43651
2019
2019
eng
16
21
article
Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
Bad Honnef und London
1
2019-07-23
2019-07-23
--
Single-trajectory spectral analysis of scaled Brownian motion
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
New Journal of Physics
10.1088/1367-2630/ab2f52
1367-2630
073043
Universität Potsdam
PA 2019_65
1618.4
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436522">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 753</a>
false
false
Vittoria Sposini
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
power spectral analysis
eng
uncontrolled
single trajectory analysis
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
44288
2019
2020
eng
24
810
postprint
1
2020-01-20
2020-01-20
--
Full distribution of first exit times in the narrow escape problem
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-44288
urn:nbn:de:kobv:517-opus4-442883
1866-8372
New Journal of Physics 21 (2019) DOI: 10.1088/1367-2630/ab5de4
122001
<a href="http://publishup.uni-potsdam.de/44287">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
810
eng
uncontrolled
narrow escape problem
eng
uncontrolled
first-passage time distribution
eng
uncontrolled
mean versus most probable reaction times
eng
uncontrolled
mixed boundary conditions
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/44288/pmnr810.pdf
44287
2019
2019
eng
23
21
article
Dt. Physikalische Ges.
Bad Honnef
1
2019-12-13
2019-12-13
--
Full distribution of first exit times in the narrow escape problem
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
New Journal of Physics
10.1088/1367-2630/ab5de4
1367-2630
Universität Potsdam
PA 2019_125
1332.80
122001
<a href="https://doi.org/10.25932/publishup-44288">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 810</a>
false
false
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
narrow escape problem
eng
uncontrolled
first-passage time distribution
eng
uncontrolled
mean versus most probable reaction times
eng
uncontrolled
mixed boundary conditions
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
47696
2020
2020
eng
27
999
postprint
1
2020-09-22
2020-09-22
--
Universal spectral features of different classes of random-diffusivity processes
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-47696
urn:nbn:de:kobv:517-opus4-476960
1866-8372
063056
<a href="http://publishup.uni-potsdam.de/47695">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
New Journal of Physics 22 (2020) 6, 063056 DOI: 10.1088/1367-2630/ab9200
false
true
Creative Commons - Namensnennung, 4.0 International
Vittoria Sposini
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Flavio Seno
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
999
eng
uncontrolled
diffusion
eng
uncontrolled
power spectrum
eng
uncontrolled
random diffusivity
eng
uncontrolled
single trajectories
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/47696/pmnr999.pdf
47695
2020
2020
eng
26
6
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-06-26
2020-06-26
--
Universal spectral features of different classes of random-diffusivity processes
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
New Journal of Physics
10.1088/1367-2630/ab9200
1367-2630
063056
<a href="https://doi.org/10.25932/publishup-47696">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 999</a>
Universität Potsdam
PA 2020_052
1357.79
false
false
Creative Commons - Namensnennung, 4.0 International
Vittoria Sposini
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Flavio Seno
eng
uncontrolled
diffusion
eng
uncontrolled
power spectrum
eng
uncontrolled
random diffusivity
eng
uncontrolled
single trajectories
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
40371
2017
2017
eng
1
11
19
article
IOP
London
1
--
2017-10-24
--
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
Westudy the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
New journal of physics
10.1088/1367-2630/aa8ed9
1367-2630
Universität Potsdam, Publikationsfonds
PA 2017_54
1299.48
online registration
WOS:000413743900003
103025
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-403726">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 391</a>
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
first passage time
eng
uncontrolled
cylindrical geometry
eng
uncontrolled
aspect ratio
eng
uncontrolled
protein search
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
42299
2018
2018
eng
12
1
article
Macmillan Publishers Limited
London
1
2018-12-13
2018-12-13
--
Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants—the inverse of the mean-first-passage-time to the reaction-event. In contradiction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly solvable model we study the effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delineated by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.
Communications Chemistry
10.1038/s42004-018-0096-x
2399-3669
96
Universität Potsdam
PA 2018_82
1785.00
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-422989">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 527</a>
Creative Commons - Namensnennung, 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Chemie und zugeordnete Wissenschaften
open_access
Referiert
Publikationsfonds der Universität Potsdam
Open Access
42429
2018
2019
eng
31
655
postprint
1
2019-02-27
2019-02-27
--
Power spectral density of a single Brownian trajectory
The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
what one can and cannot learn from it
10.25932/publishup-42429
urn:nbn:de:kobv:517-opus4-424296
1866-8372
online registration
023029
New Journal of Physics 20 (2018), Art. 023029 DOI 10.1088/1367-2630/aaa67c
false
true
Creative Commons - Namensnennung, 4.0 International
Diego Krapf
Enzo Marinari
Ralf Metzler
Gleb Oshanin
Xinran Xu
Alessio Squarcini
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
655
eng
uncontrolled
power spectral density
eng
uncontrolled
single-trajectory analysis
eng
uncontrolled
probability density function
eng
uncontrolled
exact results
Physik
open_access
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/42429/pmnr655.pdf
43652
2019
2019
eng
16
753
postprint
1
2019-10-15
2019-10-15
--
Single-trajectory spectral analysis of scaled Brownian motion
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-43652
urn:nbn:de:kobv:517-opus4-436522
1866-8372
073043
New Journal of Physics 21 (2019) Art. 073043 DOI: 10.1088/1367-2630/ab2f52
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/43651">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
Vittoria Sposini
Metzler Ralf
Gleb Oshanin
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
753
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
power spectral analysis
eng
uncontrolled
single trajectory analysis
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/43652/pmnr753.pdf
35632
2012
2012
eng
8
3
86
article
American Physical Society
College Park
1
--
--
--
First passages in bounded domains When is the mean first passage time meaningful?
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(omega) distribution of the random variable omega = tau(1)/(tau(1) + tau(2)), which is a measure for how similar the first passage times tau(1) and tau(2) are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(omega) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(omega), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.86.031143
1539-3755
wos:2011-2013
031143
WOS:000309338900001
Mattos, TG (reprint author), Max Planck Inst Intelligent Syst, Heisenbergstr 3, D-70569 Stuttgart, Germany., tgmattos@is.mpg.de
European Science Foundation; Marie Curie International Research Staff
Exchange Scheme Fellowship within the 7th European Community Framework
Programme [PIRSES-GA-2010-269139]; Academy of Finland within the FiDiPro
program; ESF Research Network "Exploring the Physics of Small Devices"
Thiago G. Mattos
Carlos Mejia-Monasterio
Ralf Metzler
Gleb Oshanin
Institut für Physik und Astronomie
Referiert
40372
2017
2017
eng
11
postprint
1
--
2017-11-16
--
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
urn:nbn:de:kobv:517-opus4-403726
online registration
New journal of physics 19 (2017). - DOI: 10.1088/1367-2630/aa8ed9
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40371">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
391
eng
uncontrolled
aspect ratio
eng
uncontrolled
cylindrical geometry
eng
uncontrolled
first passage time
eng
uncontrolled
protein search
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/40372/pmnr391_online.pdf
42298
2019
2019
eng
12
527
postprint
1
2019-01-15
2019-01-15
--
Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants—the inverse of the mean-first-passage-time to the reaction-event. In contradiction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly solvable model we study the effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delineated by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.
Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-42298
urn:nbn:de:kobv:517-opus4-422989
1866-8372
Communications Chemistry 1 (2018) Art. 96 DOI: 10.1038/s42004-018-0096-x
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/42299">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
true
true
Creative Commons - Namensnennung, 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
527
Chemie und zugeordnete Wissenschaften
open_access
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/42298/pmnr527.pdf
46250
2017
2017
eng
11
19
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry-characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. A similar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA. We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters. We analyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/aa8ed9
1367-2630
wos:2017
103025
WOS:000413743900003
Grebenkov, DS (reprint author), Univ Paris Saclay, Ecole Polytech, CNRS, Lab Phys Mat Condensee,UMR7643, F-91128 Palaiseau, France.; Grebenkov, DS (reprint author), ISCP, Bolshoy Vlasyevskiy Pereulok 11, Moscow 119002, Russia., denis.grebenkov@polytechnique.edu
French National Research Agency [ANR-13-JSV5-0006-01]; Deutsche Forschungsgemeinschaft; Potsdam University
importub
2020-04-19T23:54:01+00:00
filename=package.tar
a0cdd125e124f1705eb6953da8eab0c4
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
first passage time
eng
uncontrolled
cylindrical geometry
eng
uncontrolled
aspect ratio
eng
uncontrolled
protein search
Institut für Physik und Astronomie
Referiert
Import
45235
2016
2016
eng
19
49
article
IOP Publ. Ltd.
Bristol
1
--
--
--
A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein–Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/49/22/225601
1751-8113
1751-8121
wos2016:2019
225601
WOS:000376392100006
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam Golm, Germany., rmetzler@uni-potsdam.de
Alexander von Humboldt Fellowship; ARRS Program [P1-0002]; Academy of Finland FiDiPro grant
importub
2020-03-22T16:51:01+00:00
filename=package.tar
357ecfccb10a292ef770197c7c29f4ec
Maria Schwarzl
Aljaz Godec
Gleb Oshanin
Ralf Metzler
eng
uncontrolled
first passage process
eng
uncontrolled
diffusion
eng
uncontrolled
predator-prey model
Institut für Physik und Astronomie
Referiert
Import
48405
2020
2020
eng
29
1018
postprint
1
2020-11-24
2020-11-24
--
From single-particle stochastic kinetics to macroscopic reaction rates
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
fastest first-passage time of N random walkers
10.25932/publishup-48405
urn:nbn:de:kobv:517-opus4-484059
1866-8372
New Journal of Physics 22 (2020) Art. 103004 DOI: 10.1088/1367-2630/abb1de
103004
<a href="http://publishup.uni-potsdam.de/48404">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
Creative Commons - Namensnennung, 4.0 International
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1018
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage
eng
uncontrolled
fastest first-passage time of N walkers
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/48405/pmnr1018.pdf
48404
2020
2020
eng
28
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-10-02
2020-10-02
--
From single-particle stochastic kinetics to macroscopic reaction rates
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
New Journal of Physics
fastest first-passage time of N random walkers
10.1088/1367-2630/abb1de
1367-2630
Universität Potsdam
PA 2020_095
1418.10
103004
<a href="https://doi.org/10.25932/publishup-48405">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1018</a>
false
false
Creative Commons - Namensnennung, 4.0 International
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage
eng
uncontrolled
fastest first-passage time of N walkers
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access