Power laws in neuronal culture activity from limited availability of a shared resource

Abstract

We record spontaneous activity from a developing culture of dissociated rat hippocampal neurons in vitro using a multi electrode array. To statistically characterize activity, we look at the time intervals between recorded spikes, which, unlike neuronal avalanche sizes, do not require the selection of a time bin. The distribution of inter event intervals in our data approximate power laws at all recorded stages of development, with exponents that can be used to characterize the development of the culture. Synchronized bursting emerges as the culture matures, and these bursts show activity that decays approximately exponentially. From this, we propose a model for neuronal activity within bursts based on the consumption of a shared resource. Our model produces power law distributed avalanches in simulations, and is analytically demonstrated to produce power law distributed inter event intervals with an exponent close to that observed in our data. This indicates that power law distributions in neuronal avalanche size and other observables, can be also an artefact of exponentially decaying activity within synchronized bursts.