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Information and long term memory in calcium signals

Unicellular organisms are open metabolic systems that need to process information about their external environment in order to survive. In most types of tissues and organisms, cells use calcium signaling to carry information from the extracellular side of the plasma membrane to the different metabolic targets of their internal medium. This information might be encoded in the amplitude, frequency, duration, waveform or timing of the calcium oscillations. Thus, specific information coming from extracellular stimuli can be encoded in the calcium signal and decoded again later in different locations within the cell. Despite its cellular importance, little is known about the quantitative informative properties of the calcium concentration dynamics inside the cell. In order to understand some of these informational properties, we have studied experimental Ca2+ series of Xenopus laevis oocytes under different external pH stimulus. The data has been analyzed by means of information-theoretic approaches such as Conditional Entropy, Information Retention, and other non-linear dynamics tools such as the power spectra, the Largest Lyapunov exponent and the bridge detrended Scaled Window Variance analysis. We have quantified the biomolecular information flows of the experimental data in bits, and essential aspects of the information contained in the experimental calcium fluxes have been exhaustively analyzed. Our main result shows that inside all the studied intracellular Ca2+ flows a highly organized informational structure emerge, which exhibit deterministic chaotic behavior, long term memory and complex oscillations of the uncertainty reduction based on past values. The understanding of the informational properties of calcium signals is one of the key elements to elucidate the physiological functional coupling of the cell and the integrative dynamics of cellular life.