Structure
Determina-on
by
NMR
Note:
Good
introductory
text:
“Fundamentals
in
Protein
NMR
Spectroscopy”
by
Gordon
Rule
and
Kevin
Hitchens
(c.
2006)
For
the
NMR
spectroscopist:
“Protein
NMR
Spectroscopy”
by
Cavanagh,
Fairbrother,
Palmer
&
Skelton”
(2nd
ed.
c.
2007)
NMR
structure
determina-on
Distance
geometry
Assemble
restraints
Random
coordinates
Generate
trial
structures
Simulated
annealing
Retain
lowest
energy
structures
(10%)
Energy
minimiza-on
Evaluate
and
remove
or
revise
constraints
Inconsistent
constraints?
Addi-onal
constraints?
Determine
quality
of
final
structure
But
first
we
need
to
measure
restraints
•  Step
1:
Assign
the
spectrum
–  Use
through‐bond
correla-ons
to
transfer
magne-za-on
between
directly
bonded
atoms
–  COSY,
TOCSY
for
1H
only
(unlabeled
proteins,
up
to
about
5kD)
–  Triple
resonance
experiments
for
13C/15N
proteins
•  HNCA,
HN(CO)CA,
HNCACB,
CBCACONH,
etc.
•  Step
2:
Measure
restraints
–  Distances
between
atoms
•  Use
through
space
interac-ons
•  NOE
(Nuclear
Overhauser
Enhancement),
≤5Å
•  PRE
(Paramagne-c
Relaxa-on
Enhancement),
≈10‐30Å,
1/r6
distance
dependence
–  Orienta-ons
of
bond
vectors
•  RDC
(residual
dipolar
coupling)
–  Torsion
angles
•  3
bond
J‐coupling
Interac-ons
Between
Spins
•  Only
one
is
isotropic:
J‐coupling
–  Only
J‐coupling
is
overtly
observed
in
solu-on
NMR
experiments
(unless
it
is
decoupled)
–  Rou-nely
used
to
transfer
magne-za-on
between
spins
in
solu-on
NMR
–  THROUGH
BOND
•  Dipolar
coupling
is
anisotropic
–  Overtly
observable
in
solids
–  Contribute
to
relaxa-on
in
solu-on
NMR
–  Dipolar
coupling
is
the
basis
for
solu-on
NMR
NOE
experiments.
–  THROUGH
SPACE
Resonance
Assignment
103
123
104
130
76
10
105
106
180
86
25
101 5642
46
205
203
144
43
107
181
108
71
106
202
109
110
111
131
139
122
82
148
115
156
77
134
3
150
113
24
114
147 103
115
52 179
116
23
45 168
121
41
118 159
39
97
50
104
109
125
80
110
112
169
196
18
153 55
70
100
199
5126
129
138176
34
174
22
37 53
36 201 15
65
16
160
20089 197
192
69
161
48
154
64 193
88
102
120
54
99
126
173
167
94 57
124
27
83
91 2040 178
68 164
11
135 21 136 165
145
19
204 163 195
116
9695132 175
67
191
158
58
49
17
33 172
47
117
166
133 38
157
66
4
162
93
87
61 10798
92
35 194
151
149
59
177
112
3078
127
63
79 184
206
81186
90
182
114
111
6
2
85
62
188
137
5
183
152
117
118
119
120
185
28
108
p
p
m
121
189
122
123
124
125
126
170
72
127
105
187
29
F
1
128
129
146
130
131
132
11.0
10.5
10.0
9.5
9.0
8.5
8.0
7.5
7.0
6.5
F2 ppm
Is
it
easier
to
use
through‐bond
or
through‐space
interac-ons
to
assign
resonances?
Resonance
Assignment
•
Small
proteins
(≤5kD)
–  1H
only
–  TOCSY/COSY
to
assign
spin
systems
within
residues
(uses
J‐coupling,
through
bond
only)
–  NOESY
to
connect
residues
in
order
(uses
NOE
based
on
dipolar
interac-ons,
through
space)
and
establish
long‐range
distance
restraints
•
Medium
proteins
(≤10kD)
•
Large
proteins
(≤30
kD)
–  Same
as
small,
but
use
15N
labeling
to
increase
resolu-on
and
spread
peaks
in
3
dimensions
–  13C/15N
labeling
–  Triple
resonance
experiments
use
J‐coupling
to
specifically
walk
along
backbone
within
and
between
residues
–  Assign
side
chain
protons
and
use
NOE
distance
restraints
to
determine
structure
–  RDC,
PRE,
torsion
restraints
as
well.
•
Very
large
proteins
(≤60‐80kD)
–  Same
as
large
proteins,
but
2H
to
reduce
1H/1H
dipolar
coupling.
–  Special
pulse
sequences
(TROSY)
–  Methyl‐base
distance
restraints
(higher
sensi-vity
than
amide)
Backbone
Assignment
–
HNCO
•  ≥10
kD
protein,
requires
13C/15N
labeling
i‐1
i
i+1
H
O
H
O
O
H
N
C
N
Cα C
N
C
Cα
Cα
Hα R
Hα Cβ
Hα Cβ
C γ
HN(CA)CO
i
i‐1
i
13C’
i‐1
15N‐1H
HSQC
1H
Res
4
Hβ
HNCO
13C
Res
3
15N
1H
Backbone
Assignment
–
HNCA
i‐1
i
i+1
H
O
H
O
O
H
N
C
N
Cα C
N
C
Cα
Cα
Hα R
Hα Cβ
Hα Cβ
C γ
Hβ
HNCA
Res
3
Res
4
Res
5
HNCO
i‐1
13C
13C α
i‐1
i
13C’
15N‐1H
HSQC
15N
i
i‐1
i
i‐1
i‐1
1H
1H
1H
Side
Chain
Assignment
i‐1
i
i+1
H
Many
varia-ons
for
connec-ng
Cβ
O
H
O
O
H
N
C
N
Cα C
N
C
Cα
Cα
Hα Cβ
Hα Cβ
Hα Cβ
C γ
Hβ
HN(COCA)CB
CBCA(CO)NH
HNCACB
HN(CA)CB
i‐1
i
i+1
H
O
H
O
H
O
H
TOCSY
experiments
use
N
C
N
Cα C
N
C
N
C
C
isotropic
mixing
to
transfer
α
α
magne-za-on
throughout
the
Hα Cβ
Hα Cβ
Hα Cβ HCCH
TOCSY
spin
system
CCH
TOCSY
C H HCC(CO)NH
TOCSY
γ
β
Dipolar
coupling
*FluctuaDons
in
dipolar
coupling
as
protein
rotates
in
soluDon
creates
fluctuaDons
at
the
••F
frequency
needed
to
trigger
NOE
and
relaxaDon
in
soluDon
experiments
Dipolar
Coupling
•  Can
we
observe
dipolar
coupling
directly
in
solu-on?
–  NO!
–  Average
of
(3cos2θ‐1)/2
over
all
orienta-ons
is
0!
•  Is
the
dipolar
coupling
zero
at
any
given
instant?
–  NO!
–  Fluctua-ons
in
dipolar
coupling
as
protein
rotates
in
solu-on
create
fluctua-ng
magne-c
fields.
–  Some-mes
the
frequency
matched
the
∆hν
needed
to
trigger
transi-ons
between
spin
states.
–  This
is
the
source
of
the
nuclear
overhauser
effect
and
relaxaDon
in
soluDon
experiments.
Through
space
interac-ons:
Nuclear
Overhauser
Effect
(NOE)
o
oo
ωS
βα
ωI
ββ
ωS
ωI
o
oo
oooo
αβ
ωS
Saturate
S
spin
without
affec-ng
I
spin
βα
ωI
ωS
ωI
ωI
ooo
ooo
αβ
ωS
αα
αα
Popula-ons
of
the
energy
levels
for
2
dipolar
coupled
spins
at
equilibrium.
ββ
Note
that
the
I
spin
popula-on
difference
is
not
affected.
ωS
ωI
Through
space
interac-ons:
Nuclear
Overhauser
Effect
(NOE)
o
oo
ωS
βα
ωI
ββ
oooo
αα
Popula-ons
of
the
energy
levels
for
2
dipolar
coupled
spins
at
equilibrium.
ωS
o
oo
αβ
ωS
ωI
ββ
ωS
ωI
Saturate
S
spin
without
affec-ng
I
spin
βα
ωI
ooo
Cross
relaxaDon
ωI
ooo
αβ
ωS
αα
Cross
relaxa.on
–
as
molecule
tumbles,
dipolar
coupling
value
fluctuates.
Some
of
these
fluctuaDons
occur
at
the
right
frequency
to
cause
spin
flips,
such
as
αβ
to
βα
transiDons.
Through
space
interac-ons:
Nuclear
Overhauser
Effect
(NOE)
o
oo
ωS
βα
ωI
ββ
oooo
Saturate
S
spin
without
affec-ng
I
spin
βα
oo
Cross
relaxaDon
ωI
Popula-ons
of
the
energy
levels
for
2
dipolar
coupled
spins
at
equilibrium.
ωI
ooo
αβ
ωS
αα
αα
ωS
ωI
oo
oo
αβ
ωS
ββ
ωS
ωI
ωS
ωI
Through
space
restraints:
Nuclear
Overhauser
Effect
(NOE)
•  NOE
arises
due
to
fluctua-ons
in
magne-c
field
caused
by
dipolar
coupling
between
spins
–  Through
space
restraint
since
dipolar
coupling
is
a
through
space
interac-on
between
spins.
–  Distance
dependent
–
1/r6
•  Dipolar
coupling
is
distant
dependent
•  Closer
spins
are
more
strongly
coupled,
increased
cross‐
relaxa-on,
increased
perturba-on
of
each
other’s
spin
popula-ons,
greater
NOE
NOESY
Analysis
1H
Acquire
data
(chemical
shir,
ω2)
HB
ω1
(ppm)
Crosspeaks
arise
between
protons
within
about
5
Å.
HB N
Encode
Mixing
-me
chemical
shir
(ω1)
HA
HC
HD
HD
HC
HA
ω2
(ppm)
HB
Use
these
restraints
to
build
up
structure
using
distance
geometry.
NOESY
Analysis
•  Semi‐quan-ta-ve
distance
restraint
–  Longer
mixing
-me,
greater
NOE
buildup
–  More
complex
than
the
simple
cartoon.
•  Can
measure
NOE
as
a
func-on
of
mixing
-me
and
fit
full
equa-ons
to
accurately
determine
restraint.
Expensive
(NMR
-me,
analysis
-me)
and
s-ll
complicated
by
addi-onal
coupling
to
remote
protons.
•  Usually
es-mate
upper
and
lower
bounds
(weak,
medium,
strong
NOE).
Small
protein
assignment:
TOCSY/
NOESY
•  TOCSY
connects
all
1H
spins
within
i‐1
i
3
bonds
of
each
other:
H
O
H
–  Within
residue
connec-ons
only
N
–  Cannot
transfer
across
C=O!
•  NOESY:
typical
NOEs
observed
depending
on
the
type
of
secondary
structure.
–  β:
HN
‐
Hαi‐1,
(HN
‐
HΝi‐1
weak)
other
short
distances
are
cross‐strand!
–  α:
HN
‐
HNi±1
HN
‐
Hαi‐1
H ‐
H i‐3
N
α
plus
other
weak
NOEs
with
i+4
Cα
C
Hα Cβ
C γ
i+1
O
O
H
N
Cα C
N
Cα C
Hα Cβ
H C
α
β
Hβ
Small
protein
assignment:
TOCSY/
NOESY
H1y
0.0
5.0
10.0
10.0
TOCSY
–
through
bond
NOESY‐through
space
9.0
8.0
H1x
7.0
6.0
5.0
Other
restraints
•  NOEs
have
long
been
the
primary
restraint
for
NMR
structure
determina-on
•  Other
restraints
are
useful
when
NOEs
are
difficult
to
obtain
(large
molecules,
membrane
proteins,
disordered
molecules)
•  Secondary
structure
(chemical
shir
index,
backbone
torsion
angle)
•  Orienta-onal
restraints
(residual
dipolar
coupling,
RDC)
•  Long‐range
distance
restraints
(paramagne-c
relaxa-on
enhancement,
PRE)
–  Requires
spin
label,
thus
not
as
non‐perturbing
as
most
NMR
–  Not
as
widely
used
Typical
Chemical
Shir
Values
Chemical
shir
depends
on
‐secondary
structure
‐type
of
residue
15N
not
used
in
this
way
H‐bonding
effect
makes
it
more
complicated
Chemical
Shir
Index
Chemical
Shir
Index
Can
you
locate
the
helices
and
sheets?
J‐coupling
–
Torsion
angle
restraints
•  Depends
on
conforma-on
of
intervening
bonds
for
mul-‐bond
coupling
–  3J
couplings
used
to
determine
torsion
angles
–  Karplus
equa-on
–  Backbone
φ angle
commonly
determined
from
3JHnHa,
φ
is
the
torsional
angle
between
the
C‐N‐Ca
and
N‐Ca‐C
planes.
–  Sidechain
χ1
determined
from
3J
couplings
involving
Hβ
i‐1
i
i+1
2J
NCa,
O
H
3JHNCH,
O
H
O
1‐10
4‐9
N
C
N
Cα C
N
C
Cα
Cα
Hα R
Hα Cβ
Hα Cβ
3
H
C γ
JHCCH,
2‐14
H
β
Karplus
equa-on
9
Hz
3
Hz
Residual
Dipolar
Coupling
•  Capturing
the
extra
orienta-on‐dependent
informa-on
available
in
solid‐state
with
the
resolu-on
of
solu-on
NMR.
•  Induce
a
slight
degree
of
alignment
–  Not
enough
to
degrade
resolu-on,
just
enough
to
par-ally
align
the
sample
–  Bicelles
–  Phage
Bo
–  Carbon
nanotubes
•  Measure
the
dipolar
coupling
–  Very
small
(Hz,
not
kHz)
Residual
Dipolar
Coupling
Usual
HSQC
1H
A
1H
J
B
B
15N
15N
Isotropic
media,
decoupled
1H
ωI
J
Isotropic
media,
coupled
Decoupled
ωS
A
A
J+D
B
Both
spectral
lines
split
by
πJ
J+D
15N
ωS
ωI
Aligned
media,
coupled
Residual
Dipolar
Coupling
•  Orienta-on
dependence
from
dipolar
coupling
•  Small
values
(typically
30
Hz
or
less)
•  Need
to
know
structure
and
alignment
tensor
to
interpret
fully
–
simultaneously
op-mize
alignment
tensor
while
determining
structure
–  Regular
rela-onship
between
orienta-on
(and
thus
RDC
value)
along
a
helix
or
strand.
–  Largest
RDC
value
for
bond
vectors
parallel
to
z‐axis,
largest
value
of
opposite
sign
corresponds
to
vectors
perpendicular
to
z
(3cos2θ‐1).
RDCs
are
especially
useful
for…
•  Good
for
figuring
out
rela-ve
orienta-on
of
different
domains
–  May
not
be
a
lot
of
interdomain‐NOEs
–  If
only
a
few
NOEs,
rela-ve
posi-on
of
domains
will
be
poorly
defined
•  Very
sensi-ve
to
irregulari-es
in
secondary
structure
(kinks,
etc)
•  Useful
for
“disordered”
proteins
–  Not
a
lot
of
NOEs
if
only
transient
structure
–  May
be
able
to
pick
up
propensity
for
a
par-cular
conforma-on
•  Complementary
to
distance‐dependent
NOEs
NMR
structure
determina-on
Distance
geometry
Assemble
restraints
Random
coordinates
Generate
trial
structures
Simulated
annealing
Retain
lowest
energy
structures
(10%)
Energy
minimiza-on
Evaluate
and
remove
or
revise
constraints
Inconsistent
constraints?
Addi-onal
constraints?
Determine
quality
of
final
structure
Energy
minimiza-on
•
•
•
•
•
•
•
•
Experimental
constraints
(NOEs,
3J
torsion
restraints,
bond
orienta-ons
from
RDCs,
CSI)
Non‐experimental
restraints:
bond
lengths,
angles,
torsional
angles,
van
der
waals
interac-ons
(usual
equa-ons)
Etotal=κEexperimental+Enon‐experimental
Goal:
a
low‐energy
structure
that
fits
all
restraints
well.
ENOE:
square
well
with
harmonic
sides
to
account
for
semi‐quan-ta-ve
nature
of
NOE
ERDC:
harmonic
well
Etorsion:
Karplus
equa-on
Ini-al
structures
–
Distance
geometry:
embed
set
of
interatomic
distances
into
3D
space
to
give
atomic
coordinates
•
•
–
•
•
ξi=
‐∂E/∂xi
Good
for
minimizing
within
smooth
well
Simulated
annealing:
to
escape
entrapment
in
local
minima
–
–
–
–
•
Random
coordinates
Structures
refined
by
a
combinaDon
of
energy
minimizaDon
and
simulated
annealing
Energy
minimiza-on:
Move
atoms
in
the
direc-on
defined
by
the
gradient
of
the
energy
–
–
•
Ini-al
structures
more
likely
to
be
in
reasonable
agreement
with
experimental
restraints
Smaller
number
of
dis-nct
conforma-ons
generated
Heat
structure
by
adding
kine-c
energy
to
the
system
Slowly
lower
the
energy
to
anneal
to
the
global
minimum
Trajectory
of
the
atoms
calculated
by
molecular
mechanics
Used
ini-ally
to
regularize
the
structures
and
ensure
reasonable
covalent
geometry
(no
RDCs!)
Programs,
such
as
X‐PLOR
are
designed
to
handle
NMR
restraints
and
perform
these
calcula-ons
Example
Structure
Ini-al
structures
–
ini-al
NOE
set
and
regulariza-on
H‐bonding
added
Torsion
angles
added
RDCs
added
Example
Structure