Free Subordination and Belinschi–Nica Semigroup

We realize the Belinschi–Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these semigroups we show that a differential equation holds, generalizing the complex Burgers equation. We give examples of free multiplicative subordination and find a relation to the Markov–Krein transform, Boolean stable laws and monotone stable laws. A similar idea works for additive subordination, and in particular we study the free additive subordination associated to the Cauchy distribution and show that it is a homomorphism with respect to monotone, Boolean and free additive convolutions.     

Thermodynamically Induced Conformational Changes of the Cyanobacterial Circadian Clock Protein KaiB

Site-directed spin labeling electron spin resonance (ESR) was applied to investigate the local environment of the cyanobacterial circadian clock protein KaiB. We prepared five cysteine residue-substituted mutants of KaiB labeled with maleimide spin label (MSL). By comparing the ESR spectra of KaiBs carrying MSL at different positions (Thr64, Lys67, Tyr94, Gly98, and Ala101), local conformational changes were identified. The ESR spectra of MSL-T64C and MSL-K67C showed the relatively slow motion of MSL characterized by τ?=?79 and 59?ns at 4°C, respectively. The spectra of MSL-Y94C, MSL-G98C and MSL-A101C showed relatively fast motion characterized by τ?=?8.0, 4.1 and 3.1?ns at 4°C, respectively. These differences were explained by the local environments of the position in KaiB. On incubation at 40°C for 24?h, all ESR spectra of the labeled KaiBs changed, which can be explained by the structural relaxation of KaiB.     

Efficiently Synthesizing Lacto-Ganglio-Series Gangliosides by Using a Glucosyl Ceramide Cassette Approach: The Total Synthesis of Ganglioside X2

The first total synthesis of the hybrid ganglioside X2, which consisted of a highly branched octasaccharide and ceramide moieties, was accomplished by using a glucosyl ceramide cassette approach. With a disaccharyl donor, the heptasaccharide could not be constructed by glycosylation of the C4 hydroxy group of galactose at the reducing end of the pentasaccharide. In contrast, through an alternative approach with two branched glycan units, a GM2-core trisaccharide, and a lacto-ganglio tetrasaccharide, the heptasaccharyl donor could be prepared and subsequently joined with a glucosyl ceramide cassette to afford the protected ganglioside, X2. Finally, global deprotection completed the synthesis, thus affording the pure ganglioside X2.     

Enzyme sensor for L-lactate with a chitosan-mercury film electrode

Summary An amperometric enzyme sensor composed of a mercury film electrode and an enzyme-immobilized chitosan membrane is developed. This biosensor is based on both a mercury film electrode detecting the consumption of dissolved dioxygen following enzymatic reaction, and a chitosan membrane. The latter provides an excellent permselectivity and excludes electroactive interferents. The detection range of this biosensor was 1.0×10^–5–3.0×10^–4 mol/l and the relative standard deviation, R.S.D. at 5.0×10^–5 mol/l was 1.4% (n=3). This biosensor was applied to the direct determination of L-lactate in human serum without pretreatment.