Simple model for the DNA denaturation transition

Interstrand distance distribution of DNA near melting

The distance distribution between complementary base pairs of the two strands of a DNA molecule is studied near the melting transition. Scaling arguments are presented for a generalized Poland-Scheraga-type model that includes self-avoiding interactions. At the transition temperature and for a large distance r, the distribution decays as 1/r(kappa) with kappa=1+(c-2)/nu. Here nu is the self-avoiding walk correlation length exponent and c is the exponent associated with the entropy of an open loop in the chain. Results for the distribution function just below the melting point are also presented. Numerical simulations that fully take into account the self-avoiding interactions are in good agreement with the scaling approach.

Unzipping double-stranded DNA with a force: numerical results

A double-stranded DNA molecule pulled with a force acting on the strand terminals exhibits a partially denatured structure or can be completely unzipped when the pulling force goes beyond a critical force. It has been suggested that accompanying the unzipping transition, various power-law properties exist. Through the numerical solution to a model that contains heterogeneous bonding interactions between bases on the two strands, we evaluated the critical forces and the extension-force curves for various degree of sequence disorderliness, and compared the numerical results with predictions from analytical approaches.

Phase diagram for unzipping DNA with long-range interactions

We present a critique and extension of the mean-field approach to the mechanical pulling transition in bound polymer systems. Our model is motivated by the theoretically and experimentally important examples of adsorbed polymers and double-stranded DNA. We focus on the case in which quenched disorder in the sequence of monomers is unimportant for the statistical mechanics, but we include excluded volume interactions between monomers. Our phase diagram for the critical pulling force shows an interesting reentrant phase at low temperatures which should be observable in both disordered and homogenous polymer systems. We also consider the case of nonequilibrium pulling, in which the external force probes the molecule's local, rather than global structure. The dynamics of the pulling transition in such experiments could illuminate the polymer's loop structure, which depends on the nature of excluded volume interactions.

Scaling in DNA unzipping models: denaturated loops and end segments as branches of a block copolymer network

For a model of DNA denaturation, exponents describing the distributions of denaturated loops and unzipped end segments are determined by exact enumeration and by Monte Carlo simulations in two and three dimensions. The loop distributions are consistent with first-order thermal denaturation in both cases. Results for end segments show a coexistence of two distinct power laws in the relative distributions, which is not foreseen by a recent approach in which DNA is treated as a homogeneous network of linear polymer segments. This unexpected feature, and the discrepancies with such an approach, are explained in terms of a refined scaling picture in which a precise distinction is made between network branches representing single-stranded and effective double-stranded segments.

Roles of stiffness and excluded volume in DNA denaturation

The nature and the universal properties of DNA thermal denaturation are investigated by Monte Carlo simulations. For suitable lattice models we determine the exponent c describing the decay of the probability distribution of denaturated loops of length l, P approximately l(-c). If excluded volume effects are fully taken into account, c = 2.10(4) is consistent with a first order transition. The stiffness of the double stranded chain has the effect of sharpening the transition, if it is continuous, but not of changing its order and the value of the exponent c, which is also robust with respect to inclusion of specific base-pair sequence heterogeneities.

Dynamical scaling of the DNA unzipping transition

We report studies of the dynamics of a set of exactly solvable lattice models for the force-induced DNA unzipping transition. Besides yielding the whole equilibrium phase diagram, which reveals a reentrance, these models enable us to characterize the dynamics of the process starting from a nonequilibrium initial condition. The thermal melting of DNA displays a model dependent time evolution. On the contrary, the dynamical mechanism for the unzipping by force is very robust and the scaling behavior is independent of the details of the description and, hence, superuniversal.

Phase diagram of force-induced DNA unzipping in exactly solvable models

The mechanical separation of a double helical DNA structure induced by forces pulling apart the two DNA strands ("unzipping") has been the subject of recent experiments. Analytical results are obtained within various models of interacting pairs of directed walks in the (1,1,ellipsis,1) direction on the hypercubic lattice, and the phase diagram in the force-temperature plane is studied for a variety of cases. The scaling behavior is determined at both the unzipping and melting transitions. We confirm the existence of a cold denaturation transition recently observed in numerical simulations: for a finite range of forces, the system is unzipped by decreasing the temperature. The existence of this transition is rigorously established for generic lattice and continuum space models.

Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use a renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range 1/r2 and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.

Zipping and collapse of diblock copolymers

Using exact enumeration methods and Monte Carlo simulations, we study the phase diagram relative to the conformational transitions of a diblock copolymer in two dimensions. The polymer is made of two homogeneous strands of monomers of different species which are joined to each other at one end. We find that, depending on the values of the energy parameters in the model, there is either a first order collapse from a swollen phase to a compact phase of spiral type, or a continuous transition to an intermediate zipped phase followed by a first order collapse at lower temperatures. Critical exponents of the zipping transition are computed, and their exact values are conjectured on the basis of a mapping onto percolation geometry, thanks to recent results on path-crossing probabilities.

Why is the DNA denaturation transition first order?

We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.