Effects of temperature on modeled neurons: Bursting emergence.

<p>(A) Correction parameter Q with temperature sensitivity that multiplies every constant rate in the model. Processes are three times faster at 30°C than at 20°C where parameters were obtained by experiments in slices [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.ref067" target="_blank">67</a>]. At 40°C rates are three times faster than at 30°C. (B) Maximal conductances are also changed by parameter Q. Dotted line corresponds to a , used for HVC_<i>X</i> and HVC_<i>INT</i>, and full line to which modeled HVC_<i>RA</i>. (C) Behavior of neurons in response to an applied current of 12ms for HVC_<i>X</i> and HVC_<i>INT</i> and 16ms for HVC_<i>RA</i>. At 40°C there is a remarkable similarity with intracellular measurements in vivo, where HVC_<i>X</i> and HVC_<i>RA</i> have bursting behavior (Long et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.ref066" target="_blank">66</a>]). Decreasing temperature affects the interspike interval, which widens in all cases, leading to a reduced number of spikes. At 20°C HVC_<i>RA</i> fails to spike. (D) Exploration of longer (30ms) and higher current inputs show bursts that terminate solely by intrinsic current properties at normal temperature for HVC_<i>X</i> and HVC_<i>RA</i> having the same duration as real neurons. The latter retains bursting up to 30°C and fails to spike at 20°C. HVC_<i>X</i> loses bursting offset before, at around 36°C. The short pulses have the same duration as in (A) 50ms after long pulse for HVC_<i>X</i> and HVC_<i>INT</i> and 100ms after for HVC_<i>RA</i>, show a spike number reduction at this short latency compared with (A). Bars beneath traces show duration of pulse.</p

Effects of temperature on HVC neurons.

<p>(A) Two different types of single units were recognized in terms of their spike shape. 12 Fast Spikers (FS, orange) and 18 Regular Spikers (RS, blue) (B) Classifications were made based on peak to peak wave width (<i>p</i>2<i>p</i> width). FS (orange circles) have a more variable and higher spike rate than RS (blue triangles are the five with the highest rates, and the blue rectangles the five with the lowest rates, the eight blue circles are intermediate rates cells). (C) Widening of the spike shape of normalized waveforms across temperatures for three example FS (top) and two RS (bottom). We see that RS_<i>hf</i> units show a bigger width change than RS_<i>lf</i>. Color scale shows temperature. (D) Normalized <i>full</i> width increase of the spike shape across temperatures. FS almost doubles the spike width, while RS_<i>hf</i> and RS_<i>lf</i> only increase ∼40% and ∼20% respectively at the lowest temperature. Points are mean ± s.e.m. (p* < 0.05, p** < 0.02 values for two tailed t-test made at each temperature) (E) Normalized spike rate decrease across temperature, where we also include Multiunits (MU). We do not observe significant differences between them (two tailed t-test p> 0.1). Points are mean ± s.e.m. (F) Patterns of inter-spike-interval (ISI) activity across temperature for the single units shown in (C), left to right corresponding to top to bottom. Three different types of histogram appear for all measured FS, where ISIs change non trivially (not only a distributional shift). The first one belongs to a FS with firing rate of 5.9Hz, measured over 8 minutes. ISI depletes at intervals higher than 20ms, but retain its lower than 10ms peak at lower temperatures. Second column is a neuron with a firing rate of 3.3 Hz measured for 4.8 min. This neuron shows no bursting behavior and the ISI shifts to the right and depletes. Third column is a neuron with firing rate of 2.4Hz measured for 6.4 min, where no changes are evident across temperatures. It lacks the second timescale from around 20ms. Last two columns show the behavior of the two RS, firing at 2.4Hz and 0.7Hz measured for 4 min. We see the evolution of a clear shift to the right of the distribution over the first temperatures, until they get depleted at lower temperatures. (G) Cumulative distribution of the ISI of the three types of fast spiking neurons. The only distributions that change significantly with respect to the one at normal temperature are FS 1 and FS 2, which have the second timescale (p* < 0.0005 Kolmogorov Smirnov test, ns: not significant, alpha value is strict to account for fewer counts at lower temperatures). We can see from FS 1 that this timescale starts to disappear at 36°C and at around 10ms of ISI. Bins are 1ms.</p

Spike widening in single neuronal model.

<p>(A) Intracellular voltage evolution of a single spike for the three modeled neurons across temperatures shows an increase in its width with the same current input as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.g003" target="_blank">Fig 3C</a>. The time window used to plot is identical to the one used in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.g001" target="_blank">Fig 1A and 1C</a> for the extracellular measurements, and the positive peak is aligned to 1ms and waveforms are shifted (less than 5mV) to match at peak amplitude. (B-C) Width increase for the three neuronal types was computed for the first spike of the traces in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.g003" target="_blank">Fig 3C</a>. Width is calculated as the spike width above a threshold of 55 and 60% for HVC_<i>X</i> and HVC_<i>RA</i> and from the hyperpolarization to a uprising threshold of 30% for HVC_<i>INT</i>. These were selected to match the measured experimental width at 40°C (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.s002" target="_blank">S2A Fig</a>). In (C) we show the same normalized to the width at 40°C. We see that the widening effect is of more than 100% for HVC_<i>INT</i> and about 50 and 35% in HVC_<i>X</i> and HVC_<i>RA</i> respectively for the 10°C range explored.</p

Temperature effects from a single synaptic input produce delays.

<p>(A) Voltage traces for the three neuronal types in red, and synaptic input in blue across different temperatures are aligned to 0ms at current injection start. Single bursts can be seen for the excitatory types and a similar number of spikes for the inhibitory HVC_<i>INT</i>. All neurons present interspike interval increases and HVC_<i>RA</i> also shows a spike onset delay with decreasing temperatures. Vertical line is a reference aligned to the peak of the first spike in each trace. (B) Current inputs in blue from a single synaptic model fed with the voltage traces of HVC_<i>X</i> and HVC_<i>RA</i>. Evolution of HVC_<i>INT</i> voltage in red shows a single spike elicited after the third synaptic current peak. Latencies increase when lowering temperature. Time origin and vertical line are the same as in A. (C) Delay for spike onset for the five traces in A and B relative to the timing of the first spike at normal temperature. HVC_<i>RA</i> and HVC_<i>INT</i> only have slight delays for the constant applied current, while HVC_<i>RA</i> displays an almost 5ms delay to burst onset at 30°C. For the synaptic model HVC_<i>INT</i> has delays that go up to 6ms and 12ms for the two excitatory input types. (D) Maximum absolute synaptic current elicited decreases in a similar fashion for the two excitatory inputs and decreases more than twofold in the range of temperatures explored. The change in slope of the HVC_<i>RA</i> to HVC_<i>INT</i> curve at around 34°C is due to the slight distortion of last spike in HVC_<i>RA</i>. (E) Spiking pattern of HVC_<i>INT</i> at 40°C for decreasing current at steps of -200pA shows the characteristic sensitivity of the inhibitory interneurons to input currents. (F) Interspike interval (ISI) of HVC_<i>INT</i> for different currents and temperatures. We see that it is more sensitive to currents than temperatures. Inset panels show that at 1000 and 2000pA ISI changes less than 0.3ms for different temperatures, and shows changes above 1ms only below 500pA. Currents were generated with 25ms pulses decreasing at -100pA steps in a single simulation with 200ms intervals between pulses. ISI was computed only where there was at least two spikes, which happened below -300pA.</p

Changes in model ISI distributions from poisson excitable inputs.

<p>(A-C) Different input combinations (top) and evolution of the intracellular potential for HVC_<i>INT</i> (red) and synaptic current elicited (blue) for 40°C (middle) and 32°C (bottom). Many presynaptic inputs do not elicit spikes and spiking can happen in a “burst” like manner. (A) Input of 20 HVC_<i>RA</i> neurons and 60 HVC_<i>X</i> neurons. Firing rate at 40°C is 5.6 Hz, matching FS 1 unit in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.g001" target="_blank">Fig 1F</a>. To achieve this behavior 30% of the input was made of bursts of 3 spikes, while the rest consisted of single spike events. (B) Input of 80 HVC_<i>X</i> neurons produces a firing rate at 40°C of 2.9 Hz with no “bursting” events, matching closely FS 2 unit in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.g001" target="_blank">Fig 1F</a>. To achieve this behavior, 100% of the input was made of single spikes. (C) Input of 60 HVC_<i>RA</i> neurons and 20 HVC_<i>X</i> neurons. Firing rate at 40° is 2.4 Hz, matching FS 3 from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005699#pcbi.1005699.g001" target="_blank">Fig 1F</a>. 10% of the input was made of 3 spike bursts, 20% of 2 spike bursts while the rest consisted of a single spike. (D) ISI distributions across temperatures for connectivity in A shows a big peak at times below 10ms. (E)ISI distributions across temperatures for neuron in B shows the absence of the peak below 10ms. (F) ISI distributions across temperatures for connectivity in C shows a big peak at times below 10ms. (G-I) Cumulative distribution of the ISI of the three connectivities. The distributions with the peak below 10ms change significantly with respect to the one at normal temperature (p* < 0.0005 Kolmogorov Smirnov test, ns: not significant, alpha value is strict to account for fewer counts at lower temperatures). This is due to the slight shift to the right of this peak at lower temperatures. (J) Evolution across temperatures of the spike rate of the simulated neurons explored for different balances of HVC_<i>RA</i> neurons and HVC_<i>X</i> neurons, with a fixed total of 80. Percentage of single spike input varied in steps of 10% from 70% and double and triple spike bursts also varied in 10% steps. (K) Evolution of spike rate, but with the input rates of the excitatory neurons inversed. (L) Evolution of spike rate, with synaptic inputs stronger in 0.5nS. Data points are mean values and bars are s.e.m. ISI distributions are normalized for each temperature which is color coded in °C. Simulations were made of a duration of 4 minutes.</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

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

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