Reinhard Grebe

Erythrocyte Shape is Influenced by Free Electric and Chemical Energy

The erythrocyte membrane is built up of the phospholipid-cholesterol bilayer, sandwiched by charge carrying proteins, the glycocalix, coupled to the bilayer via the hydrophobic coil of glycophorin A, and the bulk of the extrinsic proteins, coupled via Ankyrin and Band 3. Both the extrinsic proteins and some of the phospholipids of the interior face of the membrane are also carrying charges.

Change of Local Charge Density by Change of Local Mean Curvature in Biological Bilayer Membranes

Abstract Highly positive curved parts of biological membranes show an increase in density of charge carrying molecules, while parts with less positive or negative mean curvature show a diminution. This has been shown by different investigators by marking the charge carrying molecules and examining the membranes by electron microscopy. We here give an explanation for this finding based on electrostatics field theory. Assuming free lateral mobility of charge carrying molecules the membrane forms an equipotential surface. Under this premise the socalled charge simulation method can be used for building up computer models for the electrostatic properties of different shaped membranes. These models show the same behaviour for the charge density distribution as has been observed in the distribution of charge carrying molecules in membranes. So simple electrostatic repulsion forces may also in biological membranes be the reason for local mean curvature related changes in charge carrying molecules distribution.

Numerical calculation of electric fields surrounding biological cells in three dimensions

Abstract High-frequency homogeneous and inhomogeneous electric fields can be used to apply forces on biological cells and to keep and manipulate them in well defined positions. This paper presents our software package, which was designed to optimize 3D field traps and to calculate force distributions on RBCs (red blood cells).

Closed Fluid Quadrilamina Model of the Erythrocyte Membrane

Flow properties of whole blood highly depend on erythrocyte mechanical characteristics. To describe these static and dynamic properties, erythrocyte configurations are simulated using a numerical optimization method based on importance sampling and the principle of adiabatic cooling. The erythrocyte membrane is regarded as formed by a closed fluid quadrilamina. The energy function of the fluid laminae includes (i) curvature-elastic energy terms, (ii) the compression elasticity of the quadrilaminate, and (iii) the volume elasticity related to the osmotic pressure across the membrane.

Simulation von Membranformen ohne implizite Symmetrie

Die ausere Form lebender Zellen wird wesentlich durch die physikalischen Eigenschaften ihrer umgebenden Hulle, der Zellmembran bestimmt. Dies gilt in ganz besonderem Mase fur das rote Blutkorperchen, den Erythrozyten, der sich wegen seines einfachen Aufbaus (ein mit einer Hamoglobinsuspension gefullter Membransack) und der allgegenwartigen Verfugbarkeit besonders als Modellkorper fur Experimente und theoretische Betrachtungen eignet. Die herausragende Eigenschaft des Erythrozyten ist seine leichte Verformbarkeit bei groser Formstabilitat. Er wird durch die Scherkrafte im Kreislauf bis auf das Doppelte seines ursprunglichen Durchmessers auseinandergezogen und nimmt nach Entlastung sofort wieder seine ursprungliche scheibchenformige (diskoide) Ruheform an. Nicht zuletzt diese Kombination von Eigenschaften bedingt das grose Interesse, das dem roten Blutkorperchen auch von Seiten der Biophysik entgegengebracht wird.

Numerical Simulations of Vesicular and Red Blood Cell Shapes in Three Dimensions

We present the results of 3d-computer simulations of red blood cell and vesicular morphologies using optimization methods based on simulated annealing. Two membrane models were used in the simulations, the bilayer couple model and our own closed fluid lamina model. The free energy functionals corresponding to these models include contributions from compressive elasticities, both volume and surface, and curvature elasticity. No pronounced differences have so far been found in the simulation results for these models. In the stomatocytic and discocytic domain 3d-simulations show similar axially symmetric shapes as those found in our earlier 2d-simulations.

Erythrocyte Shape Simulation by Optimization of a Closed Fluid Lamina

Abstract In our earlier work the morphology of red blood cells (RBC) was examined in terms of the mean mean curvature (MMC) of their cell membranes. A simulation of the different geometries of these shapes showed that the MMC increases from the sphero-stomatocyte to the sphero-echinocyte via the discocyte. We extend this work by using a free energy function based on curvature elasticity, curvature homogeneity and volume and area constraints in conjunction with two different simulation methods: a gradient relaxation method and a Metropolis Monte Carlo method based on importance sampling. The problem with conventional methods of simulation is that they lead to the trapping of the cell shape in a local minimum. Rather than processing the new shape after calculating each point on the surface, the new shape is only processed once every point on the old surface has been calculated. The RBC membrane is treated in the simulations as a single fluid lamina exhibiting viscoelastic characteristics. In the simulations...

Ein parallelisierter Algorithmus zum Simulated-Annealing

Die Erzeugung von Modellen physikalischer Systeme ist eine der Aufgaben, die besonders hohe Anforderungen an die eingesetzten Rechner hinsichtlich Rechengeschwindigkeit und Speicherbedarf stellt. Gerade fur diese Art von Aufgaben bietet sich der Einsatz von Transputersystemen an. Mit ihnen last sich beliebig komplexe Software auf einer Minimalkonfiguration entwickeln und austesten und dann auf einem System zum Einsatz bringen, das hinsichtlich der Leistungsfahigkeit genau an die Aufgabengrose und die gestellten Anforderungen angepast ist. Ein entsprechendes Transputersystem wird am Institut fur Physiologie zur Bild Verarbeitung und fur Simulationsaufgaben eingesetzt.