Diffusions conditionnelles. II. Générateur conditionnel. Application au filtrage

This paper is a continuation of “Diffusions conditionelles, I.” If (x_t, z_t) is a two-component diffusion process, it is shown that under appropriate conditions, the process x_t (t ? T), given (z_s, s ? T) is a nonhomogeneous strong Markov process, whose generator is explicitly found by using the theory of stochastic flows. The filtering equation is reduced to an ordinary partial differential equation.     

Carbon-13 NMR spectra of some 8,13-diazasteroids and related model isoquinolines

Carbon-13 NMR spectra of some dihydro- and tetrahydro-isoquinolines were studied and applied to the assignments of ¹³C NMR signals of some 8,13-diazasteroids related to the estrone series. Some deuterated compounds were also examined. All signals could be assigned and an important long-range isotopic effect was observed which seems to be due to an interaction between the C? H(D) bond and the nitrogen lone pairs.     

Control problems with time-lag. II

Consider a continuous time Markov chain with stationary transition probabilities. A function of the state is observed. A regular conditional probability distribution for the trajectory of the chain, given observations up to time t, is obtained. This distribution also corresponds to a Markov chain, but the conditional chain has nonstationary transition probabilities. In particular, computation of the conditional distribution of the state at time s is discussed. For s > t, we have prediction (extrapolation), while s < t corresponds to smoothing (interpolation). Equations for the conditional state distribution are given on matrix form and as recursive differential equations with varying s or t. These differential equations are closely related to Kolmogorov's forward and backward equations. Markov chains with one observed and one unobserved component are treated as a special case. In an example, the conditional distribution of the change-point is derived for a Poisson process with a changing intensity, given observations of the Poisson process.     

Cyclodextrin phosphanes as first and second coordination sphere cavitands

The binding properties of two alpha-cyclodextrins, each containing two C(5)-linked "CH(2)PPh(2)" units, L 1 (A,D-substituted) and L 2 (A,C-substituted), have been investigated. Both ligands readily form transition-metal chelate complexes in which the metal centres are immobilised at the cavity entrance. Although diphosphane L 1 displays a marked tendency to behave only as a trans-spanning ligand, the ligand possesses a certain degree of flexibility, for example, allowing the stabilisation of a trigonal silver(I) complex in which the bite angle drops to 143 degrees. Another feature of L 1 concerns its ability to function as an hemilabile ligand. Together with four methoxy groups anchored onto the primary face, the two P(III) centres of L 1 form a circularly arranged P(2)O(4) 12-electron donor set able to complex an Ag(+) ion in a dynamic way, each of the four oxygen atoms coordinating successively to the silver ion. Furthermore, the particular structures of L 1 and L 2, characterised by the presence of P(III) units lying close to the cavity entrance, lead upon complexation to complexes whereby the first coordination sphere is partly entrapped in the cyclodextrin. Thus, when treated with metal chlorides, both ligands systematically produce complexes in which the Mbond;Cl unit is maintained inside the cyclodextrin through weak Cl.H-5 interactions. The chelate complex [Ag(L 1)]BF(4) reacts with acetonitrile in excess to afford a mixture of two equilibrating complexes, [Ag(acetonitrile)(L 1)]BF(4) and [Ag(acetonitrile)(2)(L 1)]BF(4), whose coordinated nitriles lie inside the cyclodextrin cavity. The inner-cavity ligands can be substituted by a benzonitrile molecule. The present study provides the first identification of an [Ag(acetonitrile)(2)(phosphane)(2)](+) ion. The unexpected stabilisation of this species probably rests on a cavity effect, the cyclodextrin walls favouring recombination of the complex after facile dissociation of the nitrile ligands.     

Solid-phase functionalization of peptides by an alpha-hydrazinoacetyl group

A novel procedure for the preparation of alpha-hydrazinoacetyl peptides is reported on the basis of the solid-phase coupling of partially or fully Boc-protected hydrazino acetic acid derivatives. The degree of unwanted polymerization of the activated ester during both activation and coupling was found to be significant for the monoprotected derivative BocNHNHCH(2)CO(2)H but could be minimized with the diprotected derivative BocNHNH(Boc)CH(2)CO(2)H and suppressed with the fully protected acid. Despite the instability of the imidocarbonate group toward acids and bases, a low-cost and effective route was sought for the preparation of the tris(Boc)-protected derivative. The N,N,N'-tris(Boc)hydrazinoacetic acid could be introduced on the solid phase after or before peptide elongation using Fmoc/tert-butyl chemistry. In this latter case, HR MAS NMR analysis of model solid supports demonstrated the partial loss of one Boc group during the repetitive piperidine treatments. Despite this slight instability, N,N,N'-tris(Boc)hydrazinoacetic acid was found to be a highly convenient reagent for the robust and easily scalable preparation of hydrazinopeptides in good yield and high purity.     

Water Sorption Controls Extreme Single-Crystal-to-Single-Crystal Molecular Reorganization in Hydrogen Bonded Organic Frameworks

As hydrogen bonded frameworks are held together by relatively weak interactions, they often form several different frameworks under slightly different synthesis conditions and respond dynamically to stimuli such as heat and vacuum. However, these dynamic restructuring processes are often poorly understood. In this work, three isoreticular hydrogen bonded organic frameworks assembled through charge-assisted amidinium⋅⋅⋅carboxylate hydrogen bonds ( 1^C/C , 1^Si/C and 1^Si/Si ) are studied. Three distinct phases for 1^C/C and four for 1^Si/C and 1^Si/Si are fully structurally characterized. The transitions between these phases involve extreme yet recoverable molecular-level framework reorganization. It is demonstrated that these transformations are related to water content and can be controlled by humidity, and that the non-porous anhydrous phase of 1^C/C shows reversible water sorption through single crystal to crystal restructuring. This mechanistic insight opens the way for the future use of the inherent dynamism present in hydrogen bonded frameworks.     

Observation of CH⋅⋅⋅π Interactions between Methyl and Carbonyl Groups in Proteins

Protein structure and function is dependent on myriad noncovalent interactions. Direct detection and characterization of these weak interactions in large biomolecules, such as proteins, is experimentally challenging. Herein, we report the first observation and measurement of long-range “through-space” scalar couplings between methyl and backbone carbonyl groups in proteins. These J couplings are indicative of the presence of noncovalent C−H⋅⋅⋅π hydrogen-bond-like interactions involving the amide π network. Experimentally detected scalar couplings were corroborated by a natural bond orbital analysis, which revealed the orbital nature of the interaction and the origins of the through-space J couplings. The experimental observation of this type of CH⋅⋅⋅π interaction adds a new dimension to the study of protein structure, function, and dynamics by NMR spectroscopy.