Gap-junction (GJ) channels formed from connexin (Cx) proteins provide direct pathways for electrical and metabolic cell-cell communication. Earlier, we developed a stochastic 16-state model (S16SM) of voltage gating of the GJ channel containing two pairs of fast and slow gates, each operating between open (o) and closed (c) states. However, experimental data suggest that gates may in fact contain two or more closed states. We developed a model in which the slow gate operates according to a linear reaction scheme, o↔c1↔c2, where c1 and c2 are initial-closed and deep-closed states that both close the channel fully, whereas the fast gate operates between the open state and the closed state and exhibits a residual conductance. Thus, we developed a stochastic 36-state model (S36SM) of GJ channel gating that is sensitive to transjunctional voltage (Vj). To accelerate simulation and eliminate noise in simulated junctional conductance (gj) records, we transformed an S36SM into a Markov chain 36-state model (MC36SM) of GJ channel gating. This model provides an explanation for well-established experimental data, such as delayed gj recovery after Vj gating, hysteresis of gj-Vj dependence, and the low ratio of functional channels to the total number of GJ channels clustered in junctional plaques, and it has the potential to describe chemically mediated gating, which cannot be reflected using an S16SM. The MC36SM, when combined with global optimization algorithms, can be used for automated estimation of gating parameters including probabilities of c1↔c2 transitions from experimental gj-time and gj-Vj dependencies.

Connexin-36 (Cx36) protein forms gap junction (GJ) channels in pancreatic beta cells and is also the main Cx isoform forming electrical synapses in the adult mammalian brain. Cx36 GJs can be regulated by intracellular pH (pHi) and cytosolic magnesium ion concentration ([Mg2+]i), which can vary significantly under various physiological and pathological conditions. However, the combined effect and relationship of these two factors over Cx36-dependent coupling have not been previously studied in detail. Our experimental results in HeLa cells expressing Cx36 show that changes in both pHi and [Mg2+]i affect junctional conductance (gj) in an interdependent manner; in other words, intracellular acidification cause increase or decay in gj depending on whether [Mg2+]i is high or low, respectively, and intracellular alkalization cause reduction in gj independently of [Mg2+]i. Our experimental and modelling data support the hypothesis that Cx36 GJ channels contain two separate gating mechanisms, and both are differentially sensitive to changes in pHi and [Mg2+]i. Using recombinant Cx36 we found that two glutamate residues in the N-terminus could be partly responsible for the observed interrelated effect of pHi and [Mg2+]i. Mutation of glutamate at position 8 attenuated the stimulatory effect of intracellular acidification at high [Mg2+]i, while mutation at position 12 and double mutation at both positions reversed stimulatory effect to inhibition. Moreover, Cx36*E8Q lost the initial increase of gj at low [Mg2+]i and double mutation lost the sensitivity to high [Mg2+]i. These results suggest that E8 and E12 are involved in regulation of Cx36 GJ channels by Mg2+ and H+ ions.

We combined the Hodgkin–Huxley equations and a 36-state model of gap junction channel gating to simulate electrical signal transfer through electrical synapses. Differently from most previous studies, our model can account for dynamic modulation of junctional conductance during the spread of electrical signal between coupled neurons. The model of electrical synapse is based on electrical properties of the gap junction channel encompassing two fast and two slow gates triggered by the transjunctional voltage. We quantified the influence of a difference in input resistances of electrically coupled neurons and instantaneous conductance–voltage rectification of gap junctions on an asymmetry of cell-to-cell signaling. We demonstrated that such asymmetry strongly depends on junctional conductance and can lead to the unidirectional transfer of action potentials. The simulation results also revealed that voltage spikes, which develop between neighboring cells during the spread of action potentials, can induce a rapid decay of junctional conductance, thus demonstrating spiking activity-dependent short-term plasticity of electrical synapses. This conclusion was supported by experimental data obtained in HeLa cells transfected with connexin45, which is among connexin isoforms expressed in neurons. Moreover, the model allowed us to replicate the kinetics of junctional conductance under different levels of intracellular concentration of free magnesium ([Mg2+]i), which was experimentally recorded in cells expressing connexin36, a major neuronal connexin. We demonstrated that such [Mg2+]i-dependent long-term plasticity of the electrical synapse can be adequately reproduced through the changes of slow gate parameters of the 36-state model. This suggests that some types of chemical modulation of gap junctions can be executed through the underlying mechanisms of voltage gating. Overall, the developed model accounts for direction-dependent asymmetry, as well as for short- and long-term plasticity of electrical synapses. Our modeling results demonstrate that such complex behavior of the electrical synapse is important in shaping the response of coupled neurons.