Elemental gesture dynamics are encoded by song premotor cortical neurons

Abstract

Quantitative biomechanical models can identify control parameters that are used during movements, and movement parameters that are encoded by premotor neurons. We fit a mathematical dynamical systems model including subsyringeal pressure, syringeal biomechanics and upper-vocal-tract filtering to the songs of zebra finches. This reduces the dimensionality of singing dynamics, described as trajectories (motor 'gestures') in a space of syringeal pressure and tension. Here we assess model performance by characterizing the auditory response 'replay' of song premotor HVC neurons to the presentation of song variants in sleeping birds, and by examining HVC activity in singing birds. HVC projection neurons were excited and interneurons were suppressed within a few milliseconds of the extreme time points of the gesture trajectories. Thus, the HVC precisely encodes vocal motor output through activity at the times of extreme points of movement trajectories. We propose that the sequential activity of HVC neurons is used as a 'forward' model, representing the sequence of gestures in song to make predictions on expected behaviour and evaluate feedback.

Figure 1. Schematized view of a dynamical systems model describing labial dynamics and vocal tract filtering (trachea and oro-esophageal cavity, OEC)

The syringeal membrane was modeled as a mass (m) with damping (b) and a restitution (spring) force (K). Normal form equations for labial position (x(t), red line) were integrated, computing the input pressure at the vocal tract (Pi(t), green line) and ultimately the total output pressure (Pout(t), blue line). v, sound velocity; T, propagation time along trachea; γ, time constant (see Methods).

Figure 2. A low dimensional model: reconstructing gestures

Spectrographs of a bird's song (a) and model synthetic song (b). Song is described by fitted parameters α(t) and β(t), proportional to air sac pressure and labial tension, respectively (c). Each sound is generated by a continuous curve in the parameter space of the model, a "gesture" (d). Oscillations in the vicinity of a SN bifurcation present rich spectra, typical of zebra finch song. Note that the spectrally poor "high note" (green) is distant from the SN bifurcation. The gray area indicates the region of phonation. The distribution of gesture durations for five birds is displayed in (e).

Figure 3. Testing the low dimensional model

The activity of HVC selective neurons of sleeping birds in response to the presentation of BOS and modeled BOS (mBOS) was similar. The timing of the three repeated motifs that were presented is indicated by the bold horizontal lines.

Figure 4. Timing of gestures relative to bursting of projection neurons

a, song spectrograph and oscillograph (top panels); reconstructed parameters pressure and tension (middle panels), with tick marks indicating the times of all GTEs. Bottom panel, raster plots of the responses of two neurons (color coded green and orange), together with their closest GTE, indicated with lines of the same colors. The trajectories (same color coding) in parameter space are displayed in (b), with a point indicating the mean position of a burst, and arrows indicating the trajectory direction. c, distribution of time differences between consecutive GTE occurrences (N = 5 birds). d, distribution of time differences between the time of each spike (Ts) and the time of the closest GTE in sleeping birds (N = 14 HVC_(p), 5 birds). e, The same analysis of d on singing birds (N = 5 HVC_(p), 2 birds).

Figure 5. Suppressed interneuron activity is associated with GTEs

a, Organized as in Fig. 4a, but with spike count response to the song (10 ms bin, 20 repetitions; green line) for one HVC_(i), and a smoothed measure of the response (black line; see Methods). Red squares indicate the time of the minima in the smoothed measure, and the vertical lines indicated the position of the closest GTE to each minima. b, distribution of time differences between spike response minima and their closest GTE in sleeping birds (15 HVC_(i), 5 birds). c, Same analysis in singing birds (10 HVC_(i), 3 birds).

Figure 6. During singing, HVC_(p) fired in the vicinity of GTE

a, A HVC_(p) neuron bursts locked to the vicinity of a GTE even as the syllable sequence and time interval varies. b, For another bird, the burst of a HVC_(p) neuron is locked to a GTE in the vicinity of a subtle acoustic transition.