Microswimmers – From Single Particle Motion to Collective Behavior

Locomotion of autonomous microswimmers is a fascinating field at the cutting edge of science. It combines the biophysics of self-propulsion via motor proteins, artificial propulsion mechanisms, swimming strategies at low Reynolds numbers, the hydrodynamic interaction of swimmers, and the collective motion and synchronisation of large numbers of agents. The articles of this Special Issue are based on the lecture notes of an international summer school, which was organized by the DFG Priority Programme 1726 “Microswimmers – From Single Particle Motion to Collective Behaviour” in the fall of 2015. The minireviews provide a broad overview of the field, covering both elementary and advanced material, as well as selected areas from current research.     

Colloids as model systems for problems in statistical physics

Owing to their mesoscopic length scales, colloidal suspensions provide ideal model systems suitable for addressing many problems in the field of statistical physics. Exemplarily, we highlight the versatile nature of such systems by discussing experiments with stochastic resonance and a practical realization of a recently proposed ratchet cellular automaton.     

Direct measurement of entropic forces induced by rigid rods

We present the first direct depletion potential measurements for a single colloidal sphere close to a wall in a suspension of rigid colloidal rods. Since all particle interactions are as good as hard-core-like, the depletion potentials are of entirely entropic origin. We developed a density functional theory approach that accurately accounts for this experimental situation. The depletion potentials calculated for different rod number densities are in very good quantitative agreement with the experimental results.     

Rationalizing the membrane interactions of cationic amphipathic antimicrobial peptides by their molecular shape

Biophysical and structural studies of cationic amphipathic antimicrobial peptides have revealed new mechanistic details concerning their membrane interactions. In interfacial environments the peptides adopt amphipathic conformations and the resulting distribution of polar, charged and hydrophobic residues allows them to partition into the bilayer interface. For several helical peptides it was found that their long axis is oriented parallel to the membrane surface, an arrangement which results in considerable perturbations in the packing of the lipid bilayer. Within the molecular shape concept the peptides act as wedge-like structures which impose positive curvature strain on the membrane. As a consequence a wide variety of morphologies are observed of peptide–lipid mixtures which strongly depend on the detailed peptide sequence, the membrane lipid composition, buffer, temperature and other environmental parameters. Therefore, the peptide–lipid systems are best described by phase diagrams, similar to the ones of detergent–lipid mixtures, encompassing on the one extreme regions where the peptide stabilizes the bilayer and on the other extreme regions where membrane lysis occurs. The effects of peptide sequence, membrane penetration depth, lipid composition and membrane surface charge density on membrane-association, -morphology and the resulting phase boundaries are discussed.     

Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential

We study the motion of an overdamped colloidal particle in a time-dependent nonharmonic potential. We demonstrate the first lawlike balance between applied work, exchanged heat, and internal energy on the level of a single trajectory. The observed distribution of applied work is distinctly non-Gaussian in good agreement with numerical calculations. Both the Jarzynski relation and a detailed fluctuation theorem are verified with good accuracy.     

Phase behavior of two-dimensional colloidal systems in the presence of periodic light fields

We investigate the phase behavior of a two-dimensional suspension of charge stabilized polystyrene spheres in the presence of a one-dimensional periodic light field. With increasing light intensity we observe a liquid-solid followed by a solid-liquid transition which are known as laser-induced freezing and melting, respectively. Here we report on measurements where, in addition to the light intensity, the single particle density was also systematically varied. As a result, we obtain for the first time the full thermodynamic information about the system which allows comparison with numerical predictions of other authors.     

Locked-floating-solid to locked-smectic transition in colloidal systems

We investigate two-dimensional melting of a colloidal system in the presence of a one-dimensional periodic substrate potential created by two interfering laser beams. We study the commensurability ratio p=sqrt[3]a/2d=2 with a the mean particle distance and d the period of the periodic potential. In contrast with the previously investigated case p=1, here we observe that melting of the locked-floating solid occurs via a novel locked-smectic phase, predicted by recent theoretical studies.     

Einstein relation generalized to nonequilibrium

The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical generalization of the Einstein relation to the nonequilibrium regime which involves an integral over measurable velocity correlation functions.     

A Cell‐Penetrating Foldamer with a Bioreducible Linkage for Intracellular Delivery of DNA

Despite significant advances in foldamer chemistry, tailored delivery systems based on foldamer architectures, which provide a high level of control over secondary structure, are curiously rare among non‐viral technologies for transporting nucleic acids into cells. A potent pH‐responsive, bioreducible cell‐penetrating foldamer (CPF) was developed through covalent dimerization of a short (8‐mer) amphipathic oligourea sequence bearing histidine‐type units. This CPF exhibits a high capacity to assemble with pDNA and mediates efficient delivery of nucleic acids into the cell. Furthermore, it does not adversely affect cellular viability and was shown to compare favorably with a cognate peptide transfection agent based on His‐rich sequences.     

Investigations of polypeptide rotational diffusion in aligned membranes by 2H and 15N solid-state NMR spectroscopy

Transmembrane and in-plane oriented peptides have been prepared by solid-phase peptide synthesis, labeled with 3,3,3-2H3-alanine and 15N-leucine at two selected sites, and reconstituted into oriented phophatidylcholine membranes. Thereafter, proton-decoupled 15N and 2H solid-state NMR spectroscopy at sample orientations of the membrane normal parallel to the magnetic field direction have been used to characterize the tilt and rotational pitch angle of these peptides in some detail. In a second step the samples have been tilted by 90 degrees . In this setup the spectral line shapes are sensitive indicators of the rate of rotational diffusion. Whereas monomeric transmembrane peptides exhibit spectral averaging and well-defined resonances, larger complexes are characterized by broad spectral line shapes. In particular the deuterium line shape is sensitive to association of a few transmembrane helices. In contrast, the formation of much larger complexes affects the 15N chemical shift spectrum. The spectra indicate that in liquid crystalline membranes an amphipathic peptide of 14 amino acids exhibits fast rotational diffusion on both the 2H and 15N time scales (>10(-5) s). Extending the sequences to 26 amino acids results in pronounced changes of the 2H solid-state NMR spectrum, whereas the signal intensities of 15N solid-state NMR spectra degrade. Below the phase transition temperature of the phospholipid bilayers, motional averaging on the time scale of the 2H solid-state NMR spectrum ceases for transmembrane and in-plane oriented peptides. Furthermore at temperatures close to the phase transition the total signal intensities of the deuterium solid-state NMR spectra strongly decrease.