The time correlation function perspective of NMR relaxation in proteins

Area of Science:

• Biophysics
• Structural Biology
• Nuclear Magnetic Resonance (NMR) Spectroscopy

Background:

• The two-body coupled-rotator slowly relaxing local structure (SRLS) approach has been used for over a decade to analyze NMR relaxation in proteins.
• This method models protein global motion and local probe motion (e.g., (15)N-(1)H bond) using NMR relaxation data.

Purpose of the Study:

• To solve the SRLS Smoluchowski equation using established best-fit parameters.
• To derive generic time correlation functions (TCFs) and gain new insights into protein dynamics.
• To establish the relationship between SRLS and traditional model-free (MF) analysis and define the validity ranges of local motion models.

Main Methods:

• Solving the SRLS Smoluchowski equation with pre-determined best-fit parameters.
• Analyzing the resulting time correlation functions (TCFs) to understand the influence of local and global motion parameters.
• Comparing SRLS-derived TCFs with those from the model-free (MF) approach.

Main Results:

• Identified dominant TCF components for rhombic local ordering, influenced by local motion.
• Quantified the significant impact of global and local diffusion axiality on NMR relaxation analysis.
• Determined the conditions under which mode-coupling becomes relevant and specified the equivalence between MF and SRLS TCFs.
• Established the validity ranges for wobble-in-a-cone and rotation-on-a-cone models for local motions.

Conclusions:

• The SRLS approach provides a more comprehensive framework for analyzing NMR relaxation data than traditional methods.
• This study validates and extends existing stochastic theories for restricted motion in proteins.
• The findings pave the way for direct comparisons between SRLS and atomistic molecular dynamics simulations.