Bayesian Probabilistic Inference of Nonparametric Distance Distributions in DEER Spectroscopy

Area of Science:

• Biophysics
• Structural Biology
• Computational Chemistry

Background:

• Double electron-electron resonance (DEER) spectroscopy is crucial for measuring distances between spin labels in proteins, providing insights into protein dynamics and conformational changes.
• Analyzing DEER data to obtain distance distributions is challenging due to the ill-posed nature of the mathematical inversion required.
• Existing methods like bootstrapping can be computationally intensive and may underestimate uncertainty.

Purpose of the Study:

• To introduce a novel Bayesian probabilistic inference approach for analyzing DEER spectroscopic data.
• To develop a method that accurately determines distance distributions and quantifies associated uncertainties.
• To provide a faster and more robust alternative to existing DEER data analysis techniques.

Main Methods:

• A Bayesian probabilistic inference framework was employed, assuming a nonparametric distance distribution with a Tikhonov smoothness prior.
• Markov Chain Monte Carlo (MCMC) sampling, specifically a compositional Gibbs sampler, was utilized to explore the posterior probability distribution.
• The method determines the full posterior distribution over model parameters, including the distance distribution, given experimental DEER data.

Main Results:

• The Bayesian approach successfully analyzes DEER data, yielding posterior probability distributions for distance distributions.
• Uncertainty in the distance distribution is visually represented through an ensemble of posterior predictive distributions.
• The method demonstrated faster performance and provided slightly larger, more comprehensive uncertainty intervals compared to bootstrapping.

Conclusions:

• The developed Bayesian inference method provides a powerful and efficient tool for analyzing DEER data.
• This approach offers a robust quantification of uncertainty in protein distance distributions derived from DEER experiments.
• The method enhances the structural and energetic insights obtainable from DEER spectroscopy, advancing the study of protein conformational landscapes.