Mathematical model of voltage gating of unapposed connexin hemichannels.

Unapposed connexin (Cx) hemichannels serve as precursors to gap junction channels but also function independently, playing crucial roles in various physiological processes. Hemichannel gating is influenced by factors such as plasma membrane voltage and extracellular divalent ion concentrations. Excessive hemichannel opening can lead to significant leakage of ions and molecules, and mutations in genes encoding Cxs often result in aberrant gating, contributing to various pathologies. Therefore, evaluating and quantifying Cx hemichannel gating behaviours is important. To address this, we developed a mathematical/computational model describing the voltage-gating properties of Cx hemichannels. The proposed model incorporates two distinct gating mechanisms - fast and loop gating - known to regulate hemichannel closure. These gating transitions are represented within a four-state kinetic scheme, which also accounts for redistribution of voltage upon the closure of either mechanism. Using a sensitivity function matrix approach, we selected voltage protocols that provide sufficient information to constrain the proposed model. The model was then fitted to electrophysiological data recorded from Cx26 and Cx45 hemichannels. Fits to both training datasets and independent validation data indicate that the model can adequately describe the basic characteristics of Cx hemichannel currents. Further analysis using the proposed kinetic scheme provides insights into hemichannel gating behaviour, including the observed delay in current activation upon depolarization and potential discrepancies between gating kinetics of unapposed hemichannels and gap junction channels. Thus, the proposed model can serve as a valuable tool for comparing voltage-gating properties across Cx isoforms and mutants and offers insights into Cx hemichannel gating behaviours. KEY POINTS: Gating of unapposed connexin (Cx) hemichannels plays a crucial role in various physiological processes, whereas mutations in Cx genes that cause aberrant gating are linked to various pathologies. To quantify the voltage-gating properties of Cx hemichannels, we present a novel mathematical/computational model that comprises two established gating mechanisms: fast and loop gating. The validity of the proposed model is demonstrated through fits to electrophysiological data from cells expressing different Cx isoforms, Cx26 and Cx45. The proposed model can serve as a useful tool for comparing the voltage-gating properties across Cx isoforms and mutants, and offers insights into the physiologically relevant mechanistic behaviours of Cx hemichannels.