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.     

Analysis of a demodulation system for Fiber Bragg Grating sensors using two fixed filters

The analysis of a demodulation system for Fiber Bragg Grating sensors based on two fixed spectral filters has been carried out both theoretically and experimentally. Different system configurations were analyzed by modifying the spectral position of the filters as well as the optical power-level of the signal reaching the two photo-detectors. Measurements with integration times that varied from 0.01 to 1 s have been compared with the low-frequency limit predicted for long-term operation. Comparisons between simulated and experimental results show good agreement, and extrapolations indicate that it should be possible to achieve an operating spectrum range of the order of 7 nm, with uncertainties equivalent to less than 2 pm in measurements of the sensor peak position.     

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

     

Inclusion of molybdenocene dichloride (Cp2MoCl2) in 2-hydroxypropyl- and trimethyl-β-cyclodextrin: Structural and biological properties

Organometallic-cyclodextrin inclusion compounds were obtained by the treatment of molybdenocene dichloride (Cp₂MoCl₂) with the modified cyclodextrins (CDs) heptakis-2,3,6-tri-O-methyl-β-CD (TRIMEB) and 2-hydroxypropyl-β-CD (HPβCD) in aqueous solution. The products were isolated by liophilisation and characterised in the solid-state by powder XRD, thermogravimetric analysis, Raman and FTIR spectroscopy, and ¹³C CP MAS NMR spectroscopy. The results are consistent with inclusion of Cp₂MoCl₂, rather than hydrolysis products such as [Cp₂Mo(H₂O)X]⁺ (X = Cl, OH) or [Cp₂Mo(H₂O)₂]²⁺. The pure non-included metallocene Cp₂MoCl₂ and its inclusion compounds with unmodified β-CD, TRIMEB and HPβCD were screened for their potential antiproliferative and cytotoxic activity, in both human cancer and healthy cell lines. Inclusion in CD was found to enhance the cytotoxic effect of Cp₂MoCl₂, with the TRIMEB adduct displaying the highest anti-tumour activity, along with the lowest toxicity towards non-neoplastic cells.     

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.     

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.     

Single cell manipulation, analytics, and label-free protein detection in microfluidic devices for systems nanobiology

Single cell analytics for proteomic analysis is considered a key method in the framework of systems nanobiology which allows a novel proteomics without being subjected to ensemble-averaging, cell-cycle, or cell-population effects. We are currently developing a single cell analytical method for protein fingerprinting combining a structured microfluidic device with latest optical laser technology for single cell manipulation (trapping and steering), free-solution electrophoretical protein separation, and (label-free) protein detection. In this paper we report on first results of this novel analytical device focusing on three main issues. First, single biological cells were trapped, injected, steered, and deposited by means of optical tweezers in a poly(dimethylsiloxane) microfluidic device and consecutively lysed with SDS at a predefined position. Second, separation and detection of fluorescent dyes, amino acids, and proteins were achieved with LIF detection in the visible (VIS) (488 nm) as well as in the deep UV (266 nm) spectral range for label-free, native protein detection. Minute concentrations of 100 fM injected fluorescein could be detected in the VIS and a first protein separation and label-free detection could be achieved in the UV spectral range. Third, first analytical experiments with single Sf9 insect cells (Spodoptera frugiperda) in a tailored microfluidic device exhibiting distinct electropherograms of a green fluorescent protein-construct proved the validity of the concept. Thus, the presented microfluidic concept allows novel and fascinating single cell experiments for systems nanobiology in the future.