Brownian dynamics study of a multiply-occupied cation channel: application to understanding permeation in potassium channels

The behavior of a multiply-occupied cation-selective channel has been computed by Brownian dynamics. The length, cross-section, ion-ion repulsion force, and ionic mobility within the channel are all estimated from data and physical reasoning. The only free parameter is a partition energy at the mouth of the channel, defining the free energy of an ion in the channel compared to the bath. It is presumed that this partition energy is associated with the energetics of exchanging a bulk hydration environment for a channel hydration environment. Varying the partition energy alone, keeping all other parameters fixed, gives approximately the full range of magnitudes of single channel conductances seen experimentally for K channels. Setting the partition energy at -11 kT makes the computed channel look similar to a squid axon K channel with respect to magnitude of conductance, shape of the I-V curve, non-unity of Ussing flux ratio exponents, decrease of current and increase of conductance with extracellular ion accumulation, and saturation at high ion concentration in the bathing solution. The model includes no preferred binding sites (local free energy minima) for ions in the channel. Therefore it follows that none of the above-mentioned properties of K channels are strong evidence for the existence of such sites. The model does not show supersaturation of current at very high bathing concentrations nor any pronounced voltage-dependence of the Ussing flux ratio exponent, suggesting that these features would require additional details not included in the model presented herein.