Chemotaxis of Cargo-Carrying Self-Propelled Particles

Exploring the Synthesis of Self-Organization and Active Motion

Proteins, genetic material, and membranes are fundamental to all known organisms, yet these components alone do not constitute life. Life emerges from the dynamic processes of self-organization, assembly, and active motion, suggesting the existence of similar artificial systems. Against this backdrop, our Perspective explores a variety of chemical phenomena illustrating how nonequilibrium self-organization and micromotors contribute to life-like behavior and functionalities. After explaining key terms, we discuss specific examples including enzymatic motion, diffusiophoretic and bubble-driven self-propulsion, pattern-forming reaction-diffusion systems, self-assembling inorganic aggregates, and hierarchically emergent phenomena. We also provide a roadmap for combining self-organization and active motion and discuss possible outcomes through biological analogs. We suggest that this research direction, deeply rooted in physical chemistry, offers opportunities for further development with broad impacts on related sciences and technologies.

Statistics of carrier-cargo complexes

We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.

Resonant Diffusion of a Gravitactic Circle Swimmer

We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.

Screening confinement of entanglements: Role of a self-propelling end inducing ballistic chain reptation

Synthetic and natural nanomaterials with self-propelling mechanisms continue to be explored to boost chain mobility beyond normal reptation in the crowded environments of entangled chains. Here we employ scaling theory and numerical simulations to demonstrate that activating one chain end of a singular or isolated chain boosts entanglement-constrained chain reptation from the one-dimensional diffusive mobility as described by the de Gennes-Edwards-Doi model to ballistic motion along the entanglement tube contour. The active chain is effectively screened from the constraint of entanglements on length scales exceeding the tube size.

Strongly enhanced dynamics of a charged Rouse dimer by an external magnetic field

While the dynamics of dimers and polymer chains in a viscous solvent is well understood within the celebrated Rouse model, the effect of an external magnetic field on the dynamics of a charged chain is much less understood. Here, we generalize the Rouse model for a charged dimer to include the effect of an external magnetic field. Our analytically solvable model allows a fundamental insight into the magneto-generated dynamics of the dimer in the overdamped limit as induced by the Lorentz force. Surprisingly, for a dimer of oppositely charged particles, we find an enormous enhancement of the dynamics of the dimer center, which exhibits even a transient superballistic behavior. This is highly unusual in an overdamped system for there is neither inertia nor any internal or external driving. We attribute this to a significant translation and rotation coupling due to the Lorentz force. We also find that magnetic field reduces the mobility of a dimer along its orientation and its effective rotational diffusion coefficient. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.

Active colloidal molecules in activity gradients

We consider a rigid assembly of two active Brownian particles, forming an active colloidal dimer, in a gradient of activity. We show analytically that depending on the relative orientation of the two particles the active dimer accumulates in regions of either high or low activity, corresponding to, respectively, chemotaxis and antichemotaxis. Certain active dimers show both chemotactic and antichemotactic behavior, depending on the strength of the activity. Our coarse-grained Fokker-Planck approach yields an effective potential, which we use to construct a nonequilibrium phase diagram that classifies the dimers according to their tactic behavior. Moreover, we show that for certain dimers a higher persistence of the motion is achieved similar to the effect of a steering wheel in macroscopic devices. This work could be useful for designing autonomous active colloidal structures which adjust their motion depending on the local activity gradients.

Bistability in orbital trajectories of a chiral self-propelled particle interacting with an external field

In this paper, the dynamics of a self-propelled stochastic particle under the influence of an axisymmetric light field is experimentally studied. The particle under consideration has the main characteristic of carrying a light sensor in an eccentric location. For the chosen experimental conditions, the emerging trajectories are orbital, and, more interestingly, they suggest the existence of bistability. A mathematical model incorporating the key experimental components is introduced. By means of numerical simulations and theoretical analysis, it is found that, in addition to the orbiting behavior, the sensor location could produce trapped or diffusive behaviors. Furthermore, the study reveals that stochastic perturbation and the eccentric location of the sensor are responsible for inducing bistability in the orbital trajectories, supporting experimental observations.

Migration of an active colloidal cell in inhomogeneous environments

Living cells on a substrate with mechanical inhomogeneities often migrate along or against the mechanical gradient, i.e., mechanotaxis, which inspires us to ask how biomimetic cells without biochemical signaling processes respond to environmental inhomogeneity. Here, we perform computer simulations to study the migration of a 2D active colloidal cell (ACC), which consists of active particles enclosed by a passive vesicle, in a heterogeneous environment composed of two adjoining uniform regions with different attributes (influencing the persistent length of the active particle). We find that the ACC can migrate unidirectionally across the interface separating the heterogeneous region and behave tactically. Interestingly, the tactic motion of the ACC is qualitatively different from that of the constituent active particles themselves. In addition, the ACC may also experience a directed drift along the interface of the heterogeneous environment. The tactic behavior of the ACC can be explained by analyzing the pressure distribution on the cell membrane exerted by the enclosed active particles. The findings provide insights into understanding the taxis of biological cells and designing biomimetic cells with environment-sensitive capabilities.

Dynamics of active particles with space-dependent swim velocity

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

Run with the Brownian Hare, Hunt with the Deterministic Hounds

We present analytic results for mean capture time and energy expended by a pack of deterministic hounds actively chasing a randomly diffusing prey. Depending on the number of chasers, the mean capture time as a function of the prey's diffusion coefficient can be monotonically increasing, decreasing, or attain a minimum at a finite value. Optimal speed and number of chasing hounds exist and depend on each chaser's baseline power consumption. The model can serve as an analytically tractable basis for further studies with bearing on the growing field of smart microswimmers and autonomous robots.