Protein separations with induced pH gradients using cation-exchange chromatographic columns containing weak acid groups

The behavior of chromatographic columns packed with resins containing both weak and strong cation-exchange groups is investigated in order to obtain protein separations by means of internally generated pH gradients in response to step changes in buffer composition. A local equilibrium model is developed to predict pH transitions using non-adsorbed buffers, i.e. containing neutral and negatively charged buffering species, based exclusively on the resin titration curve. In agreement with experimental results, the model predicts practical, fairly linear gradients between pH 5 and 7, which are formed using suitable mixtures of acetate and phosphate buffers. The separation of mixtures of ovalbumin, albumin, and transferrin is used as a model system, but, unlike most previous work, we consider preparative conditions. Near baseline resolution is obtained with protein loads as high as 10mg/mL and mobile phase velocities at high as 460 cm/h using porous, 70-microm diameter particles. The peaks obtained with this approach are much sharper than could be obtained isocratically or using externally generated, unretained gradients as a result of the peak compression caused by the axial pH gradient formed along the column. Moreover, separation is obtained at very low ionic strengths (2-3 mS/cm). The effects of flow velocity, mobile phase composition, time of injection, and protein load on retention and elution pH are investigated systematically demonstrating a range of ways in which the separation can be controlled and optimized.     

Convergence of the eigenvalues of the p-Laplace operator as p goes to 1

Let $(\lambda ^k_p)_k$ be the usual sequence of min-max eigenvalues for the $p$ -Laplace operator with $p\in (1,\infty )$ and let $(\lambda ^k_1)_k$ be the corresponding sequence of eigenvalues of the 1-Laplace operator. For bounded $\Omega \subseteq \mathbb{R }^n$ with Lipschitz boundary the convergence $\lambda ^k_p\rightarrow \lambda ^k_1$ as $p\rightarrow 1$ is shown for all $k\in \mathbb{N }$ . The proof uses an approximation of $BV(\Omega )$ -functions by $C_0^\infty (\Omega )$ -functions in the sense of strict convergence on $\mathbb{R }^n$ .     

Magnetism, f-electron localization and superconductivity in 122-type heavy-fermion metals

Both CeCu2Si2 and YbRh2Si2 crystallize in the tetragonal ThCr2Si2 crystal structure. Recent neutron-scattering results on normal-state CeCu2Si2 reveal a slowing down of the quasielastic response which complies with the scaling expected for a quantum critical point (QCP) of itinerant, i.e., three-dimensional spin-density-wave (SDW), type. This interpretation is in full agreement with the non-Fermi-liquid behavior observed in transport and thermodynamic measurements. The momentum dependence of the magnetic excitation spectrum reveals two branches of an overdamped dispersive mode whose coupling to the heavy charge carriers is strongly retarded. These overdamped spin fluctuations are considered to be the driving force for superconductivity in CeCu2Si2 (Tc = 600 mK). The weak antiferromagnet YbRh2Si2 (TN = 70 mK) exhibits a magnetic-field-induced QCP at BN = 0.06 T (B⊥c). There is no indication of superconductivity down to T = 10 mK. The magnetic QCP appears to concur with a breakdown of the Kondo effect. Doping-induced variations of the average unit-cell volume result in a detachment of the magnetic and electronic instabilities. A comparison of the properties of these isostructural compounds suggests that 3D SDW QCPs are favorable for unconventional superconductivity. The question whether a Kondo-breakdown QCP may also give rise to superconductivity, however, remains to be clarified.     

DFT and MD studies on the influence of the orientation of ester linkage groups in banana-shaped mesogens

The influence of the direction of ester linkage groups on the structural and electronic properties of five-ring banana-shaped molecules with a central 1,3-phenylene unit has been investigated including hexyloxy and dodecyloxy terminal chains. DFT studies on the B3LYP/6-31G(d) level were performed on the conformational behaviour of the ten isomers in a systematic way. The one- and two-fold potential energy scans show that the flexibility of the wings significantly depends on the orientation of the carboxyl linkage groups. Moreover, the different directions of the carboxyl groups between the aromatic rings cause remarkable changes on the dipole moment and its components of the molecules. These findings are supported by investigations on the global charge pattern of the molecules calculated from electrostatic potential group charges. The bending angle alpha obtained from a simple model for the five-ring bent-core molecules is a characteristic structural parameter which can be correlated with experimental findings. Calculations on the bent-core molecules in an external electric dipole field related to the direction of their polar axis show remarkable effects with respect to the flexibility and polarity of the isomers. First molecular dynamics simulations on the banana-shaped molecules were carried out within the AMBER 7 package. The trajectories of relevant structural parameters support the findings of the DFT studies. The results concerning the structure and polarity revealed from the DFT and MD calculations of the ten isomers can be correlated with data from dielectric measurements and mesophase properties.     

Effects of a professional solo singer education on auditory and kinesthetic feedback—a longitudinal study of singers'' pitch control

The significance of auditory and kinesthetic feedback to pitch control in singing was described in a previous report of this project for students at the beginning of their professional solo singer education.(1) As it seems reasonable to assume that pitch control can be improved by training, the same students were reinvestigated after 3 years of professional singing education. As in the previous study, the singers sang an ascending and descending triad pattern with and without masking noise in legato and staccato and in a slow and a fast tempo. Fundamental frequency and interval sizes between adjacent tones were determined and compared with their equivalents in the equally tempered tuning. The average deviations from these values were used as estimates of intonation accuracy. Intonation accuracy was reduced by masking noise, by staccato as opposed to legato singing, and by fast as opposed to slow performance. The contribution of the auditory feedback to pitch control was not significantly improved after education, whereas the kinesthetic feedback circuit was improved in slow legato and slow staccato tasks. The results support the assumption that the kinesthetic feedback contributes substantially to intonation accuracy.     

Quantum chemical studies on the conformational behaviour of substituted banana-shaped mesogens with a central 1,3-phenylene unit

Ab initio and DFT calculations on the HF/STO-3G and B3LYP/6-31G(d) level were performed on the conformational behaviour of isolated banana-shaped molecules of 1,3-phenylene bis[4-(4-n-hexyloxyphenyliminomethyl)benzoate] systems (P-6-O-PIMB). The influence of small substituents in both the central phenyl ring and the external phenyl rings on the shape, polarity and flexibility of these molecules was investigated by one- and two-fold relaxed potential energy scans in a systematic way. The effect of substituents on the global polarity of banana-shaped mesogens was analysed by the magnitude and direction of the dipole moment and its components in relation to the long axis of the molecules. Moreover, a simple model for the calculation of the bending angle was tested for banana-shaped molecules with a central 1,3-phenylene unit. The findings for the isolated banana-shaped molecules are correlated with solid state X-ray and liquid crystalline state NMR results. Banana-shaped molecules with both hexyloxy (P-6-O-PIMB) and hexyl (P-6-PIMB) terminal chains are included to study the effect of substituents in the external phenyl rings on the flexibility of these chains. An attempt will be made to correlate the results with experimental findings on banana-shaped mesogens.