Extracellular field at spike initiation.

<p>(A)-(C), Extracellular potential (color coded) and electrical field (arrows) around the simplified neuron (white box and line), at three different times indicated in (D) and (E). (D), Intracellular voltage trace at the soma and AIS distal end. (E), Extracellular potential near the soma and AIS distal end. (F), Extracellular recording near the soma of two cortical neurons (from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.ref013" target="_blank">13</a>]). (G), Extracellular AP recording near the AIS (grey) of a cortical pyramidal cell (from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.ref014" target="_blank">14</a>]).</p

Peak current versus holding voltage in somatic voltage-clamp, using the simple model with different Nav channel conductance densities (from half to twice the initial value used in Fig 4).

<p>Peak current versus holding voltage in somatic voltage-clamp, using the simple model with different Nav channel conductance densities (from half to twice the initial value used in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.g004" target="_blank">Fig 4</a>).</p

Currents at spike initiation.

<p>(A) Somatic voltage-clamp recordings. Top: somatic membrane potential, spaced by 1 mV increments from threshold (red), with one trace just below threshold. Middle: recorded currents. Bottom: membrane potential at the AIS end. (B) Top: peak current measured in somatic voltage-clamp versus holding voltage, with and without somatic Na channels, showing a discontinuity. Bottom: peak proportion of open Na channels at the distal axonal end versus holding voltage (variable m³ representing activation is shown for the first two models; variable o representing current-passing state is shown for the third model). (C) Left, Current traces experimentally measured in somatic voltage-clamp in raphé neuron (from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.ref015" target="_blank">15</a>]). Right, Peak current vs. command voltage (red; the black curve is obtained when axonal Na channels are inactivated with a prepulse). (D) Same as (C), but in a two-electrode somatic voltage-clamp of a cat motoneuron [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.ref016" target="_blank">16</a>]. Voltage is relative to the resting potential.</p

Theories of spike initiation.

<p>(A) Standard account of spike initiation: spike initiation results from the interplay between Na current and K current (mostly leak) flowing through the membrane at the initiation site. (B) Top: The isopotential Hodgkin-Huxley model produces spikes with smooth onset (left), exhibiting a gradual increase in dV/dt as a function of membrane potential V (right: onset rapidness measured as the slope at 20 mV/ms = 5.6 ms^-1). Bottom: cortical neurons have somatic spikes with sharp onsets (left), with steep increase in dV/dt as a function of V (onset rapidness: 28.8 ms^-1; human cortical data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.ref004" target="_blank">4</a>]). (C) Backpropagation hypothesis: spikes are initiated according to the conventional account, with a local axonal current loop propagating towards the soma. (D) Critical resistive coupling hypothesis: owing to the strong resistive coupling between the two sites and the soma acting as a current sink, spike initiation results from the interplay between Na current and axial current. Spikes then initiate through a global current loop encompassing AIS and soma, which behaves as an electrical dipole.</p

Fitting procedure applied on an intracellular voltage trace.

<p><b>a</b>, Top: voltage trace (top, black) and predicted threshold (red). Bottom: steady-state threshold in the fitted model. <b>b</b>, vs. predicted threshold for the trace in (a). The identity line (red) sharply separates subthreshold fluctuations from spikes.</p

Balance of currents at spike initiation in the simple model, with different Nav channel conductance densities (from half to twice the initial value used in Fig 4).

<p>Same conventions as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.g006" target="_blank">Fig 6</a>.</p

Sharpness of spike initiation in a small simulated neuron (axon diameter: 0.3 μm).

<p>(A) Action potential in the axon (blue) and distal AIS (orange; dotted: with no somatic Na channels). (B) Corresponding phase plot of the action potential, showing onset rapidness greater than 50 ms^-1 (inset).</p

Two-compartment model.

<p>(A) Equilibrium values of the gating variables for the Na (left) and K (right) channels. (B) Voltage trace (left) and phase plot (right) of a somatic spike. (C) Voltage trace (left) and phase plot (right) of an AIS spike. (D) Left: Peak current recorded in somatic voltage-clamp as a function of holding voltage. Right: Na current in the AIS (blue) and soma (orange) during a spike in current-clamp.</p

<i>In vivo</i> intracellular recordings.

<p><b>a</b>, Intracellular recordings () in the owl's ICx, with binaural stimuli (L: left, R: right). Either ITD is varied at best IID (top) or IID is varied at best ITD (bottom). Owl picture source: <a href="http://openclipart.org/detail/17566/cartoon-owl-by-lemmling" target="_blank">http://openclipart.org/detail/17566/cartoon-owl-by-lemmling</a>. <b>b</b>, Two spikes from the traces in (a); red dots indicate the estimated spiking threshold. <b>c</b>, Trace from (a) shown in phase space: vs. . Spike threshold is detected when exceeds a fixed value (red dashed line). <b>d</b>, Distribution of subthreshold membrane potential (blue) and spike threshold (green). <b>e</b>, Spike threshold vs. average before spike. <b>f</b>, Spike threshold vs. depolarization slope before spike. <b>g</b>, Spike threshold vs. preceding interspike interval. Red lines are linear regressions.</p

Somatic onset rapidness.

<p>(A) Phase plot of a somatic spike with a large soma (orange, 10,000 μm²) and a small soma (gray, 3,000 μm²). The phase plot is linear (corresponding to locally constant phase slope) around dV/dt = 25 mV/ms in the former case and around 60 mV/ms in the latter case. Maximum phase slope is similar in both cases (39.3 and 49.5 ms^-1). (B) Left: phase plot for a large soma (10,000 μm²). The presence of somatic Na channels slightly decreases onset rapidness (orange, slope: 39 ms^-1). Without them, onset rapidness is 52.6 ms^-1. Right: phase plots at different points along the axon (dotted blue: soma; dark blue: distal end; light blue: intermediate axonal positions). The prediction of somatic onset rapidness based on resistive coupling is the maximum slope of a tangent to the phase plot intersecting the spike initiation point, which gives 50 ms^-1 at the distal end (red line). (C) Left: Somatic onset rapidness (orange) and prediction from axonal phase plots (blue) as a function of soma area for the simple model. The morphologically detailed model and the simple model with a dendrite are also shown on the right. Grey: somatic phase slope at 20 mV/ms. Right: For comparison, total somatic capacitance is shown as a function of soma area. (D) Somatic (left) and axonal (right) phase plots of a spike digitized from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175362#pone.0175362.ref007" target="_blank">7</a>]. Maximum phase slopes are similar.</p