@article{GodecMetzler2017,
  author    = {Godec, Aljaž and Metzler, Ralf},
  title     = {First passage time statistics for two-channel diffusion},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {50},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {8},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aa5204},
  pages     = {17},
  year      = {2017},
  abstract  = {We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes, which is shown to effect a non-trivial first passage behaviour. We also address the scenario of intermittent immobilisation. In both cases we prove that despite the perfectly non-recurrent motion of two-channel Markov additive diffusion in 3 dimensions the first passage statistics at long times do not display Poisson-like behaviour if none of the phases has a vanishing diffusion coefficient. This stands in stark contrast to the standard (one-channel) Markov diffusion counterpart. We also discuss the relevance of our results in the context of cellular signalling.},
  language  = {en}
}
@article{GrebenkovMetzlerOshanin2021,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes},
  series = {New Journal of Physics (NJP)},
  volume    = {23},
  journal   = {New Journal of Physics (NJP)},
  publisher = {IOP - Institute of Physics Publishing},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ac1e42},
  pages     = {18},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@misc{GrebenkovMetzlerOshanin2021,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-52194},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-521942},
  pages     = {20},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{GrebenkovMetzlerOshanin2017,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {19},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aa8ed9},
  pages     = {11},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@misc{GrebenkovMetzlerOshanin2017,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-403726},
  pages     = {11},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{GrebenkovMetzlerOshanin2017,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains},
  series = {New journal of physics},
  volume    = {19},
  journal   = {New journal of physics},
  publisher = {IOP},
  address   = {London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aa8ed9},
  pages     = {1 -- 11},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Kruesemann2016,
  author    = {Kr{\"u}semann, Henning},
  title     = {First passage phenomena and single-file motion in ageing continuous time random walks and quenched energy landscapes},
  school      = {Universit{\"a}t Potsdam},
  pages     = {122},
  year      = {2016},
  abstract  = {In der Physik gibt es viele Prozesse, die auf Grund ihrer Komplexit{\"a}t nicht durch physikalische Gleichungen beschrieben werden k{\"o}nnen, beispielsweise die Bewegung eines Staubkorns in der Luft. Durch die vielen St{\"o}ße mit Luftmolek{\"u}len f{\"u}hrt es eine Zufallsbewegung aus, die so genannte Diffusion. Auch Molek{\"u}le in biologischen Zellen diffundieren, jedoch befinden sich in einer solchen Zelle im selben Volumen viel mehr oder viel gr{\"o}ßere Molek{\"u}le. Das beobachtete Teilchen st{\"o}ßt dementsprechend {\"o}fter mit anderen zusammen und die Diffusion wird langsamer, sie wird subdiffusiv. Mit der Zeit kann sich die Charakteristik der Subdiffusion {\"a}ndern; dies wird als (mikroskopisches) Altern bezeichnet. Ich untersuche in der vorliegenden Arbeit zwei mathematische Modelle f{\"u}r eindimensionale Subdiffusion, einmal den continuous time random walk (CTRW) und einmal die Zufallsbewegung in einer eingefrorenen Energielandschaft (QEL=quenched energy landscape). Beide sind Sprungprozesse, das heißt, sie sind Abfolgen von r{\"a}umlichen Spr{\"u}ngen, die durch zufallsverteilte Wartezeiten getrennt sind. Die Wartezeiten in der QEL sind r{\"a}umlich korrelliert, w{\"a}hrend sie im CTRW unkorrelliert sind. Ich untersuche in der vorliegenden Arbeit verschiedene statistische Gr{\"o}ßen in beiden Modellen. Zun{\"a}chst untersuche ich den Einfluss des Alters und den Einfluss der Korrellationen einer QEL auf die Verteilung der Zeiten, die das diffundierendes Teilchen ben{\"o}tigt, um eine (r{\"a}umliche) Schwelle zu {\"u}berqueren. Ausserdem bestimme ich den Effekt des Alters auf Str{\"o}me von (sub)diffundierenden Partikeln, die sich auf eine absorbierende Barriere zubewegen. Zuletzt besch{\"a}ftige ich mich mit der Diffusion einer eindimensionalen Anordnung von Teilchen in einer QEL, in der diese als harte Kugeln miteinander wechselwirken. Dabei vergleiche ich die gemeinsame Bewegung in einer QEL und als individuelle CTRWs miteinander {\"u}ber die Standartabweichung von der Startposition, f{\"u}r die ich das Mittel {\"u}ber mehrere QELs untersuche. Meine Arbeit setzt sich zusammen aus theoretischen {\"U}berlegungen und Berechnungen sowie der Simulation der Zufallsprozesse. Die Ergebnisse der Simulation und, soweit vorhanden, experimentelle Daten werden mit der Theorie verglichen.},
  language  = {en}
}