Persistent Behavior in a Phase-shift Sequence of Periodical Biochemical Oscillations

Abstract

We present the analysis of a phase-shift sequence obtained from random transitions between periodic solutions of a biochemical dynamical model, formed by a system of three differential equations and which represent an instability-generating multienzymatic mechanism. The phase-shift series was studied in terms of Hurst's rescaled range analysis. We found that the data were characterized by a Hurst exponentH= 0.69, which was clearly indicative of long-term trends. This result had a high significance level, as was confirmed through Monte Carlo simulations in which the data were scrambled in the series, destroying its original ordering. For these series we obtained a Hurst exponent which was consistent with the expectation ofH= 0.5 for a random independent process. This clearly showed that, although the transitions between the periodic solutions were provoked randomly, the stochastic process obtained exhibited long-term persistence. The fractal dimension was also estimated and found to be consistent with the value of the Hurst exponent.