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.

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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