Someone argues: "The potassium channel's ring of carbonyl oxygens forms a cage sized…
PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Molecular machines, transport and bioenergetics · Molecular machines, transport and bioenergetics
Forces, Machines and Signals, Ch Channels, pumps and the resting potential
Problem
Someone argues: "The potassium channel's ring of carbonyl oxygens forms a cage sized to fit a potassium ion (crystal radius 0.133nm) snugly. Sodium (crystal radius 0.095nm) is smaller, so it rattles loosely inside the same cage and cannot be coordinated properly. The cage is therefore a rigid steric filter that excludes sodium completely, passing zero sodium ions for every potassium ion."
((a)) Find the error in this reasoning.
((b)) Using the difference in free-energy cost of passage through the filter, ΔΔG=6.9kBT (sodium's minus potassium's), calculate the actual ratio of sodium to potassium throughput, and state whether it supports "zero sodium" or a finite, small leak.