Statistical theory of force-induced unzipping of DNA

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.

Statistical mechanical model for crack growth

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

Equilibrium melting probabilities of a DNA molecule with a defect: An exact solution of the Poland-Scheraga model

In this study we derive analytically the equilibrium melting probabilities for basepairs of a DNA molecule with a defect site. We assume that the defect is characterized by a change in the Watson-Crick basepair energy of the defect basepair, and in the associated two stacking energies for the defect, as compared to the remaining parts of the DNA. The defect site could, for instance, occur due to DNA basepair mismatching, cross-linking, or by the chemical modifications when attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. Our exact solution of the Poland-Scheraga model for DNA melting provides the probability that the labeled basepair, and its neighbors, are open at different temperatures. Our work is of direct importance, for instance, for studies where fluorophore-quencher pairs are used for studying single basepair fluctuations of designed DNA molecules.

Melting of dsDNA attached with AuNPs

DNA-linked gold nanoparticles (DNA-AuNPs) are combined nanomaterials that contain the optical and electronic properties of AuNPs with the unique functions of DNA. These hybrid systems are used in various nanobiotechnology, medical, and pharmaceutical sciences (Löwe et al. in FEBS J 287(23):5039, 2020; Speer et al. in Annu Rev Biophys 51:267, 2022). In recent years, there has been an increasing interest in studying the behavior of DNA-AuNPs in the presence of molecular solvents. In the present work, we study the thermal melting of DNA-linked gold nanoparticles (DNA-AuNP). In the first part of the study, we find the melting profile of short heterogeneous DNA-linked AuNP in the presence of solvent in the solution. We also study the effect of the location of the gold nanoparticle attached to the DNA molecule. In this case, we move the location of the AuNP from one end to the other. We found that while the melting temperature is susceptible to the location of the AuNP when it is near the ends, there is a region in the middle section of the chain where the melting temperature remains constant.

Pulling short DNA with mismatch base pairs

Due to misincorporation during gene replication, the accuracy of the gene expression is often compromised. This results in a mismatch or defective pair in the DNA molecule (James et al. 2016). Here, we present our study of the stability of DNA with defects in the thermal and force ensembles. We consider DNA with a different number of defects from 2to16 and study how the denaturation process differs in both ensembles. Using a statistical model, we calculate the melting point of the DNA chain in both the ensemble. Our findings display different manifestations of DNA denaturation in thermal and force ensembles. While the DNA with defects denatures at a lower temperature than the intact DNA, the point from which the DNA is pulled is important in force ensemble.

A predictive model for the thermomechanical melting transition of double stranded DNA

By extending the classical Peyrard-Bishop model, we are able to obtain a fully analytical description for the mechanical response of DNA under stretching at variable values of temperature, number of base pairs and intrachains and interchains bonds stiffness. In order to compare elasticity and temperature effects, we first analyze the system in the zero temperature mechanical limit, important to describe several experimental effects including possible hysteresis. We then analyze temperature effects in the framework of equilibrium Statistical Mechanics. In particular, we obtain an analytical expression for the temperature-dependent melting force and unzipping assigned displacement in the thermodynamical limit, also depending on the relative stability of intra vs. inter molecular bonds. Such results coincide with the purely mechanical model in the limit of zero temperature and with the denaturation temperature that we obtain with the classical transfer integral method. Based on our analytical results, we obtain explicitly phase diagrams and cooperativity parameters, where also discreteness effect can be accounted for. The obtained results are successfully applied in reproducing the thermomechanical experimental melting of DNA and the response of DNA hairpins. Due to the generality of the model, exemplified in the proposed analysis of both overstretching and unzipping experiments, we argue that the proposed approach can be extended to other thermomechanically induced molecular melting phenomena. STATEMENT OF SIGNIFICANCE: We obtain a fully analytical description of the complex wiggly energy landscape of two stranded macromolecules under unzipping loading. Based on Equilibrium Statistical Mechanics, we describe the combined thermomechanical effects and the melting transition of double stranded molecules such as nucleic acids. This is proved by quantitatively predicting the experimental behavior of both melting of DNA and DNA hairpins opening. While analytical results have been previously attained under special conditions on the relative stiffness of the covalent vs. non-covalent bonds of the base pairs, our model is completely general in this respect, thus representing a tool in the perspective of the design at the molecular scale. We show that the obtained model can be fully inscribed in the theory of phase transitions giving a new interpretation of the thermomechanical behavior of double stranded molecules.

Structure and Dynamics of dsDNA in Cell-like Environments

Deoxyribonucleic acid (DNA) is a fundamental biomolecule for correct cellular functioning and regulation of biological processes. DNA's structure is dynamic and has the ability to adopt a variety of structural conformations in addition to its most widely known double-stranded DNA (dsDNA) helix structure. Stability and structural dynamics of dsDNA play an important role in molecular biology. In vivo, DNA molecules are folded in a tightly confined space, such as a cell chamber or a channel, and are highly dense in solution; their conformational properties are restricted, which affects their thermodynamics and mechanical properties. There are also many technical medical purposes for which DNA is placed in a confined space, such as gene therapy, DNA encapsulation, DNA mapping, etc. Physiological conditions and the nature of confined spaces have a significant influence on the opening or denaturation of DNA base pairs. In this review, we summarize the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions. We include studies on various thermal and mechanical properties of dsDNA in ionic solutions, molecular crowded environments, and confined spaces. By providing a better understanding of melting and unzipping of dsDNA in different environments, this review provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.

Melting of DNA in confined geometries

The stability of DNA molecules during viral or biotechnological encapsulation is a topic of active current research. We studied the thermal stability of double-stranded DNA molecules of different lengths in a confined space. Using a statistical model, we evaluate the melting profile of DNA molecules in two geometries: conical and cylindrical. Our results show that not only the confinement, but also the geometry of the confined space plays a prominent role in the stability and opening of the DNA duplex. We find that for more confined spaces, cylindrical confinement stabilizes the DNA, but for less confined spaces conical geometry stabilizes the DNA overall. We also analyse the interaction between DNA sequence and stability, and the evenness with which strand separation occurs. Cylindrical and conical geometries enable a better controlled tuning of the stability of DNA encapsulation and the efficiency of its eventual release, compared to spherical or quasi-spherical geometries.

Hard-wall entropic effect accelerates detachment of adsorbed polymer chains

Many previous studies of unbinding kinetics have focused on a two-state model, with fully bonded and free states, which may not extend to more complicated biopolymer dynamics involving other reactions. Here we address the kinetic rate of this process at the segment level, as it is influenced by a growing dangling end of the chain. We use the mean first-passage time approach and treat the polymer as a chain attached to a wall through a succession of spring potentials, with two distinct regions of bonded and free segments. The interaction between the wall and free-moving chain end adds an entropic repulsion to this process. We estimate the average monomer detachment rate K as a function of the free dangling length L. For a flexible polymer, we find an acceleration factor in the average detachment rate depending on L and the details of the spring bond; when L is long, this factor is a simple ratio of its breaking distance to the natural bond length. For a semiflexible filament, we examine the regime where L is shorter than persistence length L_{p}, as the limit opposite to that of the flexible chain. An enhancing factor also appears, speeding up the filament unbinding when the free length grows; for a long rigid rod, this factor becomes two, independently of the bond details. We also examine the total unbinding time of an irreversible detaching process by integrating (1/K) over polymer length and discover that its power-law scaling with chain length is smaller than one, over the commonly seen range of polymer size.

Opening of DNA chain due to force applied on different locations

We consider a homogeneous DNA molecule and investigate the effect of random force applied on the unzipping profile of the molecule. How the critical force varies as a function of the chain length or number of base pairs is the objective of this study. In general, the ratio of the critical forces that is applied on the middle of the chain to that which is applied on one of the ends is two. Our study shows that this ratio depends on the length of the chain. This means that the force which is applied to a point can be experienced by a section of the chain. Beyond a length, the base pairs have no information about the applied force. In the case when the chain length is shorter than this length, this ratio may vary. Only in the case when the chain length exceeds a critical length, this ratio is found to be two. Based on the de Gennes formulation, we developed a method to calculate these forces at zero temperature. The exact results at zero temperature match numerical calculations.

Free-energy landscape and characteristic forces for the initiation of DNA unzipping

DNA unzipping, the separation of its double helix into single strands, is crucial in modulating a host of genetic processes. Although the large-scale separation of double-stranded DNA has been studied with a variety of theoretical and experimental techniques, the minute details of the very first steps of unzipping are still unclear. Here, we use atomistic molecular-dynamics simulations, coarse-grained simulations, and a statistical-mechanical model to study the initiation of DNA unzipping by an external force. Calculation of the potential of mean force profiles for the initial separation of the first few terminal basepairs in a DNA oligomer revealed that forces ranging between 130 and 230 pN are needed to disrupt the first basepair, and these values are an order of magnitude larger than those needed to disrupt basepairs in partially unzipped DNA. The force peak has an echo of ∼50 pN at the distance that unzips the second basepair. We show that the high peak needed to initiate unzipping derives from a free-energy basin that is distinct from the basins of subsequent basepairs because of entropic contributions, and we highlight the microscopic origin of the peak. To our knowledge, our results suggest a new window of exploration for single-molecule experiments.

Pulling short DNA molecules having defects on different locations

We present a study on the role of defects on the stability of short DNA molecules. We consider short DNA molecules (16 base pairs) and investigate the thermal as well as mechanical denaturation of these molecules in the presence of defects that occur anywhere in the molecule. For the investigation, we consider four different kinds of chains. Not only are the ratios of AT to GC different in these molecules but also the distributions of AT and GC along the molecule are different. With suitable modifications in the statistical model to show the defect in a pair, we investigate the denaturation of short DNA molecules in thermal as well as constant force ensembles. In the force ensemble, we pulled the DNA molecule from each end (keeping other end free) and observed some interesting features of opening of the molecule in the presence of defects in the molecule. We calculate the probability of opening of the DNA molecule in the constant force ensemble to explain the opening of base pairs and hence the denaturation of molecules in the presence of defects.

Fluctuations in the DNA double helix: A critical review

A critical overview of the extensive literature on fluctuations in the DNA double helix is presented. Both theory and experiment are comprehensively reviewed and analyzed. Fluctuations, which open up the DNA double helix making bases accessible for hydrogen exchange and chemical modification, are the main focus of the review. Theoretical descriptions of the DNA fluctuations are discussed with special emphasis on most popular among them: the nonlinear-dynamic Peyrard-Bishop-Dauxois (PBD) model and the empirical two-state (or helix-coil) model. The experimental data on the issue are comprehensibly overviewed in the historical retrospective with main emphasis on the hydrogen exchange data and formaldehyde kinetics. The theoretical descriptions are critically evaluated from the viewpoint of their applicability to describe DNA in water environment and from the viewpoint of agreement of their predictions with the reliable experimental data. The presented analysis makes it possible to conclude that, while the two-state model is most adequate from theoretical viewpoint and its predictions, based on an empirical parametrization, agree with experimental data very well, the PBD model is inapplicable to DNA in water from theoretical viewpoint on one hand and it makes predictions totally incompatible with reliable experimental data on the other. In particular, it is argued that any oscillation movements of nucleotides, assumed by the PBD model, are severely damped in water, that no "bubbles", which the PBD model predicts, exist in reality in linear DNA well below the melting range and the lifetime of an open state in DNA is actually 5 orders of magnitude longer than the value predicted by the PBD model.

Mimicking DNA stretching with the Static Mode method: shear stress versus transverse pulling stress

DNA sequencing using nanopores is closer than ever to become a reality, but further research and development still need to be done, especially to unravel the atomic-scale mechanisms of induced DNA stretching. At this level, molecular modeling and simulation are essential to investigate DNA conformational flexibility and its response to the forces involved. In this work, through a "Static Mode" approach, we present a directed exploration of the deformations of a 27-mer subjected to externally imposed forces, as it could be in a nanopore. We show how the DNA sugar-phosphate backbone undergoes the majority of the induced deformation, before the base pairing is affected, and to what extent unzipping initiation depends on the force direction.

Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide

In this paper, we show that the coarse grain model for DNA, which has been proposed recently by Knotts et al. [J. Chem. Phys. 126, 084901 (2007)], can be adapted to describe the thermal and mechanical denaturation of long DNA sequences by adjusting slightly the base pairing contribution. The adjusted model leads to (i) critical temperatures for long homogeneous sequences that are in good agreement with both experimental ones and those obtained from statistical models, (ii) a realistic step-like denaturation behaviour for long inhomogeneous sequences, and (iii) critical forces at ambient temperature of the order of 10 pN, close to measured values. The adjusted model furthermore supports the conclusion that the thermal denaturation of long homogeneous sequences corresponds to a first-order phase transition and yields a critical exponent for the critical force equal to σ = 0.70. This model is both geometrically and energetically realistic, in the sense that the helical structure and the grooves, where most proteins bind, are satisfactorily reproduced, while the energy and the force required to break a base pair lie in the expected range. It therefore represents a promising tool for studying the dynamics of DNA-protein specific interactions at an unprecedented detail level.

Role of loop entropy in the force induced melting of DNA hairpin

Dynamics of a single stranded DNA, which can form a hairpin have been studied in the constant force ensemble. Using Langevin dynamics simulations, we obtained the force-temperature diagram, which differs from the theoretical prediction based on the lattice model. Probability analysis of the extreme bases of the stem revealed that at high temperature, the hairpin to coil transition is entropy dominated and the loop contributes significantly in its opening. However, at low temperature, the transition is force driven and the hairpin opens from the stem side. It is shown that the elastic energy plays a crucial role at high force. As a result, the force-temperature diagram differs significantly with the theoretical prediction.

Kinetic mechanism for DNA unwinding by multiple molecules of Dda helicase aligned on DNA

Helicases catalyze the separation of double-stranded nucleic acids to form single-stranded intermediates. Using transient state kinetic methods, we have determined the kinetic properties of DNA unwinding under conditions that favor a monomeric form of the Dda helicase as well as conditions that allow multiple molecules to function on the same substrate. Multiple helicase molecules can align like a train on the DNA track. The number of base pairs unwound in a single binding event for Dda is increased from approximately 19 bp for the monomeric form to approximately 64 bp when as many as four Dda molecules are aligned on the same substrate, while the kinetic step size (3.2 +/- 0.7 bp) and unwinding rate (242 +/- 25 bp/s) appear to be independent of the number of Dda molecules present on a given substrate. The data support a model in which the helicase molecules bound to the same substrate move along the DNA track independently during DNA unwinding. The observed increase in processivity arises from the increased probability that at least one of the helicases will completely unwind the DNA prior to dissociation. These results are in contrast to previous reports in which multiple Dda molecules on the same track greatly enhanced the rate and amplitude for displacement of protein blocks on the track. Therefore, only when the progress of the lead molecule in the train is impeded by some type of block, such as a protein bound to DNA, do the trailing molecules interact with the lead molecule to overcome the block. The fact that trailing helicase molecules have little impact on the lead molecule in the train during routine DNA unwinding suggests that the trailing molecules are moving at rates similar to that of the lead molecule. This result implicates a step in the translocation mechanism as contributing greatly to the overall rate-limiting step for unwinding of duplex DNA.

Force induced DNA melting

When pulled along the axis, double-strand DNA undergoes a large conformational change and elongates by roughly twice its initial contour length at a pulling force of about 70 pN. The transition to this highly overstretched form of DNA is very cooperative. Applying a force perpendicular to the DNA axis (unzipping), double-strand DNA can also be separated into two single-stranded DNA, this being a fundamental process in DNA replication. We study the DNA overstretching and unzipping transition using fully atomistic molecular dynamics (MD) simulations and argue that the conformational changes of double-strand DNA associated with either of the above mentioned processes can be viewed as force induced DNA melting. As the force at one end of the DNA is increased the DNA starts melting abruptly/smoothly above a critical force depending on the pulling direction. The critical force f(m), at which DNA melts completely decreases as the temperature of the system is increased. The melting force in the case of unzipping is smaller compared to the melting force when the DNA is pulled along the helical axis. In the case of melting through unzipping, the double-strand separation has jumps which correspond to the different energy minima arising due to sequence of different base pairs. The fraction of Watson-Crick base pair hydrogen bond breaking as a function of force does not show smooth and continuous behavior and consists of plateaus followed by sharp jumps.

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.

Probability distribution analysis of force induced unzipping of DNA

We present a semimicroscopic model of dsDNA by incorporating the directional nature of hydrogen bond to describe the force induced unzipping transition. Using exact enumeration technique, we obtain the force-temperature and the force-extension curves and compare our results with the other models of dsDNA. The model proposed by us is rich enough to describe the basic mechanism of dsDNA unzipping and predicts the existence of an "eye phase." We show oscillations in the probability distribution function during unzipping. Effects of stacking energies on the melting profile have also been studied.

Probing the mechanical unzipping of DNA

A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on unzipping speed and temperature. Our findings agree quantitatively with experimental results for homogeneous DNA, and for lamda-phage DNA we reproduce the recently obtained experimental force-temperature phase diagram. Finally, we argue that there may be fundamental differences between in vivo and in vitro DNA unzipping.

Effects of the eye phase in DNA unzipping

The onset of the "eye phase" (a phase consisting of configurations of eye-type conformations or bubbles in the double-stranded DNA) and its role during the DNA unzipping is studied when a force is applied to the interior of the chain. The directionality of the hydrogen bond introduced here shows oscillations in force-extension curve similar to a "sawtooth" kind of oscillations seen in the protein unfolding experiments. The effects of intermediates (hairpins) and stacking energies on the melting profile have also been discussed.

Effect of genome sequence on the force-induced unzipping of a DNA molecule

We considered a dsDNA polymer in which distribution of bases are random at the base pair level but ordered at a length of 18 base pairs and calculated its force elongation behaviour in the constant extension ensemble. The unzipping force F(y) vs. extension y is found to have a series of maxima and minima. By changing base pairs at selected places in the molecule we calculated the change in F(y) curve and found that the change in the value of force is of the order of few pN and the range of the effect depending on the temperature, can spread over several base pairs. We have also discussed briefly how to calculate in the constant force ensemble a pause or a jump in the extension-time curve from the knowledge of F(y).