Biomedical subjects
Publications and source records attributed to Markus Bär.
The nucleation of spiral waves at a surface defect during catalytic CO oxidation on Pt(110) has been studied with a low energy electron microscope system. It is found that reaction fronts originate from a boundary layer between the defect and the surrounding Pt(110) area. The findings are corroborated by numerical simulations within a realistic reaction-diffusion model of the surface reaction.
We study two mechanisms for the formation of protein patterns near membranes of living cells by mathematical modelling. Self-assembly of protein domains by electrostatic lipid-protein interactions is contrasted with self-organization due to a nonequilibrium biochemical reaction cycle of proteins near the membrane. While both processes lead eventually to quite similar patterns, their evolution occurs on very different length and time scales. Self-assembly produces periodic protein patterns on a spatial scale below 0.1 microm in a few seconds followed by extremely slow coarsening, whereas self-organization results in a pattern wavelength comparable to the typical cell size of 100 microm within a few minutes suggesting different biological functions for the two processes.
Cell membranes are composed of a mixture of lipids. Many biological processes require the formation of spatial domains in the lipid distribution of the plasma membrane. We have developed a mathematical model that describes the dynamic spatial distribution of acidic lipids in response to the presence of GMC proteins and regulating enzymes. The model encompasses diffusion of lipids and GMC proteins, electrostatic attraction between acidic lipids and GMC proteins as well as the kinetics of membrane attachment/detachment of GMC proteins. If the lipid-protein interaction is strong enough, phase separation occurs in the membrane as a result of free energy minimization and protein/lipid domains are formed. The picture is changed if a constant activity of enzymes is included into the model. We chose the myristoyl-electrostatic switch as a regulatory module. It consists of a protein kinase C that phosphorylates and removes the GMC proteins from the membrane and a phosphatase that dephosphorylates the proteins and enables them to rebind to the membrane. For sufficiently high enzymatic activity, the phase separation is replaced by travelling domains of acidic lipids and proteins. The latter active process is typical for nonequilibrium systems. It allows for a faster restructuring and polarization of the membrane since it acts on a larger length scale than the passive phase separation. The travelling domains can be pinned by spatial gradients in the activity; thus the membrane is able to detect spatial clues and can adapt its polarity dynamically to changes in the environment.
We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets--reaction-limited and saturated regime--are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.
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Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Recent experimental and model studies have revealed that the domain size may strongly influence the dynamics of rotating spirals in two-dimensional pattern forming chemical reactions. Hartmann et al. [Phys. Rev. Lett. 76, 1384 (1996)], report a frequency increase of spirals in circular domains with diameters substantially smaller than the spiral wavelength in a large domain for the catalytic NO+CO reaction on a microstructured platinum surface. Accompanying simulations with a simple reaction-diffusion system reproduced the behavior. Here, we supplement these studies by a numerical bifurcation and stability analysis of rotating spirals in a simple activator-inhibitor model. The problem is solved in a co-rotating frame of reference. No-flux conditions are imposed at the boundary of the circular domain. At large domain sizes, eigenvalues and eigenvectors very close to those corresponding to infinite medium translational invariance are observed. Upon decrease of domain size, we observe a simultaneous change in the rotation frequency and a deviation of these eigenvalues from being neutrally stable (zero real part). The latter phenomenon indicates that the translation symmetry of the spiral solution is appreciably broken due to the interaction with the (now nearby) wall. Various dynamical regimes are found: first, the spiral simply tries to avoid the boundary and its tip moves towards the center of the circular domain corresponding to a negative real part of the "translational" eigenvalues. This effect is noticeable at a domain radius of R<R(cr,1). The spiral subsequently exhibits an oscillatory instability: the tip trajectory displays a meandering motion, which may be characterized as boundary-induced spiral meandering. A systematic study of the spiral rotation as a function of a control parameter and the domain size reveals that the meandering instability in large domains becomes suppressed, and the spiral rotation becomes rigid, at a critical radius R(cr,0). Boundary-induced meandering arises below a second critical radius R(cr,2)<R(cr,0).
Experiments with myxobacterial aggregates reveal standing waves called rippling patterns. Here these structures are modeled with a simple discrete model based on the interplay between migration and collisions of cells. Head-to-head collisions of cells result in cell reversals. To correctly reproduce the rippling patterns, a refractory phase after each cell reversal has to be assumed, during which further reversal is prohibited. The duration of this phase determines the wavelength and period of the ripple patterns as well as the reversal frequency of single cells.
We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable periodic stripe pattern, i.e., pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than that of the critical dewetting mode, weak heterogeneities are sufficient for pinning. Our results imply a large region of coexistence between coarsening dynamics and pinning.
Drifting pattern domains (DPDs), i.e., moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this model, a region of bistability between Turing patterns and traveling waves arises from a codimension-2 Turing-wave bifurcation (TWB). DPDs are found within that region in a substantial distance from the TWB. We investigated the dynamics of single interfaces between Turing and wave patterns. It is found that DPDs exist due to a locking of the interface velocities, which is imposed by the absence of space-time defects near these interfaces.