A Visual Metric for Biological Membrane Instability: Geometric Coupling of Lateral Expansion and Acyl Chain Splay as a Geometric Precursor Signature of Packing Defects in Glutamate Transporter Splice Variant Self-assemblies

The structural integrity of the phospholipid bilayer is governed by the hydrophobic effect, which drives cohesive packing, and the entropic conformational freedom of acyl chains. While conventional metrics such as the deuterium order parameter and average Area per Lipid successfully describe the bulk phase behavior of membranes, they fail to capture the transient, rare-event geometries that govern membrane function. It is increasingly recognized that hydrophobic packing defects—localized regions where the hydrocarbon core is momentarily exposed to solvent—act as the primary nucleation sites for antimicrobial peptide insertion, viral fusion, and drug permeation. However, a unified visualization characterizing the geometric origins of these defects remains elusive. Here, we introduce the Packing Defect Geometry Plot (PDGP), a multi-dimensional analysis that correlates local Voronoi tessellation area with inter-chain splay angles, available as a Python tool via pip install lipid-plots. We first establish the physical meaning of the plot on the bulk lipid population of each bilayer, defined as lipids lying more than 16 Å from any protein atom and pooled over the four systems, which supplies the reference distributions and the defect-state thresholds (the 95th percentiles, 89.8 Ų and 75.2°); no protein-free bilayer was simulated, and the manuscript states explicitly where that limits interpretation. We test the central assumption of the method directly by correlating the PDGP coordinates of each lipid with its own solvent-accessible hydrophobic surface area: lipids in the high-area/high-splay quadrant carry 5.2–13.2 times the hydrophobic surface area of the remaining lipids, although the rank correlations with the individual coordinates are weak (Spearman ρ = 0.16–0.21 with local area, 0.03–0.10 with splay angle across four systems), indicating threshold rather than monotonic behaviour. Applying the metric to 50 ns all-atom trajectories of four glutamate transporter assemblies in POPC bilayers, analysed over the final 30 ns of each run after a 20 ns equilibration during which the box cross-section was still contracting (266,875 lipid-frames), we find that the bilayer surrounding the truncated H0Y7R2 homodimer is the most conformationally disordered of the four: mean splay angle is highest (31.9° against 21.4–29.3°), sn-2 chain order lowest (plateau |S_CD| 0.266 against 0.279–0.318) and the negative-S_CC population largest (3.93% against 1.48–2.13%). This is the opposite of the expectation that larger transmembrane assemblies impose greater packing strain. Defect-state occupancy follows the same rank order as mean splay except for EAA1 versus EAA2/A0A2R8Y642, whose occupancies are tied within their confidence intervals, but its block-averaged confidence intervals overlap between systems, and we report it as a trend rather than a resolved difference. In three of the four assemblies extreme splay events are less frequent in the first annular shell than in bulk, and in EAA1/E7EUV6 they are marginally more frequent, so the data provide at most weak evidence that these assemblies promote extreme packing geometries in the lipids they contact. Because PDGP is a per-lipid rather than a grid-projected descriptor, it complements established defect-detection tools by identifying which lipids, in which conformations, generate an exposure event, and it does so in a form that can be compared directly with experimentally accessible observables such as area per lipid and NMR order parameters.