Forces along Equidistant Particle Paths

Two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force acting between the particles. On the other hand, if particles travel at the same speed (initially parallel) along geodesics in the hyperbolic plane, then the particle paths diverge. Imagine two particles in the hyperbolic plane that are bound together at a constant distance with their center of mass traveling along a geodesic path at a constant velocity, then the force due to the curvature of the space acts to break the bond and increases as a quadratic function of the velocity. We consider this problem for the sphere and the hyperbolic plane and we give the exact formula for the apparent force between the particles. This revised version was published online in July 2006 with corrections to the Cover Date.     

Wavelength dependent photo-controlled differential release of compounds from solid phase resin

A method to effect photo-mediated differential release of bead-based compound libraries using a tuneable laser in combination with chromatically orthogonal photolabile linkers is described.     

Submanifolds of the Cayley projective plane with bounded second fundamental form

We consider totally complex submanifolds of the Cayley projective plane with estimates on the length squared of the second fundamental form. We determine those bounds for which the second fundamental form is parallel and for which the submanifold is totally geodesic. The case of totally real submanifolds is also included.     

Besicovitch triangles cover unit arcs

A long standing conjecture is that the Besicovitch triangle, i.e., an equilateral triangle with side is a worm-cover. We will show that indeed there exists a class of isosceles triangles, that includes the above equilateral triangle, where each triangle from the class is a worm-cover. These triangles are defined so that the shortest symmetric z-arc stretched from side to side and touching the base would have length one.      

Intramolecular radical additions to pyridines

Intramolecular 6-exolendo-trig and 5-exo-trig cyclisations of aryl radical intermediates to the alpha-, beta- and gamma-carbons of pyridine have been shown to be facile processes at neutral pH. The tether conjoining the radical donor to the pyridine plays an important role in determining the outcome of the reaction. When a Z-alkene is used as a tether, ortho-cyclisation proceeds in good yield. A more complex course is followed when a saturated two carbon tether is employed, leading to products derived from hydrogen atom abstraction, ipso-cyclisation and ortho-cyclisation pathways. All attempts to effect 5-exolendo-trig cyclisations failed. Tributyltin hydride, tris(trimethylsilyl)silane, tris(trimethylsilyl)germane and, in part, samarium(II) iodide can each be employed as mediators of the reaction.     

Monitoring viral DNA release with capillary electrophoresis

Viral DNA injection into host cells is one of the primary mechanisms of viral propagation. Drug development that targets viral propagation requires fast and sensitive methods for monitoring the release of viral DNA in vitro. Here we demonstrate the use of capillary electrophoresis (CE) for monitoring DNA release from virus particles. As a model for this study, we used T5 bacteriophages that infect the bacterium Escherichia coli K-12 by binding to the outer membrane FhuA receptor and then injecting DNA. DNA release from the T5 phages in vitro was induced by either elevated temperature or by interaction with the purified FhuA receptor. After DNA release, the viral samples were stained with the high affinity fluorescent dye YOYO-1, injected into the capillary and subjected to electrophoresis. YOYO-1-stained DNA generated a well-defined peak, allowing reliable detection of viral DNA from as few as 10(5) viral particles. The staining to track T5 phage DNA release exemplifies the great versatility that CE offers in studying viral systems. This CE-based method can be used to study molecular mechanisms of viral infections and to evaluate anti-viral drug candidates.