Modeling Subunit Cooperativity in Opening of Tetrameric Ion Channels

Abstract

Most potassium channels are tetramers of four homologous polypeptides (subunits). During channel gating, each subunit undergoes several conformational changes independent of the state of other subunits before reaching a permissive state, from which the channel can open. However, transition from the permissive states to the open state involves a concerted movement of all subunits. This cooperative transition must be included in Markov models of channel gating. Previously, it was implemented by considering all possible combinations of four subunit states in a much larger expanded model of channel states (e.g., 27,405 channel states versus 64 subunit states), which complicates modeling and is computationally intense, especially when accurate modeling requires a large number of subunit states. To overcome these complexities and retain the tetrameric molecular structure, a modeling approach was developed to incorporate the cooperative transition directly from the subunit models. In this approach, the open state is separated from the subunit models and represented by the net flux between the open state and the permissive states. Dynamic variations of the probability of state residencies computed using this direct approach and the expanded model were identical. Implementation of the direct approach is simple and its computational time is orders-of-magnitude shorter than the equivalent expanded model.

Conformational changes of an ion-channel during gating and emerging electrophysiologic properties: Application of a computational approach to cardiac Kv7.1

“…Representative records of single channel openings were simulated using four randomly selected motion trajectories of four voltage sensors and including a cooperative transition to the channel open state (Nekouzadeh et al, 2008). The morphology of single channel records varied from constant flickering between open and closed states to no openings (Figures 5L, 5M, 5N, and Supplemental Figure S5).…”

Entropy hysteresis and nonequilibrium thermodynamic efficiency of ion conduction in a voltage-gated potassium ion channel

“…Various experimental results reveal that a potassium ion channel is composed of four independent homologous subunits [28][29][30], where each subunit remains in several conformational states. For simplicity, we consider only two conformational states of each subunit, i.e., inactive and active [31][32][33].…”

Probability Distributions of Markovian Sodium Channel States During Propagating Axonal Impulses With or Without Recovery Supernormality

“…Further modifications may include additional I states (e.g., [17,51,61]), the consideration of transitional energy barriers (e.g., [80,15]), the roles of Ca ++ [4,34] and perhaps membrane composition in the voltage-sensitivity of rate constants [ibid. ], and the transitions of channel subunits within a given state [56]. Such kinetic schemes can also be applied to the study of excitation at Ranvier nodes (e.g., [72]), and may relate to developing models about the shifting of NaCh moieties during voltage-dependent gating, such as the "tethered ball" [4] and the "paddle" [40; cf.…”