A strategy for determining the equilibrium constants for heteromeric ion channels in a complex model

Abstract

Ligand-gated ion channels are oligomers containing several binding sites for the ligands. However, the signal transmission from the ligand binding site to the pore has not yet been fully elucidated for any of these channels. In heteromeric channels, the situation is even more complex than in homomeric channels. Using published data for concatamers of heteromeric cyclic nucleotide–gated channels, we show that, on theoretical grounds, multiple functional parameters of the individual subunits can be determined with high precision. The main components of our strategy are (1) the generation of a defined subunit composition by concatenating multiple subunits, (2) the construction of 16 concatameric channels, which differ in systematically permutated binding sites, (3) the determination of respectively differing concentration–activation relationships, and (4) a complex global fit analysis with corresponding intimately coupled Markovian state models. The amount of constraints in this approach is exceedingly high. Furthermore, we propose a stochastic fit analysis with a scaled unitary start vector of identical elements to avoid any bias arising from a specific start vector. Our approach enabled us to determine 23 free parameters, including 4 equilibrium constants for the closed–open isomerizations, 4 disabling factors for the mutations of the different subunits, and 15 virtual equilibrium-association constants in the context of a 4-D hypercube. From the virtual equilibrium-association constants, we could determine 32 equilibrium-association constants of the subunits at different degrees of ligand binding. Our strategy can be generalized and is therefore adaptable to other ion channels.

Modeling the kinetics of heteromeric potassium channels

“…Despite mechanistic differential equation modeling being a common technique for answering tough experimental neuroscience questions, little modeling of heteromeric K V channels has been done. Current modeling work for heteromeric experiments either looks at different channel families or lacks the necessary known biological specificity (Cheng et al, 2007 ; Miceli et al, 2013 , 2015 ; Benndorf et al, 2022 ).…”

“…Work by Cheng et al ( 2007 ) coupled spectroscopy-based fluorescence resonance energy transfer and computational modeling to indicate that heat-sensitive transient receptor potential channels prefer heteromeric configurations. Looking at heteromeric cyclic nucleotide–gated channels, Benndorf et al ( 2022 ) analyzed the ability to determine model parameters using concatemeric experimental data. Modeling work with heteromeric K V channels has primarily consisted of fitting Boltzmann-like equations, or in rare cases Markov Models, for channel gating to voltage clamp data of either concatemeric heteromers or cells with two or more coexpressed cDNA types (Sale et al, 2008 ; Miceli et al, 2013 , 2015 ).…”

Identifiability of equilibrium constants for receptors with two to five binding sites

“…In our previous analysis on heteroterameric channels, we eased the considerations by interpreting the 16 closed states of our HA 4 models as corners of a 4-D hypercube in which the transitions, specified by the 32 K x , form the 32 edges ( Fig. S1 B ; Benndorf et al, 2022 ).…”

“…Then for each of these seven concentrations, five data points were generated by adding a stochastic noise, n st , to the noise-free P o value according to where R is an equally distributed random number between −1 and 1. This noise level was also used as standard for previous simulations ( Benndorf et al, 2022 ). It was used herein for all simulations.…”

“…We therefore studied on theoretical grounds how this unexpectedly good identifiability of parameters could be reached ( Benndorf et al, 2022 ). We showed that with this strategy indeed multiple functional parameters of the individual subunits can be determined because the constraints in this approach are sufficiently high.…”