DNA Denaturation Transition Research Articles

Influence of disorder on DNA denaturation: the disordered generalized Poland-Scheraga model

The Poland-Scheraga model is a celebrated model for the denaturation transition of DNA, which has been widely used in the bio-physical literature to study, and investigated by mathematicians. In the original model, only opposite bases of the two strands can be paired together, but a generalized version of this model has recently been introduced, and allows for mismatches in the pairing of the two strands, and for different strand lengths. This generalized Poland-Scheraga (gPS) model has only been studied recently in the case of homogeneous interactions, then with disordered interactions perturbed by an i.i.d. field. The present paper considers a disordered version of the gPS model which is more appropriate to depict the inhomogeneous composition of the two strands (in particular interactions are perturbed in a strongly dependent manner): we study the question of the influence of disorder on the denaturation transition, and our main results provide criteria for disorder (ir)-relevance, both in terms of critical points and of order of the phase transition. Surprisingly, we find that criteria for disorder relevance depend on the law of the disorder field. We discuss this with regards to Harris’ prediction for disordered systems.

Disorder and denaturation transition in the generalized Poland–Scheraga model

We investigate the generalized Poland-Scheraga model, which is used in the bio-physical literature to model the DNA denaturation transition, in the case where the two strands are allowed to be non-complementary (and to have different lengths). The homogeneous model was recently studied from a mathematical point of view in [35, 7], via a 2-dimensional renewal approach, with a loop exponent 2+α (α > 0): it was found to undergo a localization/delocalization phase transition of order ν = min(1, α) −1 , together with – in general – other phase transitions. In this paper, we turn to the disordered model, and we address the question of the influence of disorder on the denaturation phase transition, that is whether adding an arbitrarily small amount of disorder (i.e. inhomogeneities) affects the critical properties of this transition. Our results are consistent with Harris' predictions for d-dimensional disordered systems (here d = 2). First, we prove that when α d/2), then disorder is irrelevant: the quenched and annealed critical points are equal, and the disordered denaturation phase transition is also of order ν = α −1. On the other hand, when α > 1, disorder is relevant: we prove that the quenched and annealed critical points differ. Moreover, we discuss a number of open problems, in particular the smoothing phenomenon that is expected to enter the game when disorder is relevant.

Investigation of DNA denaturation from generalized Morse potential

In this paper, we present a non-linear model for the study of DNA denaturation transition. To this end, we assume that the double-strands DNA interact via a realistic generalized Morse potential that reproduces well the features of the real interaction. Using the Transfer Matrix Method, based on the resolution of a Schrödinger equation, we first determine exactly their solution, which are found to be bound states. Second, from an exact expression of the ground state, we compute the denaturation temperature and the free energy density, in terms of the parameters of the potential.Then, we calculate the contact probability, which is the probability to find the double-strands at a (finite) distance apart, from which we determine the behaviour of the mean-distance between DNA-strands.The main conclusion is that, the present analytical study reveals that the generalized Morse potential is a good candidate for the study of DNA denaturation

Temperature-dependent conformations of exciton-coupled Cy3 dimers in double-stranded DNA.

Understanding the properties of electronically interacting molecular chromophores, which involve internally coupled electronic-vibrational motions, is important to the spectroscopy of many biologically relevant systems. Here we apply linear absorption, circular dichroism, and two-dimensional fluorescence spectroscopy to study the polarized collective excitations of excitonically coupled cyanine dimers (Cy3)2 that are rigidly positioned within the opposing sugar-phosphate backbones of the double-stranded region of a double-stranded (ds)-single-stranded (ss) DNA fork construct. We show that the exciton-coupling strength of the (Cy3)2-DNA construct can be systematically varied with temperature below the ds-ss DNA denaturation transition. We interpret spectroscopic measurements in terms of the Holstein vibronic dimer model, from which we obtain information about the local conformation of the (Cy3)2 dimer, as well as the degree of static disorder experienced by the Cy3 monomer and the (Cy3)2 dimer probe locally within their respective DNA duplex environments. The properties of the (Cy3)2-DNA construct we determine suggest that it may be employed as a useful model system to test fundamental concepts of protein-DNA interactions and the role of electronic-vibrational coherence in electronic energy migration within exciton-coupled bio-molecular arrays.

Strong disorder renewal approach to DNA denaturation and wetting: typical and large deviation properties of the free energy

For the DNA denaturation transition in the presence of random contact energies, or equivalently the disordered wetting transition, we introduce a strong disorder renewal approach to construct the optimal contacts in each disordered sample of size L. The transition is found to be of infinite order, with a correlation length diverging with the essential singularity . In the critical region, we analyze the statistics over samples of the free-energy density fL and of the contact density, which is the order parameter of the transition. At the critical point, both decay as a power-law of the length L but remain distributed, in agreement with the general phenomenon of lack of self-averaging at random critical points. We also obtain that for any real q > 0, the moment of order q of the partition function at the critical point is dominated by some exponentially rare samples displaying a finite free-energy density, i.e. by the large deviation sector of the probability distribution of the free-energy density.

Denaturation of circular DNA: Supercoils and overtwist

The denaturation transition of circular DNA is studied within a Poland-Scheraga-type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant κ associated with the overtwisting energy for any given loop entropy exponent c. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for c ≤ 2. For c > 2 and κ = 0 we find that the model exhibits a first-order transition. The transition becomes of higher order for any κ > 0. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent c.

Insight into the denaturation transition of DNA

DNA undergoes a helix-to-coil transition (also called denaturation transition) upon heating. This transition can also be facilitated by using solvent mixtures (for example water–alcohol). An increase in the hydrophobic tail of the second solvent molecule first decreases then increases the melting temperature appreciably. Measurement on 4% DNA in a series of water–alcohol mixtures shows that the helix-to-coil melting transition is driven by the solvent ability to cross the hydrophobic sugar-rich region. DNA is behaving like a cylindrical micelle.

Dynamics of DNA melting

The dynamics of loops at the DNA denaturation transition is studied. A scaling argumentis used to evaluate the asymptotic behavior of the autocorrelation function of the state ofcomplementary bases (either open or closed). The long-time asymptotic behaviorof the autocorrelation function is expressed in terms of the entropy exponent,c, of a loop. The validity of the scaling argument is tested using a microscopic model of anisolated loop and a toy model of interacting loops. This suggests a method for measuringthe entropy exponent using single-molecule experiments such as fluorescence correlationspectroscopy.

Denaturation Transition of Stretched DNA

We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent c, for which we find the new value c = 4 nu-1/2 such that the transition is second order with c = 1.85 < 2 in d = 3. We show that a finite stretching force F destabilizes DNA, corresponding to a lower melting temperature T(F), in agreement with single-molecule DNA stretching experiments.

Reaction Rate Calculation by Parallel Path Swapping

The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we devise a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We test the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor of 20.

The Denaturation Transition of DNA in Mixed Solvents

The helix-to-coil denaturation transition in DNA has been investigated in mixed solvents at high concentration using ultraviolet light absorption spectroscopy and small-angle neutron scattering. Two solvents have been used: water and ethylene glycol. The “melting” transition temperature was found to be 94°C for 4% mass fraction DNA/d-water and 38°C for 4% mass fraction DNA/d-ethylene glycol. The DNA melting transition temperature was found to vary linearly with the solvent fraction in the mixed solvents case. Deuterated solvents (d-water and d-ethylene glycol) were used to enhance the small-angle neutron scattering signal and 0.1M NaCl (or 0.0058 g/g mass fraction) salt concentration was added to screen charge interactions in all cases. DNA structural information was obtained by small-angle neutron scattering, including a correlation length characteristic of the inter-distance between the hydrogen-containing (desoxyribose sugar-amine base) groups. This correlation length was found to increase from 8.5 to 12.3 Å across the melting transition. Ethylene glycol and water mixed solvents were found to mix randomly in the solvation region in the helix phase, but nonideal solvent mixing was found in the melted coil phase. In the coil phase, solvent mixtures are more effective solvating agents than either of the individual solvents. Once melted, DNA coils behave like swollen water-soluble synthetic polymer chains.

Numerical study of a disordered model for DNA denaturation transition

We numerically study a disordered version of the model for DNA denaturation transition consisting of two interacting self-avoiding walks in three dimensions, which undergoes a first order transition in the homogeneous case. The two possible values epsilonAT and epsilonGC of the interactions between base pairs are taken as quenched random variables distributed with equal probability along the chain. We measure quantities averaged over disorder such as the energy density, the specific heat, and the probability distribution of the loop lengths. When applying the scaling laws used in the homogeneous case we find that the transition seems to be smoother in the presence of disorder, in agreement with general theoretical arguments, although we cannot rule out the possibility of a first order transition.

Poland–Scheraga Models and the DNA Denaturation Transition

Poland–Scheraga models were introduced to describe the DNA denaturation transition. We give a rigorous and refined discussion of a family of these models. We derive possible scaling functions in the neighborhood of the phase transition point and review common examples. We introduce a self-avoiding Poland–Scheraga model displaying a first order phase transition in two and three dimensions. We also discuss exactly solvable directed examples. This complements recent suggestions as to how the Poland–Scheraga class might be extended in order to display a first order transition, which is observed experimentally.

Theoretical Study on Effects of Salt and Temperature on Denaturation Transition of Double-stranded DNA**The project supported by the Doctoral Foundation of the Ministry of Education of China under Grant No. 20010614005

We investigate the statistical mechanics properties of a nonlinear dynamics model of the denaturation of the DNA double-helix and study the effects of salt concentration and temperature on denaturation transition of DNA. The specific heat, entropy, and denaturation temperature of the system versus salt concentration are obtained. These results show that the denaturation of DNA not only depends on the temperature but also is influenced by the salt concentration in the solution of DNA, which are in agreement with experimental measurement.

A simple model for DNA denaturation transition

We present a simple model of DNA in which many important aspects of the real system are disregarded, while few relevant interactions which drive the system towards a first-order phase transition, as experimentally observed, are taken into account.

Effects of intrinsic base-pair fluctuations on charge transport in DNA.

We investigate propagation of a charge carrier along intrinsically dynamically disordered double-stranded DNA. This is realized by the semiclassical coupling of the charge with a nonlinear lattice model that can accurately describe the statistical mechanics of the large amplitude fluctuations of the base pairs leading to the thermal denaturation transition of DNA. We find that the fluctuating intrinsic disorder can trap the charge and inhibit polaronic charge transport. The dependence of the mean distance covered by the charge carrier until its trapping, as a function of the energy of the fluctuations of the base pairs is also presented.

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.

Simple model for the DNA denaturation transition.

We study pairs of interacting self-avoiding walks ¿omega(1), omega(2)¿ on the 3d simple cubic lattice. They have a common origin omega(1)(0)=omega 20, and are allowed to overlap only at the same monomer position along the chain: omega(1)(i) not equal omega(2)(j) for i not equal j, while omega(1)(i)=omega(2)(i) is allowed. The latter overlaps are indeed favored by an energetic gain epsilon. This is inspired by a model introduced long ago by Poland and Sheraga [J. Chem. Phys. 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 straight 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.

Statistical Mechanics of Torque Induced Denaturation of DNA

A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Gamma is presented. Our model couples the hydrogen-bond opening and the untwisting of the helicoidal molecular structure. We show that denaturation corresponds to a first-order phase transition from B-DNA to d-DNA phases and that the coexistence region is naturally parametrized by the degree of supercoiling sigma. The denaturation free energy, the temperature dependence of the twist angle, the phase diagram in the T,Gamma plane and isotherms in the sigma, Gamma plane are calculated and show a good agreement with experimental data.

Biomolecular dynamics of DNA: statistical mechanics and dynamical models

There is a growing feeling that biomolecular structure is not sufficient to determine biological activity which is also governed by large amplitude dynamics of the molecules. The transcription of DNA or its thermal denaturation are typical examples. Traditional approaches use Ising models to describe the denaturation transition of DNA. They have to introduce phenomenological “cooperativity factors” to explain the rather sharp “melting” of this quasi one-dimensional system. We present models which describe the full dynamics of the melting. Using molecular dynamics simulations and statistical analysis, we discuss the mechanism of the denaturation, including precursor effects that can be related to large amplitude localized nonlinear excitations of the molecule in which discreteness effects play a large role. We also show the microscopic origin of the cooperativity factors.