Effects of Kinks on DNA Elasticity

We study the elastic response of a worm-like polymer chain with reversible kink-like structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of trans-gauche rotations in the backbone of the single-stranded DNA. The problem is solved both analytically and numerically by generalizing the well-known analogy to the Quantum Rotator. In the small stretching force regime, we find that the persistence length is renormalized due to the presence of the kinks. In the opposite regime, the response to the strong stretching is determined solely by the bare persistence length with exponential corrections due to the ``ideal gas of kinks''. This high-force behavior changes significantly in the limit of high bending rigidity of the chain. In that case, the leading corrections to the mechanical response are likely to be due to the formation of multi-kink structures, such as kink pairs.Comment: v1: 16 pages, 7 figures, LaTeX; submitted to Physical Review E; v2: a new subsection on soft kinks added to section Theory, sections Introduction and Conclusions expanded, references added, other minor changes; v3: a reference adde

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.Comment: 11 pages, 2 figure

Universal Formulae for Percolation Thresholds

A power law is postulated for both site and bond percolation thresholds. The formula writes $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are found to belong to only three universality classes. For first two classes $b=0$ for site dilution while $b=a$ for bond dilution. The last one associated to high dimensions is characterized by $b=2a-1$ for both sites and bonds. Classes are defined by a set of value for $\{p_0; \ a\}$. Deviations from available numerical estimates at $d \leq 7$ are within $\pm 0.008$ and $\pm 0.0004$ for high dimensional hypercubic expansions at $d \geq 8$. The formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include

Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Competition for hydrogen bond formation in the helix-coil transition and protein folding

The problem of the helix-coil transition of biopolymers in explicit solvents, like water, with the ability for hydrogen bonding with solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds. The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure; and underscores the advantage of pulling experiments for studies of DNA. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.Comment: 21 pages, 3 figures, submitted to Phys Rev

Charge renormalization and phase separation in colloidal suspensions

We explore the effects of counterion condensation on fluid-fluid phase separation in charged colloidal suspensions. It is found that formation of double layers around the colloidal particles stabilizes suspensions against phase separation. Addition of salt, however, produces an instability which, in principle, can lead to a fluid-fluid separation. The instability, however, is so weak that it should be impossible to observe a fully equilibrated coexistence experimentally.Comment: 7 pages, Europhysics Letters (in press

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

Molecular Dynamics Study of Orientational Cooperativity in Water

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower then expected (with relaxation time $>$ 50 ns) [D. P. Shelton, Phys. Rev. B {\bf 72}, 020201(R) (2005)]. Molecular dynamics simulations of SPC/E water show large vortex-like structure of dipole field at ambient conditions surviving over 300 ps [J. Higo at al. PNAS, {\bf 98} 5961 (2001)]. Both results disagree with previous results on water dipoles in similar conditions, for which autocorrelation times are a few ps. Motivated by these recent results, we study the water dipole reorientation using molecular dynamics simulations in bulk SPC/E water for temperatures ranging from ambient 300 K down to the deep supercooled region of the phase diagram at 210 K. First, we calculate the dipole autocorrelation function and find that our simulations are well-described by a stretched exponential decay, from which we calculate the {\it orientational autocorrelation time} $\tau_{a}$. Second, we define a second characteristic time, namely the time required for the randomization of molecular dipole orientation, the {\it self-dipole randomization time} $\tau_{r}$, which is an upper limit on $\tau_{a}$; we find that $\tau_{r}\approx 5 \tau_{a}$. Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time $\tau_{\rm box}$ of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge $L_{\rm box}$. We find that the {\it site-dipole randomization time} $\tau_{\rm box}\approx 2.5 \tau_{a}$ for $L_{\rm box}\approx 3$\AA, i.e. it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low $T$.Comment: 25 Pages, 10 figure

Unicyclic Components in Random Graphs

The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition. At the gelation point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a result, the total number of unicyclic components grows logarithmically with the system size.Comment: 4 pages, 2 figure