DFF) formed by the bond vectors of the protein backbone (Denny et al. 2001). The sequence of protein backbone atoms comprising C, Ca and N forms a discrete curve representing the backbone geometry in space. In general, for any discrete curve with a series of points P0…Pn+1 (Figure 2.3), if there are no three consecutive points on the same line, the DFF at point Pk can be built as Fk = (tk, nk, bk), where the DFF components are defined as Pk+1 − Pk t k−1 × t k t k = , bk = , nk = b k × t k k =1…n. (2.4) Pk+1 − Pk t k−1 × t k As in Figure 2.3, the exterior bond angle θk is defined as the angle between vector tk-1 and tk. If the torsion angle for tk-1, tk and tk+1 is φk, i.e. φk = Tor(tk-1, tk, tk+1), (2.5) we can easily obtain the rotation operation formula as below: R(bk, θk ) tk-1 = tk and R(tk, φk) bk= bk+1. (2.6) Figure 2.3. The definition of the discrete Frenet frame, the vector components and the exterior angle for a sequence of points. 28 With equation 2.6, we have bk+1 = R(bk+1, θk+1) bk+1 = R(bk+1, θk+1) R(tk, φk) bk tk+1 = R(bk+1, θk+1) tk = R(bk+1, θk+1) R(tk, φk) tk nk+1 = bk+1 × tk+1 = [R(bk+1, θk+1) R(tk, φk) bk]× [ R(bk+1, θk+1) R(tk, φk) tk] = [R(bk+1, θk+1) R(tk, φk)] ( bk × tk) = R(bk+1, θk+1) R(tk, φk) nk. Thus, we can obtain the rotation relationship from Fk to Fk+1 using the exterior angle and the torsion angle: Fk+1 = R(bk+1, θk+1) R(tk, φk) Fk. (2.7) Now the conjugacy property of a rotation matrix is introduced here in order to find the relationship between Fk and Fk+1. For a rotation matrix A belonging to a special orthogonal group, it follows AR(u, θ)At=R(Au, θ). (2.8) Then we can see that t R(bk+1, θk+1) = R(R(tk, φk) bk, θk+1) = R(tk, φk) R(bk, θk+1)R(tk, φk) . With equation 2.7, we obtain t Fk+1 = R(tk, φk) R(bk, θk+1)R(tk, φk) R(tk, φk) Fk = R(tk, φk) R(bk, θk+1) Fk. (2.9) -1 Conjugating both sides of equation 2.9 with Fk , we have -1 -1 -1 Fk Fk+1 = Fk R(tk, φk) Fk Fk R(bk, θk+1) Fk -1 -1 = R(Fk tk, φk)R(Fk bk, θk+1) = R(e1, φk)R(e3, θk+1) (2.10) since we know that tk = Fke1 and bk = Fke3 where e1 and e3 are the vector components of the standard frame. Equation 2.10 shows that the transformation can be written as the product of two Euler rotations: 1 0 0 cos( k +1) − sin( k +1) 0 R(e , φ ) = 0 cos(φ ) − sin(φ ) , R(e , θ ) = sin( ) cos( ) 0 . 1 k k k 3 k+1 k +1 k +1 0 sin(φk ) cos(φk ) 0 0 1 29 This provides a convenient means to relate two consecutive frames using the torsion angle and the exterior angle. If the first frame F0 is defined as a standard frame or an identity matrix, the DFF Fk at point k can be obtained as -1 -1 -1 Fk = F0F0 … Fk-2Fk-2 Fk-1Fk-1 Fk = R(e1, φ0)R(e3, θ 1) … R(e1, φk-1)R(e3, θk). (2.11) Therefore, if the torsion and exterior angles are known along a discrete curve, the transformation between frames can be viewed as a sequence of rotations using the torsion and exterior angles. Equation 2.11 is used extensively in the PISEMA function simulations and structural calculations. 2.4 Frames and NMR Structure calculation based on solid-state NMR data requires the transformation of different frames. Basically, they are the principal axis frame (PAF), the peptide plane frame (PPF), the helical axis frame (HAF) and the laboratory frame (LF). In the following paragraphs, the definition and transformation between these frames will be described. Only those frames related to the peptide plane nitrogen are discussed. 2.4.1 Standard Peptide Plane Geometry The protein backbone can be viewed as a discrete curve extending in space; backbone atoms are the points on the discrete curve. In section 2.3 we saw that the Euclidean motion along the protein backbone can be expressed in terms of torsion angles and exterior angles. The direction and distance of the motion is dependent upon the peptide backbone geometry. Although considerable motion in the protein or peptide results in different values for bond lengths and bond angles that have been determined by either X-ray crystallography or neutron diffraction, standard average values for them are used in our spectral simulations (Engh and Huber 1991). The bond lengths and the bond angles in the standard peptide plane are illustrated in Figure 2.4. In Figure 2.4, the exterior angles are shown on the right. We will use these parameters of standard peptide plane throughout our PISEMA-based simulations. 30 Figure 2.4. The standard peptide plane geometry. 2.4.2 Principal Axis Frame and Peptide Plane Frame As mentioned in Chapter 1, the chemical shift principal axis frame (PAF) consists of three chemical shift components: δ11, δ22 and δ33. The orientation of PAF is fixed in the molecular frame (Figure 2.5). The peptide plane frame (PPF) can be defined by any two vectors on the peptide plane using the DFF definition. For instance, the PPF at nitrogen can be written in the form of PPF = (NCα, (CN × NCα)× NCα, CN × NCα). Note that those vectors in the frame are all unit vectors. In model systems, the average O O values of αD and βD have been measured as 0 and 105 , respectively (Mai et al. 1993; Teng and Cross 1989). Thus, peptide plane and the δ11δ33 plane are planar; the angle O between δ22 vector and CN × NCα is 0 . Moreover, the polar angles of N-H vector in the PAF are O O O αΝΗ= 0 , βNH = 122 - βD = 17 . Note that PPF can be defined for any atom in the protein backbone. Another common frame is called the molecular frame (MF). This frame is defined at any atom on the molecule including backbone atoms. 31 Figure 2.5. The principal axis frame of amide 15N chemical shift and the peptide plane frame at nitrogen. 2.4.3 Helical Axis Frame and Laboratory Frame The helical axis of an α-helix in the direction from N to C terminus is usually chosen as the z axis for the helical axis frame (Figure 2.6A); the x axis is directing from the helical axis to the Cα atom of the first residue and the y axis is the cross product of z and x. Certainly the x axis can be defined using other backbone heavy atoms. Here, to keep everything consistent Denny’s definition is retained (Denny et al. 2001). The magnetic field vector B0 in the HAF can be written in terms of two polar angles: ρ and τ, also known as the rotation angle and the tilt angle of the α-helix, respectively. Note that in this frame the direction of B0 is not defined as the z axis. If the sample is placed in the magnet with the bilayer normal parallel to the magnetic field, the direction B0 often defines the z axis of laboratory frame (LF) (Figure 2.6B). The xy plane in LF is parallel to the bilayer surface. The x and y axes are defined as needed. LF usually is not very important in the simulations. It only gives you the global idea of how everything is placed in the physical world. 32 Figure 2.6. A) the helical axis frame and B) the laboratory frame. The lipid bilayers with proteins embedded is used to illustrate the sample orientation with respect to the external magnetic field. 2.5 PISEMA Powder Spectrum Simulation PISEMA experiments correlate the 15N anisotropic chemical shift and 15N-1H dipolar coupling. We use π(δ, ν) to denote the PISEMA function. Using the average magnitude for chemical shift tensors and the notation in Figure 1.8, we can write δ as: 2 2 2 δ obs = 31[sin(βB )cos(αB )] + [54 sin(βB )sin(αB )] + 202cos(βB ) . In the PAF, B0 vector and NH can be expressed as: O sin βB cosαB sinβNH cos αNH sin 71 B = sin sin , NH = sin sin = 0 . 0 βB αB βNH αNH O cosβB cosβNH cos 71 Then 2 ν = νII (3(B0 · NH) -1) O O 2 = 10.735 (3(sinβBcosαBsin17 +cosβBcos17 ) -1). Now we can write π(δ, ν) as a function of βB and αB: 33 2 2 2 π(δ, ν) = {31[sin(β B )cos(α B )] + [54 sin(β B )sin(α B )] + 202cos(β B ) , O O 2 10.735 (3(sinβBcosαBsin17 +cosβBcos17 ) -1}. (2.12) PISEMA powder pattern spectrum reflects all possible orientations of B0 in the PAF. Below we apply numerical simulations to study the shape of the PISEMA function versus the B0 polar coordinates: αB and βB. Assuming αB∈[-π, π] and βB∈[0, π], we can plot f(δ, ν, αB) and f(δ, ν, βB). In Figure 2.7a, f(δ, ν, βB) gives a symmetric double O ellipse with a mirror plane when βB is 90 . This is not unexpected because the azimuthal O angles βB and 180 -βB produce the same anisotropic chemical shift and Figure 2.7f O shows that f(δ, βB) is symmetric around the βB = 90 line. For any resonance in the O PISEMA plane (δ, ν), there are two possible βB solutions: βB and 180 -βB. The function f(δ, ν, αB) produces a boat-shape structure (Figure 2.7b). Again, for any resonance in the PISEMA plane (δ, ν), there are at most four possible αB solutions: αB, -αB, 180-αB and - (180-αB). In the case of resonances on the edge of the PISEMA powder pattern, αB appears to only have three solutions: 0, 180 and –180. We plot f(δ, αB, βB) and f(ν, αB, βB) as well in Figure 2.7c and 2.7d, respectively. Both have a similar shape. Obviously, βB has a major impact on NMR observables: it influences the chemical shift and dipolar coupling more dramatically than αB (Song et al. 2000). This observation can be understood by studying equation 2.12. Because sin17o is ~ 0.29 and cos17 o is ~ 0.96, the dipolar coupling is mainly controlled by βB. The chemical shift can be rewritten in the form as 2 2 2 δ = 31[sin(βB )] + [23 sin(β B )sin(α B )] + 202cos(βB ) . Clearly, αB only appears in the second term and the whole function is dominated by βB. The simulations are most readily analyzed by comparing the 2D plots. Figure 2.7e illustrates the typical PISEMA powder spectrum, which is a tilted ellipse. Figure 2.7f is a 15 plot of f(δ, βB). Interestingly, if only the N anisotropic chemical shift is known and is O greater than 100 ppm, βB can be determined relatively accurately within an error of ±5 . 15 Unfortunately, this rule does not hold true for the αB angle (Figure 2.7i). While the N- 1 O H dipolar coupling can also give βB within an error of ±20 (Figure 2.7g), αB is not 34 Figure 2.7. Numerical simulation of PISEMA powder patterns. 3D plots of function a) f(δ, ν, βB), b) f(δ, ν, αB), c) f(δ, αB, βB) and d) f(ν, αB, βB) and 2D plots of function e) f(δ, ν), f) f(δ, βB), g) f(ν, βB), h) f(αB, βB), i) f(δ, αB) and j) f(ν, αB). See text for details. 35 defined by dipolar coupling data alone(Figure 2.7j). Figure 2.7h aims to show that the whole (αB, βB) space is searched. The asymmetry factor η is calculated as: δ − δ = 22 33 . δ11 − δiso Here we choose some figures to compare the effect of η on the simulation (Figure 2.8). Three groups of chemical shift tensors are used: 43 0 0 31 0 0 10 0 0 0 43 0 , 0 54 0 and 0 75 0 . 0 0 202 0 0 202 0 0 202 All of them have the same δ11 and isotropic chemical shift with the asymmetry factors 0, 0.2 and 0.6, respectively. By comparing the shape of simulated spectra, we find that the PISEMA powder pattern changes from an ellipse to a mussel-like shape as η increases. In the case of η= 0, the chemical shift is completely independent of αB (Figure 2.8a) and the chemical shift is sufficient to determine βB. A small increase in η expands the (δ, βB) curve, while βB can still be defined within small errors (Figure 2.8b). A large η makes a large expansion on the low chemical shift side, which in turn contributes to a large error associated with the determination of βB using chemical shift (Figure 2.8c). 2.6 PISA Wheels 2.6.1 Transformation from PAF to HAF For oriented samples, the PISEMA observables are orientational information related to the amide nitrogen chemical shift in the PAF and NH vector interacting with the external magnetic field. It is well known that a peptide plane in an ideal α-helix undergoes a 100O skew rotation along the helical axis to reach the next one. This periodic change of peptide plane orientation leads to an interesting phenomenon in PISEMA spectra: the Polarity Index Slant Angle (PISA) wheel (Denny et al. 2001; Marassi and 36 Figure 2.8. Numerical simulation of the asymmetry factor effect on the PISEMA function f(δ, ν) (on the left) and f(δ, βB) (on the right). 37 Opella 2000;Wang et al. 2000). Before describing the PISA wheel function, we need to analyze the transformation from PAF to HAF. o 15 Since αD is 0 , the transformation of N PAF to DFF can be obtained by two rotational operations (Figure 2.9): PAF = R(z, -44 O)R(x, 90 O) DFF t t = DFF DFF R(z, -44 O) DFF DFF R(x, 90 O) DFF t t = DFF R(DFF z, -44 O)R(DFF x, 90 O) O O = DFF R(e3, -44 )R(e1, 90 ) .0 719 0 − .0 695 = DFF − .0 695 0 − .0 719 . (2.13) 0 1 0 The rotation matrix on the right side of equation 2.13 correlates the transformation between these two frames. This operation also connects the NMR experimental data to the molecular structure. Note that the second rotation angle is O ∠ δ33Nx’ = ∠ CaNH- ∠ δ33NH = ∠ CaNH- (90 - ∠ δ11NH) O O O = ∠ CaNH- [90 –( ∠ CNH-βD)] = 117 –[90 –(122-βD)] O = 149 -βD = 44 O. By the right hand rule, this rotation angle should be negative. Figure 2.9. The transformation from PAF to DFF. The dashed curve in red indicates the rotational transformation for each step. 38 Now we need to find out the relationship between DFF and HAF. Here we use the same definition of the HAF as mentioned in 2.4.3 (Figure 2.6A). There is a convenient way to calculate the rotation axis and the rotation angle if the rotation matrix R is known and the rotation angle is not 180 O. Suppose S = R - Rt. Then S is skew symmetric because of S = -St and it can be written in the form of 0 − c − b S= c 0 − a . (2.14) b a 0 The rotation axis of matrix R is a h = − b . (2.15) c The rotation angle θ can be obtained by solving Tr(R) = 1+2cosθ. (2.16) Figure 2.10 illustrates the DFFs at different backbone atoms. Recalling equation 2.10 that the transformation between two consecutive DFFs can be correlated by the torsion and exterior angles, we know i i DFF(Cα ) = DFF(N ) R1(φ)R3(γ) i i DFF(C ) = DFF(Cα ) R1(ψ)R3(α) i+1 i DFF(N ) = DFF(C ) R1(ω)R3(β) (2.17) so that the transformation from DFF(Ni) to DFF(Ni+1) is DFF(Ni+1) = DFF(Ni) M, where M = R1(φ)R3(γ)R1(ψ)R3(α)R1(ω)R3(β). For a standard peptide plane (Figure 2.4) and an ideal α-helix, we have α= 65 O β = 59 O γ =70 O φ = -65 O ψ= -40 O ω= 180 O. Thus, M can be calculated as: 39 .0 265 .0 752 .0 604 M = .0 346 .0 511 − .0 787 . (2.18) − .0 900 .0 417 − .0 124 Combining the equations from 2.14 to 2.18, we obtain the unit vector of rotation axis hz i in DFF(N ) and the rotation angle θz: .0 612 O hz = .0 764 , θz =100 . (2.19) − .0 306 Figure 2.10. The discrete Frenet frames at the backbone atoms. Three axes in red are drawn to show the frame orientation. The vector v in green is the virtual bond vector of the peptide plane. In order to define the X axis in Figure 2.6A, the coordinates of the virtual bond vector v, i i+1 i i.e. Cα Cα in DFF(N ) can be obtained: i i i i+1 DFF(N ) v = DFF(N ) Cα Cα i i i i i i+1 i i+1 i+1 = DFF(N ) Cα C + DFF(N ) C N + DFF(N )N Cα i i i i i i+1 i+1 i+1 i+1 = DFF(Cα ) Cα C + DFF(C ) C N + DFF(N ) N Cα . (2.19) 40 i i i i+1 i+1 i+1 In a standard peptide plane with | Cα C | = 1.53 Ǻ, | CN | = 1.34 Ǻ and | N Cα | = 1.45 Ǻ, using equation 2.17, we can rewrite equation 2.19 as: 53.1 34.1 45.1 i i i+1 i i i+1 DFF(N ) Cα Cα = DFF(Cα ) 0 + DFF(C ) 0 + DFF(N ) 0 0 0 0 53.1 34.1 i i = DFF(N ) R1(φ)R3(γ) 0 +DFF(N ) R1(φ)R3(γ)R1(ψ)R3(α) 0 + 0 0 45.1 i DFF(N ) R1(φ)R3(γ)R1(ψ)R3(α)R1(ω)R3(β) 0 0 .0 227 i = DFF(N ) .0 761 . − 71.3 Now the X axis of the HAF in the DFF(Ni) can be defined by Charles’ formula (Hestenes 1986): i i DFF(N ) X = DFF(N ) 1/2[cot(θz/2)( hz × v) + v – (hz · v) hz] − .1 464 i = DFF(N ) .0 746 . − .1 579 Then the HAF can be constructed by i HAF = DFF(N ) (-X/|X|, hz × -X/|X|, hz) .0 642 .0 462 .0 612 i = DFF(N ) − .0 327 − .0 556 .0 764 . (2.20) .0 693 − .0 691 − .0 206 Combining with equation 2.13, we have .0 690 .0 719 − .0 090 HAF = PAF .0 693 − .0 691 − .0 206 . (2.21) − .0 211 .0 079 − .0 975 This relationship is used repeatedly throughout PISEMA simulations. We designate T for the transformation matrix 41 .0 690 .0 719 − .0 090 T = .0 693 − .0 691 − .0 206 . (2.22) − .0 211 .0 079 − .0 975 2.6.2 PISA Wheels haf As in Figure 2.6A, B0 coordinates in the HAF is sin(τ)cos(ρ) haf HAF B0 = HAF sin(τ)sin(ρ) , cos(τ) while in the PAF, it can be written as: paf t haf haf B0 = PAF HAF B0 = T B0 . To obtain the PISEMA function π(δ, ν), we can calculate the chemical shift and dipolar coupling in the PAF: δ 33 0 0 δ = B paf ·{ 0 δ 0 ·B paf } 0 22 0 0 0 δ11 = 6.54cos2(ρ) - 6.54cos2(ρ)cos2(τ) -27.75cos(ρ)sin(ρ) +27.75cos(ρ)sin(ρ)cos2(τ) + 63.68sin(τ)cos(ρ)cos(τ) + 43.09 +151.37cos2(τ) -19.90sin(t)sin(ρ)cos(τ) (2.23) haf haf 2 ν = 10.735(3(B0 · NH ) -1)/2 haf t paf 2 =10.735{3[B0 · (T NH )] -1}/2 sin(τ)cos(ρ) sin(1 )7 t f 2 = 10.735{3[ sin(τ)sin(ρ) · (T 0 )] -1}/2 cos(τ) cos( )71 = 16.10[0.286sin(τ)sin(ρ)-0.958cos(τ)]2-5.368. (2.24) At different tilt angles τ, π(δ, ν) functions map wheel-like patterns in PISEMA spectra, which are referred to as PISA wheels (Figure 2.11). Because of the periodicity of α- helical backbone structures (i.e., the constant rotation of peptide plane around the helical 42 axis), the anisotropic chemical shift and dipolar coupling are predictable. Thus, the wheel pattern in PISEMA spectra reflects the helical structure in the protein. Figure 2.11. PISA wheels. The π(δ, ν) function is simulated at various tilt angles with a rotation angle ρ∈ (0, 2π]. Note the center of each wheel representing the tilt angle falls on a line. The simulations of PISA wheels are consistent with those in the literature (Denny et al. 2001; Marassi and Opella 2000; Wang et al. 2000). 2.7 PISEMA Waves The periodicity inherent in α-helical structure results in wave patterns for the dipolar and anisotropic chemical shift data in PISEMA spectra. These result in waves not only for dipolar couplings (so called dipolar waves, (Mesleh et al. 2003; Mesleh and 43 Opella 2003; Mesleh et al. 2002), but also for chemical shifts (Kovacs et al. 2000) and other orientational parameters. Here, we call these waves, “PISEMA waves”. Basically, a PISEMA wave is a function of NMR parameter p and residue number k of α-helix: f(p, k). This function correlates the tilt angle τ and the rotation angle ρ for the α-helix. In this section, we will discuss the change in PISEMA waves for various tilt and rotation angles. In the end, we will present an interesting way to display the PISA wheels (“PISA helix”), which directly reflects the α-helix in the NMR data. 2.7.1 PISEMA Waves For an ideal α-helix, each peptide plane rotates about 100O around the helical axis and migrates 1.5 Å along the axis. In the HAF (Figure 2.6A), the coordinates of the B0 vector in the PPF(k) can be written as sin(τ)cos(ρ − (k − 26)100) haf B0 = sin(τ)sin(ρ − (k − 26)100) . (2.25) cos(τ) Note that 26 is the first residue number and it can be other number in different cases. ρ - haf (k-26)100 describes the right handedness of the α-helix, in other words, the B0 vector rotates clockwise around the helical axis. Substituting ρ in equation 2.23 with ρ -(k- 26)100, we have f(δ, k) = 6.54cos2(ρ-(k-26)100)-6.54cos2(ρ-(k-26)100)cos2(τ) - 27.75cos(ρ-(k-26)100)sin(ρ-(k-26)100) + 27.75cos(ρ-(k-26)100)sin(ρ-(k-26)100)cos2(τ) + 63.68sin(τ)cos(ρ-(k-26)100)cos(τ)+43.09 +151.37cos2(τ) - 19.90sin(τ)sin(ρ-(k-26)100)cos(τ). (2.26) Similarly, we are able to obtain other PISEMA-wave functions such as f(ν, k), f(αB, k), f(βB, k) and f(ξ, k). Note that in the PAF (Figure 2.2 and Figure 1.6), 44 1 0 sin17O paf paf paf cos(αB) = B0 · 0 , cos(βB) = B0 · 0 and cos(ξ) = B0 · 0 . O 0 1 cos17 Figure 2.12 shows the PISEMA waves at different tilt and rotation angles. The results are summarized in Table 2.1. Basically, f(p, k) are trigonometric functions. Clearly, while PISEMA-wave functions are independent upon k in the case of τ = 0O haf t (now B0 is always [0, 0, 1] ), PISEMA-wave functions with other sets of (ρ, τ) give rise to sinusoidal curves. Although the PISEMA waves are sensitive to both the tilt angle and the rotation angle, the tilt angle appears to affect the wave pattern more dramatically than the rotation angle. While the tilt angle could change the amplitude and offset of the curves, it cannot change the phase. The rotation angle does the reverse: it can only change the phase but no other parameters. This is true because of the coordinates of B0 vector (equation 2.25). The tilt and rotational angles of a helix can be obtained by fitting NMR data to PISEMA wave functions, which in turn provides the structural information of the TM topology in the planar lipid bilayers. While the dipolar coupling usually is measured through two-dimensional experiments (e.g. PISEMA) or a series of one-dimensional experiments by varying the CP contact time (Tian and Cross 1997), the anisotropic chemical shift can be obtained by simple one-dimensional cross-polarization experiments. In this respect chemical shift waves appear to be more convenient in the membrane protein structural modeling. To obtain high-resolution protein backbone structure, however, dipolar couplings and even additional anisotropic chemical shift data from other nuclei would be very helpful. We will come back to this issue in Chapter 5 where structure determination using PISEMA data is discussed. 2.7.2 PISA Helix We discuss the PISA wheel in Section 2.6.2 and the PISEMA waves in Section 2.7.1. It would be natural to think of a three-parameter PISEMA function: π(δ, ν, k). Substituting ρ with ρ-(k-26)100 in equation 2.23 and 2.24, we have (δ, ν, k) = {6.54cos2(ρ-(k-26)100) - 6.54cos2(ρ-(k-26)100)cos2(τ) -27.75cos(ρ- 45 (k-26)100)sin(ρ-(k-26)100) +27.75cos(ρ-(k-26)100)sin(ρ-(k- 26)100)cos2(τ) + 63.68sin(τ)cos(ρ-(k-26)100)cos(τ) + 43.09+151.37cos2(τ) -19.90sin(t)sin(ρ-(k-26)100)cos(τ), 16.10[0.286sin(τ)sin(ρ-(k-26)100)-0.958cos(τ)]2-5.368, k}. (2.27) Figure 2.13 illustrates the 3-D plot of function 2.27 with two different tilt angles. They are two right-handed helices! Here we call them PISA helices. The tilt angle τ affects the helical radius as the variation of B0 vector in chemical shift and dipolar coupling PAFs is a function of τ. We also plot the experimental data of M2-TMD with amantadine in Figure 2.13b. Figure 2.13b displays different facets: the projections are the PISA wheels (Figure 2.13c), chemical shift waves (Figure 2.13d) and dipolar waves (Figure 2.14e). Please note that Figure 2.13a is not a ribbon representation of two α- helices in a protein; it is a reflection of the α-helical structure in the NMR data! Table 2.1. The effect of tilt angle and rotation angle on PISEMA wave functions PISEMA- Change of tilt angle (τ) Change of rotation angle (ρ) b wave τ= 0O Phase Offset Amplitude Phase Offset Amplitude function 192.5 f(δ, k) - + + + - - ppm 17.4 f(ν, k) - + + + - - kHz O f(αB, k) - - + + - - 89.7 O f(βB, k) - + - + - - 167.2 a f(ξ, k) - + + + - - 159.2 O a Since sin17O is very close to 0, the change of amplitude is not obvious in the simulation. However, it varies the amplitude with different tilt angles. b The result of NMR parameters with τ = 0O . Those values are independent of rotation angle. 46 Figure 2.12. PISEMA waves. For all the simulations in the left column, the rotation angle is 0o and the tilt angle varies. For those in the right column, the tilt angle is 20o and the rotation angle varies. The angle used for simulation for each sinusoidal curve is labeled with an arrow on the right. 47 Figure 2.13. PISA helices. a) The tube representation of two PISA helices. Two helices with tilt angles of 19o and 28o are shown in the figure. b) The PISA helix fitting with PISEMA experimental data (M2-TMD with amantadine). Plot c-d shows the 2-D projection of b. It can be seen that they are c) PISA wheels, d) chemical shift waves and e) dipolar waves. Pyramids in the Figure 2.13b indicate the experimental data points. 48 CHAPTER 3 HISTIDINES: HEART OF THE PROTON CHANNEL FROM THE INFLEUNZA A VIRUS Selectivity is a fundamental molecular and chemical property of channels (Burykin et al. 2003; Chakrabarti et al. 2004; de Groot et al. 2003; Doyle et al. 1998; Fu et al. 2002; Ilan et al. 2004; Tajkhorshid et al. 2002; Tian and Cross 1999). While much is known about selectivity in the aquaporins and K+ channels, little is known about the molecular origins of selectivity in H+ channels. The first proton channel to be cloned, over-expressed and purified is the M2 protein from Influenza A (Lin and Schroeder 2001; Schroeder et al. 1994; Tian et al. 2003; Tian et al. 2002), which is exquisitely H+ selective (Chizhmakov et al. 1996; Chizhmakov et al. 2003; Lin and Schroeder 2001; Mould et al. 2000a; Pinto et al. 1992; Tang et al. 2002). Recently, a second H+ channel from Influenza B virus has been recognized based on the HXXXW sequential motif in the transmembrane domain (Mould et al. 2003; Paterson et al. 2003). Two broad classes of proteins transport protons (Decoursey 2003), those that couple H+ transfer directly to biological functions (e.g. oxidative phosphorylation (Saraste 1999) and lactose permease (Abramson et al. 2003)), and proton channels, such as the M2 protein (Lamb et al. 1985) that functions solely for the conduction of protons and only indirectly for other biological activities. Both classes of proteins have regulated and selective H+ transport activities. In this chapter, we will discuss the chemical properties of the histidines in the pore of the M2 proton channel over a pH range from 5 to 8.6 by solid-state NMR spectroscopy. In the end, we propose a “histidine-lock” model to depict the closed state of the M2 channel. 49 3.1 The M2 Protein and the Influenza A Virus The M2 protein from influenza A virus has 96 amino acid residues with a single 19-residue transmembrane (TM) helix, a 23-residue extracellular segment and a 54- residue cytoplasmic tail (Figure 3.1a, (Lamb and Choppin 1981; Lamb et al. 1981; Lamb et al. 1985). Chemical cross-linking shows that the M2 protein is minimally a homotetramer and statistical analysis of the ion channel activity also indicates that the minimal active oligomer of the M2 protein is tetrameric (Holsinger and Lamb 1991; Panayotov and Schlesinger 1992; Sugrue and Hay 1991). The tetrameric bundle structure of the M2 protein is stabilized by the formation of disulfide bonds between cysteines in the N-terminal domain (Sugrue and Hay 1991). Post-translational modifications, such as palmitoylation and phosphorylation can occur in the cytoplasmic domain. Current data indicate that post-translational modifications do not significantly affect ion channel activity of M2 protein (Holsinger et al. 1995). The M2 homotetramer serves as a pH-regulated proton channel that plays an important role in the influenza A life cycle. After the influenza virus enters a cell via endocytosis, the M2 proton channel is activated by the low pH of the endosome. The proton flux into the viral interior disrupts the protein-protein interactions between the matrix protein and the ribonucleoprotein complex, a prerequisite for the uncoating process (Figure 3.1, (Chizhmakov et al. 1996). The M2 proteins demonstrate channel activities in a variety of systems including CV-1 cells, Xenopus laevis oocytes, mammalian cells, yeast cells and even lipid bilayers (Chizhmakov et al. 1996; Mould et al. 2000b; Schroeder et al. 1994; Tosteson et al. 1994; Wang et al. 1995b; Wang et al. 1993b). Recently, single-channel proton currents have been detected after the M2 protein is reconstituted into phospholipid bilayers (Vijayvergiya et al. 2004). Among the amino acid residues in the M2 protein, histidine 37 is believed to be one of the critical residues involved in the activation and selectivity of the proton channel (Pinto et al. 1992). This is because (i) the midpoint of the pH activation curve, 5.7, is near the pKa of histidine (Wang et al. 1995b), (ii) His-37 mutants alters the ion channel properties (Pinto et al. 1997; Wang et al. 1995b), and (iii) the ion channel can be inhibited by Cu2+resulting from the coordination of Cu2+ ion by the histidine side chains 50 Figure 3.1. a) The primary sequence of the M2 protein. The yellow bar represents the hydrophobic lipid bilayer where the M2 transmembrane domain is embedded. The helical wheel representation of the TM region is shown on the right and the amantadine-resistant mutants are labeled. b) The life cycle of the influenza A virus. The figure is reprinted from L. H. Pinto’s website with permission. 51 (Gandhi et al. 1999). A very recent report showed that the gating of the M2 proton channel is governed by tryptophan 41 at the C-terminus of the transmembrane domain 2+ (Tang et al. 2002). Besides Cu , the M2 protein proton channel can be blocked by an antiviral drug, amantadine (Chizhmakov et al. 1996; Wang et al. 1993b). The amantadine derivative, rimantadine, is also an anti-flu drug with fewer side effects (Dolin et al. 1982b) Two models have been proposed to explain the channel function: a proton shuttle mechanism and “swinging doors” process (Pinto et al. 1997; Sansom et al. 1997). The first model suggests that histidine residues in the channel function as a proton shuttle that transfers protons from one side of the gate to the other (Figure 3.2A). The alternative hypothesis is that the channel is opened due to the electrostatic repulsion between positively charged histidine imidazole rings (Figure 3.2B). Then protons can pass through the water-filled channel through a Grotthus mechanism. Figure 3.2. Two hypothetical mechanisms for the M2 proton conduction: A) proton shuttle mechanism and B) “Swinging doors” process. 52 3.2 pH Titration of His37 in the M2 TM Domain 3.2.1 Sample Preparation 15Nδ1 histidine and 15Nε2 histidine were purchased from Cambridge Isotope Laboratories (Cambridge, MA) and chemically protected by fluorenylmethoxycarbonyl (Fmoc) group following the literature procedure (Barlos et al. 1982; Chang et al. 1980). 22 The total yield of Fmoc-His-(trt)-OH was 73~81%. M2-TM domain (NH2-Ser -Ser-Asp- Pro-Leu-Val-Val-Ala-Ala30-Ser-Ile-Ile-Gly-Ile-Leu-(15Nδ1 or 15Nε2) His37-Leu-Ile-Leu40- Trp-Ile-Leu-Asp-Arg-Leu46-COOH) was chemically synthesized by solid-phase synthesis on an Applied Biosystems 430A Synthesizer. The peptides were purified and examined as described previously (Kovacs and Cross 1997). 15N His37 labeled M2-TM domain was incorporated into liposomes through the detergent removal technique (Mimms et al. 1981). First M2-TM domain, (1−O-octyl-β- D-glucopyranoside) OG, 1,2-dimyristoyl-sn-3-phosphocholine (DMPC), and 1,2- dimyristoyl-sn-glucero-3-[phospho-rac-(1-glycerol)] (DMPG) were co-dissolved in 20 ml 2,2,2-trifluoroethanol and chloroform (v/v: 4/1). An OG:lipid ratio of 15:1 allows for the preparation of a highly homogeneous sample in vesicles after OG is dialyzed out later in this procedure (Mimms et al. 1981). The organic solvent was evaporated from a rotary flask and then the mixture was placed under high vacuum for at least 6 hours for the further removal of residual organic solvent. 15 ml of 10 mM citrate-borate-phosphate (CBP) buffer of a specific pH with 1 mM ethylenediaminetetraacetic acid (EDTA) was added to the dried mixture and a clear solution was prepared after the flask was vortexed in a shaker for about 20 minutes. This solution was then transferred into a dialysis bag with a 3 kDa molecular weight cutoff and dialyzed at 4 oC against the same buffer. The buffer was changed at least 5 times in 5 days to ensure the extensive removal of the detergent. The M2-TM domain loaded vesicle suspension was pelleted by ultracentrifugation at 196,000 g. The pellet was packed into a 7 mm Bruker zirconia spinner with a sealing cap ready for NMR experiments. 53 3.2.2 Solid-state NMR Experiments All cross polarization (CP)/magic angle spinning (MAS) NMR experiments were conducted on a Bruker DMX-300 NMR spectrometer at 277K. The spinning rate was about 3 kHz. 2 ms cross-polarization contact time and 5 s recycle delay were used throughout the variable-pH NMR experiments. A 100 Hz exponential line broadening was applied to the FIDs before Fourier transform. 15N chemical shift of a saturated 15 15 NH4NO3 was referenced as 0 ppm for all N chemical shifts. 1 H The H spin-lattice relaxation time in the rotating frame (T1ρ ) was measured using a standard pulse sequence described previously (Blasco et al. 1997). In short, after a 90O pulse on the proton channel, the proton magnetization is spin locked for a period of time, τ, before making CP contact with 15N. With a fixed CP contact time, the 15N signals detected while proton decoupling monitor the 1H magnetization in the spin-lock field as a H function of τ, thus allowing one to measure T1ρ indirectly. For variable-contact CP experiments, CP occurs right after the first 90o 1H pulse and the contact time is varied. 15 Assuming that the CP buildup time constant (TNH) of the histidine N in M2-TM domain 15 N is much shorter than the N spin-lattice relaxation time in the rotating frame (T1ρ ), i.e. N H TNH/T1ρ ≈ 0, with the measured T1ρ we fitted the data of the variable-contact-time experiments using the following equation (Kolodziejski and Klinowski 2002): TNH −1 t t M(t) = M0 (1− H ) [exp(− H ) − exp(− )], (3.1) T1ρ T1ρ TNH where t is the variable CP contact time, M(t) is the integrated peak area of each signal and M0 is a constant that is proportional to the sample amount. Thus, the quantitative population ratio of the 15Nδ1 isomer to the 15Nδ1-H isomer was obtained from the ratio of 15 δ1 15 δ1 M0 ( N ) to M0 ( N -H). 3.2.3 Modeling of Multi-step Proton Dissociation of M2-TM Domain Histidines The functional structure of M2-TM domain is tetrameric and all four His37 imidazole rings are crowded into the channel lumen. As the electrostatic repulsion becomes more significant when more of the histidines become protonated, it is 54 reasonable to anticipate that the pKa values of the histidines in the M2 proton channel are correlated to different charge states. Here a biochemically reasonable model is used to explain the pH dependence of histidine proton affinity. The fully charged M2 channel has four dissociable protons, which are lost in discrete steps. Each step has a dissociation constant, namely, K1, K2, K3 and K4 shown in Scheme 3.1. Note that “M2” and “M2 H1- + 4 ” (Scheme 3.1) stand for the tetrameric M2-TM domain bearing different numbers of protons. + K1 + + M2 ⋅ H 4 ←→M2 ⋅ H3 + H + K 2 + + M2 ⋅ H3 ←→M2 ⋅ H2 + H + K3 + + M2 ⋅ H 2 ←→M2 ⋅ H + H K M2 ⋅ H + ←4 → M2 + H+ Scheme 3.1 Thus, each equilibrium constant can be written as: + + [M2⋅ H3 ][H ] K1 = + (3.2) [M2⋅ H 4 ] + + [M2⋅ H 2 ][H ] K 2 = + (3.3) [M2⋅ H3 ] [M2⋅ H + ][H+ ] K 3 = + (3.4) [M2⋅ H 2 ] [M2][H+ ] K = (3.5) 4 [M2⋅ H + ] Here for simplicity we use the concentration of different species instead of activities. Other useful equations (equations 3.6-3.8) shown below can be derived from equations 3.2-3.5: + + 2 [M2⋅ H 2 ][H ] K1K 2 = + (3.6) [M2⋅ H 4 ] [M2⋅ H + ][H+ ]3 K1K 2K 3 = + (3.7) [M2⋅ H 4 ] 55 [M2][H+ ]4 K1K 2K 3K 4 = + (3.8) [M2⋅ H 4 ] 15 + The N CP/MAS spectra cannot differentiate between the various M2 H 1-4 tetramers. However, the concentration ratio of neutral histidine [His] and charged histidine [HisH+] can be obtained from the NMR spectra and expressed as a function of pH from the combination of equations 3.2-3.7. [His] [M2⋅ H + ]+ 2[M2⋅ H + ] + 3[M2⋅ H + ] + 4[M2] = 3 2 + + + + + [HisH ] 4[M2⋅ H 4 ]+ 3[M2⋅ H3 ]+ 2[M2⋅ H 2 ] + [M2⋅ H ] + [M2⋅ H + ] [M2⋅ H + ] [M2⋅ H ] [M2] 3 + 2 2 + 3 + 4 [M2⋅ H + ] [M2⋅ H + ] [M2⋅ H + ] [M2⋅ H + ] = 4 4 4 4 (3.9) + + + [M2⋅ H3 ] [M2⋅ H 2 ] [M2⋅ H ] 4 + 3 + + 2 + + + [M2⋅ H 4 ] [M2⋅ H 4 ] [M2⋅ H 4 ] K1 K1K 2 K1K 2K 3 K1K 2K 3K 4 −pH + 2 −2pH + 3 −3pH + 4 −4pH = 10 10 10 10 K K K K K K 4 + 3 1 + 2 1 2 + 1 2 3 10−pH 10−2pH 10−3pH released The number of protons (Nproton ) released from a four-charged histidine complex is related to the concentration ratio of neutral histidine [His] and charged histidine [HisH+], 4 N released = (3.10) proton [HisH + ] 1+ [His] released Therefore, Nproton as a function of K1, K2, K3, and K4 is released 4 N proton = (3.11) K1 K1K 2 K1K 2K 3 4 + 3 −pH + 2 −2pH + −3pH 1+ 10 10 10 K K K K K K K K K K 1 + 2 1 2 + 3 1 2 3 + 4 1 2 3 4 10−pH 10−2pH 10−3pH 10−4pH accepted Similarly, The number of protons (Nproton ) accepted by a four-neutral histidine complex is accepted 4 N proton = 4 − . (3.12) K1 K1K 2 K1K 2K3 4 + 3 −pH + 2 −2pH + −3pH 1+ 10 10 10 K K K K K K K K K K 1 + 2 1 2 + 3 1 2 3 + 4 1 2 3 4 10−pH 10−2pH 10−3pH 10−4pH 56 The proton dissociation constants K1, K2, K3, and K4 were obtained by fitting the curve of Nproton versus pH using Origin 5.0 software (Microcal Software, Inc., Northampton, MA). 3.2.4 CP Kinetics of His37 15Nδ1 The magnetization transfer from abundant spins to dilute spins (in the present case, 1Hs and 15Ns) by cross polarization is based on heteronuclear dipolar interactions. Thus, dynamics and internuclear distances between the coupled nuclei, which dictate the dipolar interactions, affect the efficiency of CP. This efficiency is mainly governed by two processes: the CP buildup time, in our case, TNH and the proton rotating frame spin- lattice relaxation time, T1ρ. Even within a very short CP contact time, such as 100 µs, the 15Nδ1-H signal (147 ppm in Figure 3.3B) can be detected as the proton is covalently bonded to the nitrogen, whereas the CP buildup time for the non-protonated 15Nδ1 site is much longer. With a CP contact time of approximately 1 ms the 15Nδ1-H signal intensity reaches its maximum, while at longer CP contact times lower intensities are observed because of proton T1ρ relaxation. Proton T1ρ describes the magnitude of the proton magnetization in the rotating frame that is available for CP. For the protonated site it is clear from Figure 3.3A that the 15N signals decrease as the spin-lock time prior to cross polarization increases above 1 ms. 15 δ1 Proton T1ρ values of His37 protonated and nonprotonated N species are quantitated by fitting the signal intensities I as a function of spin-lock time before CP τ (Figure 3.3A) with τ I = I 0exp(− ) , T1ρ H where I0 is a constant. A single exponential fitting yields a T1ρ value of approximately 5 H ms for both protonated and nonprotonated sites (Table 3.1). Using the measured T1ρ value and the spectral intensities M(t) as a function of CP time, both M0 and TNH are determined with equation 3.1 and the results are summarized in Table 3.1. Although the H protonated and non-protonated states have very similar T1ρ , their TNH values differ by almost a factor of 70. While the signal height for the isotropic resonances of the non- protonated and protonated sites are similar, the combination of spinning side bands for 57 the non-protonated sites and their suppression in spectra obtained with a 2 ms CP contact time result in a factor of 3.5 greater value for M0 than for the protonated neutral His37 resonances. H 15 δ1 Figure 3.3. T1ρ measurement and various-contact-time experiments of N His37 H 15 M2-TM domain in DMPC/DMPG liposomes at pH 8.8. A) T1ρ measurement N CP/MAS NMR spectra at 277K. The samples were packed in a 7 mm MAS rotor and spun approximately 3 kHz using a 2 ms CP contact time. B) 15N CP/MAS NMR spectra as a function of various contact times. The sample condition was the same as for A. Asterisks indicate the spinning side bands. 58 Figure 3.4. The cross-polarization kinetics of 15Nδ1 His37 M2-TM domain in H 15 δ1 DMPC/DMPG liposomes at pH 8.8. A) T1ρ measurement of non-protonated N at 230 ppm and the protonated 15Nδ1–H at 147 ppm (Figure 3.3A) and B) fitting curves of 15N CP/MAS data extracted from various-contact-time experiments (Figure 3.3B). The filled and open squares represent the signal intensities of non-protonated 15Nδ1 and the protonated 15Nδ1–H, respectively. H Table 3.1. T1ρ and Variable-Contact-Time NMR Data of M2-TM domain Containing 15Nδ1 Labeled Histidine in DMPC/DMPG Liposomes at pH 8.8. Peak Position Peak Relative a a T1ρ (ms) TNH (µs) M0 (ppm) Assignment Amountb 230 ≥ N (His37) 5.2 ± 1.6 11443 ± 417 286 ±9 3.5 147 >N-H (His37) 5.1 ± 0.9 172 ± 25 81 ± 3 1 98 N.A. –CONH- 4.0 ± 1.0 218 ± 44 26 ± 1 0.3c a The errors are obtained from the curve fitting. b The relative amount is calculated from the ratio of M0 between different species. c Note that for this 25-residue M2-TM domain with His37 15Nδ1 98% enriched, the natural abundance signal would be approximately 0.4 based on 0.366% for 15N natural abundance. This accordance further validates the rationale that we use here to quantify CP. To determine the pKa of the histidine residues in the M2-TMD samples from the histidine data it is necessary to determine the intensities of the various protonated and 59 non-protonated resonances. To deconvolute these overlapping resonances, three parameters must be defined: peak position (υ), peak amplitude (A) and half-height linewidth (w). We fixed the chemical shift positions, as given previously, for they do not vary much with pH and set A and w as variables listed in Table 3.2. Note that the range for w was kept constant through the pH series for a given resonance. For any simulated spectrum, a difference spectrum was calculated with the observed data and judged by a standard deviation of the noise level from the real spectrum. Only those difference spectra with the standard deviation lower than 1.5 times the noise standard deviation were selected. Peak component integrals were adjusted based on CP efficiency and side band intensities so that the ratio of uncharged ([His]) to charged ([HisH+]) could be calculated. The error was calculated based on those solutions that satisfied the criteria. Typically, about 200 acceptable results were obtained from 4096 possible peak combinations. Figure 3.5 exhibits two examples of the spectral deconvolution. The quantification of [His]/[HisH+] directly derives from the integration of each peak component. Figure 3.5. Deconvolution of 15N CP/MAS NMR spectra at A) pH 6.5 and B) pH 7.0. Only one deconvolution of all the possible results is shown below the experimental NMR spectrum in blue lines. All the acceptable difference spectra of the simulated and experimental spectra are given below the experimental spectra. 60 3.2.5 15N CP/MAS NMR Titration of His37 A single histidine side chain can adopt one of three chemical states, a charged and two tautomeric neutral states, which can be distinguished by 15N isotropic chemical shifts. The δ1 and ε2 15N sites, protonated resonances occur in the vicinity of 150 ppm, while non-protonated resonances are near 230 ppm (Huang et al. 1984; Munowitz et al. 1982; Wei et al. 1999). Isotropic solid state NMR spectra of single site 15Nδ1 and 15Nε2 His37 labeled M2 TM domain in gel state liposomes are shown in Figure 3.6 as a function of pH. Observations above the phase transition temperature (data not shown) show qualitatively the same results, but the linewidths are substantially broader and sensitivity is lower. The 230 ppm resonance is a definitive marker for the neutral states, which may be protonated at either δ1 (tautomer II, 147 ppm) or ε2 (tautomer I, 144 ppm). When the histidine is charged, both 15N sites are protonated generating resonances at 156 ppm for 15Nδ1 and 153 ppm for 15Nε2. In addition, two unusal signals from a protonated state (167 ppm for 15Nδ1 and 162 ppm for 15Nε2) are observed with linewidths nearly double that of the other protonated resonances. The shift of the protonated resonance frequency towards the non-protonated frequency suggests a lengthening of the N-H covalent bond resulting from a strong hydrogen bond between imidazole rings (Smith et al. 1989; Song and McDermott 2001). Indeed, such a strong hydrogen bond is observed in co-crystals of imidazole and imidazolium (Krause et al. 1991), which has been computationally analyzed (Tatara et al. 2003), and characterized by solid state NMR (Song and McDermott 2001). 61 Table 3.2 Deconvolution parameters and pH versus Nproton and 4 - Nproton used in the fitting of equations 3.11 and 3.12. 147 ppm 156 ppm 167 ppm 230 ppm pH w w w w 4 - Nproton N proton Aa Aa Aa Aa (ppm) (ppm) (ppm) (ppm) 8, 10, 0.2, 0.4, 8, 10, 3.2, 3.4, 12, 14, 0.2, 0.4, 5.0 \ \ 3.17±0.21 0.83±0.21 12, 14 0.6, 0.8 12, 14 3.6, 3.8 16, 18 0.6, 0.8 8, 10, 0.5, 0.7, 8, 10, 2.6, 2.8, 12, 14, 0.5, 0.7, 6.0 \ \ 2.86±0.16 1.14± 0.16 12, 14 0.9, 1.1 12, 14 3.0, 3.2 16, 18 0.9, 1.1 8, 10, 2.2, 2.4, 8, 10, 3.3, 3.5, 12, 14, 0.9, 1.1, 6.5 \ \ 2.23±0.20 1.77± 0.20 12, 14 2.6, 2.8 12, 14 3.7, 3.9 16, 18 1.3, 1.5 8, 10, 2.0, 2.2, 8, 10, 3.0, 3.2, 12, 14, 1.6, 1.8, 7.0 \ \ 2.13±0.15 1.87± 0.15 12, 14 2.4, 2.6 12, 14 3.4, 3.6 16, 18 2.0, 2.2 8, 10, 2.8, 3.0, 8, 10, 2.8, 3.0, 12, 14, 1.8, 2.0, 8, 10, 1.6, 1.8, 8.0 1.37±0.10 2.72± 0.14 12, 14 3.2,3.4 12, 14 3.2,3.4 16, 18 2.2, 2.4 12, 14 2.2, 2.4 8, 10, 3.4, 3.6, 8, 10, 3.8, 4.0, 8.5 \\\\ 0.62±0.07 3.27±0.13 12, 14 3.8, 4.0 12, 14 4.2, 4.4 a Relative amplititudes for a specific spectrum. Intensities between spectra are not comparable. b Errors are calculated from the standard deviation of all possible results satisfying the criteria (see in text). 62 A 3.5:1 molar ratio of the neutral tautomers (I:II, respectively) was calculated from the high pH Nδ1 protonated vs. nonprotonated fractional resonance intensities (Table 3.1). Similarly, in aqueous solution histidine also favors tautomer I by the same ratio (Reynolds et al. 1973). The low tautomer II fraction, large anisotropy and poor cross polarization kinetics explains the missing non-protonated 15Nε2 signal in the high pH spectra of Figure 3.5B. The signals at 167 and 162 ppm from the 15Nδ1 and 15Nε2 sites, implicating the formation of strong hydrogen bonds between uncharged and charged imidazole rings, dominate the middle of the titration (Figure 3.7A) along with the other resonances associated with these histidine dimers. Because signals for both protonated Nδ1 and Nε2 sites involved in strong hydrogen bonds are observed, these bonds are likely to be formed by a bridge between Nδ1 and Nε2 sites (Figure 3.6C) as opposed to a bridge by two Nδ1 or two Nε2 sites. This is because at pH 7.0 where dimers dominate, the existence of Nδ1–H--Nδ1 or Nε2–H--Nε2 dimers is not consistent with the observation of 15Nδ1 signals at 156 ppm and 15Nε2 signals at 153 ppm. The population distribution between the two Nδ1-H-Nε2 dimers is nearly equal, thereby optimizing charge delocalization. The resonances for the nonprotonated sites in these dimers are not observed, reflecting the issues described previously and the anticipated broad linewidths based on the observed linewidths of the protonated partner resonances across the bridging hydrogen bond. The four imidazoles in the M2 channel are clustered closely together so they cannot be considered as independently titrating groups. Four equivalent sites can accept the first proton, resulting in two imidazole rings forming a dimer bridged by a strong hydrogen bond. In Figure 3.7A this is apparent, since the 156 ppm resonance (charged state) and the 167 ppm resonance (dimer state) increase simultaneously with decreasing pH. The second proton is likely to bind a position as far removed from the first as possible to minimize charge separation. Again a dimer is formed and at pH 7.1 more than 90% of the His37 sidechains are in dimeric form. At lower pH a third proton binds leaving a single neutral imidazole at one of four equivalent sites. For this third proton to be absorbed by the histidine cluster, a dimer must be disrupted, resulting in a potentially metastable state with charges in side by side imidazoles, less charge delocalization, and broken two fold symmetry. 63 Figure 3.6. 15N CPMAS NMR spectra of the M2 transmembrane domain in fully hydrated DMPC/DMPG (4:1 molar ratio) liposomes at 4°C as a function of pH. A) 15Nδ1 His37 labeled. B) 15Nε2 His37 labeled. Spectra were obtained on a Bruker DMX-300 15 NMR spectrometer at 277K. Chemical shifts are relative to NH4NO3 at 0 ppm. The weak signal around 98 ppm is due to natural abundance signals from the protein backbone. The spinning side bands are marked with an asterisk. C) Chemical states of the histidines in the M2 TM domain and associated 15N resonance frequencies. The intensities shown in Figure 3.7A can be converted to a relative distribution of charged and uncharged histidine side chains as shown in Figure 3.7B, illustrating a far more complex titration than previously suggested by UV Resonance Raman spectroscopy (Okada et al. 2001). While it is not possible to identify site specific pKas because of degeneracies in placing charges, it is still convenient to think of pKa’s associated with each protonation. In Fig. 3.7X the titration curve is shown with error bars from the deconvolution analysis. This curve is consistent with pKas: 8.2 ± 0.2, 8.2 ± 0.2, 6.3 ±0.3, and < 5.0. While three of the pKa values are well defined, the fourth is not, due to the lack of data at low pH where the tetrameric structure is less stable (Salom et al. 2000). The two high pKas conclusively demonstrates that the M2 proton channel has a very high 64 affinity for the first two protons. Despite the low dielectric, in the transmembrane environment a [H+] nearly two orders of magnitude lower than that necessary to protonate histidine in bulk aqueous solution is adequate for protonating two of these imidazoles in close proximity. The first two charges in the tetrameric structure are expected to form a repulsive interaction even though there is substantial charge delocalization, because their separation is shown to be less than 10 Å (Nishimura et al. 2002) and the dielectric constant in the histidine environs is certainly less than that in a bulk aqueous environment. For the second proton to bind with nearly the same affinity as the first, the repulsive interaction must be countered with a substantially favorable interaction. The formation of a strong hydrogen bonded imidazole dimer breaks the four-fold symmetry and results in a substantial structural distortion. Potentially, considerable stabilization energy is generated when two-fold symmetry is restored through the formation of a second imidazole dimer, suggesting the possibility of cooperative H+ binding. 3.2.6 Proton Conduction in the M2 Channel The M2 channel appears to be closed above pH 7 (Chizhmakov et al. 1996; Chizhmakov et al. 2003; Pinto et al. 1992), although insufficient electrophysiological data is available in alkaline pH environments. Now it is apparent that the closed state near pH 7 is represented by histidine dimers each sharing a charge forming a ‘histidine lock’ that occludes the pore. However, it has long been suspected that a titratable histidine is responsible for the acid gating of the channel (Pinto et al. 1992; Wang et al. 1995b). Apparently, this gating is associated with the third histidine titration. Disrupting one of the dimer structures appears to result in a high energy metastable state in which the system is willing to give up a H+ and return to the paired dimer state. This hypothesis (Figure 3.8) is supported by the fact that the second and third pKas are separated by nearly two pH units, suggesting how difficult it is to disrupt the stable ‘histidine lock’ conformation. 65 Figure 3.7. Analysis of the pH titration data for the His37 labeled M2 TM domain following corrections for cross polarization kinetics and following spectral deconvolution. Cross polarization kinetics were obtained for these samples of M2 TM domain in hydrated lipid bilayers and the deconvolution analysis utilized a fixed set of resonance frequencies and variable linewidths and heights. A) 15Nδ1 resonance intensities as a function of pH. B) Mole fractions were summed to present an overview of the charged [HisH+] vs. uncharged [His] imidazole rings. Error bars were calculated from the deconvolution analysis. C) A titration curve is generated from equations 3.11 and 3.12 that derives protonation and deprotonation curves for the four histidines from the [His]/[HisH+] results. 66 Selectivity for H+ may be achieved by either of two mechanisms using this histidine cluster. It is possible that the binding of a third proton simply breaks the ‘histidine lock’ allowing Grotthüs conductance through a water mediated proton wire (Okada et al. 2001; Smondyrev and Voth 2002). Grotthüs conductance only works for protons, but in addition, the substantial charge density associated with three charged histidines will repel cations such as Na+ and K+. Such charge density is not observed in the KcsA K+ selectivity filter (Doyle et al. 1998). Alternatively, the selectivity could be provided by a shuttle mechanism involving the protonation and deprotonation of a histidine sidechain through a relatively small rotational motion of the sidechain (Lear 2003; Pinto et al. 1997). This mechanism is also specific for protons, but it is not yet clear that the observed rate of proton conductance can be achieved by such a mechanism (Lear 2003). So while the ion selectivity mechanism is not yet clearly defined, H+ selectivity can be rationalized and the acid activation is apparently due to the protonation of the third histidine. Figure 3.8. A model illustrating the opening of the M2 proton channel. The region of the four-histidine complex is presented as a blue cylinder. Neutral and positively charged histidine residues are differentiated in green and yellow, respectively. Protons are shown as red spheres. The open state is illustrated as a small pink cylinder in the blue one. Dashed lines in histidine dimers represent the hydrogen bonds. 67 CHAPTER 4 AMANTADINE AND THE M2 PROTON CHANNEL FROM THE INFLUENZA A VIRUS 4.1 The Antiviral Drug Amantadine Although the anti-influenza virus activity of amantadine (1-adamantanamine hydrochloride) was discovered about 40 years ago (Davies et al. 1964) and its inhibition of the M2 proton channel from the influenza A virus has been demonstrated (Pinto et al. 1992), the mechanism of how it interacts with the M2 protein is still controversial. Conventionally, amantadine is regarded as a channel “blocker”. Alternatively, it may act as an allosteric inhibitor by which the binding of amantadine outside the pore region changes the conformation of the channel from the open state to closed state (Pinto and Lamb 1995; Wang et al. 1993a). The amantadine inhibition of the influenza A virus replication is strongly coupled to the proton channel function of M2 protein. At an early stage of the virus life cycle, the blockage of proton flux through the M2 channel prevents the M1 proteins from dissociating from the ribonucleoproteins (Kato and Eggers 1969; Skehel et al. 1978). Also, it has been reported that in the presence of amantadine the hemagglutinin adopts an acid-induced conformation in the trans Golgi network (where the intralumenal pH is low) due to the dysfunction of the M2 proton channel (Ciampor et al. 1992a; Ciampor et al. 1992b; Grambas and Hay 1992). Although amantadine is effective in the prophylaxis and treatment of the influenza A virus infections, its clinical use as an anti-influenza drug is limited due to its central nervous system side effects and its specific activity against influenza A virus (Skehel 1992). The structural analog of amantadine, rimantadine (α-methyl-1-adamantanemethanamine), has been considered as 68 a better anti-viral drug based on its strong activity and fewer side effects (Dolin et al. 1982a; Tsunoda et al. 1965). In addition to its anti-influenza viral activity, amantadine and its derivatives have been studied as possible drugs against the human immunodeficiency virus-1 (HIV-1) and Parkinson’s disease (Grelak et al. 1970; Kolocouris et al. 1996b; Tribl et al. 2001) (Scheme 4.1). Scheme 4.1 How amantadine inhibits the M2 proton channel is still an open question: Does it really block the channel? Does it affect the homotetramer structure and how? How does this molecule interact with the protein? Where is it in the channel? Is it charged or neutral in the channel? Most evidence favors the blocking mechanism. The channel in the model structure of the M2 TM domain seems to accommodate the drug molecule (Nishimura et al. 2002). All the amantadine-resistant M2 species mutate their hydrophobic channel- lining residues to longer polar residues indicating that the adamantyl group may interact with the channel residues via van der Waals interactions (Hay et al. 1985). Using neutron diffraction, Duff et al. suggested that amantadine binds in the pore region between Val27 and Ser31 (Duff et al. 1994). In a micellar phase, amantadine increases the tetramerization of M2-TM domain (Salom et al. 2000). It has been shown that M2-TM domain also forms amantadine-sensitive proton channels in model lipid bilayers (Duff and Ashley 1992). Since the extra-membrane domain of the M2 protein is truncated, the most possible allosteric binding sites would be at the interface between the M2-TM domain and the lipid bilayer. However, if this were true, it would be hard to understand why only one, not four or more (because the channel is symmetric or at least pseudo- symmetric, see Chapter 5), amantadine molecules bind the channel . 69 4.2 Amantadine and His37 The structure of M2 TM domain in lipid bilayers solved by solid-state NMR has a pore in the tetramer that can accommodate an amantadine molecule (Nishimura et al. 2002). It was thought that the adamantyl group interacts with Val24 and Ala27 via van der Waals interactions, while the charged amine group hydrogen bonds with Ser31 (Hay 1992; Sansom and Kerr 1993). Pinto and co-workers proposed another model: that amantadine binds deeper in the channel and its ammonium group hydrogen bonds with the His37 side chains (Gandhi et al. 1999). As we discuss in Chapter 4, His37 in the M2 protein is a critical residue involved in the proton selectivity and the functional gating of the proton channel (Wang et al. 1995a). On amantadine binding, there are a few questions regarding the histdine residue: 1) does the amino group of amantadine hydrogen bond with the histidine imidazole? 2) does it affect the pKa of histidine? and 3) what about the dynamics of the histidine side chain? With those questions, we have applied solid-state NMR spectroscopy to explore the amantadine binding effect on the M2-TMD His37. 4.2.1 Sample Preparation 15Nδ1 (or 15Nε2) labeled His37 M2-TMD was synthesized and incorporated into DMPC/DMPG liposomes as described in Chapter 3. For an M2-TMD sample with 10 mM amantadine, 46.9 mg amantadine (250 µmol) hydrochloride (Fisher Scientific, GA) in 5 ml CBP buffer was added to an M2-TMD loaded vesicle suspension (20 ml). The suspension was incubated at room temperature overnight and pelleted by ultracentrifugation (196,000 g). The M2-TMD in DMPC/DMPG liposomes with or without amantadine was packed into a 7 mm Bruker zirconia spinner with a sealing cap ready for magic angle spinning (MAS) NMR experiments. Oriented samples of the peptide in hydrated DMPC bilayers were prepared by first co-dissolving M2-TMD (~ 20 mg) and DMPC (~ 75mg) in 10 ml TFE. TFE was removed by rotary evaporation and dried further under high vacuum. A warm 15ml 2 70 mM CBP buffer (~ 37 OC, pH 8.8) with 1 mM EDTA was added to the dried mixture and vortexed in a shaker at 37 oC. This lipid suspension was bath sonicated for 10 minutes intermittently. A water bath was pre-warmed to 37 oC, which is higher than the gel to liquid crystalline phase transition temperature of DMPC (~ 23 OC) (Koynova and Caffrey 1998). The sonicated suspension was loaded into a 1 kDa MW cutoff dialysis bag. The dialysis bag was placed in a 1L 2mM CBP buffer overnight to equilibrate the pH between the M2-TMD/DMPC liposomes and the outside buffer. For the samples with amantadine, the outside buffer contained 10 mM amantadine. The liposomes were passed through a 2µm filter and pelleted by ultracentrifugation at 196, 000 g. The pellet was agitated at 37 oC for 1 hour until fluid. This thick fluid was spread onto 50 glass slides (5.7 mm × 12.0 mm) (Marienfeld Glassware, Bad Margentheim, Germany) and dried in a 70-75 % humidity chamber. The dried slides were rehydrated with 1.5µl 2mM CBP buffer followed by being stacked into a glass tube. The sample was incubated at 43 oC for 24 hours in 96 % humidity (saturated K2SO4) chamber. In the end, the glass tube was sealed at both ends with epoxy and two glass chips. 4.2.2 Solid-state NMR Experiments All the CP/MAS NMR experiments were conducted as in Chapter 3. Static 31P NMR experiments were also performed on the Bruker DMX-300 NMR spectrometer using a home-built 31P/1H double resonance probe. PISEMA experiments were performed on a 400 MHz spectrometer using a home-built 15N/1H probe. Typically, a 6s delay was applied before the 1H 90o pulse (~ 6 µs). 15N signals were built up using an 800 µs CP 15 15 contact period. N chemical shift of a saturated NH4NO3 was referenced as 0 ppm for all 15N chemical shifts. 4.2.3 Sharp Signals with Amantadine We began our study with 15N CP/MAS experiments of His37 (15Nδ1 and 15Nε2) M2-TM domain in DMPC/DMPG (4:1 molar ratio) with and without amantadine at different pH values (Figure 4.1). At high pH (8.8) without amantadine, the linewidths in the NMR spectrum are approximately twice those in the presence of amantadine. 71 Amantadine does not appear to alter the histidine 15N chemical shift frequencies. Even at pH 5.0, the signal at 230 ppm can be seen. Similar to the assignment of amantadine-free His37 signals, the 15Nδ1 resonances at 230 and 147 ppm come from tautomer I and tautomer II of neutral histidines, respectively (Figure 3.5C). Likewise, charged histidines contribute to 15Nδ1 signals at 156 ppm. Based on the amantadine binding data at different pH values, Wang et al. suggested that amantadine might favor the closed channel more than the activated channel (Wang et al. 1993b). As we discussed the M2 channel gating mechanism in Chapter 3, the closed state is not a single state, but has different states corresponding to different pH values. Since it was previously thought that in the closed M2 channel all histidines must be neutral, the term “the closed state” used in Wang’s article may stand for the four-neutral-histidine state. In this sense, our data at pH 6.5 are consistent with their hypothesis. However, we must keep in mind that the closed state is an obscure concept to describe an M2 channel state. The existence of neutral histidine signals at low pH values indicates that amantadine shifts the histidine pKa toward lower values. Before quantitative charactrerization of each frequency, as mentioned in Chapter 3, we need to correct for the scaling of the non-protonated 15Nδ1 signal at 230 ppm due to low CP efficiency, and we need to include the spinning sideband intensity. 4.2.4 Slow His37 Dynamics with Amantadine In Chapter 3, we measured the T1ρ for each signal and applied the measured T1ρ values in equation 3.1 to obtain the real ratio between non-protonated and protonated species. The measurement and the variable-contact-time experiments are shown in Figure 4.2. Figure 4.3 illustrates the fitting curves of the spectral intensities in Figure 4.2 and the CP kinetic parameters are summarized in Table 4.1. 15 δ1 Table 4.1 T1ρ and Variable-Contact-Time NMR Data of M2-TMD Containing N Labeled Histidine in DMPC/DMPG Liposomes with 10 mM Amantadine at pH 8.0 Peak Position Peak Relative a a T1ρ (ms) TNH (µs) M0 (ppm) Assignment Amountb 230 ≥ N (His37) 4.2 ± 0.9 6900 ± 600 9.9 ± 0.3 3.3 147 >N-H (His37) 4.8 ± 1.6 65 ± 30 2.97 ± 0.3 1 72 Figure 4.1. 15N CP/MAS NMR spectra of His37 (15Nδ1 and 15Nε2) M2-TM domain in DMPC/DMPG (4:1 molar ratio) with and without amantadine at different pH values. Note that the spectrum at the bottom is from His37 15Nε2 labeled sample. The samples were packed in a 7 mm rotor. Spectra were obtained on a Bruker DMX-300 NMR spectrometer at 277K with a spinning rate of 3 kHz. The spinning side bands are marked with asterisks. 100 Hz line broadening is applied to all spectra. 73 15 15 δ1 Figure 4.2 A) T1ρ measurement N CP/MAS NMR spectra of N His37 M2-TMD with 10 mM amantadine in DMPC/DMPG liposomes at pH 8.8 and 277K. A 4 mm spinning rotor is used in this case. The sample spinning rate was about 6 kHz using 2 ms CP contact times. B) 15N CP/MAS NMR spectra as a function of various contact time. The sample condition was the same as A. H 15 δ1 Figure 4.3. A) T1ρ measurement of non-protonated N at 230 ppm and the protonated 15Nδ1–H at 147 ppm with 10 mM amantadine (Figure 4.2A) and B) fitting curves of 15N CP/MAS data extracted from various-contact-time experiments (Figure 4.2B). The filled squares and open triangles represent the signal intensities of protonated 15Nδ1–H and the non-protonated 15Nδ1 sites, respectively. 74 From the data in Table 4.1 the presence of amantadine tautomer I (Figure 3.5C) is approximately three times more favorable than tautomer II. Consequently, amantadine does not significantly change the tautomer distribution. The presence of two histidine tautomers and the similar population of those tautomers as for free histidine indicate that those neutral histidines in the channel may not be involved in a hydrogen bond network that affects this population, as the catalytic triad in the serine proteases, where tautomer II is significantly favored (Hunkapiller et al. 1973). The reverse of the dilute spin signal buildup time, 1/TIS, is more often called the cross-polarization rate constant, which is predominantly controlled by the IS dipolar coupling. Roughly, the CP rate is proportional to the square of the dipolar coupling between I and S (Demco et al. 1975; Ernst et al. 1987). This explains why the signal buildup for the protonated 15N is about two orders of magnitude faster than the non- protonated one. Theoretical correlation between 1/TIS and molecular motion is complicated and associated with many assumptions and approximations (Cheung and Yaris 1980; Demco et al. 1975; Fulber et al. 1996). For a covalently bonded 15N-1H moiety in the imidazole ring, the signal buildup would be much more efficient than that for non-protonated 15N. On the other hand, the internal group motion can weaken the dipolar interaction dramatically. It is generally established that rigid groups or domains in the solid-state NMR sample cross-polarizes more rapidly than mobile ones (Alemany et al. 1983; Cory and Ritchey 1989). Both T1ρ and TNH are dependent upon molecular motion. Spin-lattice relaxation times in the rotating frame are sensitive to the molecular motions that occur in the micro- to millisecond timescale. Within the error of our measurements, T1ρ values of the two tautomers do not change significantly upon binding amantadine. However, these two T1ρ values should not be compared directly because they were measured at different rf fields. On the other hand, as discussed above, TNH can provide a qualitative description of the motional change upon amantadine binding. Here we assume that the spinning rate does not affect the TNH values (Alemany et al. 1983) and the Hartmann-Hahn condition was perfectly matched. With amantadine TNH is about half that without amantadine. In other words, the 15N signal grows approximately twice fast in the presence of amantadine, 75 suggesting the motion of the amantadine-bound histidines in the M2-TM domain is more constrained than the amantadine-free one, i.e. without amantadine, histidine side chains are more mobile. The narrow linewidth of the 15N signal in the presence of amantadine reinforces this perspective. The amantadine binding effect is even clearer in the PISEMA spectra of 15N leucine labeled M2-TMD in DMPC bilayers: the presence of amantadine tremendously improves the resolution of PISEMA spectrum (Figure 4.4). Figure 4.4. Comparison of PISEMA spectrum 515N leucine labeled M2-TM domain in the DMPC lipid bilayers A) in the absence of amantadine and B) in the presence of amantadine. Both of these two spectra were taken on a 400 MHz spectrometer. 76 4.2.5 Low Proton Affinity of His37 with Amantadine In the electrophysiological experiments, 100 µM amantadine is sufficient to block channel conductance of the intact M2 proton channel in oocytes at pH 5.8 (Mould et al. 2000a; Mould et al. 2000b; Wang et al. 1993b). The amantadine inhibition of the M2 channel is slowly reversible with an apparent binding constant of 0.3 µM (Wang et al. = [1993b). Therefore, 10 mM amantadine in the buffer results in [M2٠amantadine]/[M2 3× 104. Although M2-TM domain may have a lower binding constant of amantadine than the intact protein, it is arguable that such a high concentration of amantadine can ensure the dominant amantadine-bound state in our NMR samples. Moreover, the uniform narrow linewidth of the amantadine bound state confirms that these samples are uniformly bound with the drug. Surprisingly, the 167 ppm resonance, which reflects the formation of His-HisH+ dimer in the amantadine-free channel (Chapter 3), is absent in the CP/MAS NMR spectra of His37 with amantadine (Figure 4.1). This also confirms that with 10 mM amantadine there are no detectable amantadine-free His37 signals in the NMR spectra. After correcting the CP efficiency and taking the spinning side bands into account, as well, we summarize the [His]/[HisH+] with and without amantadine in Table 4.2. Since there is no formation of His-HisH+ dimers in the presence of amantadine, the characterization of His37 is based on a simple acid-base reaction as Ka HisH+ ⇔ His + H+ . Therefore, starting from the all-charged-histidine state, the number of protons released released from the M2-TM tetramer at a given pH, Nproton , can be calculated as 4 4 N released = = (4.1) proton [HisH+ ] 10−pH 1+ 1+ [His] Ka By fitting Equation 4.1, we obtain that the pKa of His37 in the presence of amantadine is 5.4 ± 0.2. This result suggests that the amantadine binding lowers the proton affinity of His37 by approximately three orders of magnitude! This binding effect is apparent in Figure 4.5, which compares the histidine titration curves in the presence and absence of amantadine. 77 Histidine lock, as we discussed in Chapter 3, is composed of two His-HisH+ dimers. These dimers substantially distribute two positive charges and stabilize them in the channel where the dielectric constant is low. In Figure 4.4, although the resolution of PISEMA spectrum without amantadine is low, resonance shifts indicating a structural alteration due to amantadine binding is apparent (for further discussion see Chapter 5). It seems that the M2-TM domain adopts a structure that favors amantadine binding but disrupts the formation of histidine dimers. Without the sharing of two charges by two histidine imidazole rings, the charged state of histidine in the M2-TM domain becomes less stable and the proton affinity of histidine drops dramatically. In this regard, the NMR data with amantadine reaffirm the functional importance of histidine lock. released Figure 4.5. Fitting of Nproton versus pH in the presence (dashed line) and absence released (solid line) of 10 mM amantadine. Nproton stands for the number of released protons released from the M2 transmembrane domain at a given pH value (see text). The Nproton versus pH data in the presence of 10 mM amantadine come from Table 4.2 and were fitted by Equation 4.1 with pKa of 5.4, while the fitting curve and those data without amantadine were duplicated from Chapter 3 for the purpose of comparison. 78 + released Table 4.2 [His] /[HisH ] and Nproton of the M2-TM domain with and without amantadine. With 10 mM Amantadine Without Amantadine pH + released + released [His] /[HisH ] Nproton [His] /[HisH ] Nproton 6.5 ~ 20a,b 3.81 0.79 1.77 6.0 1.78 2.56 0.41 1.14 5.0 0.62 1.53 0.27 0.83 a 15N CP/MAS NMR spectrum could not detect any signals from charged histidines. That at least 95% of the histidine is neutral is assumed in this case. b The hump around 170 ppm in the amantadine-bound spectrum (pH 6.5) is unlikely to be a real signal. 79 CHAPTER 5 STRUCTURE OF THE M2 TRANSMEMBRANE DOMAIN WITH AMANTADINE 5.1 Structure Determination Using Orientational Restraints It is well known that in liquid-state NMR, NOEs and J couplings provide distance and torsion angle restraints for the structural determination of biological macromolecules (Wagner et al. 1992). In solid-state NMR, these values are almost impossible to measure. In principle, solid-sate NMR dipolar recoupling techniques such as rotational echo double resonance (REDOR) experiment (Gullion and Schaefer 1989) can measure the distance between two spins much more accurately than liquid-state NMR. However, the presence of multiple spins significantly complicates the measurement if the local conformation is unknown. This problem impedes the development of dipolar recoupling NMR experiments in the structure determination of macromolecules. On the other hand, sometimes the distance between two atoms is critical for answering biological questions, e.g. substrate conformation in the binding site. In an oriented sample, 15N-1H PISEMA experiments measure both 15N-1H dipolar couplings and 15N anisotropic chemical shift, 15 giving the possible orientations of the magnetic vector B0 in the N PAF. For a string of peptide planes folded in space, orientation restraints of each amide nitrogen with respect to B0 constrain the peptide plane orientation and its torsion angles can thereby be determined. Usually, a membrane bound sample is placed in the probe with the lipid bilayer normal parallel to the external magnetic field direction. Thus, PISEMA experiments not only determine the membrane protein structure, but also directly define the membrane protein orientation with respect to the lipid bilayer. In this section, we 80 discuss how the model structure of M2-TMD with amantadine is calculated and what problems are associated with the structural calculation. Lastly, it should be mentioned that the implementation of residual dipolar coupling, a recently developed solution NMR technique, takes advantage of partial alignment of proteins or nucleic acids to deduce distance and orientational information (Prestegard et al. 2000; Tjandra and Bax 1997). 5.1.1 Torsion Angle Calculation In Figure 5.1 we illustrate two peptide planes to detail the computation of torsion angles using PISEMA data. Figure 5.1. The bond vectors and exterior angles used in torsion angle calculations. The computation requires the general formula that relates the torsion angle to an interval vector d (Quine and Cross 2000; Song et al. 2000): Tor(a, b, c) = Tor (a, b, d) + Tor (-d, b, c) (5.1) 81 where a, b, c and d are vectors in space. Based on the torsion angle definition (equation 2.1), we have a× b b× c τ = Tor (a, b, c) => R(b,τ ) = (5.2) a× b b× c a× b b× d τ1 = Tor (a, b, d) => R(b,τ ) = (5.3) 1 a× b b× d d- × b b× d b× c τ2 = Tor (-d, b, c)=> R(b,τ ) = R(b,τ ) = (5.4). 2 d- × b 2 b× d b× c Then, combining equations 5.3 and 5.4, we have a× b a× b b× c R(b,τ )R(b,τ ) = R(b,τ +τ ) = 2 1 a× b 1 2 a× b b× c τ = τ1 + τ2. Thus, we obtain equation 5.1. Using this equation, we can express protein torsion angles in terms of the magnetic field vector B0. φ = Tor (u1, u2, u3) = Tor (u1, u2, B0) + Tor (-B0, u2, u3) (5.5) ψ = Tor (u2, u3, u4) = Tor (u2, u3, B0) + Tor (-B0, u3, u4) (5.6) i i+1 where u1, u2, u3 and u4 are unit bond vectors. In the N and N PAF, we know i i sinβ B cosα B i i i B0 = sinβ B sin α B i cosβ B O sinβNH cos αNH sin 71 NH = sin sin = 0 βNH αNH O cosβNH cos 71 cos75o 0 sin 75o 0 sin 75o cos15o o u1 (or u4)= R2(180 -βD)δ11 = 0 1 0 0 = 0 = 0 o o o o − sin 75 0 cos75 1 cos75 sin15 cos44o 0 sin 44o 1 cos44o u2 = R2( ∠ δ33NCα)δ33 = 0 1 0 0 = 0 o o o − sin 44 0 cos44 0 − sin 44 82 o u3 (or u0)= R2(180 - ∠ NCCα) u1= cos65o 0 sin 65o sin 75o cos65o sin 75o + sin 65o cos75o sin140o cos50o 0 1 0 0 = 0 = 0 = 0 o o o o o o o o o − sin 65 0 cos65 cos75 − sin 65 sin 75 + cos65 cos75 cos140 − sin50 Equation 2.3 shows that the computation of torsion angles requires many vector dot products. With known peptide bond geometry, we can express them as o o o u1 u2 = cos59 , u2 u3 = cos70 , u3 u4 = cos65 , i i sinβ B cosα B o o i i o i i o i u1 B0 = [cos15 0 sin15 ]sinβ B sin α B = cos15 sinβ B cosα B + sin15 cosβ B i cosβ B i i sinβ B cosα B o o i i o i i o i u2 B0 = [cos44 0 − sin 44 ]sinβ B sin α B = cos44 sinβ B cosα B − sin 44 cosβ B i cosβ B u3 B0 = i+1 i+1 sinβ B cosα B o o i+1 i+1 o i+1 i+1 o i+1 [cos50 0 − sin50 ]sinβ B sin α B = cos50 sinβ B cosα B − sin50 cosβ B i+1 cosβ B u4 B0 = i+1 i+1 sinβ B cosα B o o i+1 i+1 o i+1 i+1 o i+1 [cos15 0 sin15 ]sinβ B sin α B = cos15 sinβ B cosα B + sin15 cosβ B . i+1 cosβ B Now we can write equations 5.5 and 5.6 as φ = Tor (u1, u2, u3) = Tor (u1, u2, B0) + Tor (-B0, u2, u3) = arg (-u1 ⋅ B0 + (u1 ⋅ u2)(u2 ⋅ B0), u1 ⋅ (u2 × B0)) + arg (B0⋅ u3 + (-B0 ⋅ u2)(u2 ⋅ u3), -B0 ⋅ (u2 × u3)), (5.7) ψ = Tor (u2, u3, u4) = Tor (u2, u3, B0) + Tor (-B0, u3, u4) = arg (-u1 ⋅ B0 + (u1 ⋅ u2)(u2 ⋅ B0), u1 ⋅ (u2 × B0)) + arg (B0⋅ u3 + (-B0 ⋅ u2)(u2 ⋅ u3), -B0 ⋅ (u2 × u3)). (5.8) The triple product in the argument can be computed as: 83 2 2 2 1/2 v1 ⋅ (v2 × v3) = ± (1-x -y -z -2xyz) (5.9) where x = v1 ⋅ v2, y = v2 ⋅ v3 , z = v1 ⋅ v3. Equation 5.8 indicates an degeneracy in the torsion angle calculations, which is called a chirality degeneracy (Quine 1999; Quine et al. 1997; Song et al. 2000). Other degeneracies in the torsion angle calculation are discussed in the following section. 5.1.2 Degeneracy Degeneracy is often concomitant with angular restraints. In liquid-state NMR, degeneracy occurs when the Karplus equation is used to obtain dihedral angles (Karplus 1963; Wagner et al. 1992). In aligned systems, dipolar couplings and anisotropic chemical shifts measured by solid-state NMR provide angular information of bond vectors with respect to the external magnetic fields. Due to the multiple solutions of the bond vector orientations, many possible structures correspond to one set of NMR data. However, as Cross pointed out, peptide geometry and steric hindrance could significantly reduce the amount of possible structures (Cross 1986). In this section, we discuss those degeneracies related to structural calculations using PISEMA data. Depending on the orientation of the bond vector with respect to the B0 field, dipolar coupling can be either positive or negative (Denny et al. 2001). However, 15N-1H dipolar couplings measured by PISEMA experiments do not inherently include the sign information. This leads to a sign degeneracy of dipolar couplings. However, only a small region (~18%) in the PISEMA powder pattern has degeneracies (Bertram et al. 2003). For TM helices that have an average tilt angle of 21o (Bowie 1997), the sign is often +1. A good example is gramicidin A because its helical axis is approximately parallel to the magnetic field and all backbone 15N-1H dipolar couplings are positive (Cross 1986). For a helix parallel to the bilayer plane, the sign is –1. Usually, the sign degeneracy from dipolar coupling is resolved as the majority of PISEMA resonances fall into the sign resolved region (Bertram et al. 2003; Denny et al. 2001). Even if the sign of the dipolar coupling is known, there is another source of degeneracy from the calculation B0 in the PAF. One set of PISEMA data, (σ, ν), can have four possible orientations for the magnetic field vector B0 in the PAF. The B0 vector 84 in the PAF can be represented using polar angles or Cartesian coordinates (Denny et al. 2001; Marassi and Opella 2000; Marassi and Opella 2002; Marassi and Opella 2003; Quine et al. 1997; Quine and Cross 2000; Song et al. 2000). The four possible solutions are (± αB, βB) and (± (π – αB), π – βB), or (x, y, z), (x, -y, z), (-x, y, -z) and (-x, -y, -z). Figure 5.2 illustrates the top view and side view of these solutions in the PAF. 15 Figure 5.2. Four possible solutions of B0 orientations in the N principle axis frame. Both Cartesian and polar coordinates are shown and each solution is labeled. A third degeneracy arises from the torsion angle calculation (equation 5.8) as discussed in 5.1.1. The last degeneracy is known as the Cα chirality degeneracy (Brenneman and Cross 1990; Song et al. 2000), because of its relevance to the free rotation at Cα. Given a set of (αB, βB), the exact orientation of the peptide plane is still not defined. The bond vectors can form cones with the axis of B0. Then, if we fix the orientation of one peptide plane, we can find the next one because the second peptide plane has to satisfy both the NMR orientational restraints and the molecule geometry at Cα. As shown in Figure 5.3, there are two possible orientations of the second peptide plane. One peptide plane is the mirror image of the other with respect to the plane formed by NCα and CαB0. 85 Figure 5.3. The Cα chirality degeneracy. Cone II indicates the possible orientations of the first peptide plane with given (αB, βB). Cone I represents the second. Cone III illustrates the possible orientations of CαC satisfying the fixed NCαC angle and CαC bond length. Clearly there are two possible orientations of the second peptide planes at the intersection of these cones, which correspond to two sets of torsion angles. 5.1.3 Continuity Rule Concomitant with the degeneracy is the continuity rule, in other words, the selection of degeneracy parameters should be consistent and continuous in the torsion angle calculations. As in equations 5.7 and 5.8, the torsion angle calculation is associated with two PISEMA data sets and the degeneracy parameters used in the computation of the torsion angles for a third residue should be consistent with the former ones. This is the same principle as used in the structural construction of gramicidin A (Ketchem et al. 1996). Dealing with continuity is complicated, requiring each step in the torsion angle calculations to be monitored in terms of degeneracy and mathematically those degeneracies should be explicitly defined (Asbury et al. In preparation). For a 86 transmembrane domain with a helical structural motif, it is natural to choose those torsion angles approaching the ideal helical values. However, this approach may not obey the continuity rule (data not shown). In the structural characterization using orientational restraints, this continuity rule offers another powerful tool to minimize degeneracies. 5.1.4 PISEMA Data of M2-TM Domain with Amantadine Lipid bilayers aligned between glass slides can be characterized by 31P NMR spectroscopy. Lipid-buried membrane proteins or peptides can be oriented to give rise to a single set of 15N NMR signals, if only one conformation exists. Orienting protein- incorporated lipid bilayers is by no means a simple task. In fact, it is one of the critical factors dictating the quality of the static NMR spectra, requiring much skill to make well- oriented samples. The 31P NMR spectrum in Figure 5.4 indicates a typical well-oriented sample. Since lipid head groups undergo fast rotation around the bilayer normal, the 31P chemical shift elements are motionally averaged and the strong signal on the left is from 31 P δII. The small signal on the right probably comes from the residual unoriented portion, the bilayer defects and other lipid phases (Moll and Cross 1990). Figure 5.4. The oriented sample for PISEMA experiments. The lipid bilayers are oriented between glass slides and about 50 glass sides are stacked in a glass tube. In the NMR probe, the sample is placed so that the bilayer normal is parallel to the external magnetic field. The uniform orientation of the lipid head group contributes to a sharp line in the static 31P spectrum shown on the left. 87 Theoretically, the dipolar coupling is scaled to about 0.82 (sin54.7o) in PISEMA experiments (Gu and Opella 1999; Wu et al. 1994). In reality, the scaling factor is a bit smaller than that. The actual scaling factor can be measured by comparing the dipolar coupling between PISEMA experiments and separated local field (SLF) experiments (Wu et al. 1994). Here, based on previous work and conclusions (Stark et al. 1978; van Willigen et al. 1977), we assume that the contribution from the anisotropic indirect dipole-dipole coupling between 15N-1H is small and negligible in our scaling factor estimation. SLF is another 2D NMR experiment correlating anisotropic chemical shift and dipolar coupling without any scaling factor. However, the linewidth in the dipolar coupling dimension is much broader than that in PISEMA spectrum. This is seen in Figure 4.5, which compares PISEMA and SLF spectra of 15N Leu38 labeled M2-TM domain with amantadine in DMPC. From the observed 15N-1H dipolar couplings, we can calculated the apparent scaling factor is: DC 15 1 15360 f = N− H(PISEMA) = = 0.78. DC 15 1 19629 N− H(SLF) This value is very close to the theoretical value and does not change significantly from one experiment to another. Therefore, we use this value in the PISEMA data correction. From Figure 5.5 we can also see that the PISEMA experiment dramatically improves the resolution and sensitivity of 15N and 15N-1H 2D NMR spectroscopy, which makes the static NMR experiments for multiple-site labeled samples feasible. Figure 5.6 lists all the PISEMA data for the M2 TM domain with amantadine in DMPC bilayers. To help assign the multiple site labeled resonances, single site labeled PISEMA data were also obtained. The PISEMA data in Figure 5.6 were collected in one spectrum and fitted with PISA wheels (Figure 5.7). Interestingly, the PISEMA data can be fitted with two PISA wheels with 19o and 28o tilt angles, respectively. The connection between resonances follow a helix-wheel pattern and the clockwise rotation indicates positive peptide plane tilt angles (Kim and Cross 2004). Two tilt angles imply a small kink (≥10o) in the TM helix. This tilt transition occurs around G34, I35 and L36. For technical reasons, the PISEMA data of His37 and Ser31 are missing. However, their positions can be well predicted as they fall into two different PISA wheels (Figure 5.7A). Therefore, ideal α-helical torsion angles are assumed here for these two residues. 88 5.1.5 Subunit Structure of M2-TM Domain with Amantadine Although PISA wheel and PISEMA wave analyses provide a very good illustration of the TM helical topology in the lipid bilayers, a high-resolution structure can be defined by a series of torsion angles calculated from PISEMA data. Taking into account the continuity issue associated with the degeneracy in the structural buildup in using equations 5.7 and 5.8, we summarize the most helical structure satisfying the NMR data in Table 5.3. Figure 5.5. Comparison between a PISEMA spectrum and a separated local field spectrum to obtain an experimental scaling factor. The sample is 15N labeled Leu38 M2- TM domain in DMPC with amantadine present. The slices of the chemical shift domain and dipolar coupling in the 2D spectrum are also shown on the top and right side of the spectra, respectively. 89 Figure 5.6. PISEMA data for various 15N M2-TM domain samples in DMPC with the amantadine present. Figure 5.7. A) Two PISA wheels in the M2-TM domain PISEMA spectrum. The spheres represent the PISEMA resonances. Each sphere is connected with lines based on resonance assignments. The PISEMA resonances are fitted with two PISA wheels with tilt angles of 19o and 28o. Question marks indicate the missing data points and their hypothetical positions. B) PISEMA wave simulation of the 15N M2-TMD anisotropic chemical shifts and 15N-1H dipolar couplings. For both simulations, a 0o rotational angle is applied. The arrows pointing to the waves indicate the tilt angle used for simulation. 90 Table 5.1 The PISEMA data from 15N labeled M2-TM domain in DMPC bilayers with amantadine and the torsion angles calculated from NMR data. M2-TM a b c c CS (ppm) DC (kHz) αB β B φ ψ Residues L26 174.9 14.5 ± 80.6 25.3 -46.4 -38.6 V27 154.3 17.2 ± 36.5 32.8 -99.1 -41.4 V28 121.4 9.3 ± 53.9 46.0 -47.9 -101.2 A29 165.6 5.8 ± 164.9 27.6 -20.3 -37.4 A30 176.8 11.8 ± 104.2 23.8 -65.0 -40.0 S31d / / / / -62.7 -56.7 I32 142.3 6.7 ± 90.9 39.4 -71.2 -31.2 I33 183.2 10.5 ± 154.8 19.6 -96.3 -15.5 G34 160.7 18.6 ± 38.9 28.4 -88.7 -44.2 I35 138.3 11.9 ± 56.2 39.9 -59.3 -87.2 L36 187.8 11.6 ± 168.3 16.8 -65.0 -40.0 H37d / / / / -60.8 -55.5 L38 170.1 19.7 ± 28.5 26.0 -80.0 -44.3 I39 159.9 14.2 ± 64.4 31.7 -64.3 -48.2 L40 187.8 12.7 ± 132.8 17.4 -65.0 -40.0 W41 199.7 20.0 ± 38.1 6.8 -65.2 -39.2 I42 167.2 18.6 ± 37.9 27.6 -55.7 -41.0 L43 174.3 10.4 ± 116.2 25.2 / / a All the anisotropic chemical shifts have ±10 ppm experimental error. b All the resonances have positive dipolar couplings with ±1kHz experimental error because they fall into the resolved sign region of PISEMA powder pattern (Figure 5.10B). c 15 There are four possible orientations of B0 in the N PAF. Only two of them are listed here. See text for the other two. d The resonances of Ser31 and His37 are unknown. The most α-helical torsion angles are chosen in this case. 5.1.6 His37 and Trp41 Side Chain Conformations There are two aromatic residues -His37 and Trp41- in the M2-TM domain that have side chain N-H bonds. Similar to backbone amide N-H, the PISEMA experiment 91 can provide possible orientations for these side chains with respect to the external magnetic field, or the bilayer normal if the 15N PAF of the side chain with respect to the side chain MF is known. The magnitudes and orientations of the principle elements of tryptophan 15Nε1 tensors were measured by Ramamoorthy and coworkers using 3D solid- state NMR spectroscopy (Ramamoorthy et al. 1997). Their results are consistent with the previous work from Cross and Opella but are different from those from Hu et al. (Cross and Opella 1983; Hu et al. 1993). Ramamoorthy et al. argued that this difference may come from the complication caused by the quadrupolar 2H nucleus (Ramamoorthy et al. 1997). Here we use the orientation data from Ramamoothy and coworkers to calculate the Trp41 side chain orientations with respect to the bilayer normal (Figure 5.8B). The magnitudes and orientations of the principle elements of positively charged histidine 15Nδ1 and 15Nε2 tensors are obtained by solid-state NMR methods (Harbison et al. 1981; Ramamoorthy et al. 1997; Wei et al. 1999). The results from these different groups are in general consistent. The magnitudes of neutral protonated histidine 15Nε2 tensors are available (Wei et al. 1999). The orientation of the principal axes in the molecular frame can be predicted from the charged 15Nδ1 and 15Nε2 tensor orientations (Cross and Opella 15 ε2 1983), that is, the δ 11 axis is collinear to the N –H vector and the δ22 axis is perpendicular to the imidazole plane (Figure 5.8B). Similar orientations of 15N chemical shift tensors have been observed in tryptophans and charged histidines (Ramamoorthy et al. 1997; Wei et al. 1999). For both Trp41 and Hia37, the orientation of the N-H bond 15 vector in the N chemical shift PAF is defined by two polar angles αΝΗ and βΝΗ (Figure 5.8A). The principal components and orientations for histidine 15Nε2 and tryptophan 15Nε1 are shown in Figure 5.8B and Table 5.2. Table 5.2 The 15N chemical shift principle components and orientations of histidine and tryptophan side chains. 15N Chemical Shift (ppm)a Polar Angles (degree) Side Chain δ 11 δ 22 δ33 αΝΗ βΝΗ Histidine 15Nε2 235.3 ± 5 154.3 ± 5 44.8 ± 5 0 ± 30 5 ± 3 Tryptophan 15Nε1 157.2 ± 1 106 ± 1 37.4 ± 1 0 ± 30 5 ± 3 92 a The chemical shift is adjusted for the different 15N chemical shift references. Saturated 15 NH4NO3 solution is about 23.6 ppm when liquid NH3 is referenced as 0 ppm (Bryce et al. 2001). The histidine 15Nε2-H chemical shift components are the average values of the neutral histidines (Wei et al. 1999). Depending on the substance and crystal form, the chemical shift tensor elements can differ within 9 ppm. Figure 5.8. A) Orientations of the N-H vector in the 15N chemical shift principal axis frame. The N-H vector in the PAF is defined by two polar angles: αΝΗ and βΝΗ. B) The 15N principle axis frame in the histidine and tryptophan molecular frame. Figure 5.9 shows the PISEMA spectra of His37 15Nε2 and Trp41 15Nε1 labeled M2-TM domain in DMPC bilayers with amantadine bound. We learned from the 15N CP/MAS of 15N side chain labeled experiments that tautomer I is the predominate species (Chapter 4). Therefore, His37 15Nε2 M2-TMD is labeled for PISEMA experiments. Interestingly, the dipolar coupling of Trp 15Nε1-1H is zero, which indicates that the 15Nε1 - 1H vector is at the magic angle with respect to the external magnetic field. Although the orientation of side chains can be calculated directly from equation 2.12, alternatively we can search the side chain orientations to fit the NMR data by varying χ1 and χ2 torsion angles. Technically, this can be implemented more readily. 93 Figure 5.9. PISEMA Spectra of His37 15Nε2 and Trp4115Nε1 M2-TMD in DMPC in the presence of amantadine. 5.2 Structure of the M2-TMD with Amantadine 5.2.1 Model Structure of M2-TMD with Amantadine Solid-state NMR has been successfully applied to determine the high-resolution structures of several membrane proteins or peptides in lipid bilayers (Ketchem et al. 1993; Marassi and Opella 2003; Opella et al. 1999; Wang et al. 2001). An atomic model of the M2-TMD/Amantadine complex has been built using experimental data from PISEMA experiments. Since the overall structure is a symmetric tetramer, the model was built by first creating a monomer structure that matched the data. The tetramer was then constructed by duplicating the monomer and choosing a tetrameric structure that 94 minimized stereo-chemical and non-bonded constraints. Amantadine was then placed inside the channel at a position consistent with other biochemical information (Hay, 1992; Hay et al., 1985; Duff et al., 1994). The experimental data from PISEMA experiments provide a series of orientational restraints that can be used to generate backbone torsion angles for the target peptide. Once the PISEMA data were assigned for each residue, a set of specific torsion angles were computed. However, because of the degeneracy in the analysis, this set of torsion angles is not unique. Nevertheless, both PISA wheel and PISEMA wave simulations demonstrate that the M2-TM domain with amantadine is predominantly α- helical (Figure 5.7). Therefore, with this secondary structure information it is possible to further limit these torsion angles to a unique set. The initial monomer structure without refinement was built iteratively by using the most alpha-helical torsion angles at each residue that matched the data. This was necessary to handle the continuity condition and residues that were missing in the PISEMA data. Figure 5.10B compares the experimental PISEMA and simulated data from the M2-TMD subunit structure. All calculated resonances superpose on the observed data except A30 in which the gramian is negative and very close to zero. In this case, the zero gramian is assumed to lead to a small error in the calculation. Only one possible set of the His37 and Trp41 side chain orientations is shown in Figure 5.10A. Some of the conformations are ruled out due to van der Waals overlap. During the tetramer modeling, the possible orientations are further restrained. Once the monomer was constructed, a tetramer was built with four monomers ~10Å apart and each rotated 90o to ensure symmetry. Since the helical tilt and helical rotation angle are fixed by the monomer, a rigid body conformation search was performed by varying only the rotation angle about the B0 field and crossing point. The lowest energy tetramer was chosen and then the amantadine molecule was added approximately 6Å below the interface region. Interfacial residues were added to the M2- TM structure and energy minimization was done on the entire complex using stereochemical, van der Waal’s and electrostatic interactions. Figure 5.11 illustrates the side and top view of the M2-TM/amantadine model structure. Although amantadine induces a kink and a small tilt angle on the M2-TMD backbone, the basic structure 95 feature does not alter; histidines and tryptophans are still inside the protein interior. Presumably, amantadine binds at the region around L26-S31. Interestingly, this region deviates a bit from an ideal α-helix, probably due to the accommodation of amantadine. Figure 5.10. A) The subunit structure of the M2-TMD tetramer with amantadine calculated based on the PISEMA data. Only the fragment from residue 26-43 is shown here. B) The comparison between the experimental PISEMA resonances and the calculated PISEMA resonances from the structure of Figure 5.8A. The empty square and the solid circle represent the experimental data and the calculated ones, respectively. Figure 5.11. The model structure of M2-TMD/amantadine in DMPC bilayers. Both His37 and Trp41 side chains are shown in stick representation. In the side view presentation, the front helix is removed for clear illustration. The possible location of amantadine (shown in Corey-Pauling-Koltun representation) is also presented. 96 Although the PISEMA spectrum of 15N 5-Leu M2-TMD sample without amantadine suffers from a poor resolution (Figure 4.4A), compared with the spectrum with amantadine (Figure 4.4B), a structural change due to the amantadine binding is apparent. Due to the unresolved resonances and lack of additional backbone NMR data, it is hard to quantitatively characterize the amantadine-free structure at present and thereby the conformational change upon amantadine binding. However, at least from this one spectrum the structural difference is modest. A high-resolution NMR structure of the M2- TMD without amantadine is available (Nishimura et al. 2002). However, comparison between our amantadine-bound model and the published M2-TMD structure should be done with caution because the sample preparation protocols for these two structures are different. The main difference is that the original samples were prepared directly from the organic solvent and were hydrated using pure water, whereas all the PISEMA samples in this dissertation were made from M2-TMD/liposomes in buffers. With the former protocol, the presence of amantadine seems not to affect the PISEMA spectra based on very limited data (Song et al. 2000). Both His37 CP/MAS and backbone PISEMA data, however, suggest a structural and dynamic change due to amantadine binding. In the study of membrane proteins, sample preparation really matters because it relates to how membrane proteins fold and insert into membranes (for reviews see (Kiefer 2003; Popot and Engelman 2000; White and Wimley 1999). It was recognized a long time ago that the conformation of gramicidin A in DMPC depends upon the solvent history of the sample (LoGrasso et al. 1988). The difference that we see here is probably a simple example showing how capricious membrane proteins are. 97 CHAPTER 6 CONCLUSIONS, HYPOTHESES AND FURTURE WORKS 6.1 Proton Conduction in the M2 Proton Channel Much knowledge on channels is gained from high-resolution protein structures. Many important biophysical questions are answered by correlating the structures with the functional studies. Without the high-resolution structures of KcsA K+ channel, we would never have the chance to appreciate the art of how the channel handles the dehydration of K+ in the selectivity filter (Doyle et al. 1998; Zhou and MacKinnon 2003). The basic principles of cation transport over a broad range of channels may be similar: ions must be dehydrated before entering the channel and the protein itself must provide an environment to allow ions to pass through. Ion transport presents a dilemma. On one hand, the channel must provide a chemical environment that attracts, selects and stabilizes the ions to be transported. As mentioned in the first chapter, in the selectivity filter of KcsA K+ channel two layers of four backbone oxygens mimic the hydration shell to solvate K+ in the center. On the other hand, the interaction between the protein and ion should not be very strong as the ion could “get stuck” in the protein. In fact, K+ ions permeate through the potassium channel at a rate approaching 108 ions per second under physiological conditions (Hille 1992). Therefore, acid residues like glutamate usually found in metal binding proteins are not good candidates for potassium channels. The backbone oxygen with a –0.42 charge (Garrett and Grisham 1995) seems to be the best compromise for this dilemma. Gramicidin A, another cation channel selectively conducts monovalent cations and utilizes this mechanism, as well (Ketchem et al. 1993; Tian and Cross 1999). 98 Proton channels employ different machinery from potassium channels in terms of gating and selectivity. Backbone oxygens are not capable of coordinating protons efficiently. To this end, titratable residues play a critical role in proton transfer (Decoursey 2003). Histidine is a reasonable choice due to its large variability in proton affinity (Edgcomb and Murphy 2002). Interestingly, a single mutation of arginine to histidine in the Shaker potassium channel makes it conduct protons (Starace and Bezanilla 2004). The protonation-deprotonation of titratable residues is very likely to be the essential gating mechanism of proton conduction in the proton channels. It inherently excludes metal cations and anions. In other words, selectivity is achieved. For pH- activated proton channels like the M2 proton channel, the excessive protonation on one side of the selectivity filter leads to the release of protons on the other side. A completely opened cavity commonly seen in other channels may not be necessary for proton channels since titratable residues such as histidines in the M2 channel may occlude the channel and function as a selectivity filter. The “histidine-lock” complex in the M2 proton channel -four hinged histidines tying the tetramer together- is a new model for proton conductance. This may be the “true” closed state of the M2 channel under physiological conditions, as pH never goes as high as 8.8 when all histidines are neutral. The apparent midpoint in the M2 activation curve (Wang et al. 1995b), pH 5.8, may be the pKa of the histidine-lock complex. In other words, it is pK2 of 6.3 in our model (see Chapter 3). It may appear at first glance to be absurd that a low dielectric channel can tolerate two charges inside. These two charges, however, are shared by four imidazole rings and the electrostatic repulsion may not be very strong. Recall that two potassium ions are separated by only 7.5 Å in the KcsA selectivity filter. It was suggested that the high conductance rate of K+ in K+ channels is achieved through electrostatic repulsion between two closely spaced K+ ions (Morais-Cabral et al. 2001; Zhou and MacKinnon 2003; Zhou et al. 2001). Two closely spaced charges are possible in the proton channel as long as they are well shielded or that the charge is distributed. We can roughly model the histidine lock, a four-imidazole complex with two-fold symmetry (Figure 6.1). The charged imidazole hydrogen bonds with the neutral imidazole and the two planes are almost orthogonal. This conformation has been observed in both x-ray crystal structures 99 and theoretical calculations (Krause et al. 1991; Quick and Williams 1976; Tatara et al. 2003). The distance between two opposite nitrogens in the imidazolium ring is about 9.6 Å (Figure 6.1). Figure 6.1. An imidazole-imidazolium complex modeling the histidine lock in the M2 proton channel. In the figure the non-protonated nitrogen on the neutral imidazole is hydrogen bonded with the protonated nitrogen on the imidazolium. The furthest distance between two charged nitrogens, which is 9.6 Å, is shown by dashed line. The van der Waals surface presentation of the complex is illustrated on the right side. This model is generated by Dr. Johan Bredenberg in Dr. Huan-Xiang Zhou’s lab. Hydrogen bonding between histidines is common in protein structures. For instance, the hydrogen bond between His12 and His119 at the active site in ribonuclease is believed to facilitate proton movement (Golubev et al. 1994). In Achromobacter lyticus protease I, His210 hydrogen bonds with His177 (Tsunasawa et al. 1989). Although the signal at 167 ppm in our 15N CP/MAS spectra is indicative of the ≥ N--- H—N+< hydrogen bond, direct evidence to demonstrate such an interaction is not yet available. Hennig and Geierstanger reported a modified 1H-15N HNN-COSY NMR 2 15 ε2 experiment that directly measures the JNN scalar coupling between ≥ N of His24 and 100 charged 15Nε2-H of His119 in sperm whale apomyoglobin (Hennig and Geierstanger 1999). This may be promising approach for providing direct evidence for the histidine lock in the M2 system. The truncated M2 protein is a good steppingstone toward understanding the function of the more complicated integral protein. The M2-TM domain has proven to be an excellent model system for the M2 proton channel (Duff and Ashley 1992; Salom et al. 2000; Wang et al. 2001). With the advent of high-field NMR spectrometers, it is possible to titrate the 15N histidine labeled M2 protein using CP/MAS methods. There are only three histidines in the M2 primary sequence (Figure 4.1). It would be feasible to mutate those two extra-membrane histidines and retain the TM histidine. Currently this project is under way in the lab. The opening and closing of channels are often concomitant with large conformational rearrangements (Hille 1992; Spencer and Rees 2002; Woolley and Lougheed 2003). Usually channels open by increasing the diameter of the pore (Jiang et al. 2002; Sukharev et al. 2001). For the M2 proton channel, from the histidine-all-neutral state to the histidine-all-charged state, one may naturally think that the variation of inter- histidine interactions may trigger conformational changes in the whole tetramer. Figure 6.2 shows the preliminary PISEMA spectra of M2-TM domain in DMPC at different pH values. The shifting of PISEMA resonance positions indicates that the backbone structure does change with the variation of pH. At high pH, each M2-TM helix in the tetramer appears to adopt a single conformation structure. As pH decreases, multiple signals show up in the single-site labeled PISEMA spectra. This is reasonable, because at high pH all histidines are neutral, and a symmetric (or at least pseudo-symmetric) M2-TM tetramer is favored. As more protons are accepted by histidines and the symmetry is broken, the M2- TM tetramer will adopt a different conformation to accommodate the change. As we discussed in Chapter 3, in most cases multiple protonation states of the M2 channel exist at a given pH. This leads to multiple peaks in the PISEMA spectra even for single-site labeled peptide. If individual peaks in the PISEMA spectra correspond to individual conformational state, we can estimate that the inter-conversion rate between different states to be slower than 1.3× 10-3 s-1based on the separation of the conformational peaks. To answer the question on how the structure specifically changes with pH, more structural data is required. Besides the pH titration of the amide sites, it would be also 101 worthwhile to look at the His37 and Trp42 side chains’ orientations at various pHs. In so doing we may have an atomic view of the channel gating mechanism. Figure 6.2. The PISEMA spectra of 15N single site labeled M2-TMD in DMPC bilayers at different pH values. 102 6.2 Amantadine Binding to the M2 Channel The discovery of amantadine as a drug to treat infection by influenza A virus strains was much earlier than the discovery of the M2 proton channel. Organic chemists have synthesized a number of amantadine analogues in order to find some compounds that are more efficient and have less side effects (Aldrich et al. 1971; Kolocouris et al. 1996a; Scholtissek et al. 1998). While rimantadine is a successful example, without the structure of the target protein, this hunting task is as difficult as finding an exit in a dark forest without a map. Here we are going to review the anti-viral activity of many amantadine derivatives conducted more than 30 years ago (Aldrich et al. 1971). We attempt to catch some hints on where amantadine binds in the M2 proton channel. Presumably, the binding site in the M2 channel can be divided into two regions: one that binds the charged amino group through hydrogen bonds or ionic interactions (region a in Figure 6.3A) and the other that interacts with the apolar adamantyl group via van der Waals interactions (region b in Figure 6.3A). Figure 6.3B summarizes the modifications on amantadine. For type I compounds, addition of one or two short alkyl groups, e.g. methyl, ethyl and propyl groups, does not affect the activity dramatically. However, the long hydrocarbon chains and large groups (e.g. a benzyl group) abolish the activity, however. It appears that at region a where the M2 channel interacts with the charged amino group there is still some limited space to adapt to amantadine derivatives. Interestingly, in type V compounds, addition of one carbon between the adamantyl and amino group results in similar or better activity in comparison with amantadine. Rimantadine belongs to this group. However, longer chain or larger group substitution of R gives inactive compounds, indicating the compactness and limited flexibility in region a. In type III compounds, replacement of the amino group in amantadine by H, OH, SH, COOH etc. results in chemicals with no activity at all. The hydrogen bond interaction between the head group and the protein may not be true since those type III derivatives + can possibly satisfy it. In addition, replacing –NH3 in amantadine by -NHCO- (i.e. lower basicity) dramatically reduces the activity. In a word, positively charged head group is necessary and the inner surface in region a must be negative. Type II and type IV 103 compounds can examine the chemistry at region b. For type II compounds, it turns out that addition of one methyl group to adamantyl portion is bearable but more or larger groups and polar groups extinguish the activity, which is indicative of the tightness and hydrophobicity at the bottom of region b. Basically, type IV compounds are active, implying that the shoulder in region b is variable. Figure 6.3. A) hypothetical amantadine binding model. The binding site can be described by two regions: region a (a polar environment to stabilize the charged amino group) in pink and region b (a hydrophobic cavity surrounding the apolar adamantyl group) in green. B) amantadine derivatives where R represents various functional groups. The qualitative discussion above can assist structural modeling of the M2-TM domain in the presence of amantadine. Initial models suggesting the hydrogen bond interaction between the amino head group of amantadine and Ser31 side chains cannot explain why amino-substituted amantadine derivatives do not have activity (Hay 1992; Sansom and Kerr 1993). Moreover, in those models histidine side chains that point to the lipid bilayer instead of the channel may be in a wrong position. Our histidine CP/MAS data do not support Pinto’s model in which the amino group interacts with the non- protonated nitrogens on the histidine imidazole (Gandhi et al. 1999). Otherwise, the shift 104 of the His37 15N resonances will be affected by this interaction (Figure 4.1). The binding model proposed by Arkin and coworkers is questionable as well (Astrahan et al. 2004), because it is hard to believe that the hydrophobic adamantyl group binds the N-terminal extra-transmembrane region, which is surrounded by many polar residues. As a matter of fact, almost 90% of N-terminal extra-transmembrane residues are polar. Neither can it explain why type II compounds do not inhibit the influenza A virus. Moreover, the structure of M2-TM domain they used is the one without amantadine and we know that amantadine changes the structure (Chapter 5). Based on our structural model, we believe that amantadine binds the channel pore: that the adamantyl group interacts with the channel interior residues (V28, A29 and I32, see Figure 3.1a for details) probably via van der Waals interactions and the charged amino group points towards the N-terminal bilayer interface, where polar and negatively charged residues (e.g. D21SSD24) are populated. The high density of negative charges in this region explains why the positively charged head group of amantadine is important and substitution with polar and negatively charged head groups abolishes the activities. The M2 amantadine-resistant strains mutate L26, V27, A30, S31 and G34 to polar or charged residues (Hay et al. 1985). In our model structure with amantadine, owing to the right-handed coiled-coil structure close to the N- terminus (Figure 5.11), these residues are facing the hydrophobic lipid hydrocarbon chains. Apparently, the binding of amantadine to the M2 amantadine-resistant mutants will be unfavorable. Amantadine is a small, rigid and symmetric molecule. It does not have to rearrange its conformation to enter the protein. The rigidity of the target molecule is favorable for binding interaction in terms of entropic penalty (Homans 2004). Based on the NMR relaxation measurements, we know that the M2 TM region appears to be more mobile in the absence of amantadine. The structure of M2-TM domain with amantadine is more rigid than that without the drug. In order to compensate for the entropic loss upon drug binding and retain strong binding affinity, the enthalpic interactions between amantadine and the protein (e.g. electrostatic and van der Waals interactions) would have to be strong. In our M2-TM model structure with amantadine, the exact position of amantadine in the channel is unknown. We successfully synthesized 15N-amantadine (see 105 Appendix B) and hope that distance-measurement NMR experiments, for example, REDOR, can pinpoint the position of the drug. 6.3 Solving Ambiguities and (15N, 1H, 15N-1H) 3D NMR Experiments One of the major problems in the structural determination using PISEMA is the multiple solutions associated with the calculations of orientational restraints. In the (15N, 15N-1H) 2D PISEMA experiments, generally, there are at least 4 possible orientations of B0 vector in PAF for a given set of (δ, ν) (see Figure 5.2 in Chapter 5). If another NMR observable, for instance, 1H anisotropic chemical shift, is introduced, most of the degeneracies can be eliminated. This is because one of the possible solutions satisfying the 15N chemical shift may not be a correct orientation for 1H chemical shift because both the magnitudes and orientations of the chemical shift tensors of these two nuclei are different. A unique solution is possible if combined with other structural information to solve the ambiguity problem. Figure 6.4 illustrates the relationship between the 15N PAF (denoted by PAFN) and the 1H PAF (denoted by PAFH) in the peptide plane MF (Sharma et al. 2002; Wu et al. 1995). The magnitudes of 1H chemical shift tensors in PAFH are δ H 0 0 3 0 0 33 0 H 0 = 0 8 0 . δ22 0 0 H 0 0 17 δ11 H H The δ33 vector is collinear with the N-H vector and the δ22 vector is perpendicular to N the peptide plane but points to the opposite direction of the δ22 vector. The cross product H H H of δ33 and δ22 makes the third vector δ11 , which is in the peptide plane (Sharma et al. 2002; Wu et al. 1995). By two successive rotational operations, we can obtain the relationship between principle axis frames as H N PAF = PAF R(e2, 287) R(e1, 180) or PAFN = PAFH R(e2, 107) R(e3, 180). (6.1) Once we have this relationship we can simulate the 3D PISA wheels in the (15N, 1H, 15N- 106 1H) 3D NMR spectrum for ideal α-helices (Figure 6.5d). Certainly, 2D correlation spectra can be obtained by looking at the projections. In Figure 6.5a, the PISA wheels in (1H, 15N-1H) correlation spectrum are not obvious, while those in the (1H, 15N) correlation spectrum (Figure 6.4b) share similar features to those in (15N, 15N-1H) PISEMA spectrum H (Figure 6.4c). Since δ33 is parallel to the N-H vector, small peptide tilt angles with 1 respect to B0 gives rise to small H chemical shifts. Figure 6.4b is consistent with the simulation from Vosegaard and Nielsen, which confirms the validity of the transformations in our simulations (Vosegaard and Nielsen 2002). Coincidentally, (15N, 15N-1H) PISEMA spectroscopy, which is often applied to study membrane proteins, seems to be the best choice to resolve the topology of transmembrane α-helices (Figure 6.4c). The M2 TM domain with amantadine seems to be a good system to study the 1H chemical shift related PISA wheels and in turn to use 1H chemical shift to minimize the degeneracies. Figure 6.4. Orientation of the 15N and amide 1H chemical shift tensors in a peptide plane. 107 Figure 6.5. Simulated PISA wheels of a) (1H, 15N-1H) correlation, b) (15N, 1H) correlation, c) (15N, 15N-1H) correlation and d) (15N, 1H, 15N-1H) correlation spectra for an ideal α-helix with different tilt angles. 6.4 Summary Titration of His37 of the M2 TM domain provides functional insight on how this proton channel manages to select and conduct protons. The four-histidine cluster in the channel has very high affinity for protons. We propose a unique “histidine lock” model to depict the closed state of the M2 proton channel under physiological conditions. At low 108 pH, more protons come to the histidine cluster and break the balance of hydrogen bonding. Thereby, the channel starts to conduct protons. The binding of the anti-viral drug amantadine hinders the M2-TM dynamics and gives rise to high-resolution NMR data. A ~10o kink is formed in the middle of the M2-TM helix when amantadine binds. High-resolution structure for one subunit of the M2-TM bundle with amantadine is determined based on PISEMA data. A tetrameric model of M2-TM with amantadine is also built from the NMR-determined subunit. Throughout this dissertation solid-state NMR spectroscopy is the core technology applied to improve our understanding of the structure, function and dynamics of the M2 transmembrane domain. Although still under development, solid-state NMR will continue to play an important role in the membrane protein biology. High-field magnets, sophisticated hardware, powerful computers and advanced software, and robust membrane protein biology will certainly open up new avenues for solid-state NMR research. Complementary to X-ray crystallography and liquid-state NMR, and learning from them as well, solid-state NMR will continue to shine in the field of structure biology. 109 APPENDIX A MAPLE PROGRAM CODES This section lists most of the programs in Maple used in Chapter 3, 4 and 5. Maple 8 needs to be installed in order to execute these programs. The Maple Book is an excellent book for learning the Maple commands (Garvan 2001). Refer to the text for the principles of each simulation. A.1 PISEMA Powder Pattern Simulation This program simulates 3D plots of function f(δ, ν, βB), f(δ, ν, αB), f(δ, αB, βB) and f(ν, αB, βB). By adjusting the different projections, you can get the 2D plots of function f(δ, ν), f(δ, βB), f(ν, βB), f(αB, βB), f(δ, αB) and f(ν, αB) as well. The principle components of the chemical shift can be changed in the program to see the effect on the PISEMA powder shapes. > restart; with(LinearAlgebra): with(plots): > sigma11:=31: sigma22:=54: sigma33:=202: > deg:=Pi/180: > PAF:=<<31, 0, 0>|<0, 54, 0>|<0, 0, 202>>: > B:= 110 > plot3d([sigma, upsilon, alpha], alpha=-180..180, beta=0..180, axes=boxed); > plot3d([sigma, beta, alpha], alpha=-180..180, beta=0..180, axes=boxed); > plot3d([upsilon, beta, alpha], alpha=-180..180, beta=0..180, axes=boxed); A.2 PISA Wheel Simulation Here a step-by-step simulation of PISA wheel is shown below. The results are shown in the code so we can see how it comes to those equations in Chapter 2. > restart: with(LinearAlgebra): with(plots): with(RealDomain); > deg:=Pi/180: > sigma11:=31: sigma22:=54: sigma33:=202: # Find the rotation axis (Denny et al. 2001). 111 > R1:=x-> evalf(<<1, 0, 0>|<0, cos(x*deg), sin(x*deg)>|<0, -sin(x*deg), cos(x*deg)>>); R2:=x-> evalf(< 112 > CaC:=evalf(R1(-65).R3(70).<1.53, 0, 0>); 0.523290818500000032 CaC := 0.607610830699999992 -1.30302563199999999 # F(C)CN'(C)=F(N)CN'(N), CN'(N)=F(N)'F(C)CN'(C) > CN:=evalf(R1(-65).R3(70).R1(-40).R3(65).<1.34, 0, 0>); -0.680530200500000015 CN := -0.348123970299999974 -1.10058545699999999 >NCa:=evalf(R1(- 65).R3(70).R1(40).R3(65).R1(180).R3(59).<1.45, 0, 0>); 0.384108033700000018 NCa := 0.501171344500000004 -1.30529242000000001 > v:=(CaC+CN+NCa)/VectorNorm((CaC+CN+NCa), 2); # Unit vector of the virtual bond vector. 0.0598141486589321912 v := 0.200548302313223903 -0.977856147980806334 > CaC+CN+NCa; # The vector of the vertual bond. 0.226868651700000034 0.760658204900000023 -3.70890350899999976 # Find the vector from Ca pointing to the rotation axis and build the HAF. > m:=1/2*(evalf(cot(100/2*deg))*CrossProduct(a, v)+v- DotProduct(a, v)*a); -0.385924880625257816 m := 0.196720642445611438 -0.416306840084920748 > r:=m/VectorNorm(m, 2); # This is the unit vector of the N-terminal Ca to the helix axis. In the HAF, the x axis should be -r. -0.642362548005504186 r := 0.327436709760485834 -0.692932578267066224 > HAF:=<-r|CrossProduct(a, -r)|a>; # This is the same as the equation in JD P136. 113 0.642362548005504186 0.4619485276 0.612 HAF := -0.327436709760485834 -0.5564014228 0.764 0.692932578267066224 -0.6911562531 -0.206 # Now, The equation above actually is HAF=MF. M. To get the equation of HAF=PAF A, We need the equation relating HAF and PAF. > N:=evalf(R3(-134).Transpose(<<0, 0,1>|<1, 0, 0>|<0, 1, 0>>)); # This equation should be PAF= MF N, where MF=I. 0.719339800500000016 0. -0.694658370299999994 N := -0.694658370299999994 0. -0.719339800500000016 0. 1. 0. # Then HAF=MF M, PAF=MF N, MF=PAF N', HAF=PAF N'M. > C:=evalf(Transpose(N).HAF, 4); 0.689500000000000000 0.718799999999999996 -0.0904800000000000050 C := 0.692899999999999960 -0.691200000000000037 -0.205999999999999988 -0.210699999999999998 0.0793500000000000039 -0.974700000000000010 # This equation should be written as HAF=PAF C. C is the Matrix A in the paper. > NH_mf:=evalf(<-1.024*cos(63*deg),-1.024*sin(63*deg), 0>); # This is the coordinates of NH vector in N DFF plane. Alternatively you can use PAF coordinates which are < 114 CS := 6.543711130cos ( 0.01745329252 ρ )2 − 6.543711130cos ( 0.01745329252 ρ )2 cos() 0.01745329252 τ 2 − 27.75122082cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ + 2 27.75122082cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ + 63.68562444sin ( 0.01745329252 τ ) cos() 0.01745329252 ρ cos() 0.01745329252 τ + 43.08765574 + 151.3657720cos ( 0.01745329252 τ )2 − 19.90082567sin ( 0.01745329252 τ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ > DC:=simplify(1/2*10.735*(3*(B0.NH_haf/VectorNorm(NH_haf, 2))^2-1)); DC := −1.316571304cos ( 0.01745329252 ρ )2 + 1.316571304cos ( 0.01745329252 ρ )2 cos() 0.01745329252 τ 2 + 0.001120788040cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ − 0.001120788040cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ cos()0.01745329252 τ 2 − 0.003755999735sin ( 0.01745329252 τ ) cos()0.01745329252 ρ cos() 0.01745329252 τ − 4.050928457 + 13.46935669cos ( 0.01745329252 τ )2 − 8.824224010sin ( 0.01745329252 τ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ # Use parametric plot to plot the PISA wheels. > tau:=10: p1:=plot([CS, DC, rho=-180..180], x=0..250, y=- 12..12, axes=boxed): tau:=30: p2:=plot([CS, DC, rho=-180..180], x=0..250, y=- 12..12, color=blue, axes=boxed): tau:=50: p3:=plot([CS, DC, rho=-180..180], x=0..250, y=- 12..12, color=green, axes=boxed): tau:=70: p4:=plot([CS, DC, rho=-180..180], x=0..250, y=- 12..12, color=yellow, axes=boxed): tau:=80: p5:=plot([CS, DC, rho=-180..180], x=0..250, y=- 12..12, color=black, axes=boxed): tau:=90: p6:=plot([CS, DC, rho=-180..180], x=0..250, y=- 12..12, color=cyan, axes=boxed): > display(p1, p2, p3, p4, p5, p6); 115 A.3 The PISEMA Waves Chemical Shift Waves > restart: with(LinearAlgebra): with(plots): > deg:=Pi/180: > B:= 116 > csk(0, 0); 192.4615720 > csk(a, 0); 192.4615720 > p8:=plot(csk(0, 20), k=25..35, color=red, axes=boxed): p9:=plot(csk(30, 20), k=25..35, color=blue, axes=boxed): p10:=plot(csk(60, 20), k=25..35, color=green, axes=boxed): p11:=plot(csk(90, 20), k=25..35, color=black, axes=boxed): > display(p8, p9, p10, p11); Dipolar Waves > restart; with(LinearAlgebra): with(plots): > deg:=Pi/180: > A:=<<0.690, 0.693, -0.211>|<0.719, -0.691, 0.079>|<- 0.0090, -0.206, -0.975>>: > B:=(r, t)-> > p7:=plot(evalf(10.735*(3*((A.B(0, 20)). 117 p9:=plot(evalf(10.735*(3*((A.B(60, 20)). > evalf(10.735*(3*((A.B(a, 0)). Alpha Waves > restart; with(LinearAlgebra): with(plots): with(RealDomain): > deg:=Pi/180: > T:=<<0.690, 0.693, -0.211>|<0.719, -0.691, 0.079>|<- 0.0090, -0.206, -0.975>>: > T. > p12:=plot(evalf(1/deg*arccos(B(0, 20).<1, 0, 0>)), k=26..35, color=red, axes=boxed): 118 p13:=plot(evalf(1/deg*arccos(B(30, 20).<1, 0, 0>)), k=26..35, color=blue, axes=boxed): p14:=plot(evalf(1/deg*arccos(B(60, 20).<1, 0, 0>)), k=26..35, color=green, axes=boxed): p15:=plot(evalf(1/deg*arccos(B(90, 20).<1, 0, 0>)), k=26..35, color=black, axes=boxed): > display(p12, p13, p14, p15); > evalf(1/deg*arccos(B(a, 0).<1, 0, 0>)); 90.51566892 > evalf(1/deg*arccos(B(a, 180).<1, 0, 0>)); 89.48433098 Beta Waves > restart; with(LinearAlgebra): with(plots): > deg:=Pi/180: > T:=<<0.690, 0.693, -0.211>|<0.719, -0.691, 0.079>|<- 0.0090, -0.206, -0.975>>: > T. 119 > p7:=plot(evalf(1/deg*arccos(B(0, 20).<0, 0, 1>)), k=26..35, color=red, axes=boxed): p8:=plot(evalf(1/deg*arccos(B(30, 20).<0, 0, 1>)), k=26..35, color=blue, axes=boxed): p9:=plot(evalf(1/deg*arccos(B(60, 20).<0, 0, 1>)), k=26..35, color=green, axes=boxed): p10:=plot(evalf(1/deg*arccos(B(90, 20).<0, 0, 1>)), k=26..35, color=black, axes=boxed): > display(p7, p8, p9, p10); > evalf(1/deg*arccos(B(a, 0).<0, 0, 1>)); 167.1614318 > evalf(1/deg*arccos(B(a, 180).<0, 0, 1>)); 12.83856814 Theta Waves > restart; with(LinearAlgebra): with(plots): with(RealDomain): > deg:=Pi/180: > T:=<<0.690, 0.693, -0.211>|<0.719, -0.691, 0.079>|<- 0.0090, -0.206, -0.975>>: > B:=(r, t)-> T. 120 > p7:=plot(evalf(1/deg*arccos(B(0, 20). > evalf(1/deg*arccos(B(a, 0). A.4 The PISA Helix > restart; with(LinearAlgebra): with(plots): with(RealDomain); > deg:=Pi/180: > A:=<<0.69, 0.69, -0.21>|<0.72, -0.69, 0.083>|<-0.089, - 0.21, -0.97>>: > B:=(tau, rho)-> 121 [36, 11.6], [38, 19.7], [39, 14.2], [40, 12.7], [42, 18.6], [43, 10.4]], x=25..44, style=point, color=black): > sigma:=<<31, 0, 0>|<0, 54, 0>|<0, 0, 202>>: > csk:=(tau, rho)- >evalf(Transpose(A. > m:=tubeplot([csk(28, 0), dck(28, 0), k], numpoints=200, k=25..36, axes=boxed): n:=tubeplot([csk(19, 0), dck(19, 0), k], numpoints=200, k=35..44, axes=boxed): > display(m, n); > p:=polyhedraplot(CS, symbol=point, axes=boxed): > display(M, N, p); 122 A.5 The Calculation of αB and βB Only the residue of A29 is shown here for an example. > restart: with(LinearAlgebra): with(RealDomain): > deg:=Pi/180: B:= A.6 Calculation of Torsion Angles 123 Only the calculation of torsion angles between I42 and L43 is shown here for an example. Please note that the continuity problem here is not considered here, i.e. the combination of torsion angles is random. See Chapter 5 for details. > restart: with(LinearAlgebra): with(RealDomain): > deg:=Pi/180: a1:=37.9: b1:=27.6: a2:=116.2: b2:=25.2: > u1u2:=evalf(cos(59*deg)): u1B1:=evalf(cos(15*deg)*cos(a1*deg)*sin(b1*deg)+sin(15*deg) *cos(b1*deg)): u2B1:=evalf(cos(44*deg)*cos(a1*deg)*sin(b1*deg)- sin(44*deg)*cos(b1*deg)): u2u3:=evalf(cos(70*deg)): u3u4:=evalf(cos(65*deg)): u2B2:=u2B1: u3B2:=evalf(cos(50*deg)*cos(a2*deg)*sin(b2*deg)- sin(50*deg)*cos(b2*deg)): u4B2:=evalf(cos(15*deg)*cos(a2*deg)*sin(b2*deg)+sin(15*deg) *cos(b2*deg)): > v1v2:=u1u2: v2v3:=u2B1: v1v3:=u1B1: x1:= -v1v3+v1v2*v2v3: y1:= sqrt(1-v1v2^2-v2v3^2-v1v3^2+2*v1v2*v2v3*v1v3): c1:=x1/sqrt(x1^2 + y1^2): phi1:= evalf(sign(y1)/deg*arccos(c1)): > v1v2:=-u2B1: v2v3:=u2u3: v1v3:=-u3B2: x2:= -v1v3+v1v2*v2v3: y2:= sqrt(1-v1v2^2-v2v3^2-v1v3^2+2*v1v2*v2v3*v1v3): c2:=x2/sqrt(x2^2+y2^2): phi2:= evalf(sign(y2)/deg*arccos(c2)): > phi1+phi2; -phi1+phi2; phi1-phi2; -phi1-phi2; 304.3409884 -20.2470074 20.2470074 -304.3409884 > v1v2:=u2u3: v2v3:=u3B2: v1v3:=u2B2: x3:= -v1v3+v1v2*v2v3: y3:= sqrt(1-v1v2^2-v2v3^2-v1v3^2+2*v1v2*v2v3*v1v3): c3:=x3/sqrt(x3^2 + y3^2): psi1:= evalf(sign(y3)/deg*arccos(c3)): > v1v2:=-u3B2: v2v3:=u3u4: v1v3:=-u4B2: x4:= -v1v3+v1v2*v2v3: y4:= -sqrt(1-v1v2^2-v2v3^2-v1v3^2+2*v1v2*v2v3*v1v3): c4:=x4/sqrt(x4^2 + y4^2): psi2:= evalf(sign(y4)*arccos(c4)/deg): 124 > psi1+psi2; -psi1+psi2; psi1-psi2; -psi1-psi2; 41.06243479 -123.3047550 123.3047550 -41.06243479 A.7 Spectral Deconvolution This program reads the 1D NMR data file and deconvolutes it into different frequencies. > restart; with(LinearAlgebra): with(plots): with(stats): > csnh:=146: # Chemical shift. > Rnh:=[seq((6+i*2)/2, i=1..4)]: # Half of linewidth. > Anh:=[seq((1.8+i*0.2)*10^8, i=1..4)]: # Amplitude. > mnh:=Matrix(4,4,(i, j)->[Anh[i], Rnh[j]]): nnh:=seq(seq(mnh[i, j], i=1..4), j=1..4): # Sequence of the combination of amplitude and linewidth/2. > for k from 1 to 16 do NH[k]:=nnh[k][1]*(nnh[k][2]^2/(nnh[k][2]^2+(350- (350+100)*i/1024-csnh)^2)): od: # The equations of Lorentzian lineshape with all possible combinations > csnhp:=156: > Rnhp:=[seq((6+i*2)/2, i=1..4)]: > Anhp:=[seq((2.8+i*0.2)*10^8, i=1..4)]: > mnhp:=Matrix(4,4,(i, j)->[Anhp[i], Rnhp[j]]): nnhp:=seq(seq(mnhp[i, j], i=1..4), j=1..4): > for k from 1 to 16 do NHp[k]:=nnhp[k][1]*(nnhp[k][2]^2/(nnhp[k][2]^2+(350- (350+100)*i/1024-csnhp)^2)): od: > csnhn:=167: > Rnhn:=[seq((10+i*3)/2, i=1..4)]: > Anhn:=[seq((1.4+i*0.2)*10^8, i=1..4)]: > mnhn:=Matrix(4,4,(i, j)->[Anhn[i], Rnhn[j]]): nnhn:=seq(seq(mnhn[i, j], i=1..4), j=1..4): 125 > for k from 1 to 16 do NHN[k]:=nnhn[k][1]*(nnhn[k][2]^2/(nnhn[k][2]^2+(350- (350+100)*i/1024-csnhn)^2)): od: > csam:=98: > Rnam:=8: > Anam:=0.7*10^8: > Nam:=Anam*(Rnam^2/(Rnam^2+(350-(350+100)*i/1024- csam)^2)): > SS:=[seq(seq(seq([NH[k]+NHp[j]+NHN[m]+Nam, evalf(log((1+1/1.8)*Int(NH[k], i=200..700)/(Int(NHN[m], i=200..700)+Int(NHp[j], i=200..700))), 4), [[nnh[k][1]/10^8, 2*nnh[k][2]] , [nnhp[j][1]/10^8, 2*nnhp[j][2]], [nnhn[m][1]/10^8, 2*nnhn[m][2]]]], k=1..16), j=1..16), m=1..16)]: > NMR:=readdata("C:\\Maple_files\\pH7.txt", [float, float]): # Note here this is the NMR data file needed to be input. data:=seq([i, NMR[i, 2]+2.5*10^7], i=1..1024): Noise:=seq(NMR[i, 2]+2.5*10^7, i=1..380): a:=0: NSD:=describe[standarddeviation[1]]([Noise]); for j from 1 to 4096 do b:=seq(SS[j][1], i=1..1024): DS:=seq(b[m]-data[m, 2], m=360..520): DF:=describe[standarddeviation[1]]([DS]); if DF<1.5*NSD then a:=op([a, SS[j][2]]): end if: od: > Num:=nops([a]); > d:=[seq(a[i], i=2..Num)]: > AV:=evalf(describe[mean](d), 4); SD:=evalf(describe[standarddeviation[1]](d), 4); > p:=[seq([i, d[i]], i=1..(Num-1))]: > m:=plot(p, x=1..Num, style=point): n:=plot(AV, x=1..Num, color=blue): p:=plot(AV-SD, x=1..Num, color=black): q:=plot(AV+SD, x=1..Num, color=black): > display(m, n, p, q); 126 A.8 15N, 1H, 15N-1H PISA simulation This program simulates the (15N, 1H, 15N-1H) 3D NMR spectra at various tilt angles. > restart: with(LinearAlgebra): with(plots): with(RealDomain); > deg:=Pi/180: > sigma11:=31: sigma22:=54: sigma33:=202: > R1:=x-> evalf(<<1, 0, 0>|<0, cos(x*deg), sin(x*deg)>|<0, -sin(x*deg), cos(x*deg)>>); R2:=x-> evalf(< 127 0. 0.406018347000000058 1.50422444280000001 A := -0.406018347000000058 0. -1.20448122099999999 -1.50422444280000001 1.20448122099999999 0. > B:=A/Norm(A, 2); 0. 0.206169302766098850 0.763819928008818483 B := -0.206169302766098850 0. -0.611615350299501093 -0.763819928008818483 0.611615350299501093 0. > a:=<0.612, 0.764, -0.206>; 0.612 a := 0.764 -0.206 > CaC:=evalf(R1(-65).R3(70).<1.53, 0, 0>); 0.523290818500000032 CaC := 0.607610830699999992 -1.30302563199999999 > CN:=evalf(R1(-65).R3(70).R1(-40).R3(65).<1.34, 0, 0>); -0.680530200500000015 CN := -0.348123970299999974 -1.10058545699999999 > NCa:=evalf(R1(-65).R3(70).R1(- 40).R3(65).R1(180).R3(59).<1.45, 0, 0>); 0.384108033700000018 NCa := 0.501171344500000004 -1.30529242000000001 > v:=(CaC+CN+NCa)/VectorNorm((CaC+CN+NCa), 2); 0.0598141486589321912 v := 0.200548302313223903 -0.977856147980806334 > CaC+CN+NCa; 0.226868651700000034 0.760658204900000023 -3.70890350899999976 > m:=1/2*(evalf(cot(100/2*deg))*CrossProduct(a, v)+v- DotProduct(a, v)*a); -0.385924880625257816 m := 0.196720642445611438 -0.416306840084920748 > r:=m/VectorNorm(m, 2); 128 -0.642362548005504186 r := 0.327436709760485834 -0.692932578267066224 > HAF:=<-r|CrossProduct(a, -r)|a>; 0.642362548005504186 0.4619485276 0.612 HAF := -0.327436709760485834 -0.5564014228 0.764 0.692932578267066224 -0.6911562531 -0.206 > N:=evalf(R3(-134).Transpose(<<0, 0,1>|<1, 0, 0>|<0, 1, 0>>)); 0.719339800500000016 0. -0.694658370299999994 N := -0.694658370299999994 0. -0.719339800500000016 0. 1. 0. > C:=evalf(Transpose(N).HAF, 4); 0.689500000000000000 0.718799999999999996 -0.0904800000000000050 C := 0.692899999999999960 -0.691200000000000037 -0.205999999999999988 -0.210699999999999998 0.0793500000000000039 -0.974700000000000010 > NH_mf:=evalf(<-1.024*cos(63*deg), -1.024*sin(63*deg), 0>); -0.4648862715 NH_mf := -0.9123906809 0. > NH_haf:=Transpose(HAF).NH_mf; 0.000124672676506731862 NH_haf := 0.292901944381341983 -0.981576878365600036 > B0:= 129 CS := 6.543711130cos ( 0.01745329252 ρ )2 − 6.543711130cos ( 0.01745329252 ρ )2 cos() 0.01745329252 τ 2 − 27.75122082cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ + 27.75122082cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ 2 + 63.68562444sin ( 0.01745329252 τ ) cos() 0.01745329252 ρ cos() 0.01745329252 τ + 43.08765574 + 151.3657720cos ( 0.01745329252 τ )2 − 19.90082567sin ( 0.01745329252 τ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ > DC:=simplify(1/2*10.735*(3*(B0.NH_haf/VectorNorm(NH_haf, 2))^2-1)); DC := −1.316571304cos ( 0.01745329252 ρ )2 + 1.316571304cos ( 0.01745329252 ρ )2 cos() 0.01745329252 τ 2 + 0.001120788040cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ − 0.001120788040cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ 2 − 0.003755999735sin ( 0.01745329252 τ ) cos() 0.01745329252 ρ cos() 0.01745329252 τ − 4.050928457 + 13.46935669cos ( 0.01745329252 τ )2 − 8.824224010sin ( 0.01745329252 τ ) sin() 0.01745329252 ρ cos()0.01745329252 τ > BH:=Transpose(R1(180)).Transpose(R2(287)).(C.B0); BH := τπ ρπ τπ ρπ 0.0000968783 sin cos + 0.2860395637 sin sin 180 180 180 180 τπ − 0.9585640375 cos 180 τ π ρ π τ π ρπ −0.6929000000 sin cos + 0.6912000000 sin sin 180 180 180 180 τπ + 0.2060000000 cos 180 τ π ρ π τ π ρπ 0.7209748475 sin cos + 0.6641921638 sin sin 180 180 180 180 τπ + 0.1984482463 cos 180 > HCS:=simplify(Transpose(BH).<<3, 0, 0>|<0, 8, 0>|<0, 0, 17>>.(BH)); 130 HCS := 1.110477400cos ( 0.01745329252 ρ )2 − 1.110477400cos ( 0.01745329252 ρ )2 cos() 0.01745329252 τ 2 + 8.618685281cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ − 8.618685281cos ( 0.01745329252 ρ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ 2 + 2.580235016sin ( 0.01745329252 τ ) cos() 0.01745329252 ρ cos() 0.01745329252 τ + 11.56708633 − 7.801574279cos ( 0.01745329252 τ )2 + 5.114535949sin ( 0.01745329252 τ ) sin() 0.01745329252 ρ cos() 0.01745329252 τ # Use parametric plot to plot the PISA wheels. > p1:=plot3d([CS, DC, HCS], rho=-180..180, tau=40..40.0000001, numpoints=1000, color=red, axes=boxed): p2:=plot3d([CS, DC, HCS], rho=-180..180, tau=10..10.0000001, numpoints=1000, color=blue, axes=boxed): p3:=plot3d([CS, DC, HCS], rho=-180..180, tau=20..20.0000001, numpoints=1000, color=black, axes=boxed): p4:=plot3d([CS, DC, HCS], rho=-180..180, tau=60..60.0000001, numpoints=1000, color=green, axes=boxed): p5:=plot3d([CS, DC, HCS], rho=-180..180, tau=90..90.0000001, numpoints=1000, color=cyan, axes=boxed): > display(p1, p2, p3, p4, p5); 0 > evalf(Transpose(R1(180)).Transpose(R2(287))); 0.292371704700000013 0. 0.956304755999999978 0. -1. 0. 0.956304755999999978 0. -0.292371704700000013 > evalf(R2(107).R3(180)); 0.292371704700000013 0. 0.956304755999999978 0. -1. 0. 0.956304755999999978 0. -0.292371704700000013 131 APPENDIX B CHEMICAL SYNTHESES All the synthetic procedures of the chemicals listed below can be found in the literature. To help other colleagues use these methods later, here I focus on the practical way and the things needing to be attentive rather than the method itself. B.1 Fmoc-15N-AA-OH References: (Chang et al. 1980) and (Antherton and Sheppard 1989). Mostly we follow Chang’s method using dioxane-water system although sometimes acetone-water system seems to give a high yield. Figure B.1 shows the experimental procedure. Based on my experience, dioxane-water worked very well. About 2mmol scale is good for our synthesis so a 50ml flask is fine. The reaction is very friendly so that a complicated setup is not needed. A NaCl-ice bath and a flask with a stopper work perfectly. You do not have to remove the cold bath since the reaction needs one hour at low temperature and about 6 hours at room temperature. It takes about one hour for the bath to reach room temperature. Fmoc-OSu is not very soluble in dioxane so you have to divide your total volume of dixone into three portions and use them separately to dissolve the whole Fmoc-OSu. The most important part for this experiment that I feel is that the pH value of the reaction mixture should be checked frequently by pH test paper after the adding of Fmoc-OSu is finished. It turns out the mixture is acidic after the reaction goes for a while. Add a few drops of 1M NaOH to keep pH always around 9.0. This can make a big difference without doing it. By adding concentrated basic solution it avoids 132 changing the solvent phase separation. The first extraction should be exhaustive as this is the step to remove the side products and it determines the purity of the final product. Acidification and extraction should all be done in a separation funnel. In the case of extracting Fmoc-Trp-OH, the phase separation is very slow so be patient. As far as I know, EtOAc is the best extraction solvent. Usually the product is very pure after the recrystallization in EtOAc-hexane. Fmoc-Ile-OH, Fmoc-Leu-OH and other hydrophobic amino acids form very nice snowflake crystals while amino acids such Fmoc-Gly-OH and Fmoc-Trp-OH are just powder. It is normal that Fmoc-Trp-OH is a bit yellowish. The final product can be checked by thin layer chromatography (TLC) and visualized under UV because of the aromatic Fmoc group. The develop solvent for TLC is CH3OH:CHCl3 (10:1). Fmoc-AA-OH also absorbs I2. Free amino acids can be seen in dark blue color with ninhydrin under heat. If one more spot is seen on the TLC plate, that indicates the side product from Fmoc-OSu. Usually it is not easy to remove it by recrystallization. Using fast silica gel chromatography (FSGC) can obtain the pure target product. However, special training is required to use FSGC. The elution solution is CH3OH:CHCl3 (20:1). Figure B.1. The flowchart of the synthesis of Fmoc-AA-OH. 133 B.2 Fmoc-15N(δ1 or ε2)-(Trt)-His-OH Reference: Barlos et al., 1982. The synthesis procedure is shown in Figure B.2. Since the 15Νδ1-labeled histidine from CIL is a monohydrated HCl salt, it needs to be neutralized in solution with 0.5N NaOH followed by lyophilization. The first step synthesis is a no-water experiment. Dry CH2Cl2 and Et3N should be distilled with CaH2 present because there is fairly amount of water in CH2Cl2 and Et3N. In the purification procedure, usage of CHCl3 should be avoided as I found by TLC that CHCl3 could dissolve some product in it. Instead, ethyl ether is much better and I did not find any product in it. Most of the reaction side products are in the ether phase. Another modification in the isolation step is that I used 10% Na2CO3 instead of Et3N to adjust the pH value. The yield for the first step is almost quantitative. The second step follows A.2.1 procedure. The total yield is 75-80%. O H3C O Si C O H +NCH - 3 C O H3C CH HN CH 2 H3C Cl CH2Cl2 1) Trt-Cl Si + CH2 N H3C Cl Reflux 2) CH3OH NH N NH O O + - H3 NCHC O Fmoc-N CH C OH CH2 Fmoc-OSu CH2 N 10% Na2CO3 N N N Trt Trt Figure B.2. The synthesis of Fmoc-N-His-(Trt)-OH. 134 B.3 H13CO-Val-OH Reference: Sheehan et al., 1958. As mentioned in the paper, 98% formic acid be used to retain the Cα chirality. Ice-salt bath can be used in order to get a lower temperature inside the flask. In the isolation step, the reaction mixture should be transferred to a larger flask as foam is easily formed during rotary evaporation. Again, the purity of the final product can be checked by TLC. Be sure to wear gloves, lab coat and goggles and all the experiments should be done in the hood. B.4 15N-Amantadine Reference: (Stetter et al. 1960). The synthesis is illustrated in Figure B.3. In the first step, CH3CN is not only a solvent but also a reactant. When conc. H2SO4 is added, it produces heat and the solution turns into brown. Br The mixture is stirred at r.t. for 24 huours. Pour water into the reaction solution. 1 Adjust pH by 5M NaOH. + 15 CH3CN Isolate 2 by filtration 2, colorless crytalline powder cat. H2SO4 Reflux 2 in NaOH and digol solution for 5 O hours.Pour the hot solution into water and H exact aqueous phase by ethyl ether. Dry N15 CH 3 the orgainc phase after combination overnight by KOH pellets. 2 Introduce HCl gas into the ether solution. Collect all the precipitate. 1) NaOH, digol 2) HCl, ether Recrystallization of the amantadine powder in absolute ethyl alcohol 15 + - and ether solution NH3 Cl 3, small needle cystal 3 Figure B.3. The synthesis of 15N-amantadine. 135 B.5 17O Labeled D-Leucine and Fmoc-N-D-Leu-C17O17OH Reference: (Steinschneider et al. 1981). 17 17 D-Leucine is O labeled in H2 O by acid catalyzed exchange (Figure A.2.4). Firstly, dry HCl gas can be produced by adding concentrated H2SO4 to NaCl powder. 2NaCl(s) + H2SO4(conc.) =Na2SO4(s) +2HCl(g) Note that HCl solution is avoided here to retain the water 17O enrichment. Add D- 17 17 Leucine (262mg, 2mmol) and 70% O enriched H2 O (0.5 g, 28mmol) into a small sealing vial. Use a glass pipet to deliver dry HCl gas into the glass vial. Note the tip should NOT be soaked in the solution. Water absorbs HCl fast and efficiently. Use a wet pH test paper to check whether the HCl gas is out. Dip the inside solution with a capillary and check the pH of the solution. If it is below pH 1, it indicates that it is time to stop blowing HCl gas. Seal the vial by flame. Put it into a ~100 oC oven for one day. Take out the sample from the oven and put it into a 4oC refrigerator. After the amino acid crystallized, stir it well and put back the oven again. Repeat this procedure at least three times as D-leucine does not dissolve well in water. In the end, put the sample into the refrigerator until it cools down, centrifugate the sample at 4000 rpm and suck out all the water with a glass pipet. Do not use vacuum to recycle the water. Wash the powder in the vial with a small amount of acetone 3 times and dry the solid in vacuo. Please also keep in mind this procedure is only suitable for leucine. Glycine, for instance, is much more soluble in water. Thus, the procedure could be different: you can add more amount of glycine in water although you have to sacrifice the enrichment; you do not have to do recrystalization during exchange. Fmoc-N-D-Leu-C17O17OH is synthesized as A.2.1. In order to avoid back exchange, the reaction should not take more two hours. Mass spectrum shows that the 17O enrichment doesn’t decrease even in the fairly basic aqueous environment in a short period of time. 136 O HO OH OH + + + - 17 + + OH H3 NCHCO H3 O H3 NCHC H NCHC 17 H 3 CH CH2 O 17 2 CH2 OH CHCH H CHCH3 3 + CHCH H 3 CH CH3 3 CH3 17OH 17 - 17 excess H 17O+ + OH Cl O 3 H3 NCHC + 17 17 H NCHC OH CH2 OH 3 repeated exchange CH CHCH3 2 H 17O CHCH CH3 2 3 CH3 Figure B.4. The mechanism of acid-catalyzed exchange. B.6 Cleavage of the M2 TM peptide Peptide is cleaved off the resin with a cleavage mixture of triflouroacetic acid containing 2.5% water, 1.25% ethanedithiol, 1.25% thioanisole for 1 hr in icebath and for 1 hr at room temperature. Typically, add 500 uL 1,2-ethanedithiol and 500 uL water to 1 g of peptide resin in a round-bottomed flask with a magnetic stir bar. Add 19 mL of cold TFA and stir at room temperature for 2 hr with the flask stoppered. The whole mixture turns into a dark brown color. Keep in mind that add water, EDT and thioanisole before adding neat TFA. You can adjust the amounts of cleavage reagents to the actual weight of the peptide resin. Filter through medium frit sintered glass funnel, rinse the resin with a small amount of TFA and add the rinses to the filtrate. Precipitate the peptide from the filtrate by addition of more than tenfold excess of cold ether. Collect the precipitate by centrifugation. Re-suspend in ether and collect the peptide by centrifuagtion three times. Dry the peptide under high vacuum for couple of hours. Ethanedithiol and thioanisole are stenchful chemicals so all the experiments should be done in the hood. Gloves and pipets should be left in hood for a couple of days and seal them before dump them into the garbage can. 137 APPENDIX C PERMISSION LETTERS Permissions Letter Ref # 04-1631 DATE: Friday, September 24, 2004 TO: Jun Hu National High Magnetic Field Laboratory 1800 E. Paul Dirac Dr. Tallahassee, FL 32310 FROM: Elizabeth Sandler, Rights and Permissions RE: Your request for permission dated 09/15/04 Regarding your request, we are pleased to grant you non-exclusive, non-transferable permission, but limited to print and microform formats only, and provided that you meet the criteria below. Such permission is for one-time use and therefore does not include permission for future editions, revisions, additional printings, updates, ancillaries, customized forms, any electronic forms, braille editions, translations, or promotional pieces. We must be contacted for permission each time such use is planned. This permission does not apply to figures / artwork that are credited to non-AAAS sources. This permission does not include the right to modify AAAS material. Print the required copyright credit line on the first page that the material appears: "Reprinted (abstracted/excerpted) with permission from [FULL REFERENCE CITATION]. Copyright [YEAR] AAAS." Insert the appropriate information in place of the capitalized words. Permission is limited to the single title specified or single edition of the publication. 138 AAAS must publish the full paper prior to use of any text. AAAS does not supply photos or artwork. Use of the AAAS material must not imply any endorsement by the American Association for the Advancement of Science. This permission is not valid for the use of the AAAS and/or SCIENCE logos. Permission is valid for use of the following AAAS material only: Fig 4 from Doyle et al., SCIENCE 280:69-77 (1998) In the following work only: Doctoral dissertation , Structure-Function Correlation of the M2 Proton Channel Characterized by Solid-State Nuclear Magnetic Resonance Spectroscopy (Florida State University)-in all languages AAAS agrees that UMI may supply copies of the dissertation on demand. 139 140 141 BIBLIOGRAPHY Abramson J, Smirnova I, Kasho V, Verner G, Kaback HR, Iwata S. 2003. Structure and. Membrane protein folding and stability: physical principles. Annu. Rev. Biophys. Biomol. Struct. 28:319-65. Abramson J, Smirnova I, Kasho V, Verner G, Kaback HR, Iwata S. 2003. Structure and mechanism of the lactose permease of Escherichia coli. Science 301(5633):610- 615. Agmon N. 1995. The Grotthuss Mechanism. Chem. Phys. Lett. 244(5-6):456-462. Aldrich PE, Hermann EC, Meier WE, Paulshock M, Prichard WW, Snyder JA, Watts JC. 1971. Antiviral agents. 2. Structure-activity relationships of compounds related to 1-adamantanamine. J. Med. Chem. 14(6):535-43. Alemany LB, Grant DM, Alger TD, Pugmire RJ. 1983. Cross Polarization and Magic Angle Sample Spinning Nmr-Spectra of Model Organic-Compounds .3. Effect of the C-13-H-1 Dipolar Interaction on Cross Polarization and Carbon-Proton Dephasing. J. Am. Chem. Soc. 105(22):6697-6704. Andersson H, von Heijne G. 1994. Positively charged residues influence the degree of SecA dependence in protein translocation across the E. coli inner membrane. FEBS Lett. 347(2-3):169-72. Antherton E, Sheppard RC. 1989. Solid-Phase Peptide Synthesis: a Practical Approach. Rickwood D, Hames BD, editors. Eynsham, Oxford, England: IRL Press at Oxford University Press. Asbury T, Bertram R, Achuthan S, Quine JR, Hu J, Cross TA. In preparation. Strucuture modeling using PISEMA. Astrahan P, Kass I, Cooper MA, Arkin IT. 2004. A novel method of resistance for influenza against a channel-blocking antiviral drug. Proteins 55(2):251-7. 142 Barlos K, Papaioannou D, Theodoropoulos D. 1982. Efficient One-Pot Synthesis of N- Trityl Amino-Acids. J. Org. Chem. 47(7):1324-1326. Belrhali H, Nollert P, Royant A, Menzel C, Rosenbusch JP, Landau EM, Pebay-Peyroula E. 1999. Protein, lipid and water organization in bacteriorhodopsin crystals: a molecular view of the purple membrane at 1.9 A resolution. Structure Fold Des. 7(8):909-17. Bertram R, Asbury T, Fabiola F, Quine JR, Cross TA, Chapman MS. 2003. Atomic refinement with correlated solid-state NMR restraints. J. Magn. Reson. 163(2):300-9. Blasco T, Perez-Pariente J, Kolodziejski W. 1997. A solid-state NMR study of the molecular sieve VPI-5 synthesized in the presence of a CTABr surfactant. Solid State Nucl. Magn. Reson. 8(3):185-94. Bowie JU. 1997. Helix packing in membrane proteins. J. Mol. Biol. 272(5):780-9. Braun P, von Heijne G. 1999. The aromatic residues Trp and Phe have different effects on the positioning of a transmembrane helix in the microsomal membrane. Biochemistry 38(30):9778-82. Brenneman MT, Cross TA. 1990. A Method for the Analytic Determination of Polypeptide Structure Using Solid-State Nuclear Magnetic-Resonance - the Metric Method. J. Chem. Phys. 92(2):1483-1494. Bryce DL, Bernard GM, Gee M, Lunmsden MD, Eichele K, Wasylishen RE. 2001. Practical aspects of modern routine solid-state multinuclear magnetic resonance spectroscopy: one-dimensional experiments. Can. J. Anal. Sci. Spect.(46):46-82. Burykin A, Kato M, Warshel A. 2003. Exploring the origin of the ion selectivity of the KcsA potassium channel. Proteins 52(3):412-26. Chakrabarti N, Tajkhorshid E, Roux B, Pomes R. 2004. Molecular basis of proton blockage in aquaporins. Structure (Camb) 12(1):65-74. Chang CD, Waki M, Ahmad M, Meienhofer J, Lundell EO, Haug JD. 1980. Preparation and properties of Nalpha-9-fluorenylmethyloxycarbonylamino acids bearing tert.- butyl side chain protection. Int. J. Pept. Protein. Res. 15(1):59-66. Charifson PS, Hiskey RG, Pedersen LG. 1990. Construction and Molecular Modeling of Phospholipid Surfaces. J. Comput. Chem. 11(10):1181-1186. 143 Cheung TTP, Yaris R. 1980. Dynamics of Cross Relaxation in Modulated Systems - Application to Nuclear Magnetic Double-Resonance of Glassy-Polymers. J. Chem. Phy. 72(6):3604-3616. Chiu ML, Nollert P, Loewen MC, Belrhali H, Pebay-Peyroula E, Rosenbusch JP, Landau EM. 2000. Crystallization in cubo: general applicability to membrane proteins. Acta Crystallogr. D Biol. Crystallogr. 56 ( Pt 6):781-4. Chizhmakov IV, Geraghty FM, Ogden DC, Hayhurst A, Antoniou M, Hay AJ. 1996. Selective proton permeability and pH regulation of the influenza virus M2 channel expressed in mouse erythroleukaemia cells. J. Physiol. 494 ( Pt 2):329- 36. Chizhmakov IV, Ogden DC, Geraghty FM, Hayhurst A, Skinner A, Betakova T, Hay AJ. 2003. Differences in conductance of M2 proton channels of two influenza viruses at low and high pH. J. Physiol. 546(Pt 2):427-38. Chou JJ, Kaufman JD, Stahl SJ, Wingfield PT, Bax A. 2002. Micelle-induced curvature in a water-insoluble HIV-1 Env peptide revealed by NMR dipolar coupling measurement in stretched polyacrylamide gel. J. Am. Chem. Soc. 124(11):2450-1. Ciampor F, Bayley PM, Nermut MV, Hirst EM, Sugrue RJ, Hay AJ. 1992a. Evidence that the amantadine-induced, M2-mediated conversion of influenza A virus hemagglutinin to the low pH conformation occurs in an acidic trans Golgi compartment. Virology 188(1):14-24. Ciampor F, Thompson CA, Grambas S, Hay AJ. 1992b. Regulation of Ph by the M2 Protein of Influenza-a Viruses. Virus Research 22(3):247-258. Cory DG, Ritchey WM. 1989. Inversion Recovery Cross-Polarization Nmr in Solid Semicrystalline Polymers. Macromolecules 22(4):1611-1615. Cross TA. 1986. Solid-State Nuclear-Magnetic-Resonance Approach for Determining the Structure of Gramicidin a without Model-Fitting. Biophys. J. 49(1):124-126. Cross TA, Opella SJ. 1983. Protein-Structure by Solid-State Nmr. J. Am. Chem. Soc. 105(2):306-308. Davies WL, Grunert RR, Haff RF, McGahen JW, Neumayer EM, Paulshock M, Watts JC, Wood TR, Hermann EC, Hoffmann CE. 1964. Antiviral Activity of 1- Adamantanamine (Amantadine). Science 144:862-3. 144 de Groot BL, Frigato T, Helms V, Grubmuller H. 2003. The mechanism of proton exclusion in the aquaporin-1 water channel. J. Mol. Biol. 333(2):279-93. Decoursey TE. 2003. Voltage-gated proton channels and other proton transfer pathways. Physiol. Rev. 83(2):475-579. Demco DE, Tegenfeldt J, Waugh JS. 1975. Dynamics of Cross Relaxation in Nuclear Magnetic Double-Resonance. Physical Review B 11(11):4133-4151. Denny JK, Wang J, Cross TA, Quine JR. 2001. PISEMA powder patterns and PISA wheels. J. Magn. Reson. 152(2):217-26. Dolin R, Reichman RC, Madore HP, Maynard R, Linton PN, Webberjones J. 1982a. A Controlled Trial of Amantadine and Rimantadine in the Prophylaxis of Influenza- a Infection. New England Journal of Medicine 307(10):580-584. Dolin R, Reichman RC, Madore HP, Maynard R, Linton PN, Webber-Jones J. 1982b. A controlled trial of amantadine and rimantadine in the prophylaxis of influenza A infection. N. Engl. J. Med. 307(10):580-4. Dougherty DA. 1996. Cation-pi interactions in chemistry and biology: a new view of benzene, Phe, Tyr, and Trp. Science 271(5246):163-8. Doyle DA, Morais Cabral J, Pfuetzner RA, Kuo A, Gulbis JM, Cohen SL, Chait BT, MacKinnon R. 1998. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 280(5360):69-77. Duff KC, Ashley RH. 1992. The transmembrane domain of influenza A M2 protein forms amantadine-sensitive proton channels in planar lipid bilayers. Virology 190(1):485-9. Duff KC, Gilchrist PJ, Saxena AM, Bradshaw JP. 1994. Neutron diffraction reveals the site of amantadine blockade in the influenza A M2 ion channel. Virology 202(1):287-93. Edgcomb SP, Murphy KP. 2002. Variability in the pKa of histidine side-chains correlates with burial within proteins. Proteins 49(1):1-6. Engelman DM, Zaccai G. 1980. Bacteriorhodopsin is an inside-out protein. Proc Natl Acad Sci U S A 77(10):5894-8. Engh RA, Huber R. 1991. Accurate Bond and Angle Parameters for X-Ray Protein- Structure Refinement. Acta Crystallogr. Sec. A 47:392-400. 145 Ernst RR, Bodenhausen G, Wokaun A. 1987. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Rowlinson JS, editor. Oxford: Oxford University Press. 610 p. Fernandez C, Wuthrich K. 2003. NMR solution structure determination of membrane proteins reconstituted in detergent micelles. FEBS Lett. 555(1):144-50. Fillingame RH, Girvin ME, Fraga D, Zhang Y. 1992. Correlations of structure and function in H+ translocating subunit c of F1F0 ATP synthase. Ann. N Y Acad. Sci. 671:323-33; discussion 333-4. Fu D, Libson A, Miercke LJW, Weitzman C, Nollert P, Krucinski J, Stroud RM. 2002. Structure of a Glycerol-Conducting Channel and the Basis for Its Selectivity. Science 290:481-486. Fulber C, Demco DE, Blumich B. 1996. The influence of molecular motion on cross- polarization in cross-linked elastomers. Solid State Nucl. Mag. 6(3):213-223. Gandhi CS, Shuck K, Lear JD, Dieckmann GR, DeGrado WF, Lamb RA, Pinto LH. 1999. Cu(II) inhibition of the proton translocation machinery of the influenza A virus M2 protein. J. Biol. Chem. 274(9):5474-82. Garrett RH, Grisham CM. 1995. Biochemistry: Saunders College Publishing. 166 p. Garvan F. 2001. The Maple book. Boca Raton, Lodon, New York, Washington, D.C.: Chapman & Hall /CRC. Golubev NS, Denisov GS, Gindin VA, Ligay SS, Limbach HH, Smirnov SN. 1994. The Role of Short Hydrogen-Bonds in Mechanisms of Enzymatic Action. Journal of Molecular Structure 322:83-91. Grambas S, Hay AJ. 1992. Maturation of Influenza-a Virus Hemagglutinin - Estimates of the Ph Encountered During Transport and Its Regulation by the M2 Protein. Virology 190(1):11-18. Grelak RP, Clark R, Stump JM, Vernier VG. 1970. Amantadine-dopamine interaction: possible mode of action in Parkinsonism. Science 169(941):203-4. Gu ZT, Opella SJ. 1999. Two- and three-dimensional 1H/13C PISEMA experiments and their application to backbone and side chain sites of amino acids and peptides. J. Magn. Reson. 140(2):340-6. 146 Gullion T, Schaefer J. 1989. Rotational-Echo Double-Resonance Nmr. J. Magn. Reson. 81(1):196-200. Harbison G, Herzfeld J, Griffin RG. 1981. Nitrogen-15 chemical shift tensors in L- histidine hydrochloride monohydrate. J. Am. Chem. Soc. 103:4752-4754. Hay AJ. 1992. The action of adamantanamines against influenza A viruses: Inhibition of the M2 ion channel protein. Semin. Virol. 3:21-30. Hay AJ, Wolstenholme AJ, Skehel JJ, Smith MH. 1985. The molecular basis of the specific anti-influenza action of amantadine. Embo J. 4(11):3021-4. Hennig M, Geierstanger BH. 1999. Direct detection of a histidine-histidine side chain hydrogen bond important for folding of apomyoglobin. J. Am. Chem. Soc. 121(22):5123-5126. Henry GD, Sykes BD. 1994. Methods to study membrane protein structure in solution. Methods Enzymol. 239:515-35. Hestenes D. 1986. New Foundations for Classical Mechanics. Dordrecht/Norwell, MA: Kluwer Academic. Hille B. 1992. Ionic channels of excitable membranes: Sinauer Associates Inc. 607 p. Holsinger LJ, Lamb RA. 1991. Influenza virus M2 integral membrane protein is a homotetramer stabilized by formation of disulfide bonds. Virology 183(1):32-43. Holsinger LJ, Shaughnessy MA, Micko A, Pinto LH, Lamb RA. 1995. Analysis of the posttranslational modifications of the influenza virus M2 protein. J. Virol. 69(2):1219-25. Homans SW. 2004. NMR spectroscopy tools for structure-aided drug design. Angew. Chem. Int. Ed. Engl. 43(3):290-300. Hu W, Cross TA. 1995. Tryptophan hydrogen bonding and electric dipole moments: functional roles in the gramicidin channel and implications for membrane proteins. Biochemistry 34(43):14147-55. Hu W, Lee KC, Cross TA. 1993. Tryptophans in membrane proteins: indole ring orientations and functional implications in the gramicidin channel. Biochemistry 32(27):7035-47. 147 Huang TH, Bachovchin WW, Griffin RG, Dobson CM. 1984. High-resolution nitrogen- 15 nuclear magnetic resonance studies of alpha-lytic protease in solid state. Direct comparison of enzyme structure in solution and in the solid state. Biochemistry 23(25):5933-7. Hunkapiller MW, Smallcombe SH, Whitaker DR, Richards JH. 1973. Carbon nuclear magnetic resonance studies of the histidine residue in alpha-lytic protease. Implications for the catalytic mechanism of serine proteases. Biochemistry 12(23):4732-43. Igumenova TI, McDermott AE. 2003. Improvement of resolution in solid state NMR spectra with J-decoupling: an analysis of lineshape contributions in uniformly 13C-enriched amino acids and proteins. J. Magn. Reson. 164(2):270-85. Ilan B, Tajkhorshid E, Schulten K, Voth GA. 2004. The mechanism of proton exclusion in aquaporin channels. Proteins 55(2):223-8. Jiang Y, Lee A, Chen J, Cadene M, Chait BT, MacKinnon R. 2002. The open pore conformation of potassium channels. Nature 417(6888):523-6. Kao HM, Lii KH. 2002. The first observation of heteronuclear two-bond J-coupling in the solid state: crystal structure and solid-state NMR spectroscopy of Rb(4)(NbO)(2)(Si(8)O(21)). Inorg. Chem. 41(22):5644-6. Karplus M. 1963. Vicinal Proton Coupling in Nuclear Magnetic Resonance. J. Am. Chem. Soc. 85(18):2870-&. Kato N, Eggers HJ. 1969. Inhibition of uncoating of fowl plague virus by l- adamantanamine hydrochloride. Virology 37(4):632-41. Katona G, Andreasson U, Landau EM, Andreasson LE, Neutze R. 2003. Lipidic cubic phase crystal structure of the photosynthetic reaction centre from Rhodobacter sphaeroides at 2.35A resolution. J. Mol. Biol. 331(3):681-92. Ketchem RR, Hu W, Cross TA. 1993. High-resolution conformation of gramicidin A in a lipid bilayer by solid-state NMR. Science 261(5127):1457-60. Ketchem RR, Lee KC, Huo S, Cross TA. 1996. Macromolecular structural elucidation with solid-state NMR-derived orientational constraints. J. Biomol. NMR 8(1):1- 14. 148 Khademi S, O'Connell J, 3rd, Remis J, Robles-Colmenares Y, Miercke LJ, Stroud RM. 2004. Mechanism of ammonia transport by Amt/MEP/Rh: structure of AmtB at 1.35 A. Science 305(5690):1587-94. Kiefer H. 2003. In vitro folding of alpha-helical membrane proteins. Biochim. Biophys. Acta 1610(1):57-62. Kim S, Cross TA. 2002. Uniformity, ideality, and hydrogen bonds in transmembrane alpha-helices. Biophys. J. 83(4):2084-2095. Kim S, Cross TA. 2004. 2D solid state NMR spectral simulation of 3(10), alpha, and pi- helices. J. Magn. Reson. 168(2):187-93. Kolocouris N, Kolocouris A, Foscolos GB, Fytas G, Neyts J, Padalko E, Balzarini J, Snoeck R, Andrei G, De Clercq E. 1996a. Synthesis and antiviral activity evaluation of some new aminoadamantane derivatives. 2. J. Med. Chem. 39(17):3307-18. Kolocouris N, Kolocouris A, Foscolos GB, Fytas G, Neyts J, Padalko E, Balzarini J, Snoeck R, Andrei G, DeClercq E. 1996b. Synthesis and antiviral activity evaluation of some new aminoadamantane derivatives .2. Journal of Medicinal Chemistry 39(17):3307-3318. Kolodziejski W, Klinowski J. 2002. Kinetics of cross-polarization in solid-state NMR: A guide for chemists. Chem. Rev. 102(3):613-628. Kovacs FA, Cross TA. 1997. Transmembrane four-helix bundle of influenza A M2 protein channel: structural implications from helix tilt and orientation. Biophys. J. 73(5):2511-7. Kovacs FA, Denny JK, Song Z, Quine JR, Cross TA. 2000. Helix tilt of the M2 transmembrane peptide from influenza A virus: an intrinsic property. J. Mol. Biol. 295(1):117-25. Koynova R, Caffrey M. 1998. Phases and phase transitions of the phosphatidylcholines. Biochimica Et Biophysica Acta-Reviews on Biomembranes 1376(1):91-145. Krause JA, Baures PW, Eggleston DS. 1991. Histidyl conformations and short N-H...N hydrogen bonds: structure of D,L-histidyl-L,D-histidine pentahydrate. Acta. Crystallogr. B 47 ( Pt 4):506-11. 149 Krueger-Koplin RD, Sorgen PL, Krueger-Koplin ST, Rivera-Torres IO, Cahill SM, Hicks DB, Grinius L, Krulwich TA, Girvin ME. 2004. An evaluation of detergents for NMR structural studies of membrane proteins. J. Biomol. NMR 28(1):43-57. Lamb RA, Choppin PW. 1981. Identification of a second protein (M2) encoded by RNA segment 7 of influenza virus. Virology 112(2):729-37. Lamb RA, Lai CJ, Choppin PW. 1981. Sequences of mRNAs derived from genome RNA segment 7 of influenza virus: colinear and interrupted mRNAs code for overlapping proteins. Proc. Natl. Acad. Sci. U S A 78(7):4170-4. Lamb RA, Zebedee SL, Richardson CD. 1985. Influenza virus M2 protein is an integral membrane protein expressed on the infected-cell surface. Cell 40(3):627-33. Lancaster CR. 2003. The role of electrostatics in proton-conducting membrane protein complexes. FEBS Lett. 545(1):52-60. Landau EM, Rosenbusch JP. 1996. Lipidic cubic phases: a novel concept for the crystallization of membrane proteins. Proc. Natl. Acad. Sci. U S A 93(25):14532- 5. Lear JD. 2003. Proton conduction through the M2 protein of the influenza A virus; a quantitative, mechanistic analysis of experimental data. FEBS Lett. 552(1):17-22. Levitt MH. 2001. Spin Dynamics - Basics of Nuclear Magnetic Resonance: John Wiley & Sons, LTD. 686 p. Lin TI, Schroeder C. 2001. Definitive assignment of proton selectivity and attoampere unitary current to the M2 ion channel protein of influenza A virus. J. Virol. 75(8):3647-56. LoGrasso PV, Moll F, 3rd, Cross TA. 1988. Solvent history dependence of gramicidin A conformations in hydrated lipid bilayers. Biophys. J. 54(2):259-67. Luca S, Heise H, Baldus M. 2003. High-resolution solid-state NMR applied to polypeptides and membrane proteins. Acc. Chem. Res. 36(11):858-65. Luecke H, Schobert B, Richter HT, Cartailler JP, Lanyi JK. 1999. Structure of bacteriorhodopsin at 1.55 A resolution. J. Mol. Biol. 291(4):899-911. Lundstrom K. 2004. Structural genomics on membrane proteins: mini review. Comb. Chem. High. Throughput Screen 7(5):431-9. 150 Mai W, Hu W, Wang C, Cross TA. 1993. Orientational Constraints as 3-Dimensional Structural Constraints from Chemical-Shift Anisotropy - the Polypeptide Backbone of Gramicidin-a in a Lipid Bilayer. Protein Sci. 2(4):532-542. Marassi FM, Opella SJ. 2000. A solid-state NMR index of helical membrane protein structure and topology. J. Magn. Reson. 144(1):150-5. Marassi FM, Opella SJ. 2002. Using pisa pies to resolve ambiguities in angular constraints from PISEMA spectra of aligned proteins. J. Biomol. NMR. 23(3):239- 42. Marassi FM, Opella SJ. 2003. Simultaneous assignment and structure determination of a membrane protein from NMR orientational restraints. Protein Sci. 12(3):403-11. Martin RW, Zilm KW. 2003. Preparation of protein nanocrystals and their characterization by solid state NMR. J. Magn. Reson. 165(1):162-74. Massiot D, Fayon F, Alonso B, Trebosc J, Amoureux JP. 2003. Chemical bonding differences evidenced from J-coupling in solid state NMR experiments involving quadrupolar nuclei. J. Magn. Reson. 164(1):160-4. Mehring M. 1983. Principles of High Resolution NMR in Solids. Berlin Heridelberg New York: Springer-Verlag. Mesleh MF, Lee S, Veglia G, Thiriot DS, Marassi FM, Opella SJ. 2003. Dipolar waves map the structure and topology of helices in membrane proteins. J. Am. Chem. Soc. 125(29):8928-35. Mesleh MF, Opella SJ. 2003. Dipolar Waves as NMR maps of helices in proteins. J. Magn. Reson. 163(2):288-99. Mesleh MF, Veglia G, DeSilva TM, Marassi FM, Opella SJ. 2002. Dipolar waves as NMR maps of protein structure. J. Am. Chem. Soc. 124(16):4206-7. Mimms LT, Zampighi G, Nozaki Y, Tanford C, Reynolds JA. 1981. Phospholipid vesicle formation and transmembrane protein incorporation using octyl glucoside. Biochemistry 20(4):833-40. Moll F, 3rd, Cross TA. 1990. Optimizing and characterizing alignment of oriented lipid bilayers containing gramicidin D. Biophys. J. 57(2):351-62. Morais-Cabral JH, Zhou Y, MacKinnon R. 2001. Energetic optimization of ion conduction rate by the K+ selectivity filter. Nature 414(6859):37-42. 151 Mould JA, Drury JE, Frings SM, Kaupp UB, Pekosz A, Lamb RA, Pinto LH. 2000a. Permeation and activation of the M2 ion channel of influenza A virus. J. Biol. Chem. 275(40):31038-50. Mould JA, Li HC, Dudlak CS, Lear JD, Pekosz A, Lamb RA, Pinto LH. 2000b. Mechanism for proton conduction of the M(2) ion channel of influenza A virus. J Biol Chem 275(12):8592-9. Mould JA, Paterson RG, Takeda M, Ohigashi Y, Venkataraman P, Lamb RA, Pinto LH. 2003. Influenza B virus BM2 protein has ion channel activity that conducts protons across membranes. Dev. Cell 5(1):175-84. Munowitz M, Bachovchin WW, Herzfeld J, Dobson CM, Griffin RG. 1982. Acid-Base and Tautomeric Equilibria in the Solid-State - N-15 Nmr-Spectroscopy of Histidine and Imidazole. J. Am. Chem. Soc. 104(5):1192-1196. Nishimura K, Kim S, Zhang L, Cross TA. 2002. The closed state of a H+ channel helical bundle combining precise orientational and distance restraints from solid state NMR. Biochemistry 41(44):13170-7. Nollert P, Royant A, Pebay-Peyroula E, Landau EM. 1999. Detergent-free membrane protein crystallization. FEBS Lett. 457(2):205-8. Okada A, Miura T, Takeuchi H. 2001. Protonation of histidine and histidine-tryptophan interaction in the activation of the M2 ion channel from influenza a virus. Biochemistry 40(20):6053-60. Opella SJ, Kim Y, McDonnell P. 1994. Experimental nuclear magnetic resonance studies of membrane proteins. Methods Enzymol. 239:536-60. Opella SJ, Marassi FM, Gesell JJ, Valente AP, Kim Y, Oblatt-Montal M, Montal M. 1999. Structures of the M2 channel-lining segments from nicotinic acetylcholine and NMDA receptors by NMR spectroscopy. Nat. Struct. Biol. 6(4):374-9. Panayotov PP, Schlesinger RW. 1992. Oligomeric organization and strain-specific proteolytic modification of the virion M2 protein of influenza A H1N1 viruses. Virology 186(1):352-5. Paterson RG, Takeda M, Ohigashi Y, Pinto LH, Lamb RA. 2003. Influenza B virus BM2 protein is an oligomeric integral membrane protein expressed at the cell surface. Virology 306(1):7-17. 152 Pebay-Peyroula E, Rummel G, Rosenbusch JP, Landau EM. 1997. X-ray structure of bacteriorhodopsin at 2.5 angstroms from microcrystals grown in lipidic cubic phases. Science 277(5332):1676-81. Pinto LH, Dieckmann GR, Gandhi CS, Papworth CG, Braman J, Shaughnessy MA, Lear JD, Lamb RA, DeGrado WF. 1997. A functionally defined model for the M2 proton channel of influenza A virus suggests a mechanism for its ion selectivity. Proc. Natl. Acad. Sci. U S A 94(21):11301-6. Pinto LH, Holsinger LJ, Lamb RA. 1992. Influenza virus M2 protein has ion channel activity. Cell 69(3):517-28. Pinto LH, Lamb RA. 1995. Understanding the mechanism of action of the anti-influenza virus drug amantadine. Trends Microbiol 3(7):271. Popot JL, Engelman DM. 2000. Helical membrane protein folding, stability, and evolution. Annu. Rev. Biochem. 69:881-922. Prestegard JH, al-Hashimi HM, Tolman JR. 2000. NMR structures of biomolecules using field oriented media and residual dipolar couplings. Q. Rev. Biophys. 33(4):371- 424. Prestegard JH, Bougault CM, Kishore AI. 2004. Residual dipolar couplings in structure determination of biomolecules. Chem. Rev. 104(8):3519-40. Quick A, Williams DJ. 1976. Crystal-Structure of Complex Salt Imidazole Imidazolium Perchlorate. Canadian Journal of Chemistry-Revue Canadienne De Chimie 54(15):2465-2469. Quine JR. 1999. Helix parameters and protein structures using quaternions. Theochemistry 460:53-66. Quine JR, Brenneman MT, Cross TA. 1997. Protein structural analysis from solid-state NMR-derived orientational constraints. Biophys. J. 72(5):2342-8. Quine JR, Cross TA. 2000. Protein structure in anisotropic environments: unique structural fold from orientational constraints. Concepts in Magnetic Resonance 12(2):71-82. Ramamoorthy A, Wu CH, Opella SJ. 1997. Magnitudes and orientations of the principal elements of the 1H chemical shift, 1H-15N dipolar coupling, and 15N chemical shift 15 15 interaction tensors in Nε1-tryptophan and Nπ-histidine side chains determined 153 by three-dimensional solid-state NMR spectroscopy of polycrystalline samples. J. Am. Chem. Soc. 119:10479-10486. RECOMMENDATIONS. 1976. Presentation of Nmr Data for Publication in Chemical Journals .B. Conventions Relating to Spectra from Nuclei Other Than Protons. Pure and Applied Chemistry 45(3-4):219-219. Rees DC, DeAntonio L, Eisenberg D. 1989. Hydrophobic organization of membrane proteins. Science 245(4917):510-3. Reynolds WF, Peat IR, Freedman MH, Lyerla JR. 1973. Determination of Tautomeric Form of Imidazole Ring of L-Histidine in Basic Solution by C-13 Magnetic- Resonance Spectroscopy. J. Am. Chem. Soc. 95(2):328-331. Rummel G, Hardmeyer A, Widmer C, Chiu ML, Nollert P, Locher KP, Pedruzzi II, Landau EM, Rosenbusch JP. 1998. Lipidic Cubic Phases: New Matrices for the Three-Dimensional Crystallization of Membrane Proteins. J. Struct. Biol. 121(2):82-91. Salom D, Hill BR, Lear JD, DeGrado WF. 2000. pH-dependent tetramerization and amantadine binding of the transmembrane helix of M2 from the influenza A virus. Biochemistry 39(46):14160-70. Sansom MS, Kerr ID. 1993. Influenza virus M2 protein: a molecular modelling study of the ion channel. Protein Eng. 6(1):65-74. Sansom MS, Kerr ID, Smith GR, Son HS. 1997. The influenza A virus M2 channel: a molecular modeling and simulation study. Virology 233(1):163-73. Saraste M. 1999. Oxidative phosphorylation at the fin de siecle. Science 283(5407):1488- 93. Scholtissek C, Quack G, Klenk HD, Webster RG. 1998. How to overcome resistance of influenza A viruses against adamantane derivatives. Antiviral Res. 37(2):83-95. Schroeder C, Ford CM, Wharton SA, Hay AJ. 1994. Functional reconstitution in lipid vesicles of influenza virus M2 protein expressed by baculovirus: evidence for proton transfer activity. J. Gen. Virol. 75 ( Pt 12):3477-84. Sharma Y, Kwon OY, Brooks B, Tjandra N. 2002. An ab initio study of amide proton shift tensor dependence on local protein structure. J. Am. Chem. Soc. 124(2):327- 335. 154 Shipley GG. 2000. Bilayers and nonbilayers: structure, forces and protein crystallization. Curr. Opin. Struct. Biol. 10(4):471-3. Skehel JJ. 1992. Influenza virus. Amantadine blocks the channel. Nature 358(6382):110- 1. Skehel JJ, Hay AJ, Armstrong JA. 1978. On the mechanism of inhibition of influenza virus replication by amantadine hydrochloride. J Gen Virol 38(1):97-110. Smith SO, Farr-Jones S, Griffin RG, Bachovchin WW. 1989. Crystal versus solution structures of enzymes: NMR spectroscopy of a crystalline serine protease. Science 244(4907):961-4. Smondyrev AM, Voth GA. 2002. Molecular dynamics simulation of proton transport near the surface of a phospholipid membrane. Biophys. J. 82(3):1460-8. Song XJ, McDermott AE. 2001. Proton transfer dynamics and N-H bond lengthening in N-H center dot center dot center dot N model systems: a solid-state NMR study. Magn. Reson. Chem. 39:S37-S43. Song Z, Kovacs FA, Wang J, Denny JK, Shekar SC, Quine JR, Cross TA. 2000. Transmembrane domain of M2 protein from influenza A virus studied by solid- state (15)N polarization inversion spin exchange at magic angle NMR. Biophys. J. 79(2):767-75. Spencer RH, Rees DC. 2002. The alpha-helix and the organization and gating of channels. Annu Rev Biophys Biomol Struct 31:207-33. Starace DM, Bezanilla F. 2004. A proton pore in a potassium channel voltage sensor reveals a focused electric field. Nature 427(6974):548-53. Stark RE, Haberkorn RA, Griffin RG. 1978. N-14 Nmr Determination of Nh Bond Lengths in Solids. J. Chem. Phys. 68(4):1996-1997. Steinschneider A, Burgar MI, Buku A, Fiat D. 1981. Labeling of Amino-Acids and Peptides with Isotopic Oxygen as Followed by O-17-Nmr. International Journal of Peptide and Protein Research 18(3):324-333. Stetter H, Mayer J, Schwarz M, Wulff K. 1960. Uber Verbindungen Mit Urotropin- Struktur .16. Beitrage Zur Chemie Der Adamantyl-(1)-Derivate. Chemische Berichte-Recueil 93(1):226-230. Stevens RC. 2004. Long live structural biology. Nat. Struct. Mol. Biol. 11(4):293-5. 155 Stevens TJ, Arkin IT. 1999. Are membrane proteins "inside-out" proteins? Proteins 36(1):135-43. Stowell MH, McPhillips TM, Rees DC, Soltis SM, Abresch E, Feher G. 1997. Light- induced structural changes in photosynthetic reaction center: implications for mechanism of electron-proton transfer. Science 276(5313):812-6. Sugrue RJ, Hay AJ. 1991. Structural characteristics of the M2 protein of influenza A viruses: evidence that it forms a tetrameric channel. Virology 180(2):617-24. Sukharev S, Betanzos M, Chiang CS, Guy HR. 2001. The gating mechanism of the large mechanosensitive channel MscL. Nature 409(6821):720-4. Tajkhorshid E, Nollert P, Jensen MO, Miercke LJ, O'Connell J, Stroud RM, Schulten K. 2002. Control of the selectivity of the aquaporin water channel family by global orientational tuning. Science 296(5567):525-30. Tang Y, Zaitseva F, Lamb RA, Pinto LH. 2002. The gate of the influenza virus M2 proton channel is formed by a single tryptophan residue. J. Biol. Chem. 277(42):39880-6. Tatara W, Wojcik MJ, Lindgren J, Probst M. 2003. Theoretical study of structures, energies, and vibrational spectra of the imidazole-imidazolium system. J. Phys. Chem. A 107(39):7827-7831. Teng Q, Cross TA. 1989. The Insitu Determination of the N-15 Chemical-Shift Tensor Orientation in a Polypeptide. J. Magn. Reson. 85(3):439-447. Tian C, Gao PF, Pinto LH, Lamb RA, Cross TA. 2003. Initial structural and dynamic characterization of the M2 protein transmembrane and amphipathic helices in lipid bilayers. Protein Sci. 12(11):2597-605. Tian C, Tobler K, Lamb RA, Pinto LH, Cross TA. 2002. Expression and initial structural insights from solid-state NMR of the M2 proton channel from influenza A virus. Biochemistry 41(37):11294-300. Tian F, Cross TA. 1997. Dipolar Oscillations in Cross-Polarized Peptide Samples in Oriented Lipid Bilayers. J. Magn. Reson. 125(1):220-3. Tian F, Cross TA. 1999. Cation transport: an example of structural based selectivity. J. Mol. Biol. 285(5):1993-2003. 156 Tjandra N, Bax A. 1997. Direct measurement of distances and angles in biomolecules by NMR in a dilute liquid crystalline medium. Science 278(5340):1111-4. Tosteson MT, Pinto LH, Holsinger LJ, Lamb RA. 1994. Reconstitution of the influenza virus M2 ion channel in lipid bilayers. J Membr Biol 142(1):117-26. Tribl GG, Wober C, Schonborn V, Brucke T, Deecke L, Panzer S. 2001. Amantadine in Parkinson's disease: lymphocyte subsets and IL-2 secreting T cell precursor frequencies. Experimental Gerontology 36(10):1761-1771. Tsunasawa S, Masaki T, Hirose M, Soejima M, Sakiyama F. 1989. The primary structure and structural characteristics of Achromobacter lyticus protease I, a lysine- specific serine protease. J. Biol. Chem. 264(7):3832-9. Tsunoda A, Maassab HF, Cochran KW, Eveland WC. 1965. Antiviral activity of alpha- methyl-1-adamantanemethylamine hydrochloride. Antimicrobial Agents Chemother 5:553-60. van Willigen H, Haberkorn RA, Griffin RG. 1977. 13C-13C dipolar spectra in solids. J. Chem. Phys. 67(12):5855-5860. Vijayvergiya V, Wilson R, Chorak A, Gao PF, Cross TA, Busath DD. 2004. Proton conductance of influenza virus m2 protein in planar lipid bilayers. Biophys. J. 87(3):1697-704. Vinogradova O, Sonnichsen F, Sanders CR, 2nd. 1998. On choosing a detergent for solution NMR studies of membrane proteins. J. Biomol. NMR 11(4):381-6. von Heijne G. 1992. Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J. Mol. Biol. 225(2):487-94. von Heijne G. 1999. Recent advances in the understanding of membrane protein assembly and structure. Q. Rev. Biophys. 32(4):285-307. Vosegaard T, Nielsen NC. 2002. Towards high-resolution solid-state NMR on large uniformly 15N- and [13C,15N]-labeled membrane proteins in oriented lipid bilayers. J. Biomol. NMR 22(3):225-47. Wagner G, Hyberts SG, Havel TF. 1992. NMR structure determination in solution: a critique and comparison with X-ray crystallography. Annu. Rev. Biophys. Biomol. Struct. 21:167-98. 157 Wallin E, von Heijne G. 1998. Genome-wide analysis of integral membrane proteins from eubacterial, archaean, and eukaryotic organisms. Protein Sci. 7(4):1029-38. Wang C, Lamb RA, Pinto LH. 1995. Activation of the M2 ion channel of influenza virus: a role for the transmembrane domain histidine residue. Biophys J 69(4):1363-71. Wang C, Takeuchi K, Pinto LH, Lamb RA. 1993. Ion channel activity of influenza A virus M2 protein: characterization of the amantadine block. J Virol 67(9):5585- 94. Wang J, Denny J, Tian C, Kim S, Mo Y, Kovacs F, Song Z, Nishimura K, Gan Z, Fu R and others. 2000. Imaging membrane protein helical wheels. J. Magn. Reson. 144(1):162-7. Wang J, Kim S, Kovacs F, Cross TA. 2001. Structure of the transmembrane region of the M2 protein H(+) channel. Protein Sci. 10(11):2241-50. Wei YF, de Dios AC, McDermott AE. 1999. Solid-state N-15 NMR chemical shift anisotropy of histidines: Experimental and theoretical studies of hydrogen bonding. J. Am. Chem. Soc. 121(44):10389-10394. White SH, Wimley WC. 1999. Membrane protein folding and stability: physical principles. Annu. Rev. Biophys. Biomol. Struct. 28:319-65. Wiener MC, White SH. 1992. Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. III. Complete structure. Biophys. J. 61(2):437-47. Woolley GA, Lougheed T. 2003. Modeling ion channel regulation. Curr. Opin. Chem. Biol. 7(6):710-4. Wu CH, Ramamoorthy A, Gierasch LM, Opella SJ. 1995. Simultaneous Characterization of the Amide H-1 Chemical Shift,H-1-N-15 Dipolar, and N-15 Chemical-Shift Interaction Tensors in a Peptide-Bond by 3-Dimensional Solid-State Nmr- Spectroscopy. J. Am. Chem. Soc. 117(22):6148-6149. Wu CH, Ramamoorthy A, Opella SJ. 1994. High-Resolution Heteronuclear Dipolar Solid-State Nmr-Spectroscopy. J. Magn. Reson. A 109(2):270-272. Yau WM, Wimley WC, Gawrisch K, White SH. 1998. The preference of tryptophan for membrane interfaces. Biochemistry 37(42):14713-8. 158 Zhou Y, MacKinnon R. 2003. The occupancy of ions in the K+ selectivity filter: charge balance and coupling of ion binding to a protein conformational change underlie high conduction rates. J. Mol. Biol. 333(5):965-75. Zhou Y, Morais-Cabral JH, Kaufman A, MacKinnon R. 2001. Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 A resolution. Nature 414(6859):43-8. 159 BIOGRAPHICAL SKETCH Jun Hu was born on December 25, 1972, in the City of Yichang, Hubei Province, the People’s Republic of China (PRC). He completed his Bachelor of Science degree in Marine Chemistry in 1995 at the Ocean University of Qingdao (now the name has been changed to the Ocean University of China), Qingdao, PRC. In the same year, he began his Master of Science at the Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai, PRC. There he obtained his MS degree in organic chemistry in 1998. In the fall of 1999, he was admitted by the Department of Chemistry and Biochemistry at the Florida State University and came to the United States of America to pursue his Ph.D study. In 2000, he joined Professor Timothy A. Cross lab. 160