A linkage analysis toolkit for studying allosteric networks in ion channels

A thermodynamic approach to studying allosterically regulated ion channels such as the large-conductance voltage- and Ca(2+)-dependent (BK) channel is presented, drawing from principles originally introduced to describe linkage phenomena in hemoglobin. In this paper, linkage between a principal channel component and secondary elements is derived from a four-state thermodynamic cycle. One set of parallel legs in the cycle describes the “work function,” or the free energy required to activate the principal component. The second are “lever operations” activating linked elements. The experimental embodiment of this linkage cycle is a plot of work function versus secondary force, whose asymptotes are a function of the parameters (displacements and interaction energies) of an allosteric network. Two essential work functions play a role in evaluating data from voltage-clamp experiments. The first is the conductance Hill energy W(H)([g]), which is a “local” work function for pore activation, and is defined as kT times the Hill transform of the conductance (G-V) curve. The second is the electrical capacitance energy W(C)([q]), representing “global” gating charge displacement, and is equal to the product of total gating charge per channel times the first moment (V(M)) of normalized capacitance (slope of Q-V curve). Plots of W(H)([g]) and W(C)([q]) versus voltage and Ca(2+) potential can be used to measure thermodynamic parameters in a model-independent fashion of the core gating constituents (pore, voltage-sensor, and Ca(2+)-binding domain) of BK channel. The method is easily generalized for use in studying other allosterically regulated ion channels. The feasibility of performing linkage analysis from patch-clamp data were explored by simulating gating and ionic currents of a 17-particle model BK channel in response to a slow voltage ramp, which yielded interaction energies deviating from their given values in the range of 1.3 to 7.2%.