TY - JOUR A1 - Safdari, Hadiseh A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Bodrova, Anna A1 - Metzler, Ralf T1 - Aging underdamped scaled Brownian motion BT - Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble-and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevE.95.012120 SN - 2470-0045 SN - 2470-0053 VL - 95 PB - American Physical Society CY - College Park ER - TY - GEN A1 - Metzler, Ralf T1 - Anomalous Diffusion in Membranes and the Cytoplasm of Biological Cells T2 - Biophysical journal Y1 - 2017 U6 - https://doi.org/10.1016/j.bpj.2016.11.2577 SN - 0006-3495 SN - 1542-0086 VL - 112 IS - 3 SP - 476A EP - 476A PB - Cell Press CY - Cambridge ER - TY - GEN A1 - Metzler, Ralf T1 - Gaussianity Fair BT - the Riddle of Anomalous yet Non-Gaussian Diffusion T2 - Biophysical journal Y1 - 2017 U6 - https://doi.org/10.1016/j.bpj.2016.12.019 SN - 0006-3495 SN - 1542-0086 VL - 112 IS - 3 SP - 413 EP - 415 PB - Cell Press CY - Cambridge ER - TY - JOUR A1 - Liu, Lin A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism. Y1 - 2017 U6 - https://doi.org/10.1021/acs.jpcb.6b12413 SN - 1520-6106 VL - 121 SP - 1284 EP - 1289 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Godec, Aljaž A1 - Metzler, Ralf T1 - First passage time statistics for two-channel diffusion JF - Journal of physics : A, Mathematical and theoretical N2 - 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. KW - first passage time KW - Markov additive processes KW - Fokker-Planck equation KW - random search processes KW - coupled initial boundary value problem KW - cellular signalling KW - asymptotic analysis Y1 - 2017 U6 - https://doi.org/10.1088/1751-8121/aa5204 SN - 1751-8113 SN - 1751-8121 VL - 50 IS - 8 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Norregaard, Kamilla A1 - Metzler, Ralf A1 - Ritter, Christine M. A1 - Berg-Sorensen, Kirstine A1 - Oddershede, Lene Broeng T1 - Manipulation and Motion of Organelles and Single Molecules in Living Cells JF - Chemical reviews N2 - The biomolecule is among the most important building blocks of biological systems, and a full understanding of its function forms the scaffold for describing the mechanisms of higher order structures as organelles and cells. Force is a fundamental regulatory mechanism of biomolecular interactions driving many cellular processes. The forces on a molecular scale are exactly in the range that can be manipulated and probed with single molecule force spectroscopy. The natural environment of a biomolecule is inside a living cell, hence, this is the most relevant environment for probing their function. In vivo studies are, however, challenged by the complexity of the cell. In this review, we start with presenting relevant theoretical tools for analyzing single molecule data obtained in intracellular environments followed by a description of state-of-the art visualization techniques. The most commonly used force spectroscopy techniques, namely optical tweezers, magnetic tweezers, and atomic force microscopy, are described in detail, and their strength and limitations related to in vivo experiments are discussed. Finally, recent exciting discoveries within the field of in vivo manipulation and dynamics of single molecule and organelles are reviewed. Y1 - 2017 U6 - https://doi.org/10.1021/acs.chemrev.6b00638 SN - 0009-2665 SN - 1520-6890 VL - 117 IS - 5 SP - 4342 EP - 4375 PB - American Chemical Society CY - Washington ER - TY - GEN A1 - Javanainen, Matti A1 - Martinez-Seara, Hector A1 - Metzler, Ralf A1 - Vattulainen, Ilpo Tapio T1 - Diffusion of Proteins and Lipids in Protein-Rich Membranesa T2 - Biophysical journal Y1 - 2018 U6 - https://doi.org/10.1016/j.bpj.2017.11.3009 SN - 0006-3495 SN - 1542-0086 VL - 114 IS - 3 SP - 551A EP - 551A PB - Cell Press CY - Cambridge ER - TY - GEN A1 - Gudowska-Nowak, Ewa A1 - Lindenberg, Katja A1 - Metzler, Ralf T1 - Preface: Marian Smoluchowski’s 1916 paper—a century of inspiration T2 - Journal of physics : A, Mathematical and theoretical Y1 - 2017 U6 - https://doi.org/10.1088/1751-8121/aa8529 SN - 1751-8113 SN - 1751-8121 VL - 50 IS - 38 PB - IOP Publ. Ltd. CY - Bristol 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 - Chechkin, Aleksei V. A1 - Seno, Flavio A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities JF - Physical review : X, Expanding access N2 - A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevX.7.021002 SN - 2160-3308 VL - 7 PB - American Physical Society CY - College Park ER -