Supporting information
Buckley CL, Toyoizumi T (2018) A theory of how active behavior stabilises neural activity: Neural gain
modulation by closed-loop environmental feedback. PLoS Comput Biol 14(1): e1005926.
https://doi.org/10.1371/journal.pcbi.1005926

Contents
S1 Supplementary whisker data
S2 Alternate schemes for sensory feedback in the whisker system
S3 Supplementary fish dataS1 Supplementary whisker data
We analyze if sensory input through infraorbital nerve (ION) plays a role in coordinatingwhisking behavior, thalamic spiking activity, and cortical local field potential (LFP). Previous
results based on simultaneous recording from whisker, thalamus, and cortex exhibited thatthalamic spiking rate increased and low frequency power of cortical LFP decreased duringwhisking behavior. Here, we reanalyze this data set and quantify cross-correlation functions
between (1) 5-20 Hz power of the whisker position, denoted by Whisker; (2) thalamic spiking
rate computed with 20 ms averaging window, denoted by Thalamus; (3) and 1-20 Hz cortical
LFP power, denoted by Cortex, recorded from ION-intact animals (n=22) and ION-cutanimals (n=19). Raw recordings and the three processed traces are shown in Fig. S1A foran example animal. We chose the 1-20 Hz range for the analysis of cortical LFP power
because notable brain-state-dependent changes were previously observed in this range [1].
The spectrogram was computed using 2 s window to reliably estimate the predominant 1Hz
power in cortical LFP and the window was gradually shifted in 20 ms steps.

Next, we computed cross-correlation functions between these 3 quantities: WhiskerThalamus, Whisker-Cortex, and Thalamus-Cortex. While the resulting cross-correlation
functions were noisy in each animal, a mean cross-correlation function averaged over eachanimal group exhibited clear common properties. In both ION-intact and ION-cut animals,
whisking behavior lead correlated increase in the thalamic activity and decrease in thecortical slow oscillations. Consistent with this result, the thalamic activity was negatively
correlated with the low-frequency cortical LFP fluctuations (Fig. S1B).

Notably, the position of the mean cross-correlation peaks was significantly shifted in ION-cut
animals relative to the ION-intact animals (Fig. S1B). Specifically, the peak of the WhiskerThalamus cross-correlation was delayed for 400 ms (p=0.02, bootstrap test) and the peak ofWhisker-Cortex cross-correlation was delayed for 200 ms (p=0.03, bootstrap test) in ION-cut
animals. However, the temporal relationship between the thalamic spiking activity and thelow-frequency cortical LFP power was not significantly altered as assessed by theThalamus-Cortex correlation function (p>0.05, bootstrap test). The bootstrap statistics werecomputed by randomly resampling animals from the two groups, assuming a null hypothesisthat the two animal groups are the same (see, the inset panels for the bootstrap statistics
about the difference of the cross-correlation peak locations).

These analyses suggest that the brain state transition was delayed after a whisking onset in
ION-cut animals relative to ION-intact animals. Thus, while sensory input is not necessary
for the brain state transition, it was necessary for inducing short-latency brain statetransitions.

Fig. S1 | (A) A simultaneous recording of whisker position (Top), thalamic spikes (Middle),and cortical LFP (Bottom) in an example animal [2]. Based on these raw traces (black),
brain-state-relevant quantities (red) are computed and shown in each panel: 5-20 Hz powerof the whisker position (Top), thalamic spiking rate (Middle), 1-20 Hz power of the cortical

LFP (Bottom). (B) A cross-correlation function between Whisker and Thalamus (Top),
Whisker and Cortex (Middle), and Thalamus and Cortex (Bottom) for ION-intact animals(blue) and ION-cut animals (red), where the inset panels show the bootstrap statistics about
the difference of the cross-correlation peak locations. The Whisker-Thalamus and theWhisker-Cortex correlation functions were significantly shifted by the ION cut.

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S2 Alternate schemes for sensory feedback in the whisker systemAB

CFig. S2: Three models for whisker circuits mediating a negative closed-loop sensory
feedback. (A) Net activation of the modeled cortical population drives neurons in the facial
nucleus (FN) to drive whisker protraction. This in turn reduces excitatory sensory input to themodeled cortical population because this is driven by retraction. Here negative feedback ismediated implicitly at the periphery. (B) Protraction information could be conveyed along thefull pathway but net inhibitory input to the modeled cortical population result because POm
inhibits the cortex. In either model circuit, the initial activation of cortical neurons causes
subsequent suppression of their activity by feedback through the whisker circuit, constituting
a negative sensory feedback loop. These two hypotheses are testable but not necessarily
mutually exclusive. (C) An alternative hypothesis is the whisker feedback is completed in thebrain stem and changes in cortical activity are driven by activity changes in the thalamus.

Fig. S2: Three models for whisker circuits mediating a negative closed-loop sensory
feedback. (A) Net activation of the modeled cortical population drives neurons in the facial
nucleus (FN) to drive whisker protraction. This in turn reduces excitatory sensory input to themodeled cortical population because this is driven by retraction. Here negative feedback ismediated implicitly at the periphery. (B) Protraction information could be conveyed along thefull pathway but net inhibitory input to the modeled cortical population result because POminhibits the cortex. In either model circuit, the initial activation of cortical neurons causes
subsequent suppression of their activity by feedback through the whisker circuit, constituting
a negative sensory feedback loop. These two hypotheses are testable but not necessarily
mutually exclusive. (C) An alternative hypothesis is the whisker feedback is completed in thebrain stem and changes in cortical activity are driven by activity changes in the thalamus.
Our whisker model remains abstract in terms of known vibrissa system anatomy and, inparticular, the relay stations between the cortex and a whisker. The exact concordance ofthe model with known vibrissa system anatomy is beyond the scope of this paper, but weprovide a more detailed to demonstrate a possible anatomical explanation of our model andprovide a means for the research community to experimentally examine closed-loop sensory
feedback in specific biological circuits.
In our model (Fig. S2A), we assume that projections between regions are largely excitatory(c.f.[1]). Importantly, we distinguish two subcortical pathways that signal afferent input tocortical neurons - one for transmitting reafferent input and the other for transmitting
exafferent input. This distinction could reflect the separation between a parameniscal
pathway i.e., via thalamic POm, conveying reafferent signals, and a lemniscal pathway, i.e.,
via thalamic VPM, conveying exafferent input [2,3]). Accordingly, we modeled exafferent
input to cortical neurons by using a stereotypical pulse upon each whisker contact and brief
deflection, and reafferent input proportional to whisker angle reflecting motor efference [4].
Regardless of how the properties of reaffererent input - whisking phase, absolute position, ortheir temporal derivatives - are encoded by the pathway they do not change the main
conclusion of our model as long as the closed-loop sensory feedback constitutes net
negative feedback.
In agreement with the anatomy, we assume that cortically generated motor signals modulate
whisking behavior by acting on the facial nucleus (FN) [1]. Because whisking behavior
persists after sensory denervation [5] , cortical ablation [6], or decerebration[7], we explicitly
modeled a central pattern generator (CPG) that autonomously generates whisking patternslocating exogenous to the cortical-whisker loop [8]. Thus, the FN receives input from boththe cortical population and CPG and moves the whisker in the reafference model.
We cannot rule out other biological pathways for negative closed-loop sensory feedback. For
example, negative feedback can also be mediated by dominant cortical inhibition to themodeled population of cortical neurons (Fig. S2B). In agreement, thalamocorticalconnections strongly innervate fast spiking neurons and consequently implement strong
feedforward inhibition to the cortex[9]. Other potential models arise from heterogeneity incortical populations. For example, negative closed-loop sensory feedback can be mediatedby neurons in the barrel cortex that directly drive whisker retraction with extremely shortlatencies [10].
Alternatively, the dominant negative feedback loop could be subcortcial, Fig. S2C. Here thedynamics of the cortex only indirectly reflects the stabilization of the thalamus. This scheme
is also consistent with reduced thalamic activity during whisking [11]. It is important to notethat this implementation also fundamentally relies on stabilisation of neuronal activity by
negative closed-loop sensory feedback.
At the level of the whole vibrissa system, there are likely multiple parallel and nested
feedback loops, both positive and negative [1]. However, we assume that the overall or net
feedback mediated by the cortical-whisker circuit during corresponding behavior is negative

in sign which we empirically demonstrate the presence of negative closed-loop sensory
feedback in zebrafish active sensing. These models are experimentally testable. For
example, a group of neurons that encode aspects of reafferent input, such as whisker
protraction, could be genetically labeled and used for anatomical tracing studies. We canmoreover study the physiological role of these neurons by optogenetically silencing themduring active whisking and study how brain state as well as the animal’s behavior may bealtered. This specific neuronal population could also be optogenetically activated and theensuing behaviors and changes in vibrissae information processing pathways studied.
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S3 Supplementary fish dataFig. S3 | (A) The decorrelation effect is not an artifact of measurement noise. Changes inpairwise correlations (replay-closed and change in log low frequency power (replay-closed,mean over interval [0.01 0.15] Hz) were highly correlated in the recorded neurons evenwhen the calcium traces (both cells and motor neurons) were thresholded (the threshold wasequal to the mean plus one standard deviation of the calcium signal measured over both
replay and closed loop conditions) (Spearman’s rank correlation ρ=0.57, p<10-8). (B) The
increase of motor activity in the closed-loop condition does not easily explain reduction inneural fluctuations and correlation. (B,top): Changes in mean motor activity (replay-closed)and change in log low frequency power (as in A), averaged over all cells within a given trial
are positively correlated (r=0.18, p<10-2, Spearman’s rank correlation). Specifically, on a cellby-cell basis increases in low frequency fluctuations are correlated with increases in motor
activity (replay-closed) despite the fact that on average motor activity was higher duringclosed-loop behavior and low frequency fluctuations were reduced. B(bottom): Furthermorechanges in mean motor activity (replay-closed) and changes in pairwise correlations (replayclosed) (averaged over all pairwise interactions in a given trial) are not significantly
correlated (r=0.03, p>0.5, Spearman’s rank correlation). (C) Filter describing behavioral
feedback. A linear filter that describes behavioral feedback (E→E’) is also strongly negative.
Following the kernel method outlined in the methods section we calculated the behavioral
feedback as a direct filter between the closed loop environment and environment in thereplay condition (E→E’). This also indicates that the closed-loop sensory feedback isnegative. Note: the magnitude of this closed-loop sensory feedback estimated from thebehavior is much greater than the cell self-feedback, reflecting the fact that cellular variability
was much greater than variability across animals.