# Statistical crossover and nonextensive behavior of the neuronal short-term depression

## TL;DR

This paper introduces a q-differential equation model to analyze nonextensive behavior and statistical crossover in neuronal short-term depression, revealing heterogeneity in neurotransmitter release and bridging electrophysiological and morphological data.

## Contribution

It presents a novel q-differential equation framework to characterize nonextensivity and heterogeneity in synaptic depression, advancing understanding of neuronal coding mechanisms.

## Key findings

- Evidence of nonextensivity in electrophysiological data
- Identification of statistical crossover in neurotransmission
- Simple vesicle model fits low-frequency data

## Abstract

The theoretical basis of neuronal coding, associated with short term degradation in synaptic transmission, is a matter of debate in the literature. In fact, electrophysiological signals are commonly characterized as inversely proportional to stimulus intensity. Among theoretical descriptions of this phenomenon, models based on $1/f$-dependency are employed to investigate the biophysical properties of the short term synaptic depression. In this work we formulated a model based on a paradigmatic \textit{q}-differential equation to obtain a generalized formalism useful for investigation of nonextensivity in this specific type of synaptic plasticity. Our analysis reveals nonextensivity in data from electrophysiological recordings and also a statistical crossover in neurotransmission. In particular, statistical transitions providesadditional support to the hypothesis of heterogeneous release probability of neurotransmitters. On the other hand, the simple vesicle model agrees with data only at low frequency stimulations. Thus, the present work presents a method to demonstrate that short-term depression is not only governed by random mechanisms but also by a nonextensive behavior. Our findings also conciliate morphological and electrophysiological investigations into a coherent biophysical scenario.