Critical Slowing Down Governs the Transition to Neuron Spiking

Abstract

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 system’s 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.

Critical slowing as a biomarker for seizure susceptibility

“…Critical slowing has been observed in many systems, including cell population collapse in bacterial cultures [6], crashes in financial markets [7], and earthquakes [8]. Critical transitions have been employed to describe neural systems, such as onset of depression [9], changes in perception [10], switching between motor programs [11], onset of spiking in neurons [12], and termination of epileptic seizures [13].…”

A theory of neocortical seizure spread: Insights from statistical physics

“…System dynamics ‘slows down’ near a continuous phase transition [33, 52], as observed during transition to neuronal spiking and the onset, spread and termination of seizures [24, 31, 32, 54, 55]. Building on previous reports [47, 56], we show (see Methods) that a non-saturating model ‘slows down’, i.e., that the time required for m(t) to reach its predicted value m grows exponentially near criticality, as in Fig 3B.…”

Channel-noise-induced critical slowing in the subthreshold Hodgkin-Huxley neuron

“…Having been experimentally demonstrated in the squid giant axon preparation [13], we anticipate that observation of critical slowing-down in the neurophysiological laboratory may be possible under appropriate conditions (see Ref. [33] for a recent experimental demonstration). When considering interneuron communication-a process traditionally thought to be constrained to suprathreshold actions-divergence of subthreshold voltage fluctuations just prior to spike initiation may have functional significance given the presence of gap electrical junctions that can couple one neuron to another.…”