Theory of active particle penetration through a planar elastic membrane

Abstract

With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoparticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by particle-based computer simulations, the penetration process of an active particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a selfassembled sheet of particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane particles. The active penetrating particle is assumed to interact sterically with the membrane particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the active particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario may be accompanied by a partial fragmentation of the membrane into bunches of isolated or clustered particles and creation of a hole of a size exceeding the interaction range of the membrane components. It is further demonstrated that the capability of penetration is strongly influenced by the size of the approaching particle relative to that of the membrane particles. Accordingly, active particles with larger size are more likely to remain trapped at the membrane for the same propulsion speed. Such behavior is in line with experimental observations. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-tocontinuum formulation. It well describes the system behavior in the small-deformation regime. Particularly, the theory allows to determine the membrane displacement of the particles in the trapping state. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial active particles.

Hydrodynamics can determine the optimal route for microswimmer navigation

“…Our results might be relevant for future studies on microswimmers in various complex environments involving hard walls or obstacle landscapes [65][66][67] , penetrable boundaries 68,69 , or external (viscosity) gradients [70][71][72] . For such scenarios, our results (or generalizations based on the same framework) can be used as reference calculations, e.g., to test machine-learning-based approaches to optimal microswimmer navigation 5,6 and perhaps also to help programming navigation systems for future microswimmer generations.…”

Aggregate morphology of active Brownian particles on porous, circular walls

“…It has been shown recently that the wall-adhesion properties of active particles can be utilized for sorting and trapping of such particles, by effectively tuning the wall geometry [40][41][42][43][44]. In addition, tuning the wall penetrability of particles also changes their properties near the wall, which has potential applications in specific biomedical processes involving drug delivery [45,46]. In the case of non-planar * raghu@phy.iitb.ac.in † Authors contributed equally to this work.…”

Effective interactions mediated between two permeable disks in an active fluid

“…Recent studies of semipermeable vesicles filled with active particles 37 , 49 – 54 can also be generalized straightforwardly to incorporate permeation of active particles through the enclosing vesicle membrane 47 , 48 . Such extensions can provide insight into the interplay between permeability and shape fluctuations/deformability, brining the model vesicles closer to realistic examples of soft permeable inclusions.…”

“…These structures can be utilized in a wide range of applications such as controlled internalization of polystyrene microparticles and crystallites in fibroblast cells 38 , selective entrapment of catalytically active nanoparticles within polymer stomatocytes 39 , targeted cargo/drug delivery to soft tissues (such as tumors) by means of nonactive and active particles 40 – 45 as well as biological microswimmers 45 , 46 . Despite such emerging applications, detailed modeling of active-particle penetration through flexible membranes have been considered only recently 47 , 48 , with a growing number of studies having been focused on structural and dynamical ramifications of entrapping active particles within soft semipermeable vesicles, whose deformable enclosing membranes are permeable only to the background fluid and not the active particles 49 – 54 (see also Ref. 55 for an experimental study of entrapping motile bacteria within an emulsions drop).…”