Gap junctions (GJs) are direct intercellular cytoplasmic connections permeable to ions, small molecules (< 1 kDa), and hydrophilic molecules (e.g., ATP, glucose triphosphate inositol), which are formed by two juxtapositing hemi-channels present on membranes of adjacent cells. Each of these hemi-channels or connexons, is com- posed of six connexin (Cx) subunits (arranged circularly around a central pore), of which there are 21 types, classified by molecular weight. The central nervous system (CNS) is extensively coupled by 11 different types of GJs expressed on most brain cell types, which can be joined either homo- or heterocellularly. It is evident that gap junctions are largely present in glia, especially astrocytes, however, there are also several reports of gap junctional coupling of interneurons. Cx43 in astrocytes, and Cx36 in neurons are two of the most well-studied connexin proteins. In addition to forming the GJ pore as a duo, unapposed connexons can also be present on membranes. These hemichannels, which remain closed under physiological condition to retain ion gradients and membrane integrity, have been known to open during metabolic inhibition and could exacerbate neuronal injury.
Various gating systems are in place to finely regulate GJ permeability in the short and long-term: voltage, phosphorylation, intracellular calcium and pH, adhesion proteins, extracellular matrix, and hormones. A variety of electrophysiological and imaging techniques have been used to measure channel characteristics of GJs including dye-transfer techniques (e.g., uorescence recovery after photobleaching [FRAP], microinjection) and conductance measurements by dual patch clamp.
GJs have been described as “fast-track intercellular communication routes" because of their ability to connect various cell types in order to establish a cytoplasmic continuum between them. In the heart, GJs form pores between cardiomyocytes and play a major role in propagating the cardiac action potential to adjacent cells within the required time-scale. In the CNS, GJs not only intercellular couple together neurons, astrocytes, oligodendrocytes, and ependymal cells, but there is also evidence of neuron-astrocyte and astrocyte-oligodendrocyte coupling.
Connexin genes and their corresponding proteins are named according to the molecular weight of different connexin proteins (e.g., Cx43 has a mass of 43 kilodaltons). The molecular topography of connexin proteins includes four alpha-helical transmembrane domains, intracellular N- and C- termini, two extracellular loops, and a cytoplasmic loop. There are two to three cysteine residues located in the extracellular loops, which are needed for the proper alignment of two connexons to form a continuous gap junction channel. The cytoplasmic C-terminus carries several serine, threonine, and tyrosine residues, which serve as targets for a number of protein kinases and phosphatases for posttranslational modifications. To date more than 20 different connexin genes have been identified and are expressed in many different cells and tissues in mammals.
The direct cell-to-cell communication in most vertebrate animals is accomplished through structures that line the cell membrane called gap junctions. Gap junctions are channel proteins that are composed of two half-channels (referred to as connexons) embedded in the cell membrane of adjacent cells. Each connexon is composed of six connexins, proteins that are arranged in such a way to form a pore-like structure. The linkage of connexons on adjacent cells to form gap junctions promotes the electrical coupling of cells by allowing an avenue through which charged ions may diffuse between cells.
Gap-junction coupling is thought to be the primary mechanism that allows for the propagation of the cardiac action potential, although recent experiments and modeling efforts have shown that the influence of local electric fields can also have a coupling effect on nearby cells, especially in cases where the number of gap junctions are low due to diseased state. This mode of coupling, known as ephaptic coupling, is an area of active research.
The voltage-induced changes in intracellular ionic concentrations during the onset of an action potential in cell x provide the species available to form the gap-junctional coupling current, Ij, with adjacent cell y. Ij subsequently raises the cell-membrane voltage in cell y to the threshold, which promotes the conformation of sodium channels to the open state, initializing the fast inward sodium current and resulting in the depolarization phase of the action potential.
It has been shown that at least two distinct current-producing modes, referred to as the open state and the residual state, exist for each connexon. This conception is a simplification of the actual gating dynamics of gap junctions, as it has been shown that each of the six connexin proteins comprising the connexon serve as sub-gates and a much larger number of distinct gating modes exist. In this context, gating mode refers to the channel’s particular conformation among a discrete number of possibilities. The geometry of the channel alters which ionic species are permitted to travel through and as a result its conductive properties. It has also been shown in numerous experiments that the gating dynamics of connexons, and thus gap junctions, are functions of the local gap-junctional voltage gradient.
Despite the importance of gap junctions in cardiac electrophysiology, relatively few mathematical models have been constructed to describe their gating dynamics, as many cardiac action potential models approximate the behavior with constant intercellular resistance values or smooth out their influence with continuous tissue approximation models derives a gap junction model describing the dynamics of gap junctions in ventricular myocardium cells. The conductances of each hemi-channel are derived by conceptualizing the two connexons as a series circuit experiencing a constant gap-junctional voltage Vj The rate parameters of the dynamical system governing gating proportions are modeled as exponentially decaying functions of the local voltage across each connexon. The local gap junction current, Ij, is then computed as the product of the proportion of gap junctions in each of the four gating modes and the associated conductance. The model put forth in aims to describe the propagation of an action potential along a 1D cable model with a voltage-dependent description of gap-junction gating. The model uses the voltage-dependent dynamic gating model from to compute the coupling current Ij and models the intracellular currents using the well known Luo-Rudy I model.