An SRLS Study of ²H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLC_γ1C SH2

The two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for NMR relaxation in proteins is extended to derive conformational entropy, Ŝ. This version of SRLS is applied to deuterium relaxation from the C-CDH₂ bonds of free and peptide-bound PLC_γ1C SH2. Local C-CDH₂ motion is described by a correlation time for local diffusion, τ₂, and a Maier-Saupe potential, u. On average, τ₂, which largely fulfills τ₂ ≪ τ₁ (τ₁ - correlation time for global tumbling), is 270 ± 41 ps and u is 2 ± 0.1 k_BT. The PLC_γ1C SH2 data were analyzed previously with the model-free (MF) method. SRLS is a generalization of MF, assumed so far to yield the latter for τ₂ ≪ τ₁ and simple local geometry. Despite these conditions being fulfilled, we find here that τ₂ and u differ substantially from their MF counterparts. This is shown to stem from MF (a) disregarding mode-coupling of the first type (see below) and (b) parametrizing the methyl-moiety-related spectral density function (SDF). Our main interest lies in ΔŜ, the conformational entropy difference between the peptide-bound and free PLC_γ1C SH2 forms. We find that ΔŜ is rendered inaccurate in MF because factors a and b above impair the accuracy of S_axis, the parameter on which the calculation of ΔŜ is based. Conformational entropy was obtained previously using various simple system-specific models. SRLS is unique in obtaining this important thermodynamic quantity based on a general physically well-defined local potential. It is also unique in its ability to extract the information inherent in ²H relaxation parameters from methyl moieties in protein with accuracy commensurate with data sensitivity.