Surface hydrophobicity modulates the operation of actomyosin-based dynamic nanodevices

We studied the impact of surface hydrophobicity on the motility of actin filaments moving on heavy-meromyosin (HMM)-coated surfaces. Apart from nitrocellulose (NC), which is the current standard for motility assays, all materials tested are good candidates for microfabrication: hydrophilic and hydrophobic glass, poly(methyl methacrylate) (PMMA), poly(tert-butyl methacrylate) (PtBuMA), and a copolymer of O-acryloyl acetophenone oxime with a 4-acryloyloxybenzophenone (AAPO). The most hydrophilic (hydrophilic glass, contact angle 35 degrees) and the most hydrophobic (PtBuMA, contact angle 78 degrees) surfaces do not maintain the motility of actin filaments, presumably because of the low density of adsorbed HMM protein or its high levels of denaturation, respectively. The velocity of actin filaments presents higher values in the middle of this "surface hydrophobicity motility window" (NC, PMMA), and a bimodal distribution, which is more apparent at the edges of this motility window (hydrophobic glass and AAPO). A molecular surface analysis of HMM and its S1 units suggests that the two very different, temporally separated conformations of the HMM heads could exacerbate the surface-modulated protein behavior, which is common to all microdevices using surface-immobilized proteins. An explanation for the above behavior proposes that the motility of actin filaments on HMM-functionalized surfaces is the result of the action of three populations of motors, each in a different surface-protein conformation, that is, HMM with both heads working (high velocities), working with one head (low velocities), and fully denatured HMM (no motility). It is also proposed that the molecularly dynamic nature of polymer surfaces amplifies the impact of surface hydrophobicity on protein behavior. The study demonstrates that PMMA is a good candidate for the fabrication of future actomyosin-driven dynamic nanodevices because it induces the smoothest motility of individual nano-objects with velocities comparable with those obtained on NC.     

Nonlinear programming with E-preinvex and local E-preinvex functions

In this paper, we extend the class of E-convex sets, E-convex and E-quasiconvex functions introduced by [Youness, E.A., 1999. E-convex sets, E-convex functions and E-convex programming. Journal of Optimization Theory and Applications 102, 439–450], respectively by [Syau, Yu-Ru, Lee, E. Stanley, 2005. Some properties of E-convex functions. Applied Mathematics Letters 18, 1074–1080] to E-invex set, E-preinvex, E-prequasiinvex and corresponding local concepts. Some properties of these classes are studied. As an application of our results, we consider the nonlinear programming problem for which, we establish that, under mild conditions, a local minimum is a global minimum.     

On optimality conditions for multiobjective optimization problems in topological vector space

In this paper, we are concerned with a differentiable multiobjective programming problem in topological vector spaces. An alternative theorem for generalized K subconvexlike mappings is given. This permits the establishment of optimality conditions in this context: several generalized Fritz John conditions, in line to those in Hu and Ling [Y. Hu, C. Ling, The generalized optimality conditions of multiobjective programming problem in topological vector space, J. Math. Anal. Appl. 290 (2004) 363-372] are obtained and, in the presence of the generalized Slater's constraint qualification, the Karush-Kuhn-Tucker necessary optimality conditions.     

A novel approach in cinnamic acid synthesis: direct synthesis of cinnamic acids from aromatic aldehydes and aliphatic carboxylic acids in the presence of boron tribromide

Cinnamic acids have been prepared in moderate to high yields by a new direct synthesis using aromatic aldehydes and aliphatic carboxylic acids, in the presence of boron tribromide as reagent, 4-dimethylaminopyridine (4-DMAP) and pyridine (Py) as bases and N-methyl-2-pyrolidinone (NMP) as solvent, at reflux (180-190 degrees C) for 8-12 hours.