Figure 1.
Song and Sleep-Related Firing in HVC and RA Neurons of Zebra Finches
(A) During the production of a song motif (sound spectrogram on top), RA-projecting HVC neurons (HVCRA neurons) produce at most one stereotyped spike burst (red rasters). HVC interneurons (HVCI neurons) produce dense and less-stereotyped spike patterns (green rasters). A more elaborate version of this figure was originally published in [1].
(B) Sleep-related firing in HVCRA and RA neurons. (i) Top: spike-raster plot of a simultaneously recorded HVCRA–RA pair during sleep. RA spikes (black rasters) have been time aligned to HVCRA bursts (red rasters). (i) Bottom: CSP function of the same neuron pair. Also known as the cross-intensity function, the CSP function is an estimate of the conditional RA spiking probability as a function of the time lag to HVCRA spikes (see Methods). (ii) ISI pdfs of RA neurons vary from one dataset to another. ISI pdfs have been averaged either over 29 RA neurons recorded in isolation (full line), or over 26 RA neurons recorded simultaneously with HVCRA neurons (dashed line), or over 50 RA neurons recorded simultaneously with HVCI neurons (dotted line).
Figure 2.
Markov Model of HVC Activity during Behavior and Sleep
(A) When birds are awake, but not singing, HVC activity persists in a ground state (state 0) with probability q = 1. When birds sing, groups of HVCRA neurons (numbered circles) are sequentially activated with probability p = 1 (the dashed arrows indicate song onset and offset). A single HVCRA neuron (red square) is linked with exactly one HVCRA group, and single RA and HVCI neurons (blue and green squares) are linked with random subsets of LR and LI groups, respectively.
(B) During sleep, HVCRA groups are sequentially activated with probability p < 1; with probability 1 − p, HVC activity transits into the ground state. There, it persists with probability q < 1; with probability 1 − q, it transits back into a song state.
(C) Bursts in different neuron types are modeled by the first few milliseconds of averaged song-related ISI pdfs pb(τ).
(D) Tonic firing in RA and HVCI neurons is modeled by gamma functions pa(τ) (black curves). The diversity of waking-related ISI pdfs in these neurons is illustrated by the blue and green curves, each representing a different neuron.
Table 1.
Model Parameters and Their Derivation
Figure 3.
Song-Related ISI pdfs of RA and HVCI Neurons
(A,B) Model-based fits of averaged ISI pdfs in RA and HVCI neurons during singing. The arrows delimit the ISI range of the burst models in Figure 2C, i.e., 6 ms and 10 ms, respectively. The RA-neuron data (A) were taken from [10], and the HVCI data (B) were provided courtesy of A. Kozhevnikov. LR = 12, and LI = 35.
(C,D) Raster plots of song-related spike trains in four RA and four HVCI model neurons for two different values of link counts LR/I and burst probabilities pR/I. Spikes are represented as tick marks and drawn in alternating colors for different neurons.
Figure 4.
Modeling Sleep-Related Activity (p,q < 1)
(A) An RA neuron producing few burst ISIs. A good fit is produced when the survival time of the ground state is long, compared to that of song states (light sleep, q much closer to 1 than p). DR = 80 ms, and VR = 0.7.
(B) A different RA neuron producing many burst ISIs. A good fit was produced by a relatively long survival time of sleep states (deep sleep). DR = 120 ms, and VR = 0.67.
(C,D) Spike raster plots of HVCRA and RA neurons. All HVCRA bursts (red rasters) are aligned at the center of the plots. Corresponding RA spikes (black rasters) are shown below each HVCRA burst. When p is large (strongly coherent sleep) (C), stereotyped RA bursting is observed over larger intervals than when p is small (D).
Figure 5.
Burst Epochs and Pairwise Correlations
(A) Instantaneous firing rates of a recorded HVCI neuron (top), a simulated HVCI neuron without burst epochs (middle), and a simulated HVCI neuron with burst epochs (bottom). Burst epochs are indicated by arrows.
(B) A sample raster plot of a simultaneously recorded HVCRA–HVCI pair (top) and a comparable plot from model simulations (bottom). The inclusion of burst epochs gives rise to rows with very sparse HVCI bursting (top arrow) and rows with dense HVCI bursting (bottom arrow), as is seen in real data.
(C–F) Average CSP functions in different neuron types. The functions are plotted in reference to a spike in the first pair, i.e., with respect to RA spikes in (D) and with respect to HVCRA spikes in (E).
(C) RA–RA neuron pairs (from n = 29 recorded pairs). p = 6/7, and q = 39/40.
(D) RA–HVCI pairs (n = 50 pairs). The arrow indicates an asymmetry that is reproduced by the model. p = 9/11, and q = 49/50.
(E) HVCRA–HVCI (n = 26). p = 7/8, and q = 59/60.
(F) HVCI–HVCI pairs (n = 19). HVCI neurons randomly link to 56 of the 100 HVCRA groups. p = 7/8, and q = 32/33.
In (C–F) LI = 50, pI = 0.63, DR = 240 ms, pR = 0.92, and LR = 13.
Figure 6.
HVC States Evolve Sequentially and Are Formed by Distinct HVCRA Groups
Distribution of CSPs in (n = 46) HVCRA–RA pairs in the interval −60 to 60 ms of HVCRA spikes (black histogram). With the exception of two peaks at CSPs zero and one (black arrows), the distribution is well-approximated by an exponential curve (purple line). Shown are the average CSP functions of 50 simulated HVCRA–RA pairs for three different model assumptions: (1) HVCRA neurons fire with probability pP = 0.8 in a single HVCRA group (red curve); (2) HVCRA neurons fire in two (randomly selected) HVCRA groups with probabilities 0.64 and 0.16 (green curve); and (3) activation of HVCRA groups is sequential in 80% of song-like transitions and in 20% it is random (blue curve). The green and blue arrows indicate inadequacies of model assumptions 2 and 3. p = 6/7, q = 39/40, LR = 12, pR = 1, DR = 240 ms, and pb = 0.
Figure 7.
RA-Intrinsic Dynamics and Inhibition
(A) When RA burst sequences extend beyond HVCI sequences by a random time uniformly distributed in the interval 0–15 ms, then the left flank of the average RA–HVCI CSP function gets uncharacteristically wide (arrows).
(B) Transitive suppression of tonic firing in RA neurons is explained by RA inhibition. Shown are average RA IFR curves in 1.2 s time windows in which one RA neuron does not fire a burst, and time-aligned to burst onset in a simultaneously recorded RA neuron. Conjunctively with the bursts, there is a transient reduction in firing rate of the nonbursting neuron (black curve, n = 50 RA neuron pairs). The model in which RA inhibition suppresses spontaneous firing (red curve) is able to reproduce this transient reduction, but the model in which RA neurons display a soft refractory period after bursts (blue curve) is not. p = 6/7, q = 39/40, LR = 12, pR = 1, DR = 240 ms, and pb = 0.