Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation

How environment affects active particle swarms: a case study

We investigate the collective motion of self-propelled agents in an environment filled with obstacles that are tethered to fixed positions via springs. The active particles are able to modify the environment by moving the obstacles through repulsion forces. This creates feedback interactions between the particles and the obstacles from which a breadth of patterns emerges (trails, band, clusters, honey-comb structures, etc.). We will focus on a discrete model first introduced in Aceves-Sanchez P et al. (2020, Bull. Math. Biol. 82, 125 (doi:10.1007/s11538-020-00805-z)), and derived into a continuum PDE model. As a first major novelty, we perform an in-depth investigation of pattern formation of the discrete and continuum models in two dimensions: we provide phase-diagrams and determine the key mechanisms for bifurcations to happen using linear stability analysis. As a result, we discover that the agent-agent repulsion, the agent-obstacle repulsion and the obstacle's spring stiffness are the key forces in the appearance of patterns, while alignment forces between the particles play a secondary role. The second major novelty lies in the development of an innovative methodology to compare discrete and continuum models that we apply here to perform an in-depth analysis of the agreement between the discrete and continuum models.

Autonomously Propelled Colloids for Penetration and Payload Delivery in Complex Extracellular Matrices

For effective treatment of diseases such as cancer or fibrosis, it is essential to deliver therapeutic agents such as drugs to the diseased tissue, but these diseased sites are surrounded by a dense network of fibers, cells, and proteins known as the extracellular matrix (ECM). The ECM forms a barrier between the diseased cells and blood circulation, the main route of administration of most drug delivery nanoparticles. Hence, a stiff ECM impedes drug delivery by limiting the transport of drugs to the diseased tissue. The use of self-propelled particles (SPPs) that can move in a directional manner with the application of physical or chemical forces can help in increasing the drug delivery efficiency. Here, we provide a comprehensive look at the current ECM models in use to mimic the in vivo diseased states, the different types of SPPs that have been experimentally tested in these models, and suggest directions for future research toward clinical translation of SPPs in diverse biomedical settings.

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.