Macromolecular crowding can influence polymer shapes, which is important for understanding the thermodynamic stability of polymer solutions and the structure and function of biopolymers (proteins, RNA, DNA) under confinement. We explore the influence of nanoparticle crowding on polymer shapes via Monte Carlo simulations and free-volume theory of a coarse-grained model of polymer-nanoparticle mixtures. Exploiting the geometry of random walks, we model polymer coils as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor. Accounting for the entropic cost of a nanoparticle penetrating a larger polymer coil, we compute the crowding-induced shift in the shape distributions, radius of gyration, and asphericity of ideal polymers in a theta solvent. With increased nanoparticle crowding, we find that polymers become more compact (smaller, more spherical), in agreement with predictions of free-volume theory. Our approach can be easily extended to nonideal polymers in good solvents and used to model conformations of biopolymers in crowded environments.

Depletion-induced interactions between colloids in colloid-polymer mixtures depend in range and strength on size, shape, and concentration of depletants. Crowding by colloids in turn affects shapes of polymer coils, such as biopolymers in biological cells. By simulating hard-sphere colloids and random-walk polymers, modeled as fluctuating ellipsoids, we compute depletion-induced potentials and polymer shape distributions. Comparing results with exact density-functional theory calculations, molecular simulations, and experiments, we show that polymer shape fluctuations play an important role in depletion and crowding phenomena.

Depletion forces and macromolecular crowding govern the structure and function of biopolymers in biological cells and the properties of polymer nanocomposite materials. To isolate and analyze the influence of polymer shape fluctuations and penetrability on depletion-induced interactions and crowding by nanoparticles, we model polymers as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor of an ideal random walk. Within this model, we apply Monte Carlo simulation methods to compute the depletion-induced potential of mean force between hard nanospheres and crowding-induced shape distributions of polymers in the protein limit, in which polymer coils can be easily penetrated by smaller nanospheres. By comparing depletion potentials from simulations of ellipsoidal and spherical polymer models with predictions of polymer field theory and free-volume theory, we show that polymer depletion-induced interactions and crowding depend sensitively on polymer shapes and penetrability, with important implications for bulk thermodynamic phase behavior.