Multifractality Nature of Microtubule Dynamic Instability Process

The irregularity of growing and shortening patterns observed experimentally in microtubules reflects a dynamical system that fluctuates stochastically between assembly and disassembly phases. The observed time series of microtubule lengths have been extensively analyzed to shed light on structural and dynamical properties of microtubules. Here, for the first time, Multifractal Detrended Fluctuation analysis (MFDFA) has been employed to investigate the multifractal and topological properties of both experimental and simulated microtubule time series. We find that the time dependence of microtubule length possesses true multifractal characteristics and cannot be described by monofractal distributions. Based on the multifractal spectrum profile, a set of multifractal indices have been calculated that can be related to the level of dynamical activities of microtubules. We also show that the resulting multifractal spectra for the simulated data might not be comparable with experimental data. Statement of Significance Microtubules are some of the most important subcellular structures involved in a multitude of functions in all eukaryotic cells. In addition to their cylindrical geometry, their polymerization/depolymerization dynamics, termed dynamic instability, is unique among all protein polymers. In this paper we demonstrate that there is a very specific mathematical representation of microtubule growth and shrinkage time series in terms of multifractality. We further show that using this characteristic, one can distinguish real experimental data from synthetic time series generated from computer simulations.