🔬 condensed matter

Run and tumble dynamics of a soft robotic cell

By encasing a programmable active particle within a deformable membrane, this study demonstrates how membrane softness serves as a single control parameter to continuously tune intermittent stop-and-go dynamics and transport properties, thereby establishing design principles for synthetic soft robotic cells.

Original authors: Siddhant Mohapatra, Fanny Wéry, Filip Novkoski, Piotr Nowakowski, Ana-Suncana Smith, Nicolas Vandewalle

Published 2026-06-05

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Siddhant Mohapatra, Fanny Wéry, Filip Novkoski, Piotr Nowakowski, Ana-Suncana Smith, Nicolas Vandewalle

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a tiny, self-driving robot that isn't just a hard metal box, but is wrapped in a stretchy, soft balloon. This is the "soft robotic cell" described in the paper. The scientists wanted to see what happens when you put a programmed robot inside a flexible membrane, mimicking how real living cells move.

Here is the story of what they found, explained simply:

The Setup: A Robot in a Balloon

Think of the robot (called a "GRASPion") as a small, elliptical car that can drive forward and spin around. The scientists put this car inside a large, circular paper ring that acts like a soft, stretchy skin or membrane.

The Control Knob: The size of the ring is the most important thing. A small ring is tight and stiff (hard to stretch). A large ring is loose and floppy (very soft). By just changing the size of the ring, the scientists could tune how "soft" the whole cell felt.

The Movement: Stop-and-Go

The robot inside was programmed to do two things:

Drive straight for a bit.
Spin in place for a bit.

When the robot spins, the whole "cell" stops moving forward. When the robot drives, the cell moves. This creates a "stop-and-go" pattern, similar to how a person might walk briskly, stop to tie a shoe, and then walk again.

The Big Discovery: The "Softness" Switch

The magic happens when they change the size of the ring (the softness):

The Tight Fit (Small Ring): When the ring is small and tight, the robot is squished against the walls. Every time the robot tries to drive or spin, the whole cell moves with it immediately. They are "coupled" like a passenger glued to the driver's seat. The cell moves exactly as the robot does.
The Loose Fit (Large Ring): As the ring gets bigger and softer, something interesting happens. The robot can drive around inside the cell without moving the whole cell immediately. The cell starts to wobble and deform.
- The Result: The cell starts to move differently than the robot inside. The robot might spin, but the soft cell keeps drifting forward for a moment because the "skin" is so stretchy it absorbs the movement. This creates a new, more complex way of moving that the robot wasn't explicitly programmed to do.

The "Run and Tumble" Analogy

The scientists compared this to a bacterium that "runs" (swims straight) and "tumbles" (spins to change direction).

Short Term: The cell zooms in a straight line (like a bullet).
Long Term: Because of all the spinning and the soft skin wobbling, the cell eventually starts to wander randomly, like a drunk person stumbling home (diffusion).

The key finding is that softness is the single dial that controls this. By just making the membrane softer (larger), they could smoothly tune how long the cell zooms, how often it stops, and how far it wanders.

Why It Matters (According to the Paper)

The paper claims this is a breakthrough because:

It's a New Kind of Robot: Before this, scientists could make hard robots move in specific ways, or make groups of robots move together. But they couldn't make a single soft robot that changes its own movement style just by changing how squishy it is.
It Mimics Life: Real cells (like white blood cells) change shape to move through tight spaces. This soft robot does something similar: its "skin" helps it move in a way that is different from its internal engine.
It's Predictable: The scientists built a math model (a "run-and-tumble" theory) that perfectly predicted how the soft cell would move. This means we can now design these soft robots with specific movement styles just by adjusting their softness.

In a nutshell: The paper shows that if you put a robot inside a stretchy balloon, the balloon's softness acts like a master control knob. It turns a simple "drive and spin" robot into a complex, wandering cell that can switch between zooming straight and drifting randomly, all without changing the robot's code—just by changing the size of its skin.

Technical Summary: Run and Tumble Dynamics of a Soft Robotic Cell

Problem Statement
The continuous regulation of transport properties through softness remains a longstanding challenge in the field of active matter. While living systems utilize the coupling of internal activity and membrane deformability to control locomotion (e.g., amoeboid motion), synthetic active matter has largely failed to replicate this at microscopic to mesoscopic scales. Existing synthetic Active Particle (AP) assemblies rely on many-body interactions or external cues to tune transport, and individual soft APs capable of autonomously generating and modulating locomotion as a synthetic analogue of a motile cell are currently missing. Consequently, shape deformability has not yet been explored as an internal control parameter for programmable transport regimes in single soft APs without invoking collective effects.

Methodology
The authors present a minimal soft robotic cell system combining experiments, simulations, and a theoretical framework:

Experimental Setup: A centimeter-sized, programmable, elliptical robotic AP (the "GRASPion") is confined within a deformable paper ring membrane (height 3 cm, radius $R \in [4, 13]$ cm). The membrane radius serves as the control parameter for cell softness, as the energy required for deformation scales as $R^{-3}$ . The robot is programmed with a stochastic propulsion protocol alternating between ballistic translation and rotation (about a point offset from the center) to generate intermittent stop-and-go dynamics. Motion is recorded via a top-mounted camera at 30 frames/s.
Simulations: The system is modeled as two-dimensional interacting entities evolving via overdamped dynamics. The bot is driven by force and torque, while the membrane is modeled as a closed, discretized curve subject to bending, surface tension, and bot-membrane interaction forces. A key distinction is that simulations include membrane relaxation via dissipation, whereas experiments rely on static friction which suppresses relaxation.
Theoretical Framework: The authors apply a run-and-tumble theoretical model, treating the cell as a two-state Markovian particle. Analytic expressions for the Mean Squared Displacement (MSD) are derived from velocity autocorrelation functions, assuming negligible thermal diffusion.

Key Results

Coupled vs. Decoupled Dynamics:
- Coupled Regime ( $R \approx 4-5$ cm): The geometric centers (GC) of the bot and the cell move together. The cell's stop-and-go dynamics directly reflect the bot's driving protocol.
- Decoupled Regime (Large $R$ ): As membrane softness increases (larger $R$ ), the system transitions to a decoupled state where the bot and cell GCs are effectively dissociated. The cell's motion no longer mirrors the bot's specific driving protocol, yet intermittent stop-and-go dynamics persist.
Transport Properties and Scaling:
- The synthetic cell exhibits ballistic motion at short time lags ( $\tau$ ) crossing over to diffusive motion at long time lags.
- Increasing membrane softness (increasing $R$ ) extends the crossover regime.
- In the decoupled regime, the data collapses when the MSD is scaled by $R^{1/3}$ and the time lag by $R^{-1}$ , validating the modeling approach across both experiments and simulations.
Statistical Analysis of Motion:
- Both "stop" and "go" durations follow exponential distributions, supporting the run-and-tumble model.
- The mean stop time ( $\langle \tau_s \rangle$ ) increases monotonically with $R$ , reflecting the time the bot spends moving without interacting with the membrane.
- The mean go time ( $\langle \tau_g \rangle$ ) initially increases with softness (due to membrane deformations constraining bot orientation) but saturates in the highly decoupled regime where deformations can no longer constrain the bot.
- Discrepancies between experiment and simulation in $\langle \tau_g \rangle$ are attributed to static friction in experiments, which allows deformation without center-of-mass displacement, a factor absent in simulations.
Validation of Theory:
- The theoretical run-and-tumble framework successfully reproduces the overall transport properties. The extracted ballistic velocity ( $\hat{v}_0$ ) and diffusion coefficient ( $\hat{D}$ ) from experimental and simulation data align with theoretical predictions derived from velocity moments.
- The ballistic velocity and diffusion coefficient both decrease with increasing cell size, as a larger fraction of active input is directed toward membrane deformation and frictional dissipation.

Significance and Claims
The paper claims to demonstrate that encasing a programmable active particle within a deformable membrane naturally gives rise to intermittent stop-and-go dynamics, linking internal driving to emergent locomotion. Crucially, membrane softness acts as a single control parameter that continuously tunes persistence, intermittency, and long-time transport.

The authors assert that this work establishes design principles for programmable soft active transport by realizing a minimal, programmable soft AP with continuously controllable complex transport properties. This fulfills a goal in active matter to create a synthetic analogue of a single motile cell that captures key physical properties of living systems without their full biological complexity. The system is presented as a tractable platform for studying transport in complex environments and a potential stepping stone toward studying cooperative effects in assemblies of soft robotic cells or introducing feedback mechanisms for adaptive locomotion strategies.