Typical experimental and model findings on <i>I_h</i>.

<p><b>a</b>) simulation of ZD7288 application during a 0.33 nA somatic current injection: at <i>t</i> = 500 the <i>I_h</i> was blocked by resetting the peak conductance to 0; <b>b</b>) (<i>top</i>) increase in the dendritic firing rate after <i>I_h</i> upregulation following febrile seizures induction (adapted from Fig. 2A of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036867#pone.0036867-DyhrfjeldJohnsen2" target="_blank">[3]</a>); (<i>bottom</i>) simulation of <i>I_h</i> upregulation in febrile seizures; traces are dendritic recordings during a 500 ms current injection (0.4 nA at ∼280 µm), using a 3× increase in <i>g_{h_pk}</i> (from 0.01 mS/cm²) to obtain about the same depolarization (∼3 mV) and the same increase (∼3×) in the number of APs observed in the experiments; <b>c</b>) (<i>top</i>) experimental recordings demonstrating an increase in temporal summation at the soma during distal dendritic EPSPs after ZD2288 application (taken and redrawn from Fig. 1b of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036867#pone.0036867-Magee1" target="_blank">[22]</a>, with permission by Macmillan Publishers Ltd, copyright (1999)); simulation of EPSPs temporal summation during a 50 Hz train of 5 dendritic EPSPs activated under different conditions; the bars above the plots represent the timing of <i>I_h</i> block (modeling ZD7288 application), and a somatic current injection (0.11 nA) modeling the experimental protocol to restore the original membrane resting potential after ZD7288 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036867#pone.0036867-Magee1" target="_blank">[22]</a>; traces are somatic recordings during proximal (24 µm) or distal (500 µm) stimulation of the main trunk; peak synaptic conductances (1.7 and 5 nS for proximal and distal stimulations, respectively) were adjusted to obtain the same peak somatic depolarization during the first EPSP under control conditions; <i>g_{h_pk}</i> = 0.01 mS/cm².</p

A shunting current proportional to <i>I_h</i> takes into account all experimental findings.

<p><b>a</b>) (<i>left</i>) peak somatic membrane potential as a function of synaptic stimulation strength using <i>I_lk</i> with <i>lk</i> = 0.7, i.e. 70% of the peak <i>I_h</i> conductance) under control (<i>red</i>) and no <i>I_h</i> (<i>blue</i>); inset shows somatic recordings during a 10 nS stimulus; <i>g_KM =</i>10 ms/cm²; <b>b</b>) same as in panel <i>a</i> but without <i>K_M</i>; <b>c</b>) peak somatic membrane potential as a function of synaptic input strength without <i>I_h</i> (<i>blue</i>), with <i>I_h</i> and different values of <i>lk</i> (<i>green</i> and <i>orange</i>), or with <i>v_{rev_lk}</i> = −90 mV.</p

Modeling experimental findings on lamotrigine application.

<p>(<i>left</i>) experimental recordings demonstrating a decrease in dendritic (but not somatic) firing after <i>I_h</i> up-regulation caused by application of the anticonvulsive drug Lamotrigine (adapted from Fig. 2d of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036867#pone.0036867-Poolos1" target="_blank">[4]</a>); (<i>right</i>) simulation of somatic (<i>bottom</i>) and dendritic (<i>top</i>, ∼200 µm from soma) recordings during a 500 ms current injection of 0.55 or 0.82 nA, respectively, before (control) and during LTG application (bar above plots); <i>g_{h_pk}</i> = 0.01 mS/cm², <i>lk</i> = 0.5 (control), <i>lk</i> = 0.8 (LTG).</p

Realistic modeling of puzzling experimental findings.

<p><b>a</b>) the 3D reconstruction used in most simulations (<i>left</i>, cell ri06 from the neuromorpho.org database), and model fitting (<i>green</i>) of simultaneous dendritic and somatic experimental recordings (<i>black</i>); dendritic current injection (1 nA, 200 ms, ∼200 µm from soma); cell’s scale bar is 100 µm; <b>b</b>) (<i>left</i>) Typical peak somatic depolarization reached during dendritic stimulations in an experiments with (<i>red</i>) or without (<i>blue</i>) <i>I_h</i>; inset shows somatic recordings for a 60 µA stimulus; (<i>right</i>) Peak somatic depolarization with or without <i>I_h</i> after block of <i>K_M</i>. Experimental results in panel <i>b</i> report results observed in different CA1 neurons, and were adapted from Figs. 2b and 6c of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036867#pone.0036867-George1" target="_blank">[5]</a> with permission from Macmillan Publishers Ltd, copyright (2009).</p

A dynamic interaction between <i>I_h</i> and <i>K_M</i> can show a crossover effect only in special cases.

<p><b>a</b>) (<i>left</i>) peak somatic membrane potential as a function of stimulus strength in a non spiking single-compartmental model, with (<i>red</i> traces) or without <i>I_h</i> (<i>black</i> traces) and different values for the <i>K_M</i> peak conductance, <i>g_KM</i>; note the large depolarization with <i>g_KM</i> = 0; (<i>right</i>) same as in the <i>left</i> panel but using a spiking single-compartmental model; insets show somatic potential during a current clamp of 0.5 or 0.05 nA with or without <i>K_M</i>, respectively. <b>b</b>) peak somatic membrane potential as a function of stimulus strength using the full realistic morphology with (<i>red</i> traces) or without <i>I_h</i> (<i>black</i> traces) and two different <i>K_M</i> channel distributions; insets show somatic potential during a current clamp in the two cases, respectively.</p

Parameter values best fitting the experimental traces in Fig. 1a.

<p>Parameter values best fitting the experimental traces in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036867#pone-0036867-g001" target="_blank">Fig. 1a</a>.</p

A dynamic interaction between <i>I_h</i> and <i>K_M</i> in a realistic model cannot reproduce the experimental findings.

<p>Peak somatic membrane potential as a function of synaptic input strength, without (<i>left</i>) or with (<i>right</i>) <i>K_M</i>, and with (<i>red</i>) or without (<i>blue</i>) <i>I_h</i>. Insets show somatic traces for a 7.5 nS (<i>left</i>) or a 10 nS (<i>right</i>) synaptic input.</p

Typical experimental ECG recordings showing the different arrhythmias taken into account by our model.

<p><b>A)</b> single premature ventricular beat; <b>B)</b> trigeminy complexes; <b>C)</b> bigeminy complexes; <b>D)</b> couplet episode; <b>E)</b> triplet episode; <b>F)</b> two short runs of tachyarrhythmias. In all cases, markers highlight arrhythmic complexes.</p

Specific sequences of interspike interval (ISI) define normal or abnormal behavior; X normal ISI; −, shorter than normal; +, longer than normal.

<p>Specific sequences of interspike interval (ISI) define normal or abnormal behavior; X normal ISI; −, shorter than normal; +, longer than normal.</p

Our model suggests that all kinds of arrhythmia can be explained by dynamical fluctuations of the gap junctions.

<p><b>A)</b> (top to bottom) isolated arrhythmia, trigeminy complex, bigeminy complex, couplet, triplet, short runs of tachyarrhythmias followed by a bigeminism; compare all panels with those in Fig. 2; <b>B)</b> 25 sec simulation exhibiting different types of arrhythmic behavior. In all cases, red markers highlight abnormal sequences (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0100288#pone-0100288-t001" target="_blank">Table 1</a>); traces represent the membrane potential of cell(25,100), from simulations with the following average gap junction conductance and variance: (4.7, 0.3) iPVB, (4.9, 0.3) trigeminy, bigeminy, and triplet, (4.7, 0.6) couplet, (4.7, 0.8) VT.</p