@article{PulkkinenMetzler2015,
  author    = {Pulkkinen, Otto and Metzler, Ralf},
  title     = {Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation},
  series = {Scientific reports},
  journal   = {Scientific reports},
  number    = {5},
  publisher = {Nature Publishing Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep17820},
  year      = {2015},
  abstract  = {Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.},
  language  = {en}
}
@article{MetzlerCherstvyChechkinetal.2015,
  author    = {Metzler, Ralf and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Bodrova, Anna S.},
  title     = {Ultraslow scaled Brownian motion},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {17},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {063038},
  publisher = {Dt. Physikalische Ges., IOP},
  address   = {Bad Honnef, London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/17/6/063038},
  year      = {2015},
  abstract  = {We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.},
  language  = {en}
}
@article{MetzlerBauerRasmussenetal.2015,
  author    = {Metzler, Ralf and Bauer, Maximilian and Rasmussen, Emil S. and Lomholt, Michael A.},
  title     = {Real sequence effects on the search dynamics of transcription factors on DNA},
  series = {Scientific Reports},
  volume    = {5},
  journal   = {Scientific Reports},
  number    = {10072},
  publisher = {Nature Publishing Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep10072},
  year      = {2015},
  abstract  = {Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.},
  language  = {en}
}