Phase diagrams of the vibrissa motoneuron model with <i>g</i>_h = 0.

<p>The dynamical states of the model neuron are plotted in the <i>g</i>_M-<i>I</i>_app plane (A) and in the <i>g</i>_M-<i>I</i>_app plane (B). A regime of STOs (light grey) is obtained between the regimes of quiescence and tonic firing. Red lines denote the Hopf bifurcation (HB), and blue lines denote the saddle-node of periodics (SNP) or period doubling (PD) bifurcations.</p

Properties of firing patterns without and with an intrinsic MMOs-generating mechanism.

<p>The firing rate <i>f</i>_R (I), the coefficient of variation CV (II) and the time period <i>t</i>_p, computed assuming a Bernoulli process (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0109205#pone.0109205.e009" target="_blank">Equation 3</a>) (III) are plotted as a function of <i>I</i>_app for <i>g</i>_h = 0 (A) and <i>g</i>_h = 0.3 mS/cm² (B). The colors of the lines denoting the values of σ (in µA×ms^1/2/cm²) are: black – 0, red – 0.01, green – 0.032, blue – 0.1 and orange – 0.32. The vertical dotted lines denote the <i>I</i>_app values of the transitions between different dynamical states (quiescence, STOs, MMOs and tonic firing) of the noiseless neuron.</p

Response of a motoneuron pool to periodic stimulation from a CPG and neuromodulation.

<p>50 uncoupled motoneurons are simulated, each receiving constant input <i>I</i>_app = 2 µA/cm² mimicking the excitability effects of neuromodulators such as serotonin, and periodic stimulation from a CPG with a frequency <i>f</i> = 10 Hz. The periodic stimulation is <i>I</i>_c = 0.15 µA/cm² during the first 20 ms of each cycle with a duration of <i>T</i>_per = 1/<i>f</i>, and 0 otherwise. Different neurons have different noise realizations. Additional parameters: <i>g</i>_h = 0.3 mS/cm², σ = 0.032 µA×ms^1/2/cm². Realizations of the noise are different across motoneurons. (A) The membrane potential <i>V</i> as a function of <i>t</i> for two neurons (black). The stimulus pattern is schematically plotted above each panel (red) to emphasize the synchrony of spikes with the stimulus. (B) Rastergram of the spikes (black circles) of the 50 motoneurons. The stimulus is <i>I</i>_c between each pair of adjacent red lines. (C) The total force amplitude <i>F</i>, in arbitrary units (<i>A</i> = 1, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0109205#pone.0109205.e010" target="_blank">Equation 4</a>), generated by a whole muscle whose cells are innervated by the pool of motoneurons (black). The dotted blue line denotes a similar simulation with <i>I</i>_app = 2.4 µA/cm².</p

Voltage time traces of the model neuron in response to step current injection at <i>t</i> = 0.

<p>The values of <i>I</i>_app are indicated to the right of the traces. (A) <i>g</i>_h = 0, σ = 0.01 µA×ms^1/2/cm². The noiseless neuron does not exhibit MMOs, but this level of noise generates MMOs near the transition between quiescence and tonic firing. (B) <i>g</i>_h = 0, σ = 0.1 µA×ms^1/2/cm². For this larger noise level, MMOs are generated in a more widespread <i>I</i>_app regime. (C) <i>g</i>_h = 0.3 mS/cm², σ = 0.01 µA×ms^1/2/cm². The noiseless neuron generates MMOs. This level of noise increases the <i>I</i>_app regime in which MMOs are obtained only slightly. The MMOs are less ordered, and the number of STOs between spikes varies from one inter-spike interval to another. (D) <i>g</i>_h = 0.3 mS/cm², σ = 0.1 µA×ms^1/2/cm². MMOs appear in <i>I</i>_app regimes in which the noiseless neuron is quiescent or fires tonically, and the firing patterns look less ordered.</p

Bifurcation diagrams of the vibrissa motoneuron model with <i>g</i>_h = 0.3 mS/cm².

<p>(A) The values of the membrane potential <i>V</i> (top panel) and the firing rate <i>f</i>_R (bottom panel) are plotted as functions of <i>I</i>_app for fixed points (thin lines) and limit cycles (thick lines) for <i>g</i>_M = 1 mS/cm². For limit cycles, minimal and maximal voltages during the cycle are plotted. Solid lines denote stable solutions, and dotted lines denote unstable solutions. Stable sub-threshold oscillations are shown in blue, whereas stable tonic firing states are shown in solid thick black lines. Solid circles in the top panels denote bifurcations from the following types: Hopf (HB), saddle-node of periodics (SNP) and period doubling (PD). The firing rate in the MMOs state is plotted in red in the bottom panel. (B) The firing rate <i>f</i>_R in the MMOs state is plotted as a function of <i>I</i>_app at a larger scale. The types of mixed mode states (see text, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0109205#pone-0109205-g004" target="_blank">Figure 4</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0109205#pone.0109205-Ermentrout1" target="_blank">[23]</a>) are indicated above the curve.</p

Neural network model of L4.

<p><b>(a)</b> Diagram of the recurrent model of L4 network. <b>(b)</b> Spike shape of VPM (schematic), L4E and L4I neurons. <b>(c)</b> Temporal dynamics of individual EPSPs for the different synaptic connections (T = VPM; I = L4 FS; E = L4E). The convention is that that the first letter corresponds to the post-synaptic neuron and the second letter to the presynaptic neuron. <b>(d)</b> Thalamic generating function <i>F</i>_T (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.e003" target="_blank">Eq 1</a>). The panels on the right show the same figure in a magnified scale. For simplicity, we assume that all T neurons have the same preferred phase.</p

Summary of experimental results in the object-localization task [37].

<p><b>(a)</b> Top, schematic illustrates measurement of whisker position (azimuthal angle <i>θ</i>), instances of touch and an example trace of whisker position. Protraction corresponds to positive changes in <i>θ</i>. <b>(b)</b> Schematics of the thalamocortical circuit and relevant cell-types. <b>(c)</b> Spike rate aligned to transitions from non-whisking to whisking (adapted from panel 5e in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref037" target="_blank">37</a>]). <b>(d)</b> Average spike rate as a function of whisking amplitude. <b>(e)</b> Average population response aligned to touch (adapted from panel 5c in [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref037" target="_blank">37</a>]). Data and figures corresponding to previously reported datasets [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref036" target="_blank">36</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref037" target="_blank">37</a>].</p

Network parameters in the reference parameter set: - synaptic delay, <i>K</i>_<i>αβ</i>—average number of presynaptic inputs, <i>g</i>_<i>αβ</i>—synaptic conductance, <i>V</i>_extr—the extremal value of the unitary synaptic membrane potential change.

<p>The corresponding experimental values for <i>K</i>_<i>αβ</i> and <i>V</i>_extr are written in the two right columns. Those values are taken from the following references: a—[<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref053" target="_blank">53</a>], b—[<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref056" target="_blank">56</a>], c—[<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref034" target="_blank">34</a>], d- [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref028" target="_blank">28</a>], e–[<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref057" target="_blank">57</a>], f—[<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.ref027" target="_blank">27</a>].</p

Effect of varying thalamocortical conductances on the function of L4E neurons.

<p>Symblols and lines are as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005576#pcbi.1005576.g009" target="_blank">Fig 9</a>. <b>(a)</b> Changing <i>g</i>_ET. <b>(b)</b> ν_E vs. <i>A</i>_T during whisker movements only. <b>(c)</b> R_E vs. <i>C</i>_T. <b>(d)</b> Changing <i>g</i>_IT. <b>(e-f)</b> Same as <b>b-c</b>.</p

A neural network model of L4 explains suppression of whisker movement signals in L4 excitatory neurons.

<p>The colors black, grey and red denote T, L4E and L4I neuronal populations respectively. <b>(a)</b> Example L4E and L4I membrane potential during simulated whisking (green). <b>(b)</b> The population- and time average spike rates ν_E and ν_I of the L4E and L4I neurons respectively as function of the thalamic input <i>A</i>_T in the absence of touch. L4I neurons follow linearly the thalamic input while L4E neurons increase only weakly with <i>A</i>_T beyond firing threshold. Inset, zoom in. <b>(c)</b> Membrane potential for an example neuron during whisking and touch (black dots). <b>(d)</b> Population PSTH aligned to touch onset. Inset, zoom in.</p