Direct Simulations of Phase Behavior of Mixtures of Oppositely Charged Proteins/Nanoparticles and Polyelectrolytes

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates: Insights from Molecular Simulations

Electrostatic interactions in polymeric systems are responsible for a wide range of liquid-liquid phase transitions that are of importance for biology and materials science. Such transitions are referred to as complex coacervation, and recent studies have sought to understand the underlying physics and chemistry. Most theoretical and simulation efforts to date have focused on oppositely charged linear polyelectrolytes, which adopt nearly ideal-coil conformations in the condensed phase. However, when one of the coacervate components is a globular protein, a better model of complexation should replace one of the species with a spherical charged particle or colloid. In this work, we perform coarse-grained simulations of colloid-polyelectrolyte coacervation using a spherical model for the colloid. Simulation results indicate that the electroneutral cell of the resulting (hybrid) coacervates consists of a polyelectrolyte layer adsorbed on the colloid. Power laws for the structure and the density of the condensed phase, which are extracted from simulations, are found to be consistent with the adsorption-based scaling theory of hybrid coacervation. The coacervates remain amorphous (disordered) at a moderate colloid charge, Q, while an intra-coacervate colloidal crystal is formed above a certain threshold, at Q > Q*. In the disordered coacervate, if Q is sufficiently low, colloids diffuse as neutral nonsticky nanoparticles in the semidilute polymer solution. For higher Q, adsorption is strong and colloids become effectively sticky. Our findings are relevant for the coacervation of polyelectrolytes with proteins, spherical micelles of ionic surfactants, and solid organic or inorganic nanoparticles.

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates

We develop a scaling theory for the structure and dynamics of "hybrid" complex coacervates formed from linear polyelectrolytes (PEs) and oppositely charged spherical colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. At low concentrations, in stoichiometric solutions, PEs adsorb at the colloids to form electrically neutral finite-size complexes. These clusters attract each other through bridging between the adsorbed PE layers. Above a threshold concentration, macroscopic phase separation sets in. The coacervate internal structure is defined by (i) the adsorption strength and (ii) the ratio of the resulting shell thickness to the colloid radius, H/R. A scaling diagram of different coacervate regimes is constructed in terms of the colloid charge and its radius for Θ and athermal solvents. For high charges of the colloids, the shell is thick, H ≫ R, and most of the volume of the coacervate is occupied by PEs, which determine its osmotic and rheological properties. The average density of hybrid coacervates exceeds that of their PE-PE counterparts and increases with nanoparticle charge, Q. At the same time, their osmotic moduli remain equal, and the surface tension of hybrid coacervates is lower, which is a consequence of the shell's inhomogeneous density decreasing with the distance from the colloid surface. When charge correlations are weak, hybrid coacervates remain liquid and follow Rouse/reptation dynamics with a Q-dependent viscosity, η _Rouse ∼ Q ^4/5 and η _rep ∼ Q ^28/15 for a Θ solvent. For an athermal solvent, these exponents are equal to 0.89 and 2.68, respectively. The diffusion coefficients of colloids are predicted to be strongly decreasing functions of their radius and charge. Our results on how Q affects the threshold coacervation concentration and colloidal dynamics in condensed phases are consistent with experimental observations for in vitro and in vivo studies of coacervation between supercationic green fluorescent proteins (GFPs) and RNA.

Self-assembled morphologies of polyelectrolyte-grafted nanoparticles directed by oppositely charged polymer matrices

Self-assembled structure of polymer grafted nanoparticles is an interesting and growing subject in the field of hybrid electronics and high energy density materials. In light of this, the self-assembled morphologies of polyelectrolyte (PE) sparsely grafted nanoparticles tuned by oppositely charged matrix chains are studied using molecular dynamics simulations. Our focus is to elucidate the effect of matrix chain polymerization on modulating the stretching properties of tethered PE layers, on the self-assembled structuring of nanoparticles. Through varying the matrix chain length and stiffness as well as electrostatic interaction strength, rich phase behaviors of PE coated nanoparticles are predicted, including spherical micelle-like structures being preferred with short matrix chains and percolating network morphologies favored with long matrix chains, which is more pronounced with an enhanced matrix chain rigidness. To pinpoint the mechanisms of self-assembled structure formation, the thickness of grafted layers, the gyration radius of tethered chains, and pair correlation functions between nanoparticles are analyzed carefully. Additionally, electrostatic correlations, manifested as the bridging via matrix chains, are examined by identifying three states of matrix PE chains. Our simulation results may be useful for designing smart polymer nanocomposites based on PE coated nanoparticles.

Self-assembled structure of polymer grafted nanoparticles is an interesting and growing subject in the field of hybrid electronics and high energy density materials.