Physics of Biology

Quantum Area Scaling of Natural Toxins: A Harmonic Grid Based on the Bohr Radius and Euler’s Constant

Authors: Alberto Coe

The Topological Polar Surface Area (TPSA) is a critical descriptor in pharmacology, yet itsdistribution across natural toxins has long been considered stochastic. This study proposes anovel geometric framework where TPSA is quantized as a function of the Bohr area unit (au2080² ≈ 0.28003 Ų). By applying a harmonic resonance model based on a modified Euler’s constant �� = �� − 2/3, we analyzed 28 diverse natural toxins, ranging from Hydrocyanic Acid to Maitotoxin. The results reveal a discrete double octave grid (Nodes 23 to 39) that accounts fortoxin dimensions with a mean residual of 0.18 (in node space) and a high level of significance. A Monte Carlo simulation confirms the model's validity with a significance level of P = 0.0056. These findings suggest that the chemical space of natural toxicity is governed by a fundamental area-scaling law rooted in quantum constants, offering new predictive capabilities for molecular toxicology.

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[v1] 2026-05-07 19:26:11

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