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.     

Recent developments in the synthesis of 11β-aryl-estrone derivatives

An industrial synthesis of 11β-aryl-estrone derivatives is described, based on the 1,4-addition of the aryl side-chain, as a cuprate, on to a mixture of allylic 5(10) alpha and beta epoxides, followed by hydrolysis and subsequent aromatization.     

FT–IR microspectroscopy study of blends of ester functionalized ethylene–propylene copolymer with (vinylidene fluoride-hexafluoropropene) elastomer

An ethylene—propylene (EPR) copolymer functionalized with (1,2-dicarboethoxy)ethyl groups has been blended with a vinylidene fluoride—hexafluropropene elastomer (NML). The existence of intermolecular interactions involving mainly the carbonyl groups of the side chains of the functionalized copolymer and the methylene hydrogens of the fluoroelastomer through hydrogen bonding was shown by means of FT—IR spectroscopy. The structure and composition of some microdomains in the mixture was examined by means of FT—IR microspectroscopy.     

1-Arylsulfonylamino-1,2,3-triazole derivatives from functionalyzed 1,2-cyclohexanediones

The heterocyclization reaction of arylsulfonylhydrazones from alkyl substituted 1,2-cyclohexanediones is sensitive to the steric requirements of the alkyl groups. A mechanism for the cyclization in acidic medium is also reported.     

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.     

X-ray structure and circular dichroism of pure rotamers of bis[guanosine-5'-monophosphate(-1)](N,N,N',N'-tetramethylcyclohexyl-1,2-diamine)platinum(II) complexes that have R,R and S,S configurations at the asymmetric diamine

The use of a sterically hindered diamine ligand (Me(4)DACH) has allowed for the first time, the isolation and characterization, both in the solid state (X-ray crystallography) and in solution (circular dichroism), of pure DeltaHT rotamers of [Pt(Me(4)dach)(5'-GMP)(2)] (compounds 1 and 2 for R,R and S,S configurations of the Me(4)DACH ligand, respectively). Comparison of the CD spectra obtained for each rotamer, which differ only in the chirality of the Me(4)DACH ligand (R,R or S,S) or in the chirality of the HT conformation (Delta or Lambda), allowed us to conclude that, in the 200-350 nm range, the contributions to the overall CD spectrum that stem from diamine chirality and diamine-induced chirality of platinum d--d transitions or from sugar chirality are negligible relative to the exciton chiral coupling that occurs for pi-pi* transitions of the cis guanines. Accurate molecular structures of 1.10 D(2)O and 2.14 D(2)O (conventional crystallographic agreement indexes R(1) convergent to 2.07 % and 2.18 %, respectively) revealed that the crystallized rotamers have a DeltaHT conformation that is in agreement with all previously reported X-ray structures of [Pt(diamine)(nucleos(t)ide)(2)] complexes. This conformation allows the 5'-phosphate to be located in proximity to the Me(4)DACH ligand so that (P)O...HC(N) hydrogen-bond interactions exists in both complexes. For both structures, the canting of the guanine planes on the coordination plane is right-handed (R; canting angle (Phi) of 80.9 degrees and 73.2 degrees, respectively); this indicates that the canting direction is driven by the HT conformation chirality (Delta for both compounds) and not by the chirality of the carrier ligand (different for the two compounds). Density functional theory analysis of the conformational space as a function of Phi indicated a good agreement between the computed and experimental structures. The increase in energy for Phi values below 65 degrees and 55 degrees (for 1 and 2, respectively) is mainly due to the short intramolecular contacts between C(8)H and the cis N-Me groups on the same side of the platinum coordination plane.