Titus S. van Erp, Santiago Cuesta-Lopez, Johannes-Geert Hagmann, Michel Peyrard
We show that the calculated DNA denaturation curves for finite (Peyrard-Bishop-Dauxois (PBD) chains are intrinsically undefined.
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DNA melting: intra base-pair dynamics and a vector generalization of the Peyrard-Bishop-Dauxois model
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DNA-gold nanoparticle assemblies have shown promise as an alternative technology to DNA microarrays for DNA detection and RNA profiling. Understanding the effect of DNA sequences on the melting temperature of the system is central to developing reliable detection technology. We studied the effects of DNA base-pairing defects, such as mismatches and deletions, on the melting temperature of DNA-nanoparticle assemblies. We found that, contrary to the general assumption that defects lower the melting temperature of DNA, some defects increase the melting temperature of DNA-linked nanoparticle assem…
When double-stranded DNA molecules are heated, or exposed to denaturing agents, the two strands get separated. The statistical physics of this process has a long history, and is commonly described in term of the Poland-Scheraga (PS) model. Crucial to this model is the configurational entropy for a melted region (compared to the entropy of an intact region of the same size), quantified by the loop factor. In this study we investigate how confinement affects the DNA melting transition, by using the loop factor for an ideal Gaussian chain. By subsequent numerical solutions of the PS model, we dem…
DNA nanocompartment is a typical DNA-based machine whose function is dependent of molecular collective effect. Fundamental properties of the device have been addressed via electrochemical analysis, fluorescent microscopy, and atomic force microscopy. Interesting and novel phenomena emerged during the switching of the device. We have found that DNAs in this system exhibit a much steep melting transition compared to ones in bulk solution or conventional DNA array. To achieve an understanding to this discrepancy, we introduced DNA-DNA interaction potential to the conventional Ising-like Zimm-Brag…
When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this "melting" transition have been intensively investigated. Recently there has been a surge of interest in this question, caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce, and solve a model predicting how confinement affects the melting transition for a simple model syst…
The effect of secondary structure on DNA duplex formation is poorly understood. We use a coarse-grained model of DNA to show that specific 3- and 4-base pair hairpins reduce hybridization rates by factors of 2 and 10 respectively, in good agreement with experiment. By contrast, melting rates are accelerated by factors of ~100 and ~2000. This surprisingly large speed-up occurs because hairpins form during the melting process, stabilizing partially melted states, and facilitating dissociation. These results may help guide the design of DNA devices that use hairpins to modulate hybridization and …
The conclusions presented in this Letter arXiv:cond-mat/0412591 rely on not converged calculations and should be considered with caution.
Three, interrelated biologically-relevant examples of biased random walks are presented: (1) A model for DNA melting, modelled as DNA unzipping, which provides a way to illustrate the role of the Boltzmann factor in a venue well-known to biology and pre-medical students; (2) the activity of helicase motor proteins in unzipping double-stranded DNA, for example, at the replication fork, which is an example of a Brownian ratchet; (3) force generation by actin polymerization, which is another Brownian ratchet, and for which the force and actin-concentration dependence of the velocity of actin poly…
DNA melting and hybridization is a fundamental biological process as well as a crucial step in many modern biotechnology applications. DNA confined on surfaces exhibits different behavior from that in free solutions. The system of DNA-capped gold nanoparticles exhibits unique phase transitions and represents a new class of complex fluids. Depending on the sequence of the DNA, particles can be linked to each other through direct complementary DNA sequences or via a ``linker'' DNA whose sequence is complementary to the sequence attached to the gold nanoparticles. We observed different melting tr…
Nonequilibrium Work Fluctuations in Force-induced Melting of a Short B-DNA
本研究通过对12碱基对B-DNA进行恒速拉伸实验测量非平衡功，并利用Jarzynski等式准确计算出DNA平衡态与力诱导熔解态之间的自由能差。
Despite numerous attempts, the understanding of the thermal denaturation of DNA is still a challenge due to the lack of structural data at the transition since standard experimental approaches to DNA melting are made in solution and do not provide spatial information. We report a measurement using neutron scattering from oriented DNA fibres to determine the size of the regions that stay in the double-helix conformation as the melting temperature is approached from below. A Bragg peak from the B-form of DNA has been observed as a function of temperature and its width and integrated intensity ha…
A double-stranded DNA unravels thermally through intermediate denatured bubble segments. Intrinsically, fluctuations ensue at the bubble boundaries from non-equilibrium (NE) energy exchanges with the environment. However, such details gets obscured by large population kinetics at the macroscale, associating equilibrium pathway to the unravelling landscape. In this work, we capture evidence of fluctuation energetics with picoliter samples in a microfluidic cantilever. We exploit nanomechanical resonance to measure the NE energy exchanges through dissipation, revealing a crucial pre-melting tran…
Standard DNA melting curves record the separation of the two strands versus temperature, but they do not provide any information on the location of the opening. We introduce an experimental method which adds a new dimension to the melting curves of short DNA sequences by allowing us to record the degree of opening in several positions along the molecule all at once. This adds the spatial dimension to the melting curves and allows a precise investigation of the role of the base-pair sequence on the fluctuations and denaturation of the DNA double helix. We illustrate the power of the method by i…
The melting curves of short heterogeneous DNA chains in solution are calculated on the basis of statistical thermodynamics and compared to experiments. The computation of the partition function is based on the Peyrard-Bishop hamiltonian, which has already been adopted in the theoretical description of the melting of long DNA chains. In the case of short chains it is necessary to consider not only the breaking of the hydrogen bonds between single base pairs, but also the complete dissociation of the two strands forming the double helix.
Overstretching of B-DNA is currently understood as force-induced melting. Depending on the geometry of the stretching experiment, the force threshold for the overstretching transition is around 65 or 110 pN. Although the mechanisms behind force-induced melting have been correctly described by Rouzina and Bloomfield \cite{RouzinaBloomfield2001a}, neither force threshold has been exactly calculated by theory. In this work, a detailed analysis of the force-extension curve is presented, based on a description of single-stranded DNA in terms of the discrete Kratky-Porod model, consistent with (i) t…
We report experimental observations on the effect of disorder on the phase behavior of DNA-linked nanoparticle assemblies. Variation in DNA linker lengths results in different melting temperatures of the DNA-linked nanoparticle assemblies. We observed an unusual trend of a non-monotonic ``zigzag'' pattern in the melting temperature as a function of DNAlinker length. Linker DNA resulting in unequal DNA duplex lengths introduces disorder and lowers the melting temperature of the nanoparticle system. Comparison with free DNA thermodynamics shows that such an anomalous zigzag pattern does not exis…
We investigate kinetic pathways of the DNA melting transition using variable-range versions of the Poland-Scheraga (PS) and Peyrard-Dauxois-Bishop (PDB) models of DNA. In the PS model, we construct a phi^4-field theory to calculate the critical droplet profile, the initial growth modes, and the exponent characterizing the divergence of the susceptibility near the spinodal. In the PDB model, we use a mean field analysis to calculate susceptibility exponent. We compare these theoretical results with Monte Carlo and Brownian dynamic simulations on the PS and PDB models, respectively. We find that…
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 pl…
The melting behavior of long, heterogeneous DNA chains is examined within the framework of the nonlinear lattice dynamics based Peyrard-Bishop-Dauxois (PBD) model. Data for the pBR322 plasmid and the complete T7 phage have been used to obtain model fits and determine parameter dependence on salt content. Melting curves predicted for the complete fd phage and the Y1 and Y2 fragments of the $ϕ$X174 phage without any adjustable parameters are in good agreement with experiment. The calculated probabilities for single base-pair opening are consistent with values obtained from imino proton exchange …
We propose a new statistical mechanics model for the melting transition of DNA. Base pairing and stacking are treated as separate degrees of freedom, and the interplay between pairing and stacking is described by a set of local rules which mimic the geometrical constraints in the real molecule. This microscopic mechanism intrinsically accounts for the cooperativity related to the free energy penalty of bubble nucleation. The model describes both the unpairing and unstacking parts of the spectroscopically determined experimental melting curves. Furthermore, the model explains the observed tempe…
We propose a statistical mechanics model for DNA melting in which base stacking and pairing are explicitly introduced as distinct degrees of freedom. Unlike previous approaches, this model describes thermal denaturation of DNA secondary structure in the whole experimentally accessible temperature range. Base pairing is described through a zipper model, base stacking through an Ising model. We present experimental data on the unstacking transition, obtained exploiting the observation that at moderately low pH this transition is moved down to experimentally accessible temperatures. These measure…
Understanding the melting of short DNA sequences probes DNA at the scale of the genetic code and raises questions which are very different from those posed by very long sequences, which have been extensively studied. We investigate this problem by combining experiments and theory. A new experimental method allows us to make a mapping of the opening of the guanines along the sequence as a function of temperature. The results indicate that non-local effects may be important in DNA because an AT-rich region is able to influence the opening of a base pair which is about 10 base pairs away. An earl…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free energy landscape. Melting profiles, dependence …
We investigated how the finiteness of the length of the sequence affects the phase transition that takes place at 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 non-extensive (order parameter and correlation length) thermodynamic quantities of finite sequences with open boundary conditions, and applied the modified procedure to two different dynamical models. We showed that rounding of the transition clearly takes place when the length of the sequence is d…
As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the undenatured sections can, in principle, alter the nature of the thermal denaturation process. Assuming that the strains associated with this overwinding are not relieved, we find that a simple model of strain-altered melting leads to a suppression of the melting transition when the unaltered transition is continuous. When the melting transition is first order in the …
The Peyrard-Bishop DNA model describes the molecular interactions with simple potentials which allow efficient calculations of melting temperatures. However, it is based on a Hamiltonian that does not consider the helical twist or any other relevant molecular dimensions. Here, we start from a more realistic 3D model and work out several approximations to arrive at a new non-linear 1D Hamiltonian with a twist angle dependence. Our approximations were numerically compared to full 3D calculations, and established its validity in the regime of small angles. For long DNA sequences we obtain sharp, …
Melting and hybridization of DNA-capped gold nanoparticle networks are investigated with optical absorption spectroscopy. Single-stranded, 12-base DNA-capped gold nanoparticles are linked with complementary, single-stranded, 24-base linker DNA to form particle networks. Compared to free DNA, a sharp melting transition is seen in these networked DNA-nanoparticle systems. The sharpness is explained by percolation transition phenomena.
We introduce a sequence-dependent parametrization for a coarse-grained DNA model [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Chem. Phys. 134, 085101 (2011)] originally designed to reproduce the properties of DNA molecules with average sequences. The new parametrization introduces sequence-dependent stacking and base-pairing interaction strengths chosen to reproduce the melting temperatures of short duplexes. By developing a histogram reweighting technique, we are able to fit our parameters to the melting temperatures of thousands of sequences. To demonstrate the flexibility of the mod…
DNA denaturation has long been a subject of intense study due to its relationship to DNA transcription and its fundamental importance as a nonlinear, structural transition. Many aspects of this phenomenon, however, remain poorly understood. Existing models fit quite well with experimental results on the fraction of unbound base pairs versus temperature. Yet, these same models give incorrect results for other essential quantities. For example, the predicted base pair fluctuation timescales - relevant to transcription - are orders of magnitude different from those observed experimentally. Here, …
Table of Content 1. Introduction 2. DNA fundamentals 3. Attachment of DNA to surface 4. Fabrication of nanostructures using DNA 4.1 Nanostructures of pure DNA 4.2 DNA-based assembly of metal nanoparticles 4.3 Construction of semiconductor particle arrays using DNA 4.4 DNA-directed nanowires 4.5 DNA-functionalized carbon nanotubes 4.6 Field-transistor based on DNA 4.7 Nanofabrication using artificial DNA 5. DNA-based nanostructures as biosensors 6. Properties of DNA-linked gold nanoparticles 6.1 Aggregation of DNA-modified gold nanoparticles 6.2 Melting of DNA-linked gold nanoparticle aggregati…
The homochirality of the molecules of life has been a vexing problem with no generally accepted solution to date. Since a racemic mixture of chiral nucleotides frustrates the extension and replication of RNA and DNA, understanding the origin of homochirality has important implications to the investigation of the origin of life. Here we suggest a novel solution to the homochirality problem based on a recently proposed thermodynamic dissipation theory for the origin of life. Homochirality is suggested to have been incorporated gradually into the emerging life as a result of asymmetric right- ove…
We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused on precise sequences and investigated the succession of local openings that lead to their dissociation. For this purpose, we performed Transfer Integral type calculations with two different dynamical models, namely the heterogeneous Dauxois-Peyrard-Bishop model and the model based on finite stacking enthalpies we recently proposed. It appears that, for both m…
The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e. stretches of DNA which do not carry any useful information for the protein synthesis. We have analyzed the melting behavior of randomly selected human cDNA sequences obtained from the genomic DNA by removing all introns. A clear correspondence is observed between exons and melting domains. This finding may provide new insights in the physical mechanisms underlying the evolution of genes.
The melting transition of deoxyribonucleic acid (DNA), whereby the strands of the double helix structure completely separate at a certain temperature, has been characterized using neutron scattering. A Bragg peak from B-form fibre DNA has been measured as a function of temperature, and its widths and integrated intensities have been interpreted using the Peyrard-Bishop-Dauxois (PBD) model with only one free parameter. The experiment is unique, as it gives spatial correlation along the molecule through the melting transition where other techniques cannot.
We present direct evidence for a reversible phase transition of DNA-linked colloidal gold assemblies. Transmission electron microscopy and optical absorption spectroscopy are used to monitor the colloidal gold phase transition, whose behavior is dominated by DNA interactions. We use single-stranded DNA-capped colloidal gold that is linked by complementary linker DNA to form the assemblies. We found that, compared to free DNA, a sharp melting transition is observed for the DNA-linked colloidal gold assemblies. The structure of the assemblies is non-crystalline, much like a gel phase, consistent…
Using the Langevin Dynamics simulation, we have studied the effects of the shear force on the rupture of short double stranded DNA at different temperatures. We show that the rupture force increases linearly with the chain length and approaches to the asymptotic value in accordance with the experiment. The qualitative nature of these curves almost remains same for different temperatures but with a shift in the force. We observe three different regimes in the extension of covalent bonds (back bone) under the shear force.
Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low temperature / low force compact (folded) structure and a high temperature / high force molten (unfolded) structure. The influence of c on phas…
We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with "nu_perpendicular" = - beta = 1, "nu_parallel" = gamma/2 = 2 (characteristic of short range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents "nu_…
We present a nonlinear dynamical model for DNA thermal denaturation, which is based on the finite stacking enthalpies used in thermodynamical nearest-neighbour calculations. Within this model, the finiteness of stacking enthalpies is shown to be responsible for the sharpness of calculated melting curves. Transfer-integral and molecular dynamics calculations are performed to demonstrate that the proposed model leads to good agreement with known experimental results for both homogeneous and inhomogeneous DNA.
We recently proposed a dynamical mesoscopic model for DNA, which is based, like statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present article, 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 mod…
Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conforma…
We study the influence of a THz field on thermal properties of DNA molecules. A Peyrard- Bishop-Dauxois model with the inclusion of a solvent interaction term is considered. The THz field is included as a sinusoidal driven force in the equation of mo tion. We show how under certain field and system parameters, melting transition and bubble formation are modified.
The paper uses mesoscopic, non-linear lattice dynamics based (Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA below and near the denaturation temperature. Computationally efficient notation is introduced for the relevant statistical mechanics. Computed melting profiles of long and short heterogeneous sequences are presented, using a recently introduced reparametrization of the PBD model, and critically discussed. The statistics of extended open bubbles and bound clusters is formulated and results are presented for selected examples.
The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous short sequences of DNA, i.e. $\sim 100$ base pairs, in the framework of a mesoscopic Hamiltonian model which accounts for the helicoidal geometry of the molecule. The theoretical background for the application of the path integral formalism to predictive analysis of the molecule thermodynamical properties is discussed. The base pair displacements with respec…
The force induced unzipping transition of a double stranded DNA is considered from a purely thermodynamic point of view. This analysis provides us with a set of relations that can be used to test microscopic theories and experiments. The thermodynamic approach is based on the hypothesis of impenetrability of the force in the zipped state. The melting and the unzipping transitions are considered in the same framework and compared with the existing statistical model results. The analysis is then extended to a possible continuous unzipping transition.
The mechanism of threshold elongation (overstretching) of DNA macromolecules under the action of external force is studied within the framework of phenomenological approach. When considering the task it is taken into account that double-stranded DNA is a polymorphic macromolecule with a set of metastable states. Accordingly to proposed mechanism, DNA threshold elongation can take place as a cooperative structural transition of macromolecule to metastable form, which is stabilized by the external force. For the description of DNA overstretching, the model included external (stretching) and inte…
On the effect of force on DNA in the Peyrard-Bishop-Dauxois model
本文研究了外力对DNA双螺旋断裂动力学的影响，利用PBD模型分析了力作用点对氢键断裂和变性过程的影响，并探讨了滞回现象。
We study the thermal and mechanical behavior of DNA denaturation in the frame of the mesoscopic Peyrard- Bishop-Dauxois model with the inclusion of solvent interaction. By analyzing the melting transition of a homogeneous A-T sequence, we are able to set suitable values of the parameters of the model and study the formation and stability of bubbles in the system. Then, we focus on the case of the P5 promoter sequence and use the Principal Component Analysis of the trajectories to extract the main information on the dynamical behavior of the system. We find that this analysis method gives an ex…
The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double stranded helix, released by a loop denaturation, is absorbed by \emph{supercoils}. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent $c$. However the first order transition displayed by the PS model for $c>2$ in linear DNA is replaced by a continuous transition with arbitrarily high order as $c$ approaches 2…
A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The …
We analyze the dynamics of structural transitions between normal right-handed B form and unusual left-handed Z form for a linear DNA molecule. The dynamics under the external torque in physiological buffer is modeled by a Langevin equation, with the potential term given by the authors previously [Phys. Rev. E 84, 021926 (2011)]. With this model, we first simulate the relaxation processes around B-form structure after sudden changes of the external torques, where slow relaxation $\sim t^{-1/2}$ as a function of the elapsed time $t$ is observed. Then, the dynamics of structural transition from Z…
We theoretically investigated the temperature fluctuations of DNA close to denaturation and observed a strong enhancement of these fluctuations at the critical temperature. Although in a much lower frequency range, such a sharp increase was also reported in the recent experimental work of Nagapriya et al [Phys. Rev. Lett. 96, 038102 (2006)]. We showed that there is instead no enhancement of temperature fluctuations when the dissipation coefficient in Langevin equations is assumed to be larger than a few tens of ps-1, and pointed out the possible role of the solvent in real experiments. We soug…
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