Analysis and Simulation of Hybrid Models for Reaction Networks

The dynamics of biochemical reaction networks can be described by a variety of models, like the Reaction Rate equation (RRE), the Chemical Master equation (CME) or the Fokker-Planck equation (FPE). In this thesis, the behaviour of these different models is analysed. It is shown that the FPE can be motivated as an approximation of the CME and convergence is proven. Furthermore, two hybrid models are constructed by combining different approaches and convergence properties are proven and discussed

Nuclear Charge Radius of 12^{12}Be

The nuclear charge radius of $^{12}$Be was precisely determined using the technique of collinear laser spectroscopy on the $2s_{1/2}\rightarrow 2p_{1/2, 3/2}$ transition in the Be$^{+}$ ion. The mean square charge radius increases from $^{10}$Be to $^{12}$Be by \delta ^{10,12} = 0.69(5) \fm^{2} compared to \delta ^{10,11} = 0.49(5) \fm^{2} for the one-neutron halo isotope $^{11}$Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of $^{12}$Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.Comment: 5 pages, 3 figure

Collinear laser spectroscopy of atomic cadmium

Hyperfine structure $A$ and $B$ factors of the atomic 5s\,5p\,\; ^3\rm{P}_2 \rightarrow 5s\,6s\,\; ^3\rm{S}_1 transition are determined from collinear laser spectroscopy data of $^{107-123}$Cd and $^{111m-123m}$Cd. Nuclear magnetic moments and electric quadrupole moments are extracted using reference dipole moments and calculated electric field gradients, respectively. The hyperfine structure anomaly for isotopes with $s_{1/2}$ and $d_{5/2}$ nuclear ground states and isomeric $h_{11/2}$ states is evaluated and a linear relationship is observed for all nuclear states except $s_{1/2}$. This corresponds to the Moskowitz-Lombardi rule that was established in the mercury region of the nuclear chart but in the case of cadmium the slope is distinctively smaller than for mercury. In total four atomic and ionic levels were analyzed and all of them exhibit a similar behaviour. The electric field gradient for the atomic 5s\,5p\,\; ^3\mathrm{P}_2 level is derived from multi-configuration Dirac-Hartree-Fock calculations in order to evaluate the spectroscopic nuclear quadrupole moments. The results are consistent with those obtained in an ionic transition and based on a similar calculation.Comment: 12 pages, 5 figure

Precision Test of Many-Body QED in the Be+^+ 2p2p Fine Structure Doublet Using Short-Lived Isotopes

Absolute transition frequencies of the 2s\; ^2{\rm S}_{1/2} \rightarrow 2p\;^2\mathrm{P}_{1/2,3/2} transitions in Be$^+$ were measured for the isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its isotope dependence are extracted and compared to results of \textit{ab initio} calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of $m \alpha^6$ and $m \alpha^7 \ln \alpha$. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.Comment: 5 pages, 2 figure

Error bound for piecewise deterministic processes modeling stochastic reaction systems

Biological processes involving the random interaction of d species with integer particle numbers are often modeled by a Markov jump process on N d 0. Realizations of this process can, in principle, be generated with the classical stochastic simulation algorithm proposed in [19], but for very reactive systems this method is usually inefficient. Hybrid models based on piecewise deterministic processes offer an attractive alternative which can decrease the simulation time considerably in applications where species with rather low particle numbers interact with very abundant species. We investigate the convergence of the hybrid model to the original one for a class of reaction systems with two distinct scales. Our main result is an error bound which states that, under suitable assumptions, the hybrid model approximates the marginal distribution of the discrete species and the conditional moments of the continuous species up to an error of O ` M −1 ´ where M is the scaling parameter of the partial thermodynamic limit

Chlorella virus ATCV-1 encodes a functional potassium channel of 82 amino acids

Chlorella virus PBCV-1 (Paramecium bursaria chlorella virus-1) encodes the smallest protein (94 amino acids, named Kcv) previously known to form a functional K+ channel in heterologous systems. In this paper, we characterize another chlorella virus encoded K+ channel protein (82 amino acids, named ATCV-1 Kcv) that forms a functional channel in Xenopus oocytes and rescues Saccharomyces cerevisiae mutants that lack endogenous K+ uptake systems. Compared with the larger PBCV-1 Kcv, ATCV-1 Kcv lacks a cytoplasmic N-terminus and has a reduced number of charged amino acids in its turret domain. Despite these deficiencies, ATCV-1 Kcv accomplishes all the major features of K+ channels: it assembles into a tetramer, is K+ selective and is inhibited by the canonical K+ channel blockers, barium and caesium. Single channel analyses reveal a stochastic gating behavior and a voltage-dependent conductance that resembles the macroscopic I/V relationship. One difference between PBCV-1 and ATCV-1 Kcv is that the latter is more permeable to K+ than Rb+. This difference is partially explained by the presence of a tyrosine residue in the selective filter of ATCV-1 Kcv, whereas PBCV-1 Kcv has a phenylalanine. Hence, ATCV-1 Kcv is the smallest protein to form a K+ channel and it will serve as a model for studying structure–function correlations inside the potassium channel pore

The proapoptotic influenza A virus protein PB1-F2 forms a nonselective ion channel.

The data support the idea that PB1-F2 is able to form protein channel pores with no appreciable selectivity in membranes and that the c-terminus is important for this function. This information could be important for drug development