Dietmar Plenz

In cellular automata, localized activity patterns called gliders propagate and interact to carry and transform information. Whether neuronal networks can harness this computational power remains unclear. Here, we demonstrate that a cortical network model with separate excitatory and inhibitory populations, graded cellular activity and uniform local connectivity spontaneously generates diverse, interacting gliders. An analytical reduction identifies the cellular conditions sustaining propagation of the dominant G-glider. Distinct gliders can assemble into growing structures that emit other glider types. Near excitation–inhibition balance, sparse glider dynamics coexist with high computational capacity, measured by input differentiation and generalization, with local capacity varying across space and time. Strong mutual inhibition between interneurons instead permits metastatic proliferation with low computational capacity. These findings connect cellular automata to neuronal information processing and identify interacting gliders as a candidate mechanism for dynamic plasticity: the reorganization of computation within an unchanged synaptic architecture.

Empirical evidence of scaling behaviors in neuronal avalanches suggests that neuronal populations in the brain operate near criticality. Departure from scaling in neuronal avalanches has been used as a measure of distance to criticality and linked to brain disorders. A distinct line of evidence for brain criticality has come from thermodynamic signatures in maximum entropy (ME) models. Both of these approaches have been widely applied to the analysis of neuronal data. However, the relationship between deviations from avalanche criticality and the thermodynamics of ME models of neuronal populations remains poorly understood. To address this question, we study spontaneous activity of organotypic rat cortex slice cultures in physiological and drug-induced hypo- or hyperexcitable conditions, which are classified as critical, subcritical, and supercritical based on avalanche dynamics. We find that static ME models inferred from critical cultures show signatures of criticality in thermodynamic quantities, e.g., specific heat. However, such signatures are also present and equally strong in models inferred from supercritical cultures---despite their altered dynamics and poor functional performance. On the contrary, ME models inferred from subcritical cultures do not show thermodynamic hints of criticality. Importantly, we confirm these results using an interpretable neural network model that can be tuned to and away from avalanche criticality. Our findings indicate that static maximum entropy models, although not constraining dynamical features, correctly distinguish subcritical from critical/supercritical systems. However, they may not be able to discriminate between avalanche criticality and supercriticality, suggesting that dynamics is relevant to capture the supercritical behavior and distinguish it from criticality.

Cortical neurons are sparsely and weakly connected, motivating the long-standing idea that they must act collectively, as cell assemblies, to exert substantial influence on surrounding networks. Yet a few spikes in a single pyramidal neuron can recruit thousands of cortical neurons according to a power law with exponent ∼0.285, consistent with a two-dimensional system near a critical percolation transition. Here we holographically stimulated ensembles of 1–16 layer 2/3 pyramidal neurons in visual cortex of awake mice while imaging hundreds of neighbouring neurons. Across two orders of magnitude in evoked spike count, network responses followed the same scaling law observed for single-neuron perturbations, with no detectable threshold at which co-activation produced additional amplification. Recruitment was sublinear, suppression increased with ensemble size, and ongoing scale-free avalanche dynamics remained stationary. Nevertheless, ensemble identity became increasingly decodable from surrounding activity. Thus, coordinated firing increases representational specificity without escaping the critical dynamics governing propagation: cortical ensembles convey identity without gaining disproportionate causal impact.

To guide behavior in uncertain environments, the brain must rapidly detect novel or unexpected events. The neocortex, involved with complex perception and decision-making, is thought to contribute to this computation, but underlying mechanisms are poorly understood. Here, we test how a few unanticipated action potentials influence local circuitry in the resting mouse visual cortex. Using targeted holographic stimulation, we evoked sparse “surprise” spikes in single pyramidal neurons and monitored their effects on hundreds of neighboring cells with 2-photon imaging. These novel spikes, distinct from the cortex’s ongoing large-scale activity fluctuations, produced strong, transient recruitment, following a power-law with slope 0.2–0.3, indicating that single neurons can mobilize large fractions of the surrounding network. Ongoing activity was dominated by neuronal avalanches, highly variable, scale-invariant spike cascades characteristic of systems near criticality. Yet, the information regarding the origin of our perturbations remained reliably identifiable and distributed across most of the observed network, as shown using machine-learning classifiers. Cortical network simulations confirmed that the measured scaling and distributed information matches predictions for systems operating near criticality. These results demonstrate two hallmarks of criticality, avalanche organization and amplified responses to small perturbations, suggesting that critical dynamics enhance the cortex’s ability to detect novel events.

The ability to detect and transmit novel events is essential for adaptive behavior in uncertain environments. Here, we investigate how holographically triggered, unanticipated action potentials propagate through the primary visual cortex of resting mice, focusing on pyramidal neuron communication. We find that these novel spikes — uncorrelated with ongoing activity — exert a disproportionately large influence on neighboring neurons, whose response scales as a power law (exponent ∼0.2–0.3). Even a few such spikes can recruit a large fraction of the local network, enabling robust decoding of perturbation origin despite high trial-by-trial variability and ongoing activity dominated by large activity fluctuations in the form of scale-invariant, parabolic neuronal avalanches. Simulations confirm this scaling to small, local perturbations aligns with the high susceptibility of complex systems near criticality. These results suggest that critical dynamics facilitate efficient transmission of novel signals, revealing a fundamental mechanism for cortical novelty detection.

Scaling relationships are key in characterizing complex systems at criticality. In the brain, they are evident in neuronal avalanches—scale-invariant cascades of neuronal activity quantified by power laws. Avalanches manifest at the cellular level as cascades of neuronal groups that fire action potentials simultaneously. Such spatiotemporal synchronization is vital to theories on brain function yet avalanche synchronization is often underestimated when only a fraction of neurons is observed. Here, we investigate biases from fractional sampling within a balanced network of excitatory and inhibitory neurons with all-to-all connectivity and critical branching process dynamics. We focus on how mean avalanche size scales with avalanche duration. For parabolic avalanches, this scaling is quadratic, quantified by the scaling exponent, χ = 2, reflecting rapid spatial expansion of simultaneous neuronal firing over short durations. However, in networks sampled fractionally, χ is significantly lower. We demonstrate that applying temporal coarse-graining and increasing a minimum threshold for coincident firing restores χ = 2, even when as few as 0.1% of neurons are sampled. This correction crucially depends on the network being critical and fails for near sub- and supercritical branching dynamics. Using cellular 2-photon imaging, our approach robustly identifies χ = 2 over a wide parameter regime in ongoing neuronal activity from frontal cortex of awake mice. In contrast, the common ‘crackling noise’ approach fails to determine χ under similar sampling conditions at criticality. Our findings overcome scaling bias from fractional sampling and demonstrate rapid, spatiotemporal synchronization of neuronal assemblies consistent with scale-invariant, parabolic avalanches at criticality.

Scaling relationships are key in characterizing complex systems at criticality. In the brain, they are evident in neuronal avalanches—scale-invariant cascades of neuronal activity quantified by power laws. Avalanches manifest at the cellular level as cascades of neuronal groups that fire action potentials simultaneously. Such spatiotemporal synchronization is vital to theories on brain function yet avalanche synchronization is often underestimated when only a fraction of neurons is observed. Here, we investigate biases from fractional sampling within a balanced network of excitatory and inhibitory neurons with all-to-all connectivity and critical branching process dynamics. We focus on how mean avalanche size scales with avalanche duration. For parabolic avalanches, this scaling is quadratic, quantified by the scaling exponent, χ = 2, reflecting rapid spatial expansion of simultaneous neuronal firing over short durations. However, in networks sampled fractionally, χ is significantly lower. We demonstrate that applying temporal coarse-graining and increasing a minimum threshold for coincident firing restores χ = 2, even when as few as 0.1% of neurons are sampled. This correction crucially depends on the network being critical and fails for near sub- and supercritical branching dynamics. Using cellular 2-photon imaging, our approach robustly identifies χ = 2 over a wide parameter regime in ongoing neuronal activity from frontal cortex of awake mice. In contrast, the common ’crackling noise’ approach fails to determine χ under similar sampling conditions at criticality. Our findings overcome scaling bias from fractional sampling and demonstrate rapid, spatiotemporal synchronization of neuronal assemblies consistent with scale-invariant, parabolic avalanches at criticality.

Neurons in the cerebral cortex fire coincident action potentials during ongoing activity and in response to sensory inputs. These synchronized cell assemblies are fundamental to cortex function, yet basic dynamical aspects of their size and duration are largely unknown. Using 2-photon imaging of neurons in the superficial cortex of awake mice, we show that synchronized cell assemblies organize as scale-invariant avalanches that quadratically grow with duration. The quadratic avalanche scaling was only found for correlated neurons, required temporal coarse-graining to compensate for spatial subsampling of the imaged cortex, and suggested cortical dynamics to be critical as demonstrated in simulations of balanced E/I-networks. The corresponding time course of an inverted parabola with exponent of χ = 2 described cortical avalanches of coincident firing for up to 5 s duration over an area of 1 mm². These parabolic avalanches maximized temporal complexity in the ongoing activity of prefrontal and somatosensory cortex and in visual responses of primary visual cortex. Our results identify a scale-invariant temporal order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches.

Temporal synchrony of signals arriving from different neurons or brain regions is essential for proper neural processing. Nevertheless, it is not well understood how such synchrony is achieved and maintained in a complex network of time-delayed neural interactions. Myelin plasticity, accomplished by oligodendrocytes (OLs), has been suggested as an efficient mechanism for controlling timing in brain communications through adaptive changes of axonal conduction velocity and consequently conduction time delays, or latencies; however, local rules and feedback mechanisms that OLs use to achieve synchronization are not known. We propose a mathematical model of oligodendrocyte-mediated myelin plasticity (OMP) in which OLs play an active role in providing such feedback. This is achieved without using arrival times at the synapse or modulatory signaling from astrocytes; instead, it relies on the presence of global and transient OL responses to local action potentials in the axons they myelinate. While inspired by OL morphology, we provide the theoretical underpinnings that motivated the model and explore its performance for a wide range of its parameters. Our results indicate that when the characteristic time of OL’s transient intracellular responses to neural spikes is between 10 and 40 ms and the firing rates in individual axons are relatively low (10 Hz), the OMP model efficiently synchronizes correlated and time-locked signals while latencies in axons carrying independent signals are unaffected. This suggests a novel form of selective synchronization in the CNS in which oligodendrocytes play an active role by modulating the conduction delays of correlated spike trains as they traverse to their targets.