BMB 601Chemical Exchange and NMR

Hari Hariharan Ph.D.Senior Research Investigator

Center of Magnetic Resonance & Optical ImagingDepartment of Radiology

School of MedicineUniversity 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)**B0

• (N0/N

0) = exp(-E/kT)• n = (N

0 - N0)

• n = (1-exp(-E/kT)) / (1 + exp(-E/kT))

• n ~ (E/kT) / 2• M0 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 M1 and M2:

Ignoring relaxation:

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

Single Pulse Spetra-4Slow Exchange: k << |1-2|

Note: Original assumption about no relaxation. All line width is from exchange

Single Pulse Spetra-5Fast 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: http://www.shokhirev.com/nikolai/abc/nmrtut/NMRtut4.html

Asymmetric Exchange Rate Spectra

Chemical Exchange and NMR Time Scale

Selective Preparation experiments

How to handle direct excitation effects?

AB B’

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.