@article{ThapaParkKimetal.2022,
  author    = {Thapa, Samudrajit and Park, Seongyu and Kim, Yeongjin and Jeon, Jae-Hyung and Metzler, Ralf and Lomholt, Michael A.},
  title     = {Bayesian inference of scaled versus fractional Brownian motion},
  series = {Journal of physics : A, mathematical and theoretical},
  volume    = {55},
  journal   = {Journal of physics : A, mathematical and theoretical},
  number    = {19},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ac60e7},
  pages     = {21},
  year      = {2022},
  abstract  = {We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.},
  language  = {en}
}
@article{MardoukhiJeonChechkinetal.2018,
  author    = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Fluctuations of random walks in critical random environments},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {20},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {31},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c8cp03212b},
  pages     = {20427 -- 20438},
  year      = {2018},
  abstract  = {Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.},
  language  = {en}
}
@article{JeonJavanainenMartinezSearaetal.2016,
  author    = {Jeon, Jae-Hyung and Javanainen, Matti and Martinez-Seara, Hector and Metzler, Ralf and Vattulainen, Ilpo},
  title     = {Protein Crowding in Lipid Bilayers Gives Rise to Non-Gaussian Anomalous Lateral Diffusion of Phospholipids and Proteins},
  series = {Physical review : X, Expanding access},
  volume    = {6},
  journal   = {Physical review : X, Expanding access},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2160-3308},
  doi       = {10.1103/PhysRevX.6.021006},
  pages     = {17},
  year      = {2016},
  abstract  = {Biomembranes are exceptionally crowded with proteins with typical protein-to-lipid ratios being around 1:50 - 1:100. Protein crowding has a decisive role in lateral membrane dynamics as shown by recent experimental and computational studies that have reported anomalous lateral diffusion of phospholipids and membrane proteins in crowded lipid membranes. Based on extensive simulations and stochastic modeling of the simulated trajectories, we here investigate in detail how increasing crowding by membrane proteins reshapes the stochastic characteristics of the anomalous lateral diffusion in lipid membranes. We observe that correlated Gaussian processes of the fractional Langevin equation type, identified as the stochastic mechanism behind lipid motion in noncrowded bilayer, no longer adequately describe the lipid and protein motion in crowded but otherwise identical membranes. It turns out that protein crowding gives rise to a multifractal, non-Gaussian, and spatiotemporally heterogeneous anomalous lateral diffusion on time scales from nanoseconds to, at least, tens of microseconds. Our investigation strongly suggests that the macromolecular complexity and spatiotemporal membrane heterogeneity in cellular membranes play critical roles in determining the stochastic nature of the lateral diffusion and, consequently, the associated dynamic phenomena within membranes. Clarifying the exact stochastic mechanism for various kinds of biological membranes is an important step towards a quantitative understanding of numerous intramembrane dynamic phenomena.},
  language  = {en}
}
@misc{MardoukhiJeonMetzler2015,
  author    = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Metzler, Ralf},
  title     = {Geometry controlled anomalous diffusion in random fractal geometries},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {980},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47486},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474864},
  pages     = {30134 -- 30147},
  year      = {2015},
  abstract  = {We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T-h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.},
  language  = {en}
}
@article{RevereyJeonBaoetal.2015,
  author    = {Reverey, Julia F. and Jeon, Jae-Hyung and Bao, Han and Leippe, Matthias and Metzler, Ralf and Selhuber-Unkel, Christine},
  title     = {Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii},
  series = {Scientific reports},
  volume    = {5},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep11690},
  pages     = {14},
  year      = {2015},
  abstract  = {Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.},
  language  = {en}
}
@article{MardoukhiJeonMetzler2015,
  author    = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Metzler, Ralf},
  title     = {Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {17},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {44},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c5cp03548a},
  pages     = {30134 -- 30147},
  year      = {2015},
  abstract  = {We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law similar to T-h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.},
  language  = {en}
}
@article{JeonChechkinMetzler2014,
  author    = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
  series = {Physical chemistry, chemical physics : PCCP},
  volume    = {30},
  journal   = {Physical chemistry, chemical physics : PCCP},
  number    = {16},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  doi       = {10.1039/C4CP02019G},
  pages     = {15811 -- 15817},
  year      = {2014},
  abstract  = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
  language  = {en}
}
@misc{JeonChechkinMetzler2014,
  author    = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76302},
  pages     = {15811 -- 15817},
  year      = {2014},
  abstract  = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
  language  = {en}
}
@article{JeonLeijnseOddershedeetal.2013,
  author    = {Jeon, Jae-Hyung and Leijnse, Natascha and Oddershede, Lene B. and Metzler, Ralf},
  title     = {Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {15},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {4},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/15/4/045011},
  pages     = {16},
  year      = {2013},
  abstract  = {We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that the polystyrene tracer beads of size 0.52-2.5 mu m after short-time normal diffusion turn over to perform anomalous diffusion of the form < r(2)(t)> similar or equal to t(alpha) with alpha approximate to 0.3. This free anomalous diffusion is ergodic and consistent with a description in terms of the generalized Langevin equation with a power-law memory kernel. With optical tweezers tracking, we unveil a power-law relaxation over several decades in time to the thermal plateau value under the confinement of the harmonic tweezer potential, as predicted previously (Phys. Rev. E 85 021147 (2012)). After the subdiffusive motion in the millisecond range, the motion becomes faster and turns either back to normal Brownian diffusion or to even faster superdiffusion, depending on the size of the tracer beads.},
  language  = {en}
}
@article{JeonBarkaiMetzler2013,
  author    = {Jeon, Jae-Hyung and Barkai, Eli and Metzler, Ralf},
  title     = {Noisy continuous time random walks},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {139},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {12},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.4816635},
  pages     = {15},
  year      = {2013},
  abstract  = {Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.},
  language  = {en}
}