Continuous probability distribution (CUPID) analysis of potentials for internal rotations

Area of Science:

• Biophysical Chemistry
• Structural Biology
• Computational Chemistry

Background:

• Nuclear Magnetic Resonance (NMR) spectroscopy is crucial for determining molecular structures.
• Analyzing rotamer populations from NMR data using the continuous probability distribution (CUPID) approach has limitations.

Purpose of the Study:

• To expand the CUPID method for calculating rotational potentials from NMR data.
• To address the nonnegativity problem in Fourier series expansions of probability distributions.
• To enable thermodynamic characterization of internal rotations and assess uncertainties.

Main Methods:

• Extended the CUPID approach to compute rotational potentials from Fourier coefficients of angular probability distributions.
• Developed strategies for incomplete data, including grid search, coefficient transfer, and magnitude restriction.
• Derived equations for error propagation from NMR input data to rotamer distributions.
• Utilized simulations to study error dependence and re-examined Gaussian function reconstruction.

Main Results:

• Successfully computed rotational potentials and enabled thermodynamic characterization of internal rotations in amino acids, peptides, and oligosaccharides.
• Established typical confidence intervals of +/- 30-40 degrees for dihedral angles and +/- 0.2 for rotamer populations.
• Identified C'-H beta couplings as most sensitive to uncertainties in chi 1 rotamer analysis.
• Validated the assumption of identical Gaussian peak widths.

Conclusions:

• The extended CUPID method offers a robust framework for analyzing internal rotations using NMR data.
• The approach provides reliable error estimations for dihedral angles and rotamer populations.
• The study highlights the potential of NMR cross-relaxation rates for investigating internal rotations in amino acids.