We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri J, Manghi M and Destainville N 2007 Phys. Rev. Lett. 99 088103). Our Discrete Helical Wormlike Chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite-size effects in an experimental context where polydA-polydT is clamped by two G-C strands, as well as for free polymers.
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 $c=4ν-1/2$ 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.
A statistical model of homopolymer DNA, coupling internal base pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-s…
The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillement of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and above $T^*_c$. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appear…
We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the $d = 3$ case, the…
We study the folding of RNA secondary structures with quenched sequence randomness by means of the constrained annealing method. A thermodynamic phase transition is induced by including the conformational weight of loop structures. In addition to the expected melting at high temperature, a cold melting transition appears. Our results suggest that the cold denaturation of RNA found experimentally is, in fact, a continuous phase transition triggered by quenched sequence disorder. We calculate both hot and cold melting critical temperatures for the competing energy scenario between favorable and …
Studying the properties of the solvent around proteins, we propose a much more sophisticated model of solvation than temperature-independent pairwise interactions between monomers, as is used commonly in lattice representations. We applied our model of solvation to a 16-monomer chain constrained on a two-dimensional lattice. We compute a phase diagram function of the temperature and a solvent parameter which is related to the pH of the solution. It exhibits a native state in which the chain coalesces into a unique compact conformation as well as a denatured state. Under certain solvation condi…
We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $β-$sheets in protein, by including the constant force stretching at one end of molecules as in a typical single-molecule experiment. The conformations of double-stranded regions of the chain are calculated based on polymer graph-theoretic approach [S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the unpaired single-stranded regions are treated as self-avoiding walk…
We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling double-stranded DNA at each end exerts a profound effect on the thermal denaturation, or melting, of a long segment of this molecule. We discuss the effects on this transition of a stretching force applied to opposite ends of one of the DNA strands, including full consideration of the consequences of excluded volume, the analysis of which is greatly simplified in this case. We also discuss the interplay of thermal denaturation and force-generated separation when the tension is generated by a force…
Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a 1D Ising model, which describes the internal base pair states, coupled to a discrete worm like chain model describing the chain configurations [J. Pal…
Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one knows force expansion of the extension through the $(n-1)$th power of force, it is enough information to calculate the $n$ moments of the distribution. We examine the method with three force stretching chain models, Gaussian chain, free-joined chain and excluded-volume chain on two-dimension lattice. The method reconstructs all distributions pre…
We study conformations and dynamics of active star polymers. The analysis shows that active star polymers stretching behaviour is quite different from that of active linear chains. The visual inspection of conformations and bond-bond correlations reveal a better coordination for the alignment and coordination of bonds for the star polymers than for the linear counterparts. The architecture substantially affects the chain extension transition at high values of active force. The scaling laws for the shape factor and the arm asphericity ratio established for the passive star polymers coincide wit…
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 perform Monte Carlo simulations to study the elastic properties of the helix-coil worm-like chain model of alpha-helical polypeptides. In this model the secondary structure enters as a scalar (Ising like) variable that controls the local chain bending modulus. We compute numerically the bending and stretching compliances of this molecule as well as the nonlinear interaction between stretching and torque over a wide range of model parameters. The numerical results agree well with previous mean-field and perturbative calculations where they are expected to do so. The Monte Carlo simulations a…
Langevin Dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the \textit{trans}-side. Under the influence of pre-stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields …
We discuss possible mechanisms that may impact the order of the transition between denaturated and bound DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory approach to calculate entropic exponents associated with the denaturated loop distribution. We discuss in particular variants of this transition that may occur due to the properties of the solution and may affect the self- and mutual interaction of both single and double strands. We find that the effec…
We introduce a three-state model for a single DNA chain under tension that distinguishes between B-DNA, S-DNA and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S ~ - c ln n for the entropy of a loop of length n. Force extension curves are derived exactly employing a generalized Poland-Scheraga approach and compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allo…
Double-stranded DNA `overstretches' at a pulling force of about 65 pN, increasing in length by a factor of 1.7. The nature of the overstretched state is unknown, despite its considerable importance for DNA's biological function and technological application. Overstretching is thought by some to be a force-induced denaturation, and by others to consist of a transition to an elongated, hybridized state called S-DNA. Within a statistical mechanical model we consider the effect upon overstretching of extreme sequence heterogeneity. `Chimeric' sequences possessing halves of markedly different AT co…
Single molecule experiments on B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. It has been proposed that the first transition, at forces of 60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance f…
Force-induced reversible transformations between coiled and normal polymorphs of bacterial flagella have been observed in recent optical-tweezer experiment. We introduce a discrete elastic rod model with two competing helical states governed by a fluctuating spin-like variable that represents the underlying conformational states of flagellin monomers. Using hybrid Brownian dynamics Monte-Carlo simulations, we show that a helix undergoes shape transitions dominated by domain wall nucleation and motion in response to externally applied uniaxial tension. A scaling argument for the critical force …
The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find theoreticlly and by a simple blob picture that the extension scales as fr_D where r_D is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like confor…
We examine the conformations of a model for under- and overwound DNA. The molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number. We derive a fundamental relation between the Euler angles that describe the curve and the topological linking number. Analytical expressions for the spatial configurations of the molecule in the infinite- length limit were obtained. A unique configuraion minimizes the energy for a given set of physical conditions. An elastic model incorporating thermal…
Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop formation, and salt effects. Using an iterative expression for the partition function that neglects pseudoknots, we calculate folding free energies and minimum free energy configurations based on the experimentally derived base pairing free energies. The configurational entropy of loop formation is modeled by the asymptotic expression -c ln m, where m is the length…
Nonlinear extensional flows are common in polymer processing but remain challenging theoretically because dramatic stretching of chains deforms the entanglement network far from equilibrium. Here, we present coarse-grained simulations of extensional flows in entangled polymer melts for Rouse-Weissenberg numbers $Wi_R=0.06$-$52$ and Hencky strains $ε\geq6$. Simulations reproduce experimental trends in extensional viscosity with time, rate and molecular weight. Studies of molecular structure reveal an elongation and thinning of the confining tube with increasing $Wi_R$. The rising stress is quan…
The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland-Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant r…
We study numerically the mechanical stability and elasticity properties of duplex DNA molecules within the frame of a network model incorporating microscopic degrees of freedom related with the arrangement of the base pairs. We pay special attention to the opening-closing dynamics of double-stranded DNA molecules which are forced into non-equilibrium conformations. Mechanical stress imposed at one terminal end of the DNA molecule brings it into a partially opened configuration. We examine the subsequent relaxation dynamics connected with energy exchange processes between the various degrees of…
While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting open question. Here by means of the scaling analyses and computer simulations we examine stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius $R$. Surprisingly, we reveal that the typical excursions of the polymer away from the surface scale as $Δ\sim R^β$, with the Kardar-Parisi-Zhang (KPZ) growth exponent $β=1/3$, for any …
We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering Monte Carlo simulations it is shown that the system exhibits a rich phase behavior ranging from highly ordered, compact to extended random coil structures and from desorbed to completely adsorbed or even partially embedded conformations. These findings are summarized in a pseudophase diagram indicating the predominant class of conformations as a function of the…
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to e…
How hydrodynamic interactions alter polymer stretching in turbulence
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度孟买理工学院-蒙纳士大学联合研究院）；Indian Institute of Technology Bombay（印度孟买理工学院）；Monash University（蒙纳士大学）；Université Côte d’Azur（蔚蓝海岸大学）
In order to interpret recent experimental studies of the dependence of conductance of ds-DNA as the DNA is pulled from the 3'end1-3'end2 ends, which find a sharp conductance jump for a very short (4.5 %) stretching length, we carried out multiscale modeling, to predict the conductance of dsDNA as it is mechanically stretched to promote various structural polymorphisms. We calculate the current along the stretched DNA using a combination of molecular dynamics simulations, non-equilibrium pulling simulations, quantum mechanics calculations, and kinetic Monte Carlo simulations. For 5'end1-5'end2 …
One of the major theoretical methods in understanding polymer translocation through a nanopore is the Fokker-Planck formalism based on the assumption of quasi-equilibrium of polymer conformations. The criterion for applicability of the quasi-equilibrium approximation for polymer translocation is that the average translocation time per Kuhn segment, $\langle τ\rangle/N_K$ is longer than the relaxation time $τ_0$ of the polymer. Towards an understanding of conditions that would satisfy this criterion, we have performed coarse-grained three dimensional Langevin dynamics and multi-particle collisi…
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: \textit{uniform} stretching by external forces and \textit{non-uniform} stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g. fluid in uniform motion, or uniform electric field) by a universal physical framework which leads to general conclusions on different types of polymers…
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…
Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {sufficiently large} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $<Z>\sim f$ for small $f$, and $<Z>\sim f^{2/3}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for $\la Z\ra$ as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with…
In the present work, we study the equilibrium conformations of linear polyelectrolytes tethered onto a spherical, oppositely charged core in equilibrium with an ionic reservoir of fixed concentration. Particular focus is placed on the situation of stretched chains, where the monomer concentration is known to display an inverse square-law decay far away from the spherical surface, which is then further extrapolated all the way down to the grafting core. While the equilibrium distributions of mobile ions are computed in the framework of a classical Density Functional Theory (cDFT) that incorpora…
The dynamic behavior of semi-dilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semi-dilute solutions are characterized by large fluctuations in concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In non-equilibrium flows, it is generally thought that polymer chains can self-entangle in semi-dilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress, we still lack a complete molecular-level …
By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $\sim f^{1/4}$ and the effective interaction as $\sim f^{2}$, as opposed to $\sim f^{1/5}$ and $\sim f^{3/2}$, respectively, in three dimensions. Our results de…
I propose a variation of the standard worm--like chain model to account for internal order parameter (helix/coil) fields on the polymer chain. This internal order parameter field influences polymer conformational statistics by locally modifying the persistence length of the chain. Using this model, I make predictions for the bending and stretching response of an alpha-helical domain of a protein. In particular, I show that alpha-helical protein domains will buckle under applied torque. This highly nonlinear elastic behavior may be important in the understanding of allosteric control of biochem…
An applied tension force changes the equilibrium conformations of a polymer chain tethered to a planar substrate and thus affects the adsorption transition as well as the coil-globule and crystallization transitions. Conversely, solvent quality and surface attraction are reflected in equilibrium force-extension curves that can be measured in experiments. To investigate these effects theoretically, we study tethered chains under tension with Wang-Landau simulations of a bond-fluctuation lattice model. Applying our model to pulling experiments on biological molecules we obtain a good description…
Polydisperse brushes obtained by reversible radical chain polymerization reaction onto a solid substrate with surface-attached initiators, are studied by means of an off-lattice Monte Carlo algorithm of living polymers (LP). Various properties of such brushes, like the average chain length and the conformational orientation of the polymers, or the force exerted by the brush on the opposite container wall, reveal power-law dependence on the relevant parameters. The observed molecular weight distribution (MWD) of the grafted LP decays much more slowly than the corresponding LP bulk system due to…
Stretching response of polymer chains under external force is crucial in understanding polymer dynamics under equilibrium and non-equilibrium conditions. Here we measure the elastic response of poly(ethylene glycol) using a lock-in based amplitude modulation-AFM with sub-angstrom amplitude in both low and high frequency regime. Appropriate analysis that takes into account the cantilever geometry and hydrodynamic loading effects of oscillating cantilever in liquid, relates X signal of lock-in amplifier linearly to stiffness.Stiffness data extracted from X signal was compared with stiffness from…
By extending the classical Peyrard-Bishop model, we are able to obtain a fully analytical description for the mechanical resistance 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 e…
The mechanical properties of polymer knots under stretching in a bad or good solvent are investigated by applying a given force $F$ to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer conformations on a simple cubic lattice is performed using a variant of the Wang-Landau algorithm. The results of the calculations of the specific energy, specific heat capacity and gyration radius for several knot topologies show a general trend in the behavior of short polymer knots with lengths up to seventy lattice units. At low tensile force $F$, knots can be fou…
The effect of magnesium ion Mg2+ on the dielectric relaxation of semidilute DNA aqueous solutions has been studied by means of dielectric spectroscopy in the 100 Hz-100 MHz frequency range. De Gennes-Pfeuty-Dobrynin semidilute solution correlation length is the pertinent fundamental length scale for sufficiently low concentration of added salt, describing the collective properties of Mg-DNA solutions. No relaxation fingerprint of the DNA denaturation bubbles, leading to exposed hydrophobic core scaling, was detected at low DNA concentrations, thus indicating an increased stability of the doubl…
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $ϕ_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10 well-entangled systems with $ϕ_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a fun…
We use computer simulations to study the relaxation of strongly deformed highly entangled polymer melts in the non-linear viscoelastic regime, focusing on anisotropic chain conformations after isochoric elongation. The Doi-Edwards tube model and its GLaMM extension, incorporating contour length fluctuation and convective constraint release, predict a retraction of the polymer chain extension in all directions, setting in immediately after deformation. This prediction has been challenged by experiment, simulation, and other theoretical studies, questioning the general validity of the tube conce…
We study the conformation and dynamics of a single polymer chain that is pulled by a constant force applied at its one end with the other end free. Such a situation is relevant to the growing technology of manipulating individual macromolecules, which offers a paradigm research for probing far-from-equilibrium responses of long flexible biological polymers. We first analyze the Rouse model for the Gaussian chains for which the exact analytical results can be obtained. More realistic features such as the finite extensibility, the excluded volume and the hydrodynamic interactions are taken into …
For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders. The ds-DNA is modeled by a mesoscopic Hamiltonian which accounts for the three dimensional helical structure and incorporates fluctuational effects at the level of the base pair. The computational method assumes that the base pair fluctuations are temperature dependent trajectories whose amplitudes can be spatially modulated according to the crowders distribution. We…
Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs con…
Conformations of a single-component bottle-brush polymer with a fully flexible backbone under poor solvent conditions are studied by molecular-dynamics simulations, using a coarse-grained bead-spring model with side chains of up to N=40 effective monomers. By variation of the solvent quality and the grafting density $σ$ with which side chains are grafted onto the flexible backbone, we study for backbone lengths of up to $N_b=100$ the crossover from the brush/coil regime to the dense collapsed state. At lower temperatures, where collapsed chains with a constant monomer density are observed, the…
