Hydrodynamics of cell-cell mechanical signaling in the initial stages of aggregation

Mathematical modeling of chemotaxis guided amoeboid cell swimming

Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, many modeling research has focused on the crawling-basedDictyostelium discoideum(Dd) cells migration induced by chemotaxis, yet recent experimental results reveal that even without adhesion or contact to a substrate, Dd cells can still swim to follow chemoattractant signals. In this paper, we develop a modeling framework to investigate the chemotaxis induced amoeboid cell swimming dynamics. A minimal swimming system consists of one deformable Dd amoeboid cell and a dilute suspension of bacteria, and the bacteria produce chemoattractant signals that attract the Dd cell. We use themathematical amoeba modelto generate Dd cell deformation and solve the resulting low Reynolds number flows, and use a moving mesh based finite volume method to solve the reaction-diffusion-convection equation. Using the computational model, we show that chemotaxis guides a swimming Dd cell to follow and catch bacteria, while on the other hand, bacterial rheotaxis may help the bacteria to escape from the predator Dd cell.

Active hydrodynamic imaging of a rigid spherical particle

A body with mechanical sensors may remotely detect particles suspended in the surrounding fluid via controlled agitation. Here we propose a sensory mode that relies on generating unsteady flow and sensing particle-induced distortions in the flow field. We demonstrate the basic physical principle in a simple analytical model, which consists of a small spherical particle at some distance from a plate undergoing impulsive or oscillatory motion. The model shows that changes in pressure or shear on the plate can be used to infer the location and size of the sphere. The key ingredient is to produce strong shear or strain around the sphere, which requires careful tuning of the viscous boundary layer on the moving plate. This elucidates how some organisms and devices may control their unsteady dynamics to enhance their range of perception.

Hydrodynamic object identification with artificial neural models

The lateral-line system that has evolved in many aquatic animals enables them to navigate murky fluid environments, locate and discriminate obstacles. Here, we present a data-driven model that uses artificial neural networks to process flow data originating from a stationary sensor array located away from an obstacle placed in a potential flow. The ability of neural networks to estimate complex underlying relationships between parameters, in the absence of any explicit mathematical description, is first assessed with two basic potential flow problems: single source/sink identification and doublet detection. Subsequently, we address the inverse problem of identifying an obstacle shape from distant measures of the pressure or velocity field. Using the analytical solution to the forward problem, very large training data sets are generated, allowing us to obtain the synaptic weights by means of a gradient-descent based optimization. The resulting neural network exhibits remarkable effectiveness in predicting unknown obstacle shapes, especially at relatively large distances for which classical linear regression models are completely ineffectual. These results have far-reaching implications for the design and development of artificial passive hydrodynamic sensing technology.

Physical limits on cellular directional mechanosensing

Many eukaryotic cells are able to perform directional mechanosensing by directly measuring minute spatial differences in the mechanical stress on their membranes. Here, we explore the limits of a single mechanosensitive channel activation using a two-state double-well model for the gating mechanism. We then focus on the physical limits of directional mechanosensing by a single cell having multiple mechanosensors and subjected to a shear flow inducing a nonuniform membrane tension. Our results demonstrate that the accuracy in sensing the mechanostimulus direction not only increases with cell size and exposure to a signal, but also grows for cells with a near-critical membrane prestress. Finally, the existence of a nonlinear threshold effect, fundamentally limiting the cell's ability to effectively perform directional mechanosensing at a low signal-to-noise ratio, is uncovered.