@article{JavanainenMartinezSearaMetzleretal.2017,
  author    = {Javanainen, Matti and Martinez-Seara, Hector and Metzler, Ralf and Vattulainen, Ilpo},
  title     = {Diffusion of Integral Membrane Proteins in Protein-Rich Membranes},
  series = {The journal of physical chemistry letters},
  volume    = {8},
  journal   = {The journal of physical chemistry letters},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1948-7185},
  doi       = {10.1021/acs.jpclett.7b01758},
  pages     = {4308 -- 4313},
  year      = {2017},
  abstract  = {The lateral diffusion of embedded proteins along lipid membranes in protein-poor conditions has been successfully described in terms of the Saffman-Delbruck (SD) model, which predicts that the protein diffusion coefficient D is weakly dependent on its radius R as D proportional to ln(1/R). However, instead of being protein-poor, native cell membranes are extremely crowded with proteins. On the basis of extensive molecular simulations, we here demonstrate that protein crowding of the membrane at physiological levels leads to deviations from the SD relation and to the emergence of a stronger Stokes-like dependence D proportional to 1/R. We propose that this 1/R law mainly arises due to geometrical factors: smaller proteins are able to avoid confinement effects much better than their larger counterparts. The results highlight that the lateral dynamics in the crowded setting found in native membranes is radically different from protein-poor conditions and plays a significant role in formation of functional multiprotein complexes.},
  language  = {en}
}
@article{PalyulinMantsevichKlagesetal.2017,
  author    = {Palyulin, Vladimir V. and Mantsevich, Vladimir N. and Klages, Rainer and Metzler, Ralf and Chechkin, Aleksei V.},
  title     = {Comparison of pure and combined search strategies for single and multiple targets},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {90},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2017-80372-4},
  pages     = {20 -- 37},
  year      = {2017},
  abstract  = {We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Levy searcher.},
  language  = {en}
}
@article{CaetanodeCarvalhoMetzleretal.2017,
  author    = {Caetano, Daniel L. Z. and de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.},
  title     = {Critical adsorption of periodic and random polyampholytes onto charged surfaces},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {19},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c7cp04040g},
  pages     = {23397 -- 23413},
  year      = {2017},
  abstract  = {How different are the properties of critical adsorption of polyampholytes and polyelectrolytes onto charged surfaces? How important are the details of polyampholyte charge distribution on the onset of critical adsorption transition? What are the scaling relations governing the dependence of critical surface charge density on salt concentration in the surrounding solution? Here, we employ Metropolis Monte Carlo simulations and uncover the scaling relations for critical adsorption for quenched periodic and random charge distributions along the polyampholyte chains. We also evaluate and discuss the dependence of the adsorbed layer width on solution salinity and details of the charge distribution. We contrast our findings to the known results for polyelectrolyte adsorption onto oppositely charged surfaces, in particular, their dependence on electrolyte concentration.},
  language  = {en}
}
@article{LiuCherstvyMetzler2017,
  author    = {Liu, Lin and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion},
  series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  volume    = {121},
  journal   = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1520-6106},
  doi       = {10.1021/acs.jpcb.6b12413},
  pages     = {1284 -- 1289},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@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{HerrmannMetzler2017,
  author    = {Herrmann, Carl J. J. and Metzler, Ralf},
  title     = {A self-avoiding walk with neural delays as a model of fixational eye movements},
  series = {Scientific reports},
  volume    = {7},
  journal   = {Scientific reports},
  publisher = {Springer Nature},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/s41598-017-13489-8},
  pages     = {1 -- 17},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{CherstvyVinodAghionetal.2017,
  author    = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averaging, ageing and delay analysis of financial time series},
  series = {New journal of physics},
  volume    = {19},
  journal   = {New journal of physics},
  publisher = {IOP},
  address   = {London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aa7199},
  pages     = {1 -- 11},
  year      = {2017},
  abstract  = {We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.},
  language  = {en}
}
@article{SchwarzlGodecMetzler2017,
  author    = {Schwarzl, Maria and Godec, Aljaž and Metzler, Ralf},
  title     = {Quantifying non-ergodicity of anomalous diffusion with higher order moments},
  series = {Scientific reports},
  volume    = {7},
  journal   = {Scientific reports},
  publisher = {Macmillan Publishers Limited},
  address   = {London},
  doi       = {10.1038/s41598-017-03712-x},
  pages     = {18},
  year      = {2017},
  abstract  = {Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.},
  language  = {en}
}
@article{ChechkinKantzMetzler2017,
  author    = {Chechkin, Aleksei V. and Kantz, Holger and Metzler, Ralf},
  title     = {Ageing effects in ultraslow continuous time random walks},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {90},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2017-80270-9},
  pages     = {12},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{SchwarzlGodecMetzler2017,
  author    = {Schwarzl, Maria and Godec, Aljaz and Metzler, Ralf},
  title     = {Quantifying non-ergodicity of anomalous diffusion with higher order moments},
  series = {Scientific reports},
  volume    = {7},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/s41598-017-03712-x},
  pages     = {18},
  year      = {2017},
  abstract  = {Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.},
  language  = {en}
}