Poly(2-oxazolines) in biological and biomedical application contexts.

Polyoxazolines of various architectures and chemical functionalities can be prepared in a living and therefore controlled manner via cationic ring-opening polymerisation. They have found widespread applications, ranging from coatings to pigment dispersants. Furthermore, several polyoxazolines are water-soluble or amphiphilic and relatively non-toxic, which makes them interesting as biomaterials. This paper reviews the development of polyoxazoline-based polymers in biological and biomedical application contexts since the beginning of the millennium. This includes nanoscalar systems such as membranes and nanoparticles, drug and gene delivery applications, as well as stimuli-responsive systems

Dynamics of Cell Shape and Forces on Micropatterned Substrates Predicted by a Cellular Potts Model

Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft elastic substrates. To predict the dynamics and steady states of cell shape and forces without any a priori knowledge of how the cell will spread on a given micropattern, here we extend earlier formulations of the two-dimensional cellular Potts model. The third dimension is treated as an area reservoir for spreading. To account for local contour reinforcement by peripheral bundles, we augment the cellular Potts model by elements of the tension-elasticity model. We first parameterize our model and show that it accounts for momentum conservation. We then demonstrate that it is in good agreement with experimental data for shape, spreading dynamics, and traction force patterns of cells on micropatterned substrates. We finally predict shapes and forces for micropatterns that have not yet been experimentally studied.Comment: Revtex, 32 pages, 11 PDF figures, to appear in Biophysical Journa

Effect of adhesion geometry and rigidity on cellular force distributions

The behaviour and fate of tissue cells is controlled by the rigidity and geometry of their adhesive environment, possibly through forces localized to sites of adhesion. We introduce a mechanical model that predicts cellular force distributions for cells adhering to adhesive patterns with different geometries and rigidities. For continuous adhesion along a closed contour, forces are predicted to be localized to the corners. For discrete sites of adhesion, the model predicts the forces to be mainly determined by the lateral pull of the cell contour. With increasing distance between two neighboring sites of adhesion, the adhesion force increases because cell shape results in steeper pulling directions. Softer substrates result in smaller forces. Our predictions agree well with experimental force patterns measured on pillar assays.Comment: 4 pages, Revtex with 4 figure

Unifying autocatalytic and zeroth order branching models for growing actin networks

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament number. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate, above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, this allows cells to grow stable actin networks over a large range of different conditions.Comment: revtex, 5 pages, 4 figure

Stability of freely falling granular streams

A freely falling stream of weakly cohesive granular particles is modeled and analysed with help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a function of cohesive energy. Extensional flow is an exact solution of the one-dimensional Navier-Stokes equation, corresponding to a strain rate, decaying like 1/t from its initial value, gammaDot0. Expanding around this basic state, we show that the flow is stable for short times (gammaDot0 * t << 1), whereas for long times (gammaDot0 * t >> 1) perturbations of all wavelength grow. The growthrate of a given wavelength depends on the instant of time when the fluctuation occurs, so that the observable patterns can vary considerably.Comment: 4 page, 5 figures. Submitted to PRL. Supplementary material: see http://wwwuser.gwdg.de/~sulrich/research/#Publication

Complete sets of cyclic mutually unbiased bases in even prime power dimensions

We present a construction method for complete sets of cyclic mutually unbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. In comparison to usual complete sets of MUBs, complete cyclic sets possess the additional property of being generated by a single unitary operator. The construction method is based on the idea of obtaining a partition of multi-qubit Pauli operators into maximal commuting sets of orthogonal operators with the help of a suitable element of the Clifford group. As a consequence, we explicitly obtain complete sets of cyclic MUBs generated by a single element of the Clifford group in dimensions $2^m$ for $m=1,2,...,24$.Comment: 10 page