Fluorinated NH-iminophosphonates and iminocarboxylates: novel synthons for the preparation of biorelevant α-aminophosphonates and carboxylates

A convenient synthetic approach to previously unknown N–H α-iminophosphonates and iminotrifluoropropionates was developed. The synthetic potential of N–H iminophosphonates and iminotrifluoropropionates, existing as an equilibrium mixture of E/Z-isomers, was demonstrated by their easy functionalization to afford biorelevant fluorinated α-aminophosphonic and α-aminocarboxylic acid derivatives.     

Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces

We use methods of harmonic analysis and group representation theory to study the spectral properties of the abstract parabolic operator \({\mathcal{L} = -{\rm d}/{\rm d}t + A}\) in homogeneous function spaces. We provide sufficient conditions for invertibility of such operators in terms of the spectral properties of the operator A and the semigroup generated by A. We introduce a homogeneous space of functions with absolutely summable spectrum and prove a generalization of the Gearhart–Prüss Theorem for such spaces. We use the results to prove existence and uniqueness of solutions of a certain class of non-linear equations.     

Measurable dynamics of maps on profinite groups

We study the measurable dynamics of transformations on profinite groups, in particular of those which factor through sufficiently many of the projection maps; these maps generalize the 1-Lipschitz maps on _p.     

Calculated chemical shifts as a fine tool of conformational analysis: an unambiguous solution for haouamine alkaloids

In this study, for the first time, conformational analysis by calculated chemical shifts (CCS) deals with a real conformational problem of a large biomolecule. This new methodology is applied to haouamine A, which is much more stereodynamically puzzled than the small models used to validate previous CCS-based conformational studies. Thorough NMR experiments by Zubia et al. on this exotic polyfunctional paracyclophane alkaloid could not determine which experimentally detected interconversion of this compound occurs in solution, rotation or N-inversion. The present study uses CCS to locate the lowest energy conformers and thus to identify the observed stereodynamic process. Molecular mechanics calculations were used to explore the conformational space of this polycyclic system, and then the geometry of located conformers was refined by ab initio calculations at the B3LYP/6-31G(d,p) level; an implicit model for acetone solution was employed. Calculated relative energies are considered too inaccurate to identify the lowest energy (i.e., those detectable by NMR) conformers. Instead, rational regression analysis of CCS for carbon atoms using B3LYP/6-31+G(d)//GIAO-based calculations singled out two conformers from a large set of alternative low energy structures, although solvation shell was not explicitly included in the model. For only these two conformers, the differences in CCS (Delta delta) for selected pairs of carbons are very similar to the experimental Delta delta values. Thus, the conformers monitored by NMR have now been identified; their piperideine ring is of (1)Sf and Sf 1 (sofa-shaped) geometry. This azacycle appears to be flexible despite the presence of the ethylenebiphenylene bridge in haouamines. Interconversion between the conformers probably occurs via a concerted process of inversion of the piperideine ring, N-inversion coupled with rotation around the C-N bond, and rotation around two C-C bonds in the ethylenebiphenylene bridge. This CCS method of conformational analysis is sufficiently simple and reliable that if chemical shifts for a pair of the same carbons are sufficiently different in routine (13)C NMR spectra of stereoisomers (ca. > or = 2 ppm), the "resolving power" of the CCS technique may rival that of NMR techniques.     

Spatial fluctuations affect the dynamics of motor proteins

Motor proteins are active biological molecules that perform their functions by converting chemical energy into mechanical work. They move unidirectionally along rigid protein filaments or DNA and RNA molecules in discrete steps by hydrolyzing ATP (adenosine triphsophate) or related energy-rich compounds. Recent single-molecule experiments have shown that motor proteins experience significant spatial fluctuations during its motion, leading to broad step-size distributions. The effect of these spatial fluctuations is analyzed explicitly by considering discrete-state stochastic models that allow us to compute exactly all dynamic properties. It is shown that for symmetric spatial fluctuations there is no change in mean velocities for weak external forces, while dispersions and stall forces are strongly affected at all conditions. These results are illustrated by several simple examples. Our method is also applied to analyze the effect of step-size fluctuations on dynamics of myosin V motor proteins. It is argued that spatial fluctuations might be used to control and regulate the dynamics of motor proteins.     

Modified coulomb law in a strongly magnetized vacuum

We study the electric potential of a charge placed in a strong magnetic field B>B(0) approximately 4.4x10(13) G, as modified by the vacuum polarization. In such a field the electron Larmour radius is much less than its Compton length. At the Larmour distances a scaling law occurs, with the potential determined by a magnetic-field-independent function. The scaling regime implies short-range interaction, expressed by the Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across B faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit B = infinity, the modified potential becomes the Dirac delta function plus a regular background. With this potential the ground-state energy is finite--the best pronounced effect of the vacuum polarization.     

A delicate universe: compactification obstacles to D-brane inflation

We investigate whether explicit models of warped D-brane inflation are possible in string compactifications. To this end, we study the potential for D3-brane motion in a warped conifold that includes holomorphically embedded D7-branes involved in moduli stabilization. The presence of the D7-branes significantly modifies the inflaton potential. We construct an example based on a very simple and symmetric embedding due to Kuperstein, z1= const, in which it is possible to fine-tune the potential so that slow-roll inflation can occur. The resulting model is rather delicate: inflation occurs in the vicinity of an inflection point, and the cosmological predictions are extremely sensitive to the precise shape of the potential.     

Optimal separation sequence for three-component mixtures

In this paper, the problem of finding the optimal separation sequence for a three-component mixture in a cascade of two binary separation stages is considered. The minimal energy that is needed for a separation in a two-stage mechanical separation subject to a given flow rate of the input mixture is obtained. Optimization is achieved by selecting the optimal sequence of binary separations and by distributing mass-exchange surfaces between separation stages optimally. For a heat-driven two-stage separation system, it is shown that the rate of flow of the input mixture cannot be higher than some bound. This bound (the maximal possible rate of heat-driven separation) and the separation sequence when it is achieved are derived.     

Visualization of different pathways of DNA release from interpolyelectrolyte complex

The release of double-stranded DNA from its interpolyelectrolyte complex with positively charged poly(allylamine hydrochloride) via exchange reaction with added polyanion, poly(sodium styrenesulfonate), is directly observed by fluorescence microscopy. It is shown that the pathways of DNA release depend essentially on the amount of added low-molecular-weight salt. At low salt content, the DNA release proceeds via the formation of an intermediate "beads-on-string" structure, whereas at high salt content the release goes directly from globule to coil states without any intermediate structures. The reasons for different character of DNA release are discussed.