Annu. Rev. Biophys. Biomol. Struct. Copyright ©
1992 by Annual
1992.21:25-47
Reviews Inc. All righls reserved
ANNUAL REVIEWS
Further
Quick links to online content
SOLID-STATE NMR APPROACHES Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
FOR STUDYING MEMBRANE
PROTEIN STRUCTURE Steven D. Smith and Dive B. Peersen
Department of Molecular Biophysics and Biochemistry,Yale University, New Haven, Connecticut 06511 KEY
WORDS:
rotational resonance, REDOR, magic angle spinning, peptides, dipolar interactions
CONTENTS SOLID-STATE NMR METHODS .. .......................................................................................
25 26
ORIENTATION·DEPENDENT APPROACHES
29
PERSPECTIVES AND OVERViEW........................................................................................
.....................................•........•......•.....•............
Theory Structural Studies of Membrane Proteins ................................................................
......... ............................................................................................................. .
D1STANCE·DEPENDENT APPROACHES ..............................................................................
REDORNMR ........................................................................................................ Rotational ResonanceNMR ....................................................................................
. .
CONCLUSIONS ...............................................................................................................
31 32 36 37 40 44
PERSPECTIVES AND OVERVIEW
The proteins that span the cell membrane perform an array of functions ranging from signal transduction to ion transport. In the past few years, gene sequencing of membrane proteins has yielded an abundance of amino acid sequence data that in turn has generated structural models for many of these proteins (13,14,52,61). Unfortunately, high resolution structures of integral membrane proteins in phospholipid bilayers have been notori ously difficult to obtain using either X-ray diffraction or solution NMR methods. It has generally been a challenge to grow well-ordered crystals of large hydrophobic molecules for diffraction studies, while solution NMR 25 1056-8700/92/0610-0025$02.00
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
26
SMITH &. PEERSEN
approaches for determining protein structure rely on rapid isotropic molec ular motion and are often not suitable for membrane systems in which proteins have restricted motions and exhibit broad NMR resonances. Lysolipids and detergents have been used to solubilize hydrophobic pro teins and increase mobility for solution studies, but have the drawback of forming micellar rather than bilayer structures (5, 21, 55). In comparison, solid-state NMR spectroscopy has become an effective approach for study ing membrane proteins, such as gramicidins (45, 78), rhodopsins (71), and phage-coat proteins (49, 50). Solid-state NMR approaches have the potential for obtaining accurate internuclear distances and orientations that can be translated into molecular structure, and recent advances in magic angle spinning (MAS) methods for measuring both homonuclear and heteronuclear dipolar couplings have begun to tap this potential. Currently, using specific l3C and 15N isotopic labels, distances in the range of 2-7 A can be measured within ,..., 0.5 A, and the relative orientations between peptide planes can be measured to better than 10°. This review covers several solid-state NMR methods that have emerged in the past few years for the analysis of membrane proteins, and the studies discussed serve to outline the strengths and limitations of the approaches. SOLID-STATE NMR METHODS
The NMR spectrum, in both solution and the solid-state, results from interactions of the observed nuclear spins with a large external magnetic field and many small local internal fields. These interactions are described by the nuclear spin Hamiltonian (£). 1. One must have an idea of the physical basis for each term of the spin Hamiltonian and its size before discussing the methods for extracting structural information from the NMR spectrum. In depth discussions can be found in several reviews (6, 40, 49, 7 1, 89). The Zeeman (J¥'z) and radio frequency Hamiltonians (J¥' RF) describe the interaction of nuclear spins with the external magnetic field and with local internal fields created by radio-frequency pulses in the NMR probe, respectively. The RF fields are about 103 times smaller than the field generated by the external magnet and stimulate transitions between NMR energy levels. The chemical-shift term (£cs) describes the shielding of a nuclear spin from the external field by surrounding electrons. The distribution of electrons around a nucleus is usually not uniform, and consequently the effective shielding is often anisotropic. The size of the chemical-shift anisotropy (CSA) increases with
NMR OF MEMBRANE PROTEINS
the asymmetry and number of occupied outer electron orbitals and is typically on the order of 1-20 kHz .YfD describes through-space dipolar intcractions, while.YfJ describes indirect through-bond dipolar interactions (or J couplings) that are mediated via electrons. The direct dipole-dipole coupling (D) ranges from 0-50 kHz depending on the gyromagnetic ratio (y) of each of the coupled spins, their through-space separation, and Plank's constant (h), where D hYIY2r-3. The J couplings are generally much smaller (0-200 Hz), but play an important role in solution NMR in which the larger direct dipolar interactions are averaged and only con tribute to the NMR spectrum through relaxation effects. Finally, an additional term .YfQ dominates the NMR spectra of quadrupolar nuclei, such as 2H and 14N. Deuterium NMR has been used extensively to study the dynamics of membrane lipids and proteins (12, 17, 65, 68, 70, 79) but is not covered in this review. Solid-state and solution NMR differ in the molecular motions that are effective in averaging these nuclear spin interactions. In solution, rapid isotropic rotational motion of proteins leads to averaging of dipolar inter actions to zero and chemical shifts to an isotropic value, resulting in narrow resonances with small splittings due to J couplings that are not averaged. In contrast, for molecules that have restricted or anisotropic motion, these spin interactions lead to broad NMR resonances. The broad NMR lineshapes contain a wealth of structural information because both the chemical-shift anisotropy and dipolar interactions depend directly on molecular structure and orientation with respect to the external magnetic field. This information is lost in solution studies. The challenge in solid state NMR is to counter problems of resolution and sensitivity in order to extract structural details from the NMR spectrum. One can improve both resolution and sensitivity in solid-state NMR studies in several ways. The first is by specific isotopic labeling. In protein studies, 13C and 15N enrichment is often used to great advantage to enhance the signals from single sites over natural-abundance backgrounds. A second approach is to orient or align samples relative to the external magnetic field, increasing both resolution and sensitivity as broadening resulting from differences in molecular orientation is greatly reduced. The macroscopic orientation of lipid bilayers has been accomplished by coating glass slides with phospholipid multilayers (30, 41, 67) or by the use of strong magnetic fields (62, 66, 72). Finally, narrow linewidths approaching those in solution can be obtained through magic angle spinning (MAS) (1, 37, 63). In MAS, the sample is physically rotated at high speeds in the magnetic field in order to average the nuclear-spin interactions. Structural studies of membrane proteins usually rely on isotopic labeling in com bination with either macroscopic orientation of the sample or MAS. High .
=
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
27
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
28
SMITH & PEERSEN
resolution IH NMR studies, analogous to those in solution, are severely limited in solids because of strong proton-proton dipolar interactions. Figure I illustrates the distinctive 13C lineshapes for the carboxyl and IX carbon resonances of free glycine. These line shapes arise from the random orientation of glycine molecules in a polycrystalline sample and are rep resentative of the broad NMR resonances (or powder patterns) mentioned above. A single molecule or crystallite in the sample contributes a narrow Lorentzian component to the overall lineshape at a frequency dependent on its orientation with respect to the external magnetic field. In Figure 1 (top), the powder pattern lineshapes represent the sum of all of the molec ular orientations in the sample and result solely from anisotropy in the
-20 kHz
Figure 1
Solid-state
13C
NMR spectra of glycine illustrating the broad NMR resonances
effects of magic angle spinning at 2.0 kHz (middle) and 7.2 kHz (bottom). The principal values of the chemical-shift tensor are shown for the J3C carboxyl
in static samples
(lOp) and the
resonance and correspond to the down-field inflection point (0"11), the maximum (0"22), and the up-field inflection point (0"33)' MAS collapses the bmad lineshapes into sharp centerbands at the isotropic chemical shifts
(O"i,o)
and rotational sidebands spaced at the spinning
frequency. The frequency scale is centered on the carboxyl centerband.
29
NMR OF MEMBRANE PROTEINS
chemical-shift interaction because dipolar interactions between DC and lH spins have been eliminated by proton decoupling. The glycine CSA is 15 kHz for the carboxyl resonance and 5 kHz for the methylene resonance at a magnetic field strength of 9.4 T (100.6 MHz l3C frequency). In Figure 1 (middle and bottom), the CSA has been averaged by spinning the sample at an angle () of 54.7° relative to the external magnetic field. This is the "magic angle." Both the chemical shift (.n"cs) and dipolar (.n"D) Ham iltonians have terms that contain factors of (3 cos2 () - 1),and at the magic angle, these terms vanish. The spinning speed of the sample has a pro nounced effect on the appearance of the spectrum. Spinning at a rotational frequency that is much less than the frequency width of the CSA results in each broad lineshape breaking up into a centerband at the isotropic chemical shift and into sets of spinning sidebands spaced at the rotational frequency. One can see this effect in Figure I (middle), where the spinning speed is 2.0 kHz. The relative intensities of the spinning sidebands can be used to determine the CSA while providing a substantial gain in signal-to noise over the powder pattern (27). Faster spinning collapses the line intensity into the centerband, thereby increasing sensitivity but removing information about the CSA. The standard solid-state cross-polarization (CP) pulse sequence used for observing dilute S spins, such as l3C and 15N, is shown in Figure 2 (top). The 90° pulse on the lH spins and simultaneous spin-locking pulses on the lH and S spins transfer the much larger polarization of the lH spins to the S spins, thereby increasing sensitivity (57, 63). The use of lH CP also allows for a faster pulse repetition rate governed by the shorter proton T . Proton irradiation is generally used during the acquisition period to 1 eliminate heteronuclear dipolar coupling. '"
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
'"
ORIENTATION-DEPENDENT APPROACHES
Diffraction and NMR methods differ greatly in how the data specify the three-dimensional structure of a protein. Diffraction data define the coordinates of atoms in a crystal lattice, while NMR methods yield relative distances and orientations between nuclei. Solution NMR structures are derived mainly from short ( < 5 A) 'H . . . 'H distance constraints, estimated from nuclear Overhauser effects (NOEs), and are refined using torsion angle data calculated from J couplings (6, 16,89). In solids, direct dipolar interactions and the chemical-shift anisotropy are exploited to obtain both distance and orientation information that constrain structural models. One solid-state NMR approach, developed by Opella, Cross, and coworkers focuses on the determination oftorsion angles in the polypeptide backbone of a protein as a way to generate protein structures solely from orientation
30
SMITH & PEERSEN
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
Cross Polarization
Rotational Resonance
REDOR 7th. 1H
13C
n I
CP
CP
I
Figure 2
7t
I
�
0 7t
1� rotor
DECOUPLE
7t
7t
7t
1t
7t
o n 0 DOD 0
2
3
4
Solid-state NMR pulse sequences used for orientation and distance measurements.
The standard cross-polarization sequence
(top) enhances dilute spin signals by transferring
the larger proton polarization to the dilute spins. The pulse sequence used in rotational resonance experiments (middle) adds a flip-back pulse followed by a selective inversion and a time delay to allow for magnetization exchange. The pulse sequence for REDOR experiments
(bottom) requires at least three RF channels. A 13e spectrum is collected with and without
the I5N pulse train, and the difference between them is used to determine the dipolar coupling. This figure illustrates a four-cycle REDOR experiment.
NMR OF MEMBRANE PROTEINS
31
constraints (9, 10, 50). The following two sections briefly describe the theory for this orientation-dependent approach and several applications to membrane systems.
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
Theory
The ex-carbons of adjacent amino acids in a polypeptide chain are joined by the amide C-N bonds. The six atoms that form this peptide linkage lie roughly in a plane, and the relative orientation of adjacent planes is defined by the
1992 by Annual
1992.21:25-47
Reviews Inc. All righls reserved
ANNUAL REVIEWS
Further
Quick links to online content
SOLID-STATE NMR APPROACHES Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
FOR STUDYING MEMBRANE
PROTEIN STRUCTURE Steven D. Smith and Dive B. Peersen
Department of Molecular Biophysics and Biochemistry,Yale University, New Haven, Connecticut 06511 KEY
WORDS:
rotational resonance, REDOR, magic angle spinning, peptides, dipolar interactions
CONTENTS SOLID-STATE NMR METHODS .. .......................................................................................
25 26
ORIENTATION·DEPENDENT APPROACHES
29
PERSPECTIVES AND OVERViEW........................................................................................
.....................................•........•......•.....•............
Theory Structural Studies of Membrane Proteins ................................................................
......... ............................................................................................................. .
D1STANCE·DEPENDENT APPROACHES ..............................................................................
REDORNMR ........................................................................................................ Rotational ResonanceNMR ....................................................................................
. .
CONCLUSIONS ...............................................................................................................
31 32 36 37 40 44
PERSPECTIVES AND OVERVIEW
The proteins that span the cell membrane perform an array of functions ranging from signal transduction to ion transport. In the past few years, gene sequencing of membrane proteins has yielded an abundance of amino acid sequence data that in turn has generated structural models for many of these proteins (13,14,52,61). Unfortunately, high resolution structures of integral membrane proteins in phospholipid bilayers have been notori ously difficult to obtain using either X-ray diffraction or solution NMR methods. It has generally been a challenge to grow well-ordered crystals of large hydrophobic molecules for diffraction studies, while solution NMR 25 1056-8700/92/0610-0025$02.00
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
26
SMITH &. PEERSEN
approaches for determining protein structure rely on rapid isotropic molec ular motion and are often not suitable for membrane systems in which proteins have restricted motions and exhibit broad NMR resonances. Lysolipids and detergents have been used to solubilize hydrophobic pro teins and increase mobility for solution studies, but have the drawback of forming micellar rather than bilayer structures (5, 21, 55). In comparison, solid-state NMR spectroscopy has become an effective approach for study ing membrane proteins, such as gramicidins (45, 78), rhodopsins (71), and phage-coat proteins (49, 50). Solid-state NMR approaches have the potential for obtaining accurate internuclear distances and orientations that can be translated into molecular structure, and recent advances in magic angle spinning (MAS) methods for measuring both homonuclear and heteronuclear dipolar couplings have begun to tap this potential. Currently, using specific l3C and 15N isotopic labels, distances in the range of 2-7 A can be measured within ,..., 0.5 A, and the relative orientations between peptide planes can be measured to better than 10°. This review covers several solid-state NMR methods that have emerged in the past few years for the analysis of membrane proteins, and the studies discussed serve to outline the strengths and limitations of the approaches. SOLID-STATE NMR METHODS
The NMR spectrum, in both solution and the solid-state, results from interactions of the observed nuclear spins with a large external magnetic field and many small local internal fields. These interactions are described by the nuclear spin Hamiltonian (£). 1. One must have an idea of the physical basis for each term of the spin Hamiltonian and its size before discussing the methods for extracting structural information from the NMR spectrum. In depth discussions can be found in several reviews (6, 40, 49, 7 1, 89). The Zeeman (J¥'z) and radio frequency Hamiltonians (J¥' RF) describe the interaction of nuclear spins with the external magnetic field and with local internal fields created by radio-frequency pulses in the NMR probe, respectively. The RF fields are about 103 times smaller than the field generated by the external magnet and stimulate transitions between NMR energy levels. The chemical-shift term (£cs) describes the shielding of a nuclear spin from the external field by surrounding electrons. The distribution of electrons around a nucleus is usually not uniform, and consequently the effective shielding is often anisotropic. The size of the chemical-shift anisotropy (CSA) increases with
NMR OF MEMBRANE PROTEINS
the asymmetry and number of occupied outer electron orbitals and is typically on the order of 1-20 kHz .YfD describes through-space dipolar intcractions, while.YfJ describes indirect through-bond dipolar interactions (or J couplings) that are mediated via electrons. The direct dipole-dipole coupling (D) ranges from 0-50 kHz depending on the gyromagnetic ratio (y) of each of the coupled spins, their through-space separation, and Plank's constant (h), where D hYIY2r-3. The J couplings are generally much smaller (0-200 Hz), but play an important role in solution NMR in which the larger direct dipolar interactions are averaged and only con tribute to the NMR spectrum through relaxation effects. Finally, an additional term .YfQ dominates the NMR spectra of quadrupolar nuclei, such as 2H and 14N. Deuterium NMR has been used extensively to study the dynamics of membrane lipids and proteins (12, 17, 65, 68, 70, 79) but is not covered in this review. Solid-state and solution NMR differ in the molecular motions that are effective in averaging these nuclear spin interactions. In solution, rapid isotropic rotational motion of proteins leads to averaging of dipolar inter actions to zero and chemical shifts to an isotropic value, resulting in narrow resonances with small splittings due to J couplings that are not averaged. In contrast, for molecules that have restricted or anisotropic motion, these spin interactions lead to broad NMR resonances. The broad NMR lineshapes contain a wealth of structural information because both the chemical-shift anisotropy and dipolar interactions depend directly on molecular structure and orientation with respect to the external magnetic field. This information is lost in solution studies. The challenge in solid state NMR is to counter problems of resolution and sensitivity in order to extract structural details from the NMR spectrum. One can improve both resolution and sensitivity in solid-state NMR studies in several ways. The first is by specific isotopic labeling. In protein studies, 13C and 15N enrichment is often used to great advantage to enhance the signals from single sites over natural-abundance backgrounds. A second approach is to orient or align samples relative to the external magnetic field, increasing both resolution and sensitivity as broadening resulting from differences in molecular orientation is greatly reduced. The macroscopic orientation of lipid bilayers has been accomplished by coating glass slides with phospholipid multilayers (30, 41, 67) or by the use of strong magnetic fields (62, 66, 72). Finally, narrow linewidths approaching those in solution can be obtained through magic angle spinning (MAS) (1, 37, 63). In MAS, the sample is physically rotated at high speeds in the magnetic field in order to average the nuclear-spin interactions. Structural studies of membrane proteins usually rely on isotopic labeling in com bination with either macroscopic orientation of the sample or MAS. High .
=
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
27
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
28
SMITH & PEERSEN
resolution IH NMR studies, analogous to those in solution, are severely limited in solids because of strong proton-proton dipolar interactions. Figure I illustrates the distinctive 13C lineshapes for the carboxyl and IX carbon resonances of free glycine. These line shapes arise from the random orientation of glycine molecules in a polycrystalline sample and are rep resentative of the broad NMR resonances (or powder patterns) mentioned above. A single molecule or crystallite in the sample contributes a narrow Lorentzian component to the overall lineshape at a frequency dependent on its orientation with respect to the external magnetic field. In Figure 1 (top), the powder pattern lineshapes represent the sum of all of the molec ular orientations in the sample and result solely from anisotropy in the
-20 kHz
Figure 1
Solid-state
13C
NMR spectra of glycine illustrating the broad NMR resonances
effects of magic angle spinning at 2.0 kHz (middle) and 7.2 kHz (bottom). The principal values of the chemical-shift tensor are shown for the J3C carboxyl
in static samples
(lOp) and the
resonance and correspond to the down-field inflection point (0"11), the maximum (0"22), and the up-field inflection point (0"33)' MAS collapses the bmad lineshapes into sharp centerbands at the isotropic chemical shifts
(O"i,o)
and rotational sidebands spaced at the spinning
frequency. The frequency scale is centered on the carboxyl centerband.
29
NMR OF MEMBRANE PROTEINS
chemical-shift interaction because dipolar interactions between DC and lH spins have been eliminated by proton decoupling. The glycine CSA is 15 kHz for the carboxyl resonance and 5 kHz for the methylene resonance at a magnetic field strength of 9.4 T (100.6 MHz l3C frequency). In Figure 1 (middle and bottom), the CSA has been averaged by spinning the sample at an angle () of 54.7° relative to the external magnetic field. This is the "magic angle." Both the chemical shift (.n"cs) and dipolar (.n"D) Ham iltonians have terms that contain factors of (3 cos2 () - 1),and at the magic angle, these terms vanish. The spinning speed of the sample has a pro nounced effect on the appearance of the spectrum. Spinning at a rotational frequency that is much less than the frequency width of the CSA results in each broad lineshape breaking up into a centerband at the isotropic chemical shift and into sets of spinning sidebands spaced at the rotational frequency. One can see this effect in Figure I (middle), where the spinning speed is 2.0 kHz. The relative intensities of the spinning sidebands can be used to determine the CSA while providing a substantial gain in signal-to noise over the powder pattern (27). Faster spinning collapses the line intensity into the centerband, thereby increasing sensitivity but removing information about the CSA. The standard solid-state cross-polarization (CP) pulse sequence used for observing dilute S spins, such as l3C and 15N, is shown in Figure 2 (top). The 90° pulse on the lH spins and simultaneous spin-locking pulses on the lH and S spins transfer the much larger polarization of the lH spins to the S spins, thereby increasing sensitivity (57, 63). The use of lH CP also allows for a faster pulse repetition rate governed by the shorter proton T . Proton irradiation is generally used during the acquisition period to 1 eliminate heteronuclear dipolar coupling. '"
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
'"
ORIENTATION-DEPENDENT APPROACHES
Diffraction and NMR methods differ greatly in how the data specify the three-dimensional structure of a protein. Diffraction data define the coordinates of atoms in a crystal lattice, while NMR methods yield relative distances and orientations between nuclei. Solution NMR structures are derived mainly from short ( < 5 A) 'H . . . 'H distance constraints, estimated from nuclear Overhauser effects (NOEs), and are refined using torsion angle data calculated from J couplings (6, 16,89). In solids, direct dipolar interactions and the chemical-shift anisotropy are exploited to obtain both distance and orientation information that constrain structural models. One solid-state NMR approach, developed by Opella, Cross, and coworkers focuses on the determination oftorsion angles in the polypeptide backbone of a protein as a way to generate protein structures solely from orientation
30
SMITH & PEERSEN
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
Cross Polarization
Rotational Resonance
REDOR 7th. 1H
13C
n I
CP
CP
I
Figure 2
7t
I
�
0 7t
1� rotor
DECOUPLE
7t
7t
7t
1t
7t
o n 0 DOD 0
2
3
4
Solid-state NMR pulse sequences used for orientation and distance measurements.
The standard cross-polarization sequence
(top) enhances dilute spin signals by transferring
the larger proton polarization to the dilute spins. The pulse sequence used in rotational resonance experiments (middle) adds a flip-back pulse followed by a selective inversion and a time delay to allow for magnetization exchange. The pulse sequence for REDOR experiments
(bottom) requires at least three RF channels. A 13e spectrum is collected with and without
the I5N pulse train, and the difference between them is used to determine the dipolar coupling. This figure illustrates a four-cycle REDOR experiment.
NMR OF MEMBRANE PROTEINS
31
constraints (9, 10, 50). The following two sections briefly describe the theory for this orientation-dependent approach and several applications to membrane systems.
Annu. Rev. Biophys. Biomol. Struct. 1992.21:25-47. Downloaded from www.annualreviews.org Access provided by University of Birmingham on 11/14/15. For personal use only.
Theory
The ex-carbons of adjacent amino acids in a polypeptide chain are joined by the amide C-N bonds. The six atoms that form this peptide linkage lie roughly in a plane, and the relative orientation of adjacent planes is defined by the
