## 3 Results  
### Classical MD Simulations  
In the KcsA model, conduction is estimated to reach up to maximal currents in the order of \(10^{8}\) ions per second [16; 18]. The present MD simulations can basically reproduce this result. At the single-atom scale, however, conduction appeared to follow a quite different temporal characteristic than one would expect from electro-diffusion based on continuum Poisson-Nernst-Planck (PNP) models. Here we found that, on average, an ion was transmitted only every 2 to 5 nanoseconds to the extracellular domain. Together with average occupancies of the filter between 2 and 4 ions, an ion was found to spend between 6 and 15 ns in the SF domain. Translocation between binding locations within the filter were very short and occurred within around 1 picosecond crossing distances of 0.3 nm between each site. One could expect that ions can transverse the entire SF within 5 to 10 picoseconds, but the present simulations indicated that, on average, it took about 1000 times longer compared with this theoretical option. The reason can be found within strongly extended halting times that are largely suppressed in the macroscopic approximation of a continuous ion flow. At the present scale, sub-molecular details explicit the coordination strength exerted by surrounding carbonyl charges [19]. As a result from this Coulombic coordination, currents showed a temporal substructure in which consecutive bursts of ions were interrupted by exceedingly long intervals during which no ions left the SF. Figure 2 shows the result of a simulation which covered a period of 10 \(\upmu\)s. During this interval, 1763 K\({}^{+}\) ions left the SF to the extracellular side. Although the average time between ion emissions is expected to be around 5.67 ns, more than 89% of the ions exited the SF within less than 2 ns of the previous emission. The above findings demonstrate a strong bursting characteristic, if the process is resolved to the highest level at the single-atom scale. In accord with this finding, there was a strong discrepancy between predictions based on a simulated Poisson-type (P) behavior and the present findings. As apparent from Figure 2, a sequence of 1763 random P events was compared to the emission characteristic following from our simulation.  
Finally, as seen from a 'classical perspective', the present results render a picture on the question of optimization of selective conduction, which has been at the focus of debate in previous studies. Details of these results will be published separately [20]. In short, changes in critical measures such as the length of the filter region had a strong effect on conduction. Changes of just a few percent (e.g., 4%) will halve conduction, and changes around 10% will freeze conduction completely.  
The optimum length of the SF seemed to be about 0.7% longer than the values we assumed for the present calculations.  
Figure 2: Red dots: Classical MD simulation of K\({}^{+}\) current through the SF during 10 \(\upmu\)s; 1763 K+ ions left the SF at the extracellular side, mostly in bursts with very short time between successive ions. Blue dots: A mathematical sequence of random events according to a Poisson statistic which was set to produce a mean of 1763 events in 10 \(\upmu\)s.