Effects of magnesium salt concentrations on B-DNA overstretching transition

In this study, we use optical tweezers to investigate the ionic effects of magnesium salt solutions on the overstretching transition of single B-DNA molecules. The experimental data are compared with those in sodium salt solutions. The overstretching transition force increases when the NaCl or MgCl₂ salt concentration increases. Magnesium cations have much stronger effects on the overstretching transition force than sodium cations. For both NaCl and MgCl₂ salt solutions, the overstretching transition force is linear with the natural logarithm of salt concentration, which confirms the theory proposed in previous paper. The modified ZZO model is applied to study the electrostatic contribution of magnesium salt solutions to the overstretching transition of single B-DNA molecules. The consistency between the experimental data and analytical results shows that the modified ZZO model can simulate the transition behavior of single B-DNA molecules in different NaCl and MgCl₂ salt solutions.     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Melting of columnar hexagonal DNA liquid crystals

The persistence length DNA hexagonal-cholesteric phase transition upon dilution and/or increase in solvent ionic strength is investigated with polarized light microscopy. The ionic strength dependence of the transition follows Lindemann criterion , i.e., the hexagonal lattice melts when the root-mean-square fluctuations in transverse order exceed 10% of the interaxial spacing. The spacings are derived from density and the fluctuations are estimated with a theory of undulation enhanced electrostatic interactions. Additional support for this theory is given by the DNA equation of state and anisotropic neutron radiation scattering from magnetically aligned cholesteric samples just below the phase transition. Received: 17 November 1997 / Revised: 21 January 1998 / Accepted: 25 February 1998     

Stretching DNA: Role of electrostatic interactions

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 the extension scales as where 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 conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

盐离子对DNA延伸力的影响

在Ahsan等给出的描述DNA分子弹性的两状态虫链模型的基础上,考虑到盐离子浓度对静电自由能的影响,得到了延伸力随盐浓度的变化规律,结果表明:在低力和高力范围延伸力受盐浓度的影响较小,相变延伸范围随盐浓度的增加非线性增加,与实验测量一致.     

Nanoconfinement-enhanced conformational response of single DNA molecules to changes in ionic environment

We show that the ionic environment plays a critical role in determining the configurational properties of DNA confined in silica nanochannels. The extension of DNA in the nanochannels increases as the ionic strength is reduced, almost tripling over two decades in ionic strength for channels around 100 x 100 nm in dimension. Surprisingly, we find that the variation of the persistence length alone with ionic strength is not enough to explain our results. The effect is due mainly to increasing self-avoidance created by the reduced screening of electrostatic interactions at low ionic strength. To quantify the increase in self-avoidance, we introduce a new parameter into the de Gennes theory: an effective DNA width that gives the increase in the excluded volume due to electrostatic repulsion.     

Radial distribution function of rod-like polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rod-like limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted effective persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with the strength of the electrostatic interaction and the Debye screening length. Received 4 March 2002 and Received in final form 1 July 2002 RID="a" ID="a"e-mail: jrudnick@physics.ucla.edu     

盐离子对双链DNA分子弹性影响的研究P

在DNA延伸过程中,考虑到氢键相互作用以及盐浓度(Na+)对氢键和堆积作用的影响,给出了修正的ZZO模型,得到了力-延伸曲线随盐浓度的变化规律.结果表明:随盐浓度的增加,延伸相变力非线性增加,并最终趋于稳定,理论计算结果与实验测量一致.     

Electrostatic image effects for counterions between charged planar walls

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak-coupling level the image charge effects are generally small, making their mark only in the second-order fluctuation term. However, in the strong-coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long-range image potentials.     

Parameter selection in a Peyrard-Bishop-Dauxois model for DNA dynamics

In this Letter we study possible intervals for some parameters existing in the Peyrard-Bishop-Dauxois (PBD) model for the DNA dynamics. These parameters describe longitudinal and helicoidal interactions between nucleotides and a Morse potential approximating transverse interactions. We also estimate a possible interval for a wave number of a carrier component of a modulated solitonic wave. Finally, we compare our statements with experimental value of solitonic velocity in DNA.     

Persistence length for a model semirigid polyelectrolyte as seen by small angle neutron scattering: a relevant variation of the lower bound with ionic strength

In a SANS experiment, we have directly determined for the first time the conformation of hyaluronan, a model semirigid polyelectrolyte. At high ionic strength, this is completely possible, where the scattered intensity crosses over (when decreasing q) from a q(-1) rod variation to a q(-2) and, where fitting to the "wormlike" chain model gives the backbone, intrinsic, persistence length: L0 = 86.5 A. At low ionic strength, we can safely check that the measured persistence length appears increased by at least the amount predicted by Odijk for the electrostatic contribution, L(e) (approximately kappa(-2), square of the Debye screening length). However, the intensity at the lowest q is not only due to the single chain, since it crosses over from a q(-1) to a q(-4) variation, characteristic of polymer associations.     

The electrostatic persistence length of polymers beyond the OSF limit

We use large-scale Monte Carlo simulations to test scaling theories for the electrostatic persistence length l _e of isolated, uniformly charged polymers with Debye-Hückel intrachain interactions in the limit where the screening length κ^-1 exceeds the intrinsic persistence length of the chains. Our simulations cover a significantly larger part of the parameter space than previous studies. We observe no significant deviations from the prediction l _e∝κ^-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. We show that previous results pointing into this direction are due to a combination of excluded-volume and finite chain length effects. The paper emphasizes the role of scaling arguments in the development of useful representations for experimental and simulation data. Received 12 February 2002     

Chiral electrostatics breaks the mirror symmetry of DNA supercoiling

DNA supercoiling plays a fundamental role in regulating cellular activity and in the packaging of genetic material. In this communication, we analyse the effect of attractive chiral forces on the conformation of a closed circular DNA molecule, arising due to the helical patterns of charges on the DNA. We propose a model for closed loop DNA which uses the results of the recent theory of electrostatic interactions of a braid of two free-ended DNA molecules. Our model reproduces the known features of DNA supercoiling in an environment of low ionic strength. In high salt conditions, and in the presence of counterions that have high affinity to the DNA grooves, helix-specific forces significantly affect the conformation of the molecule by favouring a state characterized by a central left-handed braided section where there is close contact between distant portions of the loop. In such an environment we predict a previously unexplored possibility that nicked or topologically relaxed DNA molecules adopt a writhed state. This prediction suggests an alternative explanation for experiments in which it was assumed that the most stable topoisomer is always an open circle. Our results also give the first plausible explanation for the occurrence of tightly interwound molecules observed in cryo-electron microscopy and atomic force microscopy in a high ionic strength environment. We suggest several new experiments to test the predictions of this theory.     

Effects of ionic strength and charge annealing in star-branched polyelectrolytes

We have developed a scaling theory that describes the conformations of weak star-branched polyelectrolytes in dilute solutions. The dependences of the overall star size on the number of branches and on the ionic strength of the solution (tuned by the addition of low molecular weight salt) are analyzed. The intrinsic structure of the polyelectrolyte stars in salt-free and salt-added solutions is discussed in terms of concentration and elastic blobs. In contrast to neutral stars, the swollen corona of the polyelectrolyte star consists of blobs which are not closely packed. We have shown that the size of star polyelectrolytes is less sensitive to the variation in the ionic strength than the size of linear polyelectrolytes. The effects of the ionization-recombination balance in the star polyelectrolyte were taken into account. For polyelectrolytes with small ionization constant, the size of the star depends nonmonotonically on the number of branches and on the ionic strength of the solution due to recombination of counterions with charged monomers. Received: 10 November 1997 / Revised: 16 February 1998 / Accepted: 1st April 1998     

Conduction transition of nano-scaled molecular wires driven by environment coupling

We propose a hybridization model to simulate a molecular wire coupling with the environmental molecules. Results reveal that the conduction transition from conducting to semiconducting depends on the coupling strength. In our simulations, the non-equilibrium Green's function method is employed to calculate the current-voltage relationship for the molecular wire through metallic contacts. Our calculations show that the band gap can be manipulated from the outside molecules coupling. Temperature dependence of the conductivity is represented in our results with strong dependence in high temperature range, which is qualitatively comparable with the experimental results of DNA. In our results, with small coupling, the current is enhanced by the exchange. On the contrary, too large a coupling results in localization of the transport carriers, leading to a semiconducting like property. We try to associate this study with the conducting property of DNA, which can be manipulated by environmental modulation.     

Folding of lattice protein chains with modified Gō potential

We propose a modified Gō model in which the pairwise interaction energies vary as local environment changes. The stability difference between the surface and the core is also well considered in this model. Thermodynamic and kinetic studies suggest that this model has improved folding cooperativity and foldability in contrast with the Gō model. The free energy landscape of this model has broad barriers and narrow denatured states, which is consistent with that of the two-state folding proteins and is lacked for the Gō model. The role of non-native interactions in protein folding is also studied. We find that appropriate consideration of the contribution of the non-native interactions may increase the folding rate around the transition temperature. Our results show that conformation-dependent interaction between the residues is a realistic representation of potential functions in protein folding. Received 10 April 2002 / Received in final form 20 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wangwei@nju.edu.cn     

Counterion vibrations in the DNA low-frequency spectra

The vibrations of univalent metal cations with respect to phosphate groups of the DNA backbone are described using the four-mass model approach (S.N. Volkov, S.N. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991)) extended in this paper. The force constant of the counterion-phosphate interaction is determined by considering the DNA with counterions as a lattice of ion crystal. For such ion-phosphate lattice the Madelung constant and the dielectric constant are estimated. The obtained value of the Madelung constant is lower than for the NaCl crystal, and its value is about 1.3. The dielectric constant is within 2.3-2.7 depending on the counterion type and form of the double helix. The calculations of the low-frequency spectra show that for the DNA with metal cations Na⁺ , K⁺ , Rb⁺ and Cs⁺ the frequency of ion-phosphate vibrations decreases from 174 to 96cm^-1 as the counterion mass increases. The obtained frequencies agree well with the vibrational spectra of polynucleotides in a dry state which prove our suggestion about the existence of the ion-phosphate lattice around the DNA double helix. The amplitudes of conformational vibrations for DNA in B -form are calculated as well. The results demonstrate that light counterions ( Na⁺ do not disturb the internal dynamics of the DNA. However, heavy counterions ( Cs⁺ have effect on the internal vibrations of the DNA structural elements.     

Loops in DNA: An overview of experimental and theoretical approaches

DNA loop formation plays a central role in many cellular processes. The aim of this paper is to present the state of the art and open problems regarding the experimental and theoretical approaches to DNA looping. A particular attention is devoted to the effects of the protein bridge size and of protein induced sharp DNA bending on DNA loop formation enhancement.