Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Vortex ring generation due to the coalescence of a water drop at a free surface

 Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which the duration of the coalescence process, τ_*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ_*∼σ^-1/2 and τ_*∼L ^3/2. Received: 22 December 1995 / Accepted: 15 October 1996     

Nanoparticles from cationic copolymer and DNA that are soluble and stable in common organic solvents

DNA by virtue of its superlative ability to self-assemble has found use beyond biological research in the design and fabrication of nanomaterials. However, developing novel DNA-based materials for chemical applications might be restricted due to the insoluble nature of DNA in most common organic solvents. In this Communication, we are reporting the first demonstration of making DNA soluble in a variety of nonbiological solvents such as acetonitrile, benzene, dimethyl sulfoxide (DMSO), and tetrahydrofuran with the help of poly(ethylene glycol) (PEG)-based cationic random copolymers. Because of complex formation between cationic copolymer and anionic DNA, nanoparticles are formed. These nanoparticles are expected to exhibit micelle-like structures with a nanometric core of cationic units neutralized by phosphate anions of DNA, surrounded by a shell of PEG segments. As PEG is soluble in the organic solvents used in this study, nanoparticles are stable in these solvents, making entrapped DNA soluble in these organic solvents.     

Low Reynolds Number Interactions between Colloidal Particles near the Entrance to a Cylindrical Pore

The interaction between stable colloidal particles arriving at a pore entrance was studied using a numerical method for the case where the particle size is smaller than but of the same order as the pore size. The numerical method was adapted from a front-tracking technique developed for studying incompressible, multifluid flow by S. O. Unverdi and G. Tryggvason (J. Comp. Phys. 100, 25, 1992). The method is based on the finite difference solution of Navier-Stokes equation on a stationary, structured, Cartesian grid and the explicit representation of the particle-liquid interface using an unstructured grid that moves through the stationary grid. The simulations are in two dimensions, considering both deformable and nondeformable particles, and include interparticle colloidal interactions. The interparticle and particle-pore hydrodynamic interactions, which are very difficult to determine using existing analytical and semi-numerical, semi-analytical techniques in microhydrodynamics, are naturally accounted for in our numerical method and need not be explicity determined. Two- and three-particle motion toward a pore has been considered in our simulations. The simulations demonstrate how the competition between hydrodynamic forces and colloidal forces acting on particles dictate their flow behavior near the pore entrance. The predicted dependence of the particle flow behavior on the flow velocity and the ratio of pore size to particle size are qualitatively consistent with the experimental observations of V. Ramachandran and H. S. Fogler (J. Fluid Mech. 385, 129, 1999). Copyright 2000 Academic Press.     

Synthesis and DNA binding properties of pyrrole amino acid-containing peptides

Dimers of the pyrrole amino acid (Paa), 5-(aminomethyl)pyrrole-2-carboxylic acid, and its derivatives having Lys anchored on N- and C-termini bind in the minor groove of DNA with considerable apparent binding affinities. When the Lys unit is attached to the C-terminus, the resulting ligand binds to ds-DNA with twice the affinity, of the order of 10⁵, than the one carrying two positive charges at the same end.     

Complexes of poly(ethylene glycol)-based cationic random copolymer and calf thymus DNA: a complete biophysical characterization

Complete biophysical characterization of complexes (polyplexes) of cationic polymers and DNA is needed to understand the mechanism underlying nonviral therapeutic gene transfer. In this article, we propose a new series of synthesized random cationic polymers (RCPs) from methoxy poly(ethylene glycol) monomethacrylate (MePEGMA) and (3-(methacryloylamino)propyl)trimethylammonium chloride with different mole ratios (32:68, 11:89, and 6:94) which could be used as a model system to address and answer the basic questions relating to the mechanism of the interaction of calf thymus DNA (CT-DNA) and cationic polymers. The solubility of the complexes of CT-DNA and RCP was followed by turbidity measurements. It has been observed that complexes of RCP with 68 mol % MePEGMA precipitate near the charge neutralization point, whereas complexes of the other two polymers are water-soluble and stable at all compositions. Dnase 1 digestion experiments show that DNA is inaccessible when it forms complexes with RCP. Ethidium bromide exclusion and gel electrophoretic mobility show that both polymers are capable of binding with CT-DNA. Atomic force microscopy images in conjunction with light scattering experiments showed that the complexes are spherical in nature and 75-100 nm in diameter. Circular dichroism spectroscopy studies indicated that the secondary structure of DNA in the complexes is not perturbed due to the presence of poly(ethylene glycol) segments in the polymer. Furthermore, we used a combination of spectroscopic and calorimetric techniques to determine complete thermodynamic profiles accompanying the helix-coil transition of CT-DNA in the complexes. UV and differential scanning calorimetry melting experiments revealed that DNA in the complexes is more stable than in the free state and the extent of stability depends on the polymer composition. Isothermal titration calorimetry experiments showed that the binding of these RCPs to CT-DNA is associated with small exothermic enthalpy changes. A complete thermodynamic profile showed that the RCP/DNA complex formation is entropically favorable. Much broader opportunities to vary the architecture of the polymers studied here make these systems promising in addressing various basic and practical problems in gene delivery systems.     

An affinity-based probe for the proteomic profiling of aspartic proteases

We have developed an affinity-based probe for the proteomic profiling of aspartic proteases. Our probe was shown to be selective towards aspartic proteases over other proteins. It was also shown that the strategy may be used to label selectively aspartic proteases in the presence of a large excess of other proteins, thus making it useful for future proteome profiling experiments.     

Stereoselective Seed-Induced Living Supramolecular Polymerization

Stereoselective and temporally controlled supramolecular polymerizations are ubiquitous in nature and are desirable attributes for the design of chiral, well-defined functional materials. Kinetically controlled, living supramolecular polymerization (LSP) has emerged recently for the synthesis of supramolecular polymers with controlled length and narrow dispersity. On the other hand, stringent design requirements for chiral-discriminating monomers precludes the stereoselective control of the supramolecular polymer structure. Herein, a synergetic stereo- and structural control of supramolecular polymerization by the realization of an unprecedented stereoselective seed-induced LSP is reported. Homochiral and seeded growth is demonstrated with bischromophoric naphthalene diimide (NDI) enantiomers with a chiral binaphthyl amine core, exhibiting strong self-recognition abilities and pathway complexity.