The transition from dendrite to soma compels the VE to converge at the soma.

<p>(A) The soma is characterized by a wider diameter and the presence of the cell nucleus. The nucleus is enclosed by two nuclear envelopes (<i>NE</i>) and occupies the majority of the cell's cross-section, at its widest diameter. The outer NE is continuous with the ER membrane and the space between the two NE is continuous with the ER lumen (<i>ER lumen</i>). The NE allows continuity between the nucleoplasm and the cytosol through pore complexes (<i>P</i>), ∼9 nm in diameter. Altogether, the structure of the nucleoplasm and the two nuclear envelopes establishes an electrical continuity with the inner cable. Thus, the electrotonic pathway from the dendritic spine to the cell nucleus may be reduced to three successive CIC systems as indicated by three grey rectangles: (a) dendritic-CIC, (b) perinuclear-CIC and (c) nuclear-CIC. (B) A simplified simulation of the transition from dendrites to soma was conducted by connecting a dendritic-CIC (labeled ‘a’) with somatic-CIC (labeled ‘b’ and ’c’). The dendritic-CIC followed the default parameters (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000036#pcbi-1000036-t002" target="_blank">Table 2</a>), whereas the somatic-CIC had a wider diameter (<i>d</i>_mP = 16 µm) and was further divided into two consecutive segments: perinuclear zone (labeled ‘b’) and nuclear zone (labeled ‘c’). The perinuclear-zone was short (0.2 λ) and characterized by a narrow cytosolic cross-section and wide ER cross-section (<i>E</i> = 0.99) and the nuclear-zone was characterized by a wide non-conductive cross-section (<i>N</i> = 0.9 and the original <i>E</i> value, <i>E</i> = 0.45). (C) <i>V</i>_mE traces of two spatially distinct synaptic sources (red and blue traces) separated by a distance of 0.2 electrotonic units, are plotted with and without the effect of the somatic-CIC (solid and dashed lines, respectively). Each trace is scaled to the EPSP amplitude at the VE-peak (nVE). Right: Vertical expansion into the region of transition from dendritic-CIC to somatic-CIC (shaded zone). The triangles mark the origin (i.e. synaptic source) of each curve by corresponding colors. Note that at the segment that follows the transition from a dendritic-CIC into a somatic-CIC, both traces, which are otherwise negative, become positive and the VE peaks reach higher levels.</p

The individual synapse can determine the VE position or its polarity at a distinct target along the cable.

<p>(A) Synaptic input initiates, simultaneously, axial currents along the cytosol (<i>I_i</i>) and along the ER lumen (<i>I_ER</i>). The ratio (<i>I</i>) between these currents at the synapse (<i>I_ER</i>_{(<i>x = 0</i>)} and <i>I_i</i>_{(<i>x = 0</i>)}, respectively), modulates the position of the VE. These currents may be modified by <i>active</i> transition of charges (<i>i</i>_mER; Eq. G1.4, G1.5) across the ER membrane, at the synapse, during synaptic activation (see text for details). The traces represent steady-state nVE introduced by 3 different synaptic signals with identical <i>V</i>_{mP(x = 0)} (i.e. potential across plasma membrane at the synapse), identical cable properties, but different <i>I</i> ratios (blue, red and black traces represent simulations of synaptic activation with positive, negative and zero <i>I</i>, respectively). (B) VE-peak position is presented as a function of <i>I</i>. Its position is represented as percent of the distance between the synapse and VE-peak when <i>I</i> = 0. Inset: The amplitude of nVE-peak as a function of <i>I</i>. Y-axis describes the percent change in the peak level of nVE, from the default (<i>I</i> = 0) level. (C) The effect of <i>I</i> on <i>V</i>_mE at several fixed distances from the synapse. Each trace represents the nVE level as a function of <i>I</i> at a fixed position (0.2, 0.6, 1, 2 space constants from the synapse; red, black blue and blue, respectively). <i>V</i>_mE amplitude at each position is described as percent of <i>V</i>_mP amplitude (EPSP) at that specific distance from the synapse. Inset: Triangles depict the sampling position of traces with corresponding color. Note that at each target, VE amplitude can reach 100% of EPSP level or drop below zero. (D) Steady-state calcium level is plotted as function of distance from a point source of calcium (1 pA). The calculations assumed basal Ca²⁺ level of 70 nM and an endogenous mobile buffer of kD = 50 µM and concentration of 0.5 mM (see text for details). The region with a significant calcium elevation was assumed to be where Ca²⁺ level raised above twice the basal level (dashed line; 12 µm). With a typical dendritic spine density <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000036#pcbi.1000036-BallesterosYanez1" target="_blank">[35]</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000036#pcbi.1000036-Major1" target="_blank">[36]</a> the estimated extent of Ca-signal spread along the dendritic shaft, is predicted to cover a region occupied by ∼20 dendritic spines.</p

The CIC system predicts a <i>Virtual-Electrode</i> along the ER membrane under realistic parameters.

<p>Steady-state description of the CIC-model prediction under the parameters described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000036#pcbi-1000036-t002" target="_blank">Table 2</a>. (A) The potential along the cytosol (blue; <i>V</i>_i) and the potential along the ER lumen (red; <i>V</i>_ER) decay at different rates along distance (<i>x</i>[λ]) given in electrotonic units. As a result, the ER transmembrane potential (green; <i>V</i>_mE, given by the difference between <i>V</i>_ER and <i>V</i>_i) generates a qualitatively unique pattern (inset). Namely, <i>V</i>_mE is negative along ∼0.65 space-constants from the synapse, where it crosses the zero line, becomes positive and then decays to zero <i>V</i>_mE. We name the positive segment (where <i>V</i>_mE>0) that follows a negative segment (where 0<<i>V</i>_mE), ‘<i>Virtual-Electrode</i>’ (<i>VE</i>; Dashed area, see text for details). Note that practically <i>V</i>_mP = <i>V</i>_i (solid red line), since we assume that <i>V</i>_e→0. (B) Comparison between the prediction of the CIC model (solid line) and the prediction of the conventional cable model (dashed line) for the transmembrane potential along the plasma membrane (<i>V</i>_mP). Both traces were normalized to <i>V</i>_mP at the synapse (<i>V</i>_{mP(<i>x</i> = 0)}). Bottom: Subtracting the prediction of the conventional cable model from the prediction of the CIC model (green line). Note that the maximal difference between the two predictions lies below 2% of <i>V</i>_{mP(<i>x</i> = 0)}. (C) The spatial pattern of the peak potential across the ER membrane (VE-peak) is compared to the EPSP amplitude at the same distance from the synapse (nVE; green) and shows that at the peak, the VE reaches ∼41% of the EPSP. A second way to compare the <i>V</i>_mE to the EPSP is presenting <i>V</i>_mE as a fraction of <i>V</i>_mP at each point along the cable. (black line) This representation of <i>V</i>_mE shows that at positions beyond the peak of the VE, the <i>V</i>_mE amplitude reaches values greater than the <i>V</i>_mP amplitude. (D) Parameter dependency of VE amplitude and pattern: <i>V</i>_mE was recalculated after increasing (blue) or decreasing (red) <i>N</i> or <i>E</i> (the non-conductive cross-section or the ER cross-section, respectively) by 15% from the default parameters (gray) provided in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000036#pcbi-1000036-t002" target="_blank">Table 2</a>. <i>V</i>_mE is presented in relation to EPSP as <i>nVE representation and</i> as a fraction of <i>V</i>_mP at each point along the cable (solid lines and dashed lines, respectively).</p

Time domain analysis of CIC system.

<p>(A) <i>V</i>_mE traces at different time points after starting to depolarize the synapse (<i>V</i>_{mP[x = 0]} = 13 mV). Note that the VE pattern is already established at <i>T</i> = 0.005 (units of time-constant; τ_m = 48 ms) and that the VE-peak virtually reaches its final position and amplitude within 1.5 τ_m (72 ms). Each of the <i>V</i>_mE traces is presented as percentage of the EPSP level at the position of the VE-peak (nVE), at the specific time point. The black trace depicts the <i>V</i>_mE at time points of <i>T</i> = 1 whereas red and blue traces depict the <i>V</i>_mE at time points lower or higher than <i>T</i> = 1, respectively. (B) For comparison, the conventional pattern of an EPSP along distance (<i>V</i>_mP(X)) is plotted for the same time points as in A. The amplitude of each of the <i>V</i>_mP traces is expressed as percentage of the potential at the signal's origin (synapse; <i>X</i> = 0). Color representation of the different time points is similar to (A). (C) The rising rate of <i>V</i>_mE or <i>V</i>_mP to steady-state level (red or blue, respectively) is simulated at the position of the VE-peak (<i>X</i> = 1.29). The amplitude is expressed as percent of the steady-state level at that position. Note that at the time <i>V</i>_mP reaches 50% of its steady-state level, <i>V</i>_mE has already reached its steady-state level and starts overshooting this after 0.6 τ_m (29 ms) <i>V</i>_mE reaching peak of ∼20% above the steady-state levels at 1 τ_m (48 ms). Note that these kinetics lies within the duration of a synaptic current influx induced by a typical glutamatergic synapse (12–24 ms; see text for details). (D) The propagation pattern and rate of electrotonic signals along the internal cable (red; <i>V</i>_mE) and along the external cable (blue; <i>V</i>_mP) compared to the prediction of the conventional cable theory (gray; <i>T</i> = 2⋅λ). Following the conventional definition for electrotonic velocity we plotted, over time, the points where the transmembrane potentials reached 50% of its steady-state level (solid lines). Dashed red line depicts the rate the VE-peak approaches its steady-state position (dashed, horizontal gray line). At different positions along the internal cable, the potential develops toward positive or toward negative directions (as demonstrated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000036#pcbi-1000036-g005" target="_blank">Figure 5A</a>). For simplicity, only the region where <i>V</i>_mE develops toward a positive direction was analyzed. This region lies above the dashed green line, which depicts the position where <i>V</i>_mE = 0 at steady-state (<i>X</i> = 0.64 λ). Note the negligible difference between the predictions of the CIC model and the conventional model for the speed of electrotonic signals along the external cable (blue and gray lines, respectively).</p