Low-dimensional criticality embedded in high-dimensional awake brain dynamics.

Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. We offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality-a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescales agrees with established theory of critical dynamics. Our results suggest that the cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.

Sensory input to cortex encoded on low-dimensional periphery-correlated subspaces.

As information about the world is conveyed from the sensory periphery to central neural circuits, it mixes with complex ongoing cortical activity. How do neural populations keep track of sensory signals, separating them from noisy ongoing activity? Here, we show that sensory signals are encoded more reliably in certain low-dimensional subspaces. These coding subspaces are defined by correlations between neural activity in the primary sensory cortex and upstream sensory brain regions; the most correlated dimensions were best for decoding. We analytically show that these correlation-based coding subspaces improve, reaching optimal limits (without an ideal observer), as noise correlations between cortex and upstream regions are reduced. We show that this principle generalizes across diverse sensory stimuli in the olfactory system and the visual system of awake mice. Our results demonstrate an algorithm the cortex may use to multiplex different functions, processing sensory input in low-dimensional subspaces separate from other ongoing functions.

Odor modality is transmitted to cortical brain regions from the olfactory bulb.

Odor perception is the impetus for important animal behaviors with two predominate modes of processing: odors pass through the front of the nose (orthonasal) while inhaling and sniffing, or through the rear (retronasal) during exhalation and while eating. Despite the importance of olfaction for an animal's well-being and that ortho and retro naturally occur, it is unknown how the modality (ortho vs. retro) is even transmitted to cortical brain regions, which could significantly affect how odors are processed and perceived. Using multielectrode array recordings in tracheotomized anesthetized rats, which decouples ortho-retro modality from breathing, we show that mitral cells in rat olfactory bulb can reliably and directly transmit orthonasal versus retronasal modality with ethyl butyrate, a common food odor. Drug manipulations affecting synaptic inhibition via GABAA lead to worse decoding of ortho versus retro, independent of whether overall inhibition increases or decreases, suggesting that the olfactory bulb circuit may naturally favor encoding this important aspect of odors. Detailed data analysis paired with a firing rate model that captures population trends in spiking statistics shows how this circuit can encode odor modality. We have not only demonstrated that ortho/retro information is encoded to downstream brain regions but also used modeling to demonstrate a plausible mechanism for this encoding; due to synaptic adaptation, it is the slower time course of the retronasal stimulation that causes retronasal responses to be stronger and less sensitive to inhibitory drug manipulations than orthonasal responses.NEW & NOTEWORTHY Whether ortho (sniffing odors) versus retro (exhalation and eating) is encoded from the olfactory bulb to other brain areas is not completely known. Using multielectrode array recordings in anesthetized rats, we show that the olfactory bulb transmits this information downstream via spikes. Altering inhibition degrades ortho/retro information on average. We use theory and computation to explain our results, which should have implications on cortical processing considering that only food odors occur retronasally.

Low dimensional criticality embedded in high dimensional awake brain dynamics.

Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. Here we offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality - a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescale agrees with established theory of critical dynamics. Our results suggest that cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.

Scale-free behavioral dynamics directly linked with scale-free cortical dynamics.

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.

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.

Collapse of complexity of brain and body activity due to excessive inhibition and MeCP2 disruption.

Complex body movements require complex dynamics and coordination among neurons in motor cortex. Conversely, a long-standing theoretical notion supposes that if many neurons in motor cortex become excessively synchronized, they may lack the necessary complexity for healthy motor coding. However, direct experimental support for this idea is rare and underlying mechanisms are unclear. Here we recorded three-dimensional body movements and spiking activity of many single neurons in motor cortex of rats with enhanced synaptic inhibition and a transgenic rat model of Rett syndrome (RTT). For both cases, we found a collapse of complexity in the motor system. Reduced complexity was apparent in lower-dimensional, stereotyped brain-body interactions, neural synchrony, and simpler behavior. Our results demonstrate how imbalanced inhibition can cause excessive synchrony among movement-related neurons and, consequently, a stereotyped motor code. Excessive inhibition and synchrony may underlie abnormal motor function in RTT.

Odor-evoked increases in olfactory bulb mitral cell spiking variability.

The spiking variability of neural networks has important implications for how information is encoded to higher brain regions. It has been well documented by numerous labs in many cortical and motor regions that spiking variability decreases with stimulus onset, yet whether this principle holds in the OB has not been tested. In stark contrast to this common view, we demonstrate that the onset of sensory input can cause an increase in the variability of neural activity in the mammalian OB. We show this in both anesthetized and awake rodents. Furthermore, we use computational models to describe the mechanisms of this phenomenon. Our findings establish sensory evoked increases in spiking variability as a viable alternative coding strategy.

Differences in olfactory bulb mitral cell spiking with ortho- and retronasal stimulation revealed by data-driven models.

The majority of olfaction studies focus on orthonasal stimulation where odors enter via the front nasal cavity, while retronasal olfaction, where odors enter the rear of the nasal cavity during feeding, is understudied. The coding of retronasal odors via coordinated spiking of neurons in the olfactory bulb (OB) is largely unknown despite evidence that higher level processing is different than orthonasal. To this end, we use multi-electrode array in vivo recordings of rat OB mitral cells (MC) in response to a food odor with both modes of stimulation, and find significant differences in evoked firing rates and spike count covariances (i.e., noise correlations). Differences in spiking activity often have implications for sensory coding, thus we develop a single-compartment biophysical OB model that is able to reproduce key properties of important OB cell types. Prior experiments in olfactory receptor neurons (ORN) showed retro stimulation yields slower and spatially smaller ORN inputs than with ortho, yet whether this is consequential for OB activity remains unknown. Indeed with these specifications for ORN inputs, our OB model captures the salient trends in our OB data. We also analyze how first and second order ORN input statistics dynamically transfer to MC spiking statistics with a phenomenological linear-nonlinear filter model, and find that retro inputs result in larger linear filters than ortho inputs. Finally, our models show that the temporal profile of ORN is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the OB. Using data-driven modeling, we detail how ORN inputs result in differences in OB dynamics and MC spiking statistics. These differences may ultimately shape how ortho and retro odors are coded.

Tuning network dynamics from criticality to an asynchronous state.

According to many experimental observations, neurons in cerebral cortex tend to operate in an asynchronous regime, firing independently of each other. In contrast, many other experimental observations reveal cortical population firing dynamics that are relatively coordinated and occasionally synchronous. These discrepant observations have naturally led to competing hypotheses. A commonly hypothesized explanation of asynchronous firing is that excitatory and inhibitory synaptic inputs are precisely correlated, nearly canceling each other, sometimes referred to as 'balanced' excitation and inhibition. On the other hand, the 'criticality' hypothesis posits an explanation of the more coordinated state that also requires a certain balance of excitatory and inhibitory interactions. Both hypotheses claim the same qualitative mechanism-properly balanced excitation and inhibition. Thus, a natural question arises: how are asynchronous population dynamics and critical dynamics related, how do they differ? Here we propose an answer to this question based on investigation of a simple, network-level computational model. We show that the strength of inhibitory synapses relative to excitatory synapses can be tuned from weak to strong to generate a family of models that spans a continuum from critical dynamics to asynchronous dynamics. Our results demonstrate that the coordinated dynamics of criticality and asynchronous dynamics can be generated by the same neural system if excitatory and inhibitory synapses are tuned appropriately.

Dynamic regulation of resource transport induces criticality in interdependent networks of excitable units.

Various functions of a network of excitable units can be enhanced if the network is in the "critical regime," where excitations are, on average, neither damped nor amplified. An important question is how can such networks self-organize to operate in the critical regime. Previously, it was shown that regulation via resource transport on a secondary network can robustly maintain the primary network dynamics in a balanced state where activity doesn't grow or decay. Here we show that this internetwork regulation process robustly produces a power-law distribution of activity avalanches, as observed in experiments, over ranges of model parameters spanning orders of magnitude. We also show that the resource transport over the secondary network protects the system against the destabilizing effect of local variations in parameters and heterogeneity in network structure. For homogeneous networks, we derive a reduced three-dimensional map which reproduces the behavior of the full system.

Selective Participation of Single Cortical Neurons in Neuronal Avalanches.

Neuronal avalanches are scale-invariant neuronal population activity patterns in the cortex that emerge in vivo in the awake state and in vitro during balanced excitation and inhibition. Theory and experiments suggest that avalanches indicate a state of cortex that improves numerous aspects of information processing by allowing for the transient and selective formation of local as well as system-wide spanning neuronal groups. If avalanches are indeed involved with information processing, one might expect that single neurons would participate in avalanche patterns selectively. Alternatively, all neurons could participate proportionally to their own activity in each avalanche as would be expected for a population rate code. Distinguishing these hypotheses, however, has been difficult as robust avalanche analysis requires technically challenging measures of their intricate organization in space and time at the population level, while also recording sub- or suprathreshold activity from individual neurons with high temporal resolution. Here, we identify repeated avalanches in the ongoing local field potential (LFP) measured with high-density microelectrode arrays in the cortex of awake nonhuman primates and in acute cortex slices from young and adult rats. We studied extracellular unit firing in vivo and intracellular responses of pyramidal neurons in vitro. We found that single neurons participate selectively in specific LFP-based avalanche patterns. Furthermore, we show in vitro that manipulating the balance of excitation and inhibition abolishes this selectivity. Our results support the view that avalanches represent the selective, scale-invariant formation of neuronal groups in line with the idea of Hebbian cell assemblies underlying cortical information processing.

Probing spatial inhomogeneity of cholinergic changes in cortical state in rat.

Acetylcholine (ACh) plays an essential role in cortical information processing. Cholinergic changes in cortical state can fundamentally change how the neurons encode sensory input and motor output. Traditionally, ACh distribution in cortex and associated changes in cortical state have been assumed to be spatially diffuse. However, recent studies demonstrate a more spatially inhomogeneous structure of cholinergic projections to cortex. Moreover, many experimental manipulations of ACh have been done at a single spatial location, which inevitably results in spatially non-uniform ACh distribution. Such non-uniform application of ACh across the spatial extent of a cortical microcircuit could have important impacts on how the firing of groups of neurons is coordinated, but this remains largely unknown. Here we describe a method for applying ACh at different spatial locations within a single cortical circuit and measuring the resulting differences in population neural activity. We use two microdialysis probes implanted at opposite ends of a microelectrode array in barrel cortex of anesthetized rats. As a demonstration of the method, we applied ACh or neostigmine in different spatial locations via the microdialysis probes while we concomitantly recorded neural activity at 32 locations with the microelectrode array. First, we show that cholinergic changes in cortical state can vary dramatically depending on where the ACh was applied. Second, we show that cholinergic changes in cortical state can vary dramatically depending on where the state-change is measured. These results suggests that previous work with single-site recordings or single-site ACh application should be interpreted with some caution, since the results could change for different spatial locations.

Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models.

Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces are considered. By assuming quasi-steady-state activity, one can neglect the complex temporal dynamics; however, in many cases the quasi-steady-state assumption fails. Here, we develop a new reduction method for a general heterogeneous firing-rate model receiving background correlated noisy inputs that accurately handles highly non-equilibrium statistics and interactions of heterogeneous cells. Our method involves solving an efficient set of nonlinear ODEs, rather than time-consuming Monte Carlo simulations or high-dimensional PDEs, and it captures the entire set of first and second order statistics while allowing significant heterogeneity in all model parameters.

Strong neuron-to-body coupling implies weak neuron-to-neuron coupling in motor cortex.

Cortical neurons can be strongly or weakly coupled to the network in which they are embedded, firing in sync with the majority or firing independently. Both these scenarios have potential computational advantages in motor cortex. Commands to the body might be more robustly conveyed by a strongly coupled population, whereas a motor code with greater information capacity could be implemented by neurons that fire more independently. Which of these scenarios prevails? Here we measure neuron-to-body coupling and neuron-to-population coupling for neurons in motor cortex of freely moving rats. We find that neurons with high and low population coupling coexist, and that population coupling was tunable by manipulating inhibitory signaling. Importantly, neurons with different population coupling tend to serve different functional roles. Those with strong population coupling are not involved with body movement. In contrast, neurons with high neuron-to-body coupling are weakly coupled to other neurons in the cortical population.

Scale-Change Symmetry in the Rules Governing Neural Systems.

Similar universal phenomena can emerge in different complex systems when those systems share a common symmetry in their governing laws. In physical systems operating near a critical phase transition, the governing physical laws obey a fractal symmetry; they are the same whether considered at fine or coarse scales. This scale-change symmetry is responsible for universal critical phenomena found across diverse systems. Experiments suggest that the cerebral cortex can also operate near a critical phase transition. Thus we hypothesize that the laws governing cortical dynamics may obey scale-change symmetry. Here we develop a practical approach to test this hypothesis. We confirm, using two different computational models, that neural dynamical laws exhibit scale-change symmetry near a dynamical phase transition. Moreover, we show that as a mouse awakens from anesthesia, scale-change symmetry emerges. Scale-change symmetry of the rules governing cortical dynamics may explain observations of similar critical phenomena across diverse neural systems.

Robust entropy requires strong and balanced excitatory and inhibitory synapses.

It is widely appreciated that balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, balance could be achieved by many possible configurations of excitatory and inhibitory synaptic strengths and relative numbers of excitatory and inhibitory neurons. For instance, a given level of excitation could be balanced by either numerous inhibitory neurons with weak synapses or a few inhibitory neurons with strong synapses. Among the continuum of different but balanced configurations, why should any particular configuration be favored? Here, we address this question in the context of the entropy of network dynamics by studying an analytically tractable network of binary neurons. We find that entropy is highest at the boundary between excitation-dominant and inhibition-dominant regimes. Entropy also varies along this boundary with a trade-off between high and robust entropy: weak synapse strengths yield high network entropy which is fragile to parameter variations, while strong synapse strengths yield a lower, but more robust, network entropy. In the case where inhibitory and excitatory synapses are constrained to have similar strength, we find that a small, but non-zero fraction of inhibitory neurons, like that seen in mammalian cortex, results in robust and relatively high entropy.

A theoretical framework for analyzing coupled neuronal networks: Application to the olfactory system.

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique to dual micro-electrode array in vivo recordings from two distinct regions: olfactory bulb (OB) and anterior piriform cortex (PC). Our analysis predicts that: i) inhibition within the afferent region (OB) has to be weaker than the inhibition within PC, ii) excitation from PC to OB is generally stronger than excitation from OB to PC, iii) excitation from PC to OB and inhibition within PC have to both be relatively strong compared to presynaptic inputs from OB. These predictions are validated in a spiking neural network model of the OB-PC pathway that satisfies the many constraints from our experimental data. We find when the derived relationships are violated, the spiking statistics no longer satisfy the constraints from the data. In principle this modeling framework can be adapted to other systems and be used to investigate relationships between other neural attributes besides network connection strengths. Thus, this work can serve as a guide to further investigations into the relationships of various neural attributes within and across different regions during sensory processing.

Adaptation towards scale-free dynamics improves cortical stimulus discrimination at the cost of reduced detection.

Fundamental to the function of nervous systems is the ability to reorganize to cope with changing sensory input. Although well-studied in single neurons, how such adaptive versatility manifests in the collective population dynamics and function of cerebral cortex remains unknown. Here we measured population neural activity with microelectrode arrays in turtle visual cortex while visually stimulating the retina. First, we found that, following the onset of stimulation, adaptation tunes the collective population dynamics towards a special regime with scale-free spatiotemporal activity, after an initial large-scale transient response. Concurrently, we observed an adaptive tradeoff between two important aspects of population coding-sensory detection and discrimination. As adaptation tuned the cortex toward scale-free dynamics, stimulus discrimination was enhanced, while stimulus detection was reduced. Finally, we used a network-level computational model to show that short-term synaptic depression was sufficient to mechanistically explain our experimental results. In the model, scale-free dynamics emerge only when the model operates near a special regime called criticality. Together our model and experimental results suggest unanticipated functional benefits and costs of adaptation near criticality in visual cortex.