Four-State Model for Simulating Kinetic and Steady-State Voltage-Dependent Gating of Gap Junctions

Modeling and analysis of voltage gating of gap junction channels at a single-channel level

The advancement of single-channel-level recording via the patch-clamp technique has provided a powerful means of assessing the detailed behaviors of various types of ion channels in native and exogenously expressed cellular environments. However, such recordings of gap junction (GJ) channels are hampered by unique challenges that are related to their unusual intercellular configuration and natural clustering into densely packed plaques. Thus, the methods for reliable cross-correlation of data recorded at macroscopic and single-channel levels are lacking in studies of GJs. To address this issue, we combined our previously published four-state model (4SM) of GJ channel gating by voltage with maximum likelihood estimation (MLE)-based analyses of electrophysiological recordings of GJ channel currents. First, we consider evaluation of single-channel characteristics and the methods for efficient stochastic simulation of single GJ channels from the kinetic scheme described by 4SM using data obtained from macroscopic recordings. We then present an MLE-based methodology for extraction of information about transition rates for GJ channels and, ultimately, gating parameters defined in 4SM from recordings with visible unitary events. The validity of the proposed methodology is illustrated using stochastic simulations of single GJ channels and is extended to electrophysiological data recorded in cells expressing connexin 43 tagged with enhanced green fluorescent protein.

The role of the Cx43/Cx45 gap junction voltage gating on wave propagation and arrhythmogenic activity in cardiac tissue

Gap junctions (GJs) formed of connexin (Cx) protein are the main conduits of electrical signals in the heart. Studies indicate that the transitional zone of the atrioventricular (AV) node contains heterotypic Cx43/Cx45 GJ channels which are highly sensitive to transjunctional voltage (Vj). To investigate the putative role of Vj gating of Cx43/Cx45 channels, we performed electrophysiological recordings in cell cultures and developed a novel mathematical/computational model which, for the first time, combines GJ channel Vj gating with a model of membrane excitability to simulate a spread of electrical pulses in 2D. Our simulation and electrophysiological data show that Vj transients during the spread of cardiac excitation can significantly affect the junctional conductance (gj) of Cx43/Cx45 GJs in a direction- and frequency-dependent manner. Subsequent simulation data indicate that such pulse-rate-dependent regulation of gj may have a physiological role in delaying impulse propagation through the AV node. We have also considered the putative role of the Cx43/Cx45 channel gating during pathological impulse propagation. Our simulation data show that Vj gating-induced changes in gj can cause the drift and subsequent termination of spiral waves of excitation. As a result, the development of fibrillation-like processes was significantly reduced in 2D clusters, which contained Vj-sensitive Cx43/Cx45 channels.

Simulation of atrial fibrillation in a non-ohmic propagation model with dynamic gap junctions

Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel-Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100  μm resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.

The Amino Terminal Domain and Modulation of Connexin36 Gap Junction Channels by Intracellular Magnesium Ions

Electrical synapses between neurons in the mammalian CNS are predominantly formed of the connexin36 (Cx36) gap junction (GJ) channel protein. Unique among GJs formed of a number of other members of the Cx gene family, Cx36 GJs possess a high sensitivity to intracellular Mg²⁺ that can robustly act to modulate the strength of electrical synaptic transmission. Although a putative Mg²⁺ binding site was previously identified to reside in the aqueous pore in the first extracellular (E1) loop domain, the involvement of the N-terminal (NT) domain in the atypical response of Cx36 GJs to pH was shown to depend on intracellular levels of Mg²⁺. In this study, we examined the impact of amino acid substitutions in the NT domain on Mg²⁺ modulation of Cx36 GJs, focusing on positions predicted to line the pore funnel, which constitutes the cytoplasmic entrance of the channel pore. We find that charge substitutions at the 8th, 13th, and 18th positions had pronounced effects on Mg²⁺ sensitivity, particularly at position 13 at which an A13K substitution completely abolished sensitivity to Mg²⁺. To assess potential mechanisms of Mg²⁺ action, we constructed and tested a series of mathematical models that took into account gating of the component hemichannels in a Cx36 GJ channel as well as Mg²⁺ binding to each hemichannel in open and/or closed states. Simultaneous model fitting of measurements of junctional conductance, g_j, and transjunctional Mg²⁺ fluxes using a fluorescent Mg²⁺ indicator suggested that the most viable mechanism for Cx36 regulation by Mg²⁺ entails the binding of Mg²⁺ to and subsequent stabilization of the closed state in each hemichannel. Reduced permeability to Mg²⁺ was also evident, particularly for the A13K substitution, but homology modeling of all charge-substituted NT variants showed only a moderate correlation between a reduction in the negative electrostatic potential and a reduction in the permeability to Mg²⁺ ions. Given the reported role of the E1 domain in Mg²⁺ binding together with the impact of NT substitutions on gating and the apparent state-dependence of Mg²⁺ binding, this study suggests that the NT domain can be an integral part of Mg²⁺ modulation of Cx36 GJs likely through the coupling of conformational changes between NT and E1 domains.