Transient pH changes drive vacuole formation in enzyme–polymer condensates

Nature Chemical Engineering · 2026-01-09 · 2 citations

Membraneless organelles are essential for cellular function. These biomolecular condensates often exhibit complex morphologies in response to biological stimuli. In vitro condensate models help elucidate how these multiphase assemblies form and their possible functions. Here we use such a model to investigate the formation of hollow internal regions, or vacuoles, within condensates in response to a pH change. Fast rates of pH decrease and larger droplet sizes promote vacuole development within the condensates. We show that vacuole formation is a non-equilibrium process driven by the diffusion-limited exchange of condensate components during a rapid pH change. We develop a physics-based model that describes how associative phase-separating systems respond to rapid changes in external conditions, specifically pH. Our qualitative model agrees with experimental results, showing that rapid pH changes shift the phase boundaries, triggering spinodal decomposition and inducing vacuole formation within the condensates. Our pH-sensitive in vitro model illustrates a mechanism of vacuole formation in associative condensates and provides insights into the regulation of multiphase condensates in vivo. Rapid pH changes can trigger hollow vacuoles in associative condensates of pH-responsive biomolecules. Using a model enzyme–polymer system, how larger droplets and faster pH changes promote vacuole formation by creating unstable non-equilibrium compositions is shown. A physics-based model reproduces these observations, showing when and how vacuoles arise through spinodal decomposition.

Self-oscillating synchronematic colloids

Nature Communications · 2026-01-23

Self-oscillators that sustain periodic dynamics under constant input are ubiquitous in natural and engineered systems, where their interactions enable spatiotemporal coordination among many individual units. New forms of organization can emerge when these self-oscillating units are free to move and rotate, linking their spatial arrangement and orientation with their oscillation frequencies and phases. Here, we report experiments and simulations on populations of Quincke colloids that behave as self-oscillating units characterized by position, orientation, frequency, and phase. Hydrodynamic interactions among these colloids drive temporal synchronization and spatial alignment of their phases and orientations, giving rise to a new form of collective order that we term synchronematic. Within finite-size crystalline clusters, these non-reciprocal interactions promote global synchronization and circular alignment, with a collective frequency that increases with cluster size. Using the theory of weakly coupled oscillators, we derive a reduced-order model that captures the coupled evolution of phase and orientation and explains how synchronematic order depends sensitively on the particle configuration. Our results establish Quincke colloids as a model system for active oscillatory matter and reveal fundamental principles by which synchronization, alignment, and structure co-emerge—offering a framework for designing adaptive, frequency-tunable materials. Self-oscillators are critical in various natural and engineered systems, as they enable complex collective behaviors through interactions among individual units. This study demonstrates that populations of Quincke colloids-self-oscillators whose back-and-forth motion defines both a phase and a nematic oscillation axis-can achieve a form of collective order, termed synchronematic order, characterized by hydrodynamic interactions that synchronize their oscillation phases and align their orientations.

Steady rotation and wall-mediated dynamics of magnetic Janus particles in oscillating fields

Soft Matter · 2026-01-01

Janus particles with a ferromagnetic patch show height-dependent rolling and hybrid dynamics in oscillating magnetic fields, where moment coupling drives continuous rotation and boundary interactions govern trajectories.

Self-oscillating synchronematic colloids

Research Square · 2025-07-31

Programmable rheotaxis of magnetic rollers in time-varying fields

Soft Matter · 2025-01-01 · 1 citations

Magnetic microrobots capable of navigating complex fluid environments typically rely on real-time feedback to adjust external fields for propulsion and guidance. As an alternative, we explore the use of field-programmable rheotaxis, in which time-periodic magnetic fields drive directional migration of ferromagnetic particles in simple shear flows. Using a deterministic model that couples magnetic torques to hydrodynamic interactions near a surface, we show that the frequency, magnitude, and waveform of the applied field can encode diverse rheotactic behaviors-including downstream, upstream, and cross-stream migration relative to the flow. We analyze the mechanisms underlying these responses for canonical fields and use this understanding to design complex waveforms that optimize migration speed and direction. Our results reveal a tradeoff between performance and robustness: high-performance designs enable upstream motion but are sensitive to system parameters, whereas robust designs operate in the linear response regime with more modest performance gains. These findings establish a general strategy for programming flow-guided navigation in magnetic colloids and suggest routes toward self-guided microrobots that respond predictably to fluid environments without external feedback.

Transient pH changes drive vacuole formation in enzyme-polymer condensates

bioRxiv (Cold Spring Harbor Laboratory) · 2025-01-21 · 3 citations

Abstract Intracellular membraneless organelles formed by the phase separation of biomolecules are essential for cellular functioning. These biomolecular condensates often exhibit complex morphologies in response to biological stimuli. In vitro condensate models help elucidate the mechanism of formation and the associated function of these hierarchical assemblies. Here, we use an in vitro model to investigate the formation of hollow internal regions, or vacuoles, within the condensate interior in response to a pH change. Our experimental system is a pH-responsive complex coacervate formed by the anionic glucose oxidase enzyme phase separating with the weak polycation, DEAE-dextran. Fast rates of pH decrease and larger droplet sizes trigger vacuole development within the coacervates. We show that the emergence of vacuoles is a non-equilibrium process caused by the diffusion-limited exchange of condensate components during a fast pH change. We develop a theoretical model that captures how a phase-separating system responds dynamically to changes in system conditions, particularly pH. Our qualitative phase diagram aligns with our experimental results, showing that rapid pH changes shift the phase boundaries, triggering spinodal decomposition and inducing vacuole formation within the condensates. Our pH-sensitive in vitro coacervate model provides a platform to modulate the internal structure of ternary phase separating systems and gain insights into the mechanisms controlling condensate organization in vivo .

Author response for "Programmable rheotaxis of magnetic rollers in time-varying fields"

2025-08-14

Self-Guided Navigation of Magnetic Microspheres on Topographic Landscapes

ACS Applied Engineering Materials · 2024-10-28 · 3 citations

The directed propulsion of magnetic microrobots through structured environments often requires real-time feedback between external sensors and the applied field. This requirement, however, can be relaxed to enable self-guided propulsion by coupling field-driven motion to gradients in the local environment. We show that rotating fields direct the migration of ferromagnetic spheres up local gradients in the topography of a solid substrate. We quantify the speed and direction of particle migration as a function of the rotation frequency and incline angle. These observations are explained by a dynamic model that describes particle motion through the fluid due to the magnetic torque and gravitational force. We demonstrate how “topotaxis” can direct the simultaneous navigation of multiple particles on patterned arrays of concave bowls and convex domes without knowledge of the particle locations or the surface topography. These results highlight opportunities for designing time-varying fields to achieve other self-guided behaviors conditioned on local environmental cues.

Analyzing Sequential Betting with a Kelly-Inspired Convective-Diffusion Equation

Entropy · 2024-07-15 · 1 citations

The purpose of this article is to analyze a sequence of independent bets by modeling it with a convective-diffusion equation (CDE). The approach follows the derivation of the Kelly Criterion (i.e., with a binomial distribution for the numbers of wins and losses in a sequence of bets) and reframes it as a CDE in the limit of many bets. The use of the CDE clarifies the role of steady growth (characterized by a velocity U) and random fluctuations (characterized by a diffusion coefficient D) to predict a probability distribution for the remaining bankroll as a function of time. Whereas the Kelly Criterion selects the investment fraction that maximizes the median bankroll (0.50 quantile), we show that the CDE formulation can readily find an optimum betting fraction f for any quantile. We also consider the effects of “ruin” using an absorbing boundary condition, which describes the termination of the betting sequence when the bankroll becomes too small. We show that the probability of ruin can be expressed by a dimensionless Péclet number characterizing the relative rates of convection and diffusion. Finally, the fractional Kelly heuristic is analyzed to show how it impacts returns and ruin. The reframing of the Kelly approach with the CDE opens new possibilities to use known results from the chemico-physical literature to address sequential betting problems.

Synchronization and alignment of model oscillators based on Quincke rotation

Physical review. E · 2023-05-22 · 5 citations

Colloidal spheres in weakly conductive fluids roll back and forth across the surface of a plane electrode when subject to strong electric fields. The so-called Quincke oscillators provide a basis for active matter based on self-oscillating units that can move, align, and synchronize within dynamic particle assemblies. Here, we develop a dynamical model for oscillations of a spherical particle and investigate the coupled dynamics of two such oscillators in the plane normal to the field. Building on existing descriptions of Quincke rotation, the model describes the dynamics of the charge, dipole, and quadrupole moments due to charge accumulation at the particle-fluid interface and particle rotation in the external field. The dynamics of the charge moments are coupled by the addition of a conductivity gradient, which describes asymmetries in the rates of charging near the electrode. We study the behavior of this model as a function of the field strength and gradient magnitude to identify the conditions required for sustained oscillations. We investigate the dynamics of two neighboring oscillators coupled by far field electric and hydrodynamic interactions in an unbounded fluid. Particles prefer to align and synchronize their rotary oscillations along the line of centers. The numerical results are reproduced and explained by accurate low-order approximations of the system dynamics based on weakly coupled oscillator theory. The coarse-grained dynamics of the oscillator phase and angle can be used to investigate collective behaviors within ensembles of many self-oscillating colloids.