Modeling Sequence-Defined Charged Biopolymers: RNA Folding, Polyampholyte Necklaces, and Coacervation

Abstract

Charged biopolymers—including RNA, intrinsically disordered proteins (IDPs), and synthetic polyampholytes—exhibit diverse structural, dynamical, and phase behaviors that are highly sensitive to their primary sequence. These macromolecules are central to cellular function, increasingly used as programmable materials, and important therapeutic targets. A fundamental challenge is to understand how sequence-defined interactions shape structures, folding landscapes, thermodynamics, and phase behavior. This thesis develops physical modeling frameworks, including coarse-grained molecular dynamics, polymer scaling theory, and random phase approximation (RPA), to investigate sequence-defined charged biopolymers from single-molecule structure and dynamics to phase behavior. Across all systems studied, behavior is governed by the balance between enthalpic interactions (base pairing, stacking, and Coulomb interactions) and entropic penalties associated with chain flexibility and backbone geometry. The first part introduces CRANBERRY, a coarse-grained RNA model that explicitly incorporates sugar puckering and noncanonical base pairing. Using a contrastive-divergence parameterization with targeted refinement of disordered ensembles, CRANBERRY achieves realistic folding cooperativity and thermodynamics, accurately captures native fluctuations and stacking free energies, and can reversibly fold challenging tetraloop motifs \textit{de novo}. The second part examines statistically neutral polyampholytes across solvent conditions. Scaling theory and molecular dynamics simulations yield a single-chain conformational phase diagram that includes globules, extended chains, and a rich family of necklace structures. Two hierarchical necklace-in-necklace regimes emerge from the interplay between short-range attractions and Coulombic interactions encoded by blocky sequences. The final part develops an analytical RPA theory for symmetric non-neutral polyampholyte coacervates, where the ensemble-averaged net charge fraction promotes cooperative electrostatic attractions. Closed-form expressions for the correlation free energy, coacervate density, and critical salt concentration clarify how charge imbalance drives crossovers between polyampholyte-like and polyelectrolyte-like regimes and enhances salt resistance. Together, these results show how sequence-defined nonbonded interactions generate the structural and thermodynamic richness of charged biopolymers and provide insight into RNA folding, polyampholyte conformations, phase separation, and the rational design of charged polymer materials