Statistical crossover and nonextensive behavior of neuronal short-term depression

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 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.

Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions

“…Thirdly, a direct mathematical relation between the NBL and GTS was deduced by Shao and Ma [46]. Finally, studies of the mammalian NMJ performed by da Silva et al showed that synaptic transmission statistics are best understood within an approach inspired by the GTS [37,47]. Altogether, these arguments form a theoretical pillar to hypothesize about the existence of a relation between the gNBL within a generalized resting potential, likely valid at mammalian temperatures.…”

Nonextensive realizations in interacting ion channels: Implications for mechano-electrical transducer mechanisms

“…As mentioned, the bridge between non-extensivity and fractals has been systematically studied by several authors ( [62,14]). In the nervous system, Silva et al evidenced that short-term plasticity, existing in the giant calyx of Held, is better modeled using a q-differential equation inspired by the GT S formalism ( [25,53]). Previous reports reinforce their results, showing thousands of vesicles sharing the exocytotic machinery.…”

“…For example, researchers recorded the existence of long-range correlations in electroencephalogram signals ( [21]). Furthermore, Silva et al presented a study of cellular communication and neuroplasticity assuming GT S premises ( [53]). Also, this theory was applied to uncover non-random mechanisms in electrocardiograms and cellular motion in two-dimensional cellular aggregates ( [1,64]).…”