Fig 1.
A) Schematic of gap junction channel enclosing fast (blue arrows) and slow (red arrows) gates and their gating transitions. The fast gate can be in the open (o) or closed (c) states. The closed state of the fast gate exhibits residual conductance. The slow gate can reside in open (o) or in one of two fully closed states: initial-closed (c1) or deep-closed (c2). Gating probabilities depend on the transjunctional voltage (Vj), which is evaluated as a difference between membrane voltages of two adjacent cells (V1 and V2). B) Schematic of four gates arranged in series in a gap junction channel. Voltage distribution across each gate depends on their unitary conductances, which can rectify.
Fig 2.
Conductance–voltage (gj–Vj) rectification in the 36SM.
(A) Emerging rectification curves of homotypic gap junction; in this case, rectification coefficients on the left and right hemichannels were equal but of opposite signs, RL = –RR. (B) The gj–Vj relationships of heterotypic gap junction; gj asymmetry at opposite Vj polarities was obtained by setting RR to a very large value (106 mV), while RL was varied as in (A). The gj values were normalized at Vj = 0 mV.
Fig 3.
Asymmetry of electrical coupling between two neurons with different input resistances, Rin,1 and Rin,2.
A) An electrical scheme of two cells connected through soma-somatic gap junctions. Membrane voltages of cell-1 and cell-2 (V1 and V2) are described by Hodgkin–Huxley equations (HH). Junctional conductance (gj) depends on transjunctional voltage (Vj) and is estimated from the 36-state model (36SM) of gap junction channel gating. An external current (Iext) can be applied to either of the cells. B–C) Simulated changes of transmembrane potential (Vm) in cell-1 and cell-2 during the external current step of –100 pA applied to cell-1 (B) or cell-2 (C); here Rin,1/Rin,2 = 2 and the junctional conductance (gj) was equal to 4 nS. D) The dependence of coupling asymmetry, K2-1/K1-2, on the ratio of input resistances, Rin,1/Rin,2, at different gjs; here K1-2 = V2/V1 and K2-1 = V1/V2.
Fig 4.
Asymmetry of AP transfer between neurons with different input resistances, Rin,1 and Rin,2.
A) AP transfer was almost 2-fold longer when a short (1 ms) external stimulus of 250 pA was applied to cell-1 (A-a) than to cell-2 (A-b); Rin,1/Rin,2 = 1.5. B) Unidirectional transfer of APs caused by repeated short stimuli between cells with Rin,1/Rin,2 = 2. In A and B, junctional conductance gj was equal to 1 nS. C) Delays between APs depending on Rin,1/Rin,2 at different gjs. Solid and dashed curves were obtained when neurons with higher and lower Rin were stimulated, respectively.
Fig 5.
Asymmetry of transjunctional transfer of APs through electrical synapses caused by gap junction channel rectification.
A–B) Delays between APs transferred through an electrical synapse composed of rectifying channels (RL = 20 mV). Short external stimuli of 250 pA were applied to cell-1 (A) and cell-2 (B). A-a and B-a show voltages in cell-1 (red) and cell-2 (blue), V1 and V2, respectively. Dashed lines show transjunctional voltage spikes (Vj); Vj = V2 –V1. A-b and B-b show resulting changes of junctional conductance (gj). C) Dependence of a delay between APs during anterograde (from cell-1 to cell-2; solid curves) and retrograde (dashed curves) excitation transfer on rectification of gap junctions. D) Dependence of electrotonic coupling asymmetry, K2-1/K1-2, on rectification coefficient, RL.
Fig 6.
Dynamic changes of junctional conductance depend on voltage sensitivity of gap junctions and neuronal spiking activity.
A-a) A decay of junctional conductance, gj, during neuronal spiking activity. The grey horizontal line shows the time interval of stimulation using periodic (70 Hz) depolarizing stimuli of 250 pA in amplitude and 1 ms in duration. Left inset shows the developed transmembrane voltages (Vm) in presynaptic (blue) and postsynaptic (red) cells, while the right inset shows junctional conductance decrease at enhanced resolution. A-b) The same as in A-a, but in a more voltage-sensitive electrical synapse. Voltage sensitivity of the gap junction was enhanced by lowering the deep-closed transition probability pc2→c1 from 0.001 to 0.0001. The left inset in A-b shows that transfer of APs alternates due to decreased gj. B) The same as in A, but applied stimuli were distributed randomly according to the Poisson law with 55 Hz rate. In B-a, pc2→c1 = 0.001, while pc2→c1 = 0.0001 in B-b.
Fig 7.
Changes of junctional conductance in HeLa cells expressing Cx45 during bipolar and monopolar stimulation.
A) Junctional current (Ij) and conductance (gj) records obtained in response to repeated bipolar voltage (Vj) stimuli of –85 and +85 mV in amplitude; amplitude and duration of voltage spikes and current responses can be seen in the insets. B) The same as in (A) but unipolar –85 mV instead of bipolar stimuli were applied. Insets (grey background) above 7A and B show applied Vj stimuli and registered Ij values at enhanced resolution. The values of gj were estimated from gj = Ij/Vj.
Fig 8.
Neuronal activity-dependent changes of junctional conductance in heterotypic gap junctions.
A) Simulated steady-state conductance–voltage (gj,st–Vj) relationship of heterotypic gap junctions that resembles experimentally measured gj,st–Vj relationship of Cx43/Cx45 gap junctions. B shows the transfer of action potentials when the cell, virtually expressing Cx45, was stimulated. B-a) Records of membrane voltage responses in cell-Cx45 (blue trace) and cell-Cx43 (red trace). B-b) Transjunctional voltage (Vj) spikes developed in the electrical synapse. B-c) Changes of junctional conductance (gj) caused by the spiking activity of neurons. C-a,b,c) The same as in B-a,b,c, but a cell, virtually expressing Cx43, was stimulated.
Fig 9.
Simulation of [Mg2+]i–mediated changes of junctional conductance (black traces) measured in RIN cells expressing Cx36.
A) [Mg2+]i decreased from 1 to 0.01 mM. The fitted junctional conductance (gj) kinetics (red trace) was obtained at ~4.5-fold V0 increase and ~1000-fold pc1→c2 decrease. Blue traces and the right Y axis show the fraction of closed gap junction channels in which at least one slow gate is in a deep-closed state (solid blue trace). B) The same as in A, but [Mg2+]i increased from 1 to 5 mM. The fitted red trace was obtained when V0 decreased ~2 fold, while pc1→c2 rose from 0.7 to 0.95. In both A and B, gj values were normalized at [Mg2+]i = 1 mM.
Fig 10.
The simulated effect of intracellular free magnesium ion concentration ([Mg2+]i) on junctional conductance and the spread of excitation through electrical synapse formed of Cx36.
A) Simulated kinetics of junctional conductance (gj) of electrical synapse formed of Cx36 under different levels of [Mg2+]i. The parameters of 36SM at [Mg2+]i = 0.8 and 1.2 mM were approximated from optimized values, as presented in S2 Text and S2 Fig. The values of gj were normalised at [Mg2+]i = 1.0 mM. B) The resulting responses between two coupled neurons at steady-state gj reached at [Mg2+]i = 0.8, 1.0 and 1.2 mM. At [Mg2+]i = 0.8 mM, ~2.2-fold increased junctional conductance (~2.2 nS) was sufficient to invoke a postsynaptic response (red curves) to each AP in the presynaptic cell (blue curves). The spread of APs was not disturbed by voltage-gating induced gj decrease (see the upper inset in 10B). At [Mg2+]i = 1.0 mM, the steady-state gj value of ~1 nS was sufficient to transfer each AP initially, but the decreased gj caused a 2-fold lower firing rate in the postsynaptic cell, as compared with [Mg2+]i = 0.8 mM. At [Mg2+]i = 1.2 mM, junctional conductance is decreased ~2.5 fold. Such synaptic strength could only invoke an electrotonic response in the postsynaptic cell.