How molecular knots can pass through each other

We propose a mechanism in which two molecular knots pass through each other and swap positions along a polymer strand. Associated free energy barriers in our simulations only amount to a few $k_{B}T$, which may enable the interchange of knots on a single DNA strand.Comment: 6 pages, 7 figure

The Nature of the H2-Emitting Gas in the Crab Nebula

Understanding how molecules and dust might have formed within a rapidly expanding young supernova remnant is important because of the obvious application to vigorous supernova activity at very high redshift. In previous papers, we found that the H2 emission is often quite strong, correlates with optical low-ionization emission lines, and has a surprisingly high excitation temperature. Here we study Knot 51, a representative, bright example, for which we have available long slit optical and NIR spectra covering emission lines from ionized, neutral, and molecular gas, as well as HST visible and SOAR Telescope NIR narrow-band images. We present a series of CLOUDY simulations to probe the excitation mechanisms, formation processes and dust content in environments that can produce the observed H2 emission. We do not try for an exact match between model and observations given Knot 51's ambiguous geometry. Rather, we aim to explain how the bright H2 emission lines can be formed from within the volume of Knot 51 that also produces the observed optical emission from ionized and neutral gas. Our models that are powered only by the Crab's synchrotron radiation are ruled out because they cannot reproduce the strong, thermal H2 emission. The simulations that come closest to fitting the observations have the core of Knot 51 almost entirely atomic with the H2 emission coming from just a trace molecular component, and in which there is extra heating. In this unusual environment, H2 forms primarily by associative detachment rather than grain catalysis. In this picture, the 55 H2-emitting cores that we have previously catalogued in the Crab have a total mass of about 0.1 M_sun, which is about 5% of the total mass of the system of filaments. We also explore the effect of varying the dust abundance. We discuss possible future observations that could further elucidate the nature of these H2 knots.Comment: 51 pages, 15 figures, accepted for publication in MNRAS, revised Figure 12 results unchange

Geometric Knot Spaces and Polygonal Isotopy

The space of n-sided polygons embedded in three-space consists of a smooth manifold in which points correspond to piecewise linear or ``geometric'' knots, while paths correspond to isotopies which preserve the geometric structure of these knots. The topology of these spaces for the case n = 6 and n = 7 is described. In both of these cases, each knot space consists of five components, but contains only three (when n = 6) or four (when n = 7) topological knot types. Therefore ``geometric knot equivalence'' is strictly stronger than topological equivalence. This point is demonstrated by the hexagonal trefoils and heptagonal figure-eight knots, which, unlike their topological counterparts, are not reversible. Extending these results to the cases n \ge 8 is also discussed.Comment: AMS LaTeX, 23 pages, 14 figures, 1 table; submitted to Journal of Knot Theory and its Ramifications, and to Proceedings of the International Knot Theory Meeting (Knots in Hellas 1998), Delphi, Greece, 7 - 15 August 1998. Also available from http://www.williams.edu/Mathematics/jcalvo/abstract.htm

Single DNA conformations and biological function

From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-looping may be related to the efficiency of the target search process of proteins for their specific binding site on the DNA molecule. And we dwell on the spontaneous formation of intermittent DNA nanobubbles and their importance for biological processes, such as transcription initiation. The physical properties of DNA may indeed turn out to be particularly suitable for the use of DNA in nanosensing applications.Comment: 53 pages, 45 figures. Slightly revised version of a review article, that is going to appear in the J. Comput. Theoret. Nanoscience; some typos correcte

Extreme radio-wave scattering associated with hot stars

We use data on extreme radio scintillation to demonstrate that this phenomenon is associated with hot stars in the solar neighbourhood. The ionized gas responsible for the scattering is found at distances up to 1.75pc from the host star, and on average must comprise 1.E5 distinct structures per star. We detect azimuthal velocities of the plasma, relative to the host star, up to 9.7 km/s, consistent with warm gas expanding at the sound speed. The circumstellar plasma structures that we infer are similar in several respects to the cometary knots seen in the Helix, and in other planetary nebulae. There the ionized gas appears as a skin around tiny molecular clumps. Our analysis suggests that molecular clumps are ubiquitous circumstellar features, unrelated to the evolutionary state of the star. The total mass in such clumps is comparable to the stellar mass.Comment: 9 pages, 1 figure, to appear in Ap