Fig 1.
Neurons and synaptic connections.
When a signal travels from the right to the left neuron along the axon, glutamate is released at the dendritic terminals. The terminals are separated from the neighboring neuron by the synaptic cleft. Signal transmission goes via release of the neurotransmitter glutamate. It binds to receptors on the postsynaptic neuron and can initiate new action potentials. The synaptic terminals are located at the dendrites of the receiving neuron. At the same time the right neuron can receive glutamate–mediated signals from other neurons through the dendritic terminals located near its own soma. The inset on the left shows additional details: glutamate is contained in vesicles and in the release process all molecules are released into the cleft at once. The inset on the right shows idealized geometry of the synapse considered in the model.
Fig 2.
Two variants of SD with intact glutamate clearance.
The left panels (a) and (c) show SD induced by perfusion with high K+, the right panels (b) and (d) are for OGD. The OGD protocol is indicated by the horizontal bar where the light sections at the beginning and the end indicate the smooth de– and reactivation of the regulatory functions. The figure shows all the familiar aspects of SD. In (a) and (b) the neuron depolarizes and the differences between Nernst potentials become very small. Depolarization is maintained for about 70 sec and ends with an abrupt repolarization drop after which the Nernst potentials slowly return to their initial values. Changes in ion concentrations in (c) and (d) correspond to the evolution of the potentials. There is, for example, a huge increase in extracellular K+ and a huge drop in extracellular Na+. The ion fluxes induce swelling of the glia cell and the neuron (see the insets), which result in shrinkage of the ECS. The time of de– and repolarization are marked by a red upward pointing and a green downward pointing triangle. These symbols will be used in the following figures to indicate these events.
Fig 3.
Glutamate dynamics for the simulations from Fig 2.
Panels (a) and (b) show a jump of the cleft glutamate concentration to about 15 mM when the neuron depolarizes. In the simulation of K+ perfusion we assume intact glutamate uptake at all times, and the high cleft concentration is brought back to a much lower level within 2 sec (see upper inset of (a)). There is a plateau concentration near 0.01 mM that is maintained as long as the neuron is depolarized, and is only cleared after repolarization (lower inset of (a)). There is no noticeable glutamate elevation in the ECS. In panel (b) we see different dynamics, because there is no glutamate clearance during OGD. The sharp jump in the cleft concentration also decays within 2 sec, but the concentration then settles to a much higher level of 5 mM (see upper inset). It keeps increasing slowly until glutamate clearance is slowly reactivated (see horizontal bar for the OGD protocol). The lower inset shows that glutamate is back to a very low level before the neuron repolarizes. The extracellular concentration goes up to more than 5 mM. When there is no glutamate clearance at all (center part of the OGD bar) the concentrations in the cleft and the ECS are equal because of diffusion. The lower panels show pathways of glutamate clearance. Glutamate that has been taken up from the cleft or the ECS by either the neuron or the glial cell, but has not yet been recycled, counts as buffered glutamate (see Eq 30). The main plots show glutamate clearance from the cleft, the inset show clearance from the ECS. For K+ perfusion, more glutamate is cleared directly from the cleft than from the ECS (see peak values in the main plot and inset of panel (c)). In the cleft, more glutamate is cleared by glia than by the neuron (compare the orange and the yellow portion of the total uptake from the cleft). In the ECS, this relation is even more pronounced (compare turquoise to blue in the second inset). In panel (d), glutamate clearance only sets in with the reactivation of regulatory functions at the end of the OGD protocol. Now more glutamate is cleared from the ECS, since there is more in the ECS than in the clefts. The relation between uptake by glia and neural uptake is consistent with (c) and Eqs (26) and (18).
Fig 4.
SD simulations with reduced uptake rates.
Panel (a) and (b) show SD for K+ perfusion with uptake rates reduced to 20% and 18% of the normal value from Table C in S1 Text. The plots show that repolarization and recovery are delayed and the delay is longer for more reduced glutamate uptake. The repolarization time with normal uptake is indicated by the vertical dashed line. Before repolarization, the system shows low amplitude membrane potential oscillations. Panel (c) shows the evolution of the glutamate concentration in the synaptic clefts during the two simulations. Delayed recovery correlates with slower glutamate clearance. Before repolarization, there are glutamate spikes because of the membrane potential oscillations. Panel (d) gives an overview of SD durations for reduced uptake rates. In our model, the effect becomes noticeable only for rates of 35% and less. Extreme durations can be up to 500 sec, and recovery fails for uptake rates of less than 16%.
Fig 5.
Phase space perspective of SD.
Panel (a) shows the evolution of slow variables. ΔNK takes extremum values at de– and repolarization. It is used as a bifurcation parameter to derive the fixed point structures in panel (b) that guide the trajectory in phase space. contributes to ΔNK and its evolution is also shown. The values at the two points of interest are indicated by colored X markers. The values are used to compute the fixed point structures that guide the dynamics near the de– and repolarization point in (b), respectively.
Fig 6.
Dependence of the fixed point structure on Gc.
Panel (a) shows the fixed point curves for three different Gc–values. The beginning of the polarized fixed point branch is shifted towards larger ΔNK–vaues as Gc increases. The depolarized and polarized branch only overlap for Gc = 0.02 mM. Scanning through all values of Gc from 0 to 0.3 mM and higher yields the red and green line indicating the beginning of the lower and the end of the upper stable fixed point branches. The green line is only a short curve connecting the triangle markers indicating the ends of the three upper fixed point branches. In panel (b) these curves are shown in the (Gc, ΔNK)–plane. As long as the lower branch begins before the upper branch ends, i.e. whenever the green curve is above the red curve, repolarization is possible. The critical value of intersection is near 0.032 mM and for higher values of Gc there is no recovery (shaded region).
Fig 7.
Membrane phase space near repolarization point.
Panel (a) shows the stable and unstable fixed points of the membrane model as ΔNK varies for extremely low Gc (set to 0.0001 mM as in Fig 2). There is a stable depolarized and a stable (hyper–)polarized state. At the repolarization point (triangle marker) the depolarized state becomes unstable. The trajectory is guided by the fixed point branches and gets close to the lower branch before ion concentrations adjust and the neuron approaches a level slightly above the lower branch. A de– and a hyperpolarized state close to but before repolarization are marked. The values are given in Table D in S1 Text. Panel (b) shows the potentials at the ends of the upper fixed point branches for all Gc–values between 0 and 0.05 mM. The other membrane fixed point states, stable hyperpolarization, and an unstable state, are also shown. The stable hyperpolarized state ceases to exist for Gc–values higher than 0.32 mM. Beyond this critical value repolarization is no longer possible (shaded region). The critical value is consistent with the value we have derived for the transmembrane model in Fig 6.
Fig 8.
Inhibitor of astrocytic glutamate transporters, TFB-TBOA, significantly increases the duration of SD.
Here we show the network and single cell properties of SD in control and TFB-TBOA treated groups. Representative time traces of membrane potential of individual pyramidal neurons (bottom trace) and network level (top trace) in layers 2-3 of visual cortex recorded using whole-cell patch clamp and extracellular recording techniques respectively in control (n = 9) and TFB-TBOA treated groups (n = 9) are shown in panels (a–c). (d-e) SD duration defined as the time from the initiation of rapid depolarization in individual neurons and network to the time when the membrane potential repolarizes to its pre-SD value. TFB-TBOA prolonged the duration of SD both at the network level (d) (n = 9, p<0.001) and single cell level (e) (n = 9, p<0.01).