Electrostatics of DNA complexes with cationic lipid membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.     

Is a small number of charge neutralizations sufficient to bend nucleosome core DNA onto its superhelical ramp?

X-ray diffraction structures of the nucleosome core particle along with a variety of experiments are consistent with the idea that an important source of the free energy holding DNA to the superhelical ramp on the histone octamer surface is obtained from a relatively small amount of electrostatic neutralization of the DNA phosphate charge by positively charged histone groups, especially arginine residues. Here we present a theoretical analysis of a simple model that emphasizes the competition between the high degree of bending of the stiff DNA molecule required for its tight curvature on the histone octamer and the neutralization of the DNA phosphate charge by basic histone residues. Our calculation accounts for the strong influence of condensed counterions on the electrostatic interactions. We find that the minimum amount of free energy required to bend DNA into axial conformity with the superhelical ramp at physiological salt concentration can be provided by a scant 6% neutralization of the phosphate charge, in close correspondence to the stoichiometric neutralization of phosphate charge by the arginine side chain that intrudes into the inward-facing minor groove of each DNA double helical turn.     

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.     

Single-chain compaction of long duplex DNA by cationic nanoparticles: modes of interaction and comparison with chromatin

The compaction of long duplex DNA by cationic nanoparticles (NP) used as a primary model of histone core particles has been investigated. We have systematically studied the effect of salt concentration, particle size, and particle charge by means of single-molecule observations-fluorescence microscopy (FM) and transmission electron microscopy (TEM)-and molecular dynamics (MD) simulations. We have found that the large-scale DNA compaction is progressive and proceeds through the formation of beads-on-a-string structures of various morphologies. The DNA adsorbed amount per particle depends weakly on NP concentration but increases significantly with an increase in particle size and is optimal at an intermediate salt concentration. Three different complexation mechanisms have been identified depending on the correlation between DNA and NPs in terms of geometry, chain rigidity, and electrostatic interactions: free DNA adsorption onto NP surface, DNA wrapping around NP, and NP collection on DNA chain.     

Effects of electrostatic screening on the conformation of single DNA molecules confined in a nanochannel

Single T4-DNA molecules were confined in rectangular-shaped channels with a depth of 300 nm and a width in the range of 150-300 nm casted in a poly(dimethylsiloxane) nanofluidic chip. The extensions of the DNA molecules were measured with fluorescence microscopy as a function of the ionic strength and composition of the buffer as well as the DNA intercalation level by the YOYO-1 dye. The data were interpreted with the scaling theory for a wormlike polymer in good solvent, including the effects of confinement, charge, and self-avoidance. It was found that the elongation of the DNA molecules with decreasing ionic strength can be interpreted in terms of an increase of the persistence length. Self-avoidance effects on the extension are moderate, due to the small correlation length imposed by the channel cross-sectional diameter. Intercalation of the dye results in an increase of the DNA contour length and a partial neutralization of the DNA charge, but besides effects of electrostatic origin it has no significant effect on the bare bending rigidity. In the presence of divalent cations, the DNA molecules were observed to contract, but they do not collapse into a condensed structure. It is proposed that this contraction results from a divalent counterion mediated attractive force between the segments of the DNA molecule.     

Electrostatic screening and energy barriers of ions in low-dielectric membranes

We present exact solutions of the linear Poisson-Boltzmann equation for several problems relevant for ion translocation across low-dielectric membranes. Our results are obtained for a finite Debye screening length, and they generalize the classical results for pure Coulombic electrostatics (Parsegian, A. Nature (London) 1969, 221, 844). We calculate the electrostatic self-energy of an ion in the middle of a low-dielectric slab, its energy inside a cylindrical high-dielectric pore, and its energy inside a high-dielectric spherical jacket. We consider also the influence of negative charges distributed on the walls of the cylindrical pore. We show that ion self-energy barriers are considerably reduced due to screening of electrolyte. We compare our results with some numerical results for screened electrostatics of ion channels and wide pores.     

Adsorption of highly charged polyelectrolytes onto an oppositely charged porous substrate

The adsorption behavior of highly charged cationic polyelectrolytes onto porous substrates is electrostatic in nature and has been shown to be highly dependent on the polyelectrolyte properties. Copolymers of acrylamide (AM) and diallyldimethylammonium chloride (DADMAC) were synthesized to have a range of macromolecular properties (i.e., charge density and molecular mass). Traditional titration methods have been complemented by fluorescence labeling techniques that were developed to directly observe the extent that fluorescently labeled poly(AM- co-DADMAC) adsorbs into the pore structure of a cellulosic substrate. Although contributing to the electrostatic driving force, the charge density acts to limit adsorption to the outermost surface under electrolyte-free conditions. However, adsorption into the pores can occur if both the molecular mass and charge density of poly(AM- co-DADMAC) are sufficiently low. Adsorption initially increases as the electrolyte concentration is increased. However, the electrostatic persistence length of poly(AM- co-DADMAC) restricts the polyelectrolyte from entering the pores. Therefore, changes in the adsorption behavior at moderate electrolyte concentrations have been attributed to swelling of the polyelectrolyte layer at the fiber exterior. The adsorption behavior changes again at high electrolyte concentrations such that poly(AM- co-DADMAC) could adsorb into the pore structure. This occurred when the electrolyte concentration was sufficient to screen the electrostatic persistence length of poly(AM- co-DADMAC), provided that the entropic driving force for adsorption still existed. It is suggested that adsorption into the pore structure is a kinetic process that is governed by localized electrostatic interactions between poly(AM- co-DADMAC) and the charges located within the pores.     

Cationic copolymer-mediated DNA immobilization: interfacial structure and composition as determined by ellipsometry, dual polarization interferometry, and neutron reflection

DNA immobilization onto support surfaces is required in biotechnological applications such as microarrays and gene delivery. This important interfacial molecular process can be mediated from a preadsobred cationic polymer. There is, however, a lack of understanding over the control of the interfacial composition and structural distribution of the DNA immobilized. We have used a combined approach of spectroscopic ellipsometry (SE), dual polarization interferometry (DPI) and neutron reflection (NR) to determine the interfacial polymer adsorption and the subsequent DNA binding. Cationic diblock copolymers incorporating 30 phosphorylcholine (PC) groups and different diethylaminoethyl groups, referred to as MPC30-DEAn, were chosen because of their well-defined molecular architecture. While our studies revealed different effects of surface charge and hydrophobicity, the amount of copolymers adsorbed on both model surfaces showed a broad trend of increase with solution pH, indicating a strong effect arising from pH-dependent charge density on the copolymers. In contrast, the copolymer structure and solution concentration showed a weak effect under the conditions studied. The subsequent DNA binding at pH 7 showed that on both surfaces the amount of DNA immobilized followed an approximate 1:1 charge interaction for all different DNA samples studied, irrespective of single or double strand, or different DNA size, indicating the dominant effect of electrostatic interaction between the two species. Both DPI and NR revealed consistent thickness increase upon DNA binding. Furthermore, with increasing DNA size, the interfacial layer became much thicker, and charge interaction drove more extensive interfacial mixing between the two species. Our results show that the amount of DNA immobilized is controlled by the amount of cationic copolymer preadsorbed that is in turn controlled by the solution pH and surface chemistry but that is barely affected by the type and concentration of DNA or cationic copolymer.     

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.     

Charged Semi-Permeable Shell with Encapsulated Polyions: Concentration Profile,Surface Potential,and Electrostatic Pressure

Summary: We study theoretically the electrostatic equilibrium for a charged shell filled with a suspension of polyions (e.g., colloids, polyelectrolytes, etc.) and immersed in an infinite salt-free reservoir. The shell is impermeable for polyions, but allows free diffusion of counterions. From the solution of the linearized Poisson-Boltzmann equation we obtain the distribution of the potential and concentration profiles for polyions. We then derive explicit formulas for the electrostatic pressure exerted by the shell. If the overall charge of the filled shell has the same sign as the surface alone the pressure on the shell increases with increase of the surface charge density. Otherwise the surface charge density suppresses the electro-osmotic pressure due to the electrostatic attraction between the oppositely charged polyions and shell.     

Phase-separation transition in liquid mixtures near curved charged objects

We study the thermodynamic behavior of nonpolar liquid mixtures in the vicinity of curved charged objects, such as electrodes or charged colloids. There is a critical value of charge (or potential), above which a phase-separation transition occurs, and the interface between high- and low-dielectric constant components becomes sharp. Analytical and numerical composition profiles are given, and the equilibrium front location as a function of charge or voltage is found. We further employ a simple Cahn-Hilliard type equation to study the dynamics of phase separation in spatially nonuniform electric fields. We find an exponential temporal relaxation of the demixing front location. We give the dependence of the steady-state location and characteristic time on the charge, mixture composition and ambient temperature.     

Electrostatic attraction between cationic-anionic assemblies with surface compositional heterogeneities

Electrostatics play a key role in biomolecular assembly. Oppositely charged biomolecules, for instance, can be coassembled into functional units, such as DNA and histone proteins into nucleosomes and actin-binding protein complexes into cytoskeleton components, at appropriate ionic conditions. These cationic-anionic coassemblies often have surface charge heterogeneities that result from the delicate balance between electrostatics and packing constraints. Despite their importance, the precise role of surface charge heterogeneities in the organization of cationic-anionic coassemblies is not well understood. We show here that coassemblies with charge heterogeneities strongly interact through polarization of the domains. We find that this leads to symmetry breaking, which is important for functional capabilities, and structural changes, which is crucial in the organization of coassemblies. We determine the range and strength of the attraction as a function of the competition between the steric and hydrophobic constraints and electrostatic interactions.     

Do monovalent mobile ions affect DNA's flexibility at high salt content?

Numerous theoretical and experimental studies disagree on the impact of surrounding mobile ions on DNA conformational flexibility at high salt content. Specifically, it is not clear how the DNA persistence length varies when concentration of monovalent mobile ions is increased beyond the physiological value of ～0.1 M. In the present Communication we address this biologically important issue computationally by means of molecular dynamics simulations. We utilize our recently developed chemically accurate coarse-grained model for the double-stranded DNA with explicit mobile ions. We find that in a range of moderate-to-high ionic concentrations, ～0.1-1 M, DNA persistence length drops noticeably by ～25%. Our results contradict some experimental works and the celebrated theory of Odijk, Skolnick and Fixman (Skolnick et al., Macromolecules, 1977, 10, 944), suggesting a negligible variation of DNA persistence length at these concentrations. On the other hand, our findings are in near quantitative agreement with a number of other theoretical and experimental studies. Combined with our recent work on elucidating the role of elastic and electrostatic effects in maintaining DNA shape, the results reported here may indicate that conceptually new understanding of DNA rigidity needs to be developed.     

Electrostatic interactions of colloidal particles in nonpolar solvents: role of surface chemistry and charge control agents

We study the electrostatic and hydrodynamic interactions of colloidal particles in nonpolar solvents. Using blinking optical tweezers, we can extract the screening length, kappa-1, the effective surface potential, |ezeta*|, and the hydrodynamic radius, ah, in a single measurement. We apply this technique to suspensions of polystyrene and poly(methyl methacrylate) particles in hexadecane with soluble charge control agents, aerosol sodium di-2-ethylhexylsulfosuccinate (AOT) and polyisobutylene succinimide (OLOA-1200). We find that the electrostatic interactions of these particles depend sensitively on surface composition as well as on the concentration and chemistry of the charge control agent.     

The incorporation of hydration forces determined by continuum electrostatics into molecular mechanics simulations

A new technique is presented for incorporating hydration forces into molecular mechanics simulations. The method assumes the classical continuum approximation, where a solvated molecule is represented as a low-dielectric cavity of arbitrary shape embedded in a continuous region of high dielectric constant. Electrostatic effects are computed by first calculating the distribution of polarization charge (induced by the configuration of solute fixed charges) at the molecular surface. The hydration force at a particular atom is then found as the sum of the coulombic interaction with the induced surface charge, plus a purely mechanical contribution that arises from the pressure of the polarized solvent as it is pulled toward the solute. A procedure is developed to use the computed hydration forces in conjunction with the CHARMM molecular mechanics package to carry out energy minimizations in which the effects of solvation are explicitly included. This new technique also allows a detailed analysis of the relative balance of coulombic, hydration, and steric energies as a function of molecular conformation. The method is applied to the test case of a zwitterionic tripeptide (LYS-GLY-GLU), and the computational results suggest that hydration effects can play a significant role in determining a stable conformation for a solvated polar molecule. The future application to larger molecules is discussed.     

The role of electrostatic interactions in protease surface diffusion and the consequence for interfacial biocatalysis

This study examines the influence of electrostatic interactions on enzyme surface diffusion and the contribution of diffusion to interfacial biocatalysis. Surface diffusion, adsorption, and reaction were investigated on an immobilized bovine serum albumin (BSA) multilayer substrate over a range of solution ionic strength values. Interfacial charge of the enzyme and substrate surface was maintained by performing the measurements at a fixed pH; therefore, electrostatic interactions were manipulated by changing the ionic strength. The interfacial processes were investigated using a combination of techniques: fluorescence recovery after photobleaching, surface plasmon resonance, and surface plasmon fluorescence spectroscopy. We used an enzyme charge ladder with a net charge ranging from -2 to +4 with respect to the parent to systematically probe the contribution of electrostatics in interfacial enzyme biocatalysis on a charged substrate. The correlation between reaction rate and adsorption was determined for each charge variant within the ladder, each of which displayed a maximum rate at an intermediate surface concentration. Both the maximum reaction rate and adsorption value at which this maximum rate occurs increased in magnitude for the more positive variants. In addition, the specific enzyme activity increased as the level of adsorption decreased, and for the lowest adsorption values, the specific enzyme activity was enhanced compared to the trend at higher surface concentrations. At a fixed level of adsorption, the specific enzyme activity increased with positive enzyme charge; however, this effect offers diminishing returns as the enzyme becomes more highly charged. We examined the effect of electrostatic interactions on surface diffusion. As the binding affinity was reduced by increasing the solution ionic strength, thus weakening electrostatic interaction, the rate of surface diffusion increased considerably. The enhancement in specific activity achieved at the lowest adsorption values is explained by the substantial rise in surface diffusion at high ionic strength due to decreased interactions with the surface. Overall, knowledge of the electrostatic interactions can be used to control surface parameters such as surface concentration and surface diffusion, which intimately correlate with surface biocatalysis. We propose that the maximum reaction rate results from a balance between adsorption and surface diffusion. The above finding suggests enzyme engineering and process design strategies for improving interfacial biocatalysis in industrial, pharmaceutical, and food applications.     

Electrostatics and the electro-optic behaviour of chiral smectics C: 'block' polarization screening of applied voltage and 'V-shaped' switching

We present a new model for the physics of thresholdless switching in chiral smectics. In the limit of high polarization, the electro-optics of chiral smectic C liquid crystals are dominated by two distinct electrostatic effects. Complete (surface to surface) 'stiffening' of the polarization field by its charge self-interaction causes the polarization to orient as a uniform block. Complete screening of applied electric field by polarization charge leads to voltage-induced orientation where the electric field in the liquid crystal is exactly zero, These effects, both operative during the 'V-shaped' portion of thresholdless transmission vs. voltage curves, combine to produce 'V-shaped' switching.     

Diffusion of cationic polyelectrolytes into cellulosic fibers

The penetration of cationic polyelectrolytes into anionic cellulosic fibers was evaluated with fluorescent imaging techniques in order to clarify the mechanism and time scales for the diffusion process. The bulk charge of the cellulosic fibers indirectly creates a driving force for diffusion into the porous fiber wall, which is entropic in nature due to a release of counterions as the polyelectrolyte adsorbs. The individual bulk charges in the fiber cell wall also interact with the diffusing polyelectrolyte, such that the polyelectrolyte diffuses to the first available charge and consequently adsorbs and remains fixed. Thus, subsequent polyelectrolyte chains must first diffuse through the adsorbed polyelectrolyte layer before adsorbing to the next available bulk charges. This behavior differs from earlier suggested diffusion mechanisms, by which polyelectrolytes were assumed to first adsorb to the outermost surface and then reptate into the pore structure. The time scales for polyelectrolyte diffusion were highly dependent on the flexibility of the chain, which was estimated from calculations of the persistence length. The persistence length ultimately depended on the charge density and electrolyte concentration. The charge density of the polyelectrolyte had a greater influence on the time scales for diffusion. High charge density polyelectrolytes were observed to diffuse on a time scale of months, whereas the diffusion of low charge density polyelectrolytes was measured on the order of hours. An influence of the chain length, that is, steric interactions due the persistence length of the polyelectrolyte and to the tortuosity of the porous structure of the fiber wall, could only be noted for low charge density polyelectrolytes. Increasing the electrolyte concentration increased the chain flexibility by screening the electrostatic contribution to the persistence length, in turn inducing a faster diffusion process. However, a significant change in the diffusion behavior was observed at high electrolyte concentrations, at which the interaction between the polyelectrolyte charges and the fiber charges was almost completely screened.     

Electrostatic interactions in biological DNA-related systems

In this perspective article, we focus on recent developments in the theory of charge effects in biological DNA-related systems. The electrostatic effects on different levels of DNA organization are considered, including the DNA-DNA interactions, DNA complexation with cationic lipid membranes, DNA condensates and DNA-dense cholesteric phases, protein-DNA recognition, DNA wrapping in nucleosomes, and inter-nucleosomal interactions. For these systems, we develop a theoretical framework to describe the physical-chemical mechanisms of structure formation and anticipate some biological consequences. General biophysical principles of DNA compaction in chromatin fibers and DNA spooling inside viral capsids are discussed in the end, with emphasis on electrostatic aspects.