Measurability of side chain rotational isomer populations: NMR and molecular mechanics of cobalt glycyl-leucine dipeptide model system

The cobalt glycyl-leucine dipeptide is a model system for studying the effects of Karplus equation calibration, molecular mechanics accuracy, backbone conformation, and thermal motions on the measurability of side chain rotational isomer populations. We analyze measurements of 8 vicinal coupling constants about the α to β-carbon and β to γ-carbon bonds of the leucine side chain and of 10 NOESY cross relaxation rates across these bonds. Molecular mechanics and peptide and protein crystallographic databases are an essential part of this analysis because they independently suggest that the trans gauche and gauche− trans rotational isomers of the leucine side chain predominate. They also both suggest that puckering of the cobalt dipeptide ring system reduces the gauche gauche rotational isomer population to less than about 10%. At the present ±1 Hz calibration accuracy of Karplus equations for vicinal coupling constants, the predominant trans gauche and gauche− trans rotational isomer populations can be measured with about 5% accuracy, but the population of the gauche gauche rotational isomer is probably very near or just below the limit of measurability. If experimental measurement error was the only source of error, then the rotational isomer populations could be measured with about 0.5% accuracy. We develop a new type of gel graphic that provides a quick graphical summary of the rotational isomer populations as well as of the measurability of these populations.