Artificial life of an active droplets system: a quantitative lifecycle analysis

TL;DR

This work addresses how simple, dye-modulated active droplets self-organize into life-like, time-evolving states and eventually a quiescent, ordered configuration. It combines a robust tracking pipeline with windowed statistical analysis to quantify how interfacial-tension differences drive demixing and collective motion across five stages. Key contributions include (i) a detailed, transferable data-processing workflow (StarDist for segmentation, Trackpy for linking, UKF/RTS for smoothing) and (ii) a comprehensive, stage-by-stage characterization of structural and dynamical properties (velocity polarization, hexatic order, TSAMSD, VACF, turning-angle distributions, and dimer density maps). The findings advance understanding of programmable active matter and provide a framework for in silico modeling and experimental design of life-like, heterogeneous active systems with potential applications in smart materials and synthetic biology.

Abstract

The study of synthetic active matter systems holds the promise for designing smart materials and devices with emergent characteristics akin to those of living organisms, eventually opening the doors to the realization of artificial life. Such an investigation, however, is challenged by the difficulty inherent in identifying the relationship between the features of the elementary constituents and the emergent properties of the whole; to this end, a key step consists in the accurate quantification of the system's observed behavior. Here, we report the study of 50 self-propelled oil droplets floating on the surface of an aqueous solution. 25 droplets are stained with a red dye, and the other 25 are stained blue: the colorants affect the droplets' interfacial tension properties differently, consequently influencing their collective dynamics. Droplet trajectories extending for up to 5 hours are extracted from video recordings with a tracking pipeline developed ad hoc. The structural and dynamical analysis of the system reveals a ``life-to-death'' cycle unfolding in qualitatively distinct stages, showcasing a complex interplay between individual droplet mobility and collective organization. The tools developed and the results obtained in our work pave the way to the in silico modelling as well as the experimental design of synthetic active matter systems displaying life-like and programmable behavior.

Figures (9)

• Figure 1: (a-e) Snapshots of the experimental setup, with progression from left to right illustrating typical droplet configurations at the onset of each evolutionary stage of the system. The images are circled with the color of the corresponding stage, as indicated in the key provided in the plots below. (f-g) Time dependence of the droplets' velocity polarization $\Phi_{\mathcal{S}}$ and hexatic order parameter $\Psi_{6,\mathcal{S}}$, respectively defined in Eq. \ref{['eq:order']} and \ref{['eq:hex_order']} of the main text. Colored vertical bars mark the onset of each evolutionary stage. (h-l) From left to right: turning angle distribution $P_{\mathcal{S}}$, see Eq. \ref{['eq:turn_angl']}, of the blue and red droplet populations at the onset of each evolutionary stage. (m-q) From left to right: blue-blue dimer distributions $D_{\mathcal{B}\mathcal{B}}$, see Eq. \ref{['eq:dimer']}, at the onset of each evolutionary stage.
• Figure 2: Example of instance segmentation and classification performed with StarDist. (a) Close-up of a portion of an original experimental image. (b) Predicted instance positions and rays overlaid on the image of panel (a).
• Figure 3: Example of instance linking between consecutive frames of an experimental video. The colors distinguish the droplet class, and the arrows connecting panels (a) and (b) represent the matching of the identities of the droplets between frames $i$ and $i+1$.
• Figure 4: Left: segment of a test droplet trajectory reconstructed by our tracking pipeline. Right: close-up of the region indicated by the green frame in the left panel. We display (i) the raw trajectory (red line); (ii) the trajectory obtained by applying the unscented Kalman filter to the raw data (blue line); and (iii) the trajectory resulting from the unscented Kalman filter combined with the Rauch–Tung–Striebel smoother, with dashed lines indicating the associated confidence interval.
• Figure 5: Temporal evolution of (a) the velocity polarization $\Phi_{\mathcal{S}}$, see Eq. \ref{['eq:order']} (b) the hexatic order parameter $\Psi_{6,\mathcal{S}}$, see Eq. \ref{['eq:hex_order']}, and (c) the average speed $V_{\mathcal{S}}$, see Eq. \ref{['eq:speed']}, of the blue droplet population (blue line), the red droplet population (red line), and overall droplet population (black line) as a function of the window running time $t_w$. Colored vertical bars indicate the onset of each evolutionary stage of the system.