Folding of Free Polymers Under Confinement by Responsive Hydrogels
Abstract
Controlling the folding of biopolymers in crowded and confined environments, such as the interior of biological cells, remains a significant challenge. Macromolecular crowding and spatial confinement can strongly influence transition pathways between folded and unfolded states of proteins. Such environments can be mimicked in experiments by confining polymers within soft, tunable media, such as hydrogels -- cross-linked polymer networks that swell by absorbing solvent and exhibit stimulus-dependent responsiveness. Here, we develop a self-consistent mean-field theory for the equilibrium swelling and internal composition of a hydrogel immersed in a solution of free polymer coils. The theory extends the Flory-Rehner framework by incorporating free polymer coils, modeled as fluctuating ellipsoids, whose sizes and shapes are characterized by the eigenvalues of the gyration tensor. Confinement of the coils within gel pores is characterized by an effective free-volume fraction, parametrized from numerical calculations for self-avoiding-walk chains between hard walls. Coupled chemical potential equilibrium conditions are solved numerically over ranges of coil molecular weight and free polymer concentration. We find that free polymers drive a non-monotonic swelling response of hydrogels, with osmotic swelling at low concentrations followed by deswelling at higher concentrations, in qualitative agreement with experiment. We further demonstrate that confinement within gel pores reduces the radius of gyration and asphericity of embedded polymer coils, driving them toward compact, globular conformations analogous to folded protein states. These results establish a theoretical foundation for using responsive hydrogels as tunable, artificial chaperone-like systems capable of inducing and controlling biopolymer folding.
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BibTeX
@misc{aryal2026folding,
title = {{Folding of Free Polymers Under Confinement by Responsive Hydrogels}},
author = {Mahesh Aryal and Alan R. Denton},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32912},
eprint = {2610.32912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32912},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Folding of Free Polymers Under Confinement by Responsive Hydrogels
AU - Mahesh Aryal
AU - Alan R. Denton
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32912
UR - https://arxiv.org/abs/2610.32912
AB - Controlling the folding of biopolymers in crowded and confined environments, such as the interior of biological cells, remains a significant challenge. Macromolecular crowding and spatial confinement can strongly influence transition pathways between folded and unfolded states of proteins. Such environments can be mimicked in experiments by confining polymers within soft, tunable media, such as hydrogels -- cross-linked polymer networks that swell by absorbing solvent and exhibit stimulus-dependent responsiveness. Here, we develop a self-consistent mean-field theory for the equilibrium swelling and internal composition of a hydrogel immersed in a solution of free polymer coils. The theory extends the Flory-Rehner framework by incorporating free polymer coils, modeled as fluctuating ellipsoids, whose sizes and shapes are characterized by the eigenvalues of the gyration tensor. Confinement of the coils within gel pores is characterized by an effective free-volume fraction, parametrized from numerical calculations for self-avoiding-walk chains between hard walls. Coupled chemical potential equilibrium conditions are solved numerically over ranges of coil molecular weight and free polymer concentration. We find that free polymers drive a non-monotonic swelling response of hydrogels, with osmotic swelling at low concentrations followed by deswelling at higher concentrations, in qualitative agreement with experiment. We further demonstrate that confinement within gel pores reduces the radius of gyration and asphericity of embedded polymer coils, driving them toward compact, globular conformations analogous to folded protein states. These results establish a theoretical foundation for using responsive hydrogels as tunable, artificial chaperone-like systems capable of inducing and controlling biopolymer folding.
ER -