On the Theory of Ion Transport Across the Nerve Membrane, III. Potassium Ion Kinetics and Cooperativity (with x = 4, 6, 9)

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Abstract
The calculations of Part II of this series have been extended to square (x = 4) and octahedral (x = 6) arrangements of subunits in a potassium channel (or gate). The conclusion is the same as before: experimental induction and superposition properties of gK(t), on depolarization, seem to rule out any significant degree of interaction or cooperativity between the (protein?) subunits of K(+) channel. Calculations for x = 4, 6, and 9 have also been made for a square lattice of interacting channels (periodic boundary conditions). Because of apparent rapid convergence with x, it seems fairly safe to conclude that this model is unsatisfactory. There is some difficulty with superposition but the principal shortcoming is a failure to produce induction behavior. Aggregation models for the K(+) channel are also discussed briefly here. They, too, appear rather unpromising (for the same reasons as seem to exclude conformational cooperativity within a channel).