24
!"#$%&' )&*+%,# -%./+&+#% 0&.1# 2'1+#13$%. &+4 533$1#&,/+. 6/ 01/7/$%#"$%. BIOCH 590: Biomacromolecules Spring 2010 Copyright: Jianhan Chen Key References: Tinoco Chapter 10; van Holde Chapter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

Nuclear Magne,c Resonance NMR Fundamentals

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Page 1: Nuclear Magne,c Resonance NMR Fundamentals

!"#$%&'()&*+%,#(-%./+&+#%(

0&.1#(2'1+#13$%.(&+4(533$1#&,/+.(6/(01/7/$%#"$%.(

BIOCH 590: Biomacromolecules Spring 2010

Copyright: Jianhan Chen

Key References: Tinoco Chapter 10; van Holde Chapter 12;

89%'91%:(

•  0&.1#(3'1+#13$%.(–  !"#$%&'(.31+;(%+%'*<($%9%$.;(#=%71#&$(.=1>(

–  ?='/"*=@A/+4(&+4(6='/"*=(.3&#%(#/"3$1+*.(–  -%$&B&,/+(,7%.(

–  C?@!)-;(3"$.%.;(DE(!)-(

–  FE(&+4(7"$,@417%+.1/+&$(!)-(%B3%'17%+6.(

•  533$1#&,/+(6/(A1/7/$%#"$%.(–  G1*=@'%./$",/+(.6'"#6"'%(4%6%'71+&,/+(

–  E<+&71#.H('%$&B&,/+(&+&$<.1.(

–  ?'&+.1%+6(1+6%'&#,/+.H(%B#16&,/+(6'&+.I%';(.31+@$&A%$1+*(–  J/$14(.6&6%H(7%7A'&+%(3'/6%1+.(

–  K+@#%$$(!)-(

–  K7&*1+*H()-K(

L#M(N1&+=&+(O=%+( F(

!)-(C"+4&7%+6&$.(

L#M(N1&+=&+(O=%+( P(

!"#$%&'(J31+(

•  J31+H(I"+4&7%+6&$(3'/3%'6<(/I(%$%7%+6&'<(3&',#$%.(–  Q$%#6'/+H(J(R(S(

•  !"#$%".H(#/+.1.6(/I(3'/6/+.(&+4(+%"6'/+.(–  L!%6M(+"#$%".(.31+(+"7A%'H(!(R(T;(S;(D;(U(

–  !/(+"#$%".(.31+(1I(%9%+(+"7A%'.(/I(+%"6'/+.("#$%3'/6/+.(

L#M(N1&+=&+(O=%+( V(

!"#$#%&' (%)*'+',-./#0123'41$5',678'/19:"&;'<5'

=1$>/1?'1@>*91*;&',A5'

4&?1BC&'(&*")BC)$.'

C:DEF''1$'6638'<'G&?9'

DG( S( FWXYZFF( [[X[\( DXTT( ZTTXT(FG( D( VXDTWW( TXTDZ( [XWZBDT@P( YWX\(DPO( S( WXYF\P( DXDT\( DXZ[BDT@F( DFZX\(DZ!( S( @FXYDFW( TXPY( DXTVBDT@P( ZTXW(D[C( S( FZXD\DZ( DTT( TX\P( VYTXW(PD2( S( TX\P[V( DTT( WXWPBDT@F( FTFXW(

Page 2: Nuclear Magne,c Resonance NMR Fundamentals

Q+%'*<(]%9%$.(

L#M(N1&+=&+(O=%+( Z(

•  !)-(7/.6$<(#/+#%'+.(S(+"#$%1H(DG;(DPO;(DZ!(%6#(

!

E"1/ 2 =12#!B0

E1/ 2 = "12#!B0

Q+%'*<(]%9%$.(•  )&*+%,#(413/$%(

–  ^H(_<'/7&*+%,#('&,/(

•  Q+%'*<($%9%$.(

•  Q+%'*<(*&3(

–  ]&'7/'(I'%`"%+#<H(&](R('0TaFb(–  J6'%+*6=(/I(7&*+%,#(c%$4(4%6%'71+%.(6=%(%+%'*<(*&3(/I(&(*19%+(+"#$%1X(

L#M(N1&+=&+(O=%+( W(

!

µz = "!mz

!

E = "µzB0 = "#!mzB0

!

"E = #!B0 = hvL

K-(3'/A%.(91A'&,/+&$(%+%'*<($%9%$.(:16=(%+%'*<(*&3.(d(W(e#&$a7/$X(

8+(&(6<31#&$(!)-(.3%#6'/7%6%';(6=%(!)-(%+%'*<(*&3(1.(d(DT@Z(e#&$a7/$X(

G1*=%'(7&*+%,#(c%$4H(1+#'%&.%(.3%#6'&$(:146=(&+4('%./$",/+((( ( ( ( ((%+=&+#%(.3%#6'&$(.%+.1,916<(

)&*+%6(J6'%+*6=(&+4(2'/6/+(C'%`"%+#<(

L#M(N1&+=&+(O=%+( Y(

~10-5 T 1.41 T 11.75 T 18.8 T 21.15 T ~ KHz 60 MHz 500 MHz 800 MHz 900 MHz

$0 $0.5m >$5m

EFNMR

!)-(J3%#6'"7(5A./'3,/+(:=%+('&41&,/+(7&6#=%.(6=%(%+%'*<(*&3(

L#M(N1&+=&+(O=%+( \(

“Complex” features of NMR spectra of chemicals

J"#=(1+1,&$$<("+3$%&.&+6(#/73$%B16<(L6/(3=<.1#1.6.M(A%#/7%.(/+%(/I(6=%(7/.6(3/:%'I"$(7%&+.(I/'(#=%71.6.(6/(3'/A%($/#&$(#=%71#&$(L&+4(.6'"#6"'&$M(%+91'/+7%+6.(/I(L&$$M(3'/6/+.(1+(&(.<.6%7f((

Page 3: Nuclear Magne,c Resonance NMR Fundamentals

O=%71#&$(J=1>(

•  ]/#&$(9&'1&,/+.(/I(((7&*+%,#(c%$4(

–  gH(.=1%$41+*(#/%h#1%+6(

•  O=%71#&$(.=1>(

–  QB3'%..%4(1+(337(

–  -%I%'%+#%(.6&+4&'4H(6%6'&7%6=<$.1$&+%((L?)JM(L/'(EEJM(•  J1+*$%6H(&$$(DF(3'/6/+.(!)-(%`"19&$%+6(

•  ?)J(1.(9%'<(.=1%$4%4(&+4('%./+&6%(&6(=1*=('%`"%+#<(

•  )/.6(#/73/"+4.(.6"41%4(A<(DG(!)-(&A./'A(4/:+c%$4(/I(6=%(?)J(.1*+&$;(6=".(6=%'%(1.("."&$$<(+/(1+6%'I%'%+#%(A%6:%%+(6=%(.6&+4&'4(&+4(6=%(.&73$%X(((

L#M(N1&+=&+(O=%+( [(

!

"s ="0(1#$)

!

"s =#s $#ref#0

%#s $#ref#ref

5(I%:(#/+I".1+*(6%'71+/$/*1%.(

•  E/:+c%$4(L=1*=(337M(9.X("3c%$4(L$/:(337M(

•  G1*=(I'%`"%+#<(L=1*=(337M(9.($/:(I'%`"%+#<(L$/:(337M(

L#M(N1&+=&+(O=%+( DT(

highfield

lowfield

lowfrequency

highfrequency

0510! ppm

1H NMR Chart Paper

TMS

highfield

lowfield

lowfrequency

highfrequency

0100200! ppm

13C NMR Chart Paper

TMS

relative intensity

Nuclei which absorb at higher field are more shielded from the applied Bo field by their respective Be fields. Forthese nuclei (Bo-Be) is smaller and correspondingly a lowerfrequency " is required to achieve resonance.

http://orgchem.colorado.edu/hndbksupport/nmrtheory/chemshift.html

less shielded more shielded

?<31#&$(O=%71#&$(J=1>.(

•  ]/#&$(.=1%$41+*H(=1*=%'(%$%#6'/+(4%+.16<(@i(7/'%(.=1%$41+*(–  Q$%#6'/+%*&,9%(."A.,6"%+6.(:16=4'&:(%$%#6'/+(&+4(6=".('%4"#%(.=1%$41+*(((

•  K+6%'&6/71#(.=1%$41+*(&+4('1+*(#"''%+6.(–  K+4"#%4(7&*+%,#(c%$4(71*=6(/33/.%(/'(%+=&+#%(%B6%'+&$(7&*+%,#(c%$4f(

L#M(N1&+=&+(O=%+( DD(

!

"s ="0(1#$)

O CH

Electronegative elementssuch as oxygen pull electron density away fromthe hydrogen nucleus.

This decreases the magnitudeof the shielding Be field and increases(Bo-Be).

Why do different protons absorb at different frequencies of the B1 field?

C O

O

CH

H H

H

H H

methylmethoxy

methyl acetate

!=2.1 ppm!=3.7 ppm

HC C

R

R R

Bo

H

Be

Be adds to Bo near the proton

Be adds to Bo near the proton

Be

C

C

H

R

Bo Be Be substractsfrom Bo near the proton

Be

BeBe

Circulation of π electrons creates magnetic fields which contribute to the Be field. The contribuiton is a function of orientation and consequently is an anisotropic effect.

http://orgchem.colorado.edu/hndbksupport/nmrtheory/chemshift.html

Page 4: Nuclear Magne,c Resonance NMR Fundamentals

012345678910! ppm

TMSCH3

H2C

CH3

RONR2

CH3CH3

OR

OCH3

RO

HR

R R

HH

RO

Ph

CH3

H

R

Cl

CH3

Ph

OH

OH

R

NHR

RCH2OH

533'/B17&6%(O=%71#&$(J=1>.(

http://orgchem.colorado.edu/hndbksupport/nmrtheory/chemshift.html

O=%71#&$(J=1>(K+4%B1+*(•  O=%71#&$(.=1>.(I"'6=%'(4%3%+4(/+(L$/#&$M(.6'"#6"'%.(

–  C/'(%B&73$%;((jTXPZ(337;(/+(&9%'&*%;(I/'(Gk(1+(=%$1#%.;(&+4(lTXVT(337;(/+(&9%'&*%;(I/'(Gk(1+(m@.=%%6.(LN17%+%n(%6(&$X(D[\YM(

•  OJKH(&(3/:%'I"$(7%&+(I/'(/A6&1+1+*(3'/6%1+(.%#/+4&'<(.6'"#6"'%.(–  O/73&'%4(6/('&+4/7(#/1$('%I%'%+#%(9&$"%.(

–  &9%'&*%.(&..1*+7%+6.(I'/7(7"$,3$%(#=%71#&$(.=1>.(LDGk;(DPOk;(DPOm(&+4(DPO′M(6/(&''19%(&6(&(#/+.%+.".(&..1*+7%+6X(

•  ]&6%.6(%B6%+.1/+.(6/('%$1&A$%(6%',&'<(.6'"#6"'%(4%6%'71+&,/+(A<(#/7A1+1+*(OJ(&+4(.6&,.,#&$(e+/:$%4*%f(L%X*X;(.%%(0&B(2!5J(FTT\M(

L#M(N1&+=&+(O=%+( DV(Mielke and Krishnan, Prog. NMR Spect (2009)

!)-(2%&e(K+6%+.16<(

•  ?=%(7&*+16"4%(/'(1+6%+.16<(/I(!)-('%./+&+#%(1.(3'/3/',/+&$(6/(6=%(7/$&'(#/+#%+6'&,/+(/I(6=%(.&73$%;(:=1#=(1.(7/.6(&##"'&6%$<(7%&."'%4(&.(1+6%*'&6%4(1+6%+.16<(L#/77/+$<(41.3$&<%4(/+(DE(!)-(.3%#6'&M(

•  K+6%*'&6%4(1+6%+.16<(1.(3'/3/',/+&$(6/(+"7A%'(/I(3'/6/+.(

L#M(N1&+=&+(O=%+( DZ(

“Complex” features of NMR spectra of chemicals (ethanol: CH3 CH2 OH shown)

J31+@J31+(O/"3$1+*(•  5XeX&X(J#&$&'(#/"3$1+*(LN@#/"3$1+*M(

•  0%6:%%+(!)-(+/+@%`"19&$%+6(+"#$%1(–  E1o%'%+6(#=%71#&$(.=1>.(

–  E1o%'%+6(#=%71#&$(%+91'/+7%+6(&+4(+/6(%+&+,/7%'1#(3&1'.(

•  ?='/"*=(#=%71#&$(A/+4.(L%$%#6'/+(.31+M(–  E%#%&.%.(:16=(7/'%(A/+4.H(+/(7/'%(6=&+(I/"'(A/+4.(

–  N(d(T(@(FT(Gn(L4%3%+4.(/+(#=%71#&$(+&6"'%(&+4(.6'"#6"'%M(

–  N(L7%&."'%4(1+(GnM(1.(c%$4(.6'%+*6=(1+4%3%+4%+6f(

•  ]%&4.(6/(.3$1p+*(/I(6=%(7&*+%,#(.31+(%+%'*<($%9%$.;(6=".;(.1*+&$.(–  K+(6=%($1716(/I(N(qq(#=%71#&$(.=1>(41o%'%+#%(Lc'.6(/'4%'a:%&e(#/"3$1+*M(

–  J3$16(1+6/(!lD(3%&e.(1I(#/"3$%4(6/(!(&4r&#%+6(%`"19&$%+6(3'/6/+.(–  ?=%(1+6%+.1,%.(/I(6=%.%(3%&e.(I/$$/:(2&.#&$s.(6'1&+*$%(

L#M(N1&+=&+(O=%+( DW(

CH3 CH2 OH

D(D(((D(

D(((F(((D((D(((P(((P(((D(

D(((V(((W(((V(((D((((((((((((((

Page 5: Nuclear Magne,c Resonance NMR Fundamentals

Q+%'*<(]%9%$.(&+4(N@O/"3$1+*(

L#M(N1&+=&+(O=%+( DY(http://www-keeler.ch.cam.ac.uk/lectures/index.html

)/'%(#/73$%B(#&.%.(/I(N@#/"3$1+*(

L#M(N1&+=&+(O=%+( D\(

Additional splitting if coupled to multiple groups of (equivalent) protons

AX2Y

Strong coupling

Weak coupling

J&73$%(!)-(J3%#6'&(

L#M(N1&+=&+(O=%+( D[(

?<31#&$(N@O/"3$1+*(O/+.6&+6.(

L#M(N1&+=&+(O=%+( FT(http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm

Page 6: Nuclear Magne,c Resonance NMR Fundamentals

N@O/"3$1+*(&+4(O/+I/'7&,/+(

•  N@#/"3$1+*(#/+.6&+6.(&'%(9%'<(.%+.1,9%(6/(#/+I/'7&,/+.(–  5(3/:%'I"$(7%&+(6/($/#&$(.6'"#6"'%.(–  )1+17&$(+%&'([T(6/'.1/+(&+4(

7&B17"7(+%&'(T(/'(D\T(6/'.1/+(

•  t&'3$".(Q`"&,/+H(G@u@v@G(–  Q731'1#&$(3&'&7%6%'.(Lcp+*M(

–  )"$,3$%(./$",/+.((

L#M(N1&+=&+(O=%+( FD(

H' I' J' K' L'

GO( OG( DY( T( DXD(

GO( !G( DF( T( TXF(

GO( 8G( DT( T( @DXT(

G!( O!G(w( WXV( @DXV( DX[(

(*: !="-60 for proteins)

-%$&B&,/+(•  ?:/(6<3%.(/I('%$&B&,/+(3'/#%..%.(

–  ?DH(J31+@$&p#%('%$&B&,/+(L$/+*16"41+&$('%$&B&,/+;%%+6=&$31#('%$&B&,/+MH('%#/9%'<(/I(%`"1$1A'1"7(3/3"$&,/+.(L&+4(6=".(&($/..(/I(.1*+&$(&+4(%+%'*<M(

–  ?FH([email protected]+('%$&B&,/+(L6'&+.9%'.%('%$&B&,/+;(%+6'/31#('%$&B&,/+MH($/.6(/I(x#/=%'%+#%y(L:16=/"6(&($/..(/I(%B#16%4(.6&6%(3/3"$&,/+(/'(%+%'*<M(

•  ?F(1.(&$:&<.(.7&$$%'(6=&+(?D(Ld(TXD(z(FT(.%#MX(

•  !)-(3%&e(:146=(1.(*%+%'&$$<(4%6%'71+%4(A<(?FX(

L#M(N1&+=&+(O=%+( FF(

#v = 1/T2

)/$%#"$&'(?"7A$1+*(&+4(-%$&B&,/+(•  0/6=(3'/#%..%.(&'%(7&1+$<('%$&6%4(6/(7/$%#"$&'(6"7A$1+*(,7%.(L"#M(

–  ?"7A$1+*(,7%(d(+.(L(/'(:a(I'%`"%+#<(/I(_GnM(

–  ]&'*%'(7/$%#"$%.(6"7A$%.(.$/:%'(&+4(6=".(7/'%(%o%#,9%(1+(1+4"#1+*('%$&B&,/+(L.=/'6%'(?D;(?FM(

–  C&.6%'('%$&B&,/+(&6(=1*=%'(c%$4.(((

L#M(N1&+=&+(O=%+( FP(

The largest component of the spectral density function, J($), is obtained when %c-1 & $0.

!"#$%&'(89%'=&".%'(Qo%#6(L!8QM(•  -C(.&6"'&,/+(/I(/+%(.31+(#&".%.(

3%'6"'A&,/+(/I(.31+(3/3"$&,/+(/I(+%&'A<(+"#$%1(91&(7&*+%,#(413/$%@413/$%(1+6%'&#,/+.X(?=1.(#=&+*%.(6=%(1+6%+.16<(/I(/6=%'(.31+.X((

•  E1o%'%+#%(.3%#6'"7(:16=(&+4(:16=/"6(-C(.&6"'&,/+(/I(.%$%#6%4(.31+X(

•  2'/914%(.3&,&$(41.6&+#%(1+I/(&.(413/$&'(#/"3$1+*(1+6%'&#6.(6='/"*=/"6(.3&#%X(

•  _%+%'&$$<(&+(%+=&+#%7%+6(%o%#6(

•  )&*+16"4%(I"'6=%'(4%3%+4.(/+(7/$%#"$&'(4<+&71#.H(.$/:(7/,/+.(Li+.M('%4"#%.(!8Q(&+4(71*=6($%&4(6/(+%*&,9%(!8Qf(

•  !8Q(A"1$4"3('&6%d(Da'W(L413/$%@413/$%M(

L#M(N1&+=&+(O=%+( FV(

Page 7: Nuclear Magne,c Resonance NMR Fundamentals

J"77&'<(/I(K+I/'7&,/+(I'/7(!)-(•  O=%71#&$(.=1>.H($/#&$(#=%71#&$(&+4(.6'"#6"'&$(%+91'/+7%+6(

•  LK+6%*'&6%4M(1+6%+.16<H(+"7A%'(/I(3'/6/+.a#/+#%+6'&,/+(

•  N@#/"3$1+*H(&4r&#%+6(3'/6/+.(&+4($/#&$(#/+I/'7&,/+.(

•  -%$&B&,/+(,7%.H(4<+&71#.(L6"7A$1+*;(1+6%'+&$(&+4(%B#=&+*%M(

•  !8QH(.=/'6@'&+*%(.3&,&$(41.6&+#%(Lq(W({M(|(L.$/:M(4<+&71#.((

L#M(N1&+=&+(O=%+( FZ(

5$$(6=%.%(`"&+,,%.(#&+(A%(&##"'&6%$<(7%&."'%4;(/>%+;(I/'(&$$(+"#$%1(1+(6=%(.<.6%7X(?=1.(1.(:=<(!)-(#&+(A%(%B6'%7%$<(3/:%'I"$X(

549&+#%4(?=%/'1%.(I/'(E%.#'1A1+*(!)-(

E%9%$/37%+6(/I(7/4%'+(FE(&+4(7"$,@417%+.1/+&$(!)-(6%#=+1`"%.(:&.(7&4%(3/..1A$%(:16=(6=%(&14(/I(.3%#1&$(})('%3'%.%+6&,/+(e+/:+(

&.(4%+.16<@7&6'1B(I/'7&$1.7X(

L#M(N1&+=&+(O=%+( FW(

Additional reading: Dr. James Keeler’s Lectures (U of Cambridge) http://www-keeler.ch.cam.ac.uk/lectures/index.html

~%#6/'()/4%$(

•  Q+%'*<($%9%$.(&+4(.%$%#,/+.(.%9%'%$<($1716%4(1+("+4%'.6&+41+*(&49&+#%4(!)-(6%#=+1`"%.(."#=(&.(3"$.%4(!)-(&+4(7"$,417%+.1/+&$(!)-((

•  ~%#6/'(7/4%$(1.(6=%($&+*"&*%(/I(!)-H(/+$<('1*/'/".(1+(&(I%:(#&.%.;(A"6(%B6'%7%$<(".%I"$(%9%+(I/'(6=%(7/.6(./3=1.,#&6%4(!)-(%B3%'17%+6.(

•  0"$e(7&*+%,n&,/+H(+%6(7&*+%,n&,/+(9%#6/'(&$1*+.(:16=(0T(

L#M(N1&+=&+(O=%+( FY(http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr2.htm

)&+13"$&,/+(&+4(E%6%#,/+(/I()/((

•  )/(71*=6(A%(x'/6&6%4y(A<(&('&41/I'%`"%+#<(3"$.%X((

•  8+#%(,$6%4(&:&<(I'/7(6=%(n(&B1.;(6=%(7&*+%,n&,/+(9%#6/'('/6&6%.(&A/"6(6=%(41'%#,/+(/I(6=%(7&*+%,#(c%$4(.:%%31+*(/"6(&(#/+%(:16=(&(#/+.6&+6(&+*$%(&6(]&'7/'(I'%`"%+#<(L]&'7/'(3'%#%..1/+MX(

•  !)-(%B3%'17%+6.(4%6%#6(6=%(3'%#%..1/+(/I(6=%(7&*+%,n&,/+(9%#6/';(."#=(&.(A<(3$&#1+*(&(.7&$$(#/1$(/I(:1'%('/"+4(6=%(.&73$%;(:16=(6=%(&B1.(/I(6=%(#/1$(&$1*+%4(1+(6=%(()@3$&+%X(

•  -%$&B&,/+.(&+4(I'%%(1+4"#,/+(4%#&<(LCKEM(

L#M(N1&+=&+(O=%+( F\(

(only x coil shown)

T2

T1

Page 8: Nuclear Magne,c Resonance NMR Fundamentals

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!

" i*# ˆ Q " jd$ %< i ˆ Q j >

2"$.%.(•  ?=%(+"#$%&'(.31+(7&*+%,n&,/+(1.(7&+13"$&6%4(A<(&33$<1+*(&(7&*+%,#(

c%$4(:=1#=(1.(L&M(6'&+.9%'.%(6/(6=%(.6&,#(7&*+%,#(c%$4(*+,X(1+(6=%(B<@3$&+%;(&+4(LAM(/.#1$$&,+*(&6(#$/.%(6/(6=%(]&'7/'(I'%`"%+#<(/I(6=%(.31+.X(

•  Å=&6(4/%.(&(3"$.%(4/H(#=&+*%(6=%(41'%#,/+(/I(7&*+%,n&,/+(9%#6/'(

L#M(N1&+=&+(O=%+( PT(

!

H =" 0Iz +"1 cos("RFt)IxH = (" 0 #"RF)Iz +"1Ix ~ "1Ix

="1I1x +"1I2x + ...

(lab frame) (rotating f.)

(multiple spins)

"3(

# = $1!p. (([T(3"$.%H(# R([T/(

D\T(3"$.%H(#(R(D\T/(LB@3"$.%;(<@3"$.%M(

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•  Q9/$",/+(/I(4%+.16<(7&6'1B(

L#M(N1&+=&+(O=%+( PD(

Additional reading: Dr. James Keeler’s Lectures (U of Cambridge) http://www-keeler.ch.cam.ac.uk/lectures/index.html

!)-(2'&#,#%(

!)-(1.(A%#/71+*(&(x.6&+4&'4y(6//$X(?=%(e%<(1.(+/:(7/'%(6/("+4%'.6&+4(:=&6(16(1.(#&3&A$%(&+4($%..(&A/"6(=/:(/+%(:/"$4(&#6"&$$<(#&''<(/"6(6=%(

L4&6&(&#`"1.1,/+M(%B3%'17%+6X(

Page 9: Nuclear Magne,c Resonance NMR Fundamentals

)/4%'+(!)-(J3%#6'/7%6%'(

L#M(N1&+=&+(O=%+( PP(

RF input RF output

C/"'1%'(?'&+.I/'7(!)-(LC?@!)-M(

•  ?=%(A&.1#(3"$.%(&+4(&#`"1'%(%B3%'17%+6(

L#M(N1&+=&+(O=%+( PV(

1.  The sample is allowed to come to equilibrium. 2.  RF power is switched on for long enough to rotate

the magnetization through 90' i.e. a 90' pulse is applied. If the pulse is broad (“powerful”) enough, all protons in the sample are exited.

3.  After the RF power is switched off we start to detect the signal which arises from the magnetization as it rotates in the transverse plane.

4.  The free induction decay contains information about oscillation of all protons. Fourier transform analysis will thus produce the whole NMR spectrum.

“pulse sequence”

x

y

z

Bo

Magnetic moments of excess nuclear spins in theground state are represented byvectors. The vectors precessabout the direction of the Bo field.

x

y

z

The sum of the individual spinvectorsis represented by a large vector in thedirection of the Bo field.

B1

x

y

z

Bo

B1

z

The B1 field issupplied as ashort pulse along the x-axis.

This causes the netmagnetization to tip offthe z-axis into the yz-planeand then precess about thez-axis. This is equivalent to ground spin states going to excited spin states by absorption of energyfrom the B1 field.

x

y

z

Bo

My

Mz

eye

The net magnetizationcan be resolved intoy- and z-axis components.The component in the xy-plane precesses about the z-axis.

x

y

z

Bo

x

yMy

Mx

magnetization in the xy plane resolved into Mx and My components

The change in magnetizationas a function of time as the netmagnetization vector in the xy-planeprecesses about the z-axisis observed along the y-axis as My.

relaxation

x

y

z

Bodetector

With time, the change in net magnetization caused by the B1 pulse decays back to the original state with no net magnetization in the xy-plane.

relaxation

x

y

z

Bo

x

y

z

Bodetector

The change in magnetizationas a function of time as the netmagnetization vector in the xy-planeprecesses about the z-axisis observed along the y-axis as My.

With time, the change in net magnetization caused by the B1 pulse decays back to the original state with no net magnetization in the xy-plane.

Intensity

time

one cycle

Fourier

Transformation

510 0! ppm

FID

Time Domain Spectrum

Frequency Domain Spectrum

My

inte

nsity

Magnetization along the y-axis as a function of time after the B1 pulse. NMR Spectrum

http://orgchem.colorado.edu/hndbksupport/nmrtheory/chemshift.html

Page 10: Nuclear Magne,c Resonance NMR Fundamentals

!)-(?D(-%$&B&,/+(

L#M(N1&+=&+(O=%+( PY(

J31+(Q#=/(

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The most famous NMR experiment: the magnetization ends up along the same axis, regardless of the values of ! and the offset, ". This is achieved by using 180 pulse as refocusing pulse.

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z

90 pulse along -x

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L#M(N1&+=&+(O=%+( VT(http://chem.ch.huji.ac.il/nmr/techniques/other/t1t2/t1t2.html

Page 11: Nuclear Magne,c Resonance NMR Fundamentals

2=&.%(O<#$1+*(•  ?/(%$171+&6%("+:&+6%4(.1*+&$.a&',I&#6.(L&+4(.%$%#6(4%.1'%4(#/=%'%+#%M(

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L#M(N1&+=&+(O=%+( VD(

These signals add up to zero! (unless receiver phase follows pulse

Artifacts that do not follow the phases will cancel out!

(;1*' M>?"&' 4&;&)C&/'

D( Ö( Ö(

F( @u( @u(

P( @Ö( @Ö(

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amide aromatic aliphatic ~8-9 ppm ~7-8 ppm <4 ppm

methyl

Multi-dimensional NMR is the work-horse in biomolecular studies.

FE(!)-(J3%#6'/.#/3<(

L#M(N1&+=&+(O=%+( VP(

Preparation detection t1

Preparation evolution t1

mixing detection t2

FID: C(t1) Spectrum I(&1) FT

FID: C(t1,t2) Spectrum I(&1,&1)FT

2D contour plot

Recording a 2D data set involves repeating a pulse sequence for increasing values of t1 and recording a FID as a function of t2 for each value of t1.

O/''%$&,/+(J3%#6'/.#/3<(LO8JuM(

L#M(N1&+=&+(O=%+( VV(

(For AX system: )

First 90 pulse:

y

x

' 6D%

Second 90 pulse:

Only last (3) and (4) terms lead to observable signals. Term 3 yields diagonal peaks ('1, '1). Term 4 contains “coherence transfer”: a ('1, '2) cross-peak modulated by '1 in t1 and by '1 in t2.

(solid rectangles denote 90 pulses)

Page 12: Nuclear Magne,c Resonance NMR Fundamentals

K+I/'7&,/+(I'/7(O8Ju(

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after t1:

2nd 90 pulse: 1)

2)

First term is “frequency labeled” and undergo NOE/chemical exchange; second term is eliminate by coherence selection (via phase cycling). The 3rd pulse detects the first term.

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L#M(N1&+=&+(O=%+( VY(

after t1:

2nd 90 pulse:

How do one “select” I1z for detection?

A simplified scheme (the actual phase cycling is more complicated):

Scan 1: apply 2nd 90 pulse along x Scan 2: apply 2nd 90 pulse along –x

At the end, subtract FIDs from two scans. Can you imagine what happens to the above two terms?

1)

2) NOESY/EXSY

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Filled rectangles represent 90° pulses and open rectangles represent 180° pulses. The delay ( =1/(2J12); all pulses have phase x unless otherwise indicated.

Page 13: Nuclear Magne,c Resonance NMR Fundamentals

)"$,@E17%+.1/+&$(!)-(

L#M(N1&+=&+(O=%+( V[(

PE(J3%#6'&(

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~1."&$1n1+*(PE(J3%#6'&(".1+*(J6'13.(

L#M(N1&+=&+(O=%+( ZD(http://www.protein-nmr.org.uk/assignment_theory.html L#M(N1&+=&+(O=%+( ZF(

… Schematic representations of dipeptides showing nuclei in residues i and i¡1, where i is the residue number, that are correlated (circled) in the HNCACB (top left) and (HB)CBCA(CO)NNH experiments (top right). The 13CB nuclei observed in the HNCACB are colored red, denoting the opposite phase of signals arising from these spins relative to phases of 13CA signals. Strip plots from the HNCACB experiment are at the 1HN(i) and 15N(i) chemical shifts for residues His 480 to Glu 488 of the Nedd4 WW domain (bottom). The negative 13CB signals are represented as red contours. Correlations between sequential 13CA/13CB resonances are indicated by dotted lines. The asterisks (¤) in the His 480 strip identify peaks with increased intensity on another plane. This spectrum was recorded at 500 MHz (1H frequency) on a 1-mM 15N=13C-labeled Nedd4 WW domain bound to the unlabeled ENaCBP2 peptide in 10 mM sodium phosphate, 90% H2O, 10% D2O, pH 6.5 at 30±C …

Multidimensional NMR Methods for Protein Structure Determination, Kay et al., IUBMB Life (2001).

Page 14: Nuclear Magne,c Resonance NMR Fundamentals

?'13$%(-%./+&+#%(2'/6%1+(!)-(

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Labeling of a protein with both 15N & 13C causes almost all of the atoms in the protein to become observable in NMR spectroscopy. More importantly, all of the atoms also become scalar coupled to each other. These homonuclear and heteronuclear scalar couplings are relatively large compared to the linewidth of the resonance lines.

Two key references:

1.  Markley (1994) Methods in Enzymology Vol 239. 2.  Bax & Grzesiek (1993), Accounts of Chemical Research, 26, 132.

http://www.intermnet.ua.es/inteRMNet/cursoRule/doublelabel.html

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)"$,417%+.1/+&$(2'/6%1+(!)-(

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01/7/$%#"$&'(!)-(533$1#&,/+.(

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WX(K7&*1+*H()-K(

((((UX(

Page 15: Nuclear Magne,c Resonance NMR Fundamentals

L#M(N1&+=&+(O=%+( ZY( L#M(N1&+=&+(O=%+( Z\(

First NMR protein structure: Proteinase inhibitor IIA by Wüthrich lab in 1984 (published on JMB 1985). (see a historical review by Wüthrich, Nature Struct Biol 8, 923 - 925 (2001))

First X-ray protein structures Hemoglobin and myoglobin, by Max Perutz and Sir John Kendrew, respectively, in 1958

Source: PDB

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L#M(N1&+=&+(O=%+( WT(Also see: http://en.wikipedia.org/wiki/Protein_nuclear_magnetic_resonance_spectroscopy

Page 16: Nuclear Magne,c Resonance NMR Fundamentals

2'/6%1+(!)-(J&73$%(-%`"1'%7%+6.(

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Finger print region (HN-HN) of 2D 1H-1H NOESY spectrum Finger print region (HN-Ha/Side chain protons) of 1H-1H TOCSY Herrera et al PROTEINS (in press)

p22 in SDS micelles KKKKP ARVGL GITTV LTMTT QS

<NL(H'

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COSY peaks TOCSY peaks

“spin lock period”

Spin-echo sequence Spin-lock sequence

Spin-lock sequence – is the Spin-echo sequence, applied continuously. The simplest spin-lock sequence is just a continuous pulse.

The Spin-lock sequence makes all spins strongly coupled (differences in chemical shifts are less than coupling constants)

J31+(]/#e(

Page 17: Nuclear Magne,c Resonance NMR Fundamentals

]&'*%'(2'/6%1+.(

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Backbone: HNCA HN(CO)CA HNCO HCACO HN(CA)CO CBCA(CO)NH HNCACB HBHA(CBCACO)NH HN(CA)HA

High resolution 1H-15N HSQC High resolution 1H-13C HSQC (aliphatic) High resolution 1H-13C HSQC (aromatic)

Side chain: 15N TOCSY-HSQC C(CO)NH-TOCSY H(CCO)NH-TOCSY CCH-TOCSY CCH-COSY HCCH-TOCSY HCCH-COSY Aromatic 1H spectra (2QF COSY and 2Q) for resonances

within aromatic rings 1H NOESY to connect Hd with Hb (marked high

intensity NOEs) (Hb)Cb(CgCd)Hd (Hb)Cb(CgCdCe)He (HC)C(C)CH-TOCSY Methionine HMBC to assign methyl group

Incomplete excerption from Wright/Dyson lab manual (The Scripps Research Institute).

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3D 15N NOESY 3D 13C NOESY 4D 15N, 13C NOESY 4D 13C, 13C NOESY 3D 15N, 15N NOESY 3D 15N HSQC-NOESY-HSQC (take two NOESY spectra at 2 or more mixing times when possible)

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•  !8Q(&..1*+7%+6.H(/9%'$&3.($%&4(6/(&7A1*"/".(!8Q.à(16%'&,9%(&..1*+7%+6(&..1.6%4(:16=(.6'"#6"'&$(I%%4A&#e.f((((

•  01++1+*(!8Q(1+6%+.1,%.H($&'*%("+#%'6&1+,%.(&+4(/+$<(`"&$16&,9%f(;?1"" ( (/&"$/1)*$' '9&";/)%B#* (wI/'(3'/6%1+(:a()'qFT(eE&( (

.6'/+* ( (DX\@FXY({ (.6'/+*(1+6%+.16<(1+(.=/'6(67(LdZT(7.wM(!8QJu(7%41"7( (DX\@PXP({ (:%&e(1+6%+.16<(1+(.=/'6(67(LdZT(7.wM(!8QJu(:%&e ( (DX\@ZXT({ (/+$<(91.1A$%(1+($/+*%'(71B1+*(,7%(!8QJu(

PE(!8QJu@GJ}O(

•  FE(DG@DG(!8QJu(#&+(A%(9%'<((#'/:4%4X(

•  5441,/+&$(417%+.1/+(=%$3.(6/(41.3%'.%(6=%(3%&e.(&+4(I&#1$16&6%(&..1*+7%+6(

•  !8QJu(I/$$/:%4(A<(GJ}O(

L#M(N1&+=&+(O=%+( WY( L#M(N1&+=&+(O=%+( W\(

3D 1H-15N NOESY-HSQC spectrum of a dimeric GpA mutant

http://www-bioc.rice.edu/~mev/spectra3.html

Page 18: Nuclear Magne,c Resonance NMR Fundamentals

5441,/+&$(J6'"#6"'&$(-%.6'&1+6.(

•  O=%71#&$(.=1>(&+&$<.1.H(OJK(

•  G<4'/*%+(A/+4.H(EF8(%B#=&+*%(%B3%'17%+6.(6/(14%+,I<(.$/:(%B#=&+*1+*(&714%.(L6=/.%(1+9/$9%4(1+(=@A/+4.M(

•  N@#/"3$1+*(#/+.6&+6.(

L#M(N1&+=&+(O=%+( W[(

Experiment Coupling constant Information HNHA 3JHN,Ha (%HA(CA)HB COSY 3JHa,Hb c1, bH stereos HNHB 3JHN,Hb c1, bH stereos 2QF COSY JHN,Ha, 3JHa,Hb confirmation 13C-{13CO} spin-echo difference ct-HSQC 3JCg,CO Ile, Thr )1, Val )1,

C* stereos 13C-{15N} spin-echo difference ct-HSQC 3JCg,N Ile, Thr )1, Val )1,

C* stereos

J6'"#6"'&$(O&$#"$&,/+(•  5$$(.6'"#6"'&$('%.6'&1+6.(173$%7%+6%4(A<(3%+&$6<(I"+#,/+.(

•  J6'"#6"'&$(#&$#"$&,/+('%@#&.6%4(&.(*$/A&$(%+%'*<(71+171n&,/+a#/+I/'7&,/+&$(.%&'#=(3'/A$%7(L:=1#=(1.(7/$%#"$&'(4<+&71#.(&$$(&A/"6fM(

•  -%.6'&1+%4(7/$%#"$&'(4<+&71#.(:16=(.17"$&6%4(&++%&$1+*(6/(*%+%'&6%(.%6.(/I(.6'"#6"'%.(6=&6(7&B17&$$<(.&,.I<(&$$('%.6'&1+6.(

•  ?:/(e%<(3/3"$&'(!)-(.6'"#6"'&$(#&$#"$&,/+(./>:&'%(–  Ou5!5aEu5!5H(=Ü3Haa:::X$&.Xr3a3'/4a#<&+&a%*(–  O!JH(=Ü3Haa#+.@/+$1+%X/'*a9DXFDa(–  Ö3$/'@!KGH((=Ü3Haa+7'X#16X+1=X*/9aB3$/'@+1=a(

L#M(N1&+=&+(O=%+( YT(

!

V = VMM" + VNMR"

Distance rij

L#M(N1&+=&+(O=%+( YD( L#M(N1&+=&+(O=%+( YF(

Internal Coordinate MD

Page 19: Nuclear Magne,c Resonance NMR Fundamentals

-%c+%7%+6(|(~&$14&,/+(

•  !)-('%.6'&1+6(91/$&,/+(.6&,.,#.H(.%$I@#/+.1.6%+#<(

•  O/+9%'*%+#%(L3'%#1.1/+MH(#&+(A%(71.$%&41+*(

•  2-8OGQOtH(2E0(.6&,.,#.(/+(*%+%'&$((a+(41.6'1A",/+.(

•  -%c+%7%+6(".1+*(&441,/+&$(1+I/'7&,/+(I'/7(–  Q731'1#&$(3'/6%1+(I/'#%(c%$4H(

./$9%+6(%o%#6.(

–  5441,/+&$(%B3%'17%+6&$(4&6&H(!)-(&+4(+/+@!)-f(

–  -%.14"&$(413/$&'(#/"3$1+*(L-EOM((

L#M(N1&+=&+(O=%+( YP(

!

V = VMM" + VNMR" + VOther"

PDB: 2KI7; Xu et al, JMB (2009)

-%c+%7%+6(1+(173$1#16(./$9%+6(#&+(A%(".%4(6/(/A6&1+((+&,9%@$1e%(7/4%$.(I'/7($1716%4(!)-(4&6&X(

Cost: ~12h wall time using 16 Intel 2.4GHz CPUs!

-%c+%7%+6(/I()&$6/.%@01+41+*(2'/6%1+(L)02M(

•  370 residues, 42 kDa !

•  1943 NOE, 45 hydrogen bonding and 555 dihedral angle restraints.!

•  Average backbone RMSD to X-ray structure is 5.5 Å (a).!

•  Improved to 3.3 Å with 940 additional dipolar coupling based restraints (b).!

Ref. Mueller et al., JMB 300, 197 (2000)!

K73$1#16(J/$9%+6(-%c+%7%+6(-%."$6.(

•  All NOE and dihedral angle restraints were used.!

•  48 replicas were simulated at 300 to 800 K until converged.!

•  Total of 1.0 ns REX/GB simulation.!

a Backbone RMSD with respect to PDB:1dmb shown. Global: residues 6-235 and 241-370; N-domain: 6-109 and 264:309; C-domain: 114-235, 241-258 and 316-370.!

! ! ! ! ! !Initial !Final!RMSD to X-ray (Å) a! Global ! ! ! ! !4.3±4.1 !2.3±2.6! N-domain ! ! ! !2.5±2.1 !2.2±1.4! C-domain ! ! ! !3.0±3.2 !2.0±1.9!(/+ space: residues (%)! Most favored ! ! !72.2 ! !84.3! Additionally allowed ! !22.8 ! !13.3! Generously allowed ! !3.8 !1.6! Disallowed ! ! ! !1.2 ! !0.8!Violation statistics! RMSD of NOEs (Å) ! !0.0047 !0.014! NOE violations ( > 0.2Å) !2.85 ! !4.42! RMSD of angles (in degrees) !0.53 ! !6.25!

Page 20: Nuclear Magne,c Resonance NMR Fundamentals

5.8 Å ! ! ! ! ! ! 2.9 Å!

5.7 Å ! ! ! ! ! ! 3.5 Å!

-%3'%.%+6&,9%(J6'"#6"'%.H()02(

RMSD values: from X-ray (PDB:1dm); backbone atoms of residues 6-235 and 241-370!

5"6/7&,#aG1*=(?='/"*=3"6(!)-(J6'"#6"'%(E%6%'71+&,/+(

L#M(N1&+=&+(O=%+( Y\(

“Automation of NMR structure determination of proteins”, Altieri and Byrd, Curr Opin Struct Biol (2004)

“The automation of protein structure determination using NMR is coming of age. The tedious processes of resonance assignment, followed by assignment of NOE (nuclear Overhauser enhancement) interactions (now intertwined with structure calculation), assembly of input files for structure calculation, intermediate analyses of incorrect assignments and bad input data, and finally structure validation are all being automated with sophisticated software tools. The robustness of the different approaches continues to deal with problems of completeness and uniqueness; nevertheless, the future is very bright for automation of NMR structure generation to approach the levels found in X-ray crystallography. Currently, near completely automated structure determination is possible for small proteins, and the prospect for medium-sized and large proteins is good.”

O5!EKE(2'/6/#/$(

L#M(N1&+=&+(O=%+( Y[(Wuthrich and coworkers, JMB (2002)

Fina

l cyc

le

cycl

e 1

FX(2'/6%1+(E<+&71#.(I'/7(-%$&B&,/+(5+&$<.1.(

L#M(N1&+=&+(O=%+( \T(

Relaxation parameters (T1, T2, NOE) determined mainly by molecular tumbling and also depends on internal dynamics They thus report on internal dynamics, even though not always in obvious ways!

~1$$&+"%9&(%6(&$X;(xK+#'%&.%(1+(6=%(#/+I/'7&,/+&$(â%B1A1$16<(/I(#F@71#'/*$/A"$1+("3/+(#/33%'(A1+41+*H(5(3/..1A$%('/$%(I/'(#/33%'(1+(41&$<.1.@'%$&6%4(&7<$/14/.1.y;(2'/6X(J#1(LFTT[MX(

blue: with Cu2+; red: without

Page 21: Nuclear Magne,c Resonance NMR Fundamentals

}"&+,6&,9%(5+&$<.1.(/I(!)-(-%$&B&,/+(

•  Å16=(L3'/6/+@3'/6/+M(#'/..@'%$&B&,/+(."33'%..%4;(&714%(!DZ('%$&B%.(3'17&'1$<(4"%(6/(413/$&'(1+6%'&#,/+(:16=(6=%(41'%#6$<(&Ü&#=%4(DG(.31+(&+4(6='/"*=(DZ!(O=%71#&$(J=1>(5+1./6'/3<X(

•  -%$&B&,/+(3&'&7%6%'.(4%6%'71+%4(A<(.3%#6'&$(4%+.1,%.H((

L#M(N1&+=&+(O=%+( \D(Chen et al., JBNMR (2004) and references therein.

rNH is the length of the N-H bond; () is the CSA of 15N; $H and $N are the Larmor frequencies of 1H and 15N

J3%#6'&$(E%+.16<(&+4(K+6%'+&$()/,/+.(•  ?=%(.3%#6'&$(4%+.16<(I"+#,/+(1.(6=%(C/"'1%'(6'&+.I/'7(/I(6=%(&+*"$&'(&"6/@

#/''%$&,/+(I"+#,/+;(OL6M;(/I(6=%(!@G(A/+4(9%#6/';(

•  ?=%(&"6/@#/''%$&,/+(I"+#,/+(4%3%+4.(/+(A/6=(/9%'&$$(6"7A$1+*(&+4(1+6%'+&$(4<+&71#.X(5.."71+*(OL6M(R(O/L6M(OKL6M;(1I(6"7A$1+*(7"#=(.$/:%'X(

•  K+(./@#&$$%4(x7/4%$@I'%%y(&+&$<.1.(L]13&'1(&+4(Jn&A/;(D[\FM;(1+6%'+&$(4<+&71#.(#=&'&#6%'1n%4(A<(L7/,/+M(7/4%$@I'%%(3&'&7%6%'.;(1+#$"41+*((–  *%+%'&$1n%4(/'4%'(3&'&7%6%'.(L(MH(&73$16"4%.(/I(6=%(1+6%'+&$(7/,/+.(

–  Qo%#,9%(,7%(#/+.6&+6.(L"MH(,7%@.#&$%.(/I(6=%(1+6%'+&$(7/,/+.(

L#M(N1&+=&+(O=%+( \F(Time (ps)

Sample CI(t) with S2=0.9, "e=50 ps

)/4%$@C'%%(5+&$<.1.(

•  )%&."'%(?D;(?F(|(!8Q;(6<31#&$$<(&6(6:/(c%$4.(L%X*X;(ZTT()Gn(&+4(WTT()GnM(

•  C/'(%&#=(!DZ;(c6(L6='%%(/'(.1BM('%$&B&,/+(4&6&(3/1+6.(6/(6/(/A6&1+(*%+%'&$1n%4(/'4%'(3&'&7%6%'.(LJM(&+4(%o%#,9%(,7%(#/+.6&+6.(L"MX(

•  ?=%.%(4<+&71#.(3&'&7%6%'.(`"&+,I<(3'/6%1+(1+6%'+&$(4<+&71#.(&+4(#&+(A%(".%(6/("+4%'.6&+4(6=%('/$%(/I(1+6%'+&$(4<+&71#.(1+(I/$41+*(&+4(A1+41+*X(

L#M(N1&+=&+(O=%+( \P(

NMR PROBES OF MOLECULAR DYNAMICS: Overview and Comparison with Other Techniques, Palmer, Annu Rev Biophys Biomol Struct (2001). L#M(N1&+=&+(O=%+( \V(

A novel view of domain flexibility in E. coli adenylate kinase based on structural mode-coupling 15N NMR relaxation, Tugarinov et al, JMB (2002).

Assumption of uncoupled tumbling and internal motions in model-free analysis likely leads to an underestimation of motions on ns timescales.

Page 22: Nuclear Magne,c Resonance NMR Fundamentals

2'/6%1+(4<+&71#.(1+(%+n<7%(#&6&$<.1.(

L#M(N1&+=&+(O=%+( \Z(A hierarchy of timescales in protein dynamics is linked to enzyme catalysis, Kern and coworkers, Nature (2007)

mesoAdk thermoAdk

thermoAdk @ 20C 50C 80C

The synergy between structure and dynamics is essential to the function of biological macromolecules. …. Here we show that pico- to nano-second timescale atomic fluctuations in hinge regions of adenylate kinase facilitate the large-scale, slower lid motions that produce a catalytically competent state. The fast, local mobilities differ between a mesophilic and hyperthermophilic adenylate kinase, but are strikingly similar at temperatures at which enzymatic activity and free energy of folding are matched.

The connection between different timescales and the corresponding amplitudes of motions in adenylate kinase and their linkage to catalytic function is likely to be a general characteristic of protein energy landscapes.

L#M(N1&+=&+(O=%+( \W(

Schnell et al, Annu Rev Biophys Biomol Struct

(2004)

O/+I/'7&,/+&$(Q+6'/3<(1+(2'/6%1+(K+6%'&#,/+(

L#M(N1&+=&+(O=%+( \Y(

Wand and coworkers, Nature (2001); Nature (2007)

Here we employ changes in conformational dynamics as a proxy for corresponding changes in conformational entropy. We find that the change in internal dynamics of the protein calmodulin varies significantly on binding a variety of target domains. Surprisingly, the apparent change in the corresponding conformational entropy is linearly related to the change in the overall binding entropy. This indicates that changes in protein conformational entropy can contribute significantly to the free energy of protein–ligand association.

rotamer conv.

intra-well

(sidechain methyl axial)

O/"3$%4(01+41+*(&+4(C/$41+*(

L#M(N1&+=&+(O=%+( \\(Wright and coworkers, Nature (2007); COSB (2009)

pKID/KIX

“Encounter Complex”

Page 23: Nuclear Magne,c Resonance NMR Fundamentals

PX(J31+@$&A%$1+*(&+4(?'&+.1%+6(K+6%'&#,/+.(•  2&'&7&*+%,#(#%+6%'.(%+=&+#%(!)-('%$&B&,/+;(6<31#&$$<("+4%.1'%4X(

•  2&'&7&*+%,#('%$&B&,/+(%+=&+#%7%+6(L2-QM(#/"3$%4(:16=(.16%@41'%#6%4(.31+@$&A%$1+*(LJEJ]M;(=/:%9%';(3'/914%.(41.6&+#%(1+I/'7&,/+("3(6/(PZ({X(–  5$$/:.(/+%(6/(4%6%#6($/+*@'&+*%(/'4%'1+*(&+4(6'&+.1%+6(.6'"#6"'%.f((((

L#M(N1&+=&+(O=%+( \[(Fanucci & Cafiso, COSB (2006); Wu et al, JMB (2009)

Structures of typical nitroxide-based spin probes

Structural Reorganization of *-Synuclein

~1."&$1n1+*(6'&+.1%+6(%9%+6.(1+((&71+/@6%'71+&$(&"6/3'/#%..1+*(/I(GK~@D(3'/6%&.%(

L#M(N1&+=&+(O=%+( [T(Tang et al, Nature (2007)

PREs were measured on a 1:1 mixture of 0.2+mM U-[2H/13C/15N]-labelled SFNFPR(D25N) and spin-labelled SFNFPR(D25N) at natural isotopic abundance.

ZX(K+@O%$$(!)-(

L#M(N1&+=&+(O=%+( [D(Protein structure determination in living cells by in-cell NMR spectroscopy, Sakakibara et al, Nature (2009).

a, Scheme of the in-cell NMR experiments using E. coli cells. b, The 1H–15N HSQC spectrum of a TTHA1718 in-cell NMR sample immediately after sample preparation. c, The 1H–15N HSQC spectrum after 6 h in an NMR tube at 37 °C. d, The 1H–15N HSQC spectrum of the supernatant of the in-cell sample used in b and c.

L#M(N1&+=&+(O=%+( [F(

a, A superposition of the 20 final structures of TTHA1718 in living E. coli cells, showing the backbone (N, Calpha, C') atoms. b, A superposition of the 20 final structures of purified TTHA1718 in vitro. c, A comparison of TTHA1718 structures in living E. coli cells and in vitro. The best fit superposition of backbone (N, Calpha, C') atoms of the two conformational ensembles are shown with the same colour code in a and b. d, Secondary structure of TTHA1718 in living E. coli cells. The side chains of Ala, Leu and Val residues, the methyl groups of which were labelled with 1H/13C, are shown in red. e, Distance restraints derived from methyl-group-correlated and other NOEs are represented in the ribbon model with red and blue lines, respectively.

Protein structure determination in living cells by in-cell NMR spectroscopy, Sakakibara et al, Nature (2009).

A putative heavy-metal binding protein TTHA1718 from Thermus thermophilus HB8 overexpressed in Escherichia coli cells.

Page 24: Nuclear Magne,c Resonance NMR Fundamentals

WX()-K(•  x7&*+%,#('%./+&+#%(6/7/*'&3=<y(

•  C1'.6()-(17&*%(1+(D[YP(

•  FTTP(!/A%$(2'1n%(

•  E%6%#6(?D(/'(?F('%$&B&,/+(/I(:&6%'(3'/6/+.(1+(A/4<(

•  O/+6'&.6(&*%+6(6/(%+=&+#%(6=%(#/+6'&.6(L1+#'%&.%(6=%(.3'%&4(/I(?Da?F(1+(,.."%.M(

•  0T(d(DXZ(?(LWT()GnM(

•  QB6%+.19%(".%(/I(7&*+%,#(c%$4(*'&41%+6(I/'(3$&+%(.%$%#,/+(

L#M(N1&+=&+(O=%+( [P(

Additional reading: http://www.cis.rit.edu/htbooks/mri/