Protein mobility affects most cellular processes, such as the rates of enzymatic reactions, signal transduction, and assembly of macromolecular complexes. Despite such importance, little systematic information is available about protein diffusion inside bacterial cells. Here we combined fluorescence recovery after photobleaching with numerical modeling to analyze mobility of a set of fluorescent protein fusions in the bacterial cytoplasm, the plasma membrane, and in the nucleoid. Estimated diffusion coefficients of cytoplasmic and membrane proteins show steep dependence on the size and on the number of transmembrane helices, respectively. Protein diffusion in both compartments is thus apparently obstructed by a network of obstacles, creating the so-called molecular sieving effect. These obstructing networks themselves, however, appear to be dynamic and allow a slow and nearly size-independent movement of large proteins and complexes. The obtained dependencies of protein mobility on the molecular mass and the number of transmembrane helices can be used as a reference to predict diffusion rates of proteins in Escherichia coli. Mobility of DNA-binding proteins apparently mainly depends on their binding specificity, with FRAP recovery kinetics being slower for the highly specific TetR repressor than for the relatively nonspecific H-NS regulator.

Abstract. An adaptive finite element method is analyzed for approximating functionals of the solution of symmetric elliptic second order boundary value problems. We show that the method converges and derive a favorable upper bound for its convergence rate and computational complexity. We illustrate our theoretical findings with numerical results. The aforementioned works all deal with AFEMs in which the error is measured in the energy norm · E := a(·, ·)

In order to determine the molecular origin of the difference in electron and hole mobilities of amorphous thin films of Alq(3) (meridional Alq(3) (tris(8-hydroxyquinoline) aluminium)) we performed multiscale simulations covering quantum mechanics, molecular mechanics and lattice models. The study includes realistic disordered morphologies, polarized site energies to describe diagonal disorder, quantum chemically calculated transfer integrals for the off-diagonal disorder, inner sphere reorganization energies and an approximative scheme for outer sphere reorganization energies. Intermolecular transfer rates were calculated via Marcus-theory and mobilities were simulated via kinetic Monte Carlo simulations and by a Master Equation approach. The difference in electron and hole mobility originates from the different localization of charge density in the radical anion (more delocalized) compared to the radical cation (more confined). This results in higher diagonal disorder for holes and less favourable overlap properties for the hole transfer integrals leading to an overall higher electron mobility.

Lévy walks as a random search strategy have recently attracted a lot of attention, and have been described in many animal species. However, very little is known about one of the most important issues, namely how Lévy walks are generated by biological organisms. We study a model of the chemotaxis signaling pathway of E. coli, and demonstrate that stochastic fluctuations and the specific design of the signaling pathway in concert enable the generation of Lévy walks. We show that Lévy walks result from the superposition of an ensemble of exponential distributions, which occurs due to the shifts in the internal enzyme concentrations following the stochastic fluctuations. With our approach we derive the power-law analytically from a model of the chemotaxis signaling pathway, and obtain a power-law exponent , which coincides with experimental results. This work provides a means to confirm Lévy walks as natural phenomenon by providing understanding on the process through which they emerge. Furthermore, our results give novel insights into the design aspects of biological systems that are capable of translating additive noise on the microscopic scale into beneficial macroscopic behavior.