Phase Boundary and Salt Partitioning in Coacervate Complexes Formed between Poly(acrylic acid) and Poly(N,N-dimethylaminoethyl methacrylate) from Detailed Atomistic Simulations Combined with Free Energy Perturbation and Thermodynamic Integration Calculations

Transfer Matrix Model of pH Effects in Polymeric Complex Coacervation

Oppositely charged polyelectrolytes can undergo an associative phase separation, in a process known as polymeric complex coacervation. This phenomenon is driven by the electrostatic attraction between polyanion and polycation species, leading to the formation of a polymer-dense coacervate phase and a coexisting polymer-dilute supernatant phase. There has been significant recent interest in the physical origin and features of coacervation; yet notably, experiments often use weak polyelectrolytes the charge state of which depends on solution pH, while theoretical or computational efforts typically assume strong polyelectrolytes that remain fully charged. There have been only a few efforts to address this limitation, and thus there has been little exploration of how pH can affect complex coacervation. In this paper, we modify a transfer matrix theory of coacervation to account for acid-base equilibria, taking advantage of its ability to directly account for some local ion correlations that will affect monomer charging. We show that coacervation can stabilize the charged state of a weak polyelectrolyte via the proximity of oppositely charged monomers, and can lead to asymmetric phase diagrams where the positively and negatively charged polyelectrolytes exhibit different behaviors near the pK_a of either chain. Specifically, there is a partitioning of one of the salt species to a coacervate to maintain electroneutrality when one of the polyelectrolytes is only partially charged. This results in the depletion of the same salt species in the supernatant, and overall can suppress phase separation. We also demonstrate that, when one of the species is only partially charged, mixtures that are off-stoichiometric in volume fraction but stoichiometric in charge exhibit the greatest propensity to form coacervate phases.

Polyelectrolyte Complex Coacervation across a Broad Range of Charge Densities

Polyelectrolyte complex coacervates of homologous (co)polyelectrolytes with a near-ideally random distribution of a charged and neutral ethylene oxide comonomer were synthesized. The unique platform provided by these building blocks enabled an investigation of the phase behavior across charge fractions 0.10 ≤ f ≤ 1.0. Experimental phase diagrams for f = 0.30-1.0 were obtained from thermogravimetric analysis of complex and supernatant phases and contrasted with molecular dynamics simulations and theoretical scaling laws. At intermediate to high f, a dependence of polymer weight fraction in the salt-free coacervate phase (w P,c) of w P,c ∼ f 0.37±0.01 was extracted; this trend was in good agreement with accompanying simulation predictions. Below f = 0.50, w P,c was found to decrease more dramatically, qualitatively in line with theory and simulations predicting an exponent of 2/3 at f ≤ 0.25. Preferential salt partitioning to either coacervate or supernatant was found to be dictated by the chemistry of the constituent (co)polyelectrolytes.

Coacervate formation studied by explicit solvent coarse-grain molecular dynamics with the Martini model

Complex coacervates are liquid-liquid phase separated systems, typically containing oppositely charged polyelectrolytes. They are widely studied for their functional properties as well as their potential involvement in cellular compartmentalization as biomolecular condensates. Diffusion and partitioning of solutes into a coacervate phase are important to address because their highly dynamic nature is one of their most important functional characteristics in real-world systems, but are difficult to study experimentally or even theoretically without an explicit representation of every molecule in the system. Here, we present an explicit-solvent, molecular dynamics coarse-grain model of complex coacervates, based on the Martini 3.0 force field. We demonstrate the accuracy of the model by reproducing the salt dependent coacervation of poly-lysine and poly-glutamate systems, and show the potential of the model by simulating the partitioning of ions and small nucleotides between the condensate and surrounding solvent phase. Our model paves the way for simulating coacervates and biomolecular condensates in a wide range of conditions, with near-atomic resolution.