Analysis of chi angle distributions in free amino acids via multiplet fitting of proton scalar couplings

Scalar couplings are a fundamental aspect of nuclear magnetic resonance (NMR) experiments and provide rich information about electron-mediated interactions between nuclei. ³ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi></mml:mrow> </mml:math> couplings are particularly useful for determining molecular structure through the Karplus relationship, a mathematical formula used for calculating ³ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi></mml:mrow> </mml:math> coupling constants from dihedral angles. In small molecules, scalar couplings are often determined through analysis of one-dimensional proton spectra. Larger proteins have typically required specialized multidimensional pulse programs designed to overcome spectral crowding and multiplet complexity. Here, we present a generalized framework for fitting scalar couplings with arbitrarily complex multiplet patterns using a weak-coupling model. The method is implemented in FitNMR and applicable to one-dimensional, two-dimensional, and three-dimensional NMR spectra. To gain insight into the proton-proton coupling patterns present in protein side chains, we analyze a set of free amino acid one-dimensional spectra. We show that the weak-coupling assumption is largely sufficient for fitting the majority of resonances, although there are notable exceptions. To enable structural interpretation of all couplings, we extend generalized and self-consistent Karplus equation parameterizations to all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>χ</mml:mi></mml:math> angles. An enhanced model of side-chain motion incorporating rotamer statistics from the Protein Data Bank (PDB) is developed. Even without stereospecific assignments of the beta hydrogens, we find that two couplings are sufficient to exclude a single-rotamer model for all amino acids except proline. While most free amino acids show rotameric populations consistent with crystal structure statistics, beta-branched valine and isoleucine deviate substantially.