Gerald S. Manning

The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides.

Although the importance of the polyelectrolyte character of DNA has been recognized for some time (Felsenfeld & Miles 1967), few of the implications have been explored, primarily because of a lag in translating the breakthroughs in polyelectrolyte theory of the last decade into a form that is well adapted to the analysis of the specialized problems of biophysical chemistry. Perhaps an analogous situation existed in the field of protein chemistry during the period after the formulation and confirmation of the Debye—Huckel theory of ionic solutions but before Scatchards incorporation of the theory into his analysis of the binding properties of proteins. An achievement for polynucleotide solutions parallel to Scatchards was recently presented by Record, Lohman, & de Haseth (1976) and further developed and reviewed by Record, Anderson & Lohman (1978).

Limiting laws and counterion condensation in polyelectrolyte solutions. IV. The approach to the limit and the extraordinary stability of the charge fraction.

The limiting laws for polyelectrolyte solutions developed in previous papers of this series have been amply confirmed by measurement. A surprising result of the accumulated data is that the limiting polyelectrolyte charge fraction (fraction of fixed charges uncompensated by condensed counterions in the limit of zero concentration), persists up to concentrations of 0.1 M or even higher. Here the theory is extended in a simple manner to finite concentrations, and the stability of the charge fraction is found to be firmly based on consequences of the long-range polyelectrolyte field. The associated counterions are assumed to translate freely in a region centered on the contour axis of the polyion. The numerical value of the free volume is determined self-consistently from the axial charge density of the polyelectrolyte and is used as the general framework within which specific binding effects are treated.

Counterion Condensation Revisited

We review some of the characteristic properties of the structure of polyelectrolyte solutions: the condensed layer of counterions that forms abruptly at a critical threshold charge density on the polymer chain; the more diffuse Debye-Hückel cloud, which is spatially distinct from the condensed layer; and the entropic release of counterions from the condensed layer as a driving force for the binding of oppositely charged ligands. We present a reminder of the basis of our current understanding in a variety of experiments, simulations, and theories; and we attempt as well to clarify some misunderstandings. We present a new analysis of a lattice model that suggests why the limiting laws for polyelectrolyte thermodynamics have proved to be accurate despite the neglect of polymer-polymer interactions in their original derivation. We sketch recent progress in constructing a potential between counterion and polyion. A counterion located in the interface between condensed layer and Debye cloud is repelled from the polyion, creating a sharp boundary between the two counterion populations.

Limiting laws and counterion condensation in polyelectrolyte solutions. V. Further development of the chemical model.

Counterion binding to polyelectrolyte chains is formulated as a chemical reaction Mz (free) leads to Mz (bound). Expressions for the chemical potentials of free and bound counterions are set equal to obtain the reaction equilibrium. The results are equivalent to those in the previous paper of this series. An additional result obtained here is that a polyion holds its bound counterion layer with a strength on the order of 100 kcal/(mole cooperative unit). The method is then applied to the calculation of the polarizability along the chain due to the bound (condensed) counterions.

An Estimate of the Extent of Folding of Nucleosomal DNA by Laterally Asymmetric Neutralization of Phosphate Groups

We attempt quantitative implementation of a previous suggestion that asymmetric charge neutralization of DNA phosphate groups may provide part of the driving force for nucleosome folding. Polyelectrolyte theory can be used to estimate the effective compressive force acting along the length of one side of the DNA surface when a fraction of the phosphate groups are neutralized by histones bound to that side. A standard engineering formula then relates the force to the bending amplitude caused by it. Calculated bending amplitudes are consistent with the curvature of nucleosomal DNA and the overall extent of charge neutralization by the histones. The relation of the model to various aspects of nucleosome folding, including the detailed path of core-particle DNA, is discussed. Several other DNA-protein complexes are listed as examples of possible asymmetric charge-induced bending.

Counterion condensation theory constructed from different models

The primitive model and the line of charges model for ionized polymers both predict the emergence of a condensed counterion layer at a critical polymer charge density, but the two models describe the condensed layer in different ways. The Zimm-Le Bret and Ramanathan distributions for the condensed layer in the primitive model are reviewed. The extended Debye-Huckel theory of the line of charges model is recast in a more general form in an attempt to make its underlying assumptions transparent. We show that the counterion-polyion potential of mean force at great distances behaves differently for the two models.

Electrostatic free energy of the DNA double helix in counterion condensation theory

Polyelectrolyte theory based on counterion condensation is extended from the standard line charge model to helical and double helical charge arrays. The number of condensed counterions turns out to be the same as for a line charge with charge density equal to the axial charge density of the helix. Also, the logarithmic salt dependence of the electrostatic free energy is the same in the range of lower salt concentration, so that the limiting laws remain unchanged. However, the internal free energy of the condensed layer of counterions and the overall electrostatic free energy depend on the helical parameters. At higher salt, the free energies of both single and double helix are negative, indicating electrostatic stabilization of the helical charge lattices due to the mixing entropy of the condensed counterions. Except at very low salt, the free energy of a single helix is higher than the free energy of a double helix with twice the charge density. With B-DNA parameters and single strands modeled as single helices, the predicted salt dependence of the free energy of transition from double helix to separated single strands has a maximum at approximately 0.2 M salt, close to the location in the laboratory of this well-known feature of the DNA strand separation transition. We also calculate the electrostatic free energy for the transition of the DNA double helix from the B to the A conformation. The B form is electrostatically stable over most of the salt range, but there is a spontaneous electrostatic transition to A near 1 M salt. The electrostatic free energy values are close to the experimental values of the overall (electrostatic plus non-electrostatic) transition free energies for A-philic base pair sequences. We are led to suggest that the experimentally observed B-to-A transition for A-philic sequences near 1 M salt in water is governed by the polyelectrolyte properties of these two conformations of the DNA double helix. The effect of ethanol, however, cannot be attributed to lowering of the bulk dielectric constant.

Is the counterion condensation point on polyelectrolytes a trigger of structural transition

Experimental data on well documented global polymer transitions can be correlated with the linear charge density critical for counterion condensation. Other data exhibit abrupt behavior at the counterion condensation point and may consistently be interpreted in terms of a transition between locally folded and extended structures. We suggest that the underlying cause of these observations is the onset of mechanical instability of locally folded structures at the counterion condensation point.

Electrostatic effects in short superhelical DNA

We present Monte Carlo simulations of the equilibrium configurations of short closed circular DNA that obeys a combined elastic, hard-sphere, and electrostatic energy potential. We employ a B-spline representation to model chain configuration and simulate the effects of salt on chain folding by varying the Debye screening parameter. We obtain global equilibrium configurations of closed circular DNA, with several imposed linking number differences, at two salt concentrations (specifically at the extremes of no added salt and the high salt regime), and for different chain lengths. Minimization of the composite elastic/long-range potential energy under the constraints of ring closure and fixed chain length is found to produce structures that are consistent with the configurations of short supercoiled DNA observed experimentally. The structures generated under the constraints of an electrostatic potential are less compact than those subjected only to an elastic term and a hard-sphere constraint. For a fixed linking number difference greater than a critical value, the interwound structures obtained under the condition of high salt are more compact than those obtained under the condition of no added salt. In the case of no added salt, the electrostatic energy plays a dominant role over the elastic energy in dictating the shape of the closed circular DNA. The DNA supercoil opens up with increasing chain length at low salt concentration. A branched three-leaf rose structure with a fixed linking number difference is higher in energy than the interwound form at both salt concentrations employed here.

Limiting Laws for Equilibrium and Transport Properties of Polyelectrolyte Solutions

It is proposed here to discuss the interactions of point ions with infinitely long line charges against the background of a dielectric continuum [1–8]. It is expected, both on a priori and empirical grounds, that this model is a good representation of a polyelectrolyte solution at low concentrations. Further discussion of the model is deferred to the end of the article. Fairly extensive comparions of published data with the predictions of the model are given in References [1] and [7]. Further comparisons are given below, but emphasis is primarily directed at data which serve to illustrate specific points.