On the transition from cellular to wavelike patterns during solutal Marangoni convection

We study characteristic convection patterns emerging during the mass transfer of acetic acid from a glycerol-water layer to a superposed acetone layer by means of experiments and numerical simulations. The patterns form as a result of the stationary Marangoni instability. The initial phase of the pattern evolution is studied using high-resolution simulations. They show hierarchically ordered cellular structures which closely resemble experimental observations. In the later stages presently accessible to the experiments, the cells are locally replaced by relaxation oscillation waves. The emergence of these structures is favored when the experiment is performed in narrow cuvettes.     

CF3 Rotation in 3-(Trifluoromethyl)phenanthrene: Solid State 19F and 1H NMR relaxation and Bloch-Wangsness-Redfield theory

We have observed and modeled the 1H and 19F solid-state nuclear spin relaxation process in polycrystalline 3-(trifluoromethyl)phenanthrene. The relaxation rates for the two spin species were observed from 85 to 300 K at the low NMR frequencies of omega/2pi = 22.5 and 53.0 MHz where CF3 rotation, characterized by a mean time tau between hops, is the only motion on the NMR time scale. All motional time scales (omegatau < 1, omegatau approximately 1, and omegatau > 1) are observed. The 1H spins are immobile on the NMR time scale but are coupled to the 19F spins via the unlike-spin dipole-dipole interaction. The temperature dependence of the observed relaxation rates (the relaxation is biexponential) shows considerable structure and a thorough analysis of Bloch-Wangsness-Redfield theory for this coupled spin system is provided. The activation energy for CF3 rotation is 11.5 +/- 0.7 kJ/mol, in excellent agreement with the calculation in a 13-molecule cluster provided in the companion paper where the crystal structure is reported and detailed ab initio electronic structure calculations are performed [Wang, X.; Mallory F. B.; Mallory, C. W; Beckmann, P. A.; Rheingold, A. L.; Francl, M. M J. Phys. Chem. A 2006, 110, 3954].     

Microarray technology as a universal tool for high-throughput analysis of biological systems

Over the last years microarray technology has become one of the principal platform technologies for the high-throughput analysis of biological systems. Starting with the construction of first DNA microarrays in the 1990s, microarray technology has flourished in the last years and many different new formats have been developed. Peptide and protein microarrays are now applied for the elucidation of interaction partners, modification sites and enzyme substrates. Antibody microarrays are envisaged to be of high importance for the high-throughput determination of protein abundances in translational profiling approaches. First cell microarrays have been constructed to transform microarray technology from an in vitro technology to an in vivo functional analysis tool. All of these approaches share a common prerequisite: the solid support on which they are generated. The demands on this solid support are thereby as manifold as the applications themselves. This review is aimed to display the recent developments in surface chemistry and derivatization, and to summarize the latest developments in the different application areas of microarray technology.     

A promiscuous glutathione transferase transformed into a selective thiolester hydrolase

Human glutathione transferase A1-1 (hGST A1-1) can be reengineered by rational design into a catalyst for thiolester hydrolysis with a catalytic proficiency of 1.4 x 10(7) M(-1). The thiolester hydrolase, A216H that was obtained by the introduction of a single histidine residue at position 216 catalyzed the hydrolysis of a substrate termed GSB, a thiolester of glutathione and benzoic acid. Here we investigate the substrate requirements of this designed enzyme by screening a thiolester library. We found that only two thiolesters out of 18 were substrates for A216H. The A216H-catalyzed hydrolysis of GS-2 (thiolester of glutathione and naphthalenecarboxylic acid) exhibits a k(cat) of 0.0032 min(-1) and a KM of 41 microM. The previously reported catalysis of GSB has a k(cat) of 0.00078 min(-1) and KM of 5 microM. The k(cat) for A216H-catalyzed hydrolysis of GS-2 is thus 4.1 times higher than for GSB. The catalytic proficiency (k(cat)/KM)/k(uncat) for GS-2 is 3 x 10(6) M(-1). The promiscuous feature of the wt protein towards a range of different substrates has not been conserved in A216H but we have obtained a selective enzyme with high demands on the substrate.     

Isolation of bovine lactoferrin, lactoperoxidase and enzymatically prepared lactoferricin from proteolytic digestion of bovine lactoferrin using adsorptive membrane chromatography

A new downstream procedure for the isolation of bovine lactoferrin (bLf), lactoperoxidase and bovine lactoferricin (LfcinB) from sweet cheese whey was developed at the laboratory scale, based on membrane adsorber technology. The procedure was upscaled later on to an industrially relevant scale for the purificationof sweet whey concentrate with a recovery yield for lactoferrin of more than 90%. Based on these results the industrial process for 1 x 10(8) kg whey per year was projected. These high-value proteins were downstreamed by using cation-exchange membrane systems (Sartobind S, Sartorius, G?ttingen, Germany). These strongly acidic membranes trap proteins in its anionic form. The dynamic loading capacity for both proteins as well as the optimal elution profiles with sodium chloride gradients were derived from laboratory experiments using membrane modules with 15-75 cm2 membrane material. Further investigations were performed with 1 m2 modules in a continuous process mode. The enzymatic preparation of LfcinB from bLf was performed by pepsin hydrolysis and the isolation of LfcinB was directly carried out from the enzymatic digest mixture. The identification of the proteins was performed with matrix-assisted laser desorption ionisation mass spectrometry (MALDI-MS). LfcinB and bLf were both tested afterwards in biological assays in order to show not only the efficiency of the downstreaming process in regard to product quantity but also to product quality (biological activity).     

Cubature over the sphere in Sobolev spaces of arbitrary order

This paper studies numerical integration (or cubature) over the unit sphere for functions in arbitrary Sobolev spaces H^s(S²), s>1. We discuss sequences of cubature rules, where (i) the rule Q_m(n) uses m(n) points and is assumed to integrate exactly all (spherical) polynomials of degree ≤n and (ii) the sequence (Q_m(n)) satisfies a certain local regularity property. This local regularity property is automatically satisfied if each Q_m(n) has positive weights. It is shown that for functions in the unit ball of the Sobolev space H^s(S²), s>1, the worst-case cubature error has the order of convergence O(n^-s), a result previously known only for the particular case . The crucial step in the extension to general s>1 is a novel representation of , where P_ℓ is the Legendre polynomial of degree ℓ, in which the dominant term is a polynomial of degree n, which is therefore integrated exactly by the rule Q_m(n). The order of convergence O(n^-s) is optimal for sequences (Q_m(n)) of cubature rules with properties (i) and (ii) if Q_m(n) uses m(n)=O(n²) points.     

A lower bound for the worst-case cubature error on spheres of arbitrary dimension

This paper is concerned with numerical integration on the unit sphere S^r of dimension r≥2 in the Euclidean space ℝ^r+1. We consider the worst-case cubature error, denoted by E(Q_m;H^s(S^r)), of an arbitrary m-point cubature rule Q_m for functions in the unit ball of the Sobolev space H^s(S^r), where s>, and show that The positive constant c_s,r in the estimate depends only on the sphere dimension r≥2 and the index s of the Sobolev space H^s(S^r). This result was previously only known for r=2, in which case the estimate is order optimal. The method of proof is constructive: we construct for each Q_m a `bad' function f_m, that is, a function which vanishes in all nodes of the cubature rule and for which Our proof uses a packing of the sphere S^r with spherical caps, as well as an interpolation result between Sobolev spaces of different indices.     

Numerical integration with polynomial exactness over a spherical cap

This paper presents rules for numerical integration over spherical caps and discusses their properties. For a spherical cap on the unit sphere \mathbbS²\mathbb{S}^2, we discuss tensor product rules with n ²/2 + O(n) nodes in the cap, positive weights, which are exact for all spherical polynomials of degree ≤ n, and can be easily and inexpensively implemented. Numerical tests illustrate the performance of these rules. A similar derivation establishes the existence of equal weight rules with degree of polynomial exactness n and O(n ³) nodes for numerical integration over spherical caps on \mathbbS²\mathbb{S}^2. For arbitrary d ≥ 2, this strategy is extended to provide rules for numerical integration over spherical caps on \mathbbS^d\mathbb{S}^d that have O(n ^d ) nodes in the cap, positive weights, and are exact for all spherical polynomials of degree ≤ n. We also show that positive weight rules for numerical integration over spherical caps on \mathbbS^d\mathbb{S}^d that are exact for all spherical polynomials of degree ≤ n have at least O(n ^d ) nodes and possess a certain regularity property.     

Supply chain design considering economies of scale and transport frequencies

In this paper we consider a 3-echelon, multi-product supply chain design model with economies of scale in transport and warehousing that explicitly takes transport frequencies into consideration. Our model simultaneously optimizes locations and sizes of tank farms, material flows, and transport frequencies within the network. We consider all relevant costs: product cost, transport cost, tank rental cost, tank throughput cost, and inventory cost. The problem is based on a real-life example from a chemical company. We show that considering economies of scale and transport frequencies in the design stage is crucial and failing to do so can lead to substantially higher costs than optimal. We solve a wide variety of problems with branch-and-bound and with the efficient solution heuristics based on iterative linearization techniques we develop. We show that the heuristics are superior to the standard branch-and-bound technique for large problems like the one of the chemical company that motivated our research.