17 March 2000 Ž . Chemical Physics Letters 319 2000 197–204 www.elsevier.nlrlocatercplett Incorporation of temporally correlated internal motions into the magnetic resonance relaxation treatment while considering interference of different relaxation mechanisms Muppirala Ravikumar ) College of Pharmacy, The UniÕersity of Michigan, Ann Arbor, MI 48109, USA Received 27 September 1999; in final form 8 February 2000 Dedicated to Prof. Aksel A. Bothner-By in honor of his contributions to NMR spectroscopy and its applications. Abstract Temporally correlated internal motions are incorporated into the magnetic resonance relaxation treatment, taking into account the interference between two different mechanisms of relaxation. The joint probability density function due to two different stochastic processes responsible for spin relaxation is approximated in terms of the individual probability density functions. A parameter indicative of the degree of temporal correlation between the two processes is introduced. Such a parameter of dynamics provides a way of observing and analyzing temporally correlated internal motions in macro- molecules. This is important in biomolecules such as proteins and nucleic acids where the temporally correlated internal motions play a significant role in their function. Expressions for cross-correlation spectral densities are given for some common interference mechanisms. q 2000 Elsevier Science B.V. All rights reserved. 1. Introduction An important step in understanding the function of biomolecules is elucidating the nature of their structure-dynamics. Significant progress has been made towards obtaining structural details of biomolecules using NMR. Considerable interest ex- ists in using NMR as a tool to probe and understand internal motions. There is also a resurrection in using Ž . interference effects or cross-correlations between different relaxation mechanisms as an effective tool to measure geometrical parameters such as bond ) Fax: q 734-936-7490; e-mail: muppiral@umich.edu angles and torsion angles. Work on the interference w x wx effects 1–3 is reviewed by Werbelow 4 and Ku- wx w x mar 5 . Some of the recent reviews 6–15 describe fairly well the progress and current understanding in the above described directions in addition to detail- ing the theoretical and experimental approaches, es- pecially in the context of application to biomolecules. However, not enough attention has been paid to cases when the internal motions are temporally cor- related. Such correlations are significant in the inte- rior of proteins and may have an important role in w x enzymatic function and folding of proteins 16 . They may also have a role in the specificity of interactions through the optimal flexibility of biomolecules. Therefore, an effort is made here to incorporate them 0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 00 00182-2