BMB 601 Chemical Exchange and NMR Hari Hariharan Ph.D. Senior Research Investigator Center of Magnetic Resonance & Optical Imaging Department of Radiology School of Medicine University of Pennsylvania

Outline Recap from relaxation Definition of Chemical Exchange and Bloch Equations Single Pulse spectra NMR Time Scale and Chemical Exchange Selective Preparation experiments Applications

Recap from relaxation Energy Equations  E = (h/2  )*  *B 0 (N  0 /N  0 ) = exp(-  E/kT) n = (N  0 - N  0 ) n = (1-exp(-  E/kT)) / (1 + exp(-  E/kT)) n ~ (  E/kT) / 2 M 0  n Relaxation Effects Spectral density for T1 & T2 Spin Diffusion for T2 Modified Bloch Equations (dMz/dt) =  (MxBy-MyBx) – R1(Mz-M0) (dMy/dt) =  (MzBx-MxBz) – R2My (dMx/dt) =  (MyBz-MzBy) – R2Mx Methods of T1 and T2 Measurements

Chemical Exchange Definition Chemical exchange refers to any process in which a nucleus exchanges between two or more environments in which its NMR parameters (e.g. chemical shift, scalar coupling, or relaxation) differ.

Types of Chemical Exchange

Chemical Exchange – McConnell Equations To describe chemical exchange, we can continue with semi-classical description and use a set of modified Bloch equations (also known as McConnell equations, after H.M. McConnell who derived them in 1958). Note: R1,R2 here are not 1/T1 and 1/T2, rather the relaxation matrix for species 1&2 with R11,R21,R12 and R22 terms.

Single Pulse Spectra 1 What happens if you apply a 90 deg pulse and try to get a spectrum with chemical exchange? Immediately after the 90 deg pulse: with further evolutions given by

Single Pulse Spectra-2 Since we are interested only is the evolution of detected signals M 1 and M 2 : Ignoring relaxation:

Single Pulse Spectra-3 These coupled differential equations have solutions of the type:

Single Pulse Spetra-4 Slow Exchange: k << |  1-  2| Note: Original assumption about no relaxation. All line width is from exchange

Single Pulse Spetra-5 Fast Exchange: k >>|  1-  2| Note: Original assumption about no relaxation. All line width is from exchange

Symmetric Exchange spectra for different exchange rates

Symmetric Exchange Simulation Spectral Simulation Source:

Asymmetric Exchange Rate Spectra

Chemical Exchange and NMR Time Scale

Selective Preparation experiments How to handle direct excitation effects? ABB’ Two experiments are run with preparation pulse placed symmetrically about observe signal position(B and B’). Now the difference in signal from the two experiments reveals the effect of Chemical Exchange without direct signal excitation effects… Z-spectrum. New endogenous contrast mechanisms.

Applications of Chemical Exchange

Strategies for probing Exchange

pH Measurements

Saturation Transfer- Chemical Kinetics Under Slow Exchange

Summary Chemical Exchange effects can be understood through modified Bloch Equations. Slow and Fast Exchange regimes are easily understood. Intermediate Exchange regimes need numerical analysis. Exchange can modify both the position as well as the line shape of the observed spectrum. Selective preparation experiments are a powerful tool to probe Chemical Exchange effects. Chemical exchange effects can be utilized to produce endogenous contrast effects. NMR is suitable to probe chemical kinetics under the slow exchange regime. More applications yet to be discovered.