## 1 Introduction  
Electrical signals generated in nerve cells are generated by membrane proteins that catalyze a selective electro-diffusion of ions across plasma membranes. The proteins are embedded in the lipid bilayer of membranes and provide currents at the pico-ampere level, combining fast conduction with a high selectivity for particular ions. In voltage-gated potassium channels, this selective control of ion conduction is organized by a specific arrangement of amino-acids within a narrow'selectivity filter' domain of the protein [1, 2]. The most frequently studied filter model is based on the bacterial-derived KcsA channel motif (KcsA, potassium crystallographically sited activation channel) where the filter construction is formed by four subunits, each composed by the same amino acid sequence TVGYG [3; 4; 5]. Ion translocation is largely coordinated by amino acid carbonyl groups pointing towards the axis of the constriction, with oxygen lone pair electrons creating a series of four potential valleys. By convention, and as shown in Figure 1, these transient cages are labeled as sites S1 to S4 as seen from outside to inside of the membrane with coordinating interactions mimicking the hydration shell of ions in bulk water [6]. The relevant caging forces are Coulombic attractions between ion and electrons, together with repulsive effects, if lone pair electrons and the inner shell of the K\({}^{+}\) ion start to overlap [2; 6]. Further, the diffusion of K\({}^{+}\) ions seems to occur in a hopping manner between potential minima, and this in turn is driven by the transmembrane field resulting from the charge concentration gradient across the cell membrane. Additional to K\({}^{+}\) ions, also water molecules diffuse through the channel, experiencing similar carbonyl-derived caging forces. The small interaction distances of temporary caging sites together with the underlying conduction strategy, as hopping from one site to the next, stimulate the question of whether quantum effects in these transitions could play a functional role. In a recent study we have provided a first assessment of this question by simulating a single site situation and simulating a K\({}^{+}\) ion as a quantum mechanical particle. We found that, due to the slow dispersion of the initially well-localized wave packet, the enclosing carbonyl oxygen atoms tend to be pushed some distance aside, and this leads to a higher probability for the particle to escape from this site within a given time [7]. In the present work, we extend this study to include the complete TVGYG sequence and permit an arbitrary number of K\({}^{+}\) ions and water molecules to permeate. Again, we find a considerable enhancement of a K\({}^{+}\) ion's probability to propagate to the next site due to its quantum mechanical nature as a wave packet. Further, the present study confirms our previous finding about an optimal decoherence time of the particles' wave-function regarding a directional 'guidance' through subsequent potential barriers provided by the surrounding electrons. Previous studies were generally based on classical MD simulations. Whereas early studies within this frame considered an alternating sequence of K\({}^{+}\) and water molecules (e.g., KwKw) passing through the constriction [4], subsequent MD simulations also revealed other conduction mechanisms with similar free energy barriers [8] and (Kw) co-translocations [9]. In addition, for high conduction rates, a direct Coulomb knock-on mechanism was suggested with direct ionic contacts [10]. A particularly important observation that strongly encouraged the present study was the observation about the  
Figure 1: A ribbon model K\({}^{+}\) channel embedded in the lipid bilayer (**left**), with two of the four subunits and the extracellular side on top (**middle**). The four binding sites (S1–S4) with four dehydrated ions in locations S1 and S3, and one partially dehydrated ion in the neighboring cavity location Scav, are demonstrated (**right**).