A geometric framework for quantum tunneling in biomolecular systems

Abstract This study introduces a geometric framework to explain how quantum particles, specifically protons, move through energy barriers in biological molecules like DNA. Rather than viewing this tunneling as a purely random event, we propose that it is governed by the structural complexity of the surrounding molecular environment. By treating the energy landscape as a geometric shape, we demonstrate that the environment acts as a regulator that either facilitates or hinders the movement of protons between genetic base pairs. We applied this model to compare the two primary building blocks of the DNA ladder: the Guanine-Cytosine (G-C) and Adenine-Thymine (A-T) pairs. Our findings reveal that the G-C pair possesses a structural configuration that makes proton movement significantly more likely compared to the A-T pair. This difference provides a clear physical explanation for why certain parts of our genetic code are more prone to spontaneous changes, or tautomeric shifts, which can lead to mutations. Furthermore, the research explores how the DNA molecule interacts with its surrounding cellular noise (e.g. water molecules and proteins). We find that the proton behaves in a hybrid manner (at times acting like a coherent wave that exists in multiple places at once), and at other times like a solid particle trapped by its environment. This dual behavior suggests that life operates at a delicate balance between quantum mechanical effects and classical stability.