Modelling intermittent anomalous diffusion with switching fractional Brownian motion

Abstract

The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due to which the motion changes along the trajectories. Such effects manifest themselves as spatiotemporal correlations. Despite the broad occurrence of heterogeneous complex systems in nature, their analysis is still quite poorly understood and tools to model them are largely missing. We contribute to tackling this problem by employing an integral representation of Mandelbrot's fractional Brownian motion that is compliant with varying motion parameters while maintaining long memory. Two types of switching fractional Brownian motion are analysed, with transitions arising from a Markovian stochastic process and scale-free intermittent processes. We obtain simple formulas for classical statistics of the processes, namely the mean squared displacement and the power spectral density. Further, a method to identify switching fractional Brownian motion based on the distribution of displacements is described. A validation of the model is given for experimental measurements of the motion of quantum dots in the cytoplasm of live mammalian cells that were obtained by single-particle tracking.

References in corpus (23)

• Anomalous transport in the crowded world of biological cells
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells
• Machine learning method for single trajectory characterization
• Spectral content of a single non-Brownian trajectory
• Inferring diffusion in single live cells at the single molecule level
• The Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Bayesian deep learning for error estimation in the analysis of anomalous diffusion
• Single-Molecule Imaging of Nav1.6 on the Surface of Hippocampal Neurons Reveals Somatic Nanoclusters
• Superdiffusive motion of membrane-targeting C2 domains
• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission
• 1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents
• Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions
• Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis
• Unravelling intermittent features in single particle trajectories by a local convex hull method
• Complex diffusion-based kinetics of photoluminescence in semiconductor nanoplatelets
• Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast moving Endosomes
• Non-Gaussian displacement distributions in models of heterogeneous active particle dynamics

Cited by in corpus (10)

• Fractional Brownian motion with fluctuating diffusivities
• Diffusion of intrinsically disordered proteins within viscoelastic membraneless droplets
• Multifractional Brownian motion with telegraphic, stochastically varying exponent
• Dynamics of switching processes: general results and applications to intermittent active motion
• Two-dimensional Brownian motion with dependent components: turning angle analysis
• Super-resolved anomalous diffusion: deciphering the joint distribution of anomalous exponent and diffusion coefficient
• Modelling cosmic-ray transport: magnetised versus unmagnetised motion in astrophysical magnetic turbulence
• Evaluating Gaussianity of heterogeneous fractional Brownian motion
• Improved mean squared displacement analysis for anomalous single particle trajectories
• Two-dimensional fractional Brownian motion: Analysis in time and frequency domains