1. Neuronal avalanches are increasingly recognized to be important for cortex function. We have now embarked on the problem of how avalanche dynamics, or critical states, might be beneficial for learning. One of the first problems we addressed was the benefit of critical dynamics to allow network landscapes to overcome existing, encrusted pathways in order to establish new input-output relationships (Alstott et al., 2015). Dynamics of complex systems are often described using weighted networks in which the position, weight and direction of links quantify how activity propagates between system elements, or nodes. Nodes with only a few outgoing links of low weight have low out-strength and thus form bottlenecks that hinder propagation. It is currently not well understood how systems can overcome limits imposed by such bottlenecks. Here, we simulate activity cascades on weighted networks and show that, for any cascade length, activity initially propagates towards high out-strength nodes before terminating in low out-strength bottlenecks. Increasing the weights of links that are active early in the cascade further enhances already strong pathways, but worsens the bottlenecks thereby limiting accessibility to other pathways in the network. In contrast, strengthening only links that propagated the activity just prior to cascade termination, i.e. links that point into bottlenecks, eventually removes these bottlenecks and increases the accessibility of all paths on the network. This local adaptation rule simply relies on the relative timing to a global failure signal and allows systems to overcome engrained structure to adapt to new challenges. 2. A closely related problem resides in the question how critical dynamics, or neuronal avalanches, are maintained in neuronal networks that incorporate fundamental plasticity rules such as short-term plasticity and spike-timing dependent plasticity. In collaboration with Hughes Research Laboratories, a new mechanism was found how avalanches stably emerge in the presence of these synaptic plasticity rules (see Stepp et al., 2014). 3. One of the hardest problems to date was the identification of neuronal avalanche dynamics at the individual cell level. We achieved this by using latest generations of genetically encoded calcium indicators and advanced 2-photon microscopy. Using these approaches we demonstrated for the first time spike avalanches in groups of pyramidal neurons to be present in the awake animal and to disappear under anesthesia. This work is part of the BRAIN initiative and has been recently featured in the Directors blog as The brains critical balance (www.nimh.nih.gov/about/director/2015/the-brains-critical-balance.shtml) (Bellay et al., 2015). Spontaneous fluctuations in neuronal activity emerge at many spatial and temporal scales in cortex. Population measures found these fluctuations to organize as scale-invariant neuronal avalanches, suggesting cortical dynamics to be critical. Macroscopic dynamics, though, depend on physiological states and are ambiguous as to their cellular composition, spatiotemporal origin, and contributions from synaptic input or action potential (AP) output. Here, we study spontaneous firing in pyramidal neurons (PNs) from rat superficial cortical layers in vivo and in vitro using 2-photon imaging. As the animal transitions from the anesthetized to awake state, spontaneous single neuron firing increases in irregularity and assembles into scale-invariant avalanches at the group level. In vitro spike avalanches emerged naturally yet required balanced excitation and inhibition. This demonstrates that neuronal avalanches are linked to the global physiological state of wakefulness and that cortical resting activity organizes as avalanches from firing of local PN groups to global population activity. 4. Critical systems that exhibit neuronal avalanches surprise through their richness in temporal outbursts. The temporal dependencies of neuronal avalanches can similarly like in earthquake reveal complex historical dependencies that open new avenues for temporal coding. This was for the first time deeper explored in collaboration with European physicists who are experts in earthquake time series analysis. (see Lombardi et al., 2014). 5. I was the co-organizer of a Special Topic in Frontiers System Neuroscience on Criticality as a signature of healthy neural systems. The topic comprised a series of articles exploring the relationship between critical dynamics in the brain and its deviations in the disease state (Massobrio et al., 2015). 6. Critical slowing down is an important feature of systems dynamics near a phase-transition or criticality. It reports the prolonged response of a system to an external input or perturbation as the dynamics approaches a phase-transition and can be interpreted as short-term memory. We succeeded to demonstrate critical slowing down in the most basic mechanism that identifies nerve cells: the action potential generation (Meisel et al., 2015). Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a systems tendency to recover more slowly from a perturbation the closer it gets to the transition, a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws. Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf-bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.
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