Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on Run-and-Tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how non-classical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

Cell migration plays an important role in physiological and pathological processes where the fibrillar morphology of extracellular matrices (ECM) could regulate the migration dynamics. To mimic the morphological characteristics of fibrillar matrix structures, low-voltage continuous electrospinning was adapted to construct straight, wavy, looped and gridded fibre patterns made of polystyrene (of fibre diameter ca. 3 μm). Cells were free to explore their different shapes in response to the directly-adhered fibre, as well as to the neighbouring patterns. For all the patterns studied, analysing cellular migration dynamics of MDA-MB-231 (a highly migratory breast cancer cell line) demonstrated two interesting findings: first, although cells dynamically adjust their shapes and migration trajectories in response to different fibrillar environments, their average step speed is minimally affected by the fibre global pattern; secondly, a switch in behaviour was observed when the pattern features approach the upper limit of the cell body’s minor axis, reflecting that cells’ ability to divert from an existing fibre track is limited by the size along the cell body’s minor axis. It is therefore concluded that the upper limit of cell body’s minor axis might act as a guide for the design of microfibre patterns for different purposes of cell migration.

The experimental characterisation of the swimming statistics of populations of micro-organisms or artificially propelled particles is essential for understanding the physics of active systems and their exploitation. Here, we construct a theoretical framework to extract information on the threedimensional motion of micro-swimmers from the intermediate scattering function (ISF) obtained from differential dynamic microscopy (DDM). We derive theoretical expressions for the ISF of helical and oscillatory breaststroke swimmers, and test the theoretical framework by applying it to video sequences generated from simulated swimmers with precisely-controlled dynamics. We then discuss how our theory can be applied to the experimental study of helical swimmers, such as active Janus colloids or suspensions of motile microalgae. In particular, we show how fitting DDM data to a simple, non-helical ISF model can be used to derive three-dimensional helical motility parameters, which can therefore be obtained without specialised 3D microscopy equipment. Finally, we discus how our results aid the study of active matter and describe applications of biological and ecological importance.

Heterogeneity among cells is a common characteristic of living systems. For mathematical modeling of heterogeneous cell populations, one typically has to reconstruct the underlying heterogeneity from measurements on the population level. Based on recent insights into the mathematical nature of this problem as an inverse problem of tomographic type, we evaluate numerical methods to perform such a reconstruction in basic case studies. We compare a kernel density based optimization approach, filtered back projection, and algebraic reconstruction techniques. The latter two are well established methods in computed tomography.

Bacteria can chemotactically migrate up attractant gradients by controlling run-and-tumble motility patterns. In addition to this well-known chemotactic behaviour, several soil and marine bacterial species perform chemokinesis; they adjust their swimming speed according to the local concentration of chemoeffector, with higher speed at higher concentration. A field of attractant then induces a spatially varying swimming speed, which results in a drift towards lower attractant concentrations—contrary to the drift created by chemotaxis. Here, to explore the biological benefits of chemokinesis and investigate its impact on the chemotactic response, we extend a Keller–Segel-type model to include chemokinesis. We apply the model to predict the dynamics of bacterial populations capable of chemokinesis and chemotaxis in chemoeffector fields inspired by microfluidic and agar plate migration assays. We find that chemokinesis combined with chemotaxis not only may enhance the population response with respect to pure chemotaxis, but also modifies it qualitatively. We conclude presenting predictions for bacteria around dynamic finite-size nutrient sources, simulating, e.g. a marine particle or a root. We show that chemokinesis can reduce the measuring bias that is created by a decaying attractant gradient. Graphic abstract