HVC cooling produces complex changes in the distribution of syllable duration.

<p>(A) Classification of syllables into three groups, depending on the number of local minima between two consecutive inspirations, denoted by “<i>i</i>”. In red we define syllables that are reminiscent to harmonic oscillations, with no minima. In this example there are six syllables separated by five inspirations. Syllables that have one or two local minima (green circles) are distinguished from those with three or more local minima (blue circles); three and two syllables are shown, respectively. The total number of syllables analyzed for this bird is 27471 (15040 red, 5830 green and 6601 blue). (B) Histograms of durations for every syllable recorded from bird #31 for different HVC temperatures. The bin size is 2.27 ms for red syllables 4.54 ms for green syllables and 9.07 ms for blue syllables. HVC temperature decreases from top to bottom (C) Individual normalized histograms of different types of syllables. Vertical dashed lines separate regions for computing statistical quantities. Bimodal red and green distributions are separated by their intermediate lowest frequency bin count, and for the remaining range limits we selected a region centered around the mean with three ssd width to each side. Distributions do not only drift to the right as expected from a stretching phenomenon, but relative quantities also change drastically due to syllable breaking and changes in the structure of the song. Colored circles and squares are used to label each region. (D) Variations with temperature of mean syllable duration distributions for regions in (C) (error bars are ssd). One red (squares) and one blue distribution indicate a slope opposite to that expected from stretching. The slopes of the linear regressions are as follows in ms/°C: red circles −0.86+−0.34, red squares 0.3+−1.4, green circles −0.71+−0.25, green squares −2.1+−1.1 and blue circles 7.4+−1.0.</p

Experimental cooling of HVC.

<p>(A) Schematic of simplified song motor pathway with cooling device. HVC, used as proper name; RA, robust nucleus of the arcopallium; nXIIts, tracheosyringeal part of the hypoglossal nucleus; expiratory premotor nucleus RAm, nucleus retroambigualis; inspiratory premotor nucleus PAm, nucleus parambigualis. The cool side of the cooling device is positioned right against the dura over HVC. (B) Calibration of the cooling device showing brain temperature change as a function of the current applied to the device. Temperature measurements at different depths below HVC show that cooling is fairly local (n = 2). (C) Syllable breaking observed in bird #31. Shaded syllable first stretches and then breaks. Durations are <i>c₀</i> = 320 ms, <i>c₁</i> = 334 ms, <i>c₂</i> = 428 ms and <i>c₃</i> = 353 ms. Syllables have a different “breaking” point, which can be seen in the third and fourth row: syllable marked with an asterisk (*) does not break within this range of temperatures, and stops stretching in the third row, syllable marked with an “x” breaks at fourth row, and remaining syllables break at third row. Syllable frequencies range from 3 Hz in the first panel to 12 Hz in last panel. HVC temperatures from top to bottom are: normal, −2.6°C, −4.7°C and −7.5°C. (D) Syllable breaking observed in bird #37. Shaded syllable first stretches and then breaks. Durations are <i>d₀</i> = 807 ms, <i>d₁</i> = 870 ms, <i>d₂</i> = 896 ms and <i>d₃</i> = 793 ms. In the third row a deep pressure modulation arises and in the fourth row the syllable is broken into multiple expiratory pressure pulses. Pressure fluctuation, or syllable frequencies during the expiration are 34 Hz, 31 Hz and 28 Hz for first three rows. In the fourth row no clear sustained pattern exists, but in the segments with syllables they occur at 27 Hz. The song segment unmarked by shading stretches and then breaks in the fourth row. The corresponding HVC temperatures are from top to bottom: normal, −3.4°C, −4.8°C and −5.5°C. The total duration of the song segment indicates clear stretching of all patterns at first (second rows in (C) and (D)). Different syllables “break” at different temperatures (third and fourth rows), and the total duration of bout segments decreases after breaking occurs. Panel pairs in each row show spectrogram on top and recorded subsyringeal air sac pressure at bottom. Frequency range is 1–7 kHz. Pressure range is 0–1 in arbitrary units.</p

Cooling induces syllable stretching, deformation, and then syllable “breaking”.

<p>Example of song from canary #31 with the following HVC temperatures: normal, −2.6°C, −4.7°C, −5.4°C, −6.6°C and −7.5°C. Stretching occurs in the top three paired panels and is accompanied by a gradual change in the morphology of the pressure pulses and accompanying sound. The onset of breaking with coexistence of the broken and “unbroken”, deformed syllables is depicted in panel 4. The broken syllables get stretched upon further cooling (panels 5 and 6). The duration of the shaded syllables is: <i>a</i>₀ 98 ms (49×2), <i>a</i>₁ = 104 ms (52×2), <i>a</i>₂ = 112 ms (56×2), <i>a</i>₃ = 187 ms (62×3), <i>a</i>₄ = 136 ms (68×2), <i>a</i>₅ = 140 ms (70×2). For syllables <i>a</i>_i duration increments are evident as the duration increases from 49–52–56–62–68–70 ms. These durations correspond to half the syllable duration for i = 0, 1 and 2, one third of the combination of coexisting long and short syllable for i = 3, and a complete syllable for i = 4 and 5. These durations represent the period of the putative periodic instruction coming from HVC (see model in main text). If put together in a linear regression, results show that the largest stretch is of 45+−10%, and that the onset of breaking occurs at 33+−7%. Dashed line in <i>a</i>₃ is at two thirds of its duration. Paired panels show the spectrogram (1–7 kHz frequency range) on top and subsyringeal air sac pressure on the bottom (0–1 in arbitrary units).</p

Dynamical model of motor pathway and simulations of canary pressure patterns during song.

<p>(A) Schematic of proposed connectivity of circuit components. At top, HVC average activity is modeled as a simple periodic instruction driving downstream neuron populations, one excitatory and one inhibitory (See Materials and Methods for complete model and parameters). Activity from the driven excitatory population is proposed to be proportional to the output motor instruction driving air sac pressure gestures. For the depicted input frequency from HVC (forcing frequency) of 16 Hz the output is a subharmonic frequency of 8 Hz. The air sac pressure range is from 0–1 in arbitrary units. (B-C) Simulations of pressure gestures that first stretch and then break (in red) compared to actual recorded data (black). Paired panels have simulated pressure gesture and the proposed driving, scaled for illustrating the locking behavior and subharmonicity. (B) Simulated syllables at 25 Hz, 20 Hz and 14 Hz of instruction frequency (with a changing amplitude 3.1, 3.0 and 2.9 to allow better matching with experimental patterns). The first two columns show locking at half the frequency of instruction (2∶1), whereas the last column shows locking at 1∶1. (C) Simulated syllables at 34 Hz, 31 Hz and 27 Hz instruction frequency (amplitude is 2.44). The first two columns are locked 1∶1 and in the last the frequency of instructions is halved (2∶1). Notice that only varying the driving frequency, (corresponding to the conjectured effect of slowing down the HVC activity), we can account for both effects of stretching and breaking. Subharmonicity appears for some frequency ranges. Dotted line corresponds to a bifurcation transition in the system, where output changes drastically as the forcing frequency changes gradually.</p

Bifurcation map of the model predicts different types of breaking.

<p>Each coordinate of the map corresponds to a pair of parameters <i>(f,A)</i> These represent the frequency and amplitude of the forcing in our model. Colored (and numbered) regions correspond to different locking regimes between the forcing frequency and the output of the model. Regions with “p” (pulsatile) labels are for output patterns with oscillations on top of a constant value (long expiration). The “+” sign is used to denote coexistence of solutions. Color code (numeration) is as follows. Red (1) corresponds to a 1∶1 locking between the forcing and the output of the model. In the region colored with green (2) there is a 2∶1 locking. This means that the output pattern will repeat itself after a time equal to twice the forcing period. The region colored with blue (3) denotes a 3∶1 locking (i.e., the output repeats itself after a time equal to three times the forcing period). The orange region presents pulsatile solutions (1p), which are locked 1∶1 with the forcing. The light red region (1+1p) gives rise to either pulsatile or harmonic looking solutions depending on the initial conditions, both locked 1∶1 to the forcing. The region colored with cyan (2+2p) gives rise to solutions of 2∶1 locking. The other colors denote regions of the parameter space with solutions in other locking regimes. Cooling is associated with horizontal arrows A-C pointing to the left (decreasing frequency), and the breaking of syllables is interpreted as bifurcation transitions between the different regions. We mapped three syllables where we found breaking from normal and cooled song, to the beginning and end of arrows respectively. (A) Syllable (same as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067814#pone-0067814-g003" target="_blank">Figure 3</a>, canary #31) originally sung in regime 2 at 10 Hz (<i>f</i> = 20 Hz) that ends at region 1 at 13.5 Hz., both with <i>A</i> = 3.15 (a.u.). (B) Syllable in regime 1p (orange colored) at 30 Hz of canary #37 crosses border to end at region 2 at 9.7 Hz (<i>f</i> = 19.4 Hz), with <i>A</i> = 2.25. In this case, at the coldest temperature, there is an experimental pattern that we matched with locking regime 3 (blue colored), which is very close at <i>f</i> = 17.2 Hz and A  = 2.0 (a.u). (C) Syllable from region 1p (same as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067814#pone-0067814-g002" target="_blank">Figure 2D</a>, canary #37) that crosses to region 2+2p (coexistence of period 2, and period 2 above a constant expiration). The cold temperature pattern shows a lack of repetitive syllable structure that can be explained with the coexistence of solutions of our model. We used two different initial conditions that we changed in the middle of the simulation, resulting in a strong resemblance with the experimental pattern. All mentioned border crossings are different bifurcations of our model that are manifested in the cooling experiment and show its predictive capability for a wide parameter range. Model pressure has on top a scaled pattern of HVC activity to visualize the locking regime. Pressure is 0–1 in arbitrary units.</p