Selectivity of the KcsA potassium channel: Analysis and computation

Abstract

Potassium (K + ) channels regulate the flux of K + ions through cell membranes and plays significant roles in many physiological functions. This work studies the KcsA potassium channel, including the selectivity and current-voltage (IV) relations. A modified Poisson-Nernst-Planck system is employed, which include the size effect by Bikerman model and solvation energy by Born model. The selectivity of KcsA for various ions (K + , Na + , Cl − , Ca 2+ and Ba 2+ ) is studied analytically, and the profiles of concentrations and electric potential are provided. The selectivity is mainly influenced by permanent negative charges in filter of channel and the ion sizes. K + is always selected compared with Na + (or Cl − ), as smaller ion size of Na + causes larger solvation energy. There is a transition for selectivity among K + and divalent ions (Ca 2+ and Ba 2+ ), when negative charge in filter exceeds a critical value determined by ion size. This explains why divalent ions can block the KcsA channel. The profiles and IV relations are studied by analytical, numerical and hybrid methods, and are cross-validated. The results show the selectivity of the channel and also the saturation of IV curve. A simple strategy is given to compute IV relations analytically, as first approximation. The numerical method deals with general structure or parameters, but the limitations and difficulties of pure numerical 1 arXiv:1902.04634v1 [physics.bio-ph] 12 Feb 2019 simulation are also pointed out. The hybrid method provides IV relations most effectively for comparison. The reason for saturation of IV relation is illustrated, and the IV curve shows agreement with the profile and scale of experimental results.

A detailed study of ion transport through the SARS-CoV-2 E protein ion channel

“…Inside the channel, spatial dependence is assigned for the diffusion coefficient based on previous studies. 27 …”

Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

“…Remember SISBM3 is designed for extremely high ion concentrations motivated by the more efficient packing shown in Figure 1 b. Actually for situations that would give rise to extremely high ion concentrations and make the steric effect not negligible, such as the Stern layer in the electric double layer (EDL) of a charged wall (discussed next) and the selectivity filter of a K channel [ 20 ], there would be ‘locally’ one species only, which is the counter-ion of the local electrostatic environment, since co-ions (and even water) would be totally expelled. Taking the K channel selectivity filter as an example, its extreme narrowness and the strong negative oxygen charges inside it would definitely justify only one species being inside the selectivity filter, which is definitely potassium.…”

A Bubble Model for the Gating of Kv Channels

“…The studies [54,55] by Weishi Liu and his group have illustrated the effects of permanent charge on current-voltage relation. With ionic size effect and the permanent charge, saturation phenomenon of current-voltage curves can be modelled as shown in [51].…”

“…Following the previous hypothesis of the hydrophobic region, we construct a specific macroscopic model of a bubble within the framework of Poisson-Nernst-Planck (PNP) systems and show how it produces the time course of single K v channels and the ensemble properties, including the Cole-Moore delay. The PNP system and its variants have been found successful in modeling and simulation of many biological processes [50,51,28,52,53,54,55], such as current-voltage curves through ion channels, the selectivity of ion channels, and ion transport processes in the cell and tissue scales. In this work, a bubble is assumed to be present in the pore (or filter) region of the K v channel, due to the properties of the gating sensor and channel walls.…”