Stretching of a single-stranded DNA: Evidence for structural transition

Recent experiments have shown that the force-extension (F-x) curve for single-stranded DNA (ssDNA) consisting only of adenine [poly(dA)] is significantly different from thymine [poly(dT)]. Here, we show that the base stacking interaction is not sufficient to describe the F-x curves as seen in the experiments. A reduction in the reaction co-ordinate arising from the formation of helix at low forces and an increase in the distance between consecutive phosphates of unstacked bases in the stretched state at high force in the proposed model, qualitatively reproduces the experimentally observed features. The multi-step plateau in the F-x curve is a signature of structural change in ssDNA.Comment: 10 pages, 4 figure

Stretching an heteropolymer

We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between successive segments induces a change in the elongation versus force characteristics, and this change can be well described by a simple renormalisation of the elastic constant. The effective coupling constant is computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur

Size, shape, and flexibility of RNA structures

Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of RNA in the Protein Data Bank we find that the size of the folded RNA structures, measured using the radius of gyration, $R_G$, follows the Flory scaling law, namely, $R_G =5.5 N^{1/3}$ \AA where N is the number of nucleotides. The shape of RNA molecules is characterized by the asphericity $\Delta$ and the shape $S$ parameters that are computed using the eigenvalues of the moment of inertia tensor. From the distribution of $\Delta$, we find that a large fraction of folded RNA structures are aspherical and the distribution of $S$ values shows that RNA molecules are prolate ($S>0$). The flexibility of folded structures is characterized by the persistence length $l_p$. By fitting the distance distribution function $P(r)$ to the worm-like chain model we extracted the persistence length $l_p$. We find that $l_p\approx 1.5 N^{0.33}$ \AA. The dependence of $l_p$ on $N$ implies the average length of helices should increases as the size of RNA grows. We also analyze packing in the structures of ribosomes (30S, 50S, and 70S) in terms of $R_G$, $\Delta$, $S$, and $l_p$. The 70S and the 50S subunits are more spherical compared to most RNA molecules. The globularity in 50S is due to the presence of an unusually large number (compared to 30S subunit) of small helices that are stitched together by bulges and loops. Comparison of the shapes of the intact 70S ribosome and the constituent particles suggests that folding of the individual molecules might occur prior to assembly.Comment: 28 pages, 8 figures, J. Chem. Phys. in pres

The Yamabe invariant for axially symmetric two Kerr black holes initial data

An explicit 3-dimensional Riemannian metric is constructed which can be interpreted as the (conformal) sum of two Kerr black holes with aligned angular momentum. When the separation distance between them is large we prove that this metric has positive Ricci scalar and hence positive Yamabe invariant. This metric can be used to construct axially symmetric initial data for two Kerr black holes with large angular momentum.Comment: 14 pages, 2 figure

A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

A variational principle for stationary, axisymmetric solutions of Einstein's equations

Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.Comment: 21 page

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

Stretching Semiflexible Polymer Chains: Evidence for the Importance of Excluded Volume Effects from Monte Carlo Simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence of excluded volume interactions, the persistence length $\ell_p$ of the polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b= \exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing, and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$ are varied over a wide range $(0.005 \leq q_b \leq 1, \; N \leq 50000$), and also a stretching force $f$ is applied to one chain end (fixing the other end at the origin). In the absence of this force, in $d=2$ a single crossover from rod-like behavior (for contour lengths less than $\ell_p$) to swollen coils occurs, invalidating the Kratky-Porod model, while in $d=3$ a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in $d=2$, while theories based on the Kratky-Porod model are found to work in $d=3$ for stiff chains in an intermediate regime of chain extensions. While for $q_b \ll 1$ in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g. bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.Comment: 23 pages, 17 figures, 2 tables, to be published in J. Chem. Phys. (2011

On the existence of initial data containing isolated black holes

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX

The Effects of Stacking on the Configurations and Elasticity of Single Stranded Nucleic Acids

Stacking interactions in single stranded nucleic acids give rise to configurations of an annealed rod-coil multiblock copolymer. Theoretical analysis identifies the resulting signatures for long homopolynucleotides: A non monotonous dependence of size on temperature, corresponding effects on cyclization and a plateau in the extension force law. Explicit numerical results for poly(dA) and poly(rU) are presented.Comment: 4 pages and 2 figures. Accepted in Phys. Rev. E Rapid Com