A Statistical Thermodynamic Model for Ligands Interacting With Ion Channels: Theoretical Model and Experimental Validation of the KCNQ2 Channel

Abstract

Ion channels are important therapeutic targets, and their pharmacology is becoming increasingly important. However, knowledge of the mechanism of interaction of the activators and ion channels is still limited due to the complexity of the mechanisms. A statistical thermodynamic model has been developed in this study to characterize the cooperative binding of activators to ion channels. By fitting experimental concentration-response data, the model gives eight parameters for revealing the mechanism of an activator potentiating an ion channel, i.e., the binding affinity (KA), the binding cooperative coefficients for two to four activator molecules interacting with one channel (γ, μ, and ν), and the channel conductance coefficients for four activator binding configurations of the channel (a, b, c, and d). Values for the model parameters and the mechanism underlying the interaction of ztz240, a proven KCNQ2 activator, with the wild-type channel have been obtained and revealed by fitting the concentration-response data of this activator potentiating the outward current amplitudes of KCNQ2. With these parameters, our model predicted an unexpected bi-sigmoid concentration-response curve of ztz240 activation of the WT-F137A mutant heteromeric channel that was in good agreement with the experimental data determined in parallel in this study, lending credence to the assumptions on which the model is based and to the model itself. Our model can provide a better fit to the measured data than the Hill equation and estimates the binding affinity, as well as the cooperative coefficients for the binding of activators and conductance coefficients for binding states, which validates its use in studying ligand-channel interaction mechanisms.

Equilibrium probability distribution for number of bound receptor-ligand complexes

“…(12), the expressions in Eqs. (13) and (14) are no longer symmetric with respect to the exchange of R and L, because we are ignoring the depletion effect of one of the two species.…”

“…This approach has been exactly followed to derive the equilibrium occupation probability of a single receptor surrounded by L ligand molecules. 3,6,12,13 The equilibrium occupation probability of the receptor is the probability that the receptor will be bound by one of the L ligand molecules in equilibrium. The resultant formula is shown to be equivalent to the one which is obtained from the chemical reaction rate equations.…”