Modeling of the glutamate and GABA cycles according to the experimental literature.

<p>(A) Main physiological principles of glutamate and GABA cycles are glutamate and GABA releases by pyramidal cells and interneurons respectively, glutamate uptake by astrocytes and GABA uptake by both neurons and astrocytes (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.s005" target="_blank">S1 File</a>). (B) The glutamate release (solid line) from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.e009" target="_blank">Eq 9</a> matches the experimental impulse response (circles) depicted in Fig 4 in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.ref040" target="_blank">40</a>] for the parameter set {<i>W</i> = 0.59, <i>w</i>_<i>1</i> = 90, <i>w</i>_<i>2</i> = 33}. (C) Comparison between the simulated glutamate uptake from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.e011" target="_blank">Eq 11</a> and Michaelis-Menten representations {<i>V</i>_<i>M</i>, <i>K</i>_<i>M</i>} obtained from the experimental literature and converted to the same unit (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.t001" target="_blank">Table 1</a>). The Michaelis-Menten representations are numbered according to the experimental literature with 1: {<i>V</i>_<i>M</i> = 9.5, <i>K</i>_<i>M</i> = 91} for [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.ref042" target="_blank">42</a>]; 2a: {<i>V</i>_<i>M</i> = 4.2, <i>K</i>_<i>M</i> = 18.6}, 2b: {<i>V</i>_<i>M</i> = 4.8, <i>K</i>_<i>M</i> = 37}, 2c: {<i>V</i>_<i>M</i> = 2, <i>K</i>_<i>M</i> = 16} for [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.ref044" target="_blank">44</a>]; 4a: {<i>V</i>_<i>M</i> = 6.8, <i>K</i>_<i>M</i> = 18.9}, 4b: {<i>V</i>_<i>M</i> = 1.5, <i>K</i>_<i>M</i> = 54.9} for [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.ref045" target="_blank">45</a>]. Setting parameters of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.e011" target="_blank">Eq 11</a> to {<i>V</i>_<i>mg</i> = 5, <i>r</i>_<i>g</i> = 0.5, <i>s</i>_<i>g</i> = 9} led to a sigmoid function (solid line), which was close to the experimental measures for the usual physiological values of extracellular glutamate concentration (below 10 <i>μM</i>). (D) Comparison between Michaelis-Menten responses of the GABA uptake from Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.e015" target="_blank">15</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147292#pone.0147292.e016" target="_blank">16</a> with {<i>V</i>_<i>m1</i> = 5, <i>K</i>_<i>m1</i> = 24} for GAT1 transport (neurons, in gray) and {<i>V</i>_<i>m1</i> = 2, <i>K</i>_<i>m1</i> = 8} for GAT3 transport (astrocytes, in black).