Melting of DNA oligomers: dynamical models and comparison with experimental results

Force-induced unzipping of DNA in the presence of solvent molecules

The melting of double-stranded DNA (dsDNA) in the presence of solvent molecules is a fundamental process with significant implications for understanding the thermal and mechanical behavior of DNA and its interactions with the surrounding environment. The solvents play an essential role in the structural transformation of DNA subjected to a pulling force. In this study, we simulate the thermal and force induced denaturation of dsDNA and elucidate the solvent dependent melting behavior, identifying key factors that influence the stability of DNA melting in presence of solvent molecules. Using a statistical model, we first find the melting profile of short heterogeneous DNA molecules in the presence of solvent molecules in Force ensemble. We also investigate the effect of solvent's strengths on the melting profile of DNA. In the force ensemble, we consider two homogeneous DNA chains and apply the force on different locations along the chain in the presence of solvent molecules. Different pathways manifest the melting of the molecule in both ensembles, and we found several interesting features of melting DNA in a constant force ensemble, such as lower critical force when the chain is pulled from the base pair close to a solvent molecule. The results provide new insights into the force-induced unzipping of DNA and could be used to develop new methods for controlling the unzipping process. By providing a better understanding of melting and unzipping of dsDNA in the presence of solvent molecules, this study provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA nanostructures.

Improving the mesoscopic modeling of DNA denaturation dynamics

Although previously developed mesoscopic DNA models have successfully reproduced thermodynamic denaturation data, recent studies show that these overestimate the rate of denaturation by orders of magnitude. Using adapted Peyrard-Bishop-Dauxois (PBD) models, we have calculated the denaturation rates of several DNA hairpins and made comparison with experimental data. We show that the addition of a barrier at the onsite potential of the PBD model gives a more accurate description of the unzipping dynamics of short DNA sequences. The new models provide a refined theoretical insight on the dynamical mechanisms of unzipping which can have implications for the understanding of transcription and replication processes. Still, this class of adapted PBD models seems to have a fundamental limitation which implies that it is not possible to get agreement with available experimental results on the dynamics of long DNA sequences and at the same time maintain the good agreement regarding its thermodynamics. The reason for this is that the denaturation rate of long DNA chains is not dramatically lowered by the additional barrier-as the base-pairs that open are more likely to remain open, facilitating the opening of the full DNA molecule. Some care has to be taken, since experimental techniques suitable to the study of denaturation rates of long sequences seem not to agree with other experimental data on short DNA sequences. Further research, both theoretical and experimental, is therefore needed to resolve these inconsistencies-which will be a starting point for new minimalistic models that are able to describe both thermodynamics and dynamics at a predictive level.

Dynamical versus statistical mesoscopic models for DNA denaturation

We recently proposed a dynamical mesoscopic model for DNA, which is based, like the statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present paper, we first describe how the parameters of this model are varied to get predictions in better agreement with experimental results that were not addressed up to now, like mechanical unzipping, the evolution of the critical temperature with sequence length and temperature resolution. We show that the model with the new parameters provides results that are in quantitative agreement with those obtained from statistical models. Investigation of the critical properties of the dynamical model suggests that DNA denaturation looks like a first-order phase transition in a broad temperature interval, but that there necessarily exists, very close to the critical temperature, a crossover to another regime. The exact nature of the melting dynamics in this second regime still has to be elucidated. We finally point out that the descriptions of the physics of the melting transition inferred from statistical and dynamical models are not completely identical and discuss the relevance of our model from the biological point of view.

Theoretical investigation of finite size effects at DNA melting

We investigated how the finiteness of the length of a sequence affects the phase transition that takes place at the DNA melting temperature. For this purpose, we modified the transfer integral method to adapt it to the calculation of both extensive (partition function, entropy, specific heat, etc.) and nonextensive (order parameter and average separation between paired bases) thermodynamic quantities of finite sequences with open boundary conditions, and applied the modified procedure to two different dynamical models. We characterized in some detail the three effects that take place when the length of the sequence is decreased, namely, (i) the decrease of the critical temperature, (ii) the decrease of the peak values of all quantities that diverge at the thermodynamic limit but remain finite for finite sequences, like the specific heat and the correlation length, and (iii) the broadening of the temperature range over which the transition affects the dynamics of the system. We also performed a finite size scaling analysis of the two models and showed that the singular part of the free energy can indeed be expressed in terms of a homogeneous function. However, Josephson's identity is satisfied for none of the investigated models, so that the derivation of the characteristic exponents which appear, for example, in the expression of the specific heat requires some care.

Bubbles and denaturation in DNA

The local opening of DNA is an intriguing phenomenon from a statistical-physics point of view, but is also essential for its biological function. For instance, the transcription and replication of our genetic code cannot take place without the unwinding of the DNA double helix. Although these biological processes are driven by proteins, there might well be a relation between these biological openings and the spontaneous bubble formation due to thermal fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois (PBD) model, have fairly accurately reproduced some experimental denaturation curves and the sharp phase transition in the thermodynamic limit. It is, hence, tempting to see whether these models could be used to predict the biological activity of DNA. In a previous study, we introduced a method that allows to obtain very accurate results on this subject, which showed that some previous claims in this direction, based on molecular-dynamics studies, were premature. This could either imply that the present PBD model should be improved or that biological activity can only be predicted in a more complex framework that involves interactions with proteins and super helical stresses. In this article, we give a detailed description of the statistical method introduced before. Moreover, for several DNA sequences, we give a thorough analysis of the bubble-statistics as a function of position and bubble size and the so-called l-denaturation curves that can be measured experimentally. These show that some important experimental observations are missing in the present model. We discuss how the present model could be improved.

Atomistic understanding of kinetic pathways for single base-pair binding and unbinding in DNA

We combine free-energy calculations and molecular dynamics to elucidate a mechanism for DNA base-pair binding and unbinding in atomic detail. Specifically, transition-path sampling is used to overcome computational limitations associated with conventional techniques to harvest many trajectories for the flipping of a terminal cytosine in a 3-bp oligomer in explicit water. Comparison with free-energy projections obtained with umbrella sampling reveals four coordinates that separate true dynamic transition states from stable reactant and product states. Unbinding proceeds via two qualitatively different pathways: one in which the flipping base breaks its intramolecular hydrogen bonds before it unstacks and another in which it ruptures both sets of interactions simultaneously. Both on- and off-pathway intermediates are observed. The relation of the results to coarse-grained models for DNA-based biosensors is discussed.

Interplay of nonlinearity and geometry in a DNA-related, Klein-Gordon model with long-range dipole-dipole interaction

Most of the studies on mathematical models of DNA are limited to next neighbor interaction. However, the coupling between base pairs is thought to be caused by dipole interaction, and, when the DNA strand is bent, the distances between base pairs become shorter, therefore the interactions with distant base pairs have to be taken into account. In this paper we analyze the existence and stability of breathers, i.e., localized oscillations in a simple model of bent DNA with long-range dipole interaction. Breathers have been suggested as precursors of the denaturation bubble.

Is DNA a nonlinear dynamical system where solitary conformational waves are possible?

DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA's nonlinear properties.

Bubble propagation in a helicoidal molecular chain

We study the propagation of very large amplitude localized excitations in a model of DNA that takes explicitly into account the helicoidal structure. These excitations represent the "transcription bubble," where the hydrogen bonds between complementary bases are disrupted, allowing access to the genetic code. We propose these kinds of excitations in alternative to kinks and breathers. The model has been introduced by Barbi et al. [Phys. Lett. A 253, 358 (1999)], and up to now it has been used to study on the one hand low amplitude breather solutions, and on the other hand the DNA melting transition. We extend the model to include the case of heterogeneous chains, in order to get closer to a description of real DNA; in fact, the Morse potential representing the interaction between complementary bases has two possible depths, one for A-T and one for G-C base pairs. We first compute the equilibrium configurations of a chain with a degree of uncoiling, and we find that a static bubble is among them; then we show, by molecular dynamics simulations, that these bubbles, once generated, can move along the chain. We find that also in the most unfavorable case, that of a heterogeneous DNA in the presence of thermal noise, the excitation can travel for well more than 1000 base pairs.