On the validation of the Newcomb-Benford Law and the Weibull distribution in neuromuscular transmission

The neuromuscular junction represents a relevant substrate for revealing important biophysical mechanisms of synaptic transmission. In this context, calcium ions are important in the synapse machinery, providing the nerve impulse transmission to the muscle fiber. In this work, we carefully investigated whether intervals of spontaneous electrical activity, recorded in seven different calcium concentrations, conform to the Newcomb-Benford Law. Our analysis revealed that electrical discharge of neuromuscular junction yields the expected values for Newcomb-Benford Law for first and second digits, for different calcium concentrations. On the other hand, first-two digits archived conformity especially for concentrations much above the physiological level. We next examined previous theoretical studies, establishing a relation between the law and lognormal and Weibull distributions. We showed that the Weibull distribution is more appropriate to fit the intervals as compared to the lognormal distribution. Altogether, the present findings strongly suggest that the electrical discharge dynamics is characterized by base-invariance and scale-invariance, being the time intervals also well described by Weibull statistics. (C) 2020 Published by Elsevier B.V.