Effects of electrostatics on charged macromolecules: single-chain conformation, multi-chain aggregation and solution thermodynamics

Charged macromolecules have ubiquitous applications in both commodity materials in our everyday life and advanced functional materials to solve emergent challenges. Many biomacromolecules, like proteins, DNA, and RNA, are essentially charged macromolecules. Their equilibrium structures as well as solution properties are determined by the interplay between the long-range electrostatic interaction and the short-range van der Waals interaction. We develop a theory that systematically includes electrostatics into polymer self-consistent field theory. The structure and free energy of a single chain or an aggregate is obtained by applying the theory to a subvolume. This information is then incorporated into the framework of dilute solution thermodynamics to reconstruct the entire solution. For a single charged macromolecule in dilute salt solutions, our theory fully captures the cascade globule-pearl necklace-coil transition. At intermediate salt concentrations, we predict the formation of a stable vesicle structure. For multi-chain aggregates, our theory predicts that the aggregation of charged macromolecules at low salt concentrations is via a two-step nucleated process involving a conformational transition from metastable spherical oligomer to elongated fibril. The scaling analysis elucidates the electrostatic origin of the conformational transition: the fibril enters the screening region much earlier than the spherical aggregate. The theoretical predictions of the kinetic pathway and the morphology of the aggregates are in good agreement with the experiments of protein aggregation. Furthermore, applying the theory to solution thermodynamics, our theory fully captures the long-standing puzzles of the non-monotonic salt concentration dependence and the specific ion effect of the protein solubility. The theoretical predictions are in quantitative agreement with experimental results for various proteins and salt ions without any fitting parameters.