## Institut für Physik und Astronomie

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#### Keywords

- ageing (1)
- anomalous diffusion (1)
- biological physics (1)
- critical avalanche dynamics (1)
- gene regulatory networks (1)
- memory and delay (1)
- neuronal networks (1)
- stochastic models (1)
- stochastic processes (1)

The plasmon resonance of metal nanoparticles determines their optical response in the visible spectral range. Many details such as the electronic properties of gold near the particle surface and the local environment of the particles influence the spectra. We show how the cheap but highly precise fabrication of composite nanolayers by spin-assisted layer-by-layer deposition of polyelectrolytes can be used to investigate the spectral response of gold nanospheres (GNS) and gold nanorods (GNR) in a self-consistent way, using the established Maxwell–Garnett effective medium (MGEM) theory beyond the limit of homogeneous media. We show that the dielectric function of gold nanoparticles differs from the bulk value and experimentally characterize the shape and the surrounding of the particles thoroughly by SEM, AFM and ellipsometry. Averaging the dielectric functions of the layered surrounding by an appropriate weighting with the electric field intensity yields excellent agreement for the spectra of several nanoparticles and nanorods with various cover-layer thicknesses.

We have investigated the electrochemical, spectroscopic and electroluminescent properties of a family of aza-aromatic complexes of ruthenium of type [RuII(bpy/phen)2(L)]2+ (4d6) with three isomeric L ligands, where, bpy = 2,2′-bipyridine, phen = 1,10-phenanthroline and the L ligands are 3-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L1), 3-(2-pyridyl[1,2,3])triazolo[1,5-a]pyridine (L2) and 2-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L3). The complexes display two bands in the visible region near 410–420 and 440–450 nm. The complexes are diamagnetic and show well defined 1H NMR lines. They are electroactive in acetonitrile solution and exhibit a well defined RuII/RuIII couple near 1.20 to 1.30 V and −1.40 to −1.50 V due to ligand reduction versus Saturated Calomel Electrode (SCE). The solutions are also luminescent, with peaks are near 600 nm. All the complexes are electroluminescent in nature with peaks lying near 580 nm. L1 and L3 ligated complexes with two bpy co-ligands show weak photoluminescence (PL) but stronger electroluminescence (EL) compared to corresponding L2 ligated analogues.

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.

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.

Stochastic Wilson
(2015)

We consider a simple Markovian class of the stochastic Wilson–Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around −1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.

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.