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?