Macrophage ion currents are fit by a fractional model and therefore are a time series with memory

We studied macroscopic ion currents from macrophages and compared their patterns of behavior using classical and fractal analysis. Peak and steady state currents were measured respectively at the beginning and end of a voltage-clamp pulse. Hurst coefficients H and fractional dimensions were calculated for the current fluctuations (I(H)) during the intervening interval; these fluctuations are usually assumed to be white noise. We show that I(H) is different from 0.5 and that the increments are stationary, indicating that the dynamic model has memory and that the intervening current fluctuations cannot be considered as white noise. I(H) is less than 0.5, implying an antipersistent pattern. In addition, we show that the relation between inactivation and I(H) versus voltage V fit an equation I(H)(V) = f(V, alpha, m, d), where alpha is associated with fractional calculus and m and d are free parameters. Fitting by a fractional model confirms that the phenomenon has memory.