Melting of persistent double-stranded polymers

Tensile elasticity of a freely jointed chain with reversible hinges

Many biopolymers exhibit reversible conformational transitions within the chain, which affect their bending stiffness and their response to a stretching force. For example, double stranded DNA may have denatured "bubbles" of unzipped single strands which open and close randomly. In other polymers, the transitions may be due to the reversible attachment and detachment of ligands on ligand-receptor complexes along the backbone. Semiflexible bundles under tension formed by the reversible attachment of cross-linkers, on a coarse-grained level, exhibit similar behaviour. The simplest theoretical model which captures what the above mentioned systems have in common is a freely jointed chain (FJC) with reversible hinges. Each hinge can be open, as in the usual FJC, or closed forcing the adjacent segments to align (stretch). In this article, we analyse it in the Gibbs ensemble. Remarkably, even though the usual FJC in the thermodynamic limit exhibits ensemble equivalence, the reversible FJC exhibits ensemble inequivalence. Even though a mean field treatment suggests a continuous phase transition to a fully hinged state at a certain force, the generating function method ("necklace model") shows that there is no phase transition. However, there is a crossover between the two states with clearly different responses. In the low force (linear response) regime, the reversible FJC has higher tensile compliance than its usual counterpart. In contrast, in the strong force regime, the tensile compliance of the reversible FJC is much lower than that of the usual FJC.

Cavity approach for modeling and fitting polymer stretching

The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly studied force-elongation relation is typically hard. Here we draw from techniques developed in the context of disordered systems to solve models for single and double-stranded DNA stretching in the limit of a long polymeric chain. Since we directly derive the marginals for the molecule local orientation, our approach allows us to readily calculate the experimental elongation as well as other observables at wish. As an example, we evaluate the correlation length as a function of the stretching force. Furthermore, we are able to fit successfully our solution to real experimental data. Although the model is admittedly phenomenological, our findings are very sound. For single-stranded DNA our solution yields the correct (monomer) scale and yet, more importantly, the right persistence length of the molecule. In the double-stranded case, our model reproduces the well-known overstretching transition and correctly captures the ratio between native DNA and overstretched DNA. Also in this case the model yields a persistence length in good agreement with consensus, and it gives interesting insights into the bending stiffness of the native and overstretched molecule, respectively.

Coarse-grained simulations of DNA overstretching

We use a recently developed coarse-grained model to simulate the overstretching of duplex DNA. Overstretching at 23 °C occurs at 74 pN in the model, about 6-7 pN higher than the experimental value at equivalent salt conditions. Furthermore, the model reproduces the temperature dependence of the overstretching force well. The mechanism of overstretching is always force-induced melting by unpeeling from the free ends. That we never see S-DNA (overstretched duplex DNA), even though there is clear experimental evidence for this mode of overstretching under certain conditions, suggests that S-DNA is not simply an unstacked but hydrogen-bonded duplex, but instead probably has a more exotic structure.

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, such as water, with the ability for hydrogen bonding with a 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.

A three-state model with loop entropy for the overstretching transition of DNA

We introduce a three-state model for a single DNA chain under tension that distinguishes among B-DNA, S-DNA, and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S approximately -c ln n for the entropy of a loop of length n. Force extension curves are derived exactly by employing a generalized Poland-Scheraga approach and then compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows us to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy (entering as a domain-wall energy between paired and unpaired bases) and the loop entropy are separated. Therefore, we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.

Different pulling modes in DNA overstretching: a theoretical analysis

We study the thermally driven denaturation of a double-stranded polymer in the presence of a stretching force via Monte-Carlo simulations. When one strand only is stretched, the denaturation transition is first order, while when both strands are stretched, melting is second order. By revisiting the Poland-Scheraga model for DNA melting, we show that at room temperature, the most likely scenario is that DNA melts as it overstretches. Our results are in general agreement with the most recent experiments and suggest how varying temperature and stretching mode may help settle the question whether S-DNA exists or not.

Physical rationale behind the nonlinear enthalpy-entropy compensation in DNA duplex stability

The physical-chemical sense of nonlinear entropy-enthalpy compensation based upon the standard thermodynamical parameters of high-temperature melting for doublet units in DNA duplexes has been considered. We are able to show that there are three, with no other constraints equally plausible, principal levels of DNA melting/hybridization description. First, DNA structure assembly/disassembly can be seen from the viewpoint of the conventional equilibrium thermodynamics without taking special care of the heat capacity DeltaC(p) value (by simply setting it equal to zero). Second, it is possible to assume that the DeltaC(p) is finite, but independent of temperature. At this approximation level the high-temperature DNA melting cannot be described, but only some special transition between metastable states of DNA duplexes in water solutions in the vicinity of ice melting point. Third, both the latter transition and the high-temperature DNA melting can be reproduced by one and the same approach, if the DeltaC(p) is assumed to be temperature dependent. These three approximation levels are equally justified from the nonlinear entropy-enthalpy compensation standpoint and by a generalized theory of temperature effects on themodynamical stability as is outlined here. Applicability of each of the approximation levels involved is discussed.

Path integral method for DNA denaturation

The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc*, whereas the fraction of unbound base pairs grows continuously around and above Tc*. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc*. The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.