The 2025 motile active matter roadmap

Abstract

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

Keywords: active matter; intelligent matter; microbots; microswimmers; non-equilibrium systems; non-reciprocal interactions; swarming.

Figure 1.

Transport in porous media. (A) Geometric criterion for optimal transport of active agents in porous media. Effective diffusivities $D_{\text{eff}}$ obtained from simulations of self-propelled polymers in 3D porous media (see right panel for a simulation snapshot) and compared to a theory. Reproduced from [12]. CC BY 4.0. (B) Corner flow in unsaturated porous media generated by surfactant-producing bacteria, which communicate via quorum sensing and where the surfactant changes wettability of the surface to drive spreading. Reproduced with permission from [13].

Figure 2.

From entanglement to chemotaxis. (A) Entangled blob of California blackworms dissolves rapidly under environmental stress (scale bar is $3$ mm). From [14]. Reprinted with permission from AAAS. (B) Crowding-enhanced diffusion of self-propelled filaments in a highly-entangled environment of other active agents. Mean-square displacements $⟨(\mathrm{\Delta }\mathbf{r}(t){)}^2⟩$ for different reduced number densities $n^{\ast }$as a function of time $t$. Reprinted figure with permission from [16], Copyright (2020) by the American Physical Society. (C) Suppression of MIPS due to chemotaxis. Here, ${\alpha }_0=M_0/D_{\text{c}}$ measures the relative importance of the active diffusivity $M_0$ and the chemical diffusivity $D_{\text{c}}$ and $P{e}_{\text{C}}={\chi }_0/M_0$ is the ratio of the chemotactic coefficient ${\chi }_0$ and $M_0$. Reprinted figure with permission from [17], Copyright (2023) by the American Physical Society.

Figure 3.

Light-controlled micromotors powered by bacteria: (a) array of 16 microfabricated rotors; (b) fluorescence image showing bacteria cell bodies, which tend to occupy microchambers distributed around the gears; (c), (d) zoomed-in view of one of the rotors. Reproduced from [21]. The Author(s). CC BY 4.0.

Figure 4.

Aggregation dynamics in a monolayer of passive sticky colloids is accelerated by swimming E. coli bacteria and gives rise to aggregate morphologies that are unlike those observed in thermal systems. Reproduced from [23]. The Author(s). CC BY 4.0.

Figure 5.

Simulations snapshots that display spontaneous trapping of active particles moving through (a) a random distribution of obstacles. Reprinted figure with permission from [34], Copyright (2013) by the American Physical Society. (b ) A random stress field. Reprinted figure with permission from [35], Copyright (2018) by the American Physical Society.

Figure 6.

Illustration of active particles moving through a random field R. In vectorial active matter, particles experience both, a random force and torque as they move through the random field R.

Figure 7.

State diagram of active vesicles as a function of Peclet number Pe and the volume fraction φ of enclosed SPPs. Three regimes are indicated: tethering (blue), fluctuating (red), and bola/prolate (green) vesicle shapes. Snapshots are displayed for the points marked by open black circles. Theoretical estimates of the critical Pe_teth for tether formation are also shown (black lines). Reproduced from [42], with permission from Springer Nature.

Figure 8.

Asphericity and reduced velocities of 2D active vesicles with enclosed self-propelled filaments. The filaments are attached to the vesicle membrane and can pull or push on it. Fluctuating (F), keratocyte-like (K), and neutrophil-like (N) vesicles are shown for various membrane properties, filament self-propulsion forces, and substrate friction on the membrane. The simulation snapshots show the vesicle shapes that correspond to the black symbols. Reproduced from [47]. © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. CC BY 3.0.

Figure 9.

Lagrangian 3D tracking methods. (a) Sketch of the tracking apparatus (after [66] and [61]) under the microscope showing a 3D (XYZ) stage driven by a computerized algorithm taking an image (80 FPS) around a tagged object within a virtual trapping area (inset). The program analyses the image and provides information to the stage such as to keep the object in the central part of the trapping area and in the focal plane. Large inset: magnification of a tracked object (a motile E.coli) when the system is working in the ‘two-colors mode’. Tracking is performed on the green fluorescent body, but in parallel the flagella bundle is visualized in red fluorescent emission. Reprinted figure with permission from [61], Copyright (Year) by the American Physical Society. (b) Example of a 500 s track of an E.coli exploring the space between two glass slides. Color code corresponds to Y-direction depth. With permission from Gaspard Junot https://hal.sorbonne-universite.fr/tel-03349693v1.

Figure 10.

Hydrodynamic bound states of the green algae Volvox carteri. Reprinted figure with permission from [76], Copyright (2009) by the American Physical Society. (a) Views from above and the side of colonies, showing stokeslet-driven flows and formation of a linear array. (b) Geometry of downward Stokeslets, interactions of spinning colonies, infalling trajectories—scaled colony separation versus scaled time, and orbital frequency versus spinning frequency (inset). Reproduced with permission from [71].

Figure 11.

Distribution of topological defects in the cellular neighborhoods of three colonies of the multicellular alga Volvox carteri, obtained by light-sheet microscopy [77]. Reproduced with permission from A. Srinivasan.

Figure 12.

Simulation snapshots of CAPs with colors representing particle orientations: (a) particles with polar alignment can self-organize into traveling bands (Ω = 0), rotating macrodroplets (Ω = 0.2) and micro-flock patterns (Ω = 3). (b) Particles with a symmetric distribution of angular frequencies can form (from left to right): traveling bands (surviving weak frequency dispersion), polar vortices (for polar alignment) and active foams (for nematic alignment). Reprinted figure with permission from [84], Copyright (2017) by the American Physical Society. Reprinted figure with permission from [85], Copyright (2021) by the American Physical Society.

Figure 13.

Active solids exist on scales ranging from the micrometer to the macroscopic, and span synthetic (a)–(c) and biological (d)–(g) realizations. Systems composed of biological building blocks taken out of their natural environment (f) even blur the boundaries between the synthetic and the living. (a) Micrometer scale robots provide a route to miniaturizing insights from macroscopic active materials. Reproduced from [95], with permission from Springer Nature. (b) Activity melts a crystal composed of chiral spinners. Reproduced from [94], with permission from Springer Nature. (c) Robotic matter mechanically couples many robotic building blocks together, forming a distributed lattice capable of actuation and locomotion. Reproduced from [92], with permission from Springer Nature. (d) Epithelial cell layers act as active elastic sheets, pulsing with mechano-chemical contraction waves. Reproduced with permission from [91]. (e) Volvox turns itself inside out via the mechanics of active thin sheets. Reproduced from [78]. The Author(s). CC BY 4.0. (f) Starfish embryos cluster to form a living chiral crystal. The elastic excitations of this crystal propagate despite their overdamped nature, a feature powered by odd elastic moduli. Reproduced from [74], with permission from Springer Nature. (g) Worms cluster as a living, reconfigurable polymer melt. From [14]. Reprinted with permission from AAAS.

Figure 14.

(a) Reconfigurable microswimmers comprising magnetic Janus cubes. From [99]. Reprinted with permission from AAAS. (b) Bioinspired magnetic soft microswimmers whose shape changes as function of sucrose concentration. From [100]. Reprinted with permission from AAAS. (c) Reconfigurable colloidal clusters comprising temperature-responsive microgels whose swimming trajectory changes as a function of temperature. Reproduced with permission from [101].

Figure 15.

(a) Example of multi-material microstructures with colloidal particles positioned in regular arrays by means of capillary assembly and connected by linkers printed by two-photon polymerization direct laser writing. (b) Assembled and printed colloidal micromachines consisting of three 2.8 μm magnetic particles (red) and two 2.8 μm SiO₂ particles (white) functionalized with DNA that are linked with printed photoresist (green). (c) Example of selective capture and release of target particles (orange) as a function of temperature during ‘walking motion’ of the colloidal micromachine. Reproduced from [104]. The Author(s). CC BY 4.0.

Figure 16.

Speed control in engineered bacteria can be used to: (a) shape density. Reproduced from [107]. The Author(s). CC BY 4.0. (b) rectify bacterial random walks for confinement with dynamical optical fields. Reproduced from [108]. The Author(s). CC BY 4.0. or (c) generate gradients of active pressure. Reproduced from [109]. The Author(s). CC BY 4.0. (d) Optical lithography of bacterial biofilms. Reproduced with permission from [112]. CC BY-NC-ND 4.0. Programmed multicellular patterns using: (e) synthetic cell–cell adhesin logic. Reproduced from [113]. The Author(s). CC BY 4.0. Or (f) a synthetic genetic circuit that couples cell density and motility. From [114]. Reprinted with permission from AAAS.

Figure 17.

A dilemma in microrobotic design. For magnetic microrobots, three types of materials are essential for in vivo applications. Adding more materials to improve one aspect will inevitably compromise performance in another aspect.

Figure 18.

Collective transport of magnetic microparticles on an artificial microtubule near a droplet.

Figure 19.

The interplay of non-reciprocal coupling with hydrodynamic modes due to Goldstone modes (rotation invariance in synchronization/flocking, left) or conservation laws (in phase separation, right) can lead to dynamic phases such as chiral rotations (left) [130] and traveling waves (right) [128, 129, 131].

Figure 20.

Formation of undulating traveling waves in the non-reciprocal Cahn–Hilliard model [131]. The undulations propagate along the wavefronts (blue dashed arrow), transversally to the direction of wave propagation (green arrow).

Figure 21.

(a) Schematic representation of vision cone and alignment neighborhood of particle i (blue) with orientation e_i, distance vector r_ji= r_j − r_i to other particles. (b) Polar orientation field (grey) with cutoff R_c, and vision cone (green) with vision angle θ and vision range R_v. (c) Steering of an iABP (blue) by adaptive vision-induced torque M_i^v, for weak and strong maneuverability Ω_v, shown by dashed and full green trajectories, respectively. (d) Steering by alignment-induced torque M_i^a, for weak and strong maneuverability Ω_a, with dashed and full grey trajectories, respectively. Reproduced from [142]. CC BY 4.0.

Figure 22.

Snapshots of emerging structures for different Peclet numbers Pe, vision angles θ, with alignment-vision ratio Ω_a/Ω_v = 4 and packing fraction φ = 0.00785. The snapshots are not to scale for better visualization. Reproduced from [142]. CC BY 4.0.

Figure 23.

Emergent dynamics and function by feedback control: (A) feedback controlled active particles that show spontaneous rotation around a central particle due to a perception reaction delay [153]. The transition to the rotational phase is governed by a pitchfork bifurcation, (B), combining particle activity (${\omega }_0$) and time delay $\delta t$. (C) Colloidal reservoir computer using single active particle rotators to provide the non-linear dynamics for physical reservoir computing [154].

Figure 24.

(A) Radial thermo-osmotic flows and temperature fields create attractive, repulsive fields and hydrodynamic polarization for self-thermophoretic Janus particles (Lisa Rohde, to be published). (B) Induced nematic ordering of ellipsoidal polystyrene particles combining thermally induced depletion forces in a polyethylene glycol/water mixture behind a self-thermophoretic Janus particle (Lisa Rohde, to be published). (C) Optically heated iron oxide doped polymer particles in water droplets induce Marangoni flows (trajectory overlay) to self-organize droplets in large arrays synchronizing their flow fields (Akshay Kallikkunnath, to be published).

Figure 25.

(A) Animals use collective strategies to overcome the limitations of the individual, e.g. to transport large objects. (B) Similarly, microscopic robot swarms could solve collective challenges. (C) In multi-agent reinforcement learning (MARL) an optimal control scheme for solving a collective task is automatically obtained by training the policies of the individual agents (microswimmers). The agents learn by exploring their environment in successive sensing and acting steps. (D) For training in MARL, the individual agents need to be rewarded. For counterfactual rewards, each agent is once removed virtually; if this decreases the swarm’s performance, the removed agent did contribute positively and thus gets a high reward and vice versa.

Figure 26.

Longhorn crazy ants confront natural puzzles. Depending on the size of the load these ants retrieve food either independently (a) or as a group (b). The challenge of maneuvering the load to the nest through tight passages is ecologically relevant in both cases. Such natural challenges can inspire scalable puzzles that could allow for a quantitative study of collective cognition.

Figure 27.

(a) Inactive to active crossover: RG flow for the incompressible Vicsek model in d = 3. Reprinted figure with permission from [178], Copyright (2021) by the American Physical Society; α is the activity effective constant and u is the interaction effective constant (see [175, 178]). (b) Schematic RG diagram of the ISM field theory of [177].

Figure 28.

Macroscopic swarming patterns created by B. subtilis wildtype (leftmost) and different mutants.

Figure 29.

Microscope images acquired at different positions within a B. subtilis swarm. This figure shows that the shape of individual cells changes dramatically between the swarm center and the swarm front.