New article in PLoS Computational Biology: Self-Organized Criticality in Developing Neuronal Networks

Author Summary

Learning depends crucially on the synaptic distribution in a neural network. Therefore, investigating the development from which a certain distribution emerges is crucial for our understanding of network function. Morphological development is controlled by many different parameters, most importantly: neuronal activity, synapse formation, and the balance between excitation and inhibition, but it is largely unknown how these parameters interact on different time scales and how they influence the developing network structure. In our work, we consider the well-known concept of self-organized criticality. We have measured how real cell cultures change their activity patterns during the first 60 days of development traversing through different stages of criticality. With a dynamic model we can reproduce the observed developmental states and predict specific time-courses for the network parameters. For example, the model predicts a delayed, overshooting onset of inhibition with a longer time to reach maturation as compared to excitation. Furthermore, we suggest that the balance of dendrites and axons in the mature state is quite sensitive to the initial conditions of development. These and several more predictions are accessible by future experimental work and can help us to better understand neuronal networks and their parameters during development and also in the mature state.

Abstract

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.

Development of the network in phase space: hysteresis curve of the mean membrane potential (red) against the mean connectivity, displayed together with its possible trajectories (blue). 

Tetzlaff C, Okujeni S, Egert U, Wörgötter F, Butz M (2010) Self-Organized Criticality in Developing Neuronal Networks. PLoS Comput Biol 6(12): e1001013. doi:10.1371/journal.pcbi.1001013