On the origin of the unusual behavior in the stretching of single-stranded DNA

Force extension curves (FECs), which quantify the response of a variety of biomolecules subject to mechanical force ($f$), are often quantitatively fit using worm-like chain (WLC) or freely-jointed chain (FJC) models. These models predict that the chain extension, $x$, normalized by the contour length increases linearly at small $f$ and at high forces scale as $x \sim (1 - f^{-\alpha})$ where $\alpha$= 0.5 for WLC and unity for FJC. In contrast, experiments on ssDNA show that over a range of $f$ and ionic concentration, $x$ scales as $x\sim\ln f$, which cannot be explained using WLC or FJC models. Using theory and simulations we show that this unusual behavior in FEC in ssDNA is due to sequence-independent polyelectrolyte effects. We show that the $x\sim \ln f$ arises because in the absence of force the tangent correlation function, quantifying chain persistence, decays algebraically on length scales on the order of the Debye length. Our theory, which is most appropriate for monovalent salts, quantitatively fits the experimental data and further predicts that such a regime is not discernible in double stranded DNA.Comment: Accepted for publication in JC

Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing

We show that Kramers rate theory gives a straightforward, accurate estimate of the closing time $\tau_c$ of a semiflexible polymer that is valid in cases of physical interest. The calculation also reveals how the time scales of chain relaxation and closing are intertwined, illuminating an apparent conflict between two ways of calculating $\tau_c$ in the flexible limit.Comment: Europhys. Lett., 2003 (in press). 8 pages, 3 figures. See also, physics/0101087 for physicist's approach to and the importance of semiflexible polymer looping, in DNA replicatio

Stretching Homopolymers

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {{sufficiently large}} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $\sim f$ for small $f$, and $\sim f^{{2/3}}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for \la Z\ra as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {{We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.Comment: 24 pages, 7 figure

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

Molecular dynamics of folding of secondary structures in Go-type models of proteins

We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic aminoacid-aminoacid potential is Lennard Jones for the native contacts and a soft repulsion for the non-native contacts. The interactions are chosen to make the target secondary structure be the native state of the system. We provide a thorough equilibrium and kinetic characterization of the sequences through the molecular dynamics simulations with the Langevin noise. Models with the steric constraints are found to be better folders and to be more stable, especially in the case of the $\beta$-structures. Phononic spectra for vibrations around the native states have low frequency gaps that correlate with the thermodynamic stability. Folding of the secondary structures proceeds through a well defined sequence of events. For instance, $\alpha$-helices fold from the ends first. The closer to the native state, the faster establishment of the contacts. Increasing the system size deteriorates the folding characteristics. We study the folding times as a function of viscous friction and find a regime of moderate friction with the linear dependence. We also consider folding when one end of a structure is pinned which imitates instantaneous conditions when a protein is being synthesized. We find that, under such circumstances, folding of helices is faster and of the $\beta$-sequences slower.Comment: REVTeX, 14 pages, EPS figures included, JCP in pres

Studies on the seasonal incidence of sugarcane internode borer, Chilo saccariphagus indicus (kapur) in Tamil Nadu, India

Internode borer (INB), Chilo saccariphagus indicus (Kapur) (Lepidoptera: Pyraustidae) is an important pest on sugarcane which inflicts yield loss of about than 45 per cent. Pest surveillance and forecasting is one of the important prerequisite tools in managing such pests. Hence, an attempt was made to study the seasonal incidence of the INB during 2007 and 2008 at Nellikuppam, Tamil Nadu, India. The study revealed that the peak incidence of INB was observed during June-July, which declined thereafter. Higher temperature and deficit or failure of rainfall during March –May are considered as the favourable factors for the rise in the incidence of INB

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical Review Letter

Magnetic field stabilization system for atomic physics experiments

Atomic physics experiments commonly use millitesla-scale magnetic fields to provide a quantization axis. As atomic transition frequencies depend on the amplitude of this field, many experiments require a stable absolute field. Most setups use electromagnets, which require a power supply stability not usually met by commercially available units. We demonstrate stabilization of a field of 14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of $\gtrsim$ 100 nT without any stabilization. The rms noise is measured using a field-dependent hyperfine transition in a single $^{43}$Ca$^+$ ion held in a Paul trap at the centre of the magnetic field coils. For the $^{43}$Ca$^+$ "atomic clock" qubit transition at 14.6 mT, which depends on the field only in second order, this would yield a projected coherence time of many hours. Our system consists of a feedback loop and a feedforward circuit that control the current through the field coils and could easily be adapted to other field amplitudes, making it suitable for other applications such as neutral atom traps.Comment: 6 pages, 5 figure