Dynamic principles of concentration buffering through liquid-liquid phase separation

TL;DR

Cells face concentration fluctuations across multiple timescales, and LLPS condensates may buffer these changes, but the dynamic limits were unclear. The authors apply control theory to LLPS and develop a two-phase dynamic model with Flory–Huggins thermodynamics, performing a frequency-domain analysis via transfer functions and Bode plots. They find that the dilute phase acts as a high-pass filter while the dense phase attenuates both slow and fast perturbations, with a characteristic cutoff set by the interphase diffusivity, $\omega_0 \approx D_e$, and buffering tuned by the interaction parameter $\chi$ and droplet volume. The work provides a quantitative framework linking LLPS parameters to dynamic concentration buffering, with implications for cellular robustness and design of programmable synthetic condensates.

Abstract

Living systems must maintain robust biochemical function despite fluctuations that span a wide range of timescales. Biomolecular condensates formed by liquid-liquid phase separation (LLPS) have been shown to buffer concentration fluctuations, but the principles governing their dynamic regulation remain unclear. We address this by probing the response of LLPS to oscillatory perturbations that mimic fluctuations across different timescales, establishing the first systematic frequency-domain analysis of concentration buffering by condensates. We find that condensates act as frequency-selective filters: the perturbed dilute phase behaves as a high-pass filter, while the dense phase attenuates both low- and high-frequency perturbations. We establish quantitative links between LLPS parameters including interaction strength, droplet size, and molecular diffusivity, and the timescale range over which condensates effectively buffer concentration fluctuations. These findings establish the fundamental dynamical limits of concentration buffering by LLPS, with implications for how cells may use LLPS to adapt to fluctuating environments and for the design of synthetic condensates with programmable control properties.

Figures (5)

• Figure 1: Schematics of LLPS-based feedback control and frequency response characterization.A Schematic of the LLPS feedback control system. A process produces an output concentration $c$ in phase I from an input concentration perturbation $u$ in phase II. We then measure the error, $e=c_{\rm{eq}}-c$, where $c_{\rm{eq}}$ is the desired concentration in phase I. The error is then operated on by a controllers and added back to the input. B Schematic of a sinusoidal input $u$ and the output $c$ showing how the gain $G$ and phase shift $\varphi$ are measured. C Bode plots are constructed by varying the input frequency and measuring $G$ and $\varphi$ as a function of $\omega$. This schematic shows the behavior of a high-pass filter that attenuates low frequency perturbations and allows high frequencies to pass through.
• Figure 2: Bode plots showing the frequency response of our LLPS system to concentration perturbations in the dilute phase. Frequency-domain analysis shows distinct filtering properties in each phase: the dense phase (A) attenuates both slow and fast fluctuations, whereas the dilute phase (B) acts as a high-pass filter, transmitting fast perturbations while suppressing slow ones . The LLPS parameters for both plots were $\chi = 2.09507$, $D_e= 1$ and $V^{\rm{I}}=0.5$. The frequency is expressed in units of $\omega/\omega_0$ where $\omega_0=D_e$
• Figure 3: The frequency response of the output to disturbance gain under different LLPS parameters. The parameters tested were A the interaction parameter $\chi$ above the critical point ($\Delta\chi=\chi-2$), B the equilibrium volume fraction of the droplet phase, $V^{\rm{I}}_{\rm{eq}}/V$, and C the effective diffusion constant $D_e$. Condensate properties tune the frequency range of effective buffering. Stronger interactions, larger droplet volumes, and faster diffusion broaden the regime of attenuation, while weak interactions or small condensates reduce buffering efficiency. Parameters for all plots are $\Delta\chi=0.3105$, $V^{\rm{I}}_{\rm{eq}}/V=0.5$, $D_e = 1$ except when a specific parameter is changed. In increasing order: (A) $\Delta\chi=0.001,\,0.00562,\,0.0316,\,0.178,\,1.0$; (B) $V^{\rm{I}}_{\rm{eq}}/V=0.1,\,0.48,\,0.7,\,0.83,\,0.9$; (C) $D_e=0.1,\,0.316,\,1.0,\,3.16,\,10.0$.
• Figure S1: Analytical control-theory predictions and numerical simulations agree, validating our linearized model as a reliable framework for frequency-domain analysis of LLPS dynamics.
• Figure S2: Transfer function coefficients depend systematically on $\chi$, droplet volume, and diffusivity. These dependencies provide the quantitative link between LLPS parameters and dynamic control properties. The parameters were set to $\chi=2.31049$, $V^{\rm{I}}_{\rm{eq}}=0.5$, $D_e = 1$ except for the specific parameter being varied.