Entropic Clustering of Stickers Induces Aging in Biocondensates

Biomolecular condensates are cellular phase-separated droplets that usually exhibit a viscoelastic mechanical response. A behavior rationalized by modeling the complex molecules that make up a condensate as stickers and spacers, which assemble into a network-like structure. Condensates usually exhibit a solidification over a long period of time (days), a phenomenon described as aging.The emergence of such a long timescale of evolution from microscopic processes, as well as the associated microscopic reorganization leading to aging, remains mostly an open question. In this article, we explore the connection between the mechanical properties of the condensates and their microscopic structure. We propose a minimal model for the dynamic of stickers and spacers, and show that entropy maximization of spacers leads to an attractive force between stickers. Our system displays a surprisingly slow relaxation toward equilibrium, reminiscent of glassy systems and consistent with the liquid-to-solid transition observed. To explain this behavior, we study the clustering dynamic of stickers and successfully explain the origin of glassy relaxation.

💡 Research Summary

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The paper tackles the long‑standing question of why biomolecular condensates, which are liquid‑like phase‑separated droplets inside cells, gradually become solid‑like over days—a process commonly referred to as aging. Building on the “sticker‑and‑spacer” picture, the authors construct a minimal yet analytically tractable model in which stickers are diffusing particles that can reversibly bind to spacers, while spacers are represented as Gaussian polymer chains. Stickers act as transient cross‑links; spacers provide flexibility and connectivity.

The dynamics are described by two coupled master equations for the probability densities of bound (p_b) and unbound (p_ub) stickers. The unbinding rate follows Kramers’ theory, k_ub = τ₀⁻¹ exp(−βE_b), where E_b is a single binding energy scale. The binding rate is derived from an entropic argument: when a sticker meets a polymer segment, the polymer loses configurational entropy S_ub and gains S_b upon binding. This entropic difference yields an effective “Casimir‑like” attraction between stickers, expressed through a meeting probability P_meet(r) that depends on the local polymer entropy. Detailed balance is enforced, guaranteeing thermodynamic consistency.

Because the equations are highly coupled (the entropy of a polymer segment depends on the positions of all other bound stickers), the authors resort to Gillespie stochastic simulations. They place N stickers homogeneously in a 3‑D box surrounding a single polymer of length L and let stickers diffuse, bind, or unbind according to the rates above. Early‑time simulations show a rapid rise in the fraction of bound stickers until a plateau is reached. The plateau height depends sharply on the binding energy and on the linear sticker density N/L, reproducing a phase‑transition‑like behavior reminiscent of the Poland‑Scheraga model of DNA melting: below a critical energy E_c ∝ log(L/N) stickers remain mostly unbound (liquid‑like response), whereas above E_c they stay bound (visco‑elastic solid‑like response).

The core of the study focuses on the “aging” regime where essentially all stickers are bound and the system’s energy is fixed, but the polymer’s configurational entropy still depends on sticker positions. The authors derive a mean‑field expression for the equilibrium pair‑distribution function of two stickers: \