Allosteric effects on substrate dissociation from cytochrome P450 3A4 in nanodiscs observed by ensemble and single-molecule fluorescence spectroscopy

Cytochrome P450 (CYP) 3A4 is a major human drug-metabolizing enzyme and displays pharmacologically relevant allosteric kinetics caused by multiple substrate and/or effector binding. Here, in the first single-molecule (SM) fluorescence studies of CYPs, we use total internal reflection fluorescence microscopy to measure residence times of the fluorescent dye Nile Red in CYP3A4 incorporated in surface-immobilized lipid Nanodiscs, with and without the effector alpha-naphthoflavone. We find direct evidence that CYP3A4 effectors can decrease substrate off-rates, providing a possible mechanism for effector-mediated enhancement of substrate metabolism. These interesting results highlight the potential of SM methods in studies of CYP allosteric mechanisms.     

Cyclic sieving, promotion, and representation theory

We prove a collection of conjectures of White [D. White, personal communication, 2007], as well as some related conjectures of Abuzzahab, Korson, Li, and Meyer [O. Abuzzahab, M. Korson, M. Li, S. Meyer, Cyclic and dihedral sieving for plane partitions, U. Minnesota REU Report, 2005] and of Reiner and White [V. Reiner, personal communication, 2007; D. White, personal communication, 2007], regarding the cyclic sieving phenomenon of Reiner, Stanton and White [V. Reiner, D. Stanton, D. White, The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (2004)] as it applies to jeu-de-taquin promotion on rectangular tableaux. To do this, we use Kazhdan-Lusztig theory and a characterization of the dual canonical basis of C[x₁₁,…,xnn] due to Skandera [M. Skandera, On the dual canonical and Kazhdan-Lusztig bases and 3412, 4231-avoiding permutations, 2006, submitted for publication]. Afterwards, we extend our results to analyzing the fixed points of a dihedral action on rectangular tableaux generated by promotion and evacuation, suggesting a possible sieving phenomenon for dihedral groups. Finally, we give applications of this theory to cyclic sieving phenomena involving reduced words for the long elements of hyperoctohedral groups and noncrossing partitions.     

Fixed and periodic point results in cone metric spaces

Huang and Zhang [L.-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] proved some fixed point theorems in cone metric spaces. In this work we prove some fixed point theorems in cone metric spaces, including results which generalize those from Haung and Zhang’s work. Given the fact that, in a cone, one has only a partial ordering, it is doubtful that their Theorem 2.1 can be further generalized. We also show that these maps have no nontrivial periodic points.     

Fluoroolefins as peptide mimetics: a computational study of structure, charge distribution, hydration, and hydrogen bonding

The design of peptide mimetic compounds is greatly facilitated by the identification of functionalities that can act as peptide replacements. The fluoroalkene moiety has recently been employed for that purpose. The purpose of this work is to characterize prototypical fluoroalkenes (fluoroethylene and 2-fluoro-2-butene) with respect to key properties of peptides (amides) including structure, charge distribution, hydration, and hydrogen bonding. The results are compared to those obtained for model peptides (formamide, N-methylacetamide). Calculations have been carried out at the MP2 and B3LYP levels of theory with the 6-311++G(2d,p) and 6-311++G(2d,2p) basis sets. The results suggest that the fluoroalkene is similar in steric requirements to a peptide bond but that there is less charge separation. Calculations of the hydration free energies with the PCM bulk continuum solvent model indicate that the fluoroalkene has much smaller hydration free energies than an amide but that the difference in solvation free energy for cis and trans isomers is comparable. In studies of complexes with water molecules, the fluoroalkene is found to engage in interactions that are analogous to backbone hydrogen-bonding interactions that govern many properties of natural peptides and proteins but with smaller interaction energies. In addition, key structural differences are noted when the fluoroalkene is playing the role of hydrogen-bond acceptor which may have implications in binding, aggregation, and conformational preferences in fluoroalkene peptidomimetics. The issue of cooperativity in hydrogen-bonding interactions in complexes with multiple waters has also been investigated. The fluoroalkene is found to exhibit cooperative effects that mirror those of the peptide but are smaller in magnitude. Thus, pairwise addivitity of interactions appears to more adequately describe the fluoroalkenes than the peptides they are intended to mimic.     

Lower bounds for some matrices,II

In a series of papers, Rhaly [6]-[8] introduced three classes of matrices which are generalizations of the Cesaro Matrix of order 1. In this paper we obtain lower bounds for these classes, under certain restrictions on p.     

1:1 alternating copolymers of 1-bicyclobutanecarbonitrile with styrene

High molecular weight, 1:1 alternating copolymers of 1-bicyclobutanecarbonitrile with styrene were prepared in tetramethylenesulfone solution by complexing the electron-poor bicyclobutane monomer with zinc chloride. Methyl 1-bicyclobutanecarboxylate under these conditions gave copolymers containing a slight excess of styrene units (ratio 1:1.3 to 1:1.8). High molecular weight homopolymers of 1-bicyclobutanecarbonitrile and of methyl 1-bicyclobutanecarboxylate were prepared similarly. The tendency of the bicyclobutane nitrile to form 1:1 alternating copolymers is as great as that of its vinyl analog, acrylonitrile, and the synthesis of other alternating copolymers from this monomer should be possible.     

Bounded sequence-to-function generalized Hausdorff transformations

Georgakis (1988) obtained the norm of the transformation

considered as an operator from the sequence space , with weights
to , with weight . As corollaries he obtained inequality statements for Borel and generalized Abel transformations. He also obtained the best constants possible for several weighted norm inequalities of Hardy and Littlewood. In this paper Georgakis' results are extended to the Endl generalized Hausdorff matrices.

     

Every conservative double Hausdorff matrix is a kth absolutely summable operator

Let A denote the set of kth absolutely summable double series. In this paper it is shown that every double conservative Hausdorff matrix is a bounded operator on A.