A canonical neural mechanism for behavioral variability

Abstract

The ability to generate variable movements is essential for learning and adjusting complex behaviours. This variability has been linked to the temporal irregularity of neuronal activity in the central nervous system. However, how neuronal irregularity actually translates into behavioural variability is unclear. Here we combine modelling, electrophysiological and behavioural studies to address this issue. We demonstrate that a model circuit comprising topographically organized and strongly recurrent neural networks can autonomously generate irregular motor behaviours. Simultaneous recordings of neurons in singing finches reveal that neural correlations increase across the circuit driving song variability, in agreement with the model predictions. Analysing behavioural data, we find remarkable similarities in the babbling statistics of 5-6-month-old human infants and juveniles from three songbird species and show that our model naturally accounts for these 'universal' statistics.

Figure 1. Fluctuations in the inputs to the effectors are very weak when noise is generated autonomously in the motor network.

(a) The motor network projects in a topographic manner to D effectors (D=10 effectors, 4 represented): each effector receives inputs from a different group of M=1,000 neurons. In spite of the large variability of the neuronal activity, the variability of the effectors (right) is extremely small (coefficient of variation of the effector averaged over the 10 effectors: ). (b) The neuronal activity in the motor network is highly irregular and the correlations across neurons are tightly distributed around zero. Left: Voltage traces for one excitatory (E, red) and one inhibitory (I, blue) neuron. Middle: Distributions of coefficient of variation of the inter-spike interval, CV_ISI. Right: probability density function (pdf) of Pearson correlation coefficients in the network.

Figure 2. A generic neural circuit driving behavioural variability.

(a) When the premotor-to-motor projections are topographically organized, fluctuations in the inputs to the effectors are large. Left: circuit architecture. In the motor network, neurons in the same group (same colour, projecting to the same effector) share a fraction f of premotor inputs (arrows coloured as the corresponding group) and have a fraction 1−f of non-shared inputs (grey arrows). Right: inputs to the effectors are variable . (b,c) In the premotor network, single neuron activity is irregular and neurons are very weakly correlated. (b) Top: Raster plots of E (red) and I (blue) premotor neurons. Bottom: instantaneous mean activity of E and I neurons (bars: 100 ms and 10 Hz). (c) Voltage of two excitatory premotor neurons (top) and their spike CCs (bottom). (d,e) In the motor network, single neuron activity is irregular and neurons are correlated. (d) Top: Raster plots of E and I populations. Bottom: instantaneous mean activity of E and I neurons (scale bar: 100 ms and 10 Hz). (e) Voltage traces of two neurons in the motor network projecting to different (top) and same (bottom) effectors. Bottom: pairs of neurons projecting to the same effector are substantially correlated (right); pairs projecting to different effectors are weakly correlated (left; see also Fig. 4). (f) The variability of the inputs to the effectors increases with the fraction of shared inputs and is substantial even if the number of inputs per effector, M, is large.This is because in the motor network the activities of the neurons belonging to the same group are correlated. (g) The circuit amplifies fluctuations. The amplification factor, , (see Methods section) measures the ratio between the variability of the effectors and of the input to the motor network . It increases linearly with the average number of synapses per neuron, K (mean±s.e.m.; see also Supplementary Fig. 3f). (h) Connection probability of two neurons in the motor network depends on their distance (see Methods section) with a footprint σ_rec. The diameter of the motor network is λ=1,000 μm. (i) decreases when narrowing the footprint of the recurrent interactions in the motor network. Red dot in the figure corresponds to the parameters used in a–e.

Figure 3. Single unit recordings in zebra finch RA nucleus and in the model motor network.

(a) Top: song motif of a zebra finch. Bottom: recordings of RA single unit over 133 repetitions of song motif, aligned to one syllable in the motif (lower panel) and the corresponding average firing rate (upper panel; 5 ms bin size). (b) Extension of the model depicted in Fig. 2a. Neurons in the motor network receives also temporally structured FF inputs, representing HVC inputs in the adult zebra finch (see main text and Methods section). (c) Raster plot and corresponding average firing rate of a neuron in the motor network of the model circuit in the presence of temporally structured FF input.

Figure 4. Correlations in the trial-to-trial neuronal variability increase along the model circuit generating motor variability.

(a,b) Noise correlations in the model. In the premotor network, noise CCs are weak. In the motor network, neurons activating the same effector have significant positive correlation coefficients. (a) Top left: example of noise CCs across two single units in the variability-generating premotor network (shaded area: 2.5 s.d. around the mean). Top right: population averaged CCs. Noise CCs are almost flat, indicating the absence of significant correlations in the activity of the premotor network. Bottom: Probability density function (pdf) of Pearson correlation coefficients in the premotor network. (b) Same as in (a) but for neurons in the motor network. Bottom: Conditional probabilities of the Pearson correlations of neurons in the same functional group (dark-blue; average correlations: ∼0.068) and neurons in different groups (light blue; average correlations: average correlations: ∼−0.0066). Note that the probability of having two neurons in a group and between groups depends on the number of groups, and by taking these priors into account, the average correlations across all neurons is close to zero (average correlations: ∼0.0008; see text and Supplementary Note 1).

Figure 5. Correlations in the trial-to-trial neuronal variability increase along the circuit generating motor variability in singing birds.

Experimental recordings in zebra finches during singing. Noise correlations are weak in LMAN but substantial in RA. (a) Area of recordings. (b) STA of the noise LFP during singing in LMAN (mean±s.e.m.). The motif-average LFP was subtracted from the LFP signal and the STA of this residual LFP was then computed separately for each single unit recording (see Methods section). (c) Noise CCs of two single units recorded simultaneously in LMAN during singing. The mean motif-related activity was subtracted from the instantaneous firing rate during singing and correlation analysis was performed on the residual trial-to-trial fluctuating signal (noise correlations, see Methods section). Noise CCs are flat after a random permutation of the spikes (grey trace, shaded area: 2.5 s.d. around the mean). (d) Single-unit pairs crosscorrelograms (blue) and average crosscorrelograms (inset) of single- versus multi-unit pairs (green) and pairs of multi-units (red) recorded from different electrodes in LMAN. (e) Distribution of Pearson correlation coefficients in LMAN. (f–j) Same as (a–e), but for neurons recorded in RA. In contrast to LMAN, RA neurons exhibit significant pairwise correlations. Crosscorrelograms are broad and their integrals are significantly larger in RA than in LMAN (see Methods and Results sections for statistical tests), reflecting the slow co-fluctuations in the activity of the simultaneously recorded units.

Figure 6. Temporal fluctuations slow down along the circuits generating motor variability (data+model).

(a,b) Decorrelation time in the activity of neurons in LMAN or RA during singing in zebra finches. (a) Two examples of noise ACs (see Methods section) for neurons recorded in LMAN (simultaneous recordings, CCs plotted in Fig. 5c). Inset: superimposed spike shapes (red: average trace). FR: average singing-related firing rate during song. (b) Same as (a) but for two RA neurons (simultaneous recordings, CCs plotted in Fig. 5h). The ACs are fitted to a decaying exponential (Orange in (a) and purple in (b); Time constant is indicated in the panels). (c) ACs are much broader in RA than in LMAN (single units and mean+s.d.). (d–f) The same as in (a–c) but in the model (, see Methods section). (d) ACs for neurons in the premotor network. (e) ACs for neurons in the motor network. (f) ACs in the premotor network decay faster than in the motor network (mean+s.d.).

Figure 7. Babbling statistics are similar across different vocal learners and in the model.

(a) Statistics of the babbling behaviour generated by the model circuit depicted in Fig. 2a–e when coupled to a minimal model of the vocal organ (see Methods section). Top: spectrogram of the vocal output signal . Bottom: probability density function (pdf) of vocal gesture durations (left) and averaged autocovariance of the envelope (ACE; right). Inset: distribution of gesture durations when the y axis is in log-scale. The distribution of gesture durations is well approximated by an exponential with a ‘scale parameter', (see Methods section). ACE decorrelates over a time duration of . Slow synaptic dynamics in the premotor-to-motor projections (red:; blue: ) results in slowly fluctuating vocal output (red: and ; blue: and ). (b–i) Statistics of the babbling behaviour in four species of vocal learners (ages of the subjects (‘babbling period') are given in Methods section). Blue: Zebra finches (Zf); Red: Swamp sparrows (Sw); Green: Canaries (Ca); Black: Human infants (Bab). Different lines of the same colour correspond to different subjects from the same species. (b–e) Same as in (a), but for the Zf (b: compare to the blue line in a), Sw (c: compare to the red line in a), Ca (d) and Bab (e). Gesture duration distributions lack any clear peak and are well fit with exponential decaying function with scale parameters (mean±s.e.m.): ; ; ; . The ACE decay time is specie-dependent: ; ; ; . (f,g) Cumulative distribution functions (cdf) of gesture duration for the four species before (f) and after (g) normalizing the gesture durations by . (h) Top: Interspecies differences in cdfs are much smaller than intraspecies differences (Kolmogorov–Smirnov statistic as a distance measure between cdfs). Bottom: Differences of cdfs in pairs of learners within (left to right: Zf–Zf, Sw–Sw,Ca–Ca, Bab–Bab) and between species (left to right: Zf–Sw, Zf–Ca, Zf–Bab, Sw–Ca, Sw–Bab, Ca–Bab). (i) Most of the interspecies differences in (h) are accounted for by normalizing the gesture durations to the scale parameter of the exponential fit of their distributions (see Results and Methods sections for statistical comparisons).