Chaos evidence in catecholamine secretion at chromaffin cells

Chromaffin cells secrete catecholamine molecules via exocytosis process. Each exocytotic event is characterized by a current spike, which corresponds to the amount of released catecholamine from secretory vesicles after fusing to plasma membrane. The current spike might be measured by the oxidation of catecholamine molecules and can be experimentally detected through amperometry technique. In this contribution, the secretion of catecholamine, namely adrenaline, of a set of bovine chromaffin cells is measured individually at each single cell. The aim is to study quantitative results of chaotic behavior in catecholamine secretion. For analysis, time series were obtained from amperometric measurements of each single chromaffin cell. Three analysis techniques were exploited: (i) A low-order attractor was generated by means of phase space reconstruction, Average Mutual Information (AMI) and False Nearest Neighbors (FNN) were used to compute embedding lag and embedding dimension, respectively. (ii) The properties of power spectrum density of time series were studied by Fast Fourier Transform (FFT) looking for possible dominant frequencies in power spectrum. (iii) Maximun Lyapunov Exponent (MLE) analysis was done to study the divergence of trajectories of the time series. Nevertheless, in order to dismiss the possibility of positiveness of MLE are due to the inherent noise in experiments, seven surrogate data sets computed using the Amplitude Adjusted Fourier Transform (AAFT) algorithm was computed. The phase space reconstruction showed that, in all cases, the trajectories lie in an embedding subspace suggesting oscillatory nature. The FFT analysis showed high dispersion of the power spectrum without any predominant frequency range. MLE analysis showed that the MLE values are positive for a given orbit time and a defined range of maximum scale values. Moreover, the trajectory of the MLE evolution of all the surrogate data are asymptotic and hold positive along the maximum scale range. These findings are preliminary evidence on detecting chaotic behavior in catecholamine secretion and, in general, their provide a first step towards a deeply understanding of nonlinear behavior of protein releasing dynamics.