Interplay of Coil-Globule Transitions and Aggregation in Homopolymer Aqueous Solutions: Simulation and Topological Insights

Abstract

We investigate the structural and topological properties of hydrophobic homopolymer chains in aqueous solutions using molecular dynamics simulations and circuit topology (CT) analysis. By combining geometric observables, such as radius of gyration and degree of aggregation, with CT data, we capture the relationship between coil-globule and aggregation transitions, resolving the system's structural changes with temperature. Our results reveal a temperature-driven collective transition from isolated coiled chains to globular aggregates. At a characteristic transition temperature $T_c$, each chain in multichain systems undergoes a rapid coil-globule collapse, coinciding with aggregation, in contrast to the gradual collapse observed in single-chain systems at infinite dilution. This collective transition is reflected in geometric descriptors and a reorganization of CT motifs, shifting from intrachain-dominated motifs at low temperatures to a diverse ensemble of multichain motifs at higher temperatures. CT motif enumeration provides contact statistics while offering a topologically detailed view of polymer organization. These findings highlight CT's utility as a structural descriptor for polymer systems and suggest applications to biopolymer aggregation and folding.

Figures (6)

• Figure 1: System configurations for different temperatures, showing the structural transition at a characteristic temperature $T_c \approx 290$, for $m=4$ polymers with $n=30$ monomers each. The polymers collapse from a dilute coiled state into a globular aggregated state.
• Figure 2: Table of single-chain circuit topology motifs. Contacts $\alpha$, $\beta$ are represented by green and purple lines connecting contact sites (white circles). Underneath each motif, a cartoon representation is shown illustrating the concomitant topology.
• Figure 3: Table of single-chain circuit topology motifs. Contacts $\alpha$, $\beta$ are represented by green and purple lines connecting contact sites (white circles). Next to each motif, a cartoon representation is shown illustrating the concomitant topology. Note that when a motif is degenerate only one example is shown.
• Figure 4: Average numbers of intrachain contacts $N_{\rm intra}$ (red circles) and interchain contacts $N_{\rm inter}$ (green squares), normalized by the total number of monomers $m\cdot n$, together with their respective fractions $r_{\rm intra}$ (red circles) and $r_{\rm inter}$ (green squares), as functions of temperature $T$. (a)$N_{\rm intra}$ and $N_{\rm inter}$ for the 4-polymer system, with $N_{\rm intra}$ from the single-chain system (orange diamonds) shown for comparison; (b)$r_{\rm intra}$ and $r_{\rm inter}$ for the 4-polymer system; (c)$N_{\rm intra}$ and $N_{\rm inter}$ for the 8-polymer system; (d)$r_{\rm intra}$ and $r_{\rm inter}$ for the 8-polymer system. Black (inner) symbols denote values obtained from eqs. \ref{['eq:nintra']} and \ref{['eq:ninter']}, confirming the direct numerical calculations. For $T < T_c$, no interchain contacts are present and $N_{\rm intra}$ grows steadily, while for $T \geq T_c$, all measures ($N_{\rm intra}$, $N_{\rm inter}$, $r_{\rm intra}$, $r_{\rm inter}$) converge to constant values in both systems.
• Figure 5: The radius of gyration $R_{\rm g}$(a) and degree of cohesion $D_{\rm c}$(b) as a function of temperature for the simulated models with $4$ (red) and $8$ (green) polymers. For reference, the single-chain values are also shown (black). $R_{\rm g}$ and $D_{\rm c}$ are rescaled by the radius of gyration of the ideal chain $R_{\rm g, ideal} = b\sqrt{(n-1)/6}$ and system size $L$, respectively.