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.     

Melting and unzipping of DNA

Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule consist of an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In the present study we take into account in an approximate way the excluded-volume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a first-order melting transition in d = 2 dimensions and above, consistent with the experimental results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach. Received 21 August 2001 and Received in final form 26 January 2002     

Adhesive emulsion bilayers under an electric field: from unzipping to fusion

Water-in-oil emulsion drops are formed and stabilized with phospholipids which can adhere and form a bilayer. Using microfluidics, adhesive drop pairs are then trapped and submitted to an ac electric field. We observe three distinct states as a function of the adhesion energy and the electric field intensity. The pair can be either stable, though slightly deformed, or unzip and separate, or coalesce. The frontiers between the different states directly reflect vesicle detachment forces and electroporation theories. The experimental approach that we propose for probing liquid interface wetting between monolayers allows us to finely tuned the tension in the bilayer and gives access to bilayer unzipping.     

Statistical theory of force-induced unzipping of DNA

The unzipping transition under the influence of external force of a dsDNA molecule has been studied using the Peyrard-Bishop Hamiltonian. The critical force F_c(T) for unzipping calculated in the constant force ensemble is found to depend on the potential parameter k which measures the stiffness associated with a single strand of DNA and on D, the well depth of the on-site potential representing the strength of hydrogen bonds in a base pair. The dependence on temperature of F_c(T) is found to be (T_D - T)^1/2 (T_D being the thermal denaturation temperature) with F_c(T_D) = 0 and F_c(0) = . We used the constant extension ensemble to calculate the average force F(y) required to stretch a base pair a y distance apart. The value of F(y) needed to stretch a base pair located far away from the ends of a dsDNA molecule is found twice the value of the force needed to stretch a base pair located at one of the ends to the same distance for y 1.0 . The force F(y) in both cases is found to have a very large value for y 0.2 compared to the critical force found from the constant force ensemble to which F(y) approaches for large values of y. It is shown that the value of F(y) at the peak depends on the value of k which measures the energy barrier associated with the reduction in DNA strand rigidity as one passes from dsDNA to ssDNA and on the value of the depth of the on-site potential. The effect of defects on the position and height of the peak in the F(y) curve is investigated by replacing some of the base pairs including the one being stretched by defect base pairs. The formation and behaviour of a loop of Y shape when one of the ends base pair is stretched and a bubble of ssDNA with the shape of an eye when a base pair far from ends is stretched are investigated.     

Deformation guided unzipping of nanotubes: A first-principles study

Aiming to make narrow nanoribbons, the unzipping process of nanotubes with deformation is studied using first-principles calculation. With the increase of deformation, the most stressed CC bonds become more and more reactive to oxygen, implying that the unzipping path can be tuned via elegant deformation modulation and this is verified.     

Comparison of the measured phase diagrams in the force-temperature plane for the unzipping of two different natural DNA sequences

In this work, we consider the critical force required to unzip two different naturally occurring sequences of double-stranded DNA (dsDNA) at temperatures ranging from 20 ^°C to 50 ^°C, where one of the sequences has a 53% average guanine-cytosine (GC) content and the other has a 40% GC content. We demonstrate that the force required to separate the dsDNA of the 53% GC sequence into single-stranded DNA (ssDNA) is approximately 0.5 pN, or approximately 5% greater than the critical force required to unzip the 40% GC sequence at the same temperature. In the temperature range between 20 and 40 ^°C the measured critical forces correspond reasonably well to predictions based on a simple theoretical homopolymeric model, but at temperatures above 40 ^°C the measured critical forces are much smaller than the predicted forces. The correspondence between theory and experiment is not improved by using Monte Carlo simulations that consider the heteropolymeric nature of the sequences.     

Micromechanics of base pair unzipping in the DNA duplex

All-atom molecular dynamics (MD) simulations of DNA duplex unzipping in a water environment were performed. The investigated DNA double helix consists of a Drew-Dickerson dodecamer sequence and a hairpin (AAG) attached to the end of the double-helix chain. The considered system is used to examine the process of DNA strand separation under the action of an external force. This process occurs in vivo and now is being intensively investigated in experiments with single molecules. The DNA dodecamer duplex is consequently unzipped pair by pair by means of the steered MD. The unzipping trajectories turn out to be similar for the duplex parts with G·C content and rather distinct for the parts with A·T content. It is shown that during the unzipping each pair experiences two types of motion: relatively quick rotation together with all the duplex and slower motion in the frame of the unzipping fork. In the course of opening, the complementary pair passes through several distinct states: (i) the closed state in the double helix, (ii) the metastable preopened state in the unzipping fork and (iii) the unbound state. The performed simulations show that water molecules participate in the stabilization of the metastable states of the preopened base pairs in the DNA unzipping fork.     

Dynamic force spectroscopy of protein-DNA interactions by unzipping DNA

We demonstrate the first site-specific single-molecule characterization of the prominent activation barrier for the disruption of a protein-DNA binding complex. We achieved this new capability by combining dynamic force spectroscopy with unzipping force analysis of protein association and used the combination to investigate restriction enzyme binding to specific DNA sites. Analysis revealed lifetimes and interaction distances for three protein-DNA interactions. This new method is able to distinguish protein-DNA binding complexes on a site-specific, single-molecule basis.     

Complete phase diagram of DNA unzipping: eye, Y fork, and triple point

We study the unzipping of double stranded DNA by applying a pulling force at a fraction s (0< or =s < or =1) from the anchored end. From exact analytical and numerical results, the complete phase diagram is presented. The phase diagram shows a strong ensemble dependence for various values of s. In addition, we show the existence of an eye phase and a triple point.     

Measurement of the phase diagram of DNA unzipping in the temperature-force plane

We separate double stranded lambda phage DNA by applying a fixed force at a constant temperature ranging from 15 to 50 degrees C, and measure the minimum force required to separate the two strands. The measurements also offer information on the free energy of double stranded DNA (dsDNA) at temperatures where dsDNA does not thermally denature in the absence of force. While parts of the phase diagram can be explained using existing models and free energy parameters, others deviate significantly. Possible reasons for the deviations between theory and experiment are considered.     

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).     

DNA unzipping and the unbinding of directed polymers in a random media

We consider the unbinding of a directed polymer in a random media from a wall in d=1+1 dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are identical up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems, a method which allows us to reduce the dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance z from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process.     

Single molecule unzipping of coiled coils: sequence resolved stability profiles

We use a high resolution atomic force microscopy technique to mechanically unzip and rezip single coiled-coil proteins. This allows us to read off the complete stability profile of the protein turn by turn. We investigated three coiled coils with different length as well as a point mutation and find force fluctuations between 9 and 15 pN that can be directly related to the amino-acid sequences. An equilibrium model previously applied to DNA fully describes the mechanical unzipping process including free-energy contributions of the individual turns and seed formation energy.     

Statistical physics approach to categorize biologic signals: from heart rate dynamics to DNA sequences

We recently proposed a novel approach to categorize information carried by symbolic sequences based on their usage of repetitive patterns. A simple quantitative index to measure the dissimilarity between two symbolic sequences can be defined. This information dissimilarity index, defined by our formula, is closely related to the Shannon entropy and rank order of the repetitive patterns in the symbolic sequences. Here we discuss the underlying statistical physics assumptions of this dissimilarity index. We use human cardiac interbeat interval time series and DNA sequences as examples to illustrate the applicability of this generic approach to real-world problems.     

Current-voltage characteristics of double-strand DNA sequences

We use a tight-binding formulation to investigate the transmissivity and the current-voltage (I-V) characteristics of sequences of double-strand DNA molecules. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare the results for the genomic DNA sequence with those of artificial sequences (the long-range correlated Fibonacci and Rudin-Shapiro one) and a random sequence, which is a kind of prototype of a short-range correlated system. The random sequence is presented here with the same first neighbors pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the transmissivity spectra, although the I-V curves seem to be mostly influenced by the short-range correlations.     

Linguistic features of noncoding DNA sequences

We extend the Zipf approach to analyzing linguistic texts to the statistical study of DNA base pair sequences and find that the noncoding regions are more similar to natural languages than the coding regions. We also adapt the Shannon approach to quantifying the "redundancy" of a linguistic text in terms of a measurable entropy function, and demonstrate that noncoding regions in eukaryotes display a smaller entropy and larger redundancy than coding regions, supporting the possibility that noncoding regions of DNA may carry biological information.     

Inference from matrix products: a heuristic spin-glass algorithm

We present an algorithm for finding ground states of two-dimensional spin-glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximation to the energy whose accuracy depends on a parameter k. We test the algorithm against exact methods on random field and random bond Ising models, and we find that accurate results require a k which scales roughly polynomially with the system size. The algorithm also performs well when tested on small systems with arbitrary interactions, where no fast, exact algorithms exist. The time required is significantly less than Monte Carlo schemes.