Chemical exchange and the McConnell Equations - …groups.chem.ubc.ca/straus/Chapter3.pdf ·...
Transcript of Chemical exchange and the McConnell Equations - …groups.chem.ubc.ca/straus/Chapter3.pdf ·...
Chemical exchangeand the
McConnell Equations
- Chapter 5, on web site: http://www.chem.ubc.ca/faculty/straus/c518_09.html
A) Derivation of the McConnell equations from the Bloch equations
B) Lineshape Analysis
1) Slow exchange2) Fast exchange
C) Exchange from 2D NMR
Intramolecular exchange– Motions of sidechains in proteins– Helix-coil transitions of nucleic acids– Unfolding of proteins– Conformational equilibria
Intermolecular exchange– Binding of small molecules to macromolecules– Protonation/deprotonation equilibria– Isotope exchange processes– Enzyme catalyzed reactions
Source: http://mccammon.ucsd.edu/gallery/
A) Derivation of the McConnell equations from the Bloch eq.
Here A1 and A2 are independent... so now let’s turn on exchange:
first order kinetics
B) Lineshape Analysis
Recall:
In lab frame:
If ignore relaxation...
The solution of which is
where
and
Two cases: 1) Slow exchange2) Fast exchange
1) Slow exchange
2) Fast exchange
In general
RT
Note error in othernotes (T missing)
C) Using 2D NMR to investigate exchange
Perturb A1 selectively (using a 180 degree pulse), so that
FT-1
∆ω
∆t
ω t
And now let us use a real 2D experiment to accomplish the same thing:
So at D, we have labelled the A1 and A2 states differently, according to theirprecession frequencies:
During τm, exchange can occur:
i.e. during τm, the equations from before apply
NO RELAXATION!!!!!
Why only T1? What about T2?