Correlation between changes in nuclear magnetic resonance order parameters and conformational entropy: Molecular dynamics simulations of native and denatured staphylococcal nuclease

Abstract

Recent work has suggested that changes in NMR order parameters may quantitatively reflect changes in the conformational entropy of a protein ensemble. The extent of the mathematical relationship between local entropy changes as seen by NMR order parameters and the full protein entropy change is a complex issue. As a step towards a fuller understanding of this problem, molecular dynamics calculations of both native and denatured staphylococcal nuclease were performed. The N-H bond vector motion, in both explicit and implicit solvent, was analyzed to estimate local and global entropy changes. The calculated N-H bond vector order parameters from simulation agreed on average with experimental values for both native and denatured structures. However, the inverted-U profile of order parameters versus residue number observed experimentally for denatured nuclease was only partially reproduced by simulation of compact denatured structures. Comparisons made across the full set of simulations revealed a correlation between the N-H order parameter-based conformational entropy change and the total quasiharmonic-based conformational entropy change between the native and denatured structures. The calculations showed that about 25% of the total entropy change was reflected by changes in simulated S2 values. This result suggests that NMR-derived order parameters may be used to provide a reasonable estimate of the total conformational entropy change on protein folding.

What Contributions to Protein Side-chain Dynamics are Probed by NMR Experiments? A Molecular Dynamics Simulation Analysis

“…Wrabl et al suggested from an analysis of MD simulations that the entropy related to amide order parameters is correlated with the total configurational entropy calculated from a quasiharmonic analysis. 67 In fact, the entropy per mode (from the quantum mechanical expression 48 ) estimated from the quasiharmonic analysis is almost identical for the two proteins (1.103 cal mol K1 K K1 mode K1 for TNfn3 and 1.101 cal mol K1 K K1 mode K1 for FNfn10), despite the substantial differences in their sidechain order parameters. Nevertheless, order parameters may still be useful for giving qualitative insights into protein configurational entropy changes upon small perturbations such as ligandbinding, 68 although of course such measurements give no information on changes in total entropy.…”

Allostery and cooperativity revisited

“…Such a model focuses on the vibrational contribution to the entropy as the origin of cooperativity, as discussed for the CAP N dimer. More generally, NMR measurements have found significant global changes in the side-chain motions upon ligand binding (Igumenova et al 2005), although the quantitative relation of such effects to the change in the system entropy is not straightforward (Wrabl et al 2000). Wall and coworkers Wall 2005, 2006) have codified this idea in terms of an ''allosteric potential'' for a given site in a protein as the difference between protein conformational distributions (approximated by a harmonic model) with and without a test (''binding'') perturbation at that site.…”

Nucleotide modifications and tRNA anticodon–mRNA codon interactions on the ribosome

“…The rotational and translational entropy are not considered here since it has been found to account for <1% of the total entropy (Wrabl et al 2000); in addition, the very small structural RNA, Vol. 17, No.…”