A developmental model for generating frequency maps in the reptilian and avian cochleas

Hair cells in the turtle cochlea are frequency-tuned by a mechanism involving the combined activation of voltage-sensitive Ca2+ channels and Ca(2+)-activated K+ (KCa) channels. The main determinants of a hair cell's characteristic frequency (Fo) are the KCa channels' density and kinetics, both of which change systematically with location in the cochlea in conjunction with the observed frequency map. We have developed a model based on the differential expression of two KCa channel subunits, which when accompanied by concurrent changes in other properties (e.g., density of Ca2+ channels and inwardly rectifying K+ channels), will generate sharp tuning at frequencies from 40 to 600 Hz. The kinetic properties of the two subunits were derived from previous single-channel analysis, and it was assumed that the subunits (A and B) combine to form five species of tetrameric channel (A4, A3B, A2B2, AB3, and B4) with intermediate kinetics and overlapping distribution. Expression of KCa and other channels was assumed to be regulated by diffusional gradients in either one or two chemicals. The results are consistent with both current- and voltage-clamp data on turtle hair cells, and they show that five channel species are sufficient to produce smooth changes in both Fo and kinetics of the macroscopic KCa current. Other schemes for varying KCa channel kinetics are examined, including one that allows extension of the model to the chick cochlea to produce hair cells with Fo's from 130 to 4000 Hz. A necessary assumption in all models is a gradient in the values of the parameters identified with the cell's cytoplasmic Ca2+ buffer.