Fig 1.
(a) A schematic of the single neuronal model dynamics. (b) The concept of undershoot is proposed here, with the total surface area of the undershoot estimated (gray area). The duration of the undershoot (“time of return”) corresponds to the time needed for [K+]o to recover to the basal level after the end of the stimulation. (c) The time series of extracellular K+ concentration after different sine stimulation periods when Kir4.1 channels are in controlled states, such as 30 s, 10 s, 100 ms, from simulation results (left) and experiments interpolated for comparison (right) from Fig 3 in Chever O et al [35]. (d) K+ concentration in the extracellular space ([K+]o) and astrocyte ([K+]A) response to Kir4.1 channel in controlled and blocked states during and after 10 s sine stimulus spike. Simulation results (1); experiments correspond to results interpolated from Fig 7 in Ballanyi K et al [36]. For other parameter values, see Table 1. In addition, ɛ = 1.2/s-1 and Kbath = 4 mM.
Fig 2.
Decreased astrocytic Kir4.1 channel conductance gkir induces spontaneous periodic epileptic seizures in the absence of external stimuli.
Time trains of the neural and astrocytic membrane potential (VN (mV)) and extracellular K+ concentration ([K+]o) (black lines); membrane potential VA (mV) and K+ concentration ([K+]A) for astrocyte (red lines) when gkir is 45.0 pS (a) and 5.0 pS (b), found from the equations presented in the model section. Kbath = 8 mM, and other parameters used are the same as in Fig 1.
Fig 3.
A conceptual diagram of the gap junction-mediated astrocytic-neural network model.
Fig 4.
(a) The decay factor t1/e is proposed here. (b) A schematic diagram of extracellular K+ concentration ([K+]o) and the decay factors t1/e as published in experimental results (see Fig. 5B from [17]). Black spots and gray spots are experimental data obtained from connexin30-/- rats and control gap junction rats, respectively. (c) The relationship between extracellular K+ concentration and decay factor t1/e in control conditions or the gap junction-deficient state. The dashed lines and solid lines denote experimental fitted curves (see Fig. 5B from [17]) and fitted curves from numerical simulation data, respectively. (d) Statistical error for experimental and numerical fitted curves for different strengths of gap junctions. (e) K+ undershoot in the extracellular space with different gap junction strengths after the same external stimuli sequence. Other parameters used are the same as in Fig 1.
Table 1.
Model parameters.
Fig 5.
(a) Decreased gap junction strength F induces spontaneous periodic epileptic seizures in the absence of external stimuli. Normal discharge states of neurons when F is 20.0; periodic spontaneous seizures present at 50 s when F is 8.0 and at 24 s when F is 0.01. Experimental dual recordings of membrane potential at a 100 μm depth within hippocampal slices in the brain (data from [41,42]) (b) Schematic relationship of gap junction strength F and extracellular K+ concentration ([K+]o) or the decay factors t1/e. Other parameters used are the same as in Fig 2.