Quantum tunneling time delay investigation of \({{\varvec{K}}}^{+}\) ion in human telomeric G-quadruplex systems

Guanine-rich quadruplex DNA (G-quadruplex) is of interest both in cell biology and nanotechnology. Its biological functions necessitate a G-quadruplex to be stabilized against escape of the monovalent metal cations. The potassium ion (\({{\varvec{K}}}^{+}\)) is particularly important as it experiences a potential energy barrier while it enters and exits the G-quadruplex systems which are normally found in human telomere. In the present work, we analyzed the time it takes for the \({{\varvec{K}}}^{+}\) cations to get in and out of the G-quadruplex. Our time estimate is based on entropic tunneling time—a time formula which gave biologically relevant results for DNA point mutation by proton tunneling. The potential energy barrier experienced by \({{\varvec{K}}}^{+}\) ions is determined from a quantum mechanical simulation study, Schrodinger equation is solved using MATLAB, and the computed eigenfunctions and eigenenergies are used in the entropic tunneling time formula to compute the time delay and charge accumulation rate during the tunneling of \({{\varvec{K}}}^{+}\) in G-quadruplex. The computations have shown that ion tunneling takes picosecond times. In addition, average \({{\varvec{K}}}^{+}\) accumulation rate is found to be in the picoampere range. Our results show that time delay during the \({{\varvec{K}}}^{+}\) ion tunneling is in the ballpark of the conformational transition times in biological systems, and it could be an important parameter for understanding its biological role in human DNA as well as for the possible applications in biotechnology. To our knowledge, for the first time in the literature, time delay during the ion tunneling from and into G-quadruplexes is computed.

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