TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Sposini, Vittoria
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
A1  - Seno, Flavio
T1  - Exact distributions of the maximum and range of random diffusivity processes
JF  - New Journal of Physics
N2  - We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.
KW  - random diffusivity
KW  - extremal values
KW  - maximum and range
KW  - diffusion
KW  - Brownian motion
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/abd313
SN  - 1367-2630
VL  - 23
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
ER  - 
TY  - GEN
A1  - Grebenkov, Denis S.
A1  - Sposini, Vittoria
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
A1  - Seno, Flavio
T1  - Exact distributions of the maximum and range of random diffusivity processes
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1142 
KW  - random diffusivity
KW  - extremal values
KW  - maximum and range
KW  - diffusion
KW  - Brownian motion
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-503976
SN  - 1866-8372
IS  - 1142
ER  - 
TY  - GEN
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Distribution of first-reaction times with target regions on boundaries of shell-like domains
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1255 
KW  - diffusion
KW  - first-passage time
KW  - first-reaction time
KW  - shell-like geometries
KW  - approximate methods
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-557542
SN  - 1866-8372
SP  - 1
EP  - 23
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Distribution of first-reaction times with target regions on boundaries of shell-like domains
JF  - New Journal of Physics (NJP)
N2  - We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
KW  - diffusion
KW  - first-passage time
KW  - first-reaction time
KW  - shell-like geometries
KW  - approximate methods
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/ac4282
SN  - 1367-2630
VL  - 2021
SP  - 1
EP  - 23
PB  - IOP Publishing
CY  - London
ET  - 23
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
JF  - New Journal of Physics (NJP)
N2  - We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.
KW  - diffusion
KW  - reaction cascade
KW  - first passage time
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/ac1e42
SN  - 1367-2630
VL  - 23
PB  - IOP - Institute of Physics Publishing
CY  - Bristol
ER  - 
TY  - GEN
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1159 
KW  - diffusion
KW  - reaction cascade
KW  - first passage time
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-521942
SN  - 1866-8372
ER  - 
TY  - JOUR
A1  - Sposini, Vittoria
A1  - Krapf, Diego
A1  - Marinari, Enzo
A1  - Sunyer, Raimon
A1  - Ritort, Felix
A1  - Taheri, Fereydoon
A1  - Selhuber-Unkel, Christine
A1  - Benelli, Rebecca
A1  - Weiss, Matthias
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Towards a robust criterion of anomalous diffusion
JF  - Communications Physics
N2  - Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.
Y1  - 2022
U6  - https://doi.org/10.1038/s42005-022-01079-8
SN  - 2399-3650
VL  - 5
PB  - Springer Nature
CY  - London
ER  - 
TY  - GEN
A1  - Sposini, Vittoria
A1  - Krapf, Diego
A1  - Marinari, Enzo
A1  - Sunyer, Raimon
A1  - Ritort, Felix
A1  - Taheri, Fereydoon
A1  - Selhuber-Unkel, Christine
A1  - Benelli, Rebecca
A1  - Weiss, Matthias
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Towards a robust criterion of anomalous diffusion
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1313 
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-585967
SN  - 1866-8372
IS  - 1313
ER  -