The Hidden Force of Growth 

Physicists discover a new type of phase separation driven by a proliferating medium that rewrites the physics of particles inside it

• A medium consisting of growing and dividing cells drastically changes the behavior of other cells or particles trying to move through it
• In such a medium, moving particles show clustering and phase separation even without specific attraction
• The findings provide valuable insights for the dynamics of tumor growth, bacterial biofilms and synthetic micro-swimmers

In physics, the spontaneous de-mixing of two substances is known as phase separation. It is an important mechanism in nature to create structure and patterns and typically requires some form of attraction between the constituents. Researchers at the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) in Göttingen, together with collaborators at the University of Edinburgh and the Institute of Physical Chemistry in Warsaw, now discovered a new route to phase separation available in systems where the constituents are inherently alive or active. In their recent study in Physical Review Research, they show that self-propelled particles – which could be crawling cells or miniature artificial agents – can spontaneously form clusters when they navigate a dense colony of dividing cells. The driving force for this unexpected clustering is not an explicit interaction between the particles themselves, but emerges entirely from the ever-renewing environment created by the growing cells around them.

Two types of activity, one surprising outcome

Using computer simulations, the researchers investigated a system that consists of a dense mixture of two kinds of particles: One type can grow, divide and die – like cells in a colony or tissue. When the researchers placed self-propelled motile particles as a second type into this living matrix, something remarkable happened: They either dispersed evenly or collapsed into tight, crystal-like clusters, depending on how strongly the particles could propel themselves. The boundary between these two behaviors is sharp – a so-called phase transition to phase separation.

Philip Bittihn, group leader at MPI-DS, comments “We were looking at a dense system where every interaction is repulsive and yet the motile particles spontaneously formed clusters. That was genuinely surprising.”

The growing medium as a hidden force

To understand the origin of this clustering, the team first studied how the growing medium affects a single non-growing, motile particle. On its own, such a particle would travel in a perfectly straight line at constant speed forever. But if surrounded by dividing, dying and rearranging cells, it is continuously pushed around. These random forces from neighboring cells act like thermal noise, making the particle’s path erratic and diffusive. The dense medium additionally creates friction-like resistance that slows the particle’s effective speed and causes it to change direction more often, reducing its persistence.

Consequently, the growing medium transforms a simple ballistic swimmer into something that behaves like an active Brownian particle – the physicists' model for a self-propelled particle with noise, friction, and finite persistence – without the particle itself having any of those properties built in.

Lukas Hupe, first author of the study: “The proliferating medium really does all the work. It’s remarkable that a living environment can so completely rewrite the physics of the objects moving through it.”

Repulsion that manifests as attraction

Noise and friction alone, however, are not enough to cause condensation – there still needs to be something that pulls particles together. Here the proliferating medium plays a second role. When two non-growing particles are in close proximity, their combined presence perturbs the local flow of dividing and dying cells around them in a coordinated way. This shared disturbance creates a statistical bias causing the two particles to be pushed towards each other by the medium. As with the noise above, no attractive force was introduced into the simulation, but it arises spontaneously from the collective dynamics of the growing bath.

The exact physical origin of the effective attraction is still an open question, but Ramin Golestanian, director at MPI-DS, points out: “What we observe is reminiscent of the Casimir effect – where altered quantum fluctuations between two plates generate attraction without any direct interaction. Just like in our system, where the presence of self-propelled particles alters the fluctuating growing medium. For now, this analogy is speculative, but it is a tantalising one.”

In a simplified model, the researchers then show that the two new properties imparted by the growing medium – behaving like active Brownian particles and emergent attraction – are sufficient to explain the phase transition.

A phase transition that runs backwards

This newly observed kind of phase separation has another counterintuitive feature. In the best-known form of phase separation in active systems, motility-induced phase separation, it is the fast swimmers that cluster. These particles pile up at collision boundaries because they slow down when they meet, and the resulting traffic jam becomes self-reinforcing.  Bartlomiej Waclaw from Edinburgh points out: “In our case, the opposite is true and it is the slow swimmers that condense. The faster a particle propels itself, the more easily it escapes the effective attraction generated by the growing medium, and the less likely it is to join a cluster.” Once the self-propulsion is strong enough, the clusters dissolve (right half of the image). In contrast, they reform when propulsion is reduced. (left half of the image).

From abstract physics to biofilms and tumors

These findings are not only of fundamental theoretical interest. Their relevance also extends to many biomedical applications. Bacterial biofilms, for example, often consist of a growing, largely stationary majority of cells through which a subpopulation of motile bacteria continuously swims. In tumors, rapidly proliferating cancer cells co-exist with cells that have undergone a transformation making them invasive and motile. Even synthetic micro-swimmers or drug-delivery particles navigating tissue might potentially find themselves moving through environments dominated by growing cells. In all these settings, the behavior of the motile agents may be fundamentally reshaped by the proliferating environment in complex ways that go far beyond simple crowding.