Large-conductance Ca 2ϩ -and voltage-dependent potassium (BK) channels exhibit functional diversity not explained by known splice variants of the single Slo ␣-subunit. Here we describe an accessory subunit (␤3) with homology to other ␤-subunits of BK channels that confers inactivation when it is coexpressed with Slo. Message encoding the ␤3 subunit is found in rat insulinoma tumor (RINm5f) cells and adrenal chromaffin cells, both of which express inactivating BK channels. Channels resulting from coexpression of Slo ␣ and ␤3 subunits exhibit properties characteristic of native inactivating BK channels. Inactivation involves multiple cytosolic, trypsin-sensitive domains. The time constant of inactivation reaches a limiting value ϳ25-30 msec at Ca 2ϩ of 10 M and positive activation potentials. Unlike Shaker N-terminal inactivation, but like native inactivating BK channels, a cytosolic channel blocker does not compete with the native inactivation process. Finally, the ␤3 subunit confers a reduced sensitivity to charybdotoxin, as seen with native inactivating BK channels. Inactivation arises from the N terminal of the ␤3 subunit. Removal of the ␤3 N terminal (33 amino acids) abolishes inactivation, whereas the addition of the ␤3 N terminal onto the ␤1 subunit confers inactivation. The ␤3 subunit shares with the ␤1 subunit an ability to shift the range of voltages over which channels are activated at a given Ca 2ϩ . Thus, the ␤-subunit family of BK channels regulates a number of critical aspects of BK channel phenotype, including inactivation and apparent Ca 2ϩ sensitivity.

The properties of Ca(2+)- and voltage-dependent K+ currents and their role in defining membrane potential were studied in cultured rat chromaffin cells. Two variants of large-conductance, Ca2+ and voltage-dependent BK channels, one noninactivating and one inactivating, were largely segregated among patches. Whole-cell noninactivating and inactivating currents resulting from each of these channels were segregated among different chromaffin cells. Cell-to-cell variation in the rate and extent of whole-cell current decay was not explained by differences in cytosolic [Ca2+] regulation among cells; rather, variation was due to differences in the intrinsic properties of the underlying BK channels. About 75% of rat chromaffin cells and patches express inactivating BK current (termed BKi) while the remainder express noninactivating BK current (termed BKs). The activation time course of both currents is similar, as is the dependence of activation on [Ca2+] and membrane potential. However, deactivation of BKi channels is slower than that of BKs channels. The functional role of these BK channel variants was studied in current-clamp recordings. Although both BKi and BKs currents contribute to action potential repolarization, cells expressing BKi current are better able to fire repetitively in response to constant current injection. Blockade of BKi current by charybdotoxin abolishes this behavior, showing that afterhyperpolarizations mediated by BKi current are permissive for repetitive firing. Thus, important properties of chromaffin cell membrane excitability are determined by the type of BK current expressed.

Auxiliary beta subunits play a major role in defining the functional properties of large-conductance, Ca2+-dependent BK-type K+ channels. In particular, both the beta1 and beta2 subunits produce strong shifts in the voltage dependence of channel activation at a given Ca2+. Beta subunits are thought to coassemble with alpha subunits in a 1:1 stoichiometry, such that a full ion channel complex may contain up to four beta subunits per channel. However, previous results raise the possibility that ion channels with less than a full complement of beta subunits may also occur. The functional consequence of channels with differing stoichiometries remains unknown. Here, using expression of alpha and beta subunits in Xenopus oocytes, we show explicitly that functional BK channels can arise with less than four beta subunits. Furthermore, the results show that, for both the beta1 and beta2 subunits, each individual beta subunit produces an essentially identical, incremental effect on the voltage dependence of gating. For channels arising from alpha + beta2 subunits, the number of beta2 subunits per channel also has a substantial impact on properties of steady-state inactivation and recovery from inactivation. Thus, the stoichiometry of alpha:beta subunit assembly can play a major functional role in defining the apparent Ca2+ dependence of activation of BK channels and in influencing the availability of BK channels for activation.

Inactivating and noninactivating variants of large-conductance, Ca2+-dependent, voltage-dependent BK-type channels are found in rat chromaffin cells and are largely segregated into different cells. Here we test the hypothesis that, within the population of cells that express inactivating BK current (BKi current), the BKi channels are largely heteromultimers composed of inactivation-competent subunits (bk(i)) and noninactivating subunits (bk(s)). Several independent types of evidence support this view. The gradual removal of inactivation by trypsin is consistent with the idea that in most cells and patches there are, on average, about two to three inactivation domains per channel. In addition, several aspects of blockade of BKi current by charybdotoxin (CTX) are consistent with the idea that BKi channels contain differing numbers (one to four) of relatively CTX-resistant bk(i) subunits. Finally, the frequency of occurrence of noninactivating BKs channels in patches with predominantly inactivating BKi channels is consistent with the binomial expectations of random, independent assembly of two distinct subunits, if most cells have, on average, about two to three bk(i) subunits per channel. These results suggest that the phenotypic properties of BKi currents and the resulting cellular electrical excitability may exhibit a continuum of behavior that arises simply from the differential expression of two distinct subunits.

We prove a spectral perturbation theorem for rank-one updated matrices of special structure. Two applications of the result are given to illustrate the usefulness of the theorem. One is for the spectrum of the Google matrix and the other is for the algebraic simplicity of the maximal eigenvalue of a positive matrix.