Phase space plots.

<p>Phase space plots of the simulations in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g005" target="_blank">Fig. 5</a>. As in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g004" target="_blank">Fig. 4</a> panels (<b>a</b>) and (<b>b</b>) contain plots of the membrane potentials, in panels (<b>c</b>) and (<b>d</b>) extracellular potassium is shown. (<b>a</b>) and (<b>c</b>) are for the reduced model, (<b>b</b>) and (<b>d</b>) for the detailed model. The trajectories of the reduced model are represented as red curves, those of the detailed model are magenta. The sections of the trajectories that belong to times before and during the stimulation are dashed. The fixed point curves from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g004" target="_blank">Fig. 4</a> are added on the plots as shaded lines whereas the fixed point continuations for the unbuffered models with dynamical chloride are slightly darker. The pair of arrows in the extracellular potassium plots indicates the direction of pure transmembrane (vertical) and pure buffering dynamics (diagonal).</p

Time series.

<p>Time series for three types of oscillatory dynamics in the bath coupled reduced model. In the left panels (<b>a</b>), (<b>c</b>) and (<b>e</b>) the membrane potential and the three Nernst potentials are shown. Ion concentrations are shown in the right panels (<b>b</b>), (<b>d</b>) and (<b>f</b>). The color code is as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g005" target="_blank">Fig. 5</a>. (<b>a</b>) and (<b>b</b>), (<b>c</b>) and (<b>d</b>), and (<b>e</b>) and (<b>f</b>) are simulations for , and , respectively. The dynamics is typical for (<b>a</b>) and (<b>b</b>) seizure–like activity, (<b>c</b>) and (<b>d</b>) tonic firing, (<b>e</b>) and (<b>f</b>) periodic SD. Note the different time scales of SLA, tonic firing and period SD and also the different oscillation amplitudes in the ionic variables.</p

Retinal SD wave segment propagating (blue arrows) with free open ends that grow (red arrow) and therefore curl in to form a double spiral.

<p>At lower susceptibility values, reaction-diffusion models of SD predict that open ends retract (green arrows) and the wave vanishes.</p

Bifurcation diagram.

<p>Different representations of the bifurcation diagram of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g008" target="_blank">Fig. 8</a>. Panel (<b>a</b>) shows the extracellular sodium concentration and includes an inset around TR4 and PD. Panel (<b>b</b>) presents the potassium gain/loss.</p

Typical propagation pattern of a visual migraine aura.

<p>(a) Right visual hemifield (dotted polar grid) with five subsequent sketched “snapshots” of a traveling visual migraine aura symptom in the shape of a crescent pattern. Numbers inside the scotom gives the time passed (in minutes) since first occurrence. Data is taken from Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0005007#pone.0005007-Lashley1" target="_blank">[1]</a> (b) Visual field disturbance shown by reversed retinotopic mapping projecting the affected area onto a flat model of the primary visual cortex.1.</p

Parameters for ion–based model.

<p>Parameters for ion–based model.</p

Time series.

<p>Time series for single SD excursions in (<b>a</b>), (<b>c</b>) the reduced and in (<b>b</b>), (<b>d</b>) the detailed model. In the reduced model SD is triggered by an interruption of the pump activity for about 10 sec (shaded region). In the detailed model the extracellular potassium concentration is increased by mM after 20 sec (vertical line). In (<b>a</b>) and (<b>b</b>) the time series of the membrane potentials (black lines) are shown. Nernst potentials for all ion species are included to the diagrams as a reference. Ion dynamics are shown in (<b>c</b>) and (<b>d</b>) where extracellular ion concentrations are in lighter color.</p

Bifurcation diagram.

<p>Bifurcation diagram of the model from Kager et al. (cf. last paragraph of Sect. Models). Like in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g002" target="_blank">Fig. 2</a> panel (<b>a</b>) shows the membrane potential and panel (<b>b</b>) shows the extracellular potassium concentration of the invariant sets, i.e., fixed points and limit cycles. The line style convention (solid for stable, dashed for unstable) and bifurcation labels are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g002" target="_blank">Fig. 2</a>. Note the similar shape to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#pcbi-1003941-g002" target="_blank">Fig. 2</a>, but also the different scale of the two figures.</p

Schematic view of the spatio-temporal course of a reaction-diffusion wave for different tissue susceptibility values σ: wave front (red), recovery phase (yellow), blue arrows indicate normal velocity, future location is dashed (red).

<p>(a) sustained wave, (b) retracting wave, indicated by green arrow heads, (c) collapsing wave, (d) no spread. The gray σ interval is defined as weakly susceptible.</p

Bifurcation diagram.

<p>Fundamental bifurcation diagram in the slowest–scale dynamics, the potassium ion gain or loss through reservoirs (i.e., the bifurcation parameter). The unit of the bifurcation parameter was chosen such that it denotes the ion concentration with respect to the extracellular volume. The actual extracellular potassium concentration is the order parameter. Shown are the stable branches and (see Sec. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003941#s3" target="_blank">Results</a>) and the directions (arrows) of two paths of ‘pure’ flux condition: fluxes exclusively across the membrane and fluxes exclusively from (or to) reservoirs. A horizontal path is caused by a particular mixture of these fluxes that induces potassium ion concentration changes exclusively to the intracellular compartment. Ionic excitability can be understood as a cyclic process in this diagram (see text).</p