Physical nature of particle transport in elastically responsive hydrogels: one and two particle microrheology
Final Report Abstract
Understanding how tracer particles diffuse through complex elastic gels—such as the cytoplasm in cells, in vitro chromatin networks, F-actin fibres, or mucus gels—has significant implications across a wide range of fields, including biophysics, rheology, medicine, materials science, and even security. Recent advances in microrheology and single-particle tracking techniques allow us to follow individual tracers in such environments with great precision. These tracers can include both passive and self-propelled particles (SPPs), such as swimming bacteria, swarming cells, or synthetic microswimmers powered by chemical, acoustic, or magnetic stimuli. Importantly, the motion of tracers is not just a passive probe of the environment; their presence can actively modify the rheological and electromagnetic properties of the gel itself. This opens up possibilities for designing hybrid smart materials, performing selective macromolecular separations, or developing diagnostic tools for targeted drug delivery. Such control requires detailed knowledge of how the tracer size compares to the gel mesh, how strongly tracers interact with the network, and how the network deforms. In this project, we performed extensive simulations to investigate the dynamics of self-propelled tracers navigating through deformable, thermally fluctuating gels. We consider tracers whose sizes are comparable to or larger than the mesh size. Our simulations reveal that at short times, active tracers often become transiently trapped in the gel network, leading to subdiffusive behaviour. Over longer periods, the network’s flexibility enables active tracers to escape these traps, giving rise to transient superdiffusive motion. These observations point to clear crossovers between distinct transport regimes. In addition, we also observe moderate nonergodicity in the tracer dynamics and non-Gaussian displacement distributions at intermediate timescales. The distribution of trapping times reveals two distinct timescales that become comparable at high tracer activity. Moreover, we find that the mean trapping time varies as a power-law with the tracer’s activity, characterised by its Péclet number. At high activity, both exponential and non-exponential trapping statistics emerge, highlighting the complex interplay between activity and network constraints. Furthermore, we develop a minimal analytical framework to understand the behaviour of a tracer confined in a viscoelastic mesh in the overdamped regime. We focus on quantifying experimentally accessible observables such as the response function and power spectrum, which together reflect the underlying non-equilibrium fluctuations. We also draw an analogy between tracer escape and barrier crossing in a double-well potential, reminiscent of transitions in biomolecular systems. In this context, we explore how the tracer’s inertia and persistent motion induced by activity influence escape rates. Our findings reveal a non-monotonic dependence of the transition-path time on the persistence time. Overall, our work sheds light on the intricate biophysical processes governing the motion of particles in complex media. We capture key trends in the diffusion of active tracers, spanning regimes of confinement, transient trapping, and activity-driven transport.
Publications
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Steering self-organisation through confinement. Soft Matter, 19(9), 1695-1704.
Araújo, Nuno A. M.; Janssen, Liesbeth M. C.; Barois, Thomas; Boffetta, Guido; Cohen, Itai; Corbetta, Alessandro; Dauchot, Olivier; Dijkstra, Marjolein; Durham, William M.; Dussutour, Audrey; Garnier, Simon; Gelderblom, Hanneke; Golestanian, Ramin; Isa, Lucio; Koenderink, Gijsje H.; Löwen, Hartmut; Metzler, Ralf; Polin, Marco; Royall, C. Patrick ... & Volpe, Giorgio
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Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times. Physical Review E, 110(4).
Goswami, Koushik; Cherstvy, Andrey G.; Godec, Aljaz & Metzler, Ralf
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Heterogeneous diffusion in an harmonic potential: the role of the interpretation. New Journal of Physics, 27(6), 064602.
Pacheco-Pozo, Adrian; Sokolov, Igor M.; Metzler, Ralf & Krapf, Diego
