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National Institute of Chemistry
Slovenia
Department for Materials Electrochemistry
SOLID-STATE NMR
-theory and pharmaceutical
applications
Aljaž Godec, Uroš Maver
General theory of NMR
For convenience the physical basis of NMR will be shown for hydrogen nuclei
(proton)
Proton ≈ spinning bar magnet with
angular momentum, I
In agreement in NMR experiments only the
z component of I is known, Iz,
(I is undetermined in the x-y plane),
and is given by
h... Planck’s constant
i...spin of the proton (1/2)
hi
Iz =
2π
General theory of NMR
The angular and magnetic momentum are related by
uv
v
µ =γI
γ... gyromagnetic ratio of the nucleus
(physical property of the nucleus)
The z component of the magnetic momentum is then given by
γ hi
µz = γ I z ≡
2π
General theory of NMR
In NMR experiments the sample is placed in a static external magnetic field, B0.
The energy of the nucleus in B0 (E of Zeeman interaction) is
hγ iB0
E = − µ z B0 ≡ −
2π
-there are two energy states
for a proton in B0:
(i = +1/2)
(i = -1/2)
↓E state
↑E state
General theory of NMR
The spinning axis of the proton cannot align exactly parallel or antiparallel with the
static external field, but is precessing about it with angular frequency ω0
(Larmor frequency)
ω0 = γ B0
hγ B0
∆E = hν =
2π
Equilibrium population ratio
N −1/ 2
=e
N +1/ 2
−∆E
kT
<1
Occurrence of bulk
magnetization in +z direction
General theory of NMR
Bulk magnetization in +z direction
M z = ( N +1/ 2 − N −1/ 2 ) µ z
Mx = 0
My = 0
The equilibrium magnetization for N magnetic moments (N=N[+1/2]+N[1/2])
per unit volume, Mz0, is given by
M z0
⎛
= ⎜e
⎝
µ z B0
kT
−e
− µ z B0
kT
− µ z B0
⎛ µkTz B0
⎞
e
− e kT
⎜
⎟ µ z ≡ N ⎜ µ z B0
− µ z B0
⎠
⎜ e kT + e kT
⎝
⎞
⎟ µ ≡ N µ tanh ⎛ µ z B0 ⎞
z
⎜ kT ⎟
⎟ z
⎝
⎠
⎟
⎠
General theory of NMR
2
1
Mz
0
µ z 2 B0
⎛ µ z B0 ⎞
= N µ z tanh ⎜
≈N
⎟
kT
⎝ kT ⎠
y=tanh(x)
0
5
0
5
y=x
-1
-2
This magnetization does not build up instantaneously when the sample is placed in
a static external field (or after a 90° electromagnetic pulse).
(
dM z 1
=
M z0 − M zt
dt
T1
)
T1 ...spin-lattice relaxation time
−t
⎛
⎞
T1
0
M z (t ) = M z ⎜1 − e ⎟
⎜
⎟
⎝
⎠
General theory of NMR
In a static field there is no transverse component of the net magnetization
(M(x)=M(y)=0).
There is a way to create such a transverse magnetization using radio frequency
pulsed magnetic fields. Suppose we apply not only a constant magnetic field B0 but
also a rotating (circularly polarized) magnetic field B1 of frequency ω, perpendicular to
B0. The total field is written as
uv
v
v
v
B(t ) = B1 cos(ωt )i + B1 sin(ωt ) j + B0 k
General theory of NMR
The analysis of magnetization in this field can best be
carried out in a noninertial rotating coordinate system, *,
[ω*=ω(B1)]
uv
v
v
v
B(t ) = B1 cos(ωt )i + B1 sin(ωt ) j + B0 k
?
uuuv
uv ⎛
uuv
⎞
ω
Bef * = B1 i* + ⎜ B0 − ⎟ k *
γ ⎠
⎝
In such a system M is stationary: dM/dt=0
uuv
uuv uv
dM
=γM ×B
dt
- this can happen only if B=0. The magnetic field is 0 (in *) if we add the effective
field –(ω/γ)k*, so that B0k*–(ω/γ)k*=0.
General theory of NMR
If B1 rotates with the Larmor frequency (condition for resonance)
uv ⎛
uuv
uuuv
⎞
ω
Bef * = B1 i* + ⎜ B0 − ⎟ k *
γ ⎠
⎝
ω (B1)= ω0= ω(*)
uuuv*
v*
Beff = B1 i
The magnetization starts to precess about
B1* at rate Ω
Ω=γB1
General theory of NMR
the time B1 is switched on
t(B1)[90°]=π/2Ω
90° pulse
N(-1/2)=N(+1/2)
t(B1)[180°]=π/Ω
180 ° pulse
N −1/ 2
=e
N +1/ 2
−∆E
kT
−∆E
N +1/ 2
= e kT
N −1/ 2
General theory of NMR
For most systems the x-y magnetization decays exponentially with time
dM x*
dt
dM y*
dt
=−
=−
M x*
T2
M y*
T2
M x* (t ) = M 0 e
−t
T2
M y* (t ) = M 0 e
T2... spin-spin relaxation time
−t
T2
General theory of NMR
The movement of the tip of the magnetization
vector after a 90° pulse in the stationary
coordinate system
transverse relaxation
M x (t ) = M 0 cos(ω0t )e
M y (t ) = M 0 sin(ω0t )e
N(-1/2)=N(+1/2)
−∆E
N −1/ 2
= e kT
N +1/ 2
−t
⎛
⎞
T1
0
M z (t ) = M z ⎜1 − e ⎟
⎜
⎟
⎝
⎠
longitudinal relaxation
−t
T2
−t
T2
General theory of NMR
Detection of the signal
FID- Free Induction Decay
The time domain signal is transformed into a
frequency domain signal using FT.
General theory of NMR
Chemical shift
B0
Bi
i
The nucleus is surrounded by electrons
which act as a 3D magnetic shield. Magnetic fields
induced by currents of electrons change the local
field (Bloc) experienced by the nucleus.
ω0i = γ Bloc i
i = A, B, C
µi
uv
uv uv
B loc = B 0 − B i
uv
uv
Bi = σ B0
uuuv uv
Bloc = B 0 (1 − σ )
σ ...shielding constant
SOLID-STATE NMR
Spectra acquired with solution NMR equipment
liquid methanol
crystalline methanol
Broadening of solid state spectra is due to:
- dipolar interactions
- chemical shift anisotropy
SOLID-STATE NMR
Dipolar interaction
E jk
DS
((
)(
)
= b jk 3I j ⋅ e jk 3Ik ⋅ e jk − I j ⋅ Ik
)
Ij in Ik... angular momenta of spins j in k
ejk ...unit vector, parallel to the internuclear vector; ejk =f(t) as the molecule rotates
Dipolar coupling
constantmeasure for the intensity
of interaction
µ0 γ j γ k h
b jk = − 2
3
8π rjk
E jk DS = min
SOLID-STATE NMR
Dipolar interaction in a static magnetic field
Homonuclear:
E jk
DS
(θ jk )= b jk
1
3cos2 θ jk −1) 3I jz Ikz − I j ⋅ Ik
(
2
(
)
Heteronuclear:
DS
E jk (θ jk )= b jk (3cos2 θ jk −1)I jz Ikz
(
)
E jk DS ∝ 3cos 2 θ jk − 1
(
)
E jk DS θ jk = 54,74o = 0
MAGIC ANGLE
In solution the interaction vanishes because of rapid reorientations of molecules
(3cos2θjk-1 is integrated over all angles of a sphere). In solid state NMR molecules are
fixed with respect to the static external field.
SOLID-STATE NMR
Chemical shift anisotropy, ∆σ
σ is orientation dependent
polycrystalline samples have a random
distribution of all orientations of a
molecule
functional group oriented
parallel to B0 (maximal
screening)
∆σ ∝
(
2
3cos
( θ −1)
r3
functional group oriented
perpendicular to B0 (minimal
screening)
)
∆σ θ = 54,74o = 0
SOLID-STATE NMR
Improving resolution in SS NMR
1. MAS- Magic angle spinning
- rapid spinning at the magic angle causes the
time average of θ to be 54,74°
- the
spinning frequency is between 1 and
some 10 kHz
- we can eliminate broadening due to dipolar
interactions and chemical shift anisotropy
SOLID-STATE NMR
Improving resolution in SS NMR
2. CP- Cross polarization
polarization = ( N +1/ 2 − N −1/ 2 ) B0
- transfer of polarization from abundant spins (1H) to rare spins (13C)
γ
- we can improve the signal/noise ratio for a factor
γ
1
13
-occurs if we set the Hartmann-Hahn match properly
γ
13
C
B13 C = γ 1 H B1 H
- 13C nuclei take over properties of 1H
nuclei
- enables more repetitions in a given time
(T1(1H)<T1(13C))
H
C
SOLID-STATE NMR
2. CP Pulse sequence
Best resolution is usually
obtained with CP MAS
‘SOLID-STATE’ NMR
Pharmaceutical applications of SS NMR
- Investigations of polymorphism
1 conformation of IM in crystal
3 conformations of IM
in crystal
13C CP/MAS NMR spectra of α (1) and γ (2) polymorphic forms of indomethacine (IM).
K. Masuda et al. / International Journal of Pharmaceutics 318 (2006) 146–153
SOLID-STATE NMR
- Investigations of pseudopolymorphism
OH
CH 3
H
H
H
HO
weight
loss
13C CP/MAS NMR spectra of pseuodopolymorphs of estradiole.
TGA
J.-S. Park et al. / European Journal of Pharmaceutics and Biopharmaceutics 60 (2005) 407–412
SOLID-STATE NMR
- Investigation of amorphous solids
- broadening of signals is due to:
- wide distribution of orientations of molecules
- changes or disruption of hydrogen bond network
- differences in intermolecular distance
- wide distribution of molecular conformations
(molecules are more flexible in amorphous phase
with respect to the crystalline phase)
13C CP/MAS NMR spectra of amorphous (upper) and crystalline form of a drug
SOLID-STATE NMR
It is possible to quantify amorphous content, xa, in a binary mixture of crystalline and
amorphous phase
noise at frequency i
spectra of amorphous form
ai = Ai + ε ia
spectra of crystalline form
ci = Ci + ε ic
spectra of binary mixture
si = Si + ε is
signal at frequency i
Si = xa Ai + (1 − xa )Ci ≡ xa ( Ai − Ci ) + Ci
Introduction of new variables
Yi= si-ci in Xi= ai-ci
Yi = xa X i + ε i
ε i = xa (ε ic − ε ia )+ (ε is − ε ic )
Linear regression
SOLID-STATE NMR
Quantification of amorphous trehalose
CH 2 OH
O
OH
HO
OH
CH 2OH
O
OH
HO
O
OH
13C CP/MAS NMR spectra of pure amorphous trehalose (6),
binary mixtures (5-2) and pure crystalline trehalose
Correlation between obtained and actual fraction
R. Lefort, et al. Int. J. Pharm., 280 (2004) 209-219
SOLID-STATE NMR
Solid-state NMR in drug design and discovery
•
1.
2.
3.
4.
Resolution afforded by solid-state NMR of structural
details at subnanometre level:
determination of structural changes after binding a
small molecule at their site of action,
intimate dynamic information and electronic details
for bound molecules,
details of the binding site,
determination of chiality or the partiotioning
characteristics of small molecules.
SOLID-STATE NMR
Computational approaches for membrane targets
• NMR can reveal important details about the major
secondary structure elements of receptor molecules
(functionally relevant for ligand binding).
• Docking programs (for example Autodock) and
molecular dynamics (coupled with simulated
annealing methods) are now regularly used.
• NMR could be used to test the results of such
simulations, and NMR-generated structural
information can be included in docking routines to
increase their use and applicability and to improve
and refine the algorithms.
SOLID-STATE NMR
Solid-state NMR of large biomolecules
•
•
•
Some new high-frequency transverse relaxation-optimized
spectroscopy (TROSY) NMR methods combined with 2H and
15N labelling might extend the limit (broadened spectral lines
due to dipolar interactions) for full structural determinations for
isolated membrane proteins in suitable small detergent micelles.
Wide-line solid-state NMR has been developed to exploit
anisotropic characteristics of large complexes and to give, in
particular, molecular orientation in ordered systems, such as
fibres or membranes.
High-resolution solid-state NMR involves mechanically
averaging the anisotropic spin interactions by rotating a sample
in a rotor.
SOLID-STATE NMR
Solid-state NMR of large biomolecules
• Spinning can lead to morphological changes
(especially those that are induced by hidration).
• The resolution of the narrow NMR spectra from
spinning the sample at the magic angle (MAS)
methods does not mach those of high-resolution
solution-state NMR spectra (mainly because of
sample disorder and slow molecular motional
effects).
• The mechanical averaging means that many of the
informative spectral features are lost.
• Heterogenous systems can also be studied.
Solid-state NMR in drug discovery
Chemical bonding,
chirality and
compositional
information in
the solid form
Nonspecific and
specific binding of
a drug to a target
can be identified in
the solid-state NMR
spectrum of a
heterogenous
macromolecular
complex
Solid-state NMR spectral
parameters for a drug that
is bound at its target site
can give detailed insight into
electronic and conformational
nature and components
of a binding site
Dissociation
constant
(Kd) values
can also be
determined
The manipulation of
bioavailibility is important,
either through solubility
or partitioning to a membrane
target through the bilayer,
which can be distinguished
using solid-state NMR
The quality
control of drug
synthesis
is readily
monitored
using
solid-state
NMR
Patent infrigement
investigations
through polymorphic
differences
of competing drugs
can be resolved
Solution-state NMR
Solid-state NMR
For drug observation only in solution
Yes
NS
For drug observation as solid
(polymorphism determinations)
NS
Yes
Nuclei observable
1
13
Observation of unbound drug
H, 13C, 15N and 19F
C, 15N, 19F, 2H and 17O
Target molecular size
For complete structure determination
Yes (if Mr<30000 unless TROSY can be
applied)
NS (except for small membrane peptides so far)
For direct drug observation at target
binding site
Yes (if Mr<40000 unless TROSY can be
applied)
No limit
For indirecrt (rapidly exchanging into
solution) drug-target observation
No limit
NS
Sample size
10-500 µl
10 µl-1 ml
Detection levels of target-drug complex
(13C,15N,19F)
nM (for Mr<30000)
>20 nmoles*
Detection levels for drug only
>1 nmol
>1 nmole*
Temperature range
Not frozen
Any
Isotopic-labelling requirements for target
None or 13C in 15N selectively and/or
uniformly
None or selective target labelling (residues of a
single type or a minimal number of types)
only
Isotopic-labelling requirements for drug
Preferable for enhanced sensitivity or to
aid assignments
Yes for assignment and sensitivity enhancements
for 13C in 15N, no for rare nuclei (such as 19F)
Kd range
mM do µM (for large targets); nmM to
nM (for small targets)
<mM (no limitations)
*With
proton cross-polarization to enchance sensitivity. Kd, dissociation constant; Mr, relative molecular mass;
NS, not suitable; TROSY, transverse relaxation-optimized spectroscopy.
SOLID-STATE NMR
Isotopic substitution for drug-target studies by solidstate NMR
•
The identification and assignment of NMR resonances
require defined chemical labelling or spectroscopic
approaches that are designed for these purposes.
• The overriding consideration in experimental design is
how many sites need labelling (too many labels might
be difficult to resolve) and where the labels should be
placed.
• Modelling methods (coupled with SS NMR) can help in
the selection of sites for labels:
1. giving a distance between nuclei and constraining a
drug structure by defining torsion angles,
2. by probing a binding site and defining the involvement
of specific moieties in the binding process.
SOLID-STATE NMR
SOLID-STATE NMR
Properties of commonly used and biologically relevant
NMR-visible isotopes
NMRvisible
isotope
Substitution Natural abundance
compared with
1H
Relative
sensitivity
Main NMR property
exploited
13C
12C
1,1 %
0,016
Dipolar couplings and
chemical shift
2H
1H
0,015 %
0,001
Anisotropic quadupolar
interactions and
dynamics
15N
14N
0,37 %
0,001
Anisotropic chemical
shifts
19F
No or 1H
100 %
0,83
Strong dipolar
couplings
31P
No
100 %
0,006
Anisotropic and
isotropic chemical
shifts
SOLID-STATE NMR
Determining Kd for ligands
• The NMR spectral line
heights for 13C-labelled,
weakly binding ligand
increase as the ligand is
added to a fixed amount
of target protein.
• The fractional ratio of
bound ligand then gives
a binding isotherm and
Kd.
• By suppressing the
NMR spectrum from
isotropic, unbound
ligand, an equilibrium Kd
is determined directly.
SOLID-STATE NMR
Distance methods in solid-state NMR
•
•
•
•
•
Ultra-high resolution (±0,05 nm - direct
result of the strong sensitivity of the
magnetic dipolar coupling (b) to distance
(r)).
Methods are available for determining b
IS
between similar nuclei and different nuclei.
For homonuclear recoupling, the
recoupling is achieved under ‘rotational
resonance’ (setting the sample spinning
rate, ωR, to multiples of the frequency
difference (νAB) between the NMR
resonances (│νA-νB│).
Mixing period (τm) Æ transfer of
magnetization (reducing the spectral
intensity).
The decay curve of the intensity reduction
as a function of the mixing time then
provides a means of quantifying the dipolar
interaction.
⎛ µ0
b = −⎜
⎝ 4π
⎞ γ Iγ S h
⎟ 3
⎠ r IS
bIS…dipolar coupling between
nuclei spins I and S
µ0…permeability of vacuum
γI,γs…are the gyromagnetic
ratios of spins I and S
h…Planck constant divided by
2π
rIS...distance between nuclear
spins I and S
SOLID-STATE NMR
SOLID-STATE NMR
Resolving drug structures at the site of action
•
•
Solid-state NMR in
combination with sitedirected mutageneseis
(SDM) and bioinformatics
approaches is used for
resolving binding sites.
The intramolecular drug
structure at the target site
can be resolved with high
resolution, as can the
electronic environment (from
NMR chemical shift
perturbations).
SOLID-STATE NMR
Identifying bound ligand environment
•
•
The agonist binding site is
shown for the nicotinic Ach
receptor, which highlights the
aromatic residues (in red)
that line the agonist-binding
pocket, within which
deuterium SS NMR studies
have shown fast rotation of
the agonist –(CH3)3 group.
b and c – both modulate
receptor function, and could
potentially bind to the
receptor through a cation-π
interaction.
SOLID-STATE NMR
Partitioning behaviour of drugs
•
•
The deuterium wide-line
NMR spectra of ligands that
can partition into a
membrane show welldefined spectra for each
motionally distinct
environment.
As long as the experimental
conditions (particularly the
relaxation delays) are
sufficient, then spectral
integration (the measured
area, Ap and Ai, for the
partitioned and isotropic
spectral components) gives
directly the relative
concentrations of the small
molecule in each phase in
equilibrium.
K p = A pVa / AiVm
Va,Vm…aqueous and membrane volumes
SOLID-STATE NMR
Differential dynamics of bound ligands
•
•
•
Parts of the drug have an average
position in or on its binding site,
rather than a highly rigid location for
the whole molecule.
Deuterium substitutions give rise to
either motionally broadened or a
motionally narrowed spectrum.
The method is sensitive enough to
differentiate unbound ligand as a
narrow (‘free’) signal from the tightly
(Kd values in the nanomolar range)
‘bound’ ouabain when the deuterium
label is carried on the steroid
nucleus of ouabain.
SOLID-STATE NMR