38215
2014
2014
eng
24128
24164
37
44
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp03465a
25297814
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000344249400001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland; Israel Science Foundation; Deutsche
Forschungsgemeinschaft [CH 707/5-1]
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
Institut für Chemie
Referiert
38257
2014
2014
eng
15811
15817
7
30
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
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 < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < 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.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp02019g
24968336
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000339628400011
Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., rmetzler@uni-potsdam.de
Jae-Hyung Jeon
Aleksei V. Chechkin
Ralf Metzler
Institut für Chemie
Referiert
38309
2014
2014
eng
6118
6128
11
13
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Diffusion of finite-size particles in two-dimensional channels with random wall configurations
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c3cp55160a
24556939
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000332474700029
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
German Federal Ministry for Education and Research; Academy of Finland
within the FiDiPro scheme
Maximilian Bauer
Aljaz Godec
Ralf Metzler
Institut für Chemie
Referiert
7711
2014
eng
1847
1858
12
17
3
article
The Royal Society of Chemistry
Cambridge
1
--
2014-11-26
--
Non-universal tracer diffusion in crowded media of non-inert obstacles
We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer–obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer–obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer–crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.
Physical Chemistry Chemical Physics
1463-9076
online registration
Au-006431
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77128">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Humanwissenschaftliche Reihe ; 186</a>
Surya K. Ghosh
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
fluorescence correlation spectroscopy
eng
uncontrolled
single-particle tracking
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
living cells
eng
uncontrolled
physiological consequences
eng
uncontrolled
langevin equation
eng
uncontrolled
infection pathway
eng
uncontrolled
excluded volume
eng
uncontrolled
brownian-motion
eng
uncontrolled
random-walks
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
7712
2014
2014
eng
1847
1858
12
postprint
The Royal Society of Chemistry
Cambridge
1
2015-05-22
2014-11-26
--
Non-universal tracer diffusion in crowded media of non-inert obstacles
We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer–obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer–obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer–crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.
urn:nbn:de:kobv:517-opus4-77128
online registration
Au-006431
Phys. Chem. Chem. Phys., 2015,17, 1847-1858. - DOI: 10.1039/C4CP03599B
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7711">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Surya K. Ghosh
Andrey G. Cherstvy
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
186
eng
uncontrolled
escence correlation spectroscopy
eng
uncontrolled
single-particle tracking
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
living cells
eng
uncontrolled
physiological consequences
eng
uncontrolled
langevin equation
eng
uncontrolled
infection pathway
eng
uncontrolled
excluded volume
eng
uncontrolled
brownian-motion
eng
uncontrolled
random-walks
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
https://publishup.uni-potsdam.de/opus4-ubp/files/7712/pmnr186.pdf
7695
2014
2014
eng
472
488
17
article
The Royal Society of Chemistry
Cambridge
1
--
2014-10-20
--
Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping–unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.
Soft Matter
1744-683X
online registration
Au-006430
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76961">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Humanwissenschaftliche Reihe ; 185</a>
Jaeoh Shin
Andrey Cherstvy
Ralf Metzler
eng
uncontrolled
gene-regulation kinetics
eng
uncontrolled
physiological consequences
eng
uncontrolled
spatial-organization
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
folding kinetics
eng
uncontrolled
living cells
eng
uncontrolled
dna coiling
eng
uncontrolled
in-vitro
eng
uncontrolled
dynamics
eng
uncontrolled
mixtures
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
7696
2014
2014
eng
472
488
17
postprint
The Royal Society of Chemistry
Cambridge
1
2015-05-19
2014-10-20
--
Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping–unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.
urn:nbn:de:kobv:517-opus4-76961
online registration
Au-006430
Soft Matter, 2015,11, 472-488.. - DOI: 10.1039/C4SM02007C
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7695">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Jaeoh Shin
Andrey Cherstvy
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
185
eng
uncontrolled
gene-regulation kinetics
eng
uncontrolled
physiological consequences
eng
uncontrolled
spatial-organization
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
folding kinetics
eng
uncontrolled
living cells
eng
uncontrolled
dna coiling
eng
uncontrolled
in-vitro
eng
uncontrolled
dynamics
eng
uncontrolled
mixtures
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
https://publishup.uni-potsdam.de/opus4-ubp/files/7696/pmnr185.pdf
7443
2014
2014
eng
24128
24164
37
16
2014
article
1
--
2014-09-22
--
Anomalous diffusion models and their properties
Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.
physical chemistry, chemical physics : PCCP
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
10.1039/c4cp03465a
1463-9076 (print), 1463-9084 (online)
online registration
Au-006611
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74448">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 174</a>
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
eng
uncontrolled
intermittent chaotic systems
eng
uncontrolled
Fokker-Planck equations
eng
uncontrolled
time random-walks
eng
uncontrolled
fluorescence photobleaching recovery
eng
uncontrolled
fluctuation-dissipation theorem
eng
uncontrolled
fractional dynamics approach
eng
uncontrolled
photon-counting statistics
eng
uncontrolled
weak ergodicity breaking
eng
uncontrolled
flight search patterns
eng
uncontrolled
levy flights
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
Universität Potsdam
7444
2014
2014
eng
24128
24164
37
postprint
1
2015-03-26
2014-09-22
--
Anomalous diffusion models and their properties
Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
urn:nbn:de:kobv:517-opus4-74448
online registration
Au-006611
Physical Chemistry, Chemical Physics (2014) 16, S. 24128-24164. - DOI: 10.1039/c4cp03465a
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7443">Bibliographieeintrag der Originalveröffentlichung/Quelle</a
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
paper 174
eng
uncontrolled
Fokker-Planck equations
eng
uncontrolled
flight search patterns
eng
uncontrolled
fluctuation-dissipation theorem
eng
uncontrolled
fluorescence photobleaching recovery
eng
uncontrolled
fractional dynamics approach
eng
uncontrolled
intermittent chaotic systems
eng
uncontrolled
levy flights
eng
uncontrolled
photon-counting statistics
eng
uncontrolled
time random-walks
deu
uncontrolled
weak ergodicity breaking
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/7444/pmnr174.pdf
7400
2014
2014
eng
1591
1601
11
10
2014
article
Royal Society of Chemistry
1
--
2014-01-02
--
Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
Soft matter
10.1039/c3sm52846d
2046-2069 (online)
online registration
Au-006605
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74021">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 168</a>
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
intracellular-transport
eng
uncontrolled
adenoassociated virus
eng
uncontrolled
infection pathway
eng
uncontrolled
escherichia-coli
eng
uncontrolled
endosomal escape
eng
uncontrolled
living cells
eng
uncontrolled
trafficking
eng
uncontrolled
cytoplasm
eng
uncontrolled
models
Chemie und zugeordnete Wissenschaften
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
RSC