Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

A Hybrid Improvement Heuristic for the One-Dimensional Bin Packing Problem

We propose in this work a hybrid improvement procedure for the bin packing problem. This heuristic has several features: the use of lower bounding strategies; the generation of initial solutions by reference to the dual min-max problem; the use of load redistribution based on dominance, differencing, and unbalancing; and the inclusion of an improvement process utilizing tabu search. Encouraging results have been obtained for a very wide range of benchmark instances, illustrating the robustness of the algorithm. The hybrid improvement procedure compares favourably with all other heuristics in the literature. It improved the best known solutions for many of the benchmark instances and found the largest number of optimal solutions with respect to the other available approximate algorithms.     

Investigation of gas chromatographic interaction mechanism on permethylated cyclodextrins by molecular modelling

Summary The capillary gas chromatographic retention behavior of -pinene and tricyclene has been investigated on stationary phases of different polarities. On all but one of the columns employed, tricyclene eluted before -pinene; only permethylated -cyclodextrins dissolved in moderately polar polisiloxanes gave a reversed elution order. The intermolecular interactions which caused the unexpected retention behavior were investigated in detail, applying methods of computer simulation. To achieve this, we have developed a calculation algorithm on the basis of molecular mechanical optimizations and programmed it in a macro. This makes it possible to systematically investigate a given configuration space in which all the possible interactions can take place. It was shown that permethylated -cyclodextrin as host molecule for both guest molecules offers an optimum cavity size. As a result the number of energetically favorable contacts between host and guest molecules as well as the strength of the interactions in this stationary phase were larger. As a consequence the elution order, normally only influenced by the vapor pressure of the compounds at a given temperature, was changed. Nonspecific interactions played an especially important role for these kinds of substances.     

Automated and enhanced extraction of a small molecule-drug conjugate using an enzyme-inhibitor interaction based SPME tool followed by direct analysis by ESI-MS

We report a novel, fast, and automatic SPME-based method capable of extracting a small molecule-drug conjugate (SMDC) from biological matrices. Our method relies on the extraction of the drug conjugate followed by direct elution into an electrospray mass spectrometer (ESI-MS) source for qualitative and quantitative analysis. We designed a tool for extracting the targeting head of a recently synthesized SMDC, which includes acetazolamide (AAZ) as high-affinity ligand specific to carbonic anhydrase IX. Specificity of the extraction was achieved through systematic optimization. The design of the extraction tool is based on noncovalent and reversible interaction between AAZ and CAII that is immobilized on the SPME extraction phase. Using this approach, we showed a 330% rise in extracted AAZ signal intensity compared to a control, which was performed in the absence of CAII. A linear dynamic range from 1.2 to 25 μg/ml was found. The limits of detection (LOD) of extracted AAZ from phosphate-buffered saline (PBS) and human plasma were 0.4 and 1.2 μg/ml, respectively. This with a relative standard deviation of less than 14% (n = 40) covers the therapeutic range.

Graphical abstract

     

Molecular and crystal structures of ruthenium and osmium arene clusters

The molecular and crystal structures of a number of ruthenium and osmium clusters of nuclearity between three and six containing arene fragments such as C₆H₆, C₆H₃Me₃, C₆H₄Me₂ and C₆H₅Me have been investigated. Attention has been focused on the relationship between the terminal ( ⁶-coordination) and face-capping ( ₃: ²: ²: ²-coordination) bonding modes. Empirical packing potential energy calculations have been employed to investigate the intermolecular organization in the crystal. It has been shown that the arene fragments in mono-arene clusters form ribbons, while in bis-arene clusters graphitic-like interactions throughout the crystal are established. The factors controlling the ease of arene reorientational motion in the solid state has also been investigated in relation to the shape, size and geometry of the molecules and of their interlocking modes.     

Cautions regarding the physical interpretation of statistically based separation of the ortho substituent effect into inductive,mesomeric, and steric components—II : Acid catalysed esterification of benzoic acids by methanol and cyclohexanol

In order to attain a better insight into the composition of Taft E_s^o, constants the rate data of hydrion catalysed esterification of both m,p-substituted and o-substiluted benzoic acids by cyclohexanol and methanol were submitted to a statistical analysis using inductive mesomeric and steric substituent constants and various dummy variables differently structured. Furthermore a principal component analysis with subsequent identification of the first principal component via multiple regression analysis was applied. It has been demonstrated that in the reactions of m,p substituted compounds some substituents capable of exerting strong mesomeric effects show peculiar characteristics deviating from the general trend. Since the same result was obtained in the correlations of ortho substituted benzoic acids this effect was taken into account using an appropriate dummy variable which in all cases improved the multiple coefficient of determination. It is concluded that the esterification rates of the ortho substituted compounds depend essentially upon inductive and steric effects (taken away OMe OEt and NO₂) as proposed by Taft. While generally the E_s^o values may be regarded as some measure of a steric effect, this is not true for the methoxy and ethoxy groups.     

Traceless solid-phase synthesis of 2,4,6-chlorodiamino and triaminopyrimidines

An effective traceless solid-phase synthesis of chloro-diaminopyrimidines via an amino-de-chlorination reaction of polymer-bound 4-alkoxycarbonylamino-2,6-dichloropyrimidines has been developed. After release from the polymer the target molecules were obtained in good to excellent purity, although with modest regiocontrol. Further reaction of solid-supported N-alkoxycarbonyl-chloro-diaminopyrimidines with secondary amines afforded triaminopyrimidines in good purity under mild conditions, whereas less nucleophilic primary amines did not perform well under the conditions explored so far.     

PMR-Spektren einiger Alkoxy-9-chlor-6-nitroacridine

The spectra of some 9-chloro-6-nitroacridines with methoxy substituents in position 1,4; 2,4; 3,4; 2,3; and ethoxy substituents in positions 1, 2, 3, were recorded. The influence of electron releasing alkoxy groups and electron withdrawing nitro groups on chemical shifts of protons in the 9-chloroacridinic cycle was discussed and PMR parameters were determined, comparatively with those of acridine and 9-chloroacridine. Good agreement between calculated and experimental values is observed. The spectrum of 9-chloro-1,2,3-triethoxyacridine shows for the four protons of the ringC. (H-5, H-6, H-7, H-8) anAMNX coupling pattern whose parameters were determined.