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Spin Diffusion and Cross Relaxation in CPMAS NMR of Proteins and Peptides. . Stowe Winter School, 2013. H. N. Using NMR relaxation in solid proteins to study molecular dynamics. 15 N T 1 (s ) vs. sequence. dynamics : straightforward separation of internal from overall motion. - PowerPoint PPT Presentation
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Spin Diffusion and Cross Relaxation inCPMAS NMR of Proteins and Peptides.
Stowe Winter School, 2013
Using NMR relaxation in solid proteins to study molecular dynamics
dynamics: straightforward separation of internal from overall motion
problem: spin diffusion in uniformly enriched proteins can mask most interesting dispersion in dynamics
activation parameters: wider accessible temperature range
15CSA NΘ
NH dipoleΘ
NH
15N T1 (s) vs. sequence
05
101520253035404550
0 10 20 30 40 50 60 70 80
N CC
H D
O
N CC
H D
O
N CC
H D
O
re s id u e ire s id u e i-1 res id u e i+ 1
R D R D R D
model for 15N-15N spin diffusion in a deuterated back-exchanged protein
240 200 160 120 80 40 0 ppm
GALala, leu amidesT1 ~ 100 s
gly amineT1 ~ 0.4 s
15N—1H 15N1H3+
Zibby Fry
184 180 176 172 168 ppm60 50 40 30 20 ppm 8000 4000 0 -4000 -8000 Hz
244 K
214 K
154 K
130 K
110 K
95 K
13C 13C 1H
H2O
13C/15N glycyl-alanyl-leucine spectra vs. T
CO CH2 CH3
ala CH3
leu CH3 synthesized u-15N, u-13C/15N and also
u-13C/15N/2H
Zibby Fry
CH
δ
S1 S2
1 2SS SI I I
S z1 S z2 D D D23 23 sI I Iz x D D
H ω S ω S H H HδS dS H H
12
12
2 3δ dd δ
when |d| << δ, S1S2
flip-flops are quenched
1 2
2So
2 123S S
12 2 12
γμ P cosθ4π rd P θ
d
cos
15N115N2
1H
1H1 2S Sr
Isotropic shift difference δ truncates SSDH
15N115N2
1H
1H
1 2SS SI I I
S z1 S z2 D D D23 23 sI I Iz x D D
H ω S ω S H H HδS dS H H
1 2S Sr
12
12
2 30 d
d 0
where δeff ~ 0, flip-flops
are un-quenched
δeff ~ 0 where lines overlap
spectral overlap un-truncates SSDH
δ
S1 S2
δ
S1 S2
15N115N2
1H
1H
where δeff ~ 0, flip-flopsare un-quenched
simple theory of spin diffusion Heinrichs, Linder and HewittJCP (85), 1986, pgs. 7077-86
1 1 2 2S S S Sg 0 f ω ω f ω ω dω
overlap function
2ij ij
πR d g(0)2 spin diffusion rate
A A A A
B B B B .
z z z z1A AB AB
z z z zAB 1B AB
M M M MR R RdM M M MR R Rdt
2D spin diffusion experiment
15N
1H
CP π2
decouple
t1 t2tπ2
π2
x y
y+x-x
decoupleCP
AA BB
AA BB
2AB BA
1Δ R R21σ R R2
D Δ R R
A A A
B B B
oZ Z ZAA AB
oZ BA BB Z Z
M M MR t R tM R t R t M M
ddt
2D spin diffusion experiment
15N
1H
CP π2
decouple
t1 t2tπ2
π2
x y
y+x-x
decoupleCP
σt o o o o oA CzA 1 zA A 1 zA zB B 1 zB zA
σt o o o o oB CzB 1 zB B 1 zB zA A 1 zA zB
σtzA 1
n RΔM t ,t e cosh Dt sinh Dt M cos ω t M sinh Dt M cos ω t M MD Dn RΔM t ,t e cosh Dt sinh Dt M cos ω t M sinh Dt M cos ω t M MD D
M t ,t e co
and
o o o o oA CzA A 1 zA zB B 1 zB zA
σt o o o o oB CzB 1 zB B 1 zB zA A 1 zA zB
n RΔsh Dt sinh Dt M cos ω t M sinh Dt M cos ω t M MD Dn RΔM t ,t e cosh Dt sinh Dt M cos ω t M sinh Dt M cos ω t M MD D
2D spin diffusion experiment
15N
1H
CP π2
decouple
t1 t2tπ2
π2
x y
y+x-x
decoupleCP
o o ozA zB z A Bassuming M M M and n n 1
zA 1 σt CA 1 B 1o
z
zB 1 σt CB 1 A 1o
z
M t ,t RΔe cosh Dt sinh Dt cos ω t sinh Dt cos ω tD DMM t ,t RΔe cosh Dt sinh Dt cos ω t sinh Dt cos ω tD DM
2D spin diffusion experiment
15N
1H
CP π2
decouple
t1 t2tπ2
π2
x y
y+x-x
decoupleCP
σt
σtC
σt
σtC
ΔAA t e cosh Dt sinh DtDRAB t e sinh DtD
ΔBB t e cosh Dt sinh DtDRBA t e sinh DtD
Cif R Δ
(σ D)t
σ D t
AA t BB t AB t BA t eAA 0 BB 0
AA t BB t AB t BA t eAA 0 BB 0
auto and cross peak intensities
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 20 40 60 80
peak
inte
nsity
mixing time (s)
15N-15N 2D spin diffusion measurements on u-15N GAL
A B
X
BBAA
ABBA
15N—1H15N1H3
+
BB
AA
AB
BA
15N @ 80 MHz, νr = 18kHz1t / T
total(AA BB AB BA) M e
SD2t / Ttotal(AA BB AB BA) M e
0
1000
2000
3000
4000
5000
6000
0 5 10 15
peak
inte
nsity
mixing time (s)
15N-15N 2D spin diffusion measurements on u-15N GAL
A B
X
BBAA
ABBA
BB
AA
AB
BAXX
XAXX
XA
15N @ 80 MHz, νr = 7 kHz
SD2t / Ttotal(AA BB AB BA) M e
1t / Ttotal(AA BB AB BA) M e
15N—1H15N1H3
+
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 20 40 60 80
7 kHz11.5 kHz15 kHz18 kHz
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 20 40 60 80
7 kHz11.5 kHz15 kHz18 kHz
ln(A
A+BB
+AB+
BB)
time (s)
T1 decay TSD decay
time (s)
TSD and T1 depend on MAS rate
ln(A
A+BB
-AB-
BB)
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.05 0.1 0.15-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 20 40 60 80
7 kHz11.5 kHz15 kHz18 kHz
R C (
s-1)
2π·103 /ωr (s)
1/TSD vs. 1/ωr TSD decay
time (s)
TSD and T1 depend on MAS rate
from initial slope
ln(A
A+BB
-AB-
BB)
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 2 4 6 8
7 kHz11.5 kHz15 kHz18 kHz
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 20 40 60 80
7 kHz11.5 kHz15 kHz18 kHz
ln(A
A+BB
+AB+
BB)
TSD decay TSD decay
time (s)
TSD decay looks like classic diffusion barrier limited kinetics
ln(A
A+BB
-AB-
BB)
1/ 2time (s )Root-time decay has same form as for nuclei
relaxed by randomly distributed paramagnetic impurities
Due to distribution of N-N vectors in rotor frame
15N spectra of gly-ala-leu 15N/13C/2H crystallized from D2O/H2O
leu NH(D)ala NH(D)
gly NH3+
(D)
138 136 134 132 130 128 126 124 122 120 118 116 ppm 34 33 32 31 30 29 28 27 26 ppm
H
H H
D
D D
short CP
long CP
138 134 130 126 122 118 ppm 34 32 30 28 26 ppm
large secondary isotopic chemical shifts
120
121
122
123
124
125
126
127
128
129
131 130 129 128 127 126 125 124 123 122 121 120 ppm
AHAD
BHBD
Amide-Amide spin diffusion is 1H driven
2D 15N-15N30 s spin exchangespectrumfor 50/50
GAL
AH-BHcrosspeaks
120
121
122
123
124
125
126
127
128
129
131 130 129 128 127 126 125 124 123 122 121 120 ppm
AHAD
BHBD
Amide-Amide spin diffusion is 1H driven
2D 15N-15N30 s spin exchangespectrumfor 50/50
GAL
AH-BDcrosspeaks
120
121
122
123
124
125
126
127
128
129
131 130 129 128 127 126 125 124 123 122 121 120 ppm
AHAD
BHBD
Amide-Amide spin diffusion is 1H driven
2D 15N-15N30 s spin exchangespectrumfor 50/50
GAL
AD-BHcrosspeaks
120
121
122
123
124
125
126
127
128
129
131 130 129 128 127 126 125 124 123 122 121 120 ppm
AHAD
BHBD
Amide-Amide spin diffusion is 1H driven
2D 15N-15N 30 s spin exchangespectrumfor 50/50
GAL
No AD-BDcrosspeaks
x
x
N CC
H D
O
N CC
H D
O
N CC
H D
O
re s id u e ire s id u e i-1 res id u e i+ 1
R D R D R D
15N-15N spin diffusion should be detected in the 15N T1 relaxation
240 200 160 120 80 40 0 ppm
GALala, leu amidesT1 ~ 100 s
gly amineT1 ~ 0.4 s
15N—1H 15N1H3+
15N T1 independent of deuterium exchange
T1 amine = 0.4 s T1 amide = 800 s as r ∞
Amide 15N T1 MAS independent if gly-15N is removed
T1 amine = 0.4 s T1 amide = 800 s as r ∞
о ala in 2-15N GALо leu in 2-15N GAL
Nuclear Cross-Relaxation Induced by Specimen RotationE.R. Andrew et al, Physics Letters (4) 1963, pg 99-100
31P spectrum of PCl5
6PCl4PCl
1H T1 and methyls - Slichter, Douglass ......
13C T1 and methyls – White, Law ......
2H T1 with relaxation sinks as CD3 – Gan, Wimperis.....
Relaxation by spin diffusion to relaxation sinks
2 4 0 2 0 0 1 6 0 1 2 0 8 0 4 0 0 p p m
CSA enabled 15N-15N spin diffusion
apparent R1 fast MAS ~ R1 NH dipolar
8000 Hz
amide amine
overlap ~ constant at slow
MAS rates
R iso3R
overlap decreases as 1 once ω Δωω
2.2 kHz
5.0 kHz
12 kHz
spin diffusion under MAS
Kubo and McDowell
rimω t12 2 12 12 m
m 1, 2d P cosθ (t) d A ed
Fourier components of SSDH
Suter and Ernst (32) 1985, 5608-27
2m m Ry r
m 1, 2SD2
Ry r Ry r Ry r Ry r
1 d A A K (mω )Td K (ω ) K ( ω ) K (2ω ) K ( 2ω )15
RyK (ω)zero quantum lineshape
powder sum
240 200 160 120 80 40 0 ppm
amine isotropic
zero quantum amplitudes are approximately the overlap integral for the amine line with the amide
sidebands
26
o2 4 2
N
1ij
μ γ1 πT 2 160π
ij ij ij
ij
d f fr T1 amine = 0.4 s T1 amide = 800 s as r ∞
0100200300400500600700800900
0 5 10 15 20 25 30
H dipolarD dipolarCSA onlyexperimental
scaled overlap function fij
vr (kHz)
TSD (s)
0100200300400500600700800900
0 5 10 15 20 25 30
CSA onlyH dipolarD dipolarexperimental
vr (kHz)
Amide T1 T1 (s)
BA 1B1B
1 R RT
T1 computed from amine overlap with r, 2r sidebands of amide
T1 amine = 0.4 s
T1 amide = 800 sas r ∞
26
o2 4 2
N
1ij
μ γ1 πT 2 160π
ij ij ij
ij
d f fr
amide linewidth
~2500 Hz
15N
1H
increase overlap to decrease T1
π2
π2
1 rω ω decouple
trelax
15N
1H
increase overlap to decrease T1
π2
π2
1 rω ω decouple
trelax
trelax (s)0.0 0.1 0.2 0.5 1 2 5 10 50 100 200 400 1000
ωr/2π = 7.0 kHz
15N
1H
increase overlap to decrease T1
π2
π2
1 rω ω decouple
trelax
trelax (s)0.0 0.1 0.2 0.5 1 2 5 10 50 100 400 1000 3000
ωr/2π = 20.0 kHz
MAS and anisotropic relaxation
H Nm m
WI
WI
W2
Wo
WS
WS
β
r oω t γ
Bo
Mθ15N
1H
I S0I S
1S r 2 2I S
2
I S0I S
1S 2 2I S
2
WτW f(β,ω t γ) and g(τ,ω) 1 ω τ
W
WτW average over t, β g(τ,ω) 1 ω τ
W
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 t
powder sum decay
decay with average T1
longest T1 component
shortest T1 component
T1
T1
T1
◦
time
11/ Te
Model like 13C T1 relaxation of a methyl group under MAS
i) internal rotation dominantii) temperature dependence of known
2
CH
Θ 69.1 f or C H vector S 0.93Θ 90 f or H H vector r = 1.106 Å
I I I I I S I S I SI I I 1 2 S 0 1I 2
SS SS I S I S I SSS S 1 2 I 0 1S 2
I S I SI S I 2 0
I S I SSI S 2 0
R 2(n 1)(W W ) n (W 2W W )R 2(n 1)(W W ) n (W 2W W )R n (W W )R n (W W )
I I
S S S
oZ Z ZII I I S
oZ Z ZSI SS
M M MR t R tM M MR t R t
ddt
θ
ΘBo
1H13C
D. Torchia and A. Szabo JMR 49, (1982) pg 107
Ottiger and Bax, JACS 121
(1999) pg 4690
AE / RT1 2 oτ 4τ τ e
τ
dipolar T1 for a 15N-1H pair freely diffusing on surface of a cone
2 12Cone
11 24
1
Θ f rom S cosΘ 1 cosΘ1τ τ f romT
2 2 22I S
1 I s61 I SMAS
42 I s
21 S
42 S
21 I S
42 I S
0.075γ γ1 {g(τ,ω ω )sin 2ΘT rg(τ ,ω ω )sin Θ3g(τ,ω )sin 2Θ3g(τ ,ω )sin Θ6g(τ,ω ω )sin Θ6g(τ ,ω ω )sin Θ}
15N
1H1H
Θ
15CSA NΘ
NH dipoleΘ
NH
-6-30369
12151821
-17 -15 -13 -11 -9 -7 -5 -3 -1
NOEamide R1amine R1
θ
Θ Bo1H
15N
15N
1H1H
Θamide in“fast” motion
limit
τc ~ 10-11s
amine in“slow” motion
limit
τc ~ 10-7s
log(τc)
R 1 (s
-1) o
r NOE
13C1H 1H
1H
13C T1 vs. MAS rate for 13C, 15N enriched GAL
150 ppm
13C O
R1 enhancementsfor fast vs. slow MAS
rates could be used tomeasure CH3 to CO rCC
or… compare natural abundance with a single 13CH3
330 s
330 s
170 s 67 s
70 s
8 s
13 12SD 1 C 1 C
1 1 1T T T
6 calcsd sdT (s) 1/ r T (s)
L(CO) 88 0.00026 183A(CO) 8.4 0.0044G(CO) 83 0.00045 81
or… compare natural abundance with a single 13CH3
303 s
21 s
111 s
2 s
13 12SD 1 C 1 C
1 1 1T T T
6 calcsd sdT (s) 1/ r T (s)
L(Ca) 175 0.0003 123A(Ca) 1.8 0.084 0.5
but some R1 enhancements are not so simple to explain
17 s
0.2 s
6 calcsd sdT (s) 1/ r T (s)
L(Cg) 5.2 0.0003 122L(Cd1) 2.1 0.00048L(Cd2) 2.2 0.00039A(Cb) 0.7 0.00007
0.3 s
0.4 s
0.6 s4 s 0.5 s
0.8 s
2ij ij
sd
1 πR d g(0)T 2
Yale University• Van Phan• Zibby Fry• Suvrajit Sengupta• Victoria Mooney• Lacey Ketzner• Shan Kuang• Josh Hernandez• Chris Bennett• Hannah Fuson• Catalina Espinosa• Josh Karli
coworkers:
Funding: NSF Experimental Physical Chemistry
Agilent Foundation