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Brain State Control by Closed-Loop Environmental Feedback

Brain state regulates sensory processing and motor control for adaptive behavior. Internal mechanisms of brain state control are well studied, but the role of external modulation from the environment is not well understood. Here, we examined the role of closed-loop environmental (CLE) feedback, in comparison to open-loop sensory input, on brain state and behavior in diverse vertebrate systems. In fictively swimming zebrafish, CLE feedback for optomotor stability controlled brain state by reducing coherent neuronal activity. The role of CLE feedback in brain state was also shown in a model of rodent active whisking, where brief interruptions in this feedback enhanced signal-to-noise ratio for detecting touch. Finally, in monkey visual fixation, artificial CLE feedback suppressed stimulus-specific neuronal activity and improved behavioral performance. Our findings show that the environment mediates continuous closed-loop feedback that controls neuronal gain, regulating brain state, and that brain function is an emergent property of brain-environment interactions.


Introduction
The repertoire of animal behavior involves both passive and active interactions of the brain with the environment. Passive interactions are driven by the environment and convey signals for passive sensing and alert. Active interactions, in contrast, are bidirectional, mediating movement and goal-directed behaviors. During active interactions sensory input from the environment is shaped by motor actions, and sensory percepts inform future motor commands, forming a closed-loop between action and perception. This closed-loop environmental (CLE) feedback is central to the production of motor control behaviors (Wolpert and Ghahramani, 2000;Kawato, 1999;Scott, 2004) and active sensing behaviors such as saccading and sniffing (Smith 1962;Von Holst, 1954;Crapse and Sommer, 2008).
Yet, how this CLE feedback impacts on brain state, i.e., brain-wide neuronal dynamics and processing, has received relatively little attention.
Brain state, typically characterized by the degree of synchronously fluctuating neuronal activity as reported by electroencephalography (EEG), local field potentials (LFP), electrocortiography (ECoG), membrane potential, and population spiking activity, is strongly modulated by behavioral context (Buzsáki et al., 2012;Harris and Thiele, 2011). One of the earliest experimental examples of this phenomenon was the demonstration that alpha frequency power (7.5-12.5Hz) in EEG recordings is enhanced when subjects close their eyes or during periods of drowsiness (Berger, 1929). More generally recent experiments in rodents have demonstrated that synchronous low-frequency fluctuations (a synchronized state) are typically suppressed (moving to a desynchronized state) when animals transition from quiet attentive behaviors, where animals are largely passive, to active behaviors such as running or whisking (Crochet and Petersen, 2006;Niel and Stryker, 2010;Schneider et al., 2014;Otazu et al., 2009;Zagha et al., 2013).
Brain states not only alter spontaneous brain dynamics, but also sensory representations, presumably allowing brain function to adapt to behavioral context. For example, it has been shown that the onset of running amplifies cortical responses to visual and auditory stimuli (Niell andStryker, 2010, Fu et al., 2014;Schneider et al., 2014;McGinley and McCormick, 2014). In addition, cortical responses to punctuate stimuli are larger during synchronized states (Poulet and Petersen, 2008;Fanselow and Nicolelis, 1999;Castro-Alamancos, 2004, Otazu et al., 2009. These brain state changes are typically thought to happen across the whole brain (Berger, 1929Fu et al., 2014;McGinley and McCormick, 2014) and are cross-modal (Otazu et al., 2009). Several internal mechanisms have been implicated in these changes including neuromodulatory pathways (Goard and Dan, 2009;Polack et al., 2012;Pinto et al., 2013;Fu et al., 2014), thalamo-cortical projections (Poulet et al., 2012), and intracortical feedback (Zagha et al., 2014;Schneider et al., 2014). Changes in the external sensory environment also play an important role. Under passive sensing conditions sensory stimulation can shift neural activity in the visual cortex between asynchronous and synchronous regimes (Tan et al., 2014) and more generally sensory stimuli quench neural variability (Churchland et al., 2010). More relevant to the present study, brain state transitions often coincide with the onset of active behaviors, which are characterized by the presence of reafferent input (sensory input resulting from one's own action, mediated by the environment). It is well known that reafferent input strongly influences neural activity (Curtis and Kleinfeld, 2009;Urbain et al., 2015;Brooks et al., 2015) and modulate sensory responses (Diamond et al., 2008). However, the role played by reafferent input in regulating brain state is not well understood. In this paper, we combine theoretical and experimental approaches to dissect the effect CLE feedback mediated by reafferent input, as oppose to sensory input per se, has on modulating brain state. In doing so we elucidate a novel function that CLE feedback plays in sensing and behavior.

Results
During active behavior, sensory input to the brain is directly shaped by motor actions, and reciprocally, motor actions are informed by prior sensations forming a closed-loop between the brain and the environment. Under such conditions, it is possible to distinguish two sources of sensory input (Von Holst, 1954), see Figure 1A. First, exafferent input describes sensory signals that originate in the environment, but which are completely external to the brain (Von Holst, 1954). Second, reafferent input describes sensory signals, which, while mediated by the environment, are a direct consequence of an animal's own actions and constitute a sensory feedback signal to the brain (Von Holst, 1954). While it is known that sensory input in general can influence brain state variability (Churchland et al., 2010), it is not clear whether exafferent and reafferent input play distinct roles in determining these changes, or whether only total synaptic input is of importance. To examine the effect of each type of input on brain state, we distinguish three types of brain-environment interaction. First, an open-loop condition, where sensory input is not coupled to motor output and thus the brain receives sensory input independent of its own activity ( Figure 1B). In this condition, reafferent input is absent and the brain receives only exafferent input. Second, a closed-loop condition, where the brain interacts with the environment in a closed-loop thus coupling motor action and sensory perception ( Figure 1C). In this condition, the brain receives reafferent input in addition to any possible exafferent input. Lastly, we define a replay condition, where again the brain operates in an open-loop but where reafferent input experienced during a prior closed-loop condition is recorded and replayed as exafferent input ( Figure 1D). In this condition, the total sensory input is identical to that in the closed-loop condition, but reafferent input is absent. Specifically, the sensory input during the replay condition is not a consequence of motor actions within that condition. Therefore, this condition serves as a strong control allowing us to distinguish precisely the contribution made by reafferent input rather than that of total sensory input, to the brain state.
To understand the possible effects that CLE feedback could have on brain activity we introduce a simple idealized model. We start by describing collective neuronal activity, e.g., an EEG signal, of an open-loop brain (denoted as ( )), in terms of a first-order differential equation, where is white noise of instantaneous variance 2 generated inside the brain, is time, and is the time constant of the system. The autocorrelation peak (instantaneous variance) of variable is given by Peak = 2 /2 (see, Figure 1B for open-loop time trace). To describe neuronal activity in the closed-loop condition (denoted as ( )), we approximate reafferent input as a linear function of the brain variable, i.e., where scales the strength of reafferent input and is again white noise of instantaneous variance 2 . (Later we also explore a more realistic reafferent input that involves filtering and delay). In this condition, the continuous cycles of reafferent input constitutes a CLE feedback signal to the brain. The presence of this CLE feedback changes the effective time constant to eff = /(1 − ) or, equivalently, it the changes the system's gain. We can quantify this change by using an expression for the autocorrelation peak of the system, as follows, In particular, we find that CLE feedback suppresses fluctuations within the brain if this feedback is negative ( < 0; see Figure 1C for closed-loop time trace).
In contrast, we can describe neuronal activity in the replay condition (denoted as ( )) as: where is again white noise of instantaneous variance 2 . Here, the brain receives the same total sensory input as in the closed-loop condition, ( ), but as exafferent input, i.e., it depends on the dynamics of ( ), and not on ( ). Again we can calculate the autocorrelation peak of the brain variable in this condition as Peak = Peak + Peak * 2 /( − 2). Notably, even though the brain receives exactly the same total sensory input in the replay and closed-loop conditions the amplitudes of fluctuations are not the same. In particular, if CLE feedback is negative, we obtain peak < peak < peak (see, Figure 1D for replay time trace). In summary, this simple model suggests that CLE feedback constituted by continuous reafferent input could have a profound effect on neuronal fluctuations and thus could be implicated in the modulation of brain state. In the next section, we examine this hypothesis using experimental data.

Negative CLE feedback suppresses synchronous neural fluctuations
We tested our predictions by analysing two-photon imaging data recorded from larval zebrafish behaving in a virtual flow simulator (Ahrens et al., 2012), a setup that allowed us to quantify the differences between the closed-loop and replay conditions directly ( Figure 1). In this setup, bouts of activity recorded from motor nerves along the spine of a paralyzed fish were translated into a backward drift of a visual grating, simulating forward swimming. This allows the fish to maintain its perceived horizontal position by swimming against water flow (Ahrens et al., 2012), (Figure 2A). In a transgenic fish expressing the calcium indicator GCaMP2 brain-wide calcium activity was monitored using a two-photon microscope to scan single planes in the brain. In a closed-loop condition, the fish actively maintain their position in the virtual environment. In a replay condition, the same fish receives a replay of the closed-loop visual stimulus without real-time visual feedback (Figure 2A), (Ahrens et al., 2012). We found that neural dynamics between the two conditions were significantly different despite the fact that both the closed-loop and replay conditions involve identical sensory input ( Figure 2B).
Notably, the only information the fish received about oncoming flow was visual, i.e., there was no proprioceptive input as the fish was paralyzed (Ahrens et al., 2012). Individual neurons were heterogeneous across the whole brain, but on average low frequency (0.01 -0.15 Hz) fluctuations were suppressed (p = 0.046, sign test) and neurons were decorrelated (p = 0.005, sign test) under the closed-loop condition compared to the replay condition ( Figure 2B). Changes in the geometric mean of low frequency fluctuations and correlation were highly correlated in each pair of cells (r=0.69, p<10 -10 , Spearman's rank correlation), suggesting a common cause (see Figure 2C). The decorrelation effect was not an artifact of measurement noise, which may dominate at high frequency because the result was robust to the removal of low-level calcium activity by thresholding (see Supplementary Figure S1A).
This change aligns with brain state transitions at the onset of active behavior that has been reported in other species (see Poulet et al., 2012 or Harris andThiele, 2011 for a review). This suppression of low frequency power and correlation could be caused by an efference copy signal (signal encoding intended motor action) that suppresses synchronous neuronal fluctuations (Zagha et al., 2014;Schneider et al., 2014). However, while motor activity levels were higher in the closed-loop condition than the replay condition, this did not explain the  While these filters are neuron-dependent, the average normalized filters showed clear net effects ( Figure 3A). On average, across cells, the interaction from the brain to the environment, B'→E' ( Figure 3A, purple solid line), was strongly positive, indicating that an increase in neural activity positively drove motor behavior. However, we found that interaction from the environment to the brain, E→B' ( Figure 3A, pink solid line), was net negative, indicating that an increase in motor behavior on average suppressed neural activity. It is reasonable to assume that the same filters (circuits) operate in the closed-loop condition. If this is the case, CLE feedback for each cell in the closed-loop condition is characterized by the convolution of the two filters, i.e., by the convolution of the B'→E' and E→B' interactions computed for each cell. The convolution of these filters was on average also negative ( Figure 3A, cyan dashed line), peaking at about 1 s. This suggests, that on average, increases in neural activity self suppressed after 1 s due to negative CLE feedback.
Notably, the negative CLE feedback interactions were also confirmed by behavioral analysis, in which the the E→E' filter was estimated directly (see Supplementary Figure S1C), which supported the robustness of our results.
Next, we considered what the consequence of this negative CLE feedback on each cell's activity would be. Our conceptual model, Figure 1, suggests that fluctuations in neural activity should decrease if a cell receives negative CLE feedback. In this case the estimated CLE feedback in each cell should predict to what extent fluctuations in low frequency power should change in the closed-loop condition relative to the replay condition (see Methods). As theoretically expected, Figure 3B demonstrates that the predicted degree to which a neuron's activity was suppressed during the closed-loop condition relative to the replay condition was highly correlated with what was actually observed (r = 0.39, p < 10 -8 , Spearman's rank correlation). Note that neural activity in the closed-loop condition was not used to fit each filter. Although the majority of cells across the fish brain were suppressed by the behavior, the top 10 percentile of cells that were both strongly suppressed, and strongly involved in, negative CLE feedback were clustered in the cerebellum ( Figure 3C), a brain area implicated in sensory-motor planning and coordination (Scott, 2004). This supports the idea that the cerebellum plays a central role mediating negative closed-loop interaction between the brain and the environment by converting sensation into action in fish during optic flow stabilization.
We then investigated whether the dynamic relation between neuronal activity and motor activity were also affected by CLE feedback. To do this, we quantified the brain/environment dynamics for each neuron by naively evaluating the E→B filter in the closed-loop condition, and compared this to the corresponding E→B' filter in the replay condition ( Figure 3D). These two filters were generally distinct in the observed neurons, but were particularly so for those cells that were strongly stabilized by CLE feedback ( Figure 3D; Inset). In these neurons, while the E→B' filter from the replay condition was approximately causal, as expected, the closed-loop filter E→B had an additional acausal component. We suggest that this latter filter reflects the closed-loop interaction between the brain B and the environment E. To test if the closed-loop interaction could explain this discrepancy, we theoretically predicted the E→B filter in the closed-loop condition based on data from the replay condition, i.e., using both the E→B' and B'→E' filters (see Methods). We found that, on average, this closed-loop effect could account for the difference between E→B and E→B' as calculated for the closed-loop stabilized cells ( Figure 3D; Inset). To quantify this for each cell, we calculated the mean square error between the predicted and E→B' filters and between the E→B and E→B' filter.
The ratio of these two error terms then quantifies the fraction of the mean square error that was explained by the prediction. This ratio was significantly less than one (median = 0.80, p < 10 -11 , sign test), indicating that the prediction was more accurate when the closed-loop effect was included, and the ratio was positively correlated (r=0.25, p<10 -13 , Spearman's rank correlation) with the degree to which individual cells were stabilized in the closed-loop condition ( Figure 3D). Altogether, these results indicated that neuronal dynamics, as well as its relation to sensory stimulus and behavior, not only depend on brain circuits, but are also dynamically shaped by the mutual interaction between the brain and the environment.

CLE feedback explains the difference between active and passive sensing
Behaviors not only induce brain state transitions, but also differentiate active sensing from passive sensing. To investigate whether these differences could be accounted for by CLE feedback, we examined a well-studied model of a brain state transition in the rodent whisker system. Specifically, we consider CLE feedback to the rodent brain mediated by whisking vibrissa. Although more precisely we should refer to this as closed-loop body/environmental feedback, we retain CLE acronym by generalizing the notion of environment to refer to all processes outside of the brain highlighting the generality of our theory. Whisking not only changes brain state (Crochet and Petersen, 2006;Poulet and Petersen, 2008), but also reduces the sensitivity of the cortex to passive whisker deflections (Crochet and Petersen, 2006;Crochet et al., 2011). However, interestingly, robust responses are maintained for active contact events when the whisker collides with an object placed in the whisk field (Crochet and Petersen, 2006;Crochet et al., 2011). Furthermore, in an active touch condition where the whisker repeatedly collides with an object both intra-neuronal correlations and low frequency power of membrane potential recovers close to their passive state values (Crochet et al., 2011). We theoretically investigated whether these phenomena could be explained by the hypothesis that vibrissa dynamics mediates negative CLE feedback to the brain, influencing cortical dynamics in a way analogous to fish swimming behavior. Notably, while multiple different mechanisms are involved in brain state transition (Goard and Dan, 2009;Polack et al., 2012;Pinto et al., 2013;Fu et al., 2014;Poulet et al., 2012;Zagha et al., 2014;Schneider et al., 2014), for which sensory input is not always necessary (Poulet and Petersen, 2008;Poulet et al., 2012), this does not exclude the role of CLE feedback under physiological conditions. Indeed, although brain state transitions can happen at whisking onset even after the sensory nerve is cut (Poulet and Petersen, 2008), our analyses revealed that the latency of brain state transition, measured by whisking-related reduction in low frequency power of cortical LFP or in thalamic spiking rate, was delayed under this condition as compared to the control condition (Supplementary Section S2). This supports a physiological role for sensory input in the brain state transition.
Here, we construct a simple model of the vibrissa system to investigate the possible role of CLE interaction. The model comprises excitatory and inhibitory cortical populations dynamically interacting with a single vibrissa ( Figure 4A; see Methods for details). In our model, synchronous membrane potential fluctuations arise endogenously from interplay between the build up of excitatory cortical activity by recurrent connections and their eventual suppression by adaptation after ca. 1 s in each cell (see Methods). To model the brain/body interaction, we assumed that cortical excitatory neurons drive whisker motor behavior and both excitatory and inhibitory neurons receive the sensory input that reflects whisker angle.
Based on our theory, Figure 1, we hypothesized that synchronous neural fluctuations could be reduced during whisking by negative CLE feedback. We modeled this by assuming that cortical excitatory neurons are activated by whisker retraction but this activation drives whisker protraction (see Figure 4A). (Note the specific biological implementation of the negative CLE feedback is not central to our claims, and there are several other plausible schemes, see Discussion and Supplementary Section 6.) We also model a central pattern generator (CPG, likely located in the brain stem) (Hill et. al, 2011) that, once turned on, rapidly cycles the position of the vibrissa back and forth at around 10Hz.
Sensory input during contact events involves both contact-related and whisker angle-related signals (Diamond et al., 2008). To capture this sensory input we modeled a single whisker as two stiff mass-less sections connected by hinges at the center and the base, which are constrained by muscles (simple torsion springs). Whisking is implemented by driving the equilibrium position of the base spring. The center spring has an equilibrium value of zero angular displacement and thus tends to align both sections (see Supplemental Information Section 3). We start with a simple non-bending stiff whisker but later vary the stiffness parameter (see Methods). A horizontal solid wall is placed above the whisker and, as the whisker collides with the wall, the whisker tip stops, see Figure 4A, interrupting CLE feedback about whisker angle. Whisker contact not only involves a modification of CLE feedback but also invokes exafferent input, or contact-detection signal, that results from the stereotypical response of pressure sensitive cells in the trigeminal ganglion (Szwed et al., 2003). We model this as a brief square wave pulses (ca. 25 ms) triggered by each contact event (see Methods).
Our key hypothesis, i.e., that whisker position mediates negative CLE feedback to cortical neurons, allowed us to reproduce rodent brain state findings that are observed under three behavioral conditions (the quiet condition, the whisking condition, and the active touch condition; Figure 4B [ Crochet et al., 2011]). Specifically, the synchronous low frequency membrane potential fluctuations generated during the quiet condition (open-loop: the whisker position is fixed at 0) were significantly suppressed during the whisking condition (closedloop: the whisker is driven by the CPG and cortex) ( Figure 4C). In effect, the negative CLE feedback reduced the gain of the cortical system, see conceptual model Figure 1, and replaced prominent (ca. 1 Hz) synchronous fluctuations of the membrane potential with fast (ca. 10 Hz), but weak, fluctuations locked into the whisking cycle. As a result, the average inter-neuronal correlation of membrane potential for pairs of neurons was also suppressed ( Figure 4D).
During the active touch condition, occasional whisker touch events stopped the whisker tip on the object's surface ( Figure 4B; touch events marked by red bars). Both the low frequency power and cross-correlation of membrane potential fluctuations were partially recovered during the active touch condition in agreement with experimental results (Crochet et al., 2011) ( Figure 4C and D, red lines). We hypothesized that this recovery was a consequence of intermittent interruption of negative CLE feedback during whisker contact events. To verify this, we examined whether this result depended on the stiffness of the whisker. We also hypothesized that, if the whisker is very flexible, then the base angle would change continuously, despite contact of the tip, fully preserving CLE feedback. In contrast, a very stiff whisker would come to complete rest on the wall during each contact maximally interrupting CLE feedback (see also Supplementary Figure S3B). We found that the recovery of 1-5 Hz power was indeed predominantly caused by the interruption of CLE feedback and not touchevoked exafferent input (see Supplementary Figure S3C) demonstrating that these transient interruptions of CLE interaction can rapidly switch the active brain state to a passive brain state.
This model also accounted for observed brain state dependent changes in sensory processing (Crochet et al., 2011) without assuming additional mechanisms (Lee et al., 2008;Nguyen and Kleinfeld, 2005). In agreement with experimental results we found that passive exafferent input evoked large sensory responses in the quiet condition but markedly smaller responses during the whisking condition ( Figure 4E) (Crochet et al., 2011). Again, this was because negative CLE feedback decreases the gain of the cortical circuit (Supplemental Section 4). However, in agreement with experimental data, cortical neurons exhibited more reliable responses to active touch events ( Figure 4B and E). This was because the negative CLE feedback, that suppressed neural fluctuations during whisking, was transiently removed during active touch events allowing endogenous brain dynamics to amplify the cortical response to exafferent input ( Figure 4E and F). Consequently, active touch events combined large sensory evoked responses (signal) and low background fluctuations (noise).
To quantify this effect, we computed a discriminability index (see Methods) that measures the separation between the distributions of membrane potentials in the presence or absence of sensory events. The value of the index was similar for perturbations in both quiet and whisking conditions, i.e., although the deflection-evoked response (signal) was greater in the quiet condition, so were background fluctuations of membrane potential (noise) (see Figure   4E and F). In contrast, the discriminability index was greater for active touch events ( Figure  4E and F). Hence, the model suggests that cortical neurons are selectively sensitive to interruption of the animal's own active sensing. All these results are intuitively reproduced in a simplified model of CLE interaction, demonstrating the robustness of our findings (Supplemental Section 4).

Neurofeedback modulates brain dynamics and behavior
We further tested a core prediction of our theory by examining the impact of an artificially constructed CLE feedback on brain dynamics. Specifically, we investigated whether we could use an ECoG-based fast neurofeedback technique to modulate brain dynamics and subsequently behavioral performance in primates. This setup allowed us to observe the impact of CLE interaction without involving efference copy signal (which can induce brain . If the decision value fell between these two thresholds, a grey screen was presented. This protocol effectively approximates negative feedback (the closed-loop condition) on the decision value dynamics of the animal (however see Discussion). To distinguish between the influence of neurofeedback from the visual stimuli alone, we used a control condition in which the monkey was presented with a recording of the visual stimuli that emerged during the closed-loop condition (a replay condition). Thus, as in our conceptual mode ( Figure 1A), and analogous to the fish experiment (see Figure 2A), corresponding closed-loop and replay conditions share identical visual stimuli and only differed by the presence of neurofeedback. Again, this allowed us to examine the exact effect of CLE feedback, rather than sensory input on brain activity and behavior.
We observed that neurofeedback immediately altered the dynamics of the decision value and thus brain dynamics, without requiring any prior training or habituation of animals. The power spectrum of the decision value below 5 Hz significantly differed under the two conditions ( Figure 5B). While the 0-1 and 3-4 Hz (summarized in Figure 5C) frequency ranges were suppressed, the 1-3 Hz frequency range was enhanced during the closed-loop condition relative to the replay condition. This oscillatory modulation of the power spectrum could have arisen from delay (ca. 100 ms) in negative CLE feedback, but it would also depend on various factors, including the kinetics of the decision value, and early visual stream processing. However, the exact mechanisms underlying the changes in the power spectrum are not the focus of this study. We found that not only were the dynamics of the decision value altered by neurofeedback, but also that there was significant improvement in the monkey's fixation performance ( Figure 5D). Specifically, the distance of the eye position from the fixation point was quantified and compared under the two conditions. The fixation performance at 1600-2100 ms after the appearance of the fixation point (about 300-900 ms after typical grating onset; Supplementary Figure S5C) in the closed-loop condition was enhanced ( Figure 5E). To establish a quantitative relationship between changes in neural dynamics and behavior, we analyzed the trial-to-trial correlation between the power spectrum of the decision value and fixation performance. The reduction of fluctuation in the decision value at specific frequencies correlated with improved fixation performance ( Figure 5F). In particular, the neurofeedback-induced reduction of decision value fluctuations in the 3-4 Hz frequency range (estimated from data before the behavioral improvement; see Supplementary Figure S5D) showed a significant correlation with improved fixation performance ( Figure 5G). Taken together, these results indicate that in primates artificial neurofeedback can change brain dynamics related to sensing and task-related behavior, which was consistent with our fish and rodent studies. Although the causal chain of events underlying these changes may also involve internal brain mechanisms for state transitions (e.g., neuromodulators; see Discussion), we assert that neurofeedback constitutes the primary cause of these changes as it is the only difference between each condition.

Discussion
Brain state transitions triggered by the onset of active interactions between the brain and environment, represent a major neuronal mechanism shaping sensing and behavior. In this study, we use both theory and experiment to support the idea that negative CLE feedback inhibits network gain, which in turn, suppresses synchronous neuronal fluctuations and sharpens sensory responses. We generalize and support the theoretical framework in three diverse animal model systems summarized in Figure 6. In each system, we show that negative CLE feedback regulated real-time brain state and animal behavior.
Specifically, CLE feedback quantitatively predicted cell-specific suppression of neural oscillations in zebrafish, enhanced signal-to-noise ratio for active sensing in rodent, and enhanced task performance in primate vision.
The importance of using naturalistic sensory stimuli to study and manipulate brain state dynamics is widely demonstrated (Felsen and Dan, 2005). However, an important prediction of our theory (Figure 1, Supplemental Information Section 7), supported by our experimental findings (Figures 2, 3, and 5), is that brain dynamics during active sensing cannot be fully recapitulated or re-encoded, even if the same sensory input is precisely recorded and replayed back into a passive brain. These results provide evidence that brain state neurometrics and behavioral psychometrics during active behaviors can only be accurately understood by a quantitative account of ongoing brain-environment interactions (O'Regan and Noë, 2001).

Neuronal gain control by CLE feedback
The formal component of our theory, i.e., that CLE feedback can modulate a system's gain, is well documented in dynamical systems theory and control theory (e.g., Aströmand Murray, 2010). This gain control occurs even though the instantaneous effect of the pathways mediating feedback is purely additive (c.f. Figure 1) because the effect of repeated cycles of feedback accumulates over time. For example, input to a linear dynamical system with feedback strength makes a first direct contribution to its response, but then also makes subsequent contributions as this initial response cycles around a feedback loop-a contribution of after one cycle, 2 after two cycles and so on.
The cumulative sum of these contributions I + + 2 +. . . = /(1 − ) is equivalent to divisively scaling the input magnitude by a factor that depends on the feedback strength, i.e., effectively changing the system's gain. Thus, a constitutively active closed-loop feedback that mediates multiple action-perception cycles is essential for the form of gain control we propose.
This means that discrete and intermittent involvement of reafferent input does not imply gain modulation. For example, the classical reafference principle explains neuronal responses by a one-time detection of the mismatch between an efference copy (predicted) and reafferent (actual) (Von Holst, 1954). However, this situation is likely an inaccurate idealization to describe the closed-loop systems studied here. For example, in the zebrafish system, swim bouts typically occur every 700 ms and this interval closely overlapped with the peak of the estimated environmental feedback interaction ( Figure   3A and Supplementary Figure S1C). Hence, the neural responses in the fish experiment suggest a more dynamic system, where neural activity evoked by many cycles of action and sensation are continuously and mutually interacting.

Neuronal mechanisms of negative CLE feedback
The presence of continuous negative CLE feedback during active behavior is fundamental for our theory. Although, as a higher order theory, it is agnostic to the detail of the neural implementation, we discuss below the implications for each system. In zebrafish, the presence of negative CLE feedback during fish swimming behavior would seem a priori necessary for optic-flow stabilization behavior because the fish must act in opposition to perceived optic flow in order to minimize horizontal displacement (Wolf et al. 1992, Fry et al., 2009. Interestingly, neurons that received strong negative CLE feedback and were substantially stabilized were located in the cerebellum ( Figure 3C) consistent with a theoretical viewpoint that the cerebellum mediates this optomotor response by converting sensation into action; e.g., by completing the action-perception cycle (Ito 1972, Lisberger et al. 1987, Kawato 1999.
Our rodent whisker model explores the overall effects of negative CLE feedback mediated by the cortical-whisker circuit during active whisking. As in the fish study, the theoretical assumption of negative CLE feedback is consistent with the idea that the barrel cortex is involved in control.
Specifically, the barrel cortex comprises a nested set of servo control loops that regulate various aspects of whisker dynamics (Ahissar and Kleinfeld, 2003). At the level of the whole vibrissa system, multiple parallel and nested feedback loops, both positive and negative (Ahissar and Kleinfeld, 2003) most likely exist. While our model is abstract in terms of the known complexities of vibrissa system anatomy and exact concordance of the model with vibrissa system anatomy is beyond the scope of this paper, we provide several possible schemes for experimentalists to examine in Supplemental Information Section 6.
The artificial CLE feedback in the primate experiment implements negative feedback, although this is less obvious than in our other studies and simple models. A system is defined to be under negative feedback if this feedback causes perturbations to the system's state to decay faster in time and suppresses fluctuations due to noise. Hence, neurofeedback in the monkey experiment is a hybrid of positive and negative feedback-the feedback is negative in the 0-1 Hz and 3-4 Hz frequency bands and positive in the 1-3 Hz frequency band, because the feedback reduces or increases fluctuations of the decision value in these frequency bands, respectively ( Figure 5B). In this experiment, the system's state was quantified by the decoder's decision value, with positive and negative values indicating vertical-like and horizontal-like brain activity patterns, respectively. Due to experimental constraints of delays in neurofeedback processes and unidentified dynamic properties of the brain, imposing purely negative neurofeedback in this experiment was not possible. However, negative CLE feedback in the 3-4 Hz frequency band is strongly correlated with enhanced fixation performance ( Figure 5F), supporting its behavioral significance.

Comparison to internal mechanisms of brain state transitions
The proposed mechanism of brain state transitions by CLE feedback is qualitatively different from the many other mechanisms governing brain state that operate inside the brain (Goard and Dan, 2009;Polack et al. 2012;Pinto et al., 2013;Poulet et al., 2012;Zagha et al., 2014). Specifically, the CLE feedback mechanism involves the dynamic coordination between brain activity and body/environmental dynamics (c.f. Figure 3D), a continuous reciprocal interaction that is critical for many forms of goal-directed behavior. In this regard, our theory directly links a mechanism of brain state transitions to behavior and is closed from an explanatory view, i.e., without assumptions about upstream causes.
In our zebrafish study, an alternative interpretation of our findings is that correlated neural fluctuations are suppressed directly by an efference copy signal (Zagha et al., 2014;Schneider et al. 2014) due to greater motor commands in the closed-loop condition (Supplementary Figure S2). However, in opposition to this view, we found that motor activity correlated positively with fluctuations in each cell, and were not associated with pairwise neuronal correlations (Supplementary Figure S2). Hence, we cannot account for the results by any known functions of efference copy signals. Moreover, the primate neurofeedback allowed us to examine the impact of CLE feedback in the absence of the overt involvement of the motor system, i.e., feedback was only dependent on readout from visual areas. This allows us to conclude that CLE feedback alone, in the absence of noticeable motor activity, is sufficient to modulate brain activity and behavior.
Importantly, brain state control by CLE feedback is not mutually exclusive with other mechanisms, such as thalamo-cortical input (Poulet et al., 2012) or neuromodulation (Goard and Dan, 2009;Polack et al. 2012;Pinto et al., 2014;Fu et al. 2014) because these may also be involved in mediating the action-perception cycle. Furthermore, brain state transitions also occur in the absence of CLE feedback, such as open-loop behaviors (e.g., the onset of running that does not change the visual screen or grooming) (Niell andStryker, 2010, Fee et al. 1997), during sleep (Vyazovskiy et. al 2011;Steriade, 2005), or under dissection of the sensory nerve (Poulet and Petersen, 2008;Poulet et al., 2012). Mechanisms underlying brain state transitions are likely to be highly redundant even in the absence of essential mechanisms, such as thalamo-cortical input (Poulet et al., 2012) or corollary discharge (Schneider et al. 2014), albeit involving further delay (see also Supplementary Section 2).
Such functional redundancy may help to maintain the stability of brain state (Fu et al. 2014;McGinley et. al, 2015;Otazu et al. 2009; although with exceptions, see Vyazovskiy et. al 2011). Furthermore, the relative importance of internal and external mechanisms might adaptively change in an experiencedependent manner (Nachestedt et. al 2014).

Reafferent feedback in active sensing and revision of the reafference principle
In the whisking model, we proposed that the regulation of cortical gain by CLE feedback could explain enhanced active touch. Specifically, negative CLE feedback during whisking reproduces suppressed fluctuations and reduces responses to passive whisker stimulation (see Figure 4F).
However, robust neuronal response to active touch events could be explained by the interruption of CLE feedback when the whisker is driven into an external object. Such events interrupt CLE feedback, transiently releasing the cortex from a low gain state and enhancing sensory responses to salient sensory stimuli ( Figure 4E, Supplemental Information Section 4). This mechanism for active touch contrasts with the account of sensory processing suggested by the reafference principle (Von Holst, 1954), which postulates that motor efference is discounted from sensory input, allowing animals to sense exafferent signals (externally caused sensory input) without being confounded by the consequences of their own motor actions. In contrast, our theory suggests that the sensory system is insensitive to pure exafference during active sensing ( Figure 4F), but sensitive to the interruption of reafference which may allow animals to focus attention on the consequences of their own motor actions.
While it is straightforward to generalize this idea to other tactile systems, its implication for other sensory modalities is less clear. However, in theory, CLE feedback could be interrupted anywhere along the action-perception cycle, thus dynamically regulating neuronal gain. The timely interruption of this feedback could serve as a general mechanism for temporarily accentuating neuronal responses against a background of reduced noise (Scott, 2004, Hafed et al., 2011. For example, cerebellum neurons, which are strongly involved in the sensory-motor cycle, could be suppressed in anticipation of salient sensory events by a relevant brain area, such as the reticular formation (Kinomura et al. 1996).

Rapid neurofeedback and virtual reality-based behavioral enhancement
The primate findings demonstrate that neurofeedback can modulate brain dynamics ( Figure   5B and C) and enhance task-related behavior ( Figure 5D, E, F, and G intervened on the fast time scale of the ongoing sensory stream. Our approach has the potential to be more stable, with more rapid, user-independent, and effective behavioral control than current conventional decoded neurofeedback methods.
The neurophysiological reason underlying the improved fixation performance is not clear. However, the high-contrast grating stimulus likely serves as a distractor for the monkey and makes fixation more difficult. During the neurofeedback protocol, the 3-4 Hz frequency component of this distractor signal was suppressed by the feedback, possibly inhibiting the formation of a grating perception. If so, it is possible that such CLE feedback may help to allocate attention in physiological settings. Specifically, our model predicts that, animals may show less attention to sensory modalities that provide ongoing negative CLE feedback. A full investigation of these issues will require further work.
These findings emphasize the importance of the development of natural and virtual reality systems that provide well-controlled quantitative measurements of CLE interactions. Such novel systems would be useful for studying how healthy and disease brain physiology emerges from real-time brain-bodyenvironment interactions and may suggest new methods for manipulating or enhancing brain physiology and behavior with neurofeedback technology.
In sum, our findings suggest that context-dependent brain function and flexible behavior may only emerge from context specific CLE interactions. This supports the idea that CLE interactions may have a broad impact on our cognition (Clark, 2008) and may also shape social interactions (Froese et al., 2014).

Materials and Methods
Simple Conceptual Model: The time traces in Figure 1 were calculated by Euler's method, integrating the equations presented in the text with = −10, = 1, and time step = 0.01.

Zebrafish experiment:
We analyzed the calcium signal (∆F/F) at various sample frequencies (ca. 23 Hz) across 1908 cells in 32 fish, see Ahrens et al. (2012) for full description of experimental method. In addition to calcium sources (putative neurons), swim vigor was measured by taking electrical recordings from motor neurons in the fish's tail. In the original study, the gain (i.e., the multiplicative factor between fictive swim power, and the speed of visual feedback) was alternated between a high and low gain condition every 30 s.
We studied cells analyzed in Ahrens et al. (2012), which showed modulations of the mean ∆F/F, depending on the gain conditions. This gain alternating protocol is not relevant to the current study. To reduce this variability in data, we subtracted the mean activity level in each gain setting in our analysis (from both brain and behavior variables). Notably, our main results were qualitatively the same, even without such subtraction of the means.
We analyzed data taken from a 6-min recording of 16 prominent calcium sources per fish, putative neurons, across 600 trials. In the first 3 min, the fish performed the closed-loop optomotor behavior. For the subsequent 3 min, each fish was presented with an open-loop stimulus (no longer actively controlling their environment), which is a repeat of what the animal experienced in the previous 3 min. In this period, sensory input to the animals was identical and the only difference was the absence of closed-loop dynamics, allowing us to study how reafferent signal affected neural activity.
In Figure 2B, low frequency power was calculated as the mean log power of a neuron in the range of 0.010.15 Hz, averaged over all recorded neurons. Correlation was calculated as the average pairwise correlation (6589 pairs of cells were analyzed) between neurons in the same fish, averaged over all trials. Figure 2C plots the change in this pairwise correlation against the change in the log low frequency power (averaged for the pair) between the closed-loop and the replay condition. Note: for fish data, non-parametric tests were used and we did not assume normality. In addition, both results reported in Figure 2B were highly significant under a paired t-test, with p values <10 -5 .
We fitted the data with linear filters that describe the interaction between individual neurons and the environmental variable. Note: here we define the environmental variable (E) as the activity of motor neurons, whose history uniquely determines the visual stimulus. We calculated the linear filter that minimizes the mean square error between a driven variable ( ) and the convolution of a driving variable ( ) and filter ( ) over time. Filters were constructed as a superposition of Laguere functions. We use Laguere functions up to the order that stopped the optimization process by choosing the best Akaike Information Criterion (Akaike, 1987). Almost all filters had an order that was mid-range between 1 and 15, indicating the robustness of the chosen order.
We inferred two filters for each cell. We determined how the environment drives the brain, ( ), by directly calculating the filter between the closed-loop environment and brain in the replay condition → ′, see Figure 3A (magenta line). We determined how the brain drives In Figure 2B In Figure 3D, we calculated the → ′ filter in the replay condition and the → filter in the closed-loop condition as above, but using the Hermite rather than the Laguere functions to capture the acausal (t<0) side of the filter. Notably, the → filter in the closed-loop condition generally has an acausal component, because the brain and the environment are mutually interacting (see below). On the other hand, the → ′ filter in the replay condition is identical to the ( ) filter defined in the previous paragraph (although with minor differences due to the use of the Hermite-rather than Laguere-based functions). Hence, the two filters ( → ′ and → ) are generally different and this difference originates from the presence of CLE feedback ( → interaction) in the closed-loop condition. Here, we quantify this difference using a simple linear model. In the closed-loop condition, the system is up/down-like oscillations (Compte et al., 2003;Gentet et al., 2010;Curto et al., 2009) in the absence of neuron/whisker interactions, is whisker angle (positive: protracted and negative: retracted) interacting with neurons with weight = 0.002, is exafferent input that takes a non-zero value upon whisker stimulation, and is independent white noise of unit variance added to each neuron. Here, we interpret as both the firing rate and membrane potential, assuming a roughly linear relationship between the two. Entries in the connectivity matrix are  Figure 4C is averaged over all neurons and a quadratic spline fitted to the data.

Chernoff discrimination:
To calculate signal-to-noise-ratios, we calculated the Chernoff distance (Cover, 2012) between two probability distributions, ( ) and 0 ( ), in the presence or absence of a sensory event, respectively. Specifically, For our model, the probability distribution for each condition is well described by a Gaussian distribution where C and are covariance matrix and vector of means, respectively. By substituting this into the expression for Chernoff distance and employing the Gaussian integral identity and expressing the Chernoff distance in terms of 0 , and 0 , , we calculate the covariance and mean between three neurons, randomly selected from the network described in the first section. We calculate covariances across ensembles of 500 networks every 10 ms for a period of 1 s, starting at the onset of the sensory event. Minimization with respect to is computed numerically.
Monkey experiment: ECoG activity was recorded from 128 subdural electrodes implanted in a macaque monkey. All experimental and surgical procedures were performed in accordance with experimental protocols (No. H24-2-203(4)) approved by the RIKEN ethics committee and the recommendations of the Weatherall report, "The use of non-human primates in research".

Subject:
One monkey (male Macaca mulatta, aged 12 years, wild-type) was used in the experiment after magnetic resonance imaging. Before the implantation of subdural ECoG electrodes, the monkey was familiarized with the experimental settings and trained with a fixation task. During the fixation task, the monkey sat in a primate chair with the head in a fixed position using a helmet custom-made for the monkey. The monkey was housed individually in the room with a 12-h lightdark cycle (lights on at 8:00 AM), and participated in the experiment in the daytime. The monkey had also participated in other experiments involving fixation and voluntary saccadic eye movements more than half a year previous to this study.
Electrode Implantation: Subdural electrodes were surgically implanted after the completion of fixation training. To anesthetize the monkey, we administered ketamine (5 mg/kg, intramuscular), atropine (0.05 mg/kg), and pentobarbital (20 mg/kg, intravenous). We adjusted the dose of pentobarbital based on monkey's response to pain and heart rate. We chronically implanted a customized 128-channel ECoG electrode array in the subdural space (Unique Medical, Tokyo, Japan; Nagasaka et al., 2011).
The monkey was rewarded only in trials for which fixation was maintained from FP onset until its disappearance. ECoG signals were recorded at a sampling rate of 1 kHz using a Cerebus data acquisition system (Blackrock, UT, USA) and down-sampled to 200 Hz. Behavioral variables, such as pupil size and eye position, were recorded with a custom eye-tracking system (Nagasaka et al., 2011). Visual stimuli were constructed in Pyschtoolbox and feedback implemented by streaming ECoG data in real-time into Matlab. We used LIBSVM (Chang and Lin, 2011) under Matlab to implement the SVM.
During a 10-min training session, the monkey passively viewed consecutive 500-ms blocks of either vertical or horizontal gratings in each trial (total of about 200 trials). We found that the stimulus was most reliably decoded by applying SVM to inter-electrode correlations. We collected 100-ms runs of ECoG data from 50 electrodes for each stimulus condition and constructed the SVM vector by calculating the correlation between electrodes and flattening half (upper right triangle) of the resulting matrix to form a vector. We trained an SVM to classify vertical and horizontal grating on all collected vectors.
Classification performance strongly depended on the time interval used for the classifier, typically reaching > 90% cross-validated classification accuracy with 400-ms-long intervals.
In order to reduce temporal delay for neurofeedback, we classified stimuli using short 100-ms intervals. This typically gave > 60% cross-validated classification accuracy which is still markedly higher than chance level. A better classification performance was also achieved from grating orientations separated by 90, rather than 180 degrees, motivating our choice for horizontal and vertical gratings for the neurofeedback.
We then estimated the decision thresholds, by calculating a distribution of the decision values for each stimulus condition from the training data. These were roughly Gaussian with a positive and negative mean for the horizontal and vertical grating stimuli, respectively. We estimated the threshold for the decision value above ( ℎ ) and below ( ) which vertical and horizontal gratings are shown, respectively (see main text), by calculating the absolute value difference between the distributions and selecting the peaks of maximal difference. No gratings were presented for at least 1 s after the fixation point onset, to avoid presenting stimulus before the monkey fixated his eyes.
During testing, we consecutively sampled 100-ms runs of ECoG data, constructed an SVM vector, and used the SVM kernel to calculate the decision variable. The Matlab processing time for classifications was shorter than 100 ms. We were able to record 50108 trials for each of the closed-loop and replay conditions per experiment. We present data from four recording days in the text. We recorded a minimum of 326 trials each under the closed-loop and replay conditions. Together with the calibration of the decoder, this added to a reasonable experimental length for the subject to maintain his attention. In addition, the number of trials was comparable to that of typical experiments performed in visual psychophysics.
The power spectrum of the decision value ( Figure 5B) was calculated from the ECoG signal within 10002800 ms after the fixation point onset. Trials in which the monkey failed to fixate his eyes for at least 2800 ms were eliminated from the data set. The improvement in the performance was measured by the difference between the positions in each condition (Replay -Closed) relative to the average position (Replay + Closed) / 2 within each time-bin.
Normality for applying the t-test ( Figure 5C) was examined using the KolmogorovSmirnov goodness-of-fit hypothesis test (P > 0.07).
The performance improvement for each trial pair was summarized by root-mean-square of this quantity measured over an interval of 16002100 ms. We computed the trial-to-trial correlation between the fixation performance improvement and the power spectrum of the decision value dynamics in the interval of 10002100 ms ( Figures 5F and 5G): the power spectrum within this time period reflects the brain dynamics that precede the behavioral change. We also confirmed that the overall trend of the power spectrum of the decision value within this period (Supplementary Figure 5D) had not changed from that derived from the whole stimulation period shown in Figure 5B. fluctuates. In the closed-loop condition (C), reafferent input constitutes a CLE feedback to the brain. If this feedback is negative, the gain of the brain is reduced and fluctuations are suppressed. In the replay condition (D), the brain receives a replay of the reafferent input in the closed-loop condition as exafferent input. Any differences from the closed-loop condition are caused by the absence of CLE feedback because the sensory input is identical to that in the closed-loop condition. In this condition, the gain of the brain is not suppressed and fluctuations are much larger than in the closed-loop condition with negative feedback.        Figure 2B).
However, the position of the mean cross-correlation peaks was significantly shifted in ION-cut animals relative to the ION-intact animals (Supplementary Figure 2B). Specifically, the peak of the On the other hand, the temporal relationship between the thalamic spiking activity and the lowfrequency cortical LFP power was not significantly altered as assessed by the Thalamus-Cortex correlation function (p>0.05, bootstrap test). The corresponding bootstrap statistics were computed by randomly resampling animals from the two groups, assuming a null hypothesis that the two animal groups are the same (see, the inset panels for the bootstrap statistics about the difference of the crosscorrelation peaks).
These analyses suggest that, after a whisking onset, the brain state transition was delayed 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 state transitions.

S4 A simple conceptual model of CLE feedback
We illustrate our whisker theory with an extension of simple conceptual model presented in the text, Figure 1. It describes the dynamic interaction between brain activity (here membrane potential of neurons) and the body (here whisker position) (Supplementary Figure   4). Specifically a simplified brain-environment system was modeled as a stochastic 1dimensional first order linear ordinary differential equation as follows, representing the collective activity of neurons (e.g. local field potential) and is the environmental variable (e.g. whisker position). Note: for simplicity we assume that the dynamics of the environment variable are much faster compared with the brain dynamics and, thus, E rapidly converges to current B. The negative CLE feedback robustly reduces neural fluctuations unless feedback delay is too large. The parameter, = 0.95, is the selfcoupling within the brain, , is the magnitude of the environmental influence on the brain, is external input and, is unit variance white noise of mean 0. An open-loop condition, i.e., the absence of environmental coupling, is modeled by setting, = 0 and the closed-loop condition by setting = 0.4. Here we have set to be close to criticality ( = 1) to show that even weak CLE feedback can significantly reduce neural fluctuations. However, this choice is not central to our theory because strong CLE feedback works likewise when the system is away from criticality. Passive sensory stimulation was modeled by setting, = 1.5 for a time period of 20. Interruption of the reafferent signal was implemented by fixing the environmental variable for the same period, i.e, setting ( ′) = ( ) for < ′ < + 20.
The replay condition is constructed by first recording the environmental variable, , in the closed-loop condition and subsequently replaying this recording to the brain at a different time. The brain activity in the replay condition, , is described by   , an environment variable mediates negative CLE feedback to the brain. In the reafferent-cut condition, (C), this feedback is briefly interrupted. In the replay condition (D), the environmental input to the brain in the closed-loop condition is recorded (denoted by Er) and played back to an identical brain (albeit with different noise) at a later time. In all conditions, in addition to the reafferent input, the brain receives a short pulse of exafferent input. (E): Traces of the brain and environment variables under different conditions. In the open loop condition (green) the brain shows large spontaneous fluctuations and large response to exafferent stimulation, which are suppressed during the closed-loop condition (red). The gray bar denotes periods of stimulation. In contrast, the brain variable exhibits large and reliable response to the same input when combined with a brief interruption of the environment (the pink bar denotes the period of stimulation and reafference interruption). In the replay condition (magenta), the brain behaves similarly to the open-loop condition despite receiving the same input from the environment as the closed-loop condition.  whisker protraction. This in turn reduces excitatory sensory input to the modeled cortical population because this is driven by retraction. Here negative CLE feedback is mediated implicitly at the periphery. (B) Protraction information could be conveyed along the full 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 the brain stem and changes in cortical activity are driven by activity changes in the thalamus.

S5 Decoding of visual stimulus based on ECoG signals
Our whisker model remains abstract in terms of known vibrissa system anatomy and, in particular, the relay stations between the cortex and a whisker. The exact concordance of the model with known vibrissa system anatomy is beyond the scope of this paper, but we provide a more detailed to demonstrate a possible anatomical explanation of our model and provide a means for the research community to experimentally examine CLE feedback in specific biological circuits.
In our model (Supplementary Figure 6A), we assume that projections between regions are largely excitatory (c.f. Ahissar 2010). Importantly, we distinguish two subcortical pathways that signal afferent input to cortical 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 (Pierret et al., 2000;Urbain et al., 2015). 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 (Szwed et al., 2003). 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 CLE 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) (Ahissar, 2010). Because whisking behavior persists after sensory denervation (Welker, 1964), cortical ablation (Semba and Komisaruk, 1984), or decerebration (Lovick, 1972), we explicitly modeled a central pattern generator (CPG) that autonomously generates whisking patterns locating exogenous to the cortical-whisker loop (Hill et al., 2011). Thus, the FN receives input from both the cortical population and CPG and moves the whisker in the reafference model.
We cannot rule out other biological pathways for negative CLE feedback. For example, negative feedback can also be mediated by dominant cortical inhibition to the modeled population of cortical neurons (Supplementary Figure 6B). In agreement, thalamocortical connections strongly innervate fast spiking neurons and consequently implement strong feedforward inhibition to the cortex (Bruno and Simons 2002). Other potential models arise from heterogeneity in cortical populations. For example, negative CLE feedback can be mediated by neurons in the barrel cortex that directly drive whisker retraction with extremely short latencies .
Alternatively, the dominant negative feedback loop could be subcortcial, Supplementary Figure 6C. Here the dynamics of the cortex only indirectly reflects the stabilization of the thalamus. This scheme is also consistent with reduced thalamic activity during whisking (Poulet et al., 2012). It is important to note that this implementation also fundamentally relies on stabilisation of neuronal activity by negative CLE feedback.