@article{JeonMetzler2012,
  author    = {Jeon, Jae-Hyung and Metzler, Ralf},
  title     = {Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {85},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.85.021147},
  pages     = {8},
  year      = {2012},
  abstract  = {Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.},
  language  = {en}
}
@article{AdamcikJeonKarczewskietal.2012,
  author    = {Adamcik, Jozef and Jeon, Jae-Hyung and Karczewski, Konrad J. and Metzler, Ralf and Dietler, Giovanni},
  title     = {Quantifying supercoiling-induced denaturation bubbles in DNA},
  series = {Soft matter},
  volume    = {8},
  journal   = {Soft matter},
  number    = {33},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1744-683X},
  doi       = {10.1039/c2sm26089a},
  pages     = {8651 -- 8658},
  year      = {2012},
  abstract  = {In both eukaryotic and prokaryotic DNA sequences of 30-100 base-pairs rich in AT base-pairs have been identified at which the double helix preferentially unwinds. Such DNA unwinding elements are commonly associated with origins for DNA replication and transcription, and with chromosomal matrix attachment regions. Here we present a quantitative study of local DNA unwinding based on extensive single DNA plasmid imaging. We demonstrate that long-lived single-stranded denaturation bubbles exist in negatively supercoiled DNA, at the expense of partial twist release. Remarkably, we observe a linear relation between the degree of supercoiling and the bubble size, in excellent agreement with statistical modelling. Furthermore, we obtain the full distribution of bubble sizes and the opening probabilities at varying salt and temperature conditions. The results presented herein underline the important role of denaturation bubbles in negatively supercoiled DNA for biological processes such as transcription and replication initiation in vivo.},
  language  = {en}
}
@article{JeonMonneJavanainenetal.2012,
  author    = {Jeon, Jae-Hyung and Monne, Hector Martinez-Seara and Javanainen, Matti and Metzler, Ralf},
  title     = {Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins},
  series = {Physical review letters},
  volume    = {109},
  journal   = {Physical review letters},
  number    = {18},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.109.188103},
  pages     = {5},
  year      = {2012},
  abstract  = {Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.},
  language  = {en}
}
@article{MetzlerJeon2012,
  author    = {Metzler, Ralf and Jeon, Jae-Hyung},
  title     = {The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories},
  series = {Physica scripta : an international journal for experimental and theoretical physics},
  volume    = {86},
  journal   = {Physica scripta : an international journal for experimental and theoretical physics},
  number    = {5},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0031-8949},
  doi       = {10.1088/0031-8949/86/05/058510},
  pages     = {5},
  year      = {2012},
  abstract  = {Single-particle experiments produce time series x(t) of individual particle trajectories, frequently revealing anomalous diffusion behaviour. Typically, individual x(t) are evaluated in terms of time-averaged quantities instead of ensemble averages. Here we discuss the behaviour of the time-averaged mean squared displacement of different stochastic processes giving rise to anomalous diffusion. In particular, we pay attention to the ergodic properties of these processes, i.e. the (non)equivalence of time and ensemble averages.},
  language  = {en}
}