Size, Conformation, and Local Domains of Single-Chain Nanoparticles with Intrachain Covalent, Dipolar, and Electrostatic Interactions: Toward Artificial Intrinsically Disordered Proteins

Herein, we develop the hierarchical scaling model of single-chain polymer nanoparticles (SCNPs) with intrachain covalent bonds (i.e., intramolecular cross-links) and dipolar and electrostatic interactions, as simplified analogues of intrinsically disordered proteins (IDPs). By combining the standard elastic single-chain nanoparticle model with the mean-field dipole theory and polyelectrolyte scaling laws, we uncover new insights into the size and conformation of SCNPs with multiple interactions at different scales in a good solvent, at high dilution, and in semidiluted solutions, the latter being the most relevant conditions to compare with experimental data. The model takes into account key parameters such as the type of monomers involved, the composition and length of the precursor chain, the elasticity characteristics of the SCNPs upon intrachain cross-linking, the interaction strengths, and both the SCNPs and (monovalent) salt concentrations in solution. Our findings reveal distinct scaling behaviors depending on the balance between attractive dipolar and repulsive excluded volume forces. Notably, we demonstrate that electrostatic interactions above a threshold of charged monomers induce extended SCNP conformations at high dilution (below the chain overlap concentration, <i>c</i>*), while salt addition screens these effects, resulting in more collapsed configurations. In semidiluted salt-free solutions (<i>c</i> > <i>c</i>*), these SCNPs adopt a random walk conformation at high concentration. We provide useful expressions to estimate the size and number of local compact domains in these complex SCNPs, which can be exploited to immobilize catalysts, luminophores, or drugs. At the scaling level of accuracy, this theoretical approach offers a comprehensive examination of how multiple short- and long-range forces affect SCNP configuration from a local to a large scale, enabling the rational design of artificial IDPs for applications in nanomedicine, antifouling coatings, and stimuli-responsive materials. As a practical example, we provide useful design principles for the construction of expanded or, conversely, compact artificial IDPs based on SCNPs with covalent, dipolar, and electrostatic interactions.