Editor's evaluation: Scale-free behavioral dynamics directly linked with scale-free cortical dynamics
Year: 2022
Type: peer-review
Abstract: Article Figures and data Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract Naturally occurring body movements and collective neural activity both exhibit complex dynamics, often with scale-free, fractal spatiotemporal structure. Scale-free dynamics of both brain and behavior are important because each is associated with functional benefits to the organism. Despite their similarities, scale-free brain activity and scale-free behavior have been studied separately, without a unified explanation. Here, we show that scale-free dynamics of mouse behavior and neurons in the visual cortex are strongly related. Surprisingly, the scale-free neural activity is limited to specific subsets of neurons, and these scale-free subsets exhibit stochastic winner-take-all competition with other neural subsets. This observation is inconsistent with prevailing theories of scale-free dynamics in neural systems, which stem from the criticality hypothesis. We develop a computational model which incorporates known cell-type-specific circuit structure, explaining our findings with a new type of critical dynamics. Our results establish neural underpinnings of scale-free behavior and clear behavioral relevance of scale-free neural activity. Editor's evaluation This paper is an important study that is of interest to neuroscientists studying the organization of neural activity and behavior. The authors present compelling evidence to link the apparently scale-free distributions of behavioral metrics with scale-free distributions of neural activity. They then explore computationally mechanistic models that could account for these observations. The simulations of mechanistic models are provocative and suggest interesting network-connectivity hypotheses to test in future experiments. https://doi.org/10.7554/eLife.79950.sa0 Decision letter Reviews on Sciety eLife's review process eLife digest As we go about our days, how often do we fidget, compared to how frequently we make larger movements, like walking down the hall? And how rare is a trek across town compared to that same walk down the hall? Animals tend to follow a mathematical law that relates the size of our movements to how often we do them. This law posits that small-to-medium movements and large-to-huge movements are related in the same way, that is, the law is ‘scale-free’, it holds the same for different scales of movement. Surprisingly, measurements of brain activity also follow this scale-free law: the level of activation of a group of neurons relates to how often they are activated in the same way for different levels of activation. Although body movements and brain activity behave in a mathematically similar way, these two facts had not previously been linked. Jones et al. studied body movements and brain activity in mice, and found that scale-free body movements were linked to scale-free brain activity, but only in certain subsets of neurons. This observation had been hidden because other subsets of neurons compete with scale-free neurons. When the scale-free neurons turn on, the competing groups turn off. When averaged together, these fluctuations cancel out. The findings of Jones et al. provide a new understanding of how brain and body dynamics are orchestrated in healthy organisms. In particular, their results suggest that the complex, multi-scale nature of behavior and body movements may emerge from brain activity operating at a critical tipping point between order and disorder, at the edge of chaos. Introduction From fidgeting to expeditions, natural body movements manifest over a very broad range of spatiotemporal scales. The complexity of such movements is often organized with fractal structure, scale-free fluctuations spanning multiple spatiotemporal orders of magnitude (Anteneodo and Chialvo, 2009; Proekt et al., 2012; Sims et al., 2008; Viswanathan et al., 1999). Such behavioral complexity may be beneficial for foraging (Garg and Kello, 2021; Sims et al., 2008; Viswanathan et al., 1999; Wosniack et al., 2017), visual search (Viswanathan et al., 1999), decision-making based on priority (Barabási, 2005; Sorribes et al., 2011), flexible switching of behavior (Abe, 2020), and perhaps more. Similarly, fluctuations of ongoing neural activity in the cerebral cortex can exhibit fractal, scale-free fluctuations like the spatiotemporal cascades sometimes referred to as ‘neuronal avalanches’ (Beggs and Plenz, 2003; Bellay et al., 2015; Ma et al., 2019; Priesemann et al., 2014; Scott et al., 2014; Shew et al., 2015; Shriki et al., 2013; Tagliazucchi et al., 2012; Yu et al., 2017) and long-range temporal correlations (Hardstone et al., 2012; Kello et al., 2010; Palva et al., 2013; Smit et al., 2013). Considering these observations of behavior and brain activity together, a simple, yet unanswered question arises. Are scale-free dynamics in cerebral cortex related to scale-free body movements? Or are these statistical similarities merely superficial, without any direct link? Two previous studies in humans have shown that temporally scale-free ongoing brain dynamics are related to some subtle aspects of behavior – fluctuations in success at rhythmic finger tapping (Smit et al., 2013) and sensory detection tasks (Palva et al., 2013). But, here, we are concerned with less subtle, larger-scale body movements and invasive measurements of brain activity with single neuron resolution. According to prevailing theories of scale-free ongoing neural activity, these dynamics are often interpreted as ‘background’ activity, not directly linked to behavior. This view arises in part because computational models of scale-free neural activity generate this type of dynamics autonomously, due to internal interactions, without explicit modeling of a body that behaves (Dalla Porta and Copelli, 2019; di Santo et al., 2018; Girardi-Schappo et al., 2020; Li and Shew, 2020; Wilting et al., 2018). Similarly, in experiments, scale-free neural activity has typically been observed in animals that are at rest, not engaged by any particular motor task or sensory input, or under anesthesia (Fontenele et al., 2019; Gautam et al., 2015; Gireesh and Plenz, 2008), or in vitro (Beggs and Plenz, 2003; Bellay et al., 2020; Shew et al., 2009; Tetzlaff et al., 2010) where there is no behavior to be observed. Based on these previous experimental observations and modeling efforts, one might naturally conclude that scale-free neural activity is internally generated, emerging spontaneously, without any link to behavior. However, recent experiments in awake mice have revealed that behaviors typically ignored by experimenters, such as whisking, eye and face movement, fidgeting, walking, and running, are strongly related to ongoing neural activity in the cortex (Clancy et al., 2019; Musall et al., 2019; Salkoff et al., 2020; Stringer et al., 2019). These studies did not address our question here about scale-free-ness of neural activity and behavior, but they suggest that if ongoing activity is scale-free, then it may be strongly related to behavior. More specifically, these studies point out the possibility that previous observations of scale-free neural activity in awake animals didn’t notice a link to behavior because those studies did not measure ongoing, spontaneous movements of the face, whiskers, and body. If this is the case, it would dramatically revise the typical interpretation of scale-free ongoing activity and provide direct evidence that scale-free behavior and scale-free brain activity are inseparably related. However, in the work by Stringer et al., 2019, the measured behaviors could explain only 10–30% of the total variance in neural activity fluctuations. Thus, the question remains: is this behaviorally-related 10–30% of neural activity scale-free? Here, our aim was to answer this question. Results Here, we analyzed simultaneous recordings of more than 10,000 pyramidal neurons during 1–2 hr in visual cortex of awake mice ( seven mice, nine recordings, recording duration 1.52 ± 0.51 hr), performed and first reported by Stringer et al., 2019. The neurons were distributed throughout a volume (300–400 μm in-depth, 0.9 × 0.935 mm in the area) and sampled at 3 Hz. In addition to the neural activity, several aspects of behavior and body movements were also recorded (Figure 1). Here, we focused on four aspects of behavior. First, we studied run speed, which was assessed using an optical sensor and a floating spherical treadmill. Second, we examined pupil diameter, which was obtained from a camera targeting the faces of the mice. Pupil diameter dynamics are associated with changes in arousal and other aspects of body movement and sensory input (Reimer et al., 2016; Reimer et al., 2014; Vinck et al., 2015). Third, we studied changes in direction of gaze by tracking the speed of the center of the pupil as the mice looked around. Finally, we used previously developed methods to study whisker motion (Stringer et al., 2019), which was also obtained from the face camera. Figure 1 Download asset Open asset Simultaneous recording of behavior and neural activity. (A) Multiplane calcium imaging measured ~10,000 neurons in shallow layers of mouse visual cortex, while a camera measured facial motion and a treadmill measured run speed. (B) Example activity time series from 15 neurons (out of 11,005 total in this recording). Notice some neurons were strongly correlated with behavior (bottom five), while others were anticorrelated (top five), and others were nearly uncorrelated (middle five). (C) The four aspects of behavior - run speed, pupil diameter, speed of changes in gaze direction, and whisker motion - tended to covary on long time scales, but differ in fast fluctuations. Scale-free behavior The behavior tended to occur in bursts; rest periods were punctuated with well-defined bouts of body movement (Figure 1C and Figure 2A). All four of the behavioral variables we studied tended to start and stop together, approximately, but differed in their detailed, fast fluctuations (Figure 1C). We first sought to determine whether the behaviors exhibited scale-free dynamics. To this end, we first defined each bout of elevated body activity, hereafter called a behavioral ‘event,’ based on a threshold (the median of the entire time series). Each behavioral event began when the behavioral time series, run speed for example (Figure 2A), exceeded the threshold and ended when it returned below the threshold. The ‘size’ of each behavioral event was defined as the area between the threshold and the variable during the event (Figure 2A). This definition of events and their sizes is motivated by previous studies of scale-free neural activity (Gautam et al., 2015; Larremore et al., 2014; Li and Shew, 2020; Poil et al., 2012), typically referred to as neuronal avalanches. In the case of run speed, the event size corresponds to an effective distance traveled during the event. If the animal behavior is scale-free, one expects the distribution Pr(s) of behavioral event sizes (s) to have a power-law form, Pr(s)~s-τ. We found that these distributions often were in the form of a power-law over a wide range of event sizes (Figure 2B). For example, the run speed event size distribution for mouse 1 was scale-free for nearly four orders of magnitude of event sizes (power-law range, r=3.9 decades). To rigorously assess the range over which the data is power-law distributed, we used a maximum likelihood fitting algorithm that accounts for the number of events observed and the possibility of a cutoff at the head and tail of the distribution (Methods). Our approach builds on that used in previous studies (Shew et al., 2015). We report the power-law range r in decades, i.e., the number of orders of magnitude. If no range meets our fit criteria for statistical significance, we report r=0. Figure 2 with 2 supplements see all Download asset Open asset Spontaneous behavior is often scale-free. (A) Behavioral events (run speed, in this example) are defined by excursions above the median; event size is the area (shaded patch) between the curve and the median. (B) Four examples of behavioral event size distributions with large power-law range r>3 dB. Black points indicate the part of the distribution that is fit well by a power law. Blue points fall outside the power-law range. Gray patch indicates the expected variability (10th to 90th percentile) of the best-fit power law. (C) Summary of power-law range for all mice and all behaviors. Gaze dynamics were least likely to have a large power-law range. All mice had at least one behavior with a very large (>3 decades) power law range. Changes in power-law fitting parameters (goodness-of-fit criteria and outlier criteria) did not change our general conclusions. Although not all behaviors were scale-free over such a large range for all recordings, we found that most of the mice exhibited scale-free behaviors, particularly for running and pupil fluctuations (Figure 2C). In addition to the power-law range for larger behavioral events, some behaviors exhibited a range of small-scale behavioral events with a flat distribution consistent with low amplitude noise in the measurement methods (Figure 2—figure supplement 1). These conclusions were robust to changes in the two most important parameters for the power-law fitting algorithm: the goodness-of-fit criterion and the outlier exclusion threshold (more on outlier exclusion in Figure 2—figure supplement 2). Scale-free neural activity Next, we turned to the neural activity to test whether it was scale-free like the behavior. First, we averaged over all neurons to obtain a single population activity time series. Then, we treated the neural data in a similar way to the behavioral data. We defined neural events with a median threshold and defined event size as the area between the threshold and the data during the event (Figure 3A). This definition of events and event sizes is well-established in previous studies of scale-free neural activity (Gautam et al., 2015; Larremore et al., 2014; Li and Shew, 2020; Poil et al., 2012). (For more discussion of why this definition was chosen over other established alternatives, see Methods). The resulting distributions of neural event sizes were not scale-free; they were poorly fit by a power-law distribution (Figure 3B). Considering all 9 recordings, we found that r=1.5 ± 0.9 decades (mean ± SD). Such a short power-law range should be interpreted as evidence against any power-law at all, because nearly any function can be fit on a short range of data (more on why a large power-law range is important below). Figure 3 with 2 supplements see all Download asset Open asset Certain subsets of neurons exhibit scale-free dynamics, but total population does not. (A) Activity of the total neural population (black) and two subsets of neurons (blue, red) are shown. Each excursion above the median is one neural event (blue shaded area for subset A). Examples in panels A, B, and C are from mouse 1. (B) For the total population, the distribution of neural event sizes is not well fit by a power law (small range rtot = 1.2 decades). Histogram of event sizes (green, same bins used for blue, black distributions) shows that head of the distribution is noisy because very few events had very small sizes. (C) Certain subsets of neurons exhibited very large power-law range (rA = 3.9 decades), while other subsets did not (rB = 1.8 decades). These two example distributions are offset vertically to aid comparison of shape. (D) Distribution of power-law range r for 1000 subsets from mouse 1 (blue). Power law range r reached 4.5 decades for some subsets but did not exceed 2.6 decades for time-shifted controls (gray) in this mouse. (E) Summary of all mice, showing the number of subsets (out of 1000) with power-law range r>3.5 decades, compared to time-shifted controls. Results were qualitatively unchanged for different group size or goodness-of-fit criteria. One note of warning: at first glance, the distribution in Figure 3B may appear to have a decent power-law fit for the small event sizes. This is a misleading artifact resulting from using logarithmic bins and very few samples to estimate probability density. The inset in Figure 3B shows the number of events rather than probability density. See also Figure 2—figure supplement 1 for more clarification of this point. We emphasize that our power-law fitting algorithm does not use any bins and accounts for sample size, thus avoiding such misleading artifacts. The lack of scale-free dynamics for the neural population was surprising considering two facts together: first, the behavior exhibited scale-free dynamics (Figure 2), and second, many neurons are strongly correlated with behavior (Figure 1 and Stringer et al., 2019). One possible explanation for this puzzling observation is that summing the entire population together obscures the scale-free dynamics of certain subsets of neurons. Next, we set out to test this possibility. Since we did not know, a priori, which neurons might be in these subsets, we adopted a brute-force, shotgun search. First, we picked a ‘seed’ neuron at random from the entire population. Then we identified the 50 neurons that were most correlated with the seed neuron (we also tried 200 neurons without major impacts on the following results, Figure 3E). We averaged the activity of these 50 neurons to obtain a single time series and proceeded to define events and examine their size distribution. Two examples of time series obtained from subsets of neurons in this way are shown in Figure 3A. We repeated this process for 1000 different seed neurons. We found that some subsets of neurons were indeed scale-free, with power-law scaling over more than four orders of magnitude, while other subsets were not scale-free (Figure 3C). With so many neurons to choose from and a shotgun approach like this, it is important to avoid chance-level false positive conclusions. As a conservative control for this possibility, we repeated the analysis, but with surrogate data, generated by applying a random time shift to each neuron’s activity time series relative to other neurons. This time-shifted control data, thus, has identical statistics to the original data at the single neuron level, but correlations among neurons occur only by chance. For time-shifted controls, we found that large power-law ranges (greater than 3.5 decades) were rare and not found at all in the majority of recordings (Figure 3D and E). This conclusion was robust for different choices of group size and goodness-of-fit criteria used for the power-law fitting (Figure 3E). Two concerns with the data analyzed here are that it was sampled at a slow time scale (3 Hz frame rate) and that the deconvolution methods used to obtain the data here from the raw GCAMP6s Ca imaging signals are likely to miss some of the underlying spike activity (Huang et al., Since our of neural events on summing activity across neurons, could it be that the activity in our observed event size To address this we analyzed some spike data recording from Stringer et al., 2019). from the spike data, we a slow similar to that we analyzed here by with a down and (Figure supplements We compared neural event size distributions to based on the original spike data no of and found that the neural event size distributions were very with the same and the same power-law range (Figure supplement 1). Thus, we conclude that our reported neural event size distributions are scale-free brain activity and behavior established that certain subsets of neurons have scale-free dynamics and that behavior has scale-free dynamics, we sought to assess how the neural and behavioral dynamics are related. We first the between each behavior time series and each neural subset time series. The was very between the total neural population time series and behavior in Figure For the subsets, we found a very wide range of behavioral from 0.9 to (Figure the subsets with the with behavior also tended to have the ranges of power-law the neural subsets with the power-law range were most often with behavior. These results strongly suggest that the scale-free subsets of neurons are directly related to scale-free behavior. is also interesting to note that many of the subsets that were strongly anticorrelated with behavior also had a large power-law range (the in Figure These findings were very robust in out of 9 recordings Figure but less for some behaviors in the recordings We note that these animals also had to run more than and 50 more than the most or less than less than the least as shown in Figure supplement 1. This observation that our findings in that are not or Figure with 1 supplement see all Download asset Open asset Scale-free neural subsets with behavior, but subsets do not. (A) Each point the power-law range r and behavioral of one neural subset from mouse 1. with large r tend to be most correlated with behavior. is a of The the total population. (B) as for the other on have thus of range, and scaling studies of scale-free neural activity have typically not reported power-law range. may why we focused our here on the power-law range. our results two to this question. First, and most only neural subsets with large power-law ranges were strongly correlated with behavior (Figure Second, any of power-law scaling is if that scaling over a range. studies often on a of that one or two decades of scaling is not For the data analyzed here, we found that a power-law range of 1–2 decades is compared to for event size distributions (Figure One previous studies of scale-free brain activity have not reported power-law range from their that scale-free activity results from the neural operating in a the tipping point of a i.e., than power-law range, these studies focused on scaling between the power-law of the event size and duration distributions as by the of critical Based on our results, we that these previous studies might be by also for power-law range. previous studies also a natural question about whether the data we analyzed here from the of Our is to answer this question. According to prevailing theories of criticality in neural systems, both the sizes and of events should be power-law the of which a broad of critical et al., that the size power-law and the duration power-law should be related to how size scales with More specifically, where = - previous observations of scale-free neural activity this with of (Fontenele et al., 2019; et al., 2021; et al., 2012; Ma et al., 2019; Shew et al., 2015). To test this we first found the best-fit power-law and for the size distribution (Figure Then, we fit a power-law to the event duration distributions for the same set of events that were in the range of power-law scaling for event sizes (Figure thus And we a best-fit by a fit to as shown in Figure We found that and dramatically across different neural subsets (Figure However, if we examined only the subsets, i.e., those with a large power-law range we found that the power-law were ± ± and fit ± (mean ± Figure Thus, we conclude that power-law scaling for both sizes and of neural events and that size scales with duration to The of these scaling is consistent with but we found that our measured of were not consistent with noise fit was not to - This was typically because was resulting in sometimes of in the of the our observations of were than which is not to previously reported from experiments – This that if the scale-free neural activity we has in it may be a type of criticality that is different than previous observations. this with the is part of the for the new model we present scaling from the experiments are compared to the model results Figure Download asset Open asset scaling for neural subsets. (A) Example neural event size distribution with of the fit power law on (B) Distribution of event with of the fit power law events as in A). (C) sizes scale with event duration to the power that the fit is not well by noise (D) Each point one neural subset – power law from mouse 1. The neural subsets with to behavior power-law exhibited consistent scaling ± ± and fit ± subsets with behavioral power-law had fit points with power-law range (E) Summary of all neural subsets with power-law range decades from all experiments. Each patch corresponds to one like the example shown in The behavioral was chosen to the behavior with the for each neural Finally, we examined the for distributions of behavioral Considering the behaviors with a large power-law range we found ± ± and fit ± These were related to the and power-law ranges for neural event but only if we the neural subsets with large power-law range decades) and to behavior We found that and were correlated for neural and behavioral events = For these we each neural subset with the type of behavior that was most correlated to that of behavioral and neural events The of correlations between neural subsets and behavior, like those in Figure the entire recording several Are the correlations in Figure due to dynamics of the neural and behavioral activity, or are there correlations at the more level of the fluctuations during a single behavioral To answer these we correlations – between the behavior time series and the neural subset time series during each behavioral for each neural subset (Figure For for 1000 neural subsets and 1000 behavioral events are typical for this we would 1 Each is based on the short time series between the start and stop of the behavioral event. These correlations were often However, the chance-level of such correlations can also be for such short time series. We account for such chance-level correlations by the for time-shifted control data which the chance-level Figure with 2 supplements see all Download asset Open asset neural events with specific
Source: eLife
Author: Gordon J Berman
Institution: Emory University
Language: English
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: gold
Estimated APC paid: $2,500
OpenAlex ID: W4320926903