Stochastic Model of Gap Junctions Exhibiting Rectification and Multiple Closed States of Slow Gates.

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.

Intracellular magnesium-dependent modulation of gap junction channels formed by neuronal connexin36.

Gap junction (GJ) channels composed of Connexin36 (Cx36) are widely expressed in the mammalian CNS and form electrical synapses between neurons. Here we describe a novel modulatory mechanism of Cx36 GJ channels dependent on intracellular free magnesium ([Mg(2+)]i). We examined junctional conductance (gj) and its dependence on transjunctional voltage (Vj) at different [Mg(2+)]i in cultures of HeLa or N2A cells expressing Cx36. We found that Cx36 GJs are partially inhibited at resting [Mg(2+)]i. Thus, gj can be augmented or reduced by lowering or increasing [Mg(2+)]i, respectively. Similar changes in gj and Vj-gating were observed using MgATP or K2ATP in pipette solutions, which increases or decreases [Mg(2+)]i, respectively. Changes in phosphorylation of Cx36 or in intracellular free calcium concentration were not involved in the observed Mg(2+)-dependent modulation of gj. Magnesium ions permeate the channel and transjunctional asymmetry in [Mg(2+)]i resulted in asymmetric Vj-gating. The gj of GJs formed of Cx26, Cx32, Cx43, Cx45, and Cx47 was also reduced by increasing [Mg(2+)]i, but was not increased by lowering [Mg(2+)]i; single-channel conductance did not change. We showed that [Mg(2+)]i affects both open probability and the number of functional channels, likely through binding in the channel lumen. Finally, we showed that Cx36-containing electrical synapses between neurons of the trigeminal mesencephalic nucleus in rat brain slices are similarly affected by changes in [Mg(2+)]i. Thus, this novel modulatory mechanism could underlie changes in neuronal synchronization under conditions in which ATP levels, and consequently [Mg(2+)]i, are modified.

Stochastic 16-state model of voltage gating of gap-junction channels enclosing fast and slow gates.

Gap-junction (GJ) channels formed of connexin (Cx) proteins provide a direct pathway for electrical and metabolic cell-cell interaction. Each hemichannel in the GJ channel contains fast and slow gates that are sensitive to transjunctional voltage (Vj). We developed a stochastic 16-state model (S16SM) that details the operation of two fast and two slow gates in series to describe the gating properties of homotypic and heterotypic GJ channels. The operation of each gate depends on the fraction of Vj that falls across the gate (VG), which varies depending on the states of three other gates in series, as well as on parameters of the fast and slow gates characterizing 1), the steepness of each gate's open probability on VG; 2), the voltage at which the open probability of each gate equals 0.5; 3), the gating polarity; and 4), the unitary conductances of the gates and their rectification depending on VG. S16SM allows for the simulation of junctional current dynamics and the dependence of steady-state junctional conductance (gj,ss) on Vj. We combined global coordinate optimization algorithms with S16SM to evaluate the gating parameters of fast and slow gates from experimentally measured gj,ss-Vj dependencies in cells expressing different Cx isoforms and forming homotypic and/or heterotypic GJ channels.

pH-dependent modulation of connexin-based gap junctional uncouplers.

Gap junction (GJ) channels formed from connexin (Cx) proteins provide a direct pathway for electrical and metabolic cell­cell communication exhibiting high sensitivity to intracellular pH (pH(i)). We examined pH(i)-dependent modulation of junctional conductance (g(j)) of GJs formed of Cx26, mCx30.2, Cx36, Cx40, Cx43, Cx45, Cx46, Cx47 and Cx50 by reagents representing several distinct groups of uncouplers, such as long carbon chain alkanols (LCCAs), arachidonic acid, carbenoxolone, isoflurane, flufenamic acid and mefloquine. We demonstrate that alkalization by NH4Cl to pH ∼8 increased g(j) in cells expressing mCx30.2 and Cx45, yet did not affect g(j) of Cx26, Cx40, Cx46, Cx47 and Cx50 and decreased it in Cx43 and Cx36 GJs. Unexpectedly, cells expressing Cx45, but not other Cxs, exhibited full coupling recovery after alkalization with NH4Cl under the continuous presence of LCCAs, isoflurane and mefloquine. There was no coupling recovery by alkalization in the presence of arachidonic acid, carbenoxolone and flufenamic acid. In cells expressing Cx45, IC50 for octanol was 0.1, 0.25 and 2.68 mm at pH(i) values of 6.9, 7.2 and 8.1, respectively. Histidine modification of Cx45 protein by N-bromosuccinimide reduced the coupling-promoting effect of NH4Cl as well as the uncoupling effect of octanol. This suggests that LCCAs and some other uncouplers may act through the formation of hydrogen bonds with the as-of-yet unidentified histidine/s of the Cx45 GJ channel protein.

A stochastic four-state model of contingent gating of gap junction channels containing two "fast" gates sensitive to transjunctional voltage.

Connexins, a family of membrane proteins, form gap junction (GJ) channels that provide a direct pathway for electrical and metabolic signaling between cells. We developed a stochastic four-state model describing gating properties of homotypic and heterotypic GJ channels each composed of two hemichannels (connexons). GJ channel contain two "fast" gates (one per hemichannel) oriented opposite in respect to applied transjunctional voltage (V(j)). The model uses a formal scheme of peace-linear aggregate and accounts for voltage distribution inside the pore of the channel depending on the state, unitary conductances and gating properties of each hemichannel. We assume that each hemichannel can be in the open state with conductance gamma(h,o) and in the residual state with conductance gamma(h,res), and that both gamma(h,o) and gamma(h,res) rectifies. Gates can exhibit the same or different gating polarities. Gating of each hemichannel is determined by the fraction of V(j) that falls across the hemichannel, and takes into account contingent gating when gating of one hemichannel depends on the state of apposed hemichannel. At the single-channel level, the model revealed the relationship between unitary conductances of hemichannels and GJ channels and how this relationship is affected by gamma(h,o) and gamma(h,res) rectification. Simulation of junctions containing up to several thousands of homotypic or heterotypic GJs has been used to reproduce experimentally measured macroscopic junctional current and V(j)-dependent gating of GJs formed from different connexin isoforms. V(j)-gating was simulated by imitating several frequently used experimental protocols: 1), consecutive V(j) steps rising in amplitude, 2), slowly rising V(j) ramps, and 3), series of V(j) steps of high frequency. The model was used to predict V(j)-gating of heterotypic GJs from characteristics of corresponding homotypic channels. The model allowed us to identify the parameters of V(j)-gates under which small changes in the difference of holding potentials between cells forming heterotypic junctions effectively modulates cell-to-cell signaling from bidirectional to unidirectional. The proposed model can also be used to simulate gating properties of unapposed hemichannels.

Reverberation of excitation in neuronal networks interconnected through voltage-gated gap junction channels.

We combined Hodgkin-Huxley equations and gating models of gap junction (GJ) channels to simulate the spread of excitation in two-dimensional networks composed of neurons interconnected by voltage-gated GJs. Each GJ channel contains two fast and slow gates, each exhibiting current-voltage (I-V) rectification and gating properties that depend on transjunctional voltage (Vj). The data obtained show how junctional conductance (gj), which is necessary for synchronization of the neuronal network, depends on its size and the intrinsic firing rate of neurons. A phase shift between action potentials (APs) of neighboring neurons creates bipolar, short-lasting Vj spikes of approximately ± 100 mV that induce Vj gating, leading to a small decay of gj, which can accumulate into larger decays during bursting activity of neurons. We show that I-V rectification of GJs in local regions of the two-dimensional network of neurons can lead to unidirectional AP transfer and consequently to reverberation of excitation. This reverberation can be initiated by a single electrical pulse and terminated by a low-amplitude pulse applied in a specific window of reverberation cycle. Thus, the model accounts for the influence of dynamically modulatable electrical synapses in shaping the function of a neuronal network and the formation of reverberation, which, as proposed earlier, may be important for the development of short-term memory and its consolidation into long-term memory.

Application of stochastic automata networks for creation of continuous time Markov chain models of voltage gating of gap junction channels.

The primary goal of this work was to study advantages of numerical methods used for the creation of continuous time Markov chain models (CTMC) of voltage gating of gap junction (GJ) channels composed of connexin protein. This task was accomplished by describing gating of GJs using the formalism of the stochastic automata networks (SANs), which allowed for very efficient building and storing of infinitesimal generator of the CTMC that allowed to produce matrices of the models containing a distinct block structure. All of that allowed us to develop efficient numerical methods for a steady-state solution of CTMC models. This allowed us to accelerate CPU time, which is necessary to solve CTMC models, ~20 times.