The irregularity of growing and shortening patterns observed experimentally in microtubules and their ensembles 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 mono-fractal distributions. Based on the multifractal spectrum profile, a set of multifractal indices have been calculated that can be related to the level of dynamical processes in microtubules. We also show that the resulting multifractal spectra for the simulated data might not be comparable with experimental data.

在微管及其集合中实验观察到的生长和缩短模式的不规则性反映了一个动态系统，该系统在组装和拆卸阶段之间随机波动。已对观察到的微管长度的时间序列进行了广泛分析，以阐明微管的结构和动力学特性。在这里，第一次，多重分形趋势波动分析（MFDFA）已被用来研究实验和模拟的微管时间序列的多重分形和拓扑特性。我们发现，微管长度的时间依赖性具有真正的多分形特征，不能用单分形分布来描述。根据多重分形谱图，已经计算出一组与微管中的动力学过程水平有关的多重分形指数。我们还表明，所得的模拟数据多重分形谱可能与实验数据不具有可比性。