Monte Carlo study of titration of linear polyelectrolytes

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.

Effect of the surface charge discretization on electric double layers: A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

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.

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.