Solid state nmr

Top Curr Chem (2012) 306: 47–88
DOI: 10.1007/128_2011_154
# Springer-Verlag Berlin Heidelberg 2011
Published online: 1 June 2011
Solid-State NMR Techniques for the Structural
Determination of Amyloid Fibrils
Jerry C.C. Chan
Abstract This review discusses the solid-state NMR techniques developed for the
study of amyloid fibrils. Literature up to the end of 2010 has been surveyed and the
materials are organized according to five categories, viz. homonuclear dipolar
recoupling and polarization transfer via J-coupling, heteronuclear dipolar recou-
pling, correlation spectroscopy, recoupling of chemical shift anisotropy, and tensor
correlation. Our emphasis is on the NMR techniques and their practical aspects. The
biological implications of the results obtained for amyloid fibrils are only briefly
discussed. Our main objective is to showcase the power of NMR in the study of
biological unoriented solids.
Keywords Amyloid fibrils Á Backbone torsion angle Á Correlation spectroscopy Á
CSA Á Dipolar recoupling Á H/D exchange Á J-coupling Á Tensor correlation
Contents
1 Introduction ................................................................................ 48
2 Homonuclear Dipolar Recoupling and J-Coupling Based Techniques ..................... 49
2.1 Rotational Resonance ................................................................ 49
2.2 Dipolar Dephasing ................................................................... 50
2.3 Constant-Time Dipolar Dephasing ................................................... 51
2.4 Multiple-Quantum NMR ............................................................. 55
2.5 Polarization Transfer Via Homonuclear J-Coupling ................................. 56
2.6 Frequency-Selective Polarization Transfer ........................................... 57
3 Heteronuclear Dipolar Recoupling Techniques ............................................ 58
3.1 REDOR .............................................................................. 58
3.2 Frequency-Selective REDOR ........................................................ 60
3.3 DSQ-REDOR ........................................................................ 61
3.4 Band-Selective TEDOR ............................................................. 62
3.5 1
H–X Dipolar Couplings ............................................................. 63
J.C.C. Chan
Department of Chemistry, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei,
Taiwan
e-mail: chanjcc@ntu.edu.tw

4 Correlation Spectroscopy .................................................................. 64
4.1 Spectral Assignment ................................................................. 64
4.2 Distance Constraints ................................................................. 68
4.3 H/D Exchange Detected by Correlation Spectroscopy ............................... 69
5 Recoupling of Chemical Shift Anisotropy ................................................. 71
5.1 Theory of ROCSA ................................................................... 71
5.2 ROCSA Spectra of Amyloid Fibrils ................................................. 73
6 Tensor Correlation Methods ............................................................... 75
6.1 Backbone Phi–Psi Angle Determination ............................................. 76
6.2 Backbone Psi Angle Determination .................................................. 77
6.3 Backbone Phi Angle Determination ................................................. 79
7 Conclusion and Outlook ................................................................... 82
References ......................................................................................83
1 Introduction
Amyloid fibrils are filamentous insoluble protein aggregates closely related to many
fatal neurodegenerative diseases including Alzheimer’s disease, type II diabetes,
Huntington’s disease, and prion diseases [1, 2]. The molecular structure of amyloid
fibrils is known to contain b-sheets that extend over the length of the fibril, created
by intermolecular hydrogen bonding of b-strand peptide segments that run perpen-
dicular to the fibril axis, which is commonly referred to as the cross-b motif. It has
been known for some years that the amyloid fibrils formed by peptide sequences of
very different biophysical properties have many structural features in common [1].
To unravel the physical principles governing this interesting phenomenon, which
can provide significant mechanistic insights into the self-assembly process of
macromolecules, it is necessary to determine the molecular structures of amyloid
fibrils formed by a large variety of proteins or their fragments. Since the pioneering
work by Griffin and co-workers [3], solid-state NMR has been established as the
major analytical tool to unravel the structural details of amyloid fibrils at the
molecular level [4, 5]. Over the years, solid-state NMR studies of amyloid fibrils
have been reviewed regularly [4–9, 11, 12]. Many cleverly designed solid-state
NMR strategies have been developed to probe the hydrogen-bond registry of
b-sheet layer, the spatial organization of the various b-sheet segments of the peptide
chain, the existence of salt bridge, the side-chain–side-chain interactions, the quater-
nary contacts between b-sheet layers, the staggering of neighboring b strands, and
the motional dynamics of the backbone. The review by Naito and Kawamura has
also included a nice exposition of the interaction between amyloidogenic protein
and membranes [12].
Biological solid-state NMR is such an active research field that many new
techniques and notions have been reported in the past few years. It is simply beyond
the scope of the present review to include all the techniques which may find fruitful
applications in the study of amyloid fibrils. Given the page limit, we will only focus
on the NMR techniques which have already been applied to the study of unoriented
solid-state samples of amyloid fibrils. As implied from the title, our emphasis will
be placed on the NMR techniques and the implications of the results obtained for
48 J.C.C. Chan

amyloid fibrils will only be briefly discussed. Our purpose is to present “what has
been done” so that one may consider “what could be done.” On a more general note,
we hope that the applications discussed for amyloid fibrils can showcase the power
of NMR in the study of biological solids. Most of the techniques discussed are
under the condition of magic-angle spinning (MAS), which consists of radiofre-
quency (rf) pulse sequences that are applied in synchrony with the MAS sample
rotation. Our discussion is largely descriptive and will include some practical hints
on the experimental aspect. For a more in-depth discussion of the techniques and
theories, readers are referred to the original literature.
2 Homonuclear Dipolar Recoupling and J-Coupling
Based Techniques
In the cross-b structural motif, the registry of the hydrogen bonds between the
b strands is determined by a delicate balance of multiple side-chain–side-chain
interactions. Experimentally, the organization of the b-sheet structure can be
determined by measuring the distance between two selected residues in adjacent
b strands. Some very useful homonuclear dipolar recoupling techniques for dis-
tance measurements and spin counting will be discussed. In addition, homonuclear
polarization transfer techniques mediated by the scalar spin–spin coupling
(J-coupling) will also be covered in the following section. The dipolar recoupling
techniques developed for homonuclear correlation spectroscopy are discussed in
Sect. 4.
2.1 Rotational Resonance
Rotational resonance (R2
) is the first solid-state NMR technique applied to study
amyloid fibrils [3, 13–15]. One common implementation is to set the spinning
frequency equal to the chemical shift difference of the spin pair of interest, say,
I and S. To the lowest order, the average Hamiltonian contains the zero-quantum
(ZQ) flip-flop term (I+SÀ + IÀS+) [16, 17]. Therefore, the density operator of the
spin system would oscillate between the terms of Iz–Sz and of the ZQ coherence
(I+SÀ – IÀS+). After a selective inversion of either polarization to the Àz axis,
which would maximize the initial polarization difference, the amplitude of Iz–Sz can
be monitored as a function of the mixing time. From the time course of the
exchange in Zeeman order, the internuclear distance could be extracted if the T2
relaxation of the ZQ coherence (T2
ZQ
) is known. Usually, T2
ZQ
is approximated by
the T2 relaxations of I and S, according to the equation (T2
ZQ
)À1
¼ (T2
I
)À1
+
(T2
S
)À1
. Interestingly, it has been suggested that T2
ZQ
can be measured directly in
a Hahn-echo like experiment, where the ZQ coherence can be refocused by the
Solid-State NMR Techniques for the Structural Determination of Amyloid Fibrils 49

composite (p/2)x À (p/2)y À (p/2)x pulse [18]. Because the chemical shift differ-
ence of the carbonyl and aliphatic regions is about130–160 ppm, distances of the
spin pairs of C0
–Ca
, C0
–Cb
, or C0
–Cg
can be estimated conveniently by R2
. This
strategy has been applied in the study of the fibrils formed by PrP106–126 [19], where
it has been shown that the fibril structure comprises a close stacking of two
neighboring b-sheets adopting the structural motif of the class 1 steric zipper
[20]. Recently, a constant-time version of the R2
experiment has been developed
[21, 22], where the dynamics of the magnetization transfer is monitored as a
function of the spinning frequency. This so-called rotational resonance width
(R2
W) technique has the advantage that its data analysis allows an independent
extraction of the internuclear distance and the T2
ZQ
parameter [21, 23]. Previously,
it has been shown that the fibrils formed by the peptide GNNQQNY have three
different polymorphs [24]. For the fibril sample formed by a 50/50 (by mass)
mixture of the peptides of [13
C0
-Gly]-NNQQNY and [13
Ca
-Gly]-NNQQNY, the
intermolecular 13
C–13
C distance has been determined by the technique of R2
W
[25]. The results lie in the range of 4.5–4.9 A˚ (with an error of Æ1.0 A˚ ), consistent
with the in-register parallel b-sheet structure.
2.2 Dipolar Dephasing
The technique of dipolar recoupling with a windowless sequence (DRAWS) has
been developed to recouple homonuclear dipole–dipole interaction under MAS
conditions [26, 27]. The lowest-order average Hamiltonian of DRAWS is propor-
tional to the terms of IxSx À IySy
À Á
and 3IzSz À I Á Sð Þ. When the transverse magne-
tization is allowed to evolve under DRAWS, the dephasing rate of the signal will
depend on the dipolar coupling constants and the T2 relaxation. By measuring the
crystalline compound of adipic acid, the upper limit of 13
C–13
C distances measur-
able by DRAWS was established to be ca. 6 A˚ [18]. In an early application of
DRAWS to the study of amyloid fibrils, the organization of the b-sheet structure for
Ab10–35 fibrils has been shown to be in-register parallel [28]. In addition, the
secondary structure of the peptide monomer has been verified to adopt b-sheet
structure by measuring the C0
(i)–C0
(i+1) distances at selected residues [18]. To mimic
the spin evolution of an “infinite” long chain as anticipated for fibrils of a few
microns in length, each of the spins in a linear chain was set to have two coupled
neighbors [18]. In particular, the spins at the two ends are “coupled” as if they were
neighbors. This implementation of periodic boundary conditions has been shown to
be an effective approach to eliminate the “edge effect” [18, 29]. DRAWS can also
be used to prepare a double-quantum filter (DQF) [30]. The advantage of the
resulting DQF–DRAWS technique is that the dipolar coupling and the relaxation
parameters can be independently extracted from the excitation profile of the DQ
signal [29]. Hence, it is possible to determine accurately by DQF–DRAWS the
interstrand distances in amyloid fibrils [25, 29, 31, 32]. While DRAWS is very well
compensated for the effect of chemical shift anisotropy (CSA) [33], the required rf
50 J.C.C. Chan

field is 8.5 times the spinning frequency, which has precluded its application in the
fast spinning regime. In addition, the implementation of windowless pulse
sequences is not trivial if phase transient problems are severe. Sometimes a damp-
ing resistor has to be added in parallel to the sample coil in order to reduce the
detrimental effect of phase glitches [18, 34].
The homonuclear dipolar recoupling technique of radio frequency-driven recou-
pling (RFDR) involves a hard p pulse per rotor period and its recoupling mecha-
nism is based on the modulation of chemical shift difference [35–37]. When the
delta-pulse approximation is relaxed so that the pulse width of the p pulse is about
one-third of the rotor period, the so-called finite-pulse RFDR (fpRFDR) could
selectively reintroduce the homonuclear dipole–dipole interaction under fast
MAS conditions [38]. Because the recoupling mechanism of fpRFDR does not
require the presence of chemical shift difference, it can be applied to study samples
with a singly labeled site. For the study of amyloid fibrils, the technique of fpRFDR
is usually applied in a constant-time framework (see below).
2.3 Constant-Time Dipolar Dephasing
To minimize the effects of various experimental imperfections such as rf inhomo-
geneity and T2 relaxation, it is highly desirable to design a recoupling experiment
where the number of rf pulses and the total pulse sequence duration are maintained
constant [39]. It has been shown that the average Hamiltonian of the fpRFDR
recoupling sequence has the same operator form as the static homonuclear dipo-
le–dipole interaction [38]. Hence, the classical WAHUHA sequence developed for
homonuclear decoupling under static condition [40], viz. t À (p/2)x À t À (p/2)y À
2t À (p/2)Ày À t À (p/2)Àx À t, can be exploited as shown in Fig. 1 to achieve
homonuclear dipolar recoupling in a constant-time manner [41]. That is, the total
duration of the pulse sequence is kept constant and the effective dipolar dephasing
time is varied by adjusting the positions of the WAHUHA pulses. In other words,
we combine two pulse sequences which have opposite effects. While fpRFDR will
reintroduce the homonuclear dipole–dipole interaction, WAHUHA will suppress it,
so that the net dipolar dephasing occurs as a result of “controlled” cancellation. This
technique, which has the acronym fpRFDR-CT, has been successfully applied to
probe the b-sheet organization of amyloid fibrils [4, 42].
For the amyloid fibrils formed by proteins or polypeptides with more than 20
amino acid residues, the fibril core usually comprises in-register parallel b-sheets
[19, 28, 43–50], although it has also been shown that a polymorph of the D23N-
Ab40 fibrils may have an antiparallel b-sheet structure [51]. The fpRFDR-CT
technique is well suited to verify whether or not a fibril system adopts the organi-
zation of in-register parallel b-sheets. For a single b-sheet layer, significant signal
dephasings of the C0
and Cb
labeled at two different residues will provide strong
evidence for in-register parallel organization. In particular, shifting the hydrogen
bond registry away from in-register alignment by one residue in either direction will

increase the nearest distance between two labeled Cb
atoms to ca. 7 A˚ , for which
there will be no significant signal dephasing observed in the fpRFDR-CT experi-
ment. To quantify the spacing between the neighboring b-strands (d), the fpRFDR-
CT data can be compared with simulations on a linear chain of six spins with d
varied from 4 to 7 A˚ . To reduce the “edge effect” of a finite spin system, the initial
density operator may include only the polarization of the central two spins, whereas
the detection operator includes all six spins [45]. Furthermore, the contribution
from the background signals must be corrected for to warrant a meaningful com-
parison between the experimental and simulation data (see below) [44]. However, if
there are two b-sheets closely interdigitated, as in the case of steric zipper [20], the
interpretation of the fpRFDR-CT data would be less straightforward [52]. Also, the
fpRFDR-CT data of Ca
is difficult to analyze quantitatively because of its fast T2
relaxation.
2.3.1 Correction of Background Signals
To illustrate the procedure of background signal correction, let us consider a
hypothetical fibril system formed by polypeptides containing 21 residues, where a
Fig. 1 Pulse sequence for fpRFDR-CT measurements. (a) The fpRFDR sequence consists of a
single p pulse of length tp centered in each MAS rotation period tR. (b) The fpRFDR sequence is
incorporated into a multiple pulse cycle based on the WAHUHA cycle, by insertion of four p/2 pulses
with the indicated phases. Homonuclear dipole–dipole couplings generated by fpRFDR are scaled
by a factor of (M À N)/(M + 2 N). (c) In the full 2D technique, 13
C magnetization created by CP
evolves under 13
C–13
C dipole–dipole couplings for an effective t1 period 2(M À N)KtR is kept
constant. 1
H–13
C couplings are removed by proton decoupling fields during t1 and t2. (Figures and
caption adapted from [41]. Copyright (2001), with permission from Elsevier)
52 J.C.C. Chan

chosen residue is 13
C labeled at the carbonyl site. Assuming that 100% of the
molecules are fibrillized and that the natural abundance signals do not dephase at
all, the uncorrected C0
fpRFDR-CT data can be written as
Sraw tð Þ
Srawð0Þ
¼
Sl;f
tð Þ þ Sna;u
Sl;fð0Þ þ Sna;u
; (1)
where t denotes the effective dipolar dephasing time, and Sl,f
and Sna,u
indicate the
signals arising from the labeled sites in fibrillar state and the sites of natural
abundance (undephased), respectively. Accordingly, the C0
fpRFDR-CT data are
corrected as
Sl;f
tð Þ
Sl;fð0Þ
¼
Sraw tð Þ À Srawð0Þ Â 20Â1:1%
1þ20Â1:1%ð Þ
Srawð0Þ Â 1 À 20Â1:1%
1þ20Â1:1%ð Þ
: (2)
In a more general case, some signals from natural abundance 13
C nuclei will
dephase (Sna,d
) because of the finite probability that they are in close proximity of
other 13
C nuclei. Furthermore, some labeled peptide molecules are unfibrillized and
we assume that their signals will not dephase (Sl,u
). Consequently, we can write
Sraw tð Þ
Srawð0Þ
¼
Sl;f
tð Þ þ Sl;u
þ Sna;d
tð Þ þ Sna;u
Sl;fð0Þ þ Sl;u þ Sna;dð0Þ þ Sna;u
: (3)
An estimation of the Sna,d
signal can be obtained by measurements of the
unlabeled fibril sample. For convenience, here we assume that 10% of the natural
abundance signal will dephase, i.e., Sna,d
¼ Sna,u
Â 0.1/0.9, so that we can write
0:1
0:9 þ 1
À Á
Sna;u
Srawð0Þ
¼
20 Â 1:1%
1 þ 20 Â 1:1%
: (4)
Similarly, we can obtain
1Àxu
xu
þ 1

Sl;u
Srawð0Þ
¼
1
1 þ 20 Â 1:1%
; (5)
where the factor xu denotes the fraction of the unfibrillized samples. For a suffi-
ciently long dephasing time (ca. 70 ms), the fraction of the residual 13
C signal that
does not decay to zero becomes
Sresidual
Srawð0Þ
¼
Sl;u
þ Sna;u
Srawð0Þ
: (6)

On the basis of (4)–(6) we can estimate xu experimentally:
xu ¼
1
0:82
Sresidual
Srawð0Þ
À 0:18 Â 0:9

: (7)
Consequently, the signal fractions of Sl,f
(t)/Sl,f
(0) can be calculated and com-
pared with simulations. For samples prepared by bacterial expression, correction of
the background signals can be carried out in a similar fashion [48, 53, 54]. It is
noteworthy that spin geometries deviated from linearity, which may occur in the
side-chain 13
C nuclei such as Cb
, would produce more rapid signal decays and
smaller residual signal fraction [55].
2.3.2 Torsion Angle Determination
The backbone torsion f angle is defined as the dihedral angle of C0
(iÀ1)N(i)Ca
(i)C0
(i).
Therefore, the f angle of the residue i can be determined by measuring the distance
between C0
(iÀ1) and C0
(i) [56] and the most sensitive region of fj j is from 40 to 140
[57]. This strategy, together with other techniques based on tensor correlations
(Sect. 6), has been applied to characterize the secondary structure of the bend region
of Ab1–40 fibrils [57]. In a similar fashion, the backbone torsion c angle of the
residue i, which is defined as the dihedral angle of N(i)Ca
(i)C0
(i)N(i+1), can be
determined by measuring the distance between N(i) and N(i+1). Not surprisingly,
the most sensitive region for cj j determination is quite comparable to that of fj j
[47, 55]. For the measurements of multiple N(i)–N(i+1) distances, one could exploit
the idea of Ca
-detection or the resolution enhancement provided by the C0
–Ca
and
Ca
–Cb
correlations [55]. For the fibril samples formed by islet amyloid polypeptides,
the c angle of the residue Phe23 extracted from the Ca
-detected 15
N fpRFDR-CT
data is consistent with a bend structure in the region of residues 18–27 [47].
2.3.3 PITHIRDS-CT
Although fpRFDR-CT is a constant-time technique, the effect of T2 relaxation is
different as the positions of the WAHUHA pulses vary. Furthermore, a strong rf
field is required to achieve the hard pulse approximation for WAHUHA, which
could present a stringent condition for proton decoupling. As an alternative to the
use of WAHUHA pulses, Tycko has developed a new approach to construct
the constant-time version of fpRFDR [55]. In general, the cyclic time displacement
of an arbitrary recoupling sequence by tn will introduce a phase factor exp(imortn)
and will rotate the average Hamiltonian as follow [55]:
Hn ¼ eimortn
Urf Mtr À tn; 0ð Þ HUrf Mtr À tn; 0ð ÞÀ1
n o
; (8)
54 J.C.C. Chan

where Mtr denotes the cycle time of the sequence and Urf is the unitary operator
defined by the rf field. We now consider the pulse sequence of fpRFDR and set
tn ¼ 2pn 3oR= , where n ¼ 0, 1, 2. Because each of the p pulses in fpRFDR has a
duration of one-third of the rotor period, it can be shown that the corresponding
operator of Urf Mtr À tn; 0ð Þ is a unity operator. Consequently, if we concatenate
H0, H1, and H2, we will have
H0 þ H1 þ H2 ¼ 1 þ eimort1
þ eimort2
È É
H ¼ 0: (9)
The novelty of (9) is that the net homonuclear dipolar dephasing can be con-
trolled by a systematic variation of the number of the H0, H1, and H2 blocks. This
technique has the acronym of PITHIRDS-CT [55] and has the virtues that the effect
of T2 is identical for all data points and that the rf field of all the pulses is only 1.67
times the spinning frequency. The only experimental concern is that very stable
spinning or active rotor synchronization may be required for the implementation of
PITHIRDS-CT.
2.4 Multiple-Quantum NMR
As discussed above, dipolar dephasing experiments can provide very valuable
structural information for the study of amyloid fibrils. However, for a given
dephasing rate, it is not trivial to deduce the number of spins constituting the spin
cluster. In this regard, multiple-quantum (MQ) NMR is a powerful technique for
spin counting because the observation of an n-quantum signal implies that there
must be at least n spins coupled in a spin network [58]. The first application of MQ
NMR to the study of amyloid fibrils was carried out under static condition [59].
With an excitation time of 14.4 ms, signals up to 5Q were observed for two singly
labeled Ab1–40 fibril samples (Ala21-13
Cb
and Ala30-13
Cb
). These observations
have firmly established that the b-sheet structure of the Ab1–40 fibrils is in-register
parallel [59]. At a magnetic field of 9.4 T, the total experimental time for each
sample (10–15 mg) is approximately 100 h, with a recycle delay of 1 s. In addition
to the issue of poor sensitivity, MQ NMR measurements for C0
under static
condition are very inefficient because of the large CSA. To tackle these problems,
Oyler and Tycko have incorporated the fpRFDR sequence into some MQ NMR
techniques developed for static solids [60]. The design principle is quite similar to
that of fpRFDR-CT. For a singly labeled Ab1–40 fibril sample (Val39-13
C0
), signals
up to 3Q were observed with an excitation time of 31.1 ms under a spinning
frequency of 18.519 kHz. The total experimental time is ca. 28 h for 8 mg of the
sample. Although the sensitivity has greatly improved under MAS condition, the
downscaling of the effective Hamiltonian leads to a substantially longer excitation
time. On the other hand, the intramolecular 3Q signal has been observed in a
uniformly 13
C labeled fibril sample with an excitation time of 1.2 ms [60].

This observation illustrates an interesting possibility of probing torsion angles by a
controlled evolution of the intramolecular MQ signals, just as discussed by Levitt
and co-workers [61].
2.5 Polarization Transfer Via Homonuclear J-Coupling
Under the high-resolution condition provided by MAS, it is possible to probe the
correlations between different nuclei via the dipole–dipole interaction or the
J-coupling [62, 63]. It is of great interest to pursue J-coupling mediated polarization
transfer in SSNMR [64–76] both because of the selectivity offered by this through-
bond interaction and because of the 100% theoretical transfer efficiency for a two-
spin system. To realize polarization transfer via J-coupling, other internal interac-
tions such as chemical shifts and homonuclear dipole–dipole coupling must be
efficiently suppressed. A very successful pulse sequence for this purpose is total
through-bond-correlation spectroscopy (TOBSY) [65]. A typical TOBSY sequence
would create the following average Hamiltonian to the lowest order:
H ¼ 2pJisoI Á S: (10)
However, typical polarization transfer efficiency reported for 13
C–13
C TOBSY
measurements of polypeptides is significantly less than the theoretical maximum.
One of the major reasons is due to the requirement of high power 1
H decoupling
during the polarization transfer, which is usually set to be three times larger than the
recoupling field [37, 77].
Many years ago, Yannoni et al. demonstrated that separate proton decoupling is
in principle unnecessary for 13
C nutation spectroscopy [78]. Recently, it has been
shown in a 13
C homonuclear dipolar recoupling experiment that MAS alone is
sufficient for good 1
H decoupling when the spinning frequency is high enough [38].
A systematic study has also shown that significant excitation of 13
C homonuclear
double-quantum coherence can be acquired without 1
H decoupling [79]. This
no-decoupling approach, coined as NO-DEC by Baldus and co-workers [79], was
first tested for dipolar recoupling experiments. Intuitively, this NO-DEC approach
can be immediately incorporated into most existing TOBSY-like sequences [65, 66,
70–73]. By numerical simulations we found that proton decoupling is indeed not
necessary for the so-called R-TOBSY method, as long as the rf recoupling field is
high enough. Experimentally, a good C0
! Ca
polarization transfer efficiency
(50%) in a uniformly labeled noncrystalline polypeptide has been achieved
without 1
H decoupling, for which the rf field was set to 125 kHz at a spinning
frequency of 25 kHz [80] (Fig. 2). Although the chemical shift difference between
C0
and Ca
becomes larger at higher magnetic field, numerical simulations based on
the R-TOBSY technique shows that the transfer efficiency at a field strength of
18.8 T is nearly identical to that at 7.05 T.
56 J.C.C. Chan

2.6 Frequency-Selective Polarization Transfer
To achieve a more selective polarization transfer, e.g., C0
$ Ca
, the so-called
multiple chemical shift precession (MCSP) could be employed to achieve frequency
selective polarization transfer based on J-coupling [81]. The design principle of
MCSP has a close analogy to the DANTE concept in the zero-quantum subspace.
Consider the ZQ coherence excited by a TOBSY pulse block. Under free precession,
the ZQ coherence will evolve at a frequency equal to the chemical shift difference
(D) of the two interacting spins. As an analogy to the DANTE concept, a train of
TOBSY pulse blocks can be used to excite selectively the desired ZQ coherence in a
multiple-spin system, provided that the free precession period between two TOBSY
blocks is set equal to the integer multiples of 1/D. That is, for other spin pairs whose
chemical shift difference is different from D, the flip-flop term of the average
Hamiltonian will be truncated. Figure 3 shows the experimental results obtained
for [U–13
C, 15
N]-alanine. The upper trace represents the regular TOBSY experi-
ment, in which a significant portion of the C0
polarization has been transferred to Ca
and Cb
. As we set the precession period equal to 1/D and increase the N from 1 to 4, a
significant increase in the Ca
polarization is produced at the expense of the Cb
polarization. The selectivity of the MCSP approach depends on the number of
precession periods. An optimum value for N has to be determined experimentally.
The idea of frequency selectivity is certainly not restricted to J-coupling
mediated polarization transfer. Furthermore, frequency selective polarization trans-
fer can also be realized by DQ recoupling techniques. For the technique of shift-
evolution-assisted selective homonuclear recoupling (SEASHORE), which
employs POST-C7 to construct an effective DQ coupling [82, 83], frequency
selective polarization can be achieved when the transmitter offset is set to the
Fig. 2 13
C–13
C correlation
spectrum measured for the
MB(i + 4)EK polypeptides at
7.05 T under 25 kHz MAS
spinning. The projection of
the shaded region is shown to
highlight the excellent
C0
! Ca transfer efficiency.
(Figures and caption adapted
from [80]. Copyright (2006),
with permission from
Elsevier)

midpoint of the chemical shifts of the spin pair of interest, i.e., oI þ oSð Þ ¼ 0 [84].
In comparison, the frequency selectivity of MCSP depends on the duration of the
free precession period, whereas SEASHORE may rely only on the transmitter
position for its selectivity. The latter approach has the advantage that the free
precession period can be set to multiples of the rotor period. Strictly speaking,
the frequency selectivity is achieved in SEASHORE when the phase factor
oI þ oSð Þntr is zero or a multiple of 2p, where ntr is the duration of the free
precession period [84]. Very recently, the technique of fpRFDR has been
incorporated in the framework of SEASHORE [85]. The resultant technique, viz.
ZQ-SEASHORE, can achieve frequency selective dipolar recoupling under very
fast MAS condition (40 kHz).
3 Heteronuclear Dipolar Recoupling Techniques
3.1 REDOR
Rotational echo double resonance (REDOR) [86] is one of the most important
techniques developed for solid-state NMR spectroscopy. The theory of REDOR is
Fig. 3 Experimental results measured for [U–13
C, 15
N]-alanine based on the MCSP approach.
The polarization of Ca
after the mixing period increases as the number of R-TOBSY mixing
periods increases to four. Accordingly, the Cb
is nulliﬁed eventually. (Figure and caption adapted
from [81]. Copyright (2006), with permission from Elsevier)
58 J.C.C. Chan

well understood [87, 88] and requires no further discussion in this review. It has
been shown that the distances along the peptide backbone obtained by 13
C{15
N}
REDOR measurements can provide useful constraints on the backbone torsion
angles [89]. Another important application of REDOR in the studies of amyloid
fibrils is the determination of the H-bond registry of the b-sheets. We will discuss
some specific details relevant to this application in the following section.
To avoid the interference from intramolecular REDOR dephasing, peptides with
15
NHi labels could be mixed with peptides with 13
COj labels in a 1:1 ratio before
fibrillization, where i and j denote the residues with isotopic enhancement at the
amide and carbonyl sites, respectively. If an in-register parallel b-sheet is consid-
ered as the hypothetical structure, the most adequate model for the analysis of the
13
C{15
N} REDOR data measured for the case of i ¼ j should be a 15
N–13
C–15
N
spin system, where the NCN angle is ca. 127
and the two 15
N–13
C distances are 5.3
and 5.5 A˚ (Fig. 4a). For the case of i ¼ j + 1, the NCN angle should be 154
and the two 15
N–13
C distances 4.2 and 5.6 A˚ . Other combinations of i and j for an
Fig. 4 (a) Model for an in-register parallel b-sheet for REDOR simulations. Only the backbone is
shown and the residue labels correspond to the sequence of Ab1À40. Relevant distances between
Phe20 amide nitrogens (blue in color) and backbone carbonyl sites (dark green in color) are
shown. (b) Model for an antiparallel b-sheet with 17 + k $ 21 À k registry. (Figure and caption
adapted from [51]. Copyright 2009 American Chemical Society)

in-register parallel b-sheet are not likely to produce any REDOR fraction (DS/S0)
larger than 0.1 [51]. For an antiparallel b-sheet (Fig. 4b), if the 15
NHi makes a
hydrogen bond to the 13
COj on a neighboring peptide chain, the REDOR dephasing
can be analyzed based on the 15
N–13
C–15
N spin system where the NCN angle is ca.
180
and the two 15
N–13
C distances are 4.2 and 5.5 A˚ . Furthermore, if the residues
i and j are not hydrogen bonded, the corresponding REDOR fractions will be
significantly smaller. Consequently, measurements of the 13
C{15
N} REDOR data
of the judiciously labeled samples can be carried out to determine the H-bond
registry. Although the spin systems are based on idealized geometry, the agreement
between the experimental and simulation data are usually quite satisfactory,
provided that the contribution of the 13
C signals arising from the unlabeled sites
has been properly accounted for. A very detailed discussion of the procedure for
background signal correction has been documented in the literature [44]. Because
the 13
C–15
N distances targeting in our REDOR experiments are in the range of
4.5–5.5 A˚ , the required dephasing time is usually up to 50 ms. To minimize the T2
relaxation of the 13
C0
signals, we find that the REDOR pulse sequence developed by
Anderson et al. [90], where the rotor synchronized p pulses are alternating between
the dephasing and observe channels, is most suitable for the study of amyloid fibrils.
Although a train of p pulses are applied in the 13
C channel, the recoupling of 13
C
homonuclear dipole–dipole interaction should be negligible for the cross-b motif
because the closest 13
C–13
C distance within the same b-sheet layer is greater than
9 A˚ , provided that the peptides with 15
N labels and those with 13
C labels are well
mixed before fibrillization. The situation is somewhat more complicated for those
fibril samples formed by the polypeptides which contain the AGAAAAGA
sequence. If this palindrome sequence is located in the core region of the fibrils,
it is very likely that the two neighboring b-sheets would be closely packed to form
the so-called steric zipper [20, 91]. As such, the interlayer distance could be as close
as 5 A˚ [52]. In any case, one can monitor the attenuation of the reference signal (S0)
as a function of the dephasing time to verify if there is any sizable homonuclear
dipolar interaction among the 13
C spins.
3.2 Frequency-Selective REDOR
Frequency-selective REDOR (fsREDOR) is a very powerful technique developed
for the study of 13
C and 15
N uniformly labeled peptides or proteins [92]. The
basic idea of this technique is to combine REDOR and soft p pulses to recouple a
selected 13
C–15
N dipole–dipole interaction in a multiple-spin system. Usually one
could use Gaussian shaped pulses to achieve the required selective p inversions.
Other band selective shaped pulses have been developed for a more uniform
excitation profile [93]. In its original implementation, fsREDOR was used to extract
the internuclear distances of several model crystalline compounds [92]. In the past
few years, this technique has proven to be very useful for the study of amyloid
fibrils as well. For the Ure2p10–39 fibril samples containing 13
C and 15
N uniformly
60 J.C.C. Chan

labeled Gln, 13
C detected fsREDOR was used to assign the 15
N signals arising from
the side chain (111 ppm) and backbone amide sites (125 ppm), without measuring
the more time-consuming 13
C/15
N correlation spectrum. Experimentally, selective
inversion of the 15
N peak at 111 ppm produced greater dephasing of the Gln18 d-
carbon and selective inversion of the 15
N NMR peak at 125 ppm produced greater
dephasing of the 13
Ca
signal [45]. For the WT Ab1–40 fibril samples with uniform
15
N and 13
C labeling at F20, D23, V24, K28, G29, A30, and I30, one can use
fsREDOR to probe selectively the salt bridge resulting from the close proximity
between D23 and K28 [51]. The viability of this method stems from the fact that the
Cg signal of D23 and Nx of K28 are well resolved from other backbone C0
and amide
15
N signals, respectively. In addition to these applications, fsREDOR has been
incorporated in other newly developed techniques as discussed below.
3.3 DSQ-REDOR
Amyloid fibrils formed by peptides and proteins that are rich in glutamine or
asparagine residues are of particular interest, both because of their involvement in
neurodegenerative disorders such as Huntingon’s disease [94] and because of the
hypothesis put forward by Perutz that these fibrils are stabilized by linear chains of
hydrogen bonds among the side-chain amide groups of glutamine or asparagine.
Perutz coined the phrase “polar zippers” to describe the putative side-chain hydro-
gen bonding interactions [95, 96]. However, it is not trivial to provide direct
experimental evidence for the formation of polar zippers in amyloid fibrils. For
each side chain the intraresidue 15
N–13
C dipole–dipole coupling amounts to
1,280 Hz, corresponding to a chemical bond distance of 1.338 A˚ [97]. If a linear
chain of hydrogen bonds among the amide groups of glutamine is formed, the
interresidue 15
N–13
C dipole–dipole coupling would be 25–78 Hz (3.4–5.0 A˚ near-
est-neighbor 15
N–13
C distance). For 13
C and 15
N uniformly labeled samples, it is
very difficult to characterize the relatively weak interresidue 15
N–13
C dipolar
coupling in the presence of the strong intraresidue 15
N–13
C coupling by regular
13
C{15
N} REDOR.
Very recently, a novel solid-state NMR technique has been developed by Tycko
et al. to probe the formation of polar zippers in amyloid fibrils [45]. This technique
is an extension of the fsREDOR techniques. Referring to Fig. 5, a short fsREDOR
pulse train is applied during the pulse sequence period t1 to prepare intraresidue,
heteronuclear “double single-quantum” (DSQ) coherences between directly-
bonded 13
C/15
N pairs in side-chain amide groups. DSQ coherences are represented
by spin density operator terms of the form I1xS1x in the standard product operator
formalism [100]. It is easy to show that the coherence I1xS1x is unaffected by the
Hamiltonian of the form I1zS1z. In other words, the intraresidue DSQ coherences are
unaffected by intraresidue 15
N–13
C couplings during the longer fsREDOR dephas-
ing period td, but can decay due to intermolecular 15
N–13
C couplings pairs if such
couplings are present. DSQ coherences at the end of td are converted to observable

carbonyl 13
C nuclear spin polarization by the final fsREDOR pulse train during
period t2. 13
C NMR signals that arise from the DSQ coherences are selected by
appropriate phase cycling of rf pulses in t1 and t2. This technique has the acronym
DSQ-REDOR. The DSQ-REDOR data obtained for the fibril sample formed by the
fragment of Ure2p prion protein (13
C and 15
N uniformly labeled at Gln18) are
consistent with the structural motif of polar zipper [45]. In addition, DSQ-REDOR
can also be used to determine the backbone f and c angles for peptide samples with
uniform 13
C and 15
N labels at two consecutive residues [101]. The idea is to create
the DSQ coherences for the 13
COi–15
NHi+1 pair. The excited DSQ coherences are
then evolved under the influence of the dipolar interactions of the 15
NHi–13
COi and
15
NHi+1–13
COi+1. Thus, the dephasing of the DSQ coherence has an implicit
dependence on the backbone torsion angles of fi+1 and ci.
3.4 Band-Selective TEDOR
Another useful technique which is closely related to fsREDOR is the band-selective
transferred echo double resonance (BASE TEDOR) [102]. As shown in Fig. 6, the
Fig. 5 Radio frequency pulse sequences for measurements of S1 and S2 in DSQ-REDOR experi-
ments. The MAS period tR is 100 ms. XY represents a train of 15
N p pulses with XY-16 phase
patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M ¼ N1 ¼ 4,
N2 + N3 ¼ 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to
9.6 ms. Signals arising from intraresidue 15
N–13
C DSQ coherence (S1) are selected by standard
phase cycling. Signal decay due to the pulse imperfection of 15
N pulses is estimated by S2. Decay
due to the intermolecular 15
N–13
C dipole–dipole couplings is calculated as S1(N2)/S2(N2). The
phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted
from [45])
62 J.C.C. Chan

13
C antiphase coherence generated in the first fsREDOR period is converted into the
15
N antiphase coherence by a pair of p/2 pulses on the 15
N and 13
C spins. With the
middle band-selective p pulse applied in the Ca
(or C0
) region, the coherence transfer
would occur between the amide nitrogen and Ca
(or C0
) only. In addition, the
selective 13
C p pulse can refocus the J-couplings between the excited spins and
other 13
C spins which are outside the bandwidth of the selective pulse. After the
chemical shift evolution in the 15
N dimension (t1 evolution), the 15
N antiphase
coherence is then transferred back to the 13
C antiphase coherence by the second
fsREDOR period [102, 103]. As discussed in the foregoing section, 15
N fpRFDR-CT
or PITHIRDS-CT can be used to probe the backbone c angle when two consecutive
amide sites are 15
N labeled. However, the spectral resolution of the amide 15
N is
rather poor compared to that of Ca
. Therefore, one can employ the BASE TEDOR
technique to transfer the 15
N signals to the directly bonded Ca
for detection, when the
samples are 15
N and 13
C uniformly labeled at multiple sites [55]. The 13
Ca
-detected
15
N fpRFDR-CT data have been acquired for fibril samples formed by islet amyloid
polypeptide, from which it has been shown that the Phe23 residue adopts a non-
b-strand conformation [47]. By a systematic variation of the fsREDOR period, the
BASE TEDOR technique can be used to probe internuclear bond distances. In
particular, the effective 15
N–13
C0
and 15
N–13
Ca
one-bond dipolar couplings
of selected residues of huPrP23–144 fibrils were determined at a MAS frequency of
11.111 kH. A variant of BASE TEDOR, known as z-filtered TEDOR, has also been
employed to determine a few dozen of the one-bond and two bond C–N distances of
the fibrils formed by the 11-residue fragment of human transthyretin [104].
3.5 1
H–X Dipolar Couplings
Any heteronuclear dipolar recoupling techniques developed for systems containing
multiple 1
H spins must have the property to suppress actively the 1
H–1
H dipolar
Fig. 6 Pulse sequence of 3D band-selective TEDOR. The selective 13
C pulses were applied in
either the Ca
region (~54 ppm) or the C0
region (~174 ppm). The short delays k ensure that the total
delay between the first and second REDOR periods is equal to an integer number of rotor cycles.
For all sequences, the p/2 and p pulses are represented by thin and thick black rectangles,
respectively, and have phase x. The p REDOR pulses on the 15
N channel (gray rectangles) were
phase cycled according to the XY-4 scheme [98]. (Figure and caption adapted from the Supporting
Information of [103]. Copyright 2010 American Chemical Society)

interaction. There are several methods to achieve this goal. In addition to the
frequency-switched LG (FSLG) technique [105, 106], symmetry-based methods
[107, 108] have also been developed for the characterization of C–H and N–H bond
lengths. Site specific one-bond dipolar couplings of 15
N–1
H and 13
Ca
–1
H have been
characterized for residues in the amyloid core region of huPrP23–144 fibrils [103].
Together with the results of the effective 15
N–13
C0
and 15
N–13
Ca
one-bond dipolar
couplings, it has been deduced that the structural dynamics at the sub-microsecond
time scale are approximately identical for residues located in different parts of the
amyloid core [103]. Other applications of the recoupling techniques for 15
N–1
HN
and 13
Ca
–1
Ha
can be found in the tensor correlation methods for the measurements
of backbone torsion angles (see Sect. 6).
4 Correlation Spectroscopy
Correlation spectroscopy is of paramount importance in solid-state NMR studies of
biological solids. On the basis of the 13
C and 15
N chemical shifts, it is possible to
estimate the backbone torsion angles if the secondary structure is in the a-helix or
b-sheet regions. This feature is particularly useful for the study of amyloid fibrils.
Furthermore, the signal line widths can provide a reliable measure on the structural
order. For well ordered fibrils, the line widths are usually in the region of 2–3 ppm
for lyophilized samples, whereas the line widths would become 0.5–1.5 ppm for
hydrated samples. Although one could rely on multidimensional techniques to
enhance spectral resolution, very often one can also reduce the ambiguities in
data analyses by comparing spectra obtained for the samples prepared with differ-
ent labeling schemes. For example, by comparing the spectra of uniformly labeled
samples with those of “diluted” samples (mixture of labeled and unlabeled sam-
ples), one can distinguish the distant constraints arising from intra- or intermolecu-
lar contacts. In this section, we will discuss some correlation techniques which have
been successfully applied to the studies of amyloid fibrils.
4.1 Spectral Assignment
The 13
C signals within a uniformly labeled residue can be assigned by broadband
13
C homonuclear correlation spectroscopy. NMR techniques commonly employed
for the spectral assignments of fibril samples include proton-driven spin diffusion
(PDSD) [109], RFDR [36, 37], fpRFDR [38], dipolar assisted rotational resonance/
rf assisted diffusion (DARR/RAD) [110–112], dipolar recoupling enhanced by
amplitude modulation (DREAM) [113], and TOBSY [65, 71, 73, 114]. It should
be noted that there does not exist a universal technique optimized for all kinds of
samples. The choice of technique largely depends on the peptide sequence, the
isotopic labeling scheme, the desired measurement temperature, the inherent signal
64 J.C.C. Chan

line width, the static field strength, and the accessibility of the desired probe head.
Below we will discuss some illustrative examples taken from the literature of
amyloid fibrils.
The simplest techniques for 13
C homonuclear correlation spectroscopy are the
PDSD and DARR, for which the polarization-transfer mechanism is illustrated in
Fig. 7. The MAS frequency for PDSD is usually adjusted to be smaller than one half
of the chemical shift difference between the carbonyl and aliphatic regions, and the
mixing time is in the range of 20–50 ms [115–117]. For DARR, the MAS frequency
is adjusted in such a way that the carbonyl and aliphatic signals are close to but not
exactly on rotational resonance, and the mixing time is in the range of 5–20 ms [19,
118], depending on whether cross peaks due to multiple-bond connectivity are
desired. Both techniques have been applied to the study of amyloid fibrils in high
field (!14.1 T). Because the MAS frequency is relatively low (ca. 10 kHz), a stable
spinning can be maintained at relatively low temperature [119]. Other techniques
listed above such as fpRFDR require the rf irradiation in the 13
C channel and they
have much higher efficiency for one-bond polarization transfer than PDSD and
DARR. The mixing time is usually in the range of 2–3 ms. The technique of
fpRFDR is a viable option for the study of amyloid fibrils formed by relatively
Fig. 7 Schematic 13
C MAS spectra of two 13
C spins under 13
C–1
H recoupling, showing various
types of spectral overlap necessary for energy conservation in 13
C–13
C polarization transfer.
Spectrum (a) represents two resonances of Cali
at d1 and C0
at d2, where Cali
denotes any methine,
methylene, and methyl carbons. The hatched peak denotes one of the spinning sidebands of the C0
peak, being overlapped with the recovered 13
C–1
H dipolar powder pattern of the Cali
resonance.
Spectrum (b) shows spectral overlap for a pair of spins whose chemical shift difference is smaller
than the 13
C–1
H dipolar broadening. Spectrum (c) shows the case when spectral overlap occurs
between two 13
C–1
H dipolar powder patterns. Spectrum (d) is similar to (a), but the 13
CH
resonance shows a sideband pattern induced by modulation of the 13
C–1
H dipolar interaction
under suitable 1
H rf irradiation. Spectral overlap is achieved for one of the spinning sidebands of
the C0
peak and one of the modulation-induced sidebands of the Cali
resonance. The vertical dotted
lines denote the position of the spinning sideband of the C0
peak. (Figure and caption adapted from
[111]. Copyright [2003], American Institute of Physics)

short peptide sequence or full-length protein [54, 120], where the spinning fre-
quency is usually in the range of 18–22 kHz. The DREAM technique is highly
optimized for probing connectivity of the carbon signals in the aliphatic region
under fast MAS frequency (25 kHz), whereas the transfer between C0
and Ca
can
also be realized under very fast MAS (40 kHz at a static field of 14.1 T) [121]. An
interesting feature of the RFDR approach is that it could be applied without proton
decoupling if the 13
C recoupling field is around 120 kHz under fast spinning
conditions [122]. Another NO-DEC technique developed for high-field and fast
spinning conditions is cosine modulated adiabatic recoupling (CMAR) [123]. Both
techniques have been applied to the study of amyloid fibrils [124, 125].
Recently, the use of paramagnetic relaxation enhancement (PRE) in biological
solid-state NMR has received considerable attention [126–128]. On the basis of
PRE, Ishii et al. have developed a very efficient strategy to carry out the 13
C
homonuclear correlation experiments (paramagnetic relaxation-assisted condensed
data collection, PACC), for which convincing results have been obtained for
amyloid fibrils [129]. In the presence of paramagnetic species (e.g., Cu-EDTA),
the proton T1 relaxation of the Ab1–40 and Ab1–42 fibril samples can be shortened
substantially. Under the condition of 40 kHz MAS, a very weak 1
H decoupling
(7 kHz, TPPM) is sufficient to provide a decent spectral resolution. Overall, the
experimental recycle delay for PACC can be cut down to 0.2 s, rendering the mea-
surements of fibril samples at the nanomole scale possible at 9.4 T. We note in
passing that the effect of PRE on the 13
C CPMAS spectra has also been used to
probe the solvent exposed regions of PrP106–126 fibrils and oligomers [130].
For fibril samples comprising relatively short peptides prepared by solid-phase
synthesis, the 13
C–13
C correlation spectra alone could provide site-specific 13
C
chemical shifts because the sequence positions of the labeled residues are known.
However, for samples prepared by bacterial expression, techniques such as
NCOCA and NCACX are required to carry out sequential assignment [121]. The
coherence transfer between 15
N and 13
C nuclei is the basic step for sequential
assignment techniques. There are two transfer mechanisms developed for the
13
C–15
N coherence transfer. For the technique of SPECIFIC CP, the 13
C spin
locking field is adjusted to be comparable to the resonance offset so that the
matching of the Hartmann–Hahn conditions would depend on the position of the
13
C transmitter [131]. As an illustration, the coherence transfer from 15
N to Ca
and
15
N to C0
can be selected by placing the 13
C transmitter at ca. 44 and 162 ppm,
respectively, when the 13
C and 15
N rf fields are set to 5 and 30 kHz, respectively,
under a MAS frequency of 25 kHz [121]. Alternatively, using the technique of
BASE TEDOR or ZF-TEDOR, frequency selective 13
C–15
N coherence transfer can
also be achieved [125, 132]. As shown in a study of Ab1–40 fibrils, an evolution
period of 2.87 ms could result in strong intraresidue 13
Ca
/15
N cross-peaks [132]. On
the other hand, a mixing period of 6 ms is optimized for two-bond 15
N(i+1)–13
C(i)
transfer, which can facilitate sequential assignment of the backbone signals [124].
The aforementioned assignment techniques based on dipole–dipole interactions
are sufficient for the fibril samples with limited structural dynamics. In the presence
of substantial dynamics, which may significantly attenuate the dipole–dipole
66 J.C.C. Chan

interactions between neighboring nuclei, the 13
C{1
H} CP signals of some residues
may become missing in the dipolar-based correlation spectra. As discussed earlier,
the homonuclear polarization transfer of TOBSY proceeds through chemical bonds.
Consequently, the TOBSY sequences have the same selectively towards both the
mobile and rigid parts of the system. This feature is an advantage in the study of
hydrated fibril samples formed by sizable proteins or polypeptides. Using INEPT or
CP as the preparation step for the subsequent TOBSY polarization transfer, one can
select the 13
C signals corresponding to either the mobile or the rigid parts, respec-
tively [133]. The latter are usually originated from the core region of the amyloid
fibrils [115, 134–136] and the mobile region is presumably solvent exposed [125].
To detect the signal arising from the mobile region of fibrils and to alleviate the
interference of the signals from monomers, one can incorporate a T2 filter before the
13
C{1
H} CP step as shown in Fig. 8 [5, 134].
It is well known that the fibrils formed by different fragments of the b-amyloid
peptide could have different molecular structures [4]. While the studies of the fibril
structures formed by a variety of protein fragments can deepen our understanding of
the underlying biophysical principles of protein folding and misfolding, the fibrils
formed by bona fide proteins remain to be the most biological relevant targets. Very
often, these targets such as prion protein have to be prepared by bacterial expres-
sion. Although the carbon sources of 1,3-13
C-glycerol and 2-13
C-glycerol could be
used to enhance the spectral resolution, signal overlap may remain a severe problem
when the molecular mass of the fibril-forming monomer becomes too large. In
particular, when the number of cross-peaks is considerably smaller than the number
of residues in the protein sequence, manual sequential assignment may become
very difficult. Furthermore, it is important to check for the existence of any
alternative sets of assignments which are consistent with the same set of spectra.
To tackle this problem, Tycko et al. have developed a computer protocol based on a
Fig. 8 Pulse sequence for the measurement of homonuclear correlation spectra with T2 filtering.
Narrows bars indicate p/2 pulses and broad bars indicate p pulses. Experimental conditions
employed for a-synuclein fibrils samples: static field strength 9.4 T; temperature À5
C; spinning
frequency 8 kHz; T2 filter 100 ms; CP contact time 2.5 ms; TOBSY mixing time 6 ms. The rf
phases can be found in the original figure and caption. (Figure and caption adapted from the
Supporting Information of [134]. Copyright (2005) National Academy of Sciences, USA)

Monte Carlo/simulated annealing (MC/SA) algorithm for sequential assignment in
uniformly 13
C, 15
N-labeled proteins [137]. The two-dimensional (2D) NCACX and
NCOCX spectra measured for the fibril samples of full-length Syrian hamster prion
protein (residues 23–231) have been analyzed by the MC/SA protocol, from which
it has been concluded that the fibril core is formed primarily in the region of
residues 173–224 [54].
4.2 Distance Constraints
When site specific 13
C and 15
N chemical shifts are available, preliminary structural
conformation of the individual polypeptide strand can be obtained by TALOS
calculations [138, 139], from which one can easily identify the b-sheet regions of
the protein sequence. To refine the backbone conformation, one can use the proton-
mediated techniques [140], viz. NHHC and CHHC, to probe the short-range HN
–Ha
and Ha
–Ha
contacts ( 3 A˚ ). Consider the framework of the NHHC pulse sequence.
After the initial 15
N{1
H} CP, the polarizations of HN
are prepared by the 1
H{15
N}
CP with a contact time of ca. 150 ms. Then, a very brief 1
H–1
H spin diffusion period
(ca. 200 ms) is used to allow the contacts of HN
–Ha
, if any. Finally, the Ha
polarizations are transferred to Ca
for detection by another brief 13
C{1
H} CP
(150 ms). The CHHC experiment can be carried out in a similar fashion. As
discussed by Baldus et al. [141], the sequential HN
(i+1)–Ha
(i) distance is less than
2.6 A˚ for the b-sheet conformation, whereas the distance is about 3 A˚ for a-helices.
Therefore, NHHC spectra are very useful for the identification of the core regions of
amyloid fibrils [49, 134]. For fibril systems with antiparallel b-sheet organization,
the CHHC experiment is well suited to determine the H-bond registry because the
nearest distance of the Ha
s between the aligned residues is ca. 2.1 A˚ [10]. Further-
more, for the fibrils formed by an equimolar mixture of 13
C labeled and 15
N labeled
monomers, only intermolecular contacts will be observed in the NHHC spectrum
[49]. Both intermolecular and nonsequential intramolecular contacts obtained by
NHHC and CHHC experiments are very important for structural determination [49].
To determine long-range homonuclear distance constraints, the techniques of
PDSD and DARR are most commonly employed. Indeed, the PDSD technique has
been employed to derive distance constraints for the first protein structure deter-
mined by solid-state NMR at 17.6 T [142]. When the mixing time is in the range of
250–1,500 ms, long-range contacts up to ca. 6 A˚ become detectable in DARR or
PDSD experiments [132]. In the DARR spectra measured for Ab1–42 fibrils, the
cross peaks corresponding to the side-chain contacts between Phe19 and Leu34
have been observed, whereas the contact between Phe19 and Gly38 is missing
[143]. This observation shows that the mature Ab1–42 fibrils have a similar b-turn-b
structure as Ab1–40 fibrils, which is not consistent with a previous conclusion based
on mutagenesis results [144]. Nonetheless, it is well known that a slight difference
in incubation conditions can result in different molecular structures for amyloid
fibrils [145]. From the DARR spectra of the samples prepared by a 1:1 mixture of
68 J.C.C. Chan

two differently labeled Ab1–42 peptides, where one peptide was labeled at the 13
Cd
-
Gln15 and the other at the 13
Ca
-Gly37, the observation of the cross-peak between
Cd
-Gln15 and Ca
-Gly37 indicates that b-strand staggering occurs in Ab1–42 fibrils
[143], just as observed for Ab1–40 fibrils [132]. Note that for a nonstaggered
geometry, the predicted distance between the labeled sites would be longer than
the detection limit of DARR.
The architecture of b-sheet is also very important in the determination of fibril
structures. Given that the side chains of even-numbered and odd-numbered residues
in the same b-sheet point in opposite directions, any side-chain contacts between
odd-numbered and even-numbered residues observed in PDSD or DARR spectra
may indicate bend structures or intersheet contacts. With this consideration, the
quaternary contacts of the basic cross-b units have been found to be different for
two morphologically distinct Ab1–40 fibrils [132, 146]. As another example, the
quaternary contacts between b-sheets of the nonfibrillar oligomers formed by
PrP106–126 are found to be similar to those in fibrillar state [130]. Very recently, it
has been shown that the band selective RFDR (BASE RFDR), where selective p
pulses are used in the RFDR recoupling pulse train, is significantly more efficient
than DARR for probing long-range contacts [147]. Another useful technique for the
measurement of long-range 13
C–13
C or 15
N–15
N distances is the proton assisted
recoupling (PAR) technique [148]. The transfer mechanism of PAR is based on the
higher order effect, for which the dipolar truncation effect [149] is largely attenu-
ated. The PAR technique has been used to probe the intermolecular backbone
contacts of GNNQQNY fibrils and the results are consistent with an in-register
parallel alignment [25].
For the determination of heteronuclear long-range contacts, ZF-TEDOR with
long mixing time is a promising approach [150]. This method has been used to
study the fibrils formed by a 50:50 mixture of [15
N,12
C]- and [14
N,13
C]-labeled
b2-microglobulin monomers [151]. At a mixing time of 16 ms, a number of
intermolecular 13
C–15
N distances in the range of 5–5.5 A˚ have been detected.
The results prove that the fibrils adopt an in-register parallel b-sheet structure [151].
4.3 H/D Exchange Detected by Correlation Spectroscopy
We have shown that correlation spectroscopy is of great utility for spectral
assignments and for measurement of distance constraints. Here, we show that
the 13
C–15
N correlation spectroscopy can also be exploited to monitor hydrogen/
deuterium (H/D) exchange experiments. H/D exchange can be used to identify
solvent-protected backbone amide protons in amyloid fibrils [144, 152, 153]. In
brief, the amyloid fibrils are first incubated in deuterated buffer. After quenching
the H/D exchange, the fibrils must be disaggregated into monomers. The residues
at which the amide protons are exchanged to deuterons can then be detected by
mass spectrometry [154] or solution-state NMR spectroscopy [155]. The most
challenging step is the rapid conversion of the fibrils into the corresponding

monomers for subsequent detection. Although d6-DMSO is a reliable solvent for
the dissolution of amyloid fibrils, it is not trivial to minimize the effect of
backward exchange [155]. Different solvent mixtures have been suggested for
different amyloid systems, showing that it is largely an empirical task to prepare
the quenching buffer for an H/D exchange experiment [156]. Recently, we find
that the dissolution of the amyloid fibrils is not necessary when 13
C–15
N correla-
tion spectroscopy is used as the detection method [50]. That is, the technique of
15
N{1
H} CPMAS can be used to select the signals of the nitrogen atoms which are
in close proximity to protons. In particular, when the CP contact time is set to
100 ms, the 15
N signals of the deuterated amide groups would be largely sup-
pressed. By this simple strategy, the in situ characterization of H/D exchange in
amyloid fibrils could be realized.
As a proof-of-principle experiment, we measured the 15
N{1
H} CP spectra of the
amyloid fibrils formed by huPrP127–147 (Ac-GYMLGSAMSRPIIHFGSDYED-
NH2), which is 15
N and 13
C labeled at P137 and S143. Figure 9 shows the spectra
of the fibril sample (without any H/D exchange) obtained at two contact times, viz.
2 ms and 100 ms. For the 2-ms spectrum, two amide nitrogen signals are observed,
in which the peaks at 135 and 117 ppm are assigned to the amide nitrogen of P137
and S143, respectively [89]. When the CP contact time is reduced to 100 ms, the 15
N
{1
H} CP signal would be dominated by the one-bond 1
H–15
N transfer, which is
referred to as the 15
NH
signal in the subsequent discussion. Accordingly, the 15
NH
signal of P137 is not detectable because proline does not have any amide proton. As
expected, the 15
NH
signal of S143 is still observable under the same experimental
condition, which has approximately the same intensity as the 2-ms 15
N{1
H} signal.
Therefore, it is plausible to monitor the H/D exchange of amide protons by
measuring the corresponding 15
NH
signals without disassembling the fibrils into
monomers. We first define the protection factor of the amide proton as the ratio of
the 15
NH
signal intensities of the sample with and without H/D exchange. After
5010015020050100150200
15
N chemical shift/ppm
a b
Fig. 9 15
N{1
H} CPMAS spectra of the fibril sample formed by huPrP127–147 (15
N labeled at P137
and S143) at a spinning frequency of 20 kHz. (a) Contact time of 100 ms. (b) Contact time of 2 ms.
(Figure and caption adapted from [50]. Copyright 2010 WILEY-VCH Verlag GmbH Co.
KGaA, Weinheim)
70 J.C.C. Chan

42-h H/D exchange, the protection factors were found to be 0.07 Æ 0.03 and
0.6 Æ 0.3 for S143 and I138, respectively. The relatively large errors are mainly
due to the uncertainty of the amount of salts left in the samples. To alleviate this
problem, we redefine the protection factor as the ratio of the signal intensities of
15
NH
and 15
N, where the contact time of the corresponding 15
N{1
H} CP experi-
ments were set to 100 ms and 2 ms, respectively. The thus obtained protection factor
for I138 is 0.65 Æ 0.1. The error bar was determined by the root-mean-square noise
of the spectrum. For measurements on uniformly labeled fibril samples, our strategy
can be easily combined with 2D 13
C{15
N} correlation spectroscopy [50].
5 Recoupling of Chemical Shift Anisotropy
Under MAS alone, anisotropic interactions such as CSA and dipole–dipole cou-
plings are averaged to zero, provided that the spinning frequency is sufficiently
high. Since anisotropic interactions usually have a direct or indirect dependence on
molecular structure, numerous techniques have been developed to reintroduce these
interactions under MAS. Various CSA recoupling techniques have been proposed
and their merits have been briefly discussed by Schmidt-Rohr and co-workers
[157]. Many of these CSA recoupling methods are not applicable to homonuclear
dipole–dipole coupled systems or at MAS frequencies higher than 15 kHz, either
because finite-pulse effects become dominant or because the required rf fields
become too high to be practical. In this section, we describe the technique of
recoupling of chemical shift anisotropy (ROCSA) [158]. The major advantages of
ROCSA are: (1) that the effects of homonuclear dipole–dipole interactions are
strongly suppressed; (2) that the lineshape of the recoupled CSA pattern is identical
to the corresponding static powder pattern; (3) that the required rf field (in kHz) is
only about four times the MAS frequency; (4) that only phase shifts in multiples of
90
are required.
5.1 Theory of ROCSA
Under MAS at frequency or ¼ 2pnr, the high-field Hamiltonian of a spin-1/2
system takes the following form in the rotating frame:
HðtÞ ¼ HrfðtÞ þ HintðtÞ; (11)
HintðtÞ ¼
X
Lml
oL
m exp imortð ÞTL
l0; (12)
where L represents various internal interactions, oL
m are the orientation-dependent
coefficients of the Fourier components of the spatial functions (À2 m 2), and

TL
l0 are irreducible tensor operators of rank l. The Hamiltonian of a static powder
sample can be easily derived from the MAS Hamiltonian by setting or ¼ 0:
Hint ¼
X
Lml
oL
mTL
l0: (13)
ROCSA makes use of the CNn
n sequences [82, 159] to generate a static CSA
powder pattern under MAS condition. The average Hamiltonian for a CNn
n sequence
is [159]
H tq
À Á
¼
X
LLmlm
ðiÞm
oL
Lmlm exp imort0ð Þ dl
m0 Àbrf
À Á
Â
X
q
exp þiq
2p
N
mn À mnð Þ

TL
lm: (14)
All the symbols carry their usual meanings. If we want to create an average
Hamiltonian similar to the static one, we just need to keep the terms associated with
TCS
20 . Furthermore, the scaling factors of those terms should be identical. With the
pulse sequence of Cn1
n [160, 161], the symmetry allowed terms are
m ¼ 0; Æ1; Æ2; m ¼ 0ð Þ for n ! 3. For convenience we deﬁne the following scaling
factors:
wl
m ¼
1
tr
ðtr
0
dl
00 Àbrf
À Á
exp imortð Þdt: (15)
We want to derive a speciﬁc subcycle for Cn1
n such that the scaling factors wl
m are
identical for m equal to Æ1 and Æ2. In general, we have wl
m ¼ wl
Àm
À ÁÃ
and therefore
the conditions wl
m ¼ wl
Àm are equivalent to the conditions that wl
m are real numbers.
In particular, if we have a mirror symmetry of
brfðtÞ ¼ brf tr À tð Þ; (16)
for 0 t tr, we can obtain
wl
m ¼
1
tr
ðtr 2=
0
dl
00 ÀbrfðtÞð Þ exp imortð Þdt þ
ðtr
tr 2=
dl
00 Àbrf tr À t0
ð Þð Þ exp imort0
ð Þdt0
8

:
9
=
;
:
(17)
Setting tr À t0
¼ t for the second integral, we then have
72 J.C.C. Chan

wl
m ¼
1
tr
Â
ðtr 2=
0
dl
00 ÀbrfðtÞð Þ exp imortð Þdt À
ð0
tr 2=
dl
00 ÀbrfðtÞð Þ exp imor tr À tð Þð Þdt
8

:
9
=
;
;
(18)
wl
m ¼
2
tr
ðtr 2=
0
dl
00 ÀbrfðtÞð Þ cos mortð Þdt
8

:
9
=
;
: (19)
Consequently, under the mirror symmetry described in (16), wl
m must be real
because
dl
00 bð Þ ¼
Xl
k¼0
À1ð Þk lð Þ! lð Þ!
l À kð Þ!k! l À kð Þ!ðkÞ!
cos b
2
2 lÀkð Þ
sin b
2
2k
; (20)
where k is an integer.
Now consider the pulse sequence in Fig. 10. Each repetition of C spans one rotor
period. Between 0 and tr/2, the composite “0p” pulse 9003601802700 is applied.
This composite pulse, which has been commonly referred to as POST, is chosen
because it has been shown to compensate for effects of rf inhomogeneity [83]. The
mirror-image composite pulse is applied between tr/2 and tr. With this particular
design of ROCSA, the homonuclear dipole–dipole interaction is considerably
suppressed relative to the CSA.
5.2 ROCSA Spectra of Amyloid Fibrils
It has been shown both theoretically and experimentally that Ca
CSA values are
useful parameters to probe the local structures of biological systems [162, 163]. By
comparison of the experimental CSA values with the calculated shielding surfaces,
one may obtain an estimation of the backbone torsion angles of the corresponding
residues. As an illustration, Fig. 11 shows the ROCSA spectra measured for the
Ab11–25 fibril sample which was uniformly 13
C, 15
N-labeled at Val18 [158].
Isotropic 13
C chemical shift data indicate that Val18, Phe19, Phe20, and Ala21
adopt b-strand conformations in Ab11–25 fibrils. The Ca
CSA values obtained by
ROCSA measurements are consistent with b-strand conformations at these resi-
dues. As illustrated in the studies of microcrystalline proteins, ROCSA can be used
to obtain structural constraints on the secondary structure by characterizing the
chemical shift tensors of the backbone carbons [163]. We expect that such an
approach should also find fruitful applications in the study of amyloid fibrils.

For polypeptides with inherent structural disorders, the 13
C signals in the
carbonyl region are usually poorly resolved. Therefore, the characterization of the
C0
CSA, which is sensitive to the C ¼ O. . .HN hydrogen bond strength, will
become very difficult if more than one carbonyl carbon are 13
C labeled. Because
the Ca
signals of polypeptides are usually better resolved than the C0
signals, one
may transfer the C0
CSA patterns to the neighboring Ca
for subsequent detection.
This “Ca
-detection” scheme has been developed on the basis of ROCSA and
R-TOBSY [164]. That is, the C0
CSA is first recoupled by ROCSA and then the
pattern is transferred to Ca
for detection by R-TOBSY. Dipolar-based polarization
transfer techniques such as fpRFDR are not suitable in the present context because
the C0
–Ca
dipolar interaction will modulate the C0
CSA pattern and such modula-
tion may depend on the relative orientation of the C0
and Ca
chemical shift tensors,
which is usually unknown. Figure 12 shows the Ca
-detected C0
CSA patterns of the
amyloid fibrils formed by the peptide fragment of PrP109–122, in which the residues
Fig. 10 ROCSA pulse sequence based on Cn1
n symmetry. The rectangular blocks in black
represent p/2 pulses. The recoupling period (t1) comprises k cycles of Cn1
n. Each complete cycle
of Cn1
n spans n rotor periods (ntR). The rf phase of each Cq subcycle is set equal to 2pq/n, where q
is an index running from 0 to n À 1. Within each Cq subcycle, atR and btR indicate the position
and the duration of the POST composite pulse, respectively. We find that the solution
(a, b) ¼ (0.0329, 0.467) is a favorable choice for the suppression of the homonuclear dipole–dipole
interaction. The bracketed and subscripted values indicate the pulse length and rf phase in radians,
respectively. (Figure and caption adapted from [158]. Copyright [2003], American Institute of
Physics)
74 J.C.C. Chan

Ala113, Gly119, and Val122 are uniformly 13
C- and 15
N-labeled [164]. The C0
signals of Ala113 and Val122 are overlapping but their Ca
signals are well resolved.
The minor distortion of the C0
CSA pattern of Val122 may be attributed to the
structural disorder at the C terminus of the polypeptide. Studies on other model
compounds indicate that the Ca
-detection scheme for C0
CSA pattern is a robust one,
as long as the spin-lattice relaxation times of the C0
and Ca
signals are significantly
longer than the polarization transfer period. Again, the idea of Ca
-detection can be
incorporated easily in existing homonuclear correlation techniques.
6 Tensor Correlation Methods
Tensor correlation methods refer to the selection of two anisotropic interactions so
that the pattern of the 2D correlation spectrum can reveal the magnitudes and
relative orientation of the two tensorial interactions. Below we will discuss many
different SSNMR techniques suggested for the determination of peptide backbone
Fig. 11 ROCSA spectra for Val-18 of Ab11–25 fibrils. The C0
spectrum was measured at 9.39 T
under a MAS frequency of 20 kHz. The other spectra were measured at 14.09 T under the
frequency of 11 kHz. Upper traces are experimental spectra. Lower traces are best-fit simulations
for one-spin system. The rf carrier frequency is at 0 Hz. (Figure and caption adapted from [158].
Copyright [2003], American Institute of Physics)

torsion angles f and c under MAS. These techniques are all based on the principle
of tensor correlation [165–167].
6.1 Backbone Phi–Psi Angle Determination
The correlation of the chemical shift tensors of two neighboring carbonyl carbons,
say, C0
(i) and C0
(i+1), can be exploited to determine the backbone torsion f and c
angles of the residue i + 1. Because of the symmetry properties of the C0
chemical
shift tensor and the peptide plane, this approach cannot distinguish the conforma-
tions corresponding to (f, c) and (Àf, Àc) [168]. That is, a unique solution for
(f, c) is not warranted in general, unless the alternative solution is not allowed
sterically. The ﬁrst technique which exploits this correlation approach is the 2D
MAS exchange experiment [168, 169]. Other useful techniques include DQDRAW
[56, 170] and DQCSA [171]. The utility of these methods relies on the assumption
that the orientation of the C0
chemical shift tensor with respect to the peptide plane
is insensitive to the variation of the peptide conformation and the formation of
hydrogen bonds. Theoretical calculations carried out for a model glycyl–glycine
dipeptide at the DFT-IGLO level lend strong support to this basic assumption [172].
On the other hand, it has been shown by NMR measurements on model peptides
that the most shielded principal component (d33) is always perpendicular to the
peptide plane, whereas the orientation of the principal components lying in the
peptide plane has a variation of about 25
[173–179]. A more comprehensive
discussion of this issue can be found in a recent review [180]. Thus, the systematic
Fig. 12 Ca-detected C0
CSA patterns of the SHPrP109–122 ﬁbril sample. The upper and lower
traces correspond to the experimental and simulated spectra, respectively. Simulations correspond
to the evolution of a one-spin system under the ROCSA sequence. The only variables are the
chemical shift anisotropy and the asymmetry parameter. A Gaussian window function of 400 Hz
was applied to the simulated spectrum before the Fourier transformation. (Figure and caption
adapted from [164]. Copyright (2007), with permission from Elsevier)
76 J.C.C. Chan

errors of the backbone torsion angles determined by the C0
(i)–C0
(i+1) approach are
mainly due to the uncertainty in the tensor orientation of the C0
carbon. Nonethe-
less, the intrinsic structural inhomogeneity commonly found in amyloid fibrils
would presumably render this uncertainty immaterial. The major disadvantage of
this method is that each labeled sample can allow the determination of one pair of
f and c angles only.
For the study of Ab1–40 fibrils, it is very important to characterize the conforma-
tion of the non-b-sheet region (residues 25–29) in order to construct the molecular
model for the fibrils. On the basis of the measurements of 2D MAS exchange and
DQCSA, site specific torsion angles were obtained for the bend region of Ab1–40
fibrils [57]. Because of the multiplicity in the sign choices for the obtained f and c
angles, however, dimensional constraints obtained from EM images and the struc-
tural constraint that corresponds to the salt bridge formed between D23 and K28 are
required to deduce a unique molecular conformation for the bend region [57].
6.2 Backbone Psi Angle Determination
A direct determination of the backbone c angle can be obtained by the tensor
correlation of the N(i)–Ca
(i) and C0
(i)–N(i+1) vectors. One possibility is to excite the
DQ coherence between Ca
(i) and C0
(i) and then let the DQ coherence evolve under
the influence of the heteronuclear 13
C–15
N dipole–dipole interaction [181, 182].
The virtue of this design is that it can be easily combined with other resolution
enhancement technique such as INADEQUATE [183]. Alternatively, the magneti-
zation of C0
(i) dephased under the 13
C–15
N dipolar coupling can be transferred to
Ca
(i) for another period of 13
C–15
N dipolar dephasing [183]. This idea can be
combined with the NCOCA experiment so that the superior resolution provided
by the Ca
(i)–N(i+1) correlation could be exploited. The overall efficiency, however,
is relatively low due to the use of two polarization-transfer steps, viz. 15
N ! 13
C
and 13
C ! 13
C [183]. In comparison with the C0
(i)–C0
(i+1) techniques, the advan-
tage of the N(i)–Ca
(i)–C0
(i)–N(i+1) is that multiple c angles can be obtained from a
uniformly labeled system [183]. Note that this so-called NCCN experiment cannot
distinguish the sign of c and the most sensitive region is cj j equal to 140–180
[181]. To remove the sign ambiguity in c, one can resort to the correlation
experiments of different symmetries such as Ha
(i)–Ca
(i)–N(i+1)–HN
(i+1) [184].
Strictly speaking, the correlation of the Ha
(i)–Ca
(i) and N(i+1)–HN
(i+1) vectors
would depend on both the backbone c and o angles, but the deviation of o from
the ideal values, i.e., 180
for trans and 0
for cis conformations, should be very
small in most cases. The above pulse frameworks are very general and different
heteronuclear or homonuclear dipolar recoupling schemes can be incorporated in
them for the backbone or side-chain torsion angle determinations [184]. The NCCN
technique has been applied to study the backbone c angles of the GNNQQNY
fibrils [25]. The results indicate that there is a localized non-b-sheet structure at
residue N8 in one of the three fibril conformers.

All the techniques we have discussed thus far for c determination require
isotopic labeling of two consecutive residues. Nevertheless, it has been demon-
strated that the backbone torsion c angle can be determined within a single
13
C uniformly-labeled residue [185, 186]. The method, with the acronym RACO
for relayed anisotropy correlation, comprises three basic modules, viz. the CSA
recoupling of C0
, the polarization transfer from C0
to Ca
, and the heteronuclear
13
Ca
–1
Ha
dipolar recoupling [186]. That is, the backbone torsion c angle can be
determined by correlating the carbonyl 13
C chemical shift and the 13
Ca
–1
Ha
dipolar
tensors within a single 13
C uniformly-labeled residue. In its original implementa-
tion, RACO requires the acquisition of a series of 2D spectra under the hetero-
nuclear dipolar recoupling condition and therefore is not applicable for systems
with multiple uniformly 13
C labeled residues. This limitation of RACO can be
easily alleviated by separating the heteronuclear dipolar recoupling and the t2
acquisition periods, and by choosing recoupling pulse sequences designed for fast
MAS [187]. However, without a detailed understanding of the basic principles of
tensor correlation, it is not trivial to obtain the optimized implementation of RACO
by trial and error because there are many different recoupling pulse sequences
reported in the literature [63].
6.2.1 Echo Formation Between Two Correlated Anisotropic Interactions
In the following, we present a simple physical picture to illustrate some general
features of the RACO approach. As mentioned above, the backbone c angle can
be determined by correlating the C0
chemical shift anisotropy and the Ca
–Ha
dipolar interaction. Both interactions are anisotropic, i.e., the NMR signal evol-
ving under the inﬂuence of either interaction will decay (or dephase) to zero in a
powder sample. After the polarization transfer between C0
and Ca
, the signal
dephased in the ﬁrst period may be partially refocused in the second period. The
extent of the “echo” formation depends on whether the orientation dependence of
the average Hamiltonians during the CSA and dipolar recoupling periods are in
close resemblance [188]. In other words, the “echo” amplitude depends on: (1) the
orientation dependence of the average Hamiltonian; (2) the durations of the two
dephasing periods; (3) the relative orientation of the two internal interactions,
which is implicitly related to the backbone c angle. When the recoupling pulse
sequences for the CSA and the heteronuclear dipolar interactions are g-encoded
where the spatial parts m ¼ 2 are selected, the extent of the resemblance of the
two average Hamiltonians has a strong dependence on the c angle, and one could
then accurately determine the c angle by comparing the experimental echo
amplitude and the results simulated based on the model spin system, which is
usually set as C0
–Ca
–Ha
. For convenience, experimentally we chose to use the
FSLG technique which is a non-g-encoded sequence for heteronuclear dipolar
recoupling. Nevertheless, g-encoded sequences such as R185
2 should be a good
alternative option [108, 189]. Furthermore, to ensure the closest resemblance of
the two average Hamiltonians, the homonuclear polarization transfer inserted
78 J.C.C. Chan

between the two recoupling periods should be isotropic. That is, the R-TOBSY
sequence is a favorable choice for the homonuclear polarization transfer in the
present context.
The experimental strategy discussed above was applied to determine the dihedral
angle of uniformly 13
C and 15
N labeled L-alanine and N-acetyl-D,L-valine (NAV)
samples. The 13
C0
! Ca
peak intensities of three separate experiments
corresponding to zero, one, and two complete cycles of CSA recoupling were
measured while the dipolar recoupling period was fixed at three rotor periods
[188]. The experimental data were normalized by the first data point (no CSA
recoupling) and then compared with the numerical simulations carried out in the
same fashion as discussed earlier. Due to the symmetry properties of the C0
CSA and
the Ca
–Ha
dipolar interactions, the plot of squared deviations (w2
) between experi-
mental and simulation data will have reflection symmetries about À150, À60, 30, and
120
[186]. Minimum w2
values for L-alanine and NAV occur at c equal to 160
(161.5) and 175 (178.2)
, respectively, where the bracketed values correspond to the
crystallographic data obtained by diffraction techniques [190, 191].
For the fibril samples formed by the H1 fragment of the Syrian hamster prion
protein (SHPrP109–122, Ac-MKHMAGAAAAGAVV-NH2), the backbone c angles
of the alanine residues in the AGAAAAGA region were determined by the tensor
correlation method based on the RACO approach [52]. The C0
CSA of A113 was
characterized by the ROCSA incorporated with the Ca
-detection scheme [164] and
it was assumed that the C0
CSAs of all the alanine residues with b-strand confor-
mation are approximately the same. Additional simulations show that the c angle
determination is indeed not sensitive to the C0
CSA. As a matter of the inherent
symmetry of the tensors being correlated, there are two set of c angles which have
the best agreement with the experimental data. One is in the range of 75–100
,
whereas another one is in the b-sheet region. In this particular case, the secondary
chemical shift (d–drandom) data have shown that the AGAAAAGA region has the
b-sheet conformation. Consequently, the c angles of the palindrome region were
obtained with high precision, which had been used as the benchmark data for the
subsequent molecular dynamics simulations [52].
6.3 Backbone Phi Angle Determination
The backbone f angle can be determined by the correlation of the N–HN
and
Ca
–Ha
dipolar tensors [184, 192, 193]. The strategy of the earliest attempt is to
create the 15
N–13
C multiple-quantum coherence by REDOR and then let the
coherence evolve under the scaled heteronuclear dipole–dipole interaction gener-
ated by MREV-8 [193]. As the technique of MREV-8 is designed for applications
under static conditions, the phase evolution will be modulated by MAS. In other
words, the dipolar dephasing during the first half of the rotor period will be
refocused in the second half. Consequently, the spinning frequency must be less
than 3 kHz so that the dephasing period is long enough to reveal the angular

dependence on f with sufficient resolution. As a logical extension of the original
approach, it has been shown that the effective dephasing time of MREV-8 can be
lengthened by insertion of rotor-synchronized p pulses in the 13
C or 15
N channels
[192]. The idea is quite similar to REDOR because the average Hamiltonian of
the heteronuclear dipole–dipole interaction generated by MREV-8 has the opera-
tor form of IzSz [193]. Consequently, the double coupling scheme can be applied
under moderate spinning condition as long as the quasi-static approximation is
still valid (ca. 10 kHz). For higher spinning frequency, the time modulation of the
spatial part of the Hamiltonian (due to MAS) will interfere with the averaging
process of MREV-8 in the spin part. That is, the averaging of the undesired
homonuclear dipole–dipole interaction will become less effective. Because the
one-bond dipolar coupling constant of N–HN
is smaller than that of Ca
–Ha
by
approximately a factor of 2, the correlation of the two tensors will have a stronger
dependence on the f angle when the dipolar dephasing period of N–HN
is
doubled compared with that of Ca
–Ha
. This double coupling scheme has been
realized by preparing two separate dephasing periods for the corresponding
antiphase signals [192].
Taking the MREV-8 as a basic C element (duration ¼ tr/5), one can generate a
g-encoded [194] version of MREV-8 by concatenating the five C elements with an
rf phase set equal to k Â 2p/5, where k ¼ 0–4 [107]. The averaged Hamiltonian
calculated to the lowest order for this so-called T-MREV method has the following
form:
HIS ¼ kom¼À1Iþ þ kÃ
om¼þ1IÀf gSz; (21)
where IÆ denote the spin operators for protons, k is the scaling factor of the pulse
sequence, and om denotes the spatial part of the average Hamiltonian [107]. The
advantage of (21) is that the time dependence of both the spatial and spin parts has
been considered and therefore the dephasing of the magnetization is cumulative
over the whole irradiation period. As the T-MREV is constructed based on MREV-
8, its application is also limited to spinning frequency under 10 kHz. This drawback
can be alleviated by using recoupling sequence such as R185
2 [108, 189]. In general,
the use of g-encoded sequences for the heteronuclear dipolar recoupling requires a
proper account of the different T2 relaxation rates of the I and S states [107]. Based
on T-MREV, a 3D 1
H–15
N–13
C–1
H dipolar chemical shift experiment has been
constructed for the f angle determination as shown in Fig. 13. In fact, the same
experimental framework can be used for the c angle determination by the
Ha
(i)–Ca
(i)–N(i+1)–HN
(i+1) correlation [184].
The molecular structure of the amyloid fibrils formed by fragment 105–115 of
transthyretin (TTR105–115, YTIAALLSPTS) has been characterized by solid-state
NMR. The fibril backbone structure was first established based on the TALOS
analysis of the 15
N and 13
C chemical shifts [89]. Using the correlation experiments
of HN
(i)–N(i)–Ca
(i)–Ha
(i), Ha
(i)–Ca
(i)–N(i+1)–HN
(i+1), and N(i)–Ca
(i)–C0
(i)–N(i+1),
a total of 41 constraints on 19 backbone torsion angles have been obtained in a
80 J.C.C. Chan

subsequent study [104]. In addition, the torsion angles of most side chains have
been constrained by the long-range C–N distances obtained by the 3D z-filtered
TEDOR. Overall, a high-resolution structure of TTR105–115 in the fibrillar state has
been obtained [104], from which there are two interesting findings. First, the
conformations of the backbone and side chains are very close to the regions of
minimum intramolecular energy. Apparently, no significant energy barrier is pres-
ent regarding to the conformational change of the monomer during the fibrillization
of TTR105–115. Second, the residues P113 and T114 have adopted the b-sheet
conformation, although the restricted f angle of proline precludes the formation
of regular intermolecular hydrogen bondings at the sites of P113 and T114.
Fig. 13 Pulse sequence for the 3D 1
H–15
N–13
C–1
H dipolar chemical shift experiment to constrain
backbone and side-chain torsion angles. Polarization was transferred from 1
H to 15
N via ramped
CP, followed by 15
N chemical shift evolution during t1. The period rt2 was a constant time dipolar
recoupling period, composed of an integer number of rotor periods during which T-MREV is
applied to the 1
H spins. Polarization was subsequently transferred from 15
N to 13
C by amplitude-
ramped SPECIFIC CP, and a second constant time T-MREV recoupling period, t2, was applied to
the transverse 13
C coherences. Signal acquisition occurred during the period t3. The ratio of
1
H–15
N to 1
H–13
C dipolar evolution (r) was a fixed integer value, optimally 2. Narrow and wide
solid rectangles represent p/2 and p pulses, respectively. The phase cycling scheme can be found
in the original figure and caption. (Figure and caption adapted from [184]. Copyright 2002
American Chemical Society)

7 Conclusion and Outlook
Thanks to the pioneering works of many research groups, solid-state NMR is now a
well established spectroscopy for the study of biological solids, particularly for
those with inherent structural disorder such as amyloid fibrils. We have provided an
overview of a rather complete set of NMR techniques which have developed for
samples prepared by chemical synthesis or protein expression. There are many
different ways to present the materials discussed in this review. We hope that the
way we have chosen can give a snapshot of some facets of the very exciting
discipline of biological solid-state NMR spectroscopy. In spite of the success of
solid-state NMR as a tool in biological study, it is not yet a “mature” technique and
there is much room for further development. Below we will speculate on a few
possibilities from our own perspective.
To maximize the information content for each sample, the isotopic labeling
scheme is preferred to be the uniform one. Because long-range contacts are the most
important structural constraints, which can only be probed by dipolar-based tech-
niques, further development in the suppression of the dipolar truncation effect and
frequency-selective techniques is highly desirable for uniformly labeled samples.
Polarization transfer between 13
C and 15
N is the key step in many pulse sequences.
Techniques such as proton assisted insensitive nuclei cross polarization (PAIN-CP)
[195] are promising candidates for the design of more efficient heteronuclear
correlation experiments. Determination of backbone and side-chain torsion angles
is always an important issue in solid-state NMR. Although some very useful
techniques have been developed as discussed in this review, it is worthwhile to
search for the possibility to characterize uniquely the f and c angles in a singly
uniformly labeled residue. It can be envisioned that other tensor correlation tech-
niques such as Ca
H–C0
N [196] and NHN
–NHN
[197], which are not covered in this
review, may find fruitful applications. A research area which is of great interest is
the regime of very fast MAS (!40 kHz). Recoupling techniques developed for this
regime are presumably less susceptible to the higher-order effects. As discussed in
the chapter by Nielsen et al. [201] the optimal control theory has opened up a new
avenue for the design of pulse sequence. The optimal control software has been
implemented in the open-source SIMPSON package [198], which may be used to
optimize the performance of many existing recoupling techniques. The importance
of 14
N is clearly underrepresented in biological NMR. Nevertheless, some
promising techniques have been reported in the literature as discussed in the chapter
by Fernandez and Pruski [199]. Needless to say, dynamic nuclear polarization
(DNP) is an exciting option for signal enhancement in the NMR studies of
biological samples [200]. All in all, it can be safely concluded that biological
solid-state NMR will remain as a vibrant field for many years to come.
Acknowledgment This work was supported by the National Science Council of Taiwan. I would
like to take this opportunity to thank Dr. Robert Tycko (NIH, Bethesda, USA) for introducing me
to the field of amyloid fibrils. I also thank my former students Yun Mou, John Chin-Hao Chao, Tim
Wen-Tin Tsai, Shin-Wen Lee, Ni-Shian Lin, Fang-Chieh Chou, Hsin-Mei Cheng, Wen-Chi Chu,
82 J.C.C. Chan

Yun-Ju Tang, Huei-Ying Lian, Hsin-Kuan Lee, Tzu-Hsueh Huang, and Yuan-Chi Huang for their
many contributions in our own study of amyloid fibrils.
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