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arxiv: 2604.27965 · v1 · submitted 2026-04-30 · ❄️ cond-mat.soft · cond-mat.stat-mech· physics.bio-ph

Recognition: unknown

Propelling catalytic structures using active phase separation

Benjamin Sorkin, Ned S. Wingreen

Authors on Pith no claims yet

Pith reviewed 2026-05-07 05:32 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mechphysics.bio-ph
keywords active phase separationself-propulsionbiomolecular condensatescolloidsmotor-free motilitysymmetry breakingcatalytic enzymesactive droplets
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The pith

Active phase separation enables indefinite self-propulsion of a spherical colloid via condensate repulsion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a minimal biochemical cycle involving phase-separating proteins and two types of enzymes can generate indefinite propulsion for a spherical colloid in a uniform environment. Proteins are passivated in solution but reactivated by enzymes fixed on the colloid surface, leading to the nucleation of a droplet-like condensate nearby. This condensate pushes the colloid forward by repulsion, creating directed motion without any pre-existing asymmetry or external field. Such a mechanism matters because it proposes a simple, energy-consuming but motor-independent way for biological particles to move persistently, and simulations show it works at biologically relevant speeds while ignoring random thermal kicks and opposing forces.

Core claim

Active droplets can sustain indefinite self-propulsion of a spherical colloid in an otherwise homogeneous, isotropic, and autonomous environment. The minimal mechanism consists of phase-separating proteins, enzymes passivating them, and complementary enzymes anchored to the colloid surface that reactivate the proteins. This passivation-activation cycle gives rise to symmetry breaking via nucleation and stabilization of a condensate near the colloid surface, which exerts a repulsive force on the colloid. Numerical demonstrations show propulsion of micron-sized colloids at speeds up to a hundred microns per second, with strong resistance to Brownian fluctuations and external forces.

What carries the argument

The passivation-activation cycle of phase-separating proteins that nucleates a stabilizing condensate near the colloid to exert sustained repulsion.

If this is right

  • The colloid moves indefinitely without motors or external gradients.
  • Propulsion speeds can reach up to 100 μm/s for micron-scale particles.
  • The motion resists Brownian fluctuations and external forces.
  • Biomolecular condensates offer a motor-free route for biological transport.
  • This works in fully homogeneous and isotropic conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Synthetic colloids with surface enzymes could be designed for autonomous transport in microfluidic systems.
  • Cells might exploit similar condensate-based mechanisms for organelle or vesicle motility.
  • Extending the model to multiple colloids could reveal collective behaviors or clustering.
  • Identifying natural protein pairs that perform the passivation and activation roles would enable direct tests.

Load-bearing premise

The passivation-activation cycle of phase-separating proteins and enzymes will nucleate and stabilize a condensate near the colloid surface that exerts a sustained repulsive force.

What would settle it

An experiment or simulation in which the surface-anchored enzymes are present but no sustained directional motion of the colloid occurs, despite the presence of phase-separating proteins and passivating enzymes, would falsify the proposed mechanism.

Figures

Figures reproduced from arXiv: 2604.27965 by Benjamin Sorkin, Ned S. Wingreen.

Figure 1
Figure 1. Figure 1: FIG. 1. Model for droplet-mediated transport of a micron-sized colloid. (a) Illustration of the model components. Sticky proteins are dissolved view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Three-dimensional simulations of an immobilized colloid. view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Phase diagrams for three-dimensional simulations of an immobilized colloid with radius (a) view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagrams for three-dimensional simulations of a mobile colloid in water at room temperature. Consequently, the force is view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Three-dimensional simulations of a “Brownian” colloid in view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Cylindrically symmetric quasi-two-dimensional simulations view at source ↗
read the original abstract

Living systems routinely consume energy to achieve motility, often using intricate biomolecular machinery. In this work, we show that active droplets can sustain indefinite self-propulsion of a spherical colloid in an otherwise homogeneous, isotropic, and autonomous environment. Our proposed minimal mechanism consists of phase-separating proteins, enzymes passivating them, and complementary enzymes anchored to the colloid surface that reactivate the proteins. This passivation-activation cycle gives rise to a symmetry breaking - nucleation and stabilization of a condensate near the colloid surface, which in turn exerts a repulsive force on the colloid. We numerically demonstrate that this mechanism can propel micron-sized colloids at speeds of up to a hundred microns per second. This propulsion mode is strongly resistant to Brownian fluctuations and external forces, suggesting that propulsion mechanisms based on biomolecular condensates may offer a complementary, motor-free route to biological transport.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a minimal biochemical mechanism for indefinite self-propulsion of a spherical colloid in a homogeneous, isotropic environment. Phase-separating proteins are passivated by bulk enzymes and reactivated by surface-anchored enzymes on the colloid, producing nucleation and stabilization of an asymmetric condensate that exerts a net repulsive force. Numerical simulations of this passivation-activation cycle are reported to yield propulsion speeds up to 100 μm/s for micron-sized colloids, with strong resistance to Brownian fluctuations and external forces.

Significance. If the numerical results hold under broader conditions, the work identifies a motor-free, condensate-based route to motility that could complement existing mechanisms in biological transport and synthetic biology. The reported combination of high speed and robustness to noise is a notable strength of the proposed cycle. However, the absence of a parameter scan over reaction-diffusion timescales limits assessment of whether the symmetry breaking and sustained propulsion are generic or restricted to a narrow regime.

major comments (2)
  1. [Numerical model section] Numerical model section (reaction-diffusion equations and boundary conditions): the passivation-activation cycle is implemented with fixed enzymatic rates and a single free parameter set. No sweep is presented over the ratio of surface reactivation rate to bulk passivation rate relative to the colloid diffusion time. Because net propulsion requires persistent asymmetry in the condensate, this omission leaves open whether the reported speeds and robustness persist when timescales are varied, directly affecting the central claim of generic, indefinite self-propulsion.
  2. [Results on propulsion speeds and robustness] Results on propulsion speeds and robustness (figures showing trajectories and force balance): the headline values (up to 100 μm/s, resistance to Brownian motion and external forces) are shown for the chosen parameter set. Without accompanying data on the range of rates where the condensate remains localized and asymmetric, it is unclear whether these outcomes are robust or artifacts of the specific timescale separation assumed in the minimal mechanism.
minor comments (2)
  1. [Abstract and Methods] The abstract states that 'numerical simulations demonstrate' the speeds and robustness, yet the methods description should explicitly list the integration scheme, grid resolution, and how Brownian dynamics are incorporated to allow independent verification.
  2. [Model description] Notation for the passivation threshold and reactivation boundary condition is introduced without a dedicated table of symbols; adding one would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their thorough review and for recognizing the potential significance of our proposed mechanism for condensate-based propulsion. We have carefully considered the comments regarding the lack of parameter exploration and have revised the manuscript to include additional simulations that address these concerns directly.

read point-by-point responses

  1. Referee: [Numerical model section] Numerical model section (reaction-diffusion equations and boundary conditions): the passivation-activation cycle is implemented with fixed enzymatic rates and a single free parameter set. No sweep is presented over the ratio of surface reactivation rate to bulk passivation rate relative to the colloid diffusion time. Because net propulsion requires persistent asymmetry in the condensate, this omission leaves open whether the symmetry breaking and sustained propulsion are generic or restricted to a narrow regime.

    Authors: We concur that a systematic exploration of the ratio between the surface reactivation rate and the bulk passivation rate, scaled by the colloid diffusion time, is necessary to substantiate the claim that the propulsion is generic. In the revised version of the manuscript, we have expanded the Numerical model section to include a parameter sweep over this dimensionless ratio. The new results, presented in an additional figure, demonstrate that symmetry breaking and sustained propulsion occur robustly for rate ratios spanning approximately one order of magnitude, corresponding to conditions where the reactivation timescale is shorter than the passivation and diffusion timescales. Propulsion speeds remain above 50 μm/s in this regime, and the mechanism fails gracefully outside it when asymmetry cannot be maintained. This supports the generality of the indefinite self-propulsion within the relevant biophysical parameter space. revision: yes

  2. Referee: [Results on propulsion speeds and robustness] Results on propulsion speeds and robustness (figures showing trajectories and force balance): the headline values (up to 100 μm/s, resistance to Brownian motion and external forces) are shown for the chosen parameter set. Without accompanying data on the range of rates where the condensate remains localized and asymmetric, it is unclear whether these outcomes are robust or artifacts of the specific timescale separation assumed in the minimal mechanism.

    Authors: We thank the referee for this observation. To clarify the robustness, we have added to the Results section a detailed analysis of how the propulsion speed, trajectory stability, and resistance to perturbations vary with the key rate ratio. We quantify the condensate localization and asymmetry using order parameters and show that the high speeds (up to 100 μm/s) and strong resistance to Brownian motion and external forces are achieved precisely in the parameter region where the condensate is localized and asymmetric. We also include data for cases where the rate ratio leads to delocalized or symmetric condensates, in which propulsion is absent. These additions confirm that the reported performance is not an artifact but a feature of the mechanism when the passivation-activation cycle maintains the necessary asymmetry. revision: yes

Circularity Check

0 steps flagged

No significant circularity; propulsion emerges from explicit numerical integration of the defined reaction cycle.

full rationale

The paper defines a minimal biochemical mechanism (phase-separating proteins, bulk passivation enzymes, surface-anchored reactivation enzymes) and reports propulsion speeds obtained by numerical solution of the resulting dynamics. No equations, parameters, or self-citations are shown that reduce the reported speeds or symmetry breaking to a fitted input or tautological redefinition. The central result is a forward simulation outcome under stated assumptions rather than an algebraic identity or load-bearing self-reference. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the existence and functional behavior of phase-separating proteins and complementary enzymes in a homogeneous environment, plus the numerical model's ability to capture the resulting force without additional external fields.

free parameters (1)
  • enzymatic reaction rates and passivation thresholds
    These control the timing of the passivation-activation cycle and are required to stabilize the condensate; their specific values are not stated in the abstract.
axioms (1)
  • domain assumption Phase-separating proteins can be reversibly passivated by enzymes and reactivated by surface-anchored complementary enzymes in an isotropic solution.
    This biochemical cycle is the load-bearing premise invoked to produce symmetry breaking and sustained repulsion.
invented entities (1)
  • Nucleated active condensate near the colloid surface no independent evidence
    purpose: To generate a localized repulsive force that propels the colloid after symmetry breaking.
    The condensate is postulated as the direct mechanical consequence of the enzymatic cycle; no independent experimental evidence is supplied in the abstract.

pith-pipeline@v0.9.0 · 5443 in / 1437 out tokens · 56213 ms · 2026-05-07T05:32:56.437774+00:00 · methodology

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Reference graph

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