Facilitated diffusion of DNA-binding proteins

The diffusion-controlled limit of reaction times for site-specific DNA-binding proteins is derived from first principles. We follow the generally accepted concept that a protein propagates via two competitive modes, a three-dimensional diffusion in space and a one-dimensional sliding along the DNA. However, our theoretical treatment of the problem is new. The accuracy of our analytical model is verified by numerical simulations. The results confirm that the unspecific binding of protein to DNA, combined with sliding, is capable to reduce the reaction times significantly.Comment: 4 pages, 2 figures Nov 22 2005 - accepted for PR

Scattering functions of knotted ring polymers

We discuss the scattering function of a Gaussian random polygon with N nodes under a given topological constraint through simulation. We obtain the Kratky plot of a Gaussian polygon of N=200 having a fixed knot for some different knots such as the trivial, trefoil and figure-eight knots. We find that some characteristic properties of the different Kratky plots are consistent with the distinct values of the mean square radius of gyration for Gaussian polygons with the different knots.Comment: 4pages, 3figures, 3table

Modeling Bacterial DNA: Simulation of Self-avoiding Supercoiled Worm-Like Chains Including Structural Transitions of the Helix

Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation bubbles and other alternative structures. Various polymer models have been developed to capture these properties, with Monte-Carlo (MC) approaches dedicated to the inference of thermodynamic properties. In this chapter, we explain how to perform such Monte-Carlo simulations, following two objectives. On one hand, we present the self-avoiding supercoiled Worm-Like Chain (ssWLC) model, which is known to capture the folding properties of supercoiled DNA, and provide a detailed explanation of a standard MC simulation method. On the other hand, we explain how to extend this ssWLC model to include structural transitions of the helix.Comment: Book chapter to appear in The Bacterial Nucleoid, Methods and Protocols, Springer serie

Observation of X-rays during heating a pyroelectric crystal by an infrared laser

A pyroelectric X-ray source is proposed, in which a lithium tantalate crystal is heated by an infrared laser with a wavelength of 10.6 μm. X-ray spectra measured during irradiation of the crystal with infrared radiation and during natural cooling of the crystal include characteristic X-ray radiation of atoms contained in the structural parts of the source, as well as bremsstrahlung of electrons with energies above 50 keV. An 8 mm sodium chloride window was used to inject 64 W infrared radiation into a vacuum chamber with the pyroelectric crystal installe

Investigation of neutron generation upon irradiation of deuterated crystalline structures with an electron beam

The possibility of neutron generation by irradiating deuterated crystalline structures with an electron beam with an energy of 20-40 keV was studied. As targets, the deuterated crystalline structures of palladium and textured CVD diamond were used. Measurements of neutron emission are presented, which were carried out by three independent methods-scintillation detectors, counters based on He-3, and track detectors CR-3

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure