Product operator analysis of the influence of chemical exchange on relaxation rates

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Measurements of chemical-exchange processes by NMR are widely used to obtain valuable information about molecular dynamics and structure. Here, a computational method is introduced to assess the influence of chemical exchange on spin relaxation rates. The method is based on the inclusion of a random exchange process in product operator calculations on a microscopic level. This product operator approach can be applied to estimate exchange contributions when using sophisticated pulse sequences that cannot be easily described analytically. The method applies to the full range of exchange times measurable by NMR and can incorporate interference effects between exchange and other processes such as scalar coupling. To demonstrate its utility, simulated relaxation data were compared with theoretical predictions of spin-locking and Carr-Purcell spin-echo sequences with hard and adiabatic pulses, using different time scales for a two-site chemical-exchange process. Finally, simulations were used to examine a system in which a second random process is superimposed on a simple two-site exchange process. The method was found to provide a simple and robust tool to analyze pulse sequences and equations commonly used to study exchange-induced relaxation.

Original languageEnglish (US)
Pages (from-to)330-337
Number of pages8
JournalJournal of Magnetic Resonance
Issue number2
StatePublished - Dec 2004

Bibliographical note

Funding Information:
The authors are grateful to the Dr. Elena Ermakova (Kazan Institute of Biochemistry and Biophysics), for the useful discussion. This research was supported by NIH Grants P41 RR08079 and RO1 CA92004.


  • Adiabatic pulses
  • Bloch-McConnell equations
  • CPMG
  • Chemical-exchange
  • Density matrix
  • NMR relaxation
  • Product operator
  • Random process
  • Simulation
  • Spin-lock


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