NOESY = Nuclear Overhauser Effect SpectroscopY

Transcription

1 NOESY = Nuclear Overhauser Effect SpectroscopY The pulse sequence: 90 x - t 1-90 x - t mix x - t 2 Memo 1: in a NOE type experiment both magnetization (I z and S z ) and the zero quantum coherence terms are important. Consider: I, S and J IS

2 [eq.] Ĥ = /2 (Î x + Š x ) [0] 90 x I z and S z -I y and -S y Ĥ = Î z ( I t 1 ) + Š z ( S t 1 ) t 1 I y cos( I t 1 ) +I x sin( I t 1 ) S y cos( S t 1 ) +S x sin( S t 1 ) Ĥ = 2Î z Š z (J IS t 1 ) I y cos( I t 1 )cos( J IS t 1 ) +2I x S z cos( I t 1 )sin( J IS t 1 ) +I x sin( I t 1 )cos( J IS t 1 ) +2I y S z sin( I t 1 )sin( J IS t 1 ) S y cos( S t 1 )cos( J IS t 1 ) +2S x I z cos( S t 1 )sin( J IS t 1 ) +S x sin( S t 1 )cos( J IS t 1 ) [t 1 ] +2S y I z sin( S t 1 )sin( J IS t 1 )

3 Ĥ = /2 (Î x + Š x ) 90 x memo.= cos( /2) = 0, sin( /2) = 1 I z cos( I t 1 )cos( J IS t 1 ) 2I x S y cos( I t 1 )sin( J IS t 1 ) +I x sin( I t 1 )cos( J IS t 1 ) 2I z S y sin( I t 1 )sin( J IS t 1 ) S z cos( S t 1 )cos( J IS t 1 ) 2S x I y cos( S t 1 )sin( J IS t 1 ) +S x sin( S t 1 )cos( J IS t 1 ) [t 1,0] 2S z I y sin( S t 1 )sin( J IS t 1 ) Memo 2. I z and S z are z magnetizations, I x, S x as well as I z S y and S z I y are single-quantum coherences, I x S y and S x I y are double-quantum coherences. Memo 3: Both Z magnetizations (I z and S z ) as well as the Zero Quantum parts (ZQ) of the Double Quantum terms (DQ) are relevant for NOE. - Note that ZQ terms can't be removed from the spectrum with phase-cycling and thus bellow we will work out only the ZQ part of the DQ term.

4 memo : I + = I x + ii y I = I x ii y S + = S x + is y S = S x is y consequently 1/2 [I + + I ]= I x and 1/(2i)[I + I ] = I y 1/2[S + + S ]= S x and 1/(2i)[S + S ] = S y therefore 2I x S y = 2{1/2 [I + + I ]1/(2i)[S + S ]}= 1/(2i) {I + S + I + S + I S + I S } only I + S + and I S are double quant. coh. (or coherence order 2), I + S and I S + are zero quant. coh. (or coherence order 0) through phase cycling the double quantum coherences are removed, while 1/(2i) { I + S + I S + } terms remain. finally: 1/(2i) [ 1{(I x + ii y )(S x is y )} + {(I x ii y )(S x + is y )}] = 1/(2i) [ I x S x ii y S x + ii x S y I y S y + I x S x ii y S x + ii x S y + I y S y ] 1/(2i) [ i2i y S x + i2i x S y ] [+I y S x I x S y ] In summary : 2I x S y cos( I t 1 )sin( J IS t 1 ) [+I y S x I x S y ] cos( I t 1 )sin( J IS t 1 ) for the same reason from the 2I y S x term, the +[I x S y I y S x ] cos( S t 1 )sin( J IS t 1 ) terms have zero quantum coherence. [+I y S x I x S y ]cos( I t 1 )sin( J IS t 1 ) [+I x S y I y S x ]cos( S t 1 )sin( J IS t 1 )

5 term A: [+I y S x I x S y ]cos( I t 1 )sin( J IS t 1 ) term B: [+I x S y I y S x ]cos( S t 1 )sin( J IS t 1 ) The result of the addition of term A plus B results in the following 4 terms: A +B term = +I y S x cos( I t 1 )sin( J IS t 1 ) I x S y cos( I t 1 )sin( J IS t 1 ) +I x S y cos( S t 1 )sin( J IS t 1 ) I y S x cos( S t 1 )sin( J IS t 1 ) Written in a condensed form: [ I y S x I x S y ] [cos( I t 1 ) cos( S t 1 )]sin( J IS t 1 ) Before the mixing starts we have the following terms with quant. number 0. I z cos( I t 1 )cos( J IS t 1 ) S z cos( S t 1 )cos( J IS t 1 ) [t 1,0] [ I y S x I x S y ] [cos( I t 1 ) cos( S t 1 )]sin( J IS t 1 ) with mix. coeff. :a I I,a I S,a S I,a SS during the mixing time ( m ) the populations ( I z a II, I z a IS, S z a SI and S z a SS ) interact, while the zero-quantum term ([I y S x I x S y ]) coherence continues to precess. after the mixing the populations are: I z a II cos( I t 1 )cos( J IS t 1 ) I z a IS cos( S t 1 )cos( J IS t 1 ) S z a SS cos( S t 1 )cos( J IS t 1 ) S z a SI cos( I t 1 )cos( J IS t 1 ) and the zero-quantum coh. term is [ I y S x I x S y ] [cos( I t 1 ) cos( S t 1 )]sin( J IS t 1 )

6 Ĥ = /2 (Î x + Š x ) 90 x memo. = cos( /2) = 0, sin( /2) = 1 I y a II cos( I t 1 )cos( J IS t 1 ) I y a IS cos( S t 1 )cos( J IS t 1 ) S y a SS cos( S t 1 )cos( J IS t 1 ) S y a SI cos( I t 1 )cos( J IS t 1 ) [I z S x I x S z ] [(cos( I t 1 ) cos( S t 1 )]sin( J IS t 1 ) The unwanted zero-quantum diagonal and cross-peaks (I z S x I x S z ) (both anti-phased and dispersive) can removed at this point. a. in small molecule several spec. are recorded with diff. mixing time and coadded. b. in large molecule they can be ignored because > zero-quant. relaxation is fast > large linewidth with antiphased disp. line shape cancel each other. I y a I I cos( I t 1 )cos( J IS t 1 ) I y a IS cos( S t 1 )cos( J IS t 1 ) S y a SS cos( S t 1 )cos( J IS t 1 ) S y a SI cos( I t 1 )cos( J IS t 1 )

7 the diagonal I y term during ACQ +I y a II cos( I t 1 )cos( J IS t 1 )cos( I t 2 )cos( J IS t 2 ) 2I x S z a II cos( I t 1 )cos( J IS t 1 )cos( I t 2 )sin( J IS t 2 ) I x a II cos( I t 1 )cos( J IS t 1 )sin( I t 2 )cos( J IS t 2 ) 2I y S z a II cos( I t 1 )cos( J IS t 1 )sin( I t 2 )sin( J IS t 2 ) the diagonal S y term during ACQ +S y a SS cos( S t 1 )cos( J IS t 1 )cos( S t 2 )cos( J IS t 2 ) 2S x I z a SS cos( S t 1 )cos( J IS t 1 )cos( S t 2 )sin( J IS t 2 ) S x a SS cos( S t 1 )cos( J IS t 1 )sin( S t 2 )cos( J IS t 2 ) 2S y I z a SS cos( S t 1 )cos( J IS t 1 )sin( S t 2 )sin( J IS t 2 ) off-diagonal I y term during ACQ +I y a IS cos( S t 1 )cos( J IS t 1 )cos( I t 2 )cos( J IS t 2 ) 2I x S z a IS cos( S t 1 )cos( J IS t 1 )cos( I t 2 )sin( J IS t 2 ) I x a IS cos( S t 1 )cos( J IS t 1 )sin( I t 2 )cos( J IS t 2 ) 2I y S z a IS cos( S t 1 )cos( J IS t 1 )sin( I t 2 )sin( J IS t 2 ) off-diagonal S y term during ACQ +S y a SI cos( S t 1 )cos( J IS t 1 )cos( I t 2 )cos( J IS t 2 ) 2S x I z a SI cos( S t 1 )cos( J IS t 1 )cos( I t 2 )sin( J IS t 2 ) S x a SI cos( S t 1 )cos( J IS t 1 )sin( I t 2 )cos( J IS t 2 ) 2S y I z a SI cos( S t 1 )cos( J IS t 1 )sin( I t 2 )sin( J IS t 2 )

8 memo 1: put the receiver on x therefore only the four x term remain I x a II cos( I t 1 )cos( J IS t 1 )sin( I t 2 )cos( J IS t 2 ) S x a SS cos( S t 1 )cos( J IS t 1 )sin( S t 2 )cos( J IS t 2 ) I x a IS cos( S t 1 )cos( J IS t 1 )sin( I t 2 )cos( J IS t 2 ) S x a SI cos( S t 1 )cos( J IS t 1 )sin( I t 2 )cos( J IS t 2 ) memo 2: sin(a)cos(b ) = 1/2[sin(A+B)+sin(A-B)] cos(a)cos(b ) = 1/2[cos(A+B)+cos(A-B)] therefore 1/4I x a II [+cos{( I + J IS )t 1 } +cos{( I J IS )t 1 }][+sin{( I + J IS )t 2 }+ sin{( I J IS )t 2 }] 1/4S x a II [+cos{( S + J IS )t 1 }+cos{( S J IS )t 1 }][+sin{( S + J IS )t 2 }+ sin{( S J IS )t 2 }] 1/4I x a IS [+cos{( S + J IS )t 1 }+cos{( S J IS )t 1 }][+sin{( I + J IS )t 2 }+ sin{( I J IS )t 2 }] 1/4S x a SI [+cos{( I + J IS )t 1 } +cos{( I J IS )t 1 } ][+sin{( S + J IS )t 2 }+ sin{( S J IS )t 2 }] the following terms can be found - I x a II [ ] at I, I - I x a IS [ ] at S, I - S x a SS [ ] at S, S - S x a SI [ ] at I, S

9 if one sets the phase that cos is absorptive (a) in t 1 sin is absorptive (a) in t 2 I x a II [+a.. +a.. +a.. +a..] at I, I I x a IS [+a.. +a.. +a..+a..] at S, I S x a SS [+a.. +a.. +a.. +a..] at S, S S x a SI [+a.. +a.. +a.. +a..] at I, S If J IS = 0 (through bond coupling ignored) then The sign of the peaks is determined by the mix. coeff. :a II, a IS, a SI, a SS

10 Summary: 1 H- 1 H NOESY the raise of an off-diagonal peak S z a SI cos( I t 1 )cos( J IS t 1 ) I I z +2I x S z cos( I t 1 )sin( J IS t 1 ) S -I y I z cos( I t 1 )cos( J IS t 1 ) +S y a SI cos( I t 1 )sin( J IS t 1 ) I S x a SI cos( I t 1 )sin( J IS t 1 ) sin( S t 2 )sin( J IS t 2 ) t 1 S 1/4S x a SI [+cos{( I + J IS )t 1 }+ cos{( I J IS )t 1 }] [+sin{( S + J IS )t 2 }+ sin{( S J IS )t 2 }] S t 2 I

11 NOESY-with bipolar gradient, water flip-back pulse and : Net magnetization form H 2 O (on-resonance) 1 H G z Phase:f 90 d0 d0 t 1 d29 d x a b b y t 2 Net magnetization form protein (off-resonance) H -H z cos( 1 t 1 ) z +H y cos( 1 t 1 ) -H y cos( 1 t 1 ) +H y -H z cos( 1 t 1 ) bipolar gradient taking care of water during evolution: a pair of gradients (typically of low power e.g. 0.5%) of increasing length covering the overall time of evolution (t1). Radiation dumping is minimized since the otherwise bulk water, as well as any other signals, are dephased and rephased in a symmetric manner during evolution. (No uniform (big) water, no radiation dumping occurs.) Gradient a : dephases all coherences of the x,y plane (general clean up before bringing magnetization back into the x,y palne) Gradient b is that of the standard watergate. The water flip back pulse The on-resonance magnetization of H 2 O, is first selectively rotated into the transverse plane (along y) by the shaped low power 90-x, and subsequently returned along z by the non-selective hard 90x. All magnetization related to off-resonance signals are simply rotated to y axis. The watergate or binominal water suppression is to remove water before acquisition

12 A szekvenciális hozzárendelés és a szerkezetszámolás alapja a nukláris Overhauser- effektus (NOE) 6Å (NOE) Távolság jellegű adatok

13 szerkezetszámolás Fehérje modul 1 H- 1 H NOESY spektruma