A Note on Differentiability in a Markov Chain Market Using Stochastic Flows

Using stochastic flows of diffeomorphisms relating to a Markov chain together with the Itô's differentiation rule, the differentiability of the price of a European-style contingent claim with respect to the underlying state variables is proved in a continuous-time Markov chain market. The differentiability results are also used to calculate the Greeks for hedging.     

Dimethyltin Dichloride-Dibenzyl Sulfoxide, a Compound Crystallizing with Seven Molecules in the Asymmetric Unit

Dimethyltin dichloride-dibenzyl sulfoxide,((CH3)2SnCl2·O=S(CH2C6H5)2),crystallizes in the orthorhombic space group P212121 with a superstructure of dimensions a = 11.9290(1),b = 19.50490(1),c = 55.7390(6) ; Z = 28. The geometry of the five-coordinated tin atom in each of the seven independent adduct molecules is a square pyramid that is displaced towards a cis-trigonal bipyramid; the extent of displacement along the Berry pseudorotation pathway ranges from 20 to 45%.     

Structure‐Based Design of Platinum(II) Complexes as c‐myc Oncogene Down‐Regulators and Luminescent Probes for G‐Quadruplex DNA

A series of platinum(II) complexes with tridentate ligands was synthesized and their interactions with G‐quadruplex DNA within the c‐myc gene promoter were evaluated. Complex 1 , which has a flat planar 2,6‐bis(benzimidazol‐2‐yl)pyridine (bzimpy) scaffold, was found to stabilize the c‐myc G‐quadruplex structure in a cell‐free system. An in silico G‐quadruplex DNA model has been constructed for structure‐based virtual screening to develop new Pt^II‐based complexes with superior inhibitory activities. By using complex 1 as the initial structure for hit‐to‐lead optimization, bzimpy and related 2,6‐bis(pyrazol‐3‐yl)pyridine (dPzPy) scaffolds containing amine side‐chains emerge as the top candidates. Six of the top‐scoring complexes were synthesized and their interactions with c‐myc G‐quadruplex DNA have been investigated. The results revealed that all of the complexes have the ability to stabilize the c‐myc G‐quadruplex. Complex 3 a ([Pt^II L2R ] ⁺ ; L2 =2,6‐bis[1‐(3‐piperidinepropyl)‐1H‐enzo[d]imidazol‐2‐yl]pyridine, R =Cl) displayed the strongest inhibition in a cell‐free system (IC₅₀=2.2 μM ) and was 3.3‐fold more potent than that of 1 . Complexes 3 a and 4 a ([Pt^II L3R ]⁺; L3 =2,6‐bis[1‐(3‐morpholinopropyl)‐1H‐pyrazol‐3‐yl]pyridine, R =Cl) were found to effectively inhibit c‐myc gene expression in human hepatocarcinoma cells with IC₅₀ values of ≈17 μM , whereas initial hit 1 displayed no significant effect on gene expression at concentrations up to 50 μM . Complexes 3 a and 4 a have a strong preference for G‐quadruplex DNA over duplex DNA, as revealed by competition dialysis experiments and absorption titration; 3 a and 4 a bind G‐quadruplex DNA with binding constants (K) of approximately 10⁶–10⁷ dm³ mol^?1, which are at least an order of magnitude higher than the K values for duplex DNA. NMR spectroscopic titration experiments and molecular modeling showed that 4 a binds c‐myc G‐quadruplex DNA through an external end‐stacking mode at the 3′‐terminal face of the G‐quadruplex. Intriguingly, binding of c‐myc G‐quadruplex DNA by 3 b is accompanied by an increase of up to 38‐fold in photoluminescence intensity at λ_max=622 nm.     

A comparison of the fragmentation pathways of [Cu(II)(Ma)(Mb)]•2+ complexes where Ma and Mb are peptides containing either a tryptophan or a tyrosine residue

[Cu^II(M_a)(M_b)]^?2+ complexes, where M_a and M_b are dipeptides or tripeptides each containing either a tryptophan (W) or tyrosine (Y) residue, have been examined by means of electrospray tandem mass spectrometry. Collision‐induced dissociations (CIDs) of complexes containing identical peptides having a tryptophan residue generated abundant radical cations of the peptides; by contrast, for complexes containing peptides having a tyrosine residue, the main fragmentation channel is dissociative proton transfer to give [M_a + H]⁺ and [Cu^II(M_b – H)]^?+. When there are two different peptides in the complex, each containing a tryptophan residue, radical cations are again the major products, with their relative abundances depending on the locations of the tryptophan residue in the peptides. In the CIDs of mixed complexes, where one peptide contains a tryptophan residue and the other a tyrosine residue, the main fragmentation channel is formation of the radical cation of the tryptophan‐containing peptide and not proton transfer from the tyrosine‐containing peptide to give a protonated peptide. Copyright © 2010 John Wiley & Sons, Ltd.     

An Amphiphilic Polymer‐ and Carbon Nanotube‐Modified Indium Tin Oxide Electrode for Sensitive Electrochemical DNA Detection with Low Nonspecific Binding

We herein report an amphiphilic polymer‐, carboxylated multiwalled carbon nanotube (CNT)‐, silane polymer‐, and streptavidin‐modified indium tin oxide (ITO) electrode that allows low nonspecific binding and efficient immobilization of DNA, along with good electrocatalytic activities and low background‐current levels. The low nonspecific binding results from the well‐covering of the CNT and ITO surface with the amphiphilic polymer and silane polymer, as well as the poly(ethylene glycol) groups of the polymers. The streptavidin for DNA immobilization is covalently attached to the carboxylic acid groups of the amphiphilic polymer and CNT. A low surface coverage of CNT on the ITO electrode provides the good electrocatalytic activities and low background‐current levels. The fabricated electrode enables us to achieve a detection limit of 100 pM in DNA detection.     

The extent and effects of peptide sequence scrambling via formation of macrocyclic <Emphasis Type="Italic">b</Emphasis> ions in model proteins

The extent and effects of sequence scrambling in peptide ions during tandem mass spectrometry (MS/MS) have been examined using tryptic peptides from model proteins. Sequencescrambled b ions appeared in about 35% of 43 tryptic peptides examined under MS/MS conditions. In general, these ions had relatively low abundances with averages of 8% and 16%, depending on the instrumentation used. A few tryptic peptides gave abundant scrambled b ions in MS/MS. However, peptide and protein identifications under proteomic conditions with Mascot were not affected, even for these peptides wherein scrambling was prominent. From the 43 tryptic peptides that have been investigated, the conclusion is that sequence scrambling is unlikely to impact negatively on the accuracy of automated peptide and protein identifications in proteomics.     

MR findings of focal eosinophilic liver disease using gadoxetic acid

Purpose

The purpose of this study was to describe magnetic resonance (MR) findings of focal eosinophilic liver disease using gadoxetic acid (Gd-EOB-DTPA).

Materials and Methods

Nineteen patients (M:F=14:5; age range, 26–66 years; mean age, 50 years) with 35 focal eosinophilic liver lesions were included after reviewing the medical records of 482 patients who underwent Gd-EOB-DTPA-enhanced MR imaging (MRI) on a 3.0-T unit between April 2008 and June 2009. The diagnosis of focal eosinophilic liver disease was established by means of percutaneous liver biopsy or surgery and consistent clinical findings. Two radiologists retrospectively reviewed MR images with consensus. Margin, shape and distribution of the lesions were analyzed. We also evaluated signal intensity of focal hepatic lesions on T₁- and T₂-weighted images and patterns of enhancement in dynamic contrast study.

Results

The mean diameter of the lesions was 1.7 cm (range, 0.7–6.1 cm). Most of the focal eosinophilic liver lesions [n=31/35 (88.6%)] had poorly defined margins. They were usually isointense or slightly hypointense [n=34/35 (97.2%)] on T₁-weighted images and hyperintense [n=32/35 (91.4%)] on T₂-weighted images. Dynamic study showed enhancement (rim or homogeneous) on the arterial phase [n=21/35 (60%)] and hypointensity on the late venous phase [n=31/35 (88.6%)]. All the lesions were hypointense on the hepatobiliary phase images.

Conclusion

Focal eosinophilic liver lesions tend to be hyperintense on the arterial phase and hypointense on the late venous phase during dynamic study of Gd-EOB-DTPA-enhanced MRI. Although these findings mimic other focal hepatic lesions, poorly defined margins of the lesions and peripheral eosinophilia might help distinguish focal eosinophilic liver disease from other hepatic lesions.     

Kinetics for tautomerizations and dissociations of triglycine radical cations

Fragmentations of tautomers of the α-centered radical triglycine radical cation, [GGG^•]⁺, [GG^•G]⁺, and [G^•GG]⁺, are charge-driven, giving b-type ions; these are processes that are facilitated by a mobile proton, as in the fragmentation of protonated triglycine (Rodriquez, C. F. et al. J. Am. Chem. Soc. 2001, 123, 3006–3012). By contrast, radical centers are less mobile. Two mechanisms have been examined theoretically utilizing density functional theory and Rice-Ramsperger-Kassel-Marcus modeling: (1) a direct hydrogen-atom migration between two α-carbons, and (2) a two-step proton migration involving canonical [GGG]^•+ as an intermediate. Predictions employing the latter mechanism are in good agreement with results of recent CID experiments (Chu, I. K. et al. J. Am. Chem. Soc. 2008, 130, 7862–7872).     

Direct electrochemistry of cytochrome P450 27B1 in surfactant films

We report the first direct electrochemistry of cytochrome P450 27B1 (CYP27B1) immobilized on an edge-plane pyrolytic graphite (EPG) electrode coated with a film of didodecyldimethylammonium bromide (DDAB). Cyclic voltammetry (CV) in a deoxygenated solution revealed excellent electrochemical reversibility with an average midpoint potential of −180 ± 5 mV vs. Ag/AgCl and an apparent surface coverage of (7.0 ± 2.5) × 10¹³ molecules per cm². The rate of heterogeneous electron transfer between CYP27B1 and the EPG electrode was determined to be 3.5 ± 0.6 s⁻¹. Upon addition of oxygen, a significant increase in cathodic current occurred, likely due to electrocatalytic reduction of dioxygen to peroxide and/or water by CYP27B1. Characterization of the electrochemical properties of CYP27B1 is an important first step toward developing a bioelectrochemical method for measuring vitamin D in serum.     

Ab initio molecular dynamics studies of ionic dissolution and precipitation of sodium chloride and silver chloride in water clusters, NaCl(H2O)n and AgCl(H2O)n, n = 6, 10, and 14

An ab initio molecular dynamics method was used to compare the ionic dissolution of soluble sodium chloride (NaCl) in water clusters with the highly insoluble silver chloride (AgCl). The investigations focused on the solvation structures, dynamics, and energetics of the contact ion pair (CIP) and of the solvent-separated ion pair (SSIP) in NaCl(H(2)O)(n) and AgCl(H(2)O)(n) with cluster sizes of n = 6, 10 and 14. We found that the minimum cluster size required to stabilize the SSIP configuration in NaCl(H(2)O)(n) is temperature-dependent. For n = 6, both configurations are present as two distinct local minima on the free-energy profile at 100 K, whereas SSIP is unstable at 300 K. Both configurations, separated by a low barrier (<10 kJ mol(-1)), are identifiable on the free energy profiles of NaCl(H(2)O)(n) for n = 10 and 14 at 300 K, with the Na(+)/Cl(-) pairs being internally solvated in the water cluster and the SSIP configuration being slightly higher in energy (<5 kJ mol(-1)). In agreement with the low bulk solubility of AgCl, no SSIP minimum is observed on the free-energy profiles of finite AgCl(H(2)O)(n) clusters. The AgCl interaction is more covalent in nature, and is less affected by the water solvent. Unlike NaCl, AgCl is mainly solvated on the surface in finite water clusters, and ionic dissolution requires a significant reorganization of the solvent structure.