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

Abstract

Gap junction (GJ) channels, formed of connexin (Cx) proteins, provide a direct pathway for metabolic and electrical cell-to-cell communication. These specialized channels are not just passive conduits for the passage of ions and metabolites, but have been shown to gate robustly in response to transjunctional voltage, Vj, the voltage difference between two coupled cells and are regulated by various chemical factors. Voltage gating of GJs may play a physiological role, particularly in excitable cells which can exhibit large transients in membrane potential during the generation of an action potential. We present a mathematical/computational model of GJ channel voltage gating to assess properties of GJ channels that takes into account contingent gating of two series hemichannels and the distribution of Vj across each hemichannel. From electrophysiological recordings in cell cultures transfected with Cx43 and Cx45, isoforms that are expressed in cardiac tissue, data sets were fit simultaneously using global optimization. The results showed that the model is capable of describing both steady-state and kinetic properties of homotypic and heterotypic GJ channels composed of these connexins. Moreover, mathematical analyses showed that the model can be simplified to a reversible two-state system and solved analytically, using a rapid equilibrium assumption. Given that excitable cells are arranged in interconnected networks, the equilibrium assumption allows for a substantial reduction in computation time, which is useful in simulations of large clusters of coupled cells. Overall, this model can serve not just as a modeling tool, but also to provide a means of testing GJ channel gating behavior. SignificanceGap junction (GJ) channels gate in response to transjunctional voltage which provides the capacity for dynamic regulation of intercellular coupling. Kinetic properties of GJs in modeling studies have been infrequently addressed and we present a computational model of voltage gating that can account for both kinetic and steady-state changes in junctional conductance, gj. Although GJs possess two gating mechanisms, our analysis indicates that changes in gj for each voltage polarity can be adequately described by a kinetic scheme describing a single mechanism in each of the hemichannels, suggesting functional dominance of one mechanism over a substantial voltage range. This property allowed for model simplification that can be applied for efficient simulation of sizeable cell clusters and analyses of electrophysiological data.

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

“…Simulations using parameters for these channels obtained from fits to the data in Figure 4 are shown in Figures 5C,D . Because rate constants k 1 and k 2 can be interpreted as opening and closing rates of V j -dependent gating, it follows from our previously published V j -gating model ( Snipas et al, 2020 ) that the values of k 1 and k 2 of a hemichannel should increase or decrease exponentially with V j (depending on the sign of V j and V j -gating polarity of Cx isoform) during the application of V j ramp. The black solid lines ( Figures 5C,D ) show the predicted changes in g j over time when a V j ramp is applied with the channels exposed to symmetric 5 mM Mg 2+ conditions.…”

“…Such stochastic gating was demonstrated for Cx26 hemichannels for which single channel data is available ( Sanchez et al, 2013 ). Modeling of data using our recently published gating model, 4SM, that takes into account contingent gating of two series hemichannels and the distribution of Vj across each hemichannel ( Snipas et al, 2020 ) indicates that such stochastic gating at V j = 0 mV would be sufficient to drive a Mg 2+ -dependent reduction in g j caused by Mg 2+ binding to the closed state. Moreover, as mentioned in the results, the estimated values of model parameters k 1 and k 2 of different variants correlated well with the observed changes in V j sensitivity at high Mg 2+ concentrations.…”

Conductance heterogeneities induced by multistability in the dynamics of coupled cardiac gap junctions

“…These more complex models are based on a Markov formalism from 4 up to 16 states. 21,33,34 In those models, the transition probabilities depend on the intercellular potential. The conductance is then obtained as the average of a stochastic ensemble of GJs.…”

“…Detailed models of gap junction dynamics usually consider several open and closed configurations of the connexins that compose the gap junctions. 21,33,34 However, the physical meaning of the factor of shrinking, FS, can be better understood assuming a simple twostate system of high and low conductance. Then, we can consider an effective free energy difference between these two states that depends on the intercellular potential as follows:…”

Diversity in connexin biology

“…In addition to GJIC being regulated by channel composition, channels are further governed by gating mechanisms in response to changes in pH, voltage, ion concentrations, protein interactions, phosphorylation states, and other mechanisms ( 52 , 61 , 62 ). GJ channel gating mechanisms have been discussed extensively elsewhere ( 63 , 64 , 65 , 66 , 67 , 68 ). Given the extensive number of family members, oligomeric combinations, and regulatory mechanisms, it is not surprising that from an evolutionary standpoint connexins are well positioned to support a multitude of essential cellular functions.…”