In this article, we review our results on diffusion and phase separation in lipid membranes, as well as on interaction of membranes with colloidal particles, biomacromolecules, and supramolecular assemblies, which were obtained within the framework of the Saxon Research Unit FOR 877 “From Local Constraints to Macroscopic Transport”.

A central part of soft matter physics is the investigation of effects in an active environment. These systems are driven out of equilibrium by a constant energy consumption. In biological systems, for instance, energy is consumed in the dynamic polymerization process of cytoskeletal filaments or by motor-filament interactions. These active processes convert chemical energy into mechanical work and impede a trapping of cellular structures in thermodynamically frozen states. Thus, active soft matter is crucial for biological systems to fulfill a broad range of tasks. Inherent physical principles relying on entropy maximizing arguments, however, cannot be easily switched off even in active systems. Cells might even employ these principles to accomplish certain tasks without the need to arrange elaborate, energy dissipating structures. Within the presented studies we demonstrate possibilities how biological relevant forces can be generated in the absence of any active accessory proteins. The presented studies are based on the cytoskeletal key components actin and microtubules. We demonstrate different approaches ranging from light induced softening to cross-linker expansion, which realize entropy driven contractions of the according system.

Experiments are described on the electrophoretic mobility of a single isolated colloid and the electro-osmotic response of the surrounding medium. For that optical tweezers are employed which enable one to trap a particle without any mechanical contact and to measure its position and the forces acting on it with high resolution (±2 nm, ±200 fN). In a custom-made microfluidic cell, the two effects are separated using the identical colloid. The electrophoretic response is found to be ~ 5 times stronger than the electroosmotic effect. It is phase-shifted with respect to the external electric field, hence giving rise to a complex electrophoretic mobility which can be theoretically described by a strongly damped driven harmonic oscillator model. The measured electrophoretic mobility in monovalent salt is found to be in agreement with computations combining primitive model molecular dynamics simulations of the ionic double layer with the standard electrokinetic model. Mobility reversal of a single colloid is observed for trivalent ionic solutions (LaCl3) at ionic strengths > 10−2 mol/l. The latter is in quantitative agreement with a numerical model in which ion specific attractive forces are taken into consideration.

Using a combination of analytical theory and newly developed numerical algorithms, we analyze the most pertinent conformational characteristics of three paradigmatic types of polymers in disordered environments: (i) flexible polymers in quenched, self-similar disorder as represented by a self-avoiding random walk on a critical percolation cluster, (ii) semiflexible polymers in quenched, steric disorder as represented by an equilibrium hard-disk fluid and (iii) semiflexible polymers subject to the random energy landscape that emerges from a surrounding network of similar semiflexible polymers.

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