Bacteria-Polymer Active Phase Separation

• Bacteria-polymer active phase separation systems are defined by the interplay of motile bacteria and passive polymers, leading to nonequilibrium demixing phenomena such as MIPS.
• Rapid nucleation and arrested droplet coarsening emerge from bacterial self-propulsion, enabling accelerated condensation and stabilization of microscale droplet sizes.
• The system is modeled using kinetic flux-balance, continuum spinodal theory, and active-phase-field equations to elucidate partitioning, interface dynamics, and material design.

A bacteria-polymer active phase separation system consists of mixtures in which self-propelled bacterial cells (active matter) interact with polymers or colloidal particles (passive matter), giving rise to rich nonequilibrium phase behaviors far from equilibrium thermodynamic predictions. These systems bridge active matter physics, soft condensed matter, cell biology, and the engineering of synthetic membraneless organelles and materials. The presence of bacterial motility introduces fundamentally new mechanisms for nucleation, morphology, and arrest of phase separation, leading to phenomena such as motility-induced phase separation (MIPS), activity-tuned partitioning, stable active droplets, and dynamic self-assembly.

1. Motility-Induced Phase Separation in Bacteria-Polymer Mixtures

Motility-induced phase separation (MIPS) is a nonequilibrium phenomenon in which a mixture of active and passive particles spontaneously demixes into a dense and a dilute phase when the activity (quantified by the Péclet number, Pe) and overall particle fraction exceed critical values. In 2D Brownian-dynamics simulations at total packing fraction $\phi_0 = 0.6$, phase separation occurs for active-particle fractions as low as $x_A \simeq 0.15$ (i.e. $\phi_A = \phi_0 x_A \simeq 0.09$), provided the activity is sufficiently strong (Pe $\gtrsim 500$ for $x_A=0.15$; by contrast, for pure active systems $x_A=1$, Pe $\gtrsim 60$ suffices).

The onset of MIPS is analytically predicted by two main approaches:

• Kinetic flux-balance: Phase separation occurs above the binodal

$\phi_0 x_A = \frac{3\pi^2 \kappa}{4\text{Pe}}$

with $\kappa \approx 4.05$, making $x_A \sim \text{Pe}^{-1}$ at fixed $\phi_0$.

• Continuum spinodal theory: Instability arises when the density-dependence of swimming speed satisfies

$\frac{d\ln v(\rho)}{d\ln \rho} < -1$

For active–passive mixtures, assuming $v=v_0[1-a\phi_A-b\phi_P]$ (with $a\simeq 1.08$, $b\simeq 1.21$), the spinodal is

$\phi_0 > \frac{1}{2a x_A + b(1-x_A)}$

In bacteria-polymer experimental design, motile bacteria (size $\sigma \sim 1$–2 μm, $v_0 \sim 10$–30 μm/s, $D_r \sim 0.05$–0.1 s⁻¹) yield Pe $=3v_0/(\sigma D_r)$ in the $O(100)$–$O(1000)$ range, allowing access to MIPS at $\phi_0\approx 0.4$–$0.6$, $x_A \gtrsim 0.1$ with experimentally feasible polymer concentrations (∼1–3 wt% for 100 kDa polymers) (Stenhammar et al., 2014).

2. Nonequilibrium Effects and Arrested Phase Separation

When motile bacteria are embedded within a phase-separating polymer system, nonequilibrium effects dominate late-stage morphology:

• Rapid nucleation: Bacterial self-propulsion accelerates the early-stage condensation of gelatin-rich or dextran-rich droplets, with micrometer-scale sizes reached within $~1$ min, compared to $\lesssim$5 μm droplets in passive mixtures.
• Arrested coarsening: Active droplets arrest Ostwald ripening, stabilizing at mean radii $R\approx 20$–$40$ μm for $\gtrsim 2$ h, with narrow size distributions (polydispersity $\approx 0.15$), in contrast to indefinitely coarsening passive droplets.
• Mechanism of arrest: Anti-phase entrainment of long-wavelength interface undulations between neighboring droplets suppresses inter-droplet contact and coalescence. Shape fluctuation correlations $\langle \delta R_1(k)\,\delta R_2(-k)\rangle<0$ (for low mode numbers $k$) mediate effective repulsion, as confirmed by direct tracking and stochastic simulations (Liu et al., 6 Nov 2025).
• Active stress–driven phenomena: Persistent collective flows, enhanced droplet transport (mean-square displacement with ballistic and diffusive regimes), and dominant long-wavelength interface fluctuations ($\langle |a_l|^2\rangle/R^2 \sim l^{-3}$) are observed.

A minimal theoretical description couples a generalized Cahn–Hilliard equation for the order parameter $\phi(\mathbf{r},t)$ to advection by the active velocity field $\mathbf{v}_\mathrm{active}$, and hydrodynamics with active stresses proportional to cell density and force dipole strength.

3. Partitioning and Interfacial Interactions in Aqueous Two-Phase Bacteria-Polymer Systems

Experimental ATPSs (e.g. PEG/dextran) demonstrate how bacterial motility tunes partitioning between coexisting polymer-rich phases via competition between active propulsion and soft interfacial confinement:

• Non-motile cells are confined exclusively to the dextran-rich phase, with partition ratio $$n_\mathrm{DEX}/(n_\mathrm{DEX}+n_\mathrm{PEG})=1.00$$ for all dextran concentrations tested; thermal fluctuations ($k_B T/\mu \rm m \sim 10^{-3}$ pN) are negligible compared to the interfacial force.
• Motile cells exhibit graded partitioning:
  • $w_\mathrm{DEX}=1.5\%$: $$n_\mathrm{DEX}/(n_\mathrm{DEX}+n_\mathrm{PEG})=0.58\pm0.10$$
  • $3.2\%$: $0.78\pm0.08$
  • $8.0\%$: $1.00\pm0.00$
• Optical tweezer measurements show interfacial confinement forces $F_\mathrm{max}$ of $1$–$10$ pN, compared to bacterial propulsive forces $F_\mathrm{prop}\simeq10$ pN. The theoretical escape condition is $F_\mathrm{prop} > F_\mathrm{max}$.
• Modeling with dilute active rods in periodic soft confinement captures the transition from partitioning (motile cells in both phases) in the weak-barrier regime ($w_\mathrm{DEX}\lesssim3\%$) to trapping in DEX at strong barriers ($w_\mathrm{DEX}\gtrsim8\%$). Dimensionless groups include a Péclet number Pe $=F_\mathrm{prop} L/k_B T\sim5\times10^5$ and a confinement number $\beta=F_\mathrm{prop}L/\Delta U$ (Cheon et al., 14 May 2024).

4. Activity-Driven Self-Assembly and Functional Structures

The non-equilibrium dynamics of bacteria-polymer phase separation enable new modes of self-assembly and mesoscale function:

• Active-passive segregation: In dense coexisting phases, active particles accumulate at interfaces, while passive components form interior “rafts” of typical size $~20\sigma$.
• Directed self-assembly: Preparing a segregated core–shell geometry (passive disk surrounded by active “corona”) results in inward-traveling compression waves launched by active pressure $P_a$, leading to crystallization of the passive core, as confirmed by order parameter measurements (e.g. hexatic order parameter $\psi_6$), and persistent active coronas stabilized at the interface.
• Rotor self-assembly: Slightly below critical attraction, motile bacteria nucleate rotationally persistent finite clusters (“micro-rotors”) characterized by unidirectional collective rotation. The angular speed follows $\Omega \sim R^{-1}$, as expected from the random summation of surface torques imparted by boundary-localized active particles (Schwarz-Linek et al., 2012).
• Suppression of bulk phase separation: Motility systematically raises the threshold for bulk phase separation, requiring stronger attractive interactions (polymer concentration or potential well depth) to achieve demixing. Empirically, phase-separation binodals shift upwards by factors $1.4$–$3$, depending on activity parameters.

5. Theoretical Descriptions: Virial, Continuum, and Polymer-Bound Particle Models

A hierarchy of theoretical models describes different regimes of active phase separation:

• Second-virial approximation: For dilute active–passive mixtures, the system can be mapped to diffusion in two heat baths at temperatures $T_A$ (active) and $T_P$ (passive); chemical potentials and osmotic pressures acquire non-equilibrium corrections. Phase boundaries are determined by generalized chemical-potential equality and non-equilibrium pressure matching (Grosberg et al., 2015).
• Active-phase-field and hydrodynamics: Minimal continuum models couple Cahn–Hilliard order-parameter dynamics to active advection and active stress, as in

$$\frac{\partial\phi}{\partial t} = \nabla\cdot [ M \nabla(\delta F/\delta\phi) - \mathbf{v}_\mathrm{active} \phi ]$$

and Stokes flow with active stress injection (Liu et al., 6 Nov 2025).

• Polymer-bound active particle models: For protein–DNA partition complexes (e.g. ParABS), fluctuating polymers with attached particles generate an effective one-dimensional lattice gas with emergent long-range interactions from polymer looping. Variational solutions, beyond mean-field, yield full occupation–temperature phase diagrams and explain the nucleation, stability, and spatial localization of condensates (David et al., 2018, Guilhas et al., 2020).

6. Biological and Engineering Significance

Bacteria-polymer active phase separation systems provide biophysically validated models for understanding intracellular organization, developing synthetic assets, and designing programmable biomaterials:

• Cellular LLPS and organelles: Many cell compartments (e.g. nucleolus, stress granules, ParB droplets) display suppression of coarsening and arrested Ostwald ripening; a plausible implication is that active matter (motors, metabolic activity) underlies the stability and dynamics of these membraneless organelles (Liu et al., 6 Nov 2025, Guilhas et al., 2020).
• Patterning and segregation: Minimal reconstituted systems (bacteria-polymers, DNA–protein mixtures) allow experimental access to controlled LLPS and spatial positioning, mirroring bacterial DNA segregation machinery (ParABS).
• Material design: Embedding motile bacteria, enzyme nanomotors, or Janus swimmers in polymer matrices enables creation of droplets of tunable size ($10$–$100$ μm), enhanced cargo transport, micro-reactors, and potentially programmable release devices. Activity, propulsion, and interaction parameters determine the arrest, size, and internal structure of these architectures [(Liu et al., 6 Nov 2025); (Schwarz-Linek et al., 2012)].
• Design principles: Phase behavior is controlled by tuning Pe (via swimming speed or viscosity), $x_A$ (cell fraction), total packing fraction $\phi_0$ (polymer concentration), and starting geometry (if directed self-assembly is needed) (Stenhammar et al., 2014).

Bacteria-polymer active phase separation systems constitute a robust experimental and theoretical platform for the paper of nonequilibrium LLPS, programmable self-assembly, and the interplay between activity and polymeric environments, relevant to both fundamental biology and soft materials engineering.