title: Quantitative analysis of single particle trajectories: mean maximal excursion method.
abstract: An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss what we believe are new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions (MMEs), i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean-squared displacement we show that the MME analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the MME method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics such as diffusion on fractals, continuous time random walks, and fractional Brownian motion.
authors.affiliation: Physics Department, Technical University of Munich, Garching, Germany.
authors.forename: Vincent
authors.initials: V
authors.lastname: Tejedor
authors.forename: Olivier
authors.initials: O
authors.lastname: Bénichou
authors.forename: Raphael
authors.initials: R
authors.lastname: Voituriez
authors.forename: Ralf
authors.initials: R
authors.lastname: Jungmann
authors.forename: Friedrich
authors.initials: F
authors.lastname: Simmel
authors.forename: Christine
authors.initials: C
authors.lastname: Selhuber-Unkel
authors.forename: Lene B
authors.initials: LB
authors.lastname: Oddershede
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D004058:Diffusion; D017709:Fractals; D008055:Lipids / Q000737:chemistry; D008954:Models, Biological; D008968:Molecular Conformation; D009038:Motion; D015203:Reproducibility of Results; D013269:Stochastic Processes; D013997:Time Factors
chemical_list: D008055:Lipids