The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data collected at the individual neuron level using the framework of nonequilibrium phase transitions. Among the most striking predictions confirmed is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.

The performance of complex networks, like the brain, depends on how effectively their elements communicate. Despite the importance of communication, it is virtually unknown how information is transferred in local cortical networks, consisting of hundreds of closely spaced neurons. To address this, it is important to record simultaneously from hundreds of neurons at a spacing that matches typical axonal connection distances, and at a temporal resolution that matches synaptic delays. We used a 512-electrode array (60 μm spacing) to record spontaneous activity at 20 kHz from up to 500 neurons simultaneously in slice cultures of mouse somatosensory cortex for 1 h at a time. We applied a previously validated version of transfer entropy to quantify information transfer. Similar toin vivoreports, we found an approximately lognormal distribution of firing rates. Pairwise information transfer strengths also were nearly lognormally distributed, similar to reports of synaptic strengths. Some neurons transferred and received much more information than others, which is consistent with previous predictions. Neurons with the highest outgoing and incoming information transfer were more strongly connected to each other than chance, thus forming a “rich club.” We found similar results in networks recordedin vivofrom rodent cortex, suggesting the generality of these findings. A rich-club structure has been found previously in large-scale human brain networks and is thought to facilitate communication between cortical regions. The discovery of a small, but information-rich, subset of neurons within cortical regions suggests that this population will play a vital role in communication, learning, and memory.SIGNIFICANCE STATEMENTMany studies have focused on communication networks between cortical brain regions. In contrast, very few studies have examined communication networks within a cortical region. This is the first study to combine such a large number of neurons (several hundred at a time) with such high temporal resolution (so we can know the direction of communication between neurons) for mapping networks within cortex. We found that information was not transferred equally through all neurons. Instead, ∼70% of the information passed through only 20% of the neurons. Network models suggest that this highly concentrated pattern of information transfer would be both efficient and robust to damage. Therefore, this work may help in understanding how the cortex processes information and responds to neurodegenerative diseases.

Although relationships between networks of different scales have been observed in macroscopic brain studies, relationships between structures of different scales in networks of neurons are unknown. To address this, we recorded from up to 500 neurons simultaneously from slice cultures of rodent somatosensory cortex. We then measured directed effective networks with transfer entropy, previously validated in simulated cortical networks. These effective networks enabled us to evaluate distinctive nonrandom structures of connectivity at 2 different scales. We have 4 main findings. First, at the scale of 3–6 neurons (clusters), we found that high numbers of connections occurred significantly more often than expected by chance. Second, the distribution of the number of connections per neuron (degree distribution) had a long tail, indicating that the network contained distinctively high-degree neurons, or hubs. Third, at the scale of tens to hundreds of neurons, we typically found 2–3 significantly large communities. Finally, we demonstrated that communities were relatively more robust than clusters against shuffling of connections. We conclude the microconnectome of the cortex has specific organization at different scales, as revealed by differences in robustness. We suggest that this information will help us to understand how the microconnectome is robust against damage.

Recent work has shown that functional connectivity among cortical neurons is highly varied, with a small percentage of neurons having many more connections than others. Also, recent theoretical developments now make it possible to quantify how neurons modify information from the connections they receive. Therefore, it is now possible to investigate how information modification, or computation, depends on the number of connections a neuron receives (in-degree) or sends out (out-degree). To do this, we recorded the simultaneous spiking activity of hundreds of neurons in cortico-hippocampal slice cultures using a high-density 512-electrode array. This preparation and recording method combination produced large numbers of neurons recorded at temporal and spatial resolutions that are not currently available in any in vivo recording system. We utilized transfer entropy (a well-established method for detecting linear and nonlinear interactions in time series) and the partial information decomposition (a powerful, recently developed tool for dissecting multivariate information processing into distinct parts) to quantify computation between neurons where information flows converged. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to receive connections from high out-degree neurons. However, the in-degree of a neuron was not related to the amount of information it computed. To gain insight into these findings, we developed a simple feedforward network model. We found that a degree-modified Hebbian wiring rule best reproduced the pattern of computation and degree correlation results seen in the real data. Interestingly, this rule also maximized signal propagation in the presence of network-wide correlations, suggesting a mechanism by which cortex could deal with common random background input. These are the first results to show that the extent to which a neuron modifies incoming information streams depends on its topological location in the surrounding functional network. We recorded the electrical activity of hundreds of neurons simultaneously in brain tissue from mice and we analyzed these signals using state-of-the-art tools from information theory. These tools allowed us to ascertain which neurons were transmitting information to other neurons and to characterize the computations performed by neurons using the inputs they received from two or more other neurons. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to be recipients of information from neurons with a large number of outgoing connections. Interestingly, the number of incoming connections to a neuron was not related to the amount of information that neuron computed. To better understand these results, we built a network model to match the data. Unexpectedly, the model also maximized information transfer in the presence of network-wide correlations. This suggested a way that networks of cortical neurons could deal with common random background input. These results are the first to show that the amount of information computed by a neuron depends on where it is located in the surrounding network.

The brain is a network system in which excitatory and inhibitory neurons keep activity balanced in the highly non-random connectivity pattern of the microconnectome. It is well known that the relative percentage of inhibitory neurons is much smaller than excitatory neurons in the cortex. So, in general, how inhibitory neurons can keep the balance with the surrounding excitatory neurons is an important question. There is much accumulated knowledge about this fundamental question. This study quantitatively evaluated the relatively higher functional contribution of inhibitory neurons in terms of not only properties of individual neurons, such as firing rate, but also in terms of topological mechanisms and controlling ability on other excitatory neurons. We combined simultaneous electrical recording (~2.5 hours) of ~1000 neurons in vitro, and quantitative evaluation of neuronal interactions including excitatory-inhibitory categorization. This study accurately defined recording brain anatomical targets, such as brain regions and cortical layers, by inter-referring MRI and immunostaining recordings. The interaction networks enabled us to quantify topological influence of individual neurons, in terms of controlling ability to other neurons. Especially, the result indicated that highly influential inhibitory neurons show higher controlling ability of other neurons than excitatory neurons, and are relatively often distributed in deeper layers of the cortex. Furthermore, the neurons having high controlling ability are more effectively limited in number than central nodes of k-cores, and these neurons also participate in more clustered motifs. In summary, this study suggested that the high controlling ability of inhibitory neurons is a key mechanism to keep balance with a large number of other excitatory neurons beyond simple higher firing rate. Application of the selection method of limited important neurons would be also applicable for the ability to effectively and selectively stimulate E/I imbalanced disease states.

It has been notoriously difficult to understand interactions in the basal ganglia because of multiple recurrent loops. Another complication is that activity there is strongly dependent on behavior, suggesting that directional interactions, or effective connections, can dynamically change. A simplifying approach would be to examine just the direct, monosynaptic projections from cortex to striatum and contrast this with the polysynaptic feedback connections from striatum to cortex. Previous work by others on effective connectivity in this pathway indicated that activity in cortex could be used to predict activity in striatum, but that striatal activity could not predict cortical activity. However, this work was conducted in anesthetized or seizing animals, making it impossible to know how free behavior might influence effective connectivity. To address this issue, we applied Granger causality to local field potential signals from cortex and striatum in freely behaving rats. Consistent with previous results, we found that effective connectivity was largely unidirectional, from cortex to striatum, during anesthetized and resting states. Interestingly, we found that effective connectivity became bidirectional during free behaviors. These results are the first to our knowledge to show that striatal influence on cortex can be as strong as cortical influence on striatum. In addition, these findings highlight how behavioral states can affect basal ganglia interactions. Finally, we suggest that this approach may be useful for studies of Parkinson's or Huntington's diseases, in which effective connectivity may change during movement.