Stochasticity plays a crucial role in various biological processes, enabling adaptive responses to fluctuating conditions. Nature has evolved mechanisms to harness this stochasticity, as seen in noise dampening in neuronal development and the autonomous motion of motor proteins. While stochastic processes are observed in synthetic systems like nanomotors, they have not been intentionally employed to control system features. This research aimed to integrate stochasticity as a design element in a micromotor system to enhance life-like behavior in active matter. The micromotor was designed using a coacervate microdroplet with a fluidic polymer membrane, where enzymes served as propulsive units. The unexpected observation that motility was not simply a function of enzyme density led to the development of a physical model and in silico analysis to reveal the underlying stochastic process governing the motile behavior. This model provided the necessary insight to direct the motile behavior according to model-derived guidelines. The core hypothesis was that transient asymmetry in enzyme distribution, enabled by the fluidic membrane, would lead to various organizational states, with some exhibiting sufficient polarization to drive propulsion.

Previous research has established the importance of asymmetry (e.g., shape, catalyst distribution) for autonomous motion in micromotors. Janus particles, hemi-spherically covered with active catalysts, and Marangoni flow-driven motion have been investigated. Studies by Sanchez et al. and Sen et al. demonstrated micromotor propulsion via random surface enzyme distribution, inspiring this study's focus on transient, dynamic asymmetry. However, unlike natural systems, these studies did not utilize stochasticity as an intentional design element for controlling system features.

The study employed coacervate microdroplets formed by spontaneous coacervation of oppositely charged polyelectrolytes, stabilized by a polymer membrane. Catalase (CAT) and urease (UR) were selected as propulsive units, tethered to the membrane using azide-functionalized polymer and dibenzocyclooctyne-modified enzymes. Confocal microscopy confirmed enzyme-membrane coupling, exhibiting a ring-like distribution. Fluorescence recovery after photobleaching (FRAP) analysis verified the enzymes' lateral diffusion along the fluidic membrane. Motility was assessed by recording coacervate motion in the presence and absence of substrate (H2O2 for CAT, urea for UR) via bright-field microscopy. A custom Python script analyzed trajectories to calculate mean square displacement (MSD). The impact of enzyme density (low, medium, high) on motility was investigated, revealing a non-monotonic relationship. To explain this, a stochastic mechanical model, based on the active Brownian particle (ABP) model, was developed, incorporating enzyme mobility and distribution fluctuations. The model's parameters were fitted using experimental data, enabling the simulation of coacervate motion. The Damköhler number was calculated to rule out local substrate depletion as a cause for the observed non-monotonic relationship between enzyme density and motility. Enzyme lateral diffusivity was further tuned through in situ crosslinking with glutaraldehyde to validate the model predictions.

The study's primary finding is that stochastic enzyme distribution on the coacervate membrane produces transient asymmetry, leading to autonomous motility. This motility was not simply proportional to enzyme density; instead, a non-monotonic relationship was observed, with medium enzyme density yielding the highest velocity. This was attributed to an optimal balance between the probability of achieving asymmetric enzyme organization and the number of enzymes contributing to propulsion. The stochastic model accurately predicted this non-monotonic relationship, demonstrating the importance of transient asymmetry in driving coacervate motion. The model, derived from the ABP model, incorporated the lateral diffusion of enzymes as a key factor influencing the lifetime of the transient asymmetry and therefore the motility. The MSD derived from the model accurately matched the experimental data across short (ballistic) and long (diffusive) timescales. Experimental manipulation of enzyme diffusivity by crosslinking confirmed the model's predictions: decreasing enzyme diffusivity (by crosslinking) increased MSD and motility. Interestingly, about 10% of non-crosslinked coacervates exhibited run-and-tumble motion, a phenomenon typically observed in bacteria, indicating another level of stochasticity within the system.

The results demonstrate the successful engineering of a motile system fully governed by stochasticity. The close agreement between experimental data and model predictions confirms a high degree of control over this stochastic process. The non-monotonic relationship between enzyme density and motility highlights the complexity of stochastic systems and underscores the importance of considering the interplay between different factors. The observed run-and-tumble motion suggests further levels of stochasticity that warrant future investigation, potentially involving the stochastic release of oxygen microbubbles. This work represents a shift in design philosophy for synthetic systems, embracing stochasticity as a valuable tool for engineering life-like behaviors.

This research successfully engineered a micromotor system where motility is driven by the stochastic distribution of enzymes on a fluidic membrane. A stochastic model accurately predicted the non-monotonic relationship between enzyme density and velocity, validating the central role of transient asymmetry. The ability to modulate motility by tuning enzyme diffusivity further strengthens this conclusion. The observation of run-and-tumble behavior highlights potential for even more complex, non-linear behaviors. This study paves the way for designing other adaptive systems using stochasticity as a key design parameter.

The run-and-tumble behavior observed in a subset of coacervates was not fully explained by the model. Future research is necessary to fully characterize this phenomenon and integrate it into a more comprehensive model. The current model focuses on the average behavior of the coacervates, but further investigation into the individual trajectories might reveal additional details about the stochasticity. While the study successfully demonstrates control over motility through enzyme density and diffusivity, the exploration of other parameters influencing stochasticity warrants further investigation.