Spectral Coherence Index: A Model-Free Metric for Protein Structural Ensemble Quality Assessment

Abstract

Protein structural ensembles from NMR spectroscopy capture biologically important conformational heterogeneity, but it remains difficult to determine whether observed variation reflects coordinated motion or noise-like artifacts. We evaluate the Spectral Coherence Index (SCI), a model-free, rotation-invariant summary derived from the participation-ratio effective rank of the inter-model pairwise distance-variance matrix. Under grouped primary analysis of a Main110 cohort of 110 NMR ensembles (30--403 residues; 10--30 models per entry), SCI separated experimental ensembles from matched synthetic incoherent controls with AUC-ROC $= 0.973$ and Cliff's $δ= -0.945$. Relative to an internal 27-protein pilot, discrimination softened modestly, showing that pilot-era thresholds do not transfer perfectly to a larger, more heterogeneous cohort: the primary operating point $τ= 0.811$ yielded 95.5\% sensitivity and 89.1\% specificity. PDB-level sensitivity remained nearly unchanged (AUC $= 0.972$), and an independent 11-protein holdout reached AUC $= 0.983$. Across 5-fold grouped stratified cross-validation and leave-one-function-class-out testing, SCI remained strong (AUC $= 0.968$ and $0.971$), although $σ_{R_g}$ was the stronger single-feature discriminator and a QC-augmented multifeature model generalized best (AUC $= 0.989$ and $0.990$). Residue-level validation linked SCI-derived contributions to experimental RMSF across 110 proteins and showed broad concordance with GNM-based flexibility patterns. Rescue analyses showed that Main110 softening arose mainly from size and ensemble normalization rather than from loss of spectral signal. Together, these results establish SCI as an interpretable, bounded coherence summary that is most useful when embedded in a multimetric QC workflow for heterogeneous protein ensembles.

Figures (8)

• Figure 1: Conceptual overview of the SCI workflow. Starting from an NMR ensemble of $M$ conformers, pairwise distance variation is summarized in the distance-variance matrix $V$, eigendecomposed to obtain the normalized positive-spectrum weights $\tau_k$, compressed into the bounded score $\mathrm{SCI}=1-r_\mathrm{eff}/d$, and finally interpreted jointly with $\sigma_{R_g}$ in a multimetric QC plane. The SCI anchors shown in Stage 4 correspond to the current Main110 mean SCI for NMR ensembles (0.870) and matched synthetic incoherent controls (0.533), and the QC plane in Stage 5 uses the current Main110 data with the manuscript's screening thresholds.
• Figure 2: Main results. (a) SCI distribution across the Main110 NMR cohort, matched synthetic incoherent controls, and 40 AlphaFold single-structure proxies. Brackets indicate pairwise Cliff's $\delta$ and corrected $p$-values. (b) SCI versus mean pLDDT for the AlphaFold reference structures, showing a weak non-significant association. (c) ROC curve for the grouped primary Main110 task (AUC $= 0.973$); the star marks the Youden-$J$ operating point ($\tau = 0.811$).
• Figure 3: Spectral diagnostics. (a) SCI distribution for Main110 NMR ensembles versus matched synthetic incoherent controls. (b) SCI versus PCA first-component variance ratio. (c) Rank-correlation between SCI and PCA variance ratio. (d) Participation-ratio SCI versus entropy-based SCI, illustrating that the main ranking is driven by the distance-variance representation rather than the specific effective-rank formula.
• Figure 4: Baseline metric comparison. The current manuscript emphasizes grouped CV, leave-one-function-class-out, and independent holdout performance for SCI, $\sigma_{R_g}$, SCI+$\sigma_{R_g}$, and QC-full.
• Figure 5: Robustness analysis. (a) AUC-ROC versus injected noise level. (b) Cliff's $\delta$ versus injected noise. (c) Contact-based SCI versus contact threshold across NMR, matched synthetic incoherent controls, and AlphaFold references.