## Appendix A Numerical Parameters of the Particles and of the Selectivity Filter  
The 'particles' involved in the MD simulations are K\({}^{+}\) ions, water molecules, and carbonyl groups. All particles were modeled as point particles carrying a partial charge and a typical radial extension where mutual repulsion would set in if any two particles were close. The K\({}^{+}\) ions carried a charge of +1 q\({}_{0}\), where q\({}_{0}\) is the electric unit of charge (1.602176634 \(\times\) 10\({}^{-19}\) Coulombs). The H\({}_{2}\)O molecules were simulated as three separate charges located at the corners of a rigid triangle, and the usual parameters were assumed, i.e., an angle of 104.5\({}^{\circ}\) between the two arms to the H-atoms and a distance O-H of 95.84 pm. The partial charge on O was \(-\)0.7 q\({}_{0}\) and that on each of the H-atoms was + 0.35 q\({}_{0}\)[27]. In carbonyl groups the distance between C and O was set to the usual report of 0.123 nm. The C-atom carried a partial charge of +0.38 q\({}_{0}\)[28]. The O-atom carried a partial charge of \(-\)0.38 q\({}_{0}\)[28], of which 30% were located at the center point of the O-atom and 70% were located at an effective charge center, representing the lone pair electrons. (This distribution was estimated from trial and error to obtain the potential distributions as shown in [9] and [10].) The distance between the center of the O-atom and the lone pair charge point was set to 1.4 R\({}_{0}\), where R\({}_{0}\) is the covalent radius of the O-atom when in double bond (58.9 pm). The lone pair charge point was always fixed on the extension of the C-O-line following the vibrational axis of the O-atom. The dimensions of the selectivity filter were set by the fixed positions of the carbonyl C-atoms. We adopted values following [PERSON] et al. [29]. For each amino strand, the C-atoms of the neighboring carbonyls had a constant distance to the central axis of the SF of 0.38 nm, and the four strands were arranged in a quadratic outline. Therefore, C-atoms of a given ring were located at corners of a square with side lengths of 0.5374 nm. The distances along the axis of the SF (z-axis) between the different rings were as follows: Thr74-Thr75 0.3 nm, Thr75-Val76 0.32 nm, Val76-Gly77 0.28 nm, Gly77-Tyr78 0.31 nm, and Tyr78-Gly79 0.35 nm. The orientations of the C-O axes in the relaxed condition point more or less to the central axis of the SF, although in most depictions of the KcsA filter one can find certain deviations [9; 30; 31]. For the present calculations the angles of the C-O axes were the same for each of the four carbonyls of a given ring, but could differ from one ring to the next. We set the angles as follows (\(\boldsymbol{\varphi}\dots\) angle in the xy-plane, a value of 0 indicates that C-O points to the central axis; \(\boldsymbol{\theta}\dots\) tilt angle of C-O out of the xy-plane): At Thr74 \(\boldsymbol{\varphi}=+22.5^{\circ}\), \(\boldsymbol{\theta}=0^{\circ}\); at Thr75 \(\boldsymbol{\varphi}=+22.5^{\circ}\), \(\boldsymbol{\theta}=0^{\circ}\); at Val76 \(\boldsymbol{\varphi}=-22.5^{\circ}\), \(\boldsymbol{\theta}=0^{\circ}\); at Gly77 \(\boldsymbol{\varphi}=+22.5^{\circ}\), \(\boldsymbol{\theta}=0^{\circ}\); at Tyr78 \(\boldsymbol{\varphi}=-22.5^{\circ}\), \(\boldsymbol{\theta}=0^{\circ}\); and at Gly79 \(\boldsymbol{\varphi}=0^{\circ}\), \(\boldsymbol{\theta}=70^{\circ}\). These orientations can be roughly inferred from the right image of Figure 1 (in this and all other figures of our model of the SF the lower ring is Thr74 and the top is Gly79). Oscillations of carbonyl O-atoms with their relaxed values of \(\boldsymbol{\varphi}\) and \(\boldsymbol{\theta}\) follow a linear Hooke's law in which the spring constant is set to result in a vibrational frequency with a wavenumber of 500 cm\({}^{-1}\). This is in the range of wave numbers established for carbonyl groups within similar molecular environments [32; 33]. The damping constant of the vibration was set to \(1\times 10^{-13}\) kg/s.