Processes of DNA condensation induced by multivalent cations： Approximate annealing experiments and molecular dynamics simulations

The condensation of DNA induced by spermine is studied by atomic force microscopy （AFM） and molecular dynamics （MD） simulation in this paper. In our experiments, an equivalent amount of multivalent cations is added to the DNA solutions in different numbers of steps, and we find that the process of DNA condensation strongly depends on the speed of adding cations. That is, the slower the spermine cations are added, the slower the DNA aggregates. The MD and steered molecular dynamics （SMD） simulation results agree well with the experimental results, and the simulation data also show that the more steps of adding multivalent cations there are, the more compact the condensed DNA structure will be. This investigation can help us to control DNA condensation and understand the complicated structures of DNA--cation complexes.     

Optimal cell approach to osmotic properties of finite stiff-chain polyelectrolytes

We propose a self-consistent geometry optimized cell model approach to study osmotic properties of stiff-chain polyelectrolyte solutions. In contrast with the usual monotonic Poisson-Boltzmann prediction, the cell model predicts the correct nonmonotonic dependence of the osmotic coefficient on concentration. A lower degree of polymerization is found to reduce significantly the counterion condensation in a typical dilute strong polyelectrolyte. The results agree quantitatively with simulations of a corresponding many-body bulk system up to a dense semidilute regime.     

水合作用与pH调控聚电解质刷的构象转变

我们基于Flory-Huggins理论,建立理论模型研究水合作用与pH调控聚电解质刷的构象转变.理论模型考虑聚电解质链与水分子间的作用(聚电解质链的水合作用)、体系中的静电作用.研究发现,随着水合作用的改变,聚电解质刷出现由溶胀到塌缩的构象转变.由此表明了水合作用可在很大程度调节聚电解质刷的相变.通过分析pH的调控效应我们还发现,在碱性环境中(pH=8),聚电解质链单体的解离度增大,静电排斥会使得聚电解质刷溶胀.由此表明,聚电解质刷内水合作用与静电效应的耦合,将会共同决定聚电解质刷的构象转变特性.理论结果深刻揭示了水合作用的改变,会使得聚电解质刷体系发生相变,pH可在很大程度上改变其相变特性.     

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.     

Scaling Theory of Strongly Charged Cylindrical Polyelectrolyte Brushes

Scaling theory of charged cylindrical polyelectrolyte brushes is developed. The dependence of brush thickness on the grafting density, charge fraction, and chain length is analyzed. A full phase diagram is established. Characteristics and boundaries between different regimes of cylindrical polyelectrolyte brushes are summarized. Special attentions are paid to electrostatic interaction induced stiffening and counterion condensation effects. If the Bjerrum length of the solution is larger than the Kuhn length of the polyelectrolyte chains, counterion condensation occurs in the strongly charged polyelectrolyte brushes. On the contrary, the electrostatic interaction stretches the strongly charged grafted polyelectrolyte chains to their contour length.     

Effects of Ionic Dependence of DNA Persistence Length on the DNA Condensation at Room Temperature

DNA persistence length is a key parameter for quantitative interpretation of the conformational properties of DNA and related to the bending rigidity of DNA.A series of experiments pointed out that,in the DNA condensation process by multivalent cations,the condensed DNA takes elongated coil or compact globule states and the population of the compact globule states increases with an increase in ionic concentration.At the same time,single molecule experiments carried out in solution with multivalent cations(such as spermidine,spermine)indicated that DNA persistence length strongly depends on the ionic concentration.In order to revolve the effects of ionic concentration dependence of persistence length on DNA condensation,a model including the ionic concentration dependence of persistence length and strong correlation of multivalent cation on DNA is provided.The autocorrelation function of the tangent vectors is found as an effective way to detect the ionic concentration dependence of toroidal conformations.With an increase in ion concentration,the first periodic oscillation contained in the autocorrelation function shifts,the number of segment contained in the first periodic oscillation decreases gradually.According to the experiments,the average long-axis length is defined to estimate the ionic concentration dependence of condensation process further.The relation between long-axis length and ionic concentration matches the experimental results qualitatively.     

Molecular dynamics simulations of end-grafted centipede-like polymers with stiff charged side chains

We use molecular dynamics simulations to investigate centipede-like polymers with stiff charged side chains, end-grafted to a planar wall. The effect of the grafting density and the Bjerrum length on the conformational behaviour of the brush is examined in detail. In addition, we make a comparison of centipede-like polyelectrolyte (CPE) brushes with neutral centipede-like polymer (NCP) and linear polyelectrolyte (LPE) brushes. At weak electrostatic interaction, the main chains of the CPE chains adopt a strongly stretched conformation, and the monomer density profiles of side chains exhibit a clear oscillatory behaviour. With increasing Bjerrum length, the CPE brush undergoes a collapse transition. Compared to the CPE brushes, the counterion condensation effect is stronger for the LPE brushes, regardless of whether the electrostatic interaction is weak or strong and of whether the grafting density is low or high. Additionally, it is shown that the architecture of the grafted chains makes a weak contribution to the counterion condensation at strong electrostatic interaction. We also find that the electrostatic repulsion between charged side chains can enhance the stiffness of the main chains and thus limit the range of movement of the free-end monomers.     

Swelling behavior and viscoelasticity of ultrathin grafted hyaluronic acid films

In this paper we study the effect of monovalent and divalent ions on the swelling behavior and viscoelastic parameters of ultrathin layers of the natural polyelectrolyte hyaluronic acid covalently coupled to glass substrates. A colloidal probe technique is applied for this purpose based on latex beads, hovering over the polymer cushion. By analyzing the vertical Brownian motion of these beads with reflection interference contrast microscopy (RICM) we determined the equilibrium layer thickness (with 3 nm vertical resolution), the interfacial interaction potential, and the characteristic mesh size limiting the hydrodynamic flow within the polyelectrolyte film as a function of the ionic strength. The experimental results are interpreted in terms of three different theoretical models: the polyelectrolyte brush approximation of Pincus [#!ref1!#], a modified polyelectrolyte brush approximation in the high salt concentration limit of Ross and Pincus [#!ref2!#] and the simple scaling approximation for neutral adsorbed polymers of de Gennes [#!ref3!#]. Within experimental error all of these different models fit our experimental data and yield comparable results for the equilibrium layer thickness. Moreover we determine a thickness dependent, effective surface coverage from both brush models. The hydrodynamic properties of the films are interpreted in terms of the Brinkmann model of elastic porous media by assuming an effective mesh size, which depends linearly on the Debye screening length. The salt induced condensation of the polyelectrolyte films can be described microscopically in terms of a progressive contraction of the mesh size with increasing salt concentration. Received 10 September 1998 and Received in final form 30 November 1998     

Bicyclic diironcryptates with mobile guest cations: A new class of solid ionic conductors

Polycrystalline bicyclic diironcryptates with different mobile guest cations were synthesized and characterized by XRD analysis, IR spectroscopy, FAB-mass spectroscopy, elemental analysis, electrical conductivity spectroscopy and ion exchange experiments. We find strong indication that the guest cations exhibit a long-range mobility and that their mobility is governed by their size relative to the size of the cryptand molecules. On the other hand, the valence of the guest cations seems to play a minor role for the mobility. These results are discussed in comparison to the properties of conventional solid cationic conductors.     

Single Molecule Fluorescence Imaging and Its Application to the Study of DNA Condensation

Single molecule fluorescence imaging incorporated with optical tweezers and a laminar flow cell has been used to monitor the kinetic process of DNA condensation induced by spermidine. It was found that at least two steps were involved in the condensation process of the hydrodynamically-stretched linear DNA; a lag period followed by a rapid collapse of DNA. The lag time increased with the flow speed and the collapse time remained short within the range of the flow speed studied. The effect of salt concentration on the condensation process was examined, and the results suggest that the longer lag time observed in the higher salt buffer probably results from the displacement of bound cations and rearrangement of spermidine on the DNA. The flow-speed dependence of the lag time suggests that a nucleation event at the free end of the DNA, i.e. formation of a loop, may play a vital role in the kinetic process of condensation.     

Low-force DNA condensation and discontinuous high-force decondensation reveal a loop-stabilizing function of the protein Fis

We report single-DNA-stretching experiments showing that the protein Fis, an abundant bacterial chromosome protein of E. coli, mediates a dramatic DNA condensation to zero length. This condensation occurs abruptly when DNA tension is reduced below a protein-concentration-dependent threshold f* < 1 pN. Following condensation, reopening under larger forces proceeds via a series of discrete jumps, indicating that Fis is able to stabilize DNA crossings. Our experiments suggest that Fis may play a role in vivo stabilizing the "loop-domain" structure of the bacterial chromosome.     

Frustrated polyelectrolyte bundles and T= 0 Josephson-junction arrays

We establish a one-to-one mapping between a model for hexagonal polyelectrolyte bundles and a model for two-dimensional, frustrated Josephson-junction arrays. We find that the T = 0 insulator-to-superconductor transition of the quantum system corresponds to a continuous liquid-to-solid transition of the condensed charge in the finite-temperature classical system. We find that the role of the vector potential in the quantum system is played by elastic strain in the classical system. Exploiting this correspondence we show that the transition is accompanied by a spontaneous breaking of a discrete symmetry associated with the chiral patterning of the array and that at the transition the polyelectrolyte bundle adopts a universal response to shear.     

Bose-Einstein condensation in relativistic field theories far from equilibrium

The formation of Bose condensates far from equilibrium can play an important role in our understanding of collision experiments of heavy nuclei or for the evolution of the early Universe. In the relativistic quantum world particle number changing processes can counteract Bose condensation, and there is a considerable debate about the relevance of this phenomenon in this context. We show that the involved question of Bose condensation from initial overpopulation can be answered for the example of scalar field theories. Condensate formation occurs as a consequence of an inverse particle cascade with a universal power-law spectrum. This particle transport towards low momenta is part of a dual cascade, in which energy is also transferred by weak wave turbulence towards higher momenta. To highlight the importance of number changing processes for the subsequent decay of the condensate, we also compare to nonrelativistic theories with exact number conservation. We discuss the relevance of these results for non-Abelian gauge theories.     

Solubility of highly charged anionic polyelectrolytes in presence of multivalent cations: Specific interaction effect

Studies performed on strong polyelectrolytes and on a weak polyelectrolyte, sodium poly(acrylate), show that their stability in presence of multivalent cations depends on the chemical nature of the charged side groups of the polymer. For sulfonate groups (SO₃ ^-) or sulfate groups (OSO₃ ^-) phase separation generally occurs in presence of inorganic cations of valency 3 (as La³⁺) or larger and a resolubilization takes place at high salt concentration. The interactions of the polyelectrolyte with multivalent cations are of electrostatic origin and the phase diagrams are weakly dependent on the chemical nature of the polymer backbone and on the specificity of the counterions. For acrylate groups, (COO^-), the phase separation was observed with inorganic cations of valency 2 (as Ca²⁺) or larger without resolubilization at high salt concentration. The phase separation is due to a chemical association between cations and acrylate groups of two neighboring monomers of the same chain. This chemical association creates a hydrophobic complex by dehydrating both monomer and cation. With organic trivalent cation, as spermidine ⁺H₃N(CH₂)₄NH₂ ⁺(CH₂)₃NH₃ ⁺, where no chemical association occurs with the charged side groups COO^- or SO₃ ^- of the polyelectrolyte, similar phase diagrams were observed whatever was the polyelectrolyte with a resolubilization at high trivalent cation concentration. Received 3 March 1999 and Received in final form 2 September 1999     

水蒸气诱导聚电解质刷的构象转变

我们把Flory-Huggins模型(association models)推广应用到暴露于水蒸气中的聚电解质刷体系,考虑聚电解质-水氢键(P-W氢键)与水-水氢键(W-W氢键)、形成氢键与聚电解质链构象的耦合特性,研究水蒸气诱导的聚电解质刷构象转变的机理.研究发现,当P-W氢键效应起主导作用时,随着水蒸气浓度的增加,聚电解质刷会单调溶胀;P-W和W-W两种氢键效应,则会导致随着水蒸气浓度的增加,聚电解质刷的构象首先塌缩,然后开始溶胀的反常转变行为.基于本文的分析,可以预言,由于P-W氢键效应,聚电解质刷可以吸附水蒸气,吸附能力随聚电解质链长的增加而增强;当聚电解质链接枝密度足够高时,由于P-W和W-W两种氢键效应,增加体系中的水蒸气,会在聚电解质刷体系中形成由P-W氢键和W-W氢键交错链接的三维网络状凝胶结构.     

水蒸气诱导聚电解质刷的构象转变

我们把 Flory−Huggins 模型(association models)推广应用暴露于水蒸气中的聚电解质刷体系,考虑聚电解质-水氢键(P-W氢键)与水-水氢键(W-W氢键)、形成氢键与聚电解质链构象的耦合特性,研究水蒸气诱导的聚电解质刷构象转变的机理.研究发现,当 P-W 氢键效应起主导作用时,随着水蒸气浓度的增加,聚电解质刷会单调溶胀;P-W 和 W-W 两种氢键效应,则会导致随着水蒸气浓度的增加,聚电解质刷的构象首先塌缩,然后开始溶胀的反常转变行为。基于本文的分析,可以预言,由于 P-W 氢键效应,聚电解质刷可以吸附水蒸气,吸附能力随聚电解质链长的增加而增强;当聚电解质链接枝密度足够高时,由于 P-W 和 W-W 两种氢键效应,增加体系中的水蒸气,会在聚电解质刷体系中形成由 P-W 氢键和 W-W 氢键交错链接的三维网络状凝胶结构。     

Dynamical clustering of counterions on flexible polyelectrolytes

Molecular dynamics simulations are used to study the spatiotemporal dynamics of charge fluctuations around a polyelectrolyte molecule at charge densities above and below the classic counterion condensation threshold. Surprisingly, the counterions form weakly interacting clusters which exhibit slowly decaying short range orientational order. Local charge fluctuations create energy fluctuations at the order of k_(B)T that is sufficient to affect the polyelectrolyte interaction with an approaching ligand molecule. The predictions of the classical theory appear to be appropriate only over much longer time scales.     

Scaling equations for a biopolymer in salt solution

The effect of the simultaneous presence of monovalent and divalent cations on the thermodynamics of polyelectrolyte solutions is an incompletely solved problem. In physiological conditions, combinations of these ions affect structure formation in biopolymer systems. Dynamic light scattering measurements of the collective diffusion coefficient D and the osmotic compressibility of semidilute hyaluronan solutions containing different ratios of sodium and calcium ions are compared with simple polyelectrolyte models. Scaling relationships are proposed in terms of polymer concentration and ionic strength J of the added salt. Differences in the effects of sodium and calcium ions are found to be expressed only through J.     

Polyelectrolyte adsorption

The problem of charged polymer chains (polyelectrolytes) as they adsorb on a planar surface is addressed theoretically. We review the basic mechanisms and theory underlying polyelectrolyte adsorption on a single surface in two situations: adsorption of a single charged chain, and adsorption from a bulk solution in θ solvent conditions. The behavior of flexible and semi-rigid chains is discussed separately and is expressed as function of the polymer and surface charges, ionic strength of the solution and polymer bulk concentration. We mainly review mean-field results and briefly comment about fluctuation effects. The phenomenon of polyelectrolyte adsorption on a planar surface as presented here is of relevance to the stabilization of colloidal suspensions. In this respect we also mention calculations of the inter-plate force between two planar surfaces in presence of polyelectrolyte. Finally, we comment on the problem of charge overcompensation and its implication to multi-layers formation of alternating positive and negative polyelectrolytes on planar surfaces and colloidal particles.