We calculate the entropic part of partition function of a bubble embedded in a double stranded DNA (dsDNA) by considering the total weights of possible configurations of a system of two single stranded DNA (ssDNA) of given length which start from a point along the contour of dsDNA and reunite at a position vector {\bf r} measured from the first point and the distribution function of the position vector {\bf r} which separates the two zipper forks of the bubble in dsDNA. For the distribution function of position vector {\bf r} we use the distribution of the end-to-end vector {\bf r} of strands of given length of dsDNA found from the wormlike chain model. We show that when the chains forming the bubble are assumed to be Gaussian the so called loop closure exponent $c$ is 3 and when we made correction by including self avoidence in each chain the value of $c$ becames 3.2.
Using Monte Carlo simulations, we study the hysteresis in unzipping of a double stranded block copolymer DNA with $-A_n B_n-$ repeat units. Here $A$ and $B$ represent two different types of base pairs having two- and three-bonds, respectively, and $2n$ represents the number of such base pairs in a unit. The end of the DNA are subjected to a time dependent periodic force with frequency ($ω$) and amplitude ($g_0$) keeping the other end fixed. We find that the equilibrium force-temperature phase diagram for the static force is independent of the DNA sequence. For the periodic force case, the resu…
The presence of a thermodynamic phase of a three-stranded DNA, namely, a mixed phase of bubbles of two bound strands and a single one, is established for large dimensions ($d\geq 5$) by using exact real space renormalization group (RG) transformations and exact computations of specific heat for finite length chains. Similar exact computations for the fractal Sierpinski gasket of dimension $d<2$ establish the stability of the phase in presence of repulsive three chain interaction. In contrast to the Efimov DNA, where three strands are bound though no two are bound, the mixed phase appears on th…
Using analytical approach and Monte-Carlo (MC) simulations, we study the elastic behaviour of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than 3D conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in 2D, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-be…
We present a new method for calculating internal forces in DNA structures using coarse-grained models and demonstrate its utility with the oxDNA model. The instantaneous forces on individual nucleotides are explored and related to model potentials, and using our framework, internal forces are calculated for two simple DNA systems and for a recently-published nanoscopic force clamp. Our results highlight some pitfalls associated with conventional methods for estimating internal forces, which are based on elastic polymer models, and emphasise the importance of carefully considering secondary str…
Bubble dynamics in double stranded DNA : A Rouse chain based approach
我们提出了一个双链DNA局部变性区（气泡）的波动动力学模型。在我们的公式中，DNA链被建模为一个一维的劳斯链限制在两端。当链的横向位移达到一个临界值时，气泡形成。这个简单的模型有效地再现了自相关函数的标记的碱基对的DNA链中所测量的种子单分子实验Altan-Bonnet等。al（Phys. Rev. Lett. 90，138101（2003））。虽然我们的模型在数学上类似于Chatterjee等人提出的模型（J.Chem.Phys.127，155104（2007）），但它通过将链动力学通过受限的Rouse链结合而超越了单个反应坐标描述，从而考虑了动力学的集体性质。我们的模型还表明，自相关函数是非常敏感的正常模式的链的弛豫时间，这是显而易见的，因为气泡的波动动力学有来自不同的正常模式的链的贡献。
Solid-state nanopores are single molecule sensors that measure changes in ionic current as charged polymers such as DNA pass through. Here, we present comprehensive experiments on the length, voltage and salt dependence of the frequency of double-stranded DNA translocations through conical quartz nanopores with mean opening diameter 15 nm. We observe an entropic barrier limited, length dependent translocation frequency at 4M LiCl salt concentration and a drift-dominated, length independent translocation frequency at 1M KCl salt concentration. These observations are described by a unifying conv…
Recent magnetic tweezers experiments have reported systematic deviations of the twist response of double-stranded DNA from the predictions of the twistable worm-like chain model. Here we show, by means of analytical results and computer simulations, that these discrepancies can be resolved if a coupling between twist and bend is introduced. We obtain an estimate of 40 $\pm$ 10 nm for the twist-bend coupling constant. Our simulations are in good agreement with high-resolution, magnetic-tweezers torque data. Although the existence of twist-bend coupling was predicted long ago (Marko and Siggia, …
The folding of biological macromolecules is a fundamental process of which we lack a full comprehension. Mostly studied in proteins and RNA, single-stranded DNA (ssDNA) also folds, at physiological salt conditions, by forming non-specific secondary structures that are difficult to characterize with biophysical techniques. Here we present a helix-coil model for secondary structure formation, where ssDNA bases are organized in two different types of domains (compact and free). The model contains two parameters: the energy gain per base in a compact domain, $ε$, and the cooperativity related to t…
We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well-known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segm…
We develop a robust coarse-grained model for single and double stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data B…
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 accurate knowledge of the elastic properties of single-stranded DNA (ssDNA) is key to characterize the thermodynamics of molecular reactions that are studied by force spectroscopy methods where DNA is mechanically unfolded. Examples range from DNA hybridization, DNA ligand binding, DNA unwinding by helicases, etc. To date, ssDNA elasticity has been studied with different methods in molecules of varying sequence and contour length. A dispersion of results has been reported and the value of the persistence length has been found to be larger for shorter ssDNA molecules. We carried out pulling…
