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.     

Cross-approximate entropy of cortical local field potentials quantifies effects of anesthesia - a pilot study in rats

Background

Anesthetics dose-dependently shift electroencephalographic (EEG) activity towards high-amplitude, slow rhythms, indicative of a synchronization of neuronal activity in thalamocortical networks. Additionally, they uncouple brain areas in higher (gamma) frequency ranges possibly underlying conscious perception. It is currently thought that both effects may impair brain function by impeding proper information exchange between cortical areas. But what happens at the local network level? Local networks with strong excitatory interconnections may be more resilient towards global changes in brain rhythms, but depend heavily on locally projecting, inhibitory interneurons. As anesthetics bias cortical networks towards inhibition, we hypothesized that they may cause excessive synchrony and compromise information processing already on a small spatial scale. Using a recently introduced measure of signal independence, cross-approximate entropy (XApEn), we investigated to what degree anesthetics synchronized local cortical network activity. We recorded local field potentials (LFP) from the somatosensory cortex of three rats chronically implanted with multielectrode arrays and compared activity patterns under control (awake state) with those at increasing concentrations of isoflurane, enflurane and halothane.

Results

Cortical LFP signals were more synchronous, as expressed by XApEn, in the presence of anesthetics. Specifically, XApEn was a monotonously declining function of anesthetic concentration. Isoflurane and enflurane were indistinguishable; at a concentration of 1 MAC (the minimum alveolar concentration required to suppress movement in response to noxious stimuli in 50% of subjects) both volatile agents reduced XApEn by about 70%, whereas halothane was less potent (50% reduction).

Conclusions

The results suggest that anesthetics strongly diminish the independence of operation of local cortical neuronal populations, and that the quantification of these effects in terms of XApEn has a similar discriminatory power as changes of spontaneous action potential rates. Thus, XApEn of field potentials recorded from local cortical networks provides valuable information on the anesthetic state of the brain.

     

Advanced flicker spectroscopy of fluid membranes

The bending elasticity of a fluid membrane is characterized by its modulus and spontaneous curvature. We present a new method, advanced flicker spectroscopy of giant nonspherical vesicles, which makes it possible to simultaneously measure both parameters for the first time. Our analysis is based on the generation of a large set of reference data from Monte Carlo simulations of randomly triangulated surfaces. As an example of the potential of the procedure, we monitor thermal trajectories of vesicle shapes and discuss the elastic response of zwitterionic membranes to transmembrane pH gradients. Our technique makes it possible to easily characterize membrane curvature as a function of environmental conditions.     

Über den Untergruppenverband einer Abelschen Operatorgruppe Teil I: m-Verbände

Ohne Zusammenfassung     

Die Fehlordnung des Natriumazides und deren Einfluß auf die thermische Zersetzung, 2. Mitt.: Berechnung der Polarisationsenergie für den Ausbau eines Ionenpaares aus Natriumazid

Zusammenfassung Zur Berechnung der Polarisationsenergie nach dem Konzept eines starren Gitters wird zuerst die Polarisierbarkeit des N₃ ^– in NaN₃ berechnet. Mit den bekannten Daten für die Brechungsindizes in den Hauptachsen kann nach einer Methode vonMott der erforderliche Polarisierbarkeitstensor aufgestellt werden. Um Argumente für die Berechtigung des Verfahrens zu erhalten, wird die Polarisierbarkeit des Chlorions in NaCl analog berechnet. Unter Zugrundelegung der vonPauling gegebenen Strukturdaten des NaN₃ wird dann die Polarisationsenergie mit Hilfe verallgemeinerter Grundlagen für den Ausbau eines Ionenpaares aus NaN₃ und NaCl berechnet, während Dipol—Dipol-Wechselwirkungen abgeschätzt werden. Vernachlässigt man den Beitrag der Verschiebungspolarisation, so erhält man für die gesamte Polarisationsenergie bei NaN₃ 3,4 eV und bei NaCl 4,2 eV, wasSchottky-Fehlordnung vermuten läßt. Der Zusammenhang mit der Fehlerbildungsenergie wird im Anschluß daran diskutiert.

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For the determination of the polarization energy based upon the model of a rigid lattice, the polarizability of the azide ion in sodium azide is calculated. WithMott's method and the known data for the refractive indices along the main directions the polarizability tensor can be constructed. An analogous calculation is performed for the polarizability of the chlorine ion in NaCl in order to test arguments of our method. WithPauling's data of the NaN₃ structure, the polarization energy for the removal of an ion pair from both NaN₃ and NaCl is calculated by means of a generalized basis estimating dipole—dipole interactions. Neglecting the displacement polarization, one obtains for the total polarization energy a value of 3,4 eV for NaN₃, and 4,2 eV for NaCl, resp., pointing atSchottky-disorder. The connection with the energy of defect formation is discussed hereupon.

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Mit 6 Abbildungen     

Lösungsmitteleinfluß auf das Redoxverhalten des Hexakismethylisonitrilmangan (I) ions

The redox behaviour of hexakismethylisonitrilmanganese(I) [MnL ₆ ⁺] has been studied in acetic acid, dichloromethane, 1,2-dichloroethane, propylenecarbonate, butyrolactone, methanol, ethanol, nitromethane, acetonitrile, N-methyl-2-pyrrolidinone, dimethylformamide, dimethyl sulfoxide and water. The reversible diffusion-controlled oxidation MnL ₆ ⁺/MnL ₆ ²⁺ could be observed in all solvents studied, on both the dropping mercury electrode and the stationary platinum electrode. Employing tetrabutylammonium perchlorate as supporting electrolyte, the oxidation MnL ₆ ²⁺/MnL ₆ ³⁺ was observable only in acetic acid, nitromethane, 1,2-dichloroethane, dichloromethane, propylenecarbonate, butyrolactone and acetonitrile. In all other solvents oxidation of the solvent preceded the oxidation MnL ₆ ²⁺/MnL ₆ ³⁺. Poorly defined polarographic waves attributable to the one electron reduction of the MnL ₆ ⁺ were observed in butyrolactone, propylenecarbonate, acetonitrile, dimethylformamide, N-methyl-2-pyrrolidinone and dimethyl sulfoxide. All potential values were recorded versus bisbiphenylchromium(I)-iodide [BBCr(I)J], the problems of measuring against external aqueous reference electrodes are discussed. The redox potential of the process MnL ₆ ⁺/MnL ₆ ²⁺ was found to be a function of the donor properties of the solvents used; the effects of outer sphere coordination on the redox behaviour of this couple are discussed. No effect of the supporting electrolytes tetrabutylammonium perchlorate, tetraethylammonium nitrate and tetraethylammonium perchlorate on the redox behaviour of MnL ₆ ⁺ was found. The UV-spectrum of MnL ₆(PF₆)₂ has been recorded.

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Mit 3 Abbildungen     

L?sungsmitteleinflu? auf das Redoxverhalten des Hexakismethylisonitrilmangan (I) ions

The redox behaviour of hexakismethylisonitrilmanganese(I) [MnL ₆ ⁺] has been studied in acetic acid, dichloromethane, 1,2-dichloroethane, propylenecarbonate, butyrolactone, methanol, ethanol, nitromethane, acetonitrile, N-methyl-2-pyrrolidinone, dimethylformamide, dimethyl sulfoxide and water. The reversible diffusion-controlled oxidation MnL ₆ ⁺/MnL ₆ ²⁺ could be observed in all solvents studied, on both the dropping mercury electrode and the stationary platinum electrode. Employing tetrabutylammonium perchlorate as supporting electrolyte, the oxidation MnL ₆ ²⁺/MnL ₆ ³⁺ was observable only in acetic acid, nitromethane, 1,2-dichloroethane, dichloromethane, propylenecarbonate, butyrolactone and acetonitrile. In all other solvents oxidation of the solvent preceded the oxidation MnL ₆ ²⁺/MnL ₆ ³⁺. Poorly defined polarographic waves attributable to the one electron reduction of the MnL ₆ ⁺ were observed in butyrolactone, propylenecarbonate, acetonitrile, dimethylformamide, N-methyl-2-pyrrolidinone and dimethyl sulfoxide. All potential values were recorded versus bisbiphenylchromium(I)-iodide [BBCr(I)J], the problems of measuring against external aqueous reference electrodes are discussed. The redox potential of the process MnL ₆ ⁺/MnL ₆ ²⁺ was found to be a function of the donor properties of the solvents used; the effects of outer sphere coordination on the redox behaviour of this couple are discussed. No effect of the supporting electrolytes tetrabutylammonium perchlorate, tetraethylammonium nitrate and tetraethylammonium perchlorate on the redox behaviour of MnL ₆ ⁺ was found. The UV-spectrum of MnL ₆(PF₆)₂ has been recorded.     

Organische Schwefelverbindungen. IX—Ringkontraktion Statt Carben-Eliminierung von Neutralteilen Bei der Elektronenstossinduzierten Fragmentierung von Thiaspirofuranonen

During the fragmentation of thiaspirofuranone under electron-impact a process is presumed to occur that is best rationalised as a ring contraction of the neutral particle C₆H₁₀. A carbene structure for this neutral fragment can be excluded.     

Eine neue photometrische Eisenbestimmung mit Äthylendiamintetraessigsäure

Zusammenfassung Es wird gezeigt, daß man mit Hilfe von Komplexon-III Eisen-III-Verbindungen nach Überführung in gelbgefärbte Komplexverbindungen, deren Absorptionsmaximum unterhalb 366 m liegt, photometrisch bestimmen kann. Die Extinktion ist bei gleicher Eisenkonzentration vomph-Wert abhängig und in denph-Bereichen zwischen 0,80 und 2,80 sowie zwischen 3,92 und 5,10 konstant, so daß beide Bereiche zur Bestimmung geeignet sind. Es ist beachtlich, daß die komplexe Bindung erst oberhalbph 10,5 zerfällt und Eisenhydroxyd ausflockt. DasLambert-Beersche Gesetz ist in dem Konzentrationsbereich zwischen 4g und 500g Eisen/ml streng erfüllt. Die Bestimmung ist vielen anderen bisher bekannten photometrischen Eisenbestimmungsverfahren überlegen, da schwächere Komplexbildner (z. B. Weinsäure) und sonstige Lösungspartner nicht stören.

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Summary It was found that iron (III) compounds can be determined photometrically by the aid of complexone III. The yellow complex compound has an absorption maximum below 366 m. The extinction, at equal iron concentration, is dependent on theph value. It is constant inph ranges between 0.80 and 2.80 and also between 3.92 and 5.10, so that either of these ranges is suitable for this determination. It should be noted that the complex decomposes only aboveph = 10.5; iron hydroxide separates. TheLambert-Beer law is strictly followed in the concentration range 4g and 500g iron/ml. This method of determination is far superior to many familiar photometric procedures for iron because weaker complex-formers (e. g. tartaric acid) and other cosolutes do not interfere.

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Résumé On montre que les composés du fer-III peuvent être dosés photométriquement à l'aide de la complexone-III après transformation en un complexe coloré en jaune dont l'absorption maximum se trouve au-dessous de 366 m. L'extinction dépend duph pour des concentrations égales en fer et se montre constante entre 0,80 et 2,80, de même qu'entre 3,92 et 5,10, de sorte que ces deux domaines conviennent pour le dosage. Il faut remarquer que le complexe ne se détruit qu'au-dessus deph 10,5 et l'hydroxyde ferrique flocule. La loi deLambert-Beer est satisfaite dans le domaine de concentration entre 4 g et 500 g de fer/ml. La méthode de dosage est de beaucoup supérieure aux méthodes connues jusqu'ici pour la détermination colorimétrique du fer du fait que les complexants les plus faibles, comme l'acide tartrique, ne gênent pas.

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