Fingerprints of a second order critical line in developing neural networks

Abstract

Patterns of biological activity with properties similar to critical states of statistical mechanics have received much attention, as they were mostly seen as indicators of computational optimality. Commonly, a single regime around an isolated critical point is expected. Our experimental data and our network simulations of developing neural cultures indicate the possibility of transitions between different critical regimes. In the latter, the addition of further fundamental neurophysiological principles to the standard neurodynamics branching model generates steeper power laws that have been observed in various experiments. Our analysis exhibits two populations of neurons, each composed of inhibitory and excitatory sites, that have distinct dynamical and topological properties. This generates a line of second order critical points, similar to what is known from the thermodynamics of two-component alloys. An analysis of two major critical regimes found in the experiments suggests that different critical regimes may express distinct computational roles.

Excess entropies reveal higher organization levels in developing neuron cultures

“…3b). In a previous study of the cell culture data [29] we found first fingerprints of avalanche criticality after 10 DIV, where our mean excess entropy shows a prominent increase, in agreement with what the logistic map example suggests (Fig. 2).…”

“…After criticality at W 0.13, multiple modes of independent subnetworks emerge that, upon the increase of W , are bound by and then are released from sets that share synchronization in an intermittent-like manner [8], rather similar to what we observe in the biological example. The failure of this model to reach the experimental excess entropy levels suggests that its parameter W should be changed into a temporally variable quantity [29].…”

“…We, moreover, previously showed that from around DIV 9 onwards, cultures start to exhibit power-law neural avalanche size and lifetime distributions in their firing patterns, where in Fig. 3 c, we have marked only the most prominent 'late' critical regime [29]. To apply the excess entropy measure, each electrode was associated with a unique state.…”

“…A detailed description of the experimental setup and measurement protocol can be found in Ref. [29]. Our previous analysis of these recordings showed sparse or absent neural activity for DIV 5, leading to the exclusion of this data from the analysis.…”

Avalanche criticality in individuals, fluid intelligence and working memory

“…Furthermore, it is not clear whether deviations from criticality caused by different intervention methods follow an identical phase 5 / 44 transition trajectory. Recent studies have proposed the concept of a "critical line" instead of a "critical point" and suggested that multiple phase transition trajectories may exist (Kanders et al, 2020). Therefore, the successful recovery of the phase transition trajectory from a large-scale brain network will not only help to answer key questions regarding what the phase transition is if the brain is critical but also have important implications in brain functional imaging and large-scale brain modeling.…”