Zum Stufenaufbau der Inzidenzstrukturen mit Ähnlichkeitsrelation

Leißner [2] proved that the class of all incidence structures with similarity-relation coinzides with, the class of the algebraically defined geometries [F,T], where F denotes a neardomain over a subdomain T.In this paper we characterize those geometries, where F is a near-resp. (skew-) field by additional similarity axioms. At first we show that a subdomain T of a neardomain F is itself a neardomain iff–1T and characterize this fact geometrically. As a consequence every subdomain of a near-resp.(skew-) field has to be a near-resp. (skew-) field too. In §4 we get as a corollary that projective planes admit no sharply twice transitive groups of collineations.     

Mixed electrolytes in hydrophobic interaction chromatography†

An essential part of the modulation of protein‐binding capacity in hydrophobic interaction chromatography is the buffer‐salt system. Besides using “single” electrolytes, multicomponent electrolyte mixtures may be used as an additional tool. Both the protein solubility and the binding capacity depend on the position of a salt in the so‐called Hofmeister series. Specific interactions are observed for an individual protein‐salt combination. For salt mixtures, selectivity, recovery, and binding capacity do not behave like for the single salts that are positioned in between the two mixed components in the Hofmeister series, as the continuous correlation would suggest. Thus, finding strategies for mixed salts could potentially lead to improved capacities in hydrophobic interaction chromatography. Mixtures of ammonium sulfate, sodium citrate, sodium sulfate, sodium chloride, sodium acetate, and glycine were used to investigate the binding capacities for lysozyme and a monoclonal antibody on various hydrophobic resins. Resin capacity for two investigated proteins increases when mixtures consisting of a chaotropic and a kosmotropic salt are applied. It seems to be related to the rather basic isoelectric points of the proteins.     

Analytical and preparative separation of PEGylated lysozyme for the characterization of chromatography media

The effect of PEGylation on cation exchange chromatography was studied with poly(ethylene glycol) of different chain lengths (5 kDa, 10 kDa and 30 kDa) using lysozyme as a model system. A stable binding via reduction of a Schiff base was formed during random PEGylation on lysine residues with methoxy-PEG-aldehyde. A purification method for PEGylated proteins using cation exchange chromatography was developed, and different isoforms of mono-PEGylated lysozyme were isolated. TSKgel SP-5PW and Toyopearl GigaCap S-650M showed the best performance of all tested cation exchange resins, and the separation of PEGylated lysozyme could be also scaled up to semi-preparative level. Size-exclusion chromatography, SDS-PAGE and MALDI-TOF mass spectrometry were used for analysis. Separated mono-PEGylated lysozyme of different sizes was used to determine dynamic binding capacities (DBC) and selectivity of cation exchange chromatography resins. An optimization of binding conditions resulted in a more than 20-fold increase of DBC for Toyopearl GigaCap S-650M with 30 kDa mono-PEGylated lysozyme.     

Excitation pulse deconvolution in luminescence lifetime analysis for oxygen measurements in vivo

Oxygen-dependent quenching of phosphorescence has been proven to be a valuable tool for the measurement of oxygen concentrations both in vitro and in vivo. For biological measurements the relatively long lifetimes of phosphorescence have promoted time-domain-based devices using xenon arc flashlamps as the most common excitation light source. The resulting complex form of the excitation pulse leads to complications in the analysis of phosphorescence lifetimes and ultimately to errors in the recovered pO2 values. Although the problem has been recognized, the consequences on in vivo phosphorescence lifetime measurements have been neglected so far. In this study, the consequences of finite excitation flash duration are analyzed using computer simulations, and a method for the recovery of phosphorescence decay times from complex photometric signals is presented. The analysis provides an explanation as to why different calibration constants are reported in the literature and presents a unified explanation whereby calibration constants are not solely a property of the dye but also of the measuring device. It is concluded that complex excitation pulse patterns without appropriate analysis methods lead to device-specific calibration constants and nonlinearity and can be a potent source of errors when applied in vivo. The method of analysis presented in this article allows reliable phosphorescence lifetime measurements to be made for oxygen pressure measurements and can easily be applied to existing phosphorimeters.     

Electrochemical probing of ground state electronic interactions in polynuclear complexes of a new heteroditopic ligand

The synthesis and electronic properties of dinuclear ([(bipy)2Ru(I)M(terpy)][PF6]4(bipy = 2,2'-bipyridine, terpy = 2,2':6',2'-terpyridine; M = Ru, Os)) and trinuclear ([[(bipy)2Ru(I)]2M][PF6]6 M = Ru, Os, Fe, Co) complexes bridged by 4'-(2,2'-bipyridin-4-yl)-2,2':6',2'-terpyridine (I) have been investigated and are compared with those of mononuclear model complexes. The electrochemical analysis using cyclic voltammetry and differential pulse voltammetry reveals that there are no interactions in the ground state between adjacent metal centres. However, there is strong electronic communication between the 2,2'-bipyridine and 2,2':6',2'-terpyridine components of the bridging ligand. This conclusion is supported by a step-by-step reduction of the dinuclear and trinuclear complexes and the assignment of each electrochemical process to localised ligand sites within the didentate and terdentate domains. The investigation of the electronic absorption and emission spectra reveals an energy transfer in the excited state from the terminating bipy-bound metal centres to the central terpy-bound metal centre. This indicates that the bridge is able to facilitate energy transfer in the excited state between the metal centres despite the lack of interactions in the ground state.     

Two-photon absorption in quadrupolar pi-conjugated molecules: influence of the nature of the conjugated bridge and the donor-acceptor separation

Quadrupolar-type substitution of pi-conjugated chromophores with donor and acceptor groups has been shown to increase their two-photon absorption (TPA) response by up to two orders of magnitude. Here, we apply highly correlated quantum-chemical calculations to evaluate the impact of the nature of conjugated bridge and the charge-transfer distance on that enhancement. We compare chromophores with phenylenevinylene-, thienylenevinylene-, polyene-, and indenofluorene-type backbones substituted by dimethylamino and cyano groups. In all compounds, we find a strongly TPA-active A(g) state (either 2A(g) or 3A(g)) in the low-energy region, as well as a higher lying TPA-active state (mA(g)) at close to twice the energy of the lowest lying one-photon allowed state; the smaller energy detuning in the mA(g) states results in very large TPA cross sections delta. We also investigate the influence of the degree of ground-state polarization on TPA. Independent of the nature of the backbone and the donor-acceptor separation, delta displays the same qualitative evolution with a maximum before the cyanine-like limit; the highest TPA cross sections are calculated for distirylbenzene- and polyene-based systems.     

Combinatorial theorems on contractive mappings in power sets

We prove that to every positive integer n there exists a positive integer h such that the following holds: If S is a set of h elements and ƒ a mapping of the power set of S into such that ƒ(T)T for all T , then there exists a strictly increasing sequence T₁T_n of subsets of S such that one of the following three possibilities holds: (a) all sets ƒ(T_i), i= 1,…,n, are equal; (b) for all i=1,…, n, we have ƒ(T_i)=T_i; (c) T_i=ƒ(T_i+1) for all i= 1,…,n-1. This theorem generalizes theorems of the author, Rado, and Leeb. It has applications for subtrees in power sets.