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.     

Internal standardization for the determination of cadmium,cobalt, chromium and manganese in saline produced water from petroleum industry by inductively coupled plasma optical emission spectrometry after cloud point extraction

In the present paper a procedure is proposed for the determination of traces of Cd, Co, Mn and Cr in petroleum industry produced water by inductively coupled plasma optical emission spectrometry. The procedure is based on cloud point extraction of these metals, as their dithizonate complexes, into the surfactant-rich phase of octylphenoxypolyethoxyethanol surfactant (Triton X-114). Extractions were carried out in solutions with salinities between 10‰ and 70‰. Since residual salinity in the surfactant-rich phase caused differences in its transport to the plasma, yttrium was used as an internal standard to correct for this effect. The simultaneous metal extraction procedure was optimized by response surface methodology using a Doehlert design and desirability function. Enhancement factors of 21, 21, 9 and 19, along with limits of quantification of 0.093, 0.20, 0.73 and 1.2 μg L^− 1, and precision expressed as relative standard deviation (n = 8, 20.0 μg L^− 1) of 5.8, 1.2, 1.7 and 5.7% were obtained for Cd, Co, Mn and Cr, respectively. The accuracy was evaluated by spike recovery tests on the high salinity water samples with salinity of 40 and 63‰.     

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.     

In situ Fourier transform infrared spectroscopy as an efficient tool for determination of reaction kinetics

The performance of new FTIR-based monitoring technology to representatively determine reaction kinetics has been demonstrated on an example of homogeneously catalyzed liquid-phase sucrose hydrolysis to fructose and glucose. The reaction kinetics were investigated by using the ReactIR 1000 reaction analysis system, which enables determination of the component concentration from its characteristic FTIR spectrum. During the sucrose inversion, the ReactIR 1000 instrument connected to a computer controlled standard glass batch reactor provided the required operating conditions and information about the component concentration in real-time. We have studied the influence of hydrogen ion concentration, temperature and initial concentration of sucrose on the sucrose disappearance rate. It was found out that the inversion of sucrose is an irreversible reaction, which is not affected by the formation of fructose and glucose in the liquid-phase. Then, the parameters of the kinetic model (i.e., reaction rate constant and activation energy) were calculated. A comparison of the model output and the measured data showed that the kinetics of the sucrose inversion could be well described by means of the pseudo first-order kinetic model. Finally, the method of determining the kinetic model by FTIR spectroscopy was verified by comparing the results obtained in the batch reactor with the results obtained in the continuously stirred tank reactor.     

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.