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 - JOUR A1 - Herrmann, Carl J. J. A1 - Metzler, Ralf T1 - A self-avoiding walk with neural delays as a model of fixational eye movements JF - Scientific reports N2 - Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-13489-8 SN - 2045-2322 VL - 7 SP - 1 EP - 17 PB - Springer Nature CY - London ER - TY - JOUR A1 - Herrmann, Carl J. J. A1 - Metzler, Ralf A1 - Engbert, Ralf T1 - A self-avoiding walk with neural delays as a model of fixational eye movements JF - Scientific reports N2 - Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-13489-8 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Schwarzl, Maria A1 - Godec, Aljaz A1 - Oshanin, Gleb A1 - Metzler, Ralf T1 - A single predator charging a herd of prey: effects of self volume and predator-prey decision-making JF - Journal of physics : A, Mathematical and theoretical N2 - 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. KW - first passage process KW - diffusion KW - predator-prey model Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/22/225601 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Sereshki, L. E. A1 - Lomholt, M. A. A1 - Metzler, Ralf T1 - A solution to the subdiffusion-efficiency paradox inactive states enhance reaction efficiency at subdiffusion conditions in living cells JF - epl : a letters journal exploring the frontiers of physics N2 - Macromolecular crowding in living biological cells effects subdiffusion of larger biomolecules such as proteins and enzymes. Mimicking this subdiffusion in terms of random walks on a critical percolation cluster, we here present a case study of EcoRV restriction enzymes involved in vital cellular defence. We show that due to its so far elusive propensity to an inactive state the enzyme avoids non-specific binding and remains well-distributed in the bulk cytoplasm of the cell. Despite the reduced volume exploration capability of subdiffusion processes, this mechanism guarantees a high efficiency of the enzyme. By variation of the non-specific binding constant and the bond occupation probability on the percolation network, we demonstrate that reduced nonspecific binding are beneficial for efficient subdiffusive enzyme activity even in relatively small bacteria cells. Our results corroborate a more local picture of cellular regulation. Y1 - 2012 U6 - https://doi.org/10.1209/0295-5075/97/20008 SN - 0295-5075 VL - 97 IS - 2 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Guggenberger, Tobias A1 - Chechkin, Aleksei A1 - Metzler, Ralf T1 - Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials JF - New journal of physics : the open-access journal for physics N2 - We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials. KW - diffusion KW - Boltzmann distribution KW - fractional Brownian motion Y1 - 2022 U6 - https://doi.org/10.1088/1367-2630/ac7b3c SN - 1367-2630 VL - 24 IS - 7 PB - Dt. Physikalische Ges. CY - [Bad Honnef] ER - TY - JOUR A1 - Kar, Prathitha A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Acceleration of bursty multiprotein target search kinetics on DNA by colocalisation JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - Proteins are capable of locating specific targets on DNA by employing a facilitated diffusion process with intermittent 1D and 3D search steps. Gene colocalisation and coregulation-i.e. the spatial proximity of two communicating genes-is one factor capable of accelerating the target search process along the DNA. We perform Monte Carlo computer simulations and demonstrate the benefits of gene colocalisation for minimising the search time in a model DNA-protein system. We use a simple diffusion model to mimic the search for targets by proteins, produced initially in bursts of multiple proteins and performing the first-passage search on the DNA chain. The behaviour of the mean first-passage times to the target is studied as a function of distance between the initial position of proteins and the DNA target position, as well as versus the concentration of proteins. We also examine the properties of bursty target search kinetics for varying physical-chemical protein-DNA binding affinity. Our findings underline the relevance of colocalisation of production and binding sites for protein search inside biological cells. Y1 - 2017 U6 - https://doi.org/10.1039/c7cp06922g SN - 1463-9076 SN - 1463-9084 VL - 20 IS - 12 SP - 7931 EP - 7946 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Godec, Aljaz A1 - Metzler, Ralf T1 - Active transport improves the precision of linear long distance molecular signalling JF - Journal of physics : A, Mathematical and theoretical N2 - Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related to the noise correlation time. In addition to passive thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can transiently bind to molecular motors and are actively transported across biological cells. Active transport is most beneficial when trafficking occurs over large distances, for instance up to the order of 1 metre in neurons. Here we explain how intermittent active transport allows for faster equilibration upon a change in concentration triggered by biochemical stimuli. Moreover, we show how intermittent active excursions induce qualitative changes in the noise in effectively one-dimensional systems such as dendrites. Thereby they allow for significantly improved signalling precision in the sense of a smaller relative deviation in the concentration read-out by the receptor. On the basis of linear response theory we derive the exact mean field precision limit for counting actively transported molecules. We explain how intermittent active excursions disrupt the recurrence in the molecular motion, thereby facilitating improved signalling accuracy. Our results provide a deeper understanding of how recurrence affects molecular signalling precision in biological cells and novel medical-diagnostic devices. KW - noise in biochemical signalling KW - Brownian motion KW - active transport KW - linear response theory KW - fluctuation-dissipation theorem KW - generalised Langevin equation KW - recurrence Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/36/364001 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Ageing and confinement in non-ergodic heterogeneous diffusion processes JF - Journal of physics : A, Mathematical and theoretical N2 - We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement. KW - stochastic processes KW - anomalous diffusion KW - ageing KW - weak ergodicity breaking Y1 - 2014 U6 - https://doi.org/10.1088/1751-8113/47/48/485002 SN - 1751-8113 SN - 1751-8121 VL - 47 IS - 48 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Chechkin, Aleksei V. A1 - Kantz, Holger A1 - Metzler, Ralf T1 - Ageing effects in ultraslow continuous time random walks JF - The European physical journal : B, Condensed matter and complex systems N2 - In ageing systems physical observables explicitly depend on the time span elapsing between the original initiation of the system and the actual start of the recording of the particle motion. We here study the signatures of ageing in the framework of ultraslow continuous time random walk processes with super-heavy tailed waiting time densities. We derive the density for the forward or recurrent waiting time of the motion as function of the ageing time, generalise the Montroll-Weiss equation for this process, and analyse the ageing behaviour of the ensemble and time averaged mean squared displacements. Y1 - 2017 U6 - https://doi.org/10.1140/epjb/e2017-80270-9 SN - 1434-6028 SN - 1434-6036 VL - 90 PB - Springer CY - New York ER -