Dynamics of Alpha-Helix Formation in the CSAW Model

We study the folding dynamics of polyalanine (Ala$_{20}$), a protein fragment with 20 residues whose native state is a single alpha helix. We use the CSAW model (conditioned self-avoiding walk), which treats the protein molecule as a chain in Brownian motion, with interactions that include hydrophobic forces and internal hydrogen bonding. We find that large scale structures form before small scale structures, and obtain the relevant relaxation times. We find that helix nucleation occurs at two separate points on the protein chain. The evolution of small and large scale structures involve different mechanisms. While the former can be describe by rate equations governing the growth of helical content, the latter is akin to the relaxation of an elastic solid.Comment: 18 pages, 10 figure

A Simple Model for the DNA Denaturation Transition

We study pairs of interacting self-avoiding walks on the 3d simple cubic lattice. They have a common origin and are allowed to overlap only at the same monomer position along the chain. The latter overlaps are indeed favored by an energetic gain. This is inspired by a model introduced long ago by Poland and Sheraga [J. Chem. Phys. {\bf 45}, 1464 (1966)] for the denaturation transition in DNA where, however, self avoidance was not fully taken into account. For both models, there exists a temperature T_m above which the entropic advantage to open up overcomes the energy gained by forming tightly bound two-stranded structures. Numerical simulations of our model indicate that the transition is of first order (the energy density is discontinuous), but the analog of the surface tension vanishes and the scaling laws near the transition point are exactly those of a second order transition with crossover exponent \phi=1. Numerical and exact analytic results show that the transition is second order in modified models where the self-avoidance is partially or completely neglected.Comment: 29 pages, LaTeX, 20 postscript figure

Unfolding Rates for the Diffusion-Collision Model

In the diffusion-collision model, the unfolding rates are given by the likelihood of secondary structural cluster dissociation. In this work, we introduce an unfolding rate calculation for proteins whose secondary structural elements are $\alpha$-helices, modeled from thermal escape over a barrier which arises from the free energy in buried hydrophobic residues. Our results are in good agreement with currently accepted values for the attempt rate.Comment: Shorter version of cond-mat/0011024 accepted for publication in PR

Theory of High-Force DNA Stretching and Overstretching

Single molecule experiments on single- and double stranded DNA have sparked a renewed interest in the force-extension of polymers. The extensible Freely Jointed Chain (FJC) model is frequently invoked to explain the observed behavior of single-stranded DNA. We demonstrate that this model does not satisfactorily describe recent high-force stretching data. We instead propose a model (the Discrete Persistent Chain, or ``DPC'') that borrows features from both the FJC and the Wormlike Chain, and show that it resembles the data more closely. We find that most of the high-force behavior previously attributed to stretch elasticity is really a feature of the corrected entropic elasticity; the true stretch compliance of single-stranded DNA is several times smaller than that found by previous authors. Next we elaborate our model to allow coexistence of two conformational states of DNA, each with its own stretch and bend elastic constants. Our model is computationally simple, and gives an excellent fit through the entire overstretching transition of nicked, double-stranded DNA. The fit gives the first values for the elastic constants of the stretched state. In particular we find the effective bend stiffness for DNA in this state to be about 10 nm*kbt, a value quite different from either B-form or single-stranded DNAComment: 33 pages, 11 figures. High-quality figures available upon reques

Exotic trees

We discuss the scaling properties of free branched polymers. The scaling behaviour of the model is classified by the Hausdorff dimensions for the internal geometry: d_L and d_H, and for the external one: D_L and D_H. The dimensions d_H and D_H characterize the behaviour for long distances while d_L and D_L for short distances. We show that the internal Hausdorff dimension is d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal two for generic trees and to vary between two and infinity for scale-free trees. We show that the external Hausdorff dimension D_H is directly related to the internal one as D_H = \alpha d_H, where \alpha is the stability index of the embedding weights for the nearest-vertex interactions. The index is \alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for those from the L\'evy domain of attraction. If the dimension D of the target space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter result means that the fractal structure cannot develop in a target space which has too low dimension.Comment: 33 pages, 6 eps figure

Kinetic Arrest in Polyion-Induced Inhomogeneously-Charged Colloidal Particle Aggregation

Polymer chains adsorbed onto oppositely charged spherical colloidal particles can significantly modify the particle-particle interactions. For sufficient amounts of added polymers, the original electrostatic repulsion can even turn into an effective attraction and relatively large kinetically stable aggregates can form which display several unexpected and interesting peculiarities and some intriguing biotechnological implications. The attractive interaction contribution between two oppositely particles arises from the correlated adsorption of polyions at the oppositely charged particle surfaces, resulting in a non-homogeneous surface charge distribution. Here, we investigate the aggregation kinetics of polyion-induced colloidal complexes through Monte Carlo simulation, in which the effect of charge anisotropy is taken into account by a DLVO-like intra-particle potential, as recentely proposed by Velegol and Thwar [D. Velegol and P.K. Thwar, Langmuir, 17, 2001]. The results reveal that in the presence of a charge heterogeneity the aggregation process slows down due to the progressive increase of the potential barrier height upon clustering. Within this framework, the experimentally observed cluster phases in polyelectrolyte-liposomes solutions should be considered as a kinetic arrested state.Comment: 9 pages. 11 figure

Effective interaction between helical bio-molecules

The effective interaction between two parallel strands of helical bio-molecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than $6\AA$ it can be both attractive and repulsive. Furthermore we report a nonmonotonic behaviour of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the bio-molecules is suitably renormalized.Comment: 18 pages, 18 figures included in text, 100 bibliog

A Quantum-mechanical Approach for Constrained Macromolecular Chains

Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been treated by different researchers for decades. QMa address a fundamental issue (constraints versus the uncertainty principle) and are versatile: they also yield classical descriptions (which may not coincide with those from cCHDa, although they may agree for certain relevant quantities). Open issues include whether QMa have enough practical consequences which differ from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special Topics) Vol. 200, pp. 225-258 (2011