Comparison of distance dependence of vibration frequency and force component ratios.

<p>Red, the rate of change of fundamental vibrational frequency against contact distance along the whisker length. Blue, the rate of change of force ratios against contact distance along the whisker length. Log base 10 y-axis. There is little change in axial-to-lateral force, <i>F</i>_ax/<i>F</i>_lat, (< 1% / mm) in proximal contact positions due to whisker stiffness preventing substantial curvature during touch. However, the fundamental frequency of vibration changes substantially (5 – 10% / mm) with contact position for a large range of contacts out to <i>c</i>/<i>L</i> = 0.3. At more distal contact positions, the first eigenfrequency falls and is degenerate with proximal frequencies. The rate of change of force component ratios accelerates towards the tip.</p

Model response to touch.

<p>A. Time dependent profile of the applied force modeled by a truncated Gaussian (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006032#pcbi.1006032.e094" target="_blank">Eq (77)</a>) and a smooth connecting function <i>F</i>_<i>s</i>(<i>t</i>) (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006032#pcbi.1006032.e099" target="_blank">Eq (79)</a>) that models the touching event at early times, 0 ≤ <i>t</i> ≤ <i>τ</i>. For clarity, <i>τ</i> is exaggerated in the figure. B. Amplitudes of the eigenmodes excited by pole impact as a function of the eigenmode number calculated for different <i>τ</i>. C. The relative excitation of eigenmodes is dependent on location of contact along the whisker. D. Touch onset propagates a vibrational wave towards the base of the whisker. E. Bending moment and shear force at the follicle during, 0 ≤ <i>t</i> ≤ 10 ms, and after, <i>t</i> > 10 ms, touch calculated for pole position <i>c</i>/<i>L</i> = 0.6. F-I. Time-dependent displacement of a 5% trimmed whisker during and after typical interactions with pole located at <i>c</i>/<i>L</i> = 0.6. F. Top: steady state component, <i>y</i>_<i>s</i>(<i>x</i>, <i>t</i>), of the whisker displacement during contact with pole, 0 ≤ <i>t</i> ≤ <i>t</i>_<i>f</i>, <i>t</i>_<i>f</i> = 10 ms. Bottom: solid and dashed lines show <i>y</i>_<i>s</i>(<i>x</i>, <i>t</i>) sampled with 0.5 ms steps during the forward and backward motion, respectively. G. Top: vibrational component of the whisker displacement, <i>y</i>_<i>e</i>(<i>x</i>, <i>t</i>), during contact with pole. Bottom: vibrational component <i>y</i>_<i>e</i>(<i>x</i>, <i>t</i>) sampled with 0.5 ms steps. H. Top: sum of the steady-state and vibrational components. Bottom: solid and dashed lines show the total whisker shape sampled with 0.5 ms steps during the increase and decrease of the force, respectively. The time colorbar shown in F applies to all bottom panels F-I. I. Top: free whisker motion after the pole detachment, <i>t</i> > <i>t</i>_<i>f</i>. Bottom: whisker shape for the same time interval sampled with 0.5 ms time steps. The value <i>τ</i> = 0.1 ms was used in panels C-I.</p

Four lowest eigenmodes for a full-length conical whisker with fixed-base free-tip boundary conditions.

<p>A, Pole located at <i>c</i>/<i>L</i> = 0.3, as indicated by arrow. B, Free vibration of the whisker in absence of the pole. Insets: The same four eigenmodes magnified for clarity.</p

Comparing model and observation.

<p>Traced high speed imaging (4000 fps) of whisker displacement and deformation during touch. Each line is a whisker position during the first 5 ms from onset (0.25ms timesteps). Y-axis is expanded. This whisker had an intrinsic curvature that bent towards the anterior of the head, in the direction of protraction. Compass indicates anteroposterior and mediolateral axes. Inset, zero free parameter model predictions and observed vibrational deformation through time at eight color coded locations along the whisker during this example touch.</p

Dependencies of eigenfrequencies.

<p>A, The dependence of the five lowest dimensionless eigenfrequencies, <i>β</i>_<i>j</i>, on pole position for a full-length conical whisker. B, The dependence of the five lowest dimensionless eigenfrequencies on the truncation length for a fixed pole position <i>c</i>/<i>L</i> = 0.6.</p

Fitting whisker damping.

<p>A, Single tracked whisker over time, immediately before and after a slip-off (time between snapshots, 1 ms). B, Post-slip vibration for the example in (A). C, Best fit and 0.95 confidence intervals for 8 whisker slips.</p

Dynamic cues for whisker-based object localization: An analytical solution to vibration during active whisker touch - Fig 9

<p>A. Touches evoke quasi-static and vibrational bending moments at the base. The ratio of quasi-static and dynamic bending moments increases dramatically toward the tip. B. Similarly, the ratio of quasi-static and dynamic shear forces increases dramatically toward the tip.</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

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

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