## 4 Discussion
The new localization can be expected to be localized primarily within the original site. As coherence time gets longer, the wave packet will spread more and can eventually reach into the neighboring site initiating some chance for the next localization to evolve at this new location. This is the point where an actual change in conduction can occur. In the present simulations, we found coherence times for a K\({}^{+}\) ion in site S1 to range between 0.1 and 0.4 ps with shorter times being more frequent. During such a short time, the wave packet would usually spread into site S0 with a weight between \(10^{-5}\) and \(10^{-3}\). Here we investigate the two configurations of K\({}^{+}\) and H\({}_{2}\)O in the filter with the most extended non-conductive time intervals and with both configurations where a K\({}^{+}\) ion in located in S1 and a vacancy in S0. In both cases we found that the K\({}^{+}\) as a quantum mechanical wave packet can transverse from site S1 to site S0 in typically one-fourth to one-third of the time it takes a classical particle for the same transition. These results offer an important implication on a possible functional role of a quantum mechanical behavior for ionic transport in proteins. It predicts that ionic currents can be higher on the order of 1.8 times compared to an all-classical MD simulation. This gain in conductance also emerges if just one of the engaged ions is treated as a quantum particle in motion and potential barriers are unchanged, maintaining selectivity for the conspecific ion. It is certainly an important question to what extent the predicted gain in ion currents is supported by physiological experiments. At the moment, this question cannot be answered with certainty because classical MD simulations, as well as the present quantum mechanical simulation of ion motion, are based on a choice of parameters shaping the potentials between the engaged particles. In both approaches, the involved parameters vary over certain ranges provided by other, e.g., structural considerations. It is a tradition to choose the set of electro-chemical parameters in a way that renders ion currents in agreement with the observed values. However, physiological observations provide conduction rates close to the diffusion limit of up to \(10^{8}\) ions/s. As was mentioned in the introduction, these physiological measures are at variance with the predictions from Nernst-Planck estimates and the potential barriers obtained by classical potential mean force estimates, e.g., [11]. The present simulation offers a way to explain these fast conductions without violating the barrier heights of more than 5 kT at 300 K necessary to maintain ion coordination and selectivity. Here we show that within a'standard setting' the QM wave packet of an ion with the mass of a K\({}^{+}\) ion can spread beyond the width of a single coordination site of the KcsA filter domain during just a single coherence time interval. This is strongly suggestive that the underlying dynamics in the filter region of these ion channels involves an important quantum mechanical aspect. We expect that quantum properties become even more important if all ions occupying the channel are described as wave packets, as this will influence the mutual forces and will moderate the random fluctuations exerted by the atomic channel structure. The present results suggest a number of future investigations. One topic to address is how the quantum mechanical behavior of a K\({}^{+}\) ion located at different sites of the selectivity filter will influence current flow, particularly within situations where adjacent locations are occupied by another ion, involving a direct Coulombic knock on. Another aspect involves the description of the K\({}^{+}\) ion employing a density matrix approach. Finally, we expect to gain further insight on the conspicuous burst-like behavior of current flow with all K\({}^{+}\) ions in the selectivity filter treated as quantum particles.