How
to
find
out
everything
you
wanted
to
know
about
the
structure
and
dynamics
of
your
molecule.
Goals
•  Strengths
and
weaknesses
of
NMR
–  What
types
of
problems
is
NMR
good
for?
–  When
is
NMR
not
useful?
•  How
to
read
and
evaluate
a
paper
that
uses
NMR
as
a
technique.
•  What’s
hot
in
protein
NMR
right
now?
–  What
problems
can
NMR
address
beCer
than
other
currently
available
techniques?
What’s
Hot
in
NMR
•
•
•
•
•
•
•
Membrane
proteins
Unstructured
proteins
Protein
dynamics
Things
that
don’t
crystallize
Low
affinity
binding/interacKon
complexes
DNA/RNA
binding
proteins
In‐cell
NMR
PracKcal
NMR
•  I
want
to
use
NMR
to
study
my
favorite
protein!
–
–
–
–
What
quesKon(s)
do
you
want
to
address?
How
big
is
your
protein?
How
much
can
you
make?
(mg
quanKKes)
How
do
you
make
it?
•  E.
coli
best
for
isotopic
labeling,
but
problemaKc
for
eukaryoKc,
post‐
translaKonally
modified
proteins
•  In
vitro
increasingly
popular
(no
purificaKon
needed),
but
does
your
protein
fold
properly?
$$$$
•  May
be
able
to
address
specific
quesKons
without
labeling,
or
with
less
than
uniform
labeling
•  NMR
can
address
quesKons
of
structure,
dynamics,
thermodynamics,
kineKcs,
binding,
diffusion,
etc.
It
depends
on
the
system
if
it
will
be
easy
or
impossibly
difficult…
NMR
is
a
spectroscopic
technique
Energy
β,
spin
down,
anKparallel
to
Bo
∆E=hν
α,
spin
up,
parallel
to
Bo
MagneKc
field
strength
(Bo)
By
conven=on,
Bo
defines
the
z‐axis
•  Unique
features:
–  Energy
levels
are
based
on
nuclear
spin
–  #
of
energy
levels
depends
on
the
spin
quantum
number
(I)
of
the
nucleus
–  ∆E
between
states
depends
on
the
strength
of
the
magneKc
field
#
of
Energy
Levels
depends
on
I
•  Nuclear
spin
(I)
is
analogous
to
electron
spin
(S).
–  S=1/2,
mS=‐1/2,
+1/2
(2
states,
electron
is
spin
up
or
spin
down)
–  mI
ranges
from
–I
to
+I
in
steps
of
1
•  I=0
–  1
state,
no
∆E,
not
NMR
acKve
–  Ex.
12C
•  I=1/2
–  2
states,
just
like
electron:
±1/2
–  Ex.
1H,
15N,13C,
19F,
31P
•  I=1
–
–
–
–
3
states,
2
transiKons
2
lines
in
spectrum
for
each
nucleus!
Quadrupolar
(more
complex)
Ex.
2H
•  I>1,
someKmes
used
in
solid‐state
NMR,
big
mess!
∆E
depends
on
Bo
•  Nuclei
with
non‐zero
spin
angular
momentum
have
nuclear
magneKc
moments:
 
µ = γI
µ z = γI z
•  γ=gyromagneKc
raKo
of
nucleus
•  Energy
of
a
nucleus
with
nuclear
magneKc
moment
µ
in
a
staKc
magneKc
field,
B
:
€ 
€
o


E = −µ • B
E = −µ z Bo
E = −γm I Bo
For
spin
½,
mI=
±1/2,
∆mI=±1
(selecKon
rule)
ΔE = γBo
€
Spin
½
Nuclei
Energy
β,
spin
down,
mI=‐1/2
∆E=hν=γħΒο
α,
spin
up,
mI=+1/2
ElectromagneKc
radiaKon
corresponding
to
the
transiKon
between
these
two
states
has
a
parKcular
frequency.
MagneKc
field
strength
(Bo)
ΔE = hν = γBo
γBo
This
is
called
the
Larmor
frequency,
or
v=
resonance
frequency,
of
the
nucleus.
It
2π
varies
with
the
type
of
nucleus
(13C,
ω = γBo
1H,
etc)
and
the
magneKc
field
strength.
It
is
radio
frequency.
Spin
½
Nuclei
Nucleus
Gyromagne0c
ra0o
in
(Ts)‐1
Natural
abundance
(%)
1H
2.6752
x
108
99.98
13C
6.728
x
107
1.11
15N
‐2.712
x
107
0.36
31P
1.0841
x
108
100.00
19F
2.5181
x
108
100.00
Spectrometer
are
named
according
to
the
1H
Larmor
frequency:
A
“600
MHz”
spectrometer
operates
at
14.1
T
(Tesla)
Earth’s
magneKc
field
30
–
60
µT
Typical
MRI
1.5
–
3
T
Typical
protein
NMR:
11.74
T
(500MHz)
up
to
22.3
T
(950
MHz)
Why
is
NMR
so
insensiKve?
•  NMR
is
an
inherently
insensiKve
technique.
•  To
overcome
this,
we
use
mg
quanKKes
of
protein,
mM
protein
soluKons,
isotopic
enrichment,
signal
averaging,
cryoprobes.
•  Bulk
magneKc
moment
is
what
we
manipulate
in
an
NMR
experiment.
The
bulk
magneKc
moment
of
a
sample
depends
on
the
populaKon
difference
between
the
2
states.
Energy
z
(Bo)
β
ΔE = γBo
α
Nβ
€
α
β
€
 −ΔE 
= exp

 kT 
Nα
SensiKvity
 −(1.055 ×10−34 Js)(2.6752 ×10 8 s−1T −1 )(14.1T) 
Nβ
 −γBo 
= exp
 = exp

 kT 
Nα
(1.381×10−23 JK −1 )(298K)


Nβ
= 0.999904
Nα
(for
protons
on
a
600MHz
instrument)
•  Small
∆E,
therefore
small
populaKon
difference
between
the
two
states
according
to
Boltzmann,
and
small
bulk
magneKc
moment.
•  In
an
NMR
experiment
we
manipulate
the
bulk
magneKc
moment:
Equalizing
the
populaKons
of
the
two
states,
or
even
inverKng
the
populaKons,
sKll
creates
only
a
small
signal.
•  Higher
field
magnets
will
always
have
be4er
sensi5vity.
•  Nuclei
with
higher
γ
will
always
have
be4er
sensi5vity.
ManipulaKng
Spins
to
Get
a
Spectrum
•  Full
understanding
of
NMR
requires
quantum
mechanics
–
nuclear
spin
is
a
purely
quantum
property.
But
we
can
gain
a
lot
of
insight
from
a
classical
approximaKon…
•  We
can
think
of
spin
½
nuclei
like
liCle
bar
magnets
(dipoles)
in
a
much
larger
magneKc
field
(spectrometer).
•  We
will
apply
smaller
magneKc
fields
(radio
frequency
–
why?)
perpendicular
to
the
staKc
spectrometer
field
to
manipulate
the
bulk
magneKc
moment.
•  We
will
observe
what
happens
and
record
a
spectrum.
Basic
Physics
Reminders
•  Ampere‐Maxwell
EquaKon:
Current
in
a
wire
produces
a
magne0c
field
near
the
wire.
(How
we
create
B1
fields
to
manipulate
the
spins)
•  Faraday’s
Law
of
InducKon:
A
changing
magne0c
flux
will
set
up
a
current
in
a
closed
loop
of
wire.
(How
we
are
able
to
observe
the
NMR
signal
using
a
coil
of
wire)
•  Lenz’s
Law:
An
induced
current
is
always
in
a
direc0on
to
oppose
the
mo0on
or
change
causing
it.
(Why
the
electron
cloud
shields
the
nucleus
from
Bo)
Spectrometer
Hardware
magnet
console
Probe
•  Tuned
RLC
circuit
–  Resonance
condiKon:
ω 0 ≈ 1 LC
€
Teng,
Structural
Biology:
Prac=cal
NMR
Applica=ons
ManipulaKng
Spins
•  Since
the
nuclear
spins
have
angular
momentum,
applicaKon
of
an
external
field
generates
a
torque.
•  Bloch
EquaKons:


dM(t) 
= M(t) × γB(t)
dt
•  This
torque
causes
the
bulk
magneKc
moment
to
precess
around
the
applied
field.
€
ManipulaKng
Spins
•  In
the
case
of
Bo
(staKc
spectrometer
field),
the
spin
precess
at
their
Larmor
frequency,
ωo=‐γBo.
**This
is
exactly
the
same
as
the
frequency
required
to
excite
transiKons
between
the
energy
levels.**
•  This
is
called
the
chemical
shiv.
Chemical
Shiv
•  We
do
not
study
nuclei
in
isolaKon.
•  The
electron
cloud
shields
the
nucleus
from
the
magneKc
field.
Beff=(1‐σ)Bo
•  The
electron
cloud
surrounding
a
HN
atom
is
different
than
the
electron
cloud
surrounding
Hα.
This
leads
to
different
chemical
shivs
of
different
types
of
nuclei.
•  Differences
in
chemical
shiv
arise
due
to
variaKon
in
the
environment
of
a
nucleus
(H‐bonding,
backbone
torsion
angle,
side
chain
torsion
angle,
long‐range
electrostaKcs,
ring
currents).
aromaKc
NH
CH
CH2
CH3
Reduced
electron
density,
less
shielding,
increased
Beff
Chemical
Shiv
z
(Bo)
•  Chemical
shiv
is
a
precession
frequency
(ν
in
Hz,
or
n
Rad/s)
•  Scales
with
magneKc
field:
ω=γBo
Net
magneKc
moment
Precession
at
chemical
shiv
frequency
–  ResoluKon
improves
at
higher
magneKc
field
since
∆ω scales
with
Bo
–  How
to
compare
spectra
taken
at
different
field
strengths?
δ ( ppm) = ν − ν o ×10 6
νo
Basic
Physics
Reminders
•  Ampere‐Maxwell
EquaKon:
Current
in
a
wire
produces
a
magne0c
field
near
the
wire.
(How
we
create
B1
fields
to
manipulate
the
spins)
•  Faraday’s
Law
of
InducKon:
A
changing
magne0c
flux
will
set
up
a
current
in
a
closed
loop
of
wire.
(How
we
are
able
to
observe
the
NMR
signal
using
a
coil
of
wire)
•  Lenz’s
Law:
An
induced
current
is
always
in
a
direc0on
to
oppose
the
mo0on
or
change
causing
it.
(Why
the
electron
cloud
shields
the
nucleus
from
Bo)
ManipulaKng
Spins
•  In
order
to
obtain
an
NMR
spectrum
we
need
to
Kp
the
bulk
magneKc
moment
off
the
z‐axis
so
we
can
observe
the
chemical
shiv
precession.
•  We
must
apply
a
magneKc
field
perpendicular
to
the
staKc
magneKc
field
in
order
to
do
this.

–  Radiofrequency
pulse
applied

dM(t) 
to
probe
coil
creates
transverse
= M(t) × γB(t)
dt
field,
B1.
–  This
field
must
be
applied
on‐resonance
(rotaKng
frame
transformaKon),
ωRF=ωo,
so
it
oscillates
at
the
Larmor
frequency
of
the
spins
you
are
trying
to
manipulate
€
–  How
long
should
this
field
be
applied
(pulse
length)?
ManipulaKng
Spins


dM(t) 
= M(t) × γB(t)
dt
Net
magneKc
moment
z
(Bo)
z
(Bo)
z
(Bo)
€
y
x
Apply
B1
field
along
y‐axis
for
Kme
τ90
Let
magneKzaKon
evolve
and
Precession
at
chemical
observe
chemical
shiv
shiv
frequency
1
Pulse
NMR
experiment
Acquire
FID
1H
Fourier
Transform
Kme
frequency
Line
Width
and
RelaxaKon
•  FID
is
not
an
infinite
sine
wave.
It
oscillates
within
an
exponenKally
decaying
envelope.
exp(−t /T2 )
•  This
is
due
to
relaxa=on.
RelaxaKon
in
the
x/y
plane
occurs
due
to
loss
of
coherence.
–  Called
T2
or
transverse
relaxaKon
in
NMR.
€
–  Over
Kme,
spins
get
slightly
out
of
phase
with
each
other,
reducing
the
bulk
magneKc
moment.
–  Leads
to
Lorentzian
lineshape.
R2
Re(
ω
)
=
–  Faster
relaxaKon
leads
to
a
R2 2 + (ω o − ω ) 2
broader
line.
–  SensiKve
to
molecular
moKon
–
larger
molecules
tumble
more
slowly
and
have
broader
lines.
€
Size
limitaKons
in
NMR
•  #
of
peaks
(#
of
amino
acids)
•  Size
–
relaxaKon
Kme
affects
linewidth,
and
relaxaKon
Kme
depends
on
molecular
weight
(global
tumbling
Kme)
•  Field
strength
–
improved
resoluKon
since
∆ω
is
proporKonal
to
Bo
•  Temperature
&
solvent
viscosity
–
faster
tumbling,
slower
relaxaKon,
narrower
lines
Size
limitaKons
in
NMR
•  No
limit
in
solid‐state
NMR
in
theory…
In
pracKce,
limited
to
small
and/or
rigid
or
repeaKng
systems
(microcrystalline,
polymers,
small
membrane
proteins,
etc.)
•  SoluKon
NMR
most
established,
wide
variety
of
techniques
–  ≤30
kD,
monomeric,
rouKne
structure
and
dynamics
–  ≤60‐80kD,
monomeric,
probably
OK,
but
will
take
some
Kme
&
effort
–  ≥100kD,
may
be
able
to
address
specific
quesKons
(see
work
of
Lewis
Kay
at
U.
Toronto)
–  MulKmeric
–
complicates
the
analysis
of
NMR
spectra,
depending
on
symmetry
may
be
do‐able
–  Membrane
protein
–
can
you
solubilize
it?
How
big
is
the
solubilized
form?
–  MulKple
conformaKonal
states:
it
depends
on
the
populaKons
and
lifeKmes
•  For
NMR,
a
“solid”
is
anything
that
does
not
tumble
fast
enough
to
average
out
anisotropic
interac5ons
MulKdimensional
NMR
•  Add
an
addiKonal
dimension
to
improve
resoluKon.
•  MagneKzaKon
transferred
between
spins
via
J‐
coupling
(through
bonds)
or
dipolar
coupling
(through
space)
•  Isolated
2
spin
system
is
simplest.
•  15N‐1H
provides
a
nice
nearly‐isolated
2‐spin
system
with
the
protein
backbone.
•  HSQC:
observe
directly
bonded
pairs
of
nuclei
MulKdimensional
NMR
HSQC
Transfer
magneKzaKon
from
1H
to
15N
Record
chemical
shiv
in
indirect
dimension
(t1),
15N
frequency
in
this
case
Transfer
magneKzaKon
from
15N
to
1H
Record
chemical
shiv
in
directly
detected
dimension
(t2),
1H
frequency
in
this
case
HSQC
104
105
106
107
108
109
110
111
112
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
11.0
10.5
10.0
9.5
9.0
8.5
F2 ppm
1H
(ppm)
8.0
7.5
7.0
6.5
F
1
p
p
m
15N
(ppm)
113
Temperature
Dependence
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
11.0
10.5
10.0
9.5
9.0
8.5
F2 ppm
1H
8.0
7.5
7.0
6.5
F
1
p
p
m
15N
NMR
Strengths
and
Weaknesses
Strengths
Weaknesses
•Atomic
resolu0on
•Structural
informa0on:
chemical
shiv,
torsion
angle,
distance
restraints,
relaKve
orientaKons.
•Dynamic
informa0on:
Kmescale
(ps‐
hours),
order
parameter
for
fast
Kmescales
(ps‐ns),
populaKons
of
interconverKng
states
for
slow
exchange
(µs‐ms
and
slower).
•In
solu0on:
“naKve”
environment
for
soluble
proteins,
no
need
to
crystallize,
can
watch
equilibria/kineKcs
directly.
•Can
observe
disordered
regions
•Temperature
controlled
(4‐60C
widely
available,
enKre
range
of
liquid
water
accessible.
•Bundle
of
structures:
less
intuiKve
than
a
single
crystal
structure,
but
does
a
protein
really
exist
in
one
single
state?
How
do
we
handle
mulKple
conformaKons?
•How
to
quan0fy
disorder?
•Sensi0vity:
need
mg
quanKKes
and
high
concentraKon
soluKons
–
solubility
oven
an
issue.
•Size
limita0ons