Simulations of the Titration of Linear Polyelectrolytes with Explicit Simple Ions: Comparisons with Screened Coulomb Models and Experiments

On the Validity of Constant pH Simulations

Constant pH (cpH) simulations are now a standard tool for investigating charge regulation in coarse-grained models of polyelectrolytes and colloidal systems. Originally developed for studying solutions with implicit ions, extending this method to systems with explicit ions or solvents presents several challenges. Ensuring proper charge neutrality within the simulation cell requires performing titration moves in sync with the insertion or deletion of ions, a crucial aspect often overlooked in the literature. Contrary to the prevailing views, cpH simulations are inherently grand-canonical, meaning that the controlled pH is that of the reservoir. The presence of the Donnan potential between the implicit reservoir and the simulation cell introduces significant differences between titration curves calculated for open and closed systems; the pH of an isolated (closed) system is different from the pH of the reservoir for the same protonation state of the polyelectrolyte. To underscore this point, in this paper, we will compare the titration curves calculated using the usual cpH algorithm with those from the exact canonical simulation algorithm. In the latter case, titration moves adhere to the correct detailed balance condition, and pH is calculated using the recently introduced surface Widom insertion algorithm. Our findings reveal a very significant difference between the titration isotherms obtained using the standard cpH algorithm and the canonical titration algorithm, emphasizing the importance of using the correct simulation approach when studying charge regulation of polyelectrolytes, proteins, and colloidal particles.

Protein-like particles through nanoprecipitation of mixtures of polymers of opposite charge

HYPOTHESIS

Polymer nanoparticles (NPs) have a very high potential for applications notably in the biomedical field. However, synthetic polymer NPs cannot yet concurrence the functionalities of proteins, their natural counterparts, notably in terms of size, control over internal structure and interactions with biological environments. We hypothesize that kinetic trapping of polymers bearing oppositely charged groups in NPs could bring a new level of control and allow mimicking the surfaces of proteins.

EXPERIMENTS

Here, the assembly of mixed-charge polymer NPs through nanoprecipitation of mixtures of oppositely charged polymers is studied. Two series of copolymers made of ethyl methacrylate and 1 to 25 mol% of either methacrylic acid or a trimethylammonium bearing methacrylate are synthesized. These carboxylic acid or trimethylammonium bearing polymers are then mixed in different ratios and nanoprecipitated. The influence of the charge fraction, mixing ratio of the polymers, and precipitation conditions on NP size and surface charge is studied.

FINDINGS

Using this approach, NPs of less than 25 nm with tunable surface charge from +40 mV to -40 mV are assembled. The resulting NPs are sensitive to pH and certain NP formulations have an isoelectric point allowing repeated charge reversal. Encapsulation of fluorescent dyes yields very bright fluorescent NPs, whose interactions with cells are studied through fluorescence microscopy. The obtained results show the potential of nanoprecipitation of oppositely charged polymers for the design of NPs with precisely tuned surface properties.

Monte Carlo simulations of weak polyampholyte microgels: pH-dependence of conformation and ionization

We performed Metropolis Monte Carlo simulations to investigate the impact of varying acid and base dissociation constants on the pH-dependent ionization and conformation of weak polyampholyte microgels under salt-free conditions and under explicit consideration of the chemical ionization equilibria of the acidic and basic groups and their electrostatic interaction. Irrespective of their relative acid and base dissociation constant, all of the microgels undergo a pH-dependent charge reversal from positive to negative with a neutral charge at the isoelectric point. This charge reversal is accompanied by a U-shaped swelling transition of the microgels with a minimum of their size at the point of charge neutrality. The width of the U-shaped swelling transition, however, is found to depend on the chosen relative acid and base dissociation constants through which the extent of the favorable electrostatic intramolecular interaction of the ionized acidic and basic groups is altered. The pH-dependent swelling transition of the microgels is found to become broader, the stronger the intramolecular electrostatic interaction of the oppositely charged ionized species is. In addition, the intramolecular charge compensation of the acidic and basic groups of the microgels allows their counterions to abandon the microgel and the associated gain in translational entropy further amplifies the broadening of the pH-dependent swelling transition. The analysis of the radial ionization profiles of the acidic and basic groups of the differently composed microgels reveals a variety of radial ionization patterns with a dependence on the overall charge of the microgels.

On the distribution of hydrophilic polyelectrolytes and their counterions around zwitterionic micelles: the possible impact on the charge density in solution

Despite their charge neutrality, micelles composed of surfactants with zwitterionic headgroups selectively accumulate anions at their hydrophobic core/solution interphase due to electrostatic interactions if headgroup positive moieties are the innermost. This tendency may be markedly enhanced if polyions substitute simple ions. To investigate this possibility, solutions composed of zwitterionic micelles and hydrophilic polyanions have been investigated with Monte Carlo simulations representing the studied systems via primitive electrolyte models. Structural and energetic properties are obtained to highlight the impact of connecting simple ions into polyions on the interactions between electrolytes and micelles. Despite the latter, polyanions conserve their conformational properties. A marked increase in the concentration of charged species inside the micellar corona is, instead, found when polyions are present independently of their charge sign or the headgroup structure. Thus, polyelectrolytes act as "shuttle" for all charged species, with the potential of increasing reactions rates involving the latter due to mass effects. Besides, results for the polyions/micelles mixing free energy and Helmholtz energy profiles indicate that the critical micelle concentration is impacted minimally by hydrophilic polyelectrolytes, an outcome agreeing with experiments. This finding is entirely due to weak enthalpic effects while mixing hydrophilic polyions and micelles. A strong reduction in the screening of the micelle negative charge, acquired following the adsorption of anions in the corona and due to counterions layering just outside it (the so called "chameleon effect"), is forecasted when polyanions substitute monovalent anions.

Role of pKA in Charge Regulation and Conformation of Various Peptide Sequences

Peptides containing amino acids with ionisable side chains represent a typical example of weak ampholytes, that is, molecules with multiple titratable acid and base groups, which generally exhibit charge regulating properties upon changes in pH. Charged groups on an ampholyte interact electrostatically with each other, and their interaction is coupled to conformation of the (macro)molecule, resulting in a complex feedback loop. Their charge-regulating properties are primarily determined by the pKA of individual ionisable side-chains, modulated by electrostatic interactions between the charged groups. The latter is determined by the amino acid sequence in the peptide chain. In our previous work we introduced a simple coarse-grained model of a flexible peptide. We validated it against experiments, demonstrating its ability to quantitatively predict charge on various peptides in a broad range of pH. In the current work, we investigated two types of peptide sequences: diblock and alternating, each of them consisting of an equal number of amino acids with acid and base side-chains. We showed that changing the sequence while keeping the same overall composition has a profound effect on the conformation, whereas it practically does not affect total charge on the peptide. Nevertheless, the sequence significantly affects the charge state of individual groups, showing that the zero net effect on the total charge is a consequence of unexpected cancellation of effects. Furthermore, we investigated how the difference between the pKA of acid and base side chains affects the charge and conformation of the peptide, showing that it is possible to tune the charge-regulating properties by following simple guiding principles based on the pKA and on the amino acid sequence. Our current results provide a theoretical basis for understanding of the complex coupling between the ionisation and conformation in flexible polyampholytes, including synthetic polymers, biomimetic materials and biological molecules, such as intrinsically disordered proteins, whose function can be regulated by changes in the pH.

Interface Counterion Localization Induces a Switch between Tight and Loose Configurations of Knotted Weak Polyacid Rings despite Intermonomer Coulomb Repulsions

Stochastic simulations have been used to investigate the conformational behavior of knotted weak polyacid rings as a function of pH. Different from the commonly expected ionization-repulsion-expansion scheme upon increasing pH, theoretical results suggest a nonmonotonic behavior of the gyration radius R_g². Polyelectrolyte recontraction at high ionization is induced by the weakening of Coulomb repulsion due to counterions (CIs) localizing at the interphase between the polymer and solvent, and the more marked it appears, the more complex is the knot topology. Compared with strong polyelectrolytic species of identical ionization, weak polyacids present tighter knots due to their ability to localize neutral monomers inside the tangled part. Increasing the solvent Bjerrum length enhances CIs localization, lowering the pH at which polyacids start decreasing their average size. A similar effect is also obtained by increasing the amount of "localizable" cations by adding salts.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Osmotic pressure in polyelectrolyte solutions: cell-model and bulk simulations

The osmotic pressure of polyelectrolyte solutions as a function of concentration has been calculated by Monte Carlo simulations of a spherical cell model and by molecular dynamics simulations with periodic boundary conditions. The results for the coarse-grained polyelectrolyte model are in good agreement with experimental results for sodium polyacrylate and the cell model is validated by the bulk simulations. The cell model offers an alternative perspective on osmotic pressure and also forms a direct link to even simpler models in the form of the Poisson-Boltzmann approximation applied to cylindrical and spherical geometries. As a result, the non-monotonic behaviour of the osmotic coefficient seen in simulated salt-free solutions is shown not to rely on a transition between a dilute and semi-dilute regime, as is often suggested when the polyion is modelled as a linear flexible chain. The non-monotonic behaviour is better described as the combination of a finite-size effect and a double-layer effect. Parameters that represent the linear nature of the polyion, including an alternative to monomer concentration, make it possible to display a generalised behaviour of equivalent chains, at least at low concentrations. At high concentrations, local interactions become significant and the exact details of the model become important. The effects of added salt are also discussed and one conclusion is that the empirical additivity rule, treating the contributions from the polyelectrolyte and any salt separately, is a reasonable approximation, which justifies the study of salt-free solutions.

Monte Carlo simulations of weak polyelectrolyte microgels: pH-dependence of conformation and ionization

In this study, we investigated the effect of pH on single weak acidic polyelectrolyte microgels under salt-free conditions with (i) varying microgel concentration, (ii) varying content of acidic groups and (iii) different crosslinking densities using Monte Carlo simulations under explicit consideration of the protonation/deprotonation reaction. We assessed both global properties, such as the degree of ionization, the degree of swelling and the counterion distribution, and local properties such as the radial network ionization profile and the ionization along the polymer chains as a function of pH. We found a pronounced suppression of the pH-dependent ionization of the microgels, as compared to the ideal titration behavior and a shift of the titration curve to a higher pH originating in the proximity of acidic groups in the microgel. In contrast to macroscopic gels, counterions can leave the microgel, resulting in an effective charge of the network, which hinders the ionization. A decreasing microgel concentration leads to an increased effective charge of the microgel and a more pronounced shift of the titration curve. The number of acidic groups showed only a weak effect on the ionization behavior of the microgels. For two different microgels with different crosslinking densities, similar scaling of the gel size was observed. A distinct transition from an uncharged and unswollen to a highly charged and expanded polymer network was observed for all investigated microgels. The degree of swelling mainly depends on the degree of ionization. An inhomogeneous distribution of the degree of ionization along the radial profile of the microgel was found.

Local pH and effective pKA of weak polyelectrolytes - insights from computer simulations

In this work we study the titration behavior of weak polyelectrolytes by computer simulations. We analyze the local pH near the chains at various conditions and provide molecular-level insight which complements the recent experimental determination of this quantity. Next, we analyze the non-ideal titration behaviour of weak polyelectrolytes in solution, calculate the effective ionization constant and compare the simulation results with theoretical predictions. In contrast with the universal behaviour with respect to chain length, we find non-universality and deviations from theory with respect to polymer concentration and permittivity of the solvent. The latter we explain in terms of counterion condensation and ion correlation effects, which lead to reversal of the non-ideal titration behaviour at very low permittivities. We discuss the impact of these findings on the interpretation of experimental results.

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A- + H⁺. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge-both monomer and ionic-is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

An accurate coarse-grained model for chitosan polysaccharides in aqueous solution

Computational models can provide detailed information about molecular conformations and interactions in solution, which is currently inaccessible by other means in many cases. Here we describe an efficient and precise coarse-grained model for long polysaccharides in aqueous solution at different physico-chemical conditions such as pH and ionic strength. The Model is carefully constructed based on all-atom simulations of small saccharides and metadynamics sampling of the dihedral angles in the glycosidic links, which represent the most flexible degrees of freedom of the polysaccharides. The model is validated against experimental data for Chitosan molecules in solution with various degree of deacetylation, and is shown to closely reproduce the available experimental data. For long polymers, subtle differences of the free energy maps of the glycosidic links are found to significantly affect the measurable polymer properties. Therefore, for titratable monomers the free energy maps of the corresponding links are updated according to the current charge of the monomers. We then characterize the microscopic and mesoscopic structural properties of large chitosan polysaccharides in solution for a wide range of solvent pH and ionic strength, and investigate the effect of polymer length and degree and pattern of deacetylation on the polymer properties.

Polyelectrolyte pKa from experiment and molecular dynamics simulation

The pK_a of a polyelectrolyte has been determined experimentally by potentiometric titration and computed using Molecular Dynamics (MD) constant pH (CpH) methodology, which allows the pK_a of each titratable site along the polymer backbone.

Calcium mediated polyelectrolyte adsorption on like-charged surfaces

Monte Carlo simulations within the primitive model of calcium-mediated adsorption of linear and comb polyelectrolytes onto like-charged surfaces are described, focusing on the effect of calcium and polyion concentrations as well as on the ion pairing between polymers and calcium ions. We use a combination of Monte Carlo simulations and experimental data from titration and calcium binding to quantify the ion pairing. The polymer adsorption is shown to occur as a result of surface overcharging by Ca(2+) and ion pairing between charged monomers and Ca(2+). In agreement with experimental observations, the simulations predict that the polymer adsorption isotherm goes through a maximum as the calcium or the polymer concentration is increased. The non-Langmuir isotherms are rationalized in terms of charge-charge correlations.

Understanding the protonation behavior of linear polyethylenimine in solutions through Monte Carlo simulations

The success of polyethyleneimine (PEI) as a nonviral-based gene delivery vector has been attributed to its proton buffering capacity. Despite the great interest in PEI for its use in nonviral-based gene delivery, the protonation behavior of PEI in solution is not well understood. Earlier experimental studies have reported inconsistent values of the protonation state of PEI. In this work, we report our investigation of the protonation behavior of a realistic linear PEI (lPEI) with computational approaches. Reported experimental pK(a) values of several diamine compounds are first examined. A screened Coulombic interaction with a distance dependence dielectric is shown to reproduce the shifted pK(a) values of the model diamine compounds. Then atomistic molecular dynamic simulations of lPEI chain with 20 repeating units are performed and the results are used to provide parameters for a coarse-grained polyamine model. The screened Coulombic interaction is then incorporated in the coarse-grained lPEI chain and computational titrations are performed. The obtained computational titration curves of lPEI in solutions were found to be in best agreement with experimental results by Smits et al., but the computational titration curves have too strong of a dependence on salt concentration compared to the experimental results by Smits et al. Disregarding the discrepancy in the salt dependence, our computational titrations reveal that approximately 55% of the lPEI amine groups are protonated under physiological conditions in solution with a nearly alternating arrangement of protonated and nonprotonated amines. Titrations of lPEI in the presence of a polyanion are also performed to determine how the charge state of lPEI could be affected by complexation with DNA in gene therapy preparations. While the presence of the polyanion increases the degree of protonation of the PEI, many of PEI amines remain unprotonated under physiological conditions, providing evidence that PEI complexed with DNA could still have proton buffering capacity. Potential sources of error that have resulted in the inconsistency of previously reported protonation states of PEI were also discussed.

A Monte Carlo Study of Weak Polyampholytes: Stiffness and Primary Structure Influences on Titration Curves and Chain Conformations

The conformation and titration curves of weak polyampholytes are examined using Monte Carlo simulations with screened Coulomb potentials in the Grand Canonical ensemble. Two different types of monomers are considered. Depending on the solution pH, monomers A are weak acidic sites that can either be negatively charged or uncharged (as carboxylic groups), whereas monomers B are weak basic sites that can either be positively charged or uncharged (as amino groups). The influence of the chain stiffness, primary structure, and ionic concentration on the acid/base properties of the polyampholyte chains are systematically investigated. By adjusting the pH values, titration curves and then the fractions of positively and negatively ionized charged monomers are calculated. Stiffness influence is estimated by comparing two models of chain: a fully flexible and a rod-like polyampholyte. Different primary structures such as statistical (diblock, octablock, and alternating) and random polyampholytes are also considered. We demonstrate that the primary structure plays important roles in the acid/base properties as well as the charge distribution along the polymer backbone of a statistical rod-like polyampholyte. When flexible polyampholytes are considered, polyampholyte conformations promote the attractive electrostatic interactions between positively and negatively charged monomers, hence leading to more or less compact conformations and acid/base properties relatively different in comparison to the rod-like polyampholytes. Various conformations such as extended, globular, and pearl-necklace conformations are found in good agreement with the literature by adjusting the interaction parameter between monomers and monomer stoichiometry.

Colloidal complexes from poly(vinyl amine) and carboxymethyl cellulose mixtures

The phase behaviors of polyelectrolyte complexes formed from dilute solutions of poly(vinyl amine) (PVAm) and carboxymethyl cellulose (CMC) were determined as a function of overall composition and pH. The phase diagram included regions with soluble complexes, colloidal complexes, and macroscopic precipitates. Colloidal complexes were stable when either polymer was in sufficient excess to give electrosteric stabilization. The polymer mixing ratios giving complexes with an isoelectric point of 7 could be predicted from a simple model using the degree of ionization vs pH data for PVAm and CMC. The model failed at extreme pH values because not all added polymer was incorporated into the complexes. At pH 7, essentially all the added polymer was incorporated into the colloidal complex or precipitate, as long as the mixing ratio was within +/-10% of charge stoichiometry. The interaction of PVAm and CMC at pH 7 was endothermic, supporting the generally accepted viewpoint that the interaction of oppositely charged polyelectrolytes is entropy-driven. Although the colloidal complexes had a broad particle size distribution, the average particle size was rather insensitive to mixing ratio. By contrast, complex size was sensitive to electrolyte concentration with no complex formation when the NaCl concentration was > or =2 M.

Structure of polyelectrolyte complexes by Brownian dynamics simulation: Effects of the bond length asymmetry of the polyelectrolytes

Brownian dynamics simulations were performed to study the structure of polyelectrolyte complexes formed by two flexible, oppositely charged polyelectrolyte chains. The distribution of monomers in the complex as well as the radius of gyration and structure factor of complexes and individual polyelectrolytes are reported. These structural properties were calculated for polyelectrolyte chains with equal number of monomers, keeping constant the bond length of the negative chain and increasing the bond length of the positive chain. This introduces an asymmetry in the length of the chains that modulates the final structure of the complexes. In the symmetric case the distribution of positive and negative monomers in the complex are identical, producing clusters that are locally and globally neutral. Deviations from the symmetric case lead to nonuniform, asymmetric monomer distributions, producing net charge oscillations inside the complex and large changes in the radius of gyration of the complex and individual chains. From the radius of gyration of the polyelectrolyte chains it is shown that the positive chain is much more folded than the negative chain when the chains are asymmetric, which is also confirmed through the scaling behavior of the structure factors.

Nanoparticle Adsorption on a Weak Polyelectrolyte. Stiffness, pH, Charge Mobility, and Ionic Concentration Effects Investigated by Monte Carlo Simulations

Monte Carlo simulations have been used to study two different models for a weak linear polyelectrolyte in the presence of nanoparticles: (i) a rodlike and (ii) a flexible polyelectrolytes. The use of simulated annealing has made it possible to simulate a polyelectrolyte chain in the presence of several nanoparticles by improving conformation sampling and avoiding multiple minima problems when dense conformations are produced. Nanoparticle distributions along the polymer backbone were analyzed versus the ionic concentration, polyelectrolyte stiffness, and nanoparticle surface charge. Titration curves were calculated and the influences of the ionic concentration, solution pH, and number of adsorbed nanoparticles on the acid/base polyelectrolyte properties have been systematically investigated. The subtle balance of attractive and repulsive interactions has been discussed, and some characteristic conformations are presented. The comparison of the two limit models provides a good representation of the stiffness influence on the complex formation. In some conditions, overcharging was obtained and presented with respect to both the polyelectrolyte and nanoparticle as the central element. Finally, the charge mobility influence along the polyelectrolyte backbone was investigated by considering annealed and quenched polyelectrolyte chains.

A coarse-grained molecular model for glycosaminoglycans: application to chondroitin, chondroitin sulfate, and hyaluronic acid

A coarse-grained molecular model is presented for the study of the equilibrium conformation and titration behavior of chondroitin (CH), chondroitin sulfate (CS), and hyaluronic acid (HA)-glycosaminoglycans (GAGs) that play a central role in determining the structure and biomechanical properties of the extracellular matrix of articular cartilage. Systematic coarse-graining from an all-atom description of the disaccharide building blocks retains the polyelectrolytes' specific chemical properties while enabling the simulation of high molecular weight chains that are inaccessible to all-atom representations. Results are presented for the characteristic ratio, the ionic strength-dependent persistence length, the pH-dependent expansion factor for the end-to-end distance, and the titration behavior of the GAGs. Although 4-sulfation of the N-acetyl-D-galactosamine residue is found to increase significantly the intrinsic stiffness of CH with respect to 6-sulfation, only small differences in the titration behavior of the two sulfated forms of CH are found. Persistence length expressions are presented for each type of GAG using a macroscopic (wormlike chain-based) and a microscopic (bond vector correlation-based) definition. Model predictions agree quantitatively with experimental conformation and titration measurements, which support use of the model in the investigation of equilibrium solution properties of GAGs.

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.

Monte Carlo simulation of an inhomogeneous dielectric continuum model for B-DNA

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA. Primitive model results are verified against other simulation reports and a comparison of barbarous model predictions with experimental data is discussed. The internal energy, osmotic coefficient, radial distributions and the population ratio of counterions in the geometrically resolved major and minor grooves are all found to strongly depend on the dielectric boundary position. This suggests that a self-consistent development of the model should consider a free surface problem where the boundary is not specified a priori.

pH as a trigger of peptide beta-sheet self-assembly and reversible switching between nematic and isotropic phases

The hierarchical self-assembly of rationally designed synthetic peptides into beta-sheet tapes, ribbons, fibrils, and fibers opens up potentially useful routes to soft-solidlike materials such as hydrogels, organogels, or liquid crystals. Here, it is shown how incorporation of Glu (-CH(2)CH(2)COOH) or Orn (-CH(2)CH(2)CH(2)NH(2)) into the primary structure of an 11 amino acid peptide enables self-assembly to be rapidly (seconds) and reversibly controlled by simply changing pH. Solutions of monomeric peptide, typically at concentrations in excess of 0.003 v/v, can be switched within seconds to, for example, nematic gel states comprised of interconnected orientationally ordered arrays of fibrils or vice versa. This is to be compared with the lyophilized peptide dissolution route to nematic fluids and gels which is impracticably long, taking many hours or even days. An important design principle, that stabilization of fibrillar dispersions requires of the order of one unit of net positive or negative charge per peptide molecule, is first demonstrated and then used to design an 11 amino acid peptide P(11)-3 (CH(3)CO-Gln-Gln-Arg-Phe-Gln-Trp-Gln-Phe-Gln-Gln-Gln-NH(2)) whose self-assembly behavior is independent of pH (1 < pH < 10). pH control is then incorporated by appropriately positioning Glu or Orn side chains so that the peptide-peptide free energy of interaction in the tapelike substructure is strongly influenced by direct electrostatic forces between gamma-COO(-) in Glu(-) or delta-NH(3)(+) in Orn(+), respectively. This design principle is illustrated by the behavior of two peptides: P(11)-4 (CH(3)CO-Gln-Gln-Arg-Phe-Glu-Trp-Glu-Phe-Glu-Gln-Gln-NH(2)) which can be switched from its nematic to its isotropic fluid state by increasing pH and P(11)-5 (CH(3)CO-Gln-Gln-Orn-Phe-Orn-Trp-Orn-Phe-Gln-Gln-Gln-NH(2)) designed to exhibit the converse behavior. Acid-base titrations of fibrillar dispersions reveal deprotonation of the gamma-COOH of Glu or of the delta-NH(3)(+) of Orn(+) occurs over wide bands of up to 5 pH units, a feature of polyelectrolytes. The values of the energy parameters controlling self-assembly can therefore be smoothly and continuously varied by changing pH. This enables isotropic fluid-to-nematic transitions to be triggered by relatively small additions of acid or base, typically 1 part in 10(3) by volume of 1 M HCl or NaOH.

Dissolution of a polyelectrolyte-macroion complex by addition of salt

The dissolution of complexes formed by a linear polyelectrolyte and oppositely charged macroions by addition of salt has been examined by employing a simple model with focus on the electrostatic interactions and solved by Monte Carlo simulations. In the absence of salt an overcharged complex appears. Upon addition of salt, the number of complexed macroions is continuously decreasing, the effect being similar for flexible and stiff polyelectrolytes. Regarding the flexible polyelectrolyte, the number of polyelectrolyte-macroion contacts is reduced, whereas it remains nearly constant for the stiff polyelectrolyte as the salt content is increased. A screened Coulomb potential of the Debye-Hückel type, in which the small ions are only indirectly described, displays a good representation of the system.