Reduced surface accumulation of swimming bacteria in viscoelastic polymer fluids.

Surface-associated bacterial communities flourish in nature and in the body of animal hosts with abundant macromolecular polymers. It is unclear how the endowed viscoelasticity of polymeric fluids influences bacterial motile behavior in such environments. Here, we combined experiment and theory to study near-surface swimming of flagellated bacteria in viscoelastic polymer fluids. In contrast to the swimming behavior in Newtonian fluids, we discovered that cells swim in less curved trajectories and display reduced near-surface accumulation. Using a theoretical analysis of the non-Newtonian hydrodynamic forces, we demonstrated the existence of a generic lift force acting on a rotating filament near a rigid surface, which arises from the elastic tension generated along curved flow streamlines. This viscoelastic lift force weakens the hydrodynamic interaction between flagellated swimmers and solid surfaces and contributes to a decrease in surface accumulation. Our findings reveal previously unrecognized facets of bacterial transport and surface exploration in polymer-rich environments that are pertinent to diverse microbial processes and may inform the design of artificial microswimmers capable of navigating through complex geometries.

Rebound and scattering of motile Chlamydomonas algae in confined chambers.

Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.

Osmotic and electroosmotic fluid transport across the retinal pigment epithelium: A mathematical model.

The retinal pigment epithelium (RPE) is the outermost cell layer of the retina. It has several important physiological functions, among which is removal of excess fluid from the sub-retinal space by pumping it isotonically towards the choroid. Failure of this pumping leads to fluid accumulation, which is closely associated with several pathological conditions, such as age-related macular degeneration, macular oedema and retinal detachment. In the present work we study mechanisms responsible for fluid transport across the RPE with the aim of understanding how fluid accumulation can be prevented. We focus on two possible mechanisms, osmosis and electroosmosis, and develop a spatially resolved mathematical model that couples fluid and ion transport across the epithelium, accounting for the presence of Na+,K+ and Cl- ions. Our model predicts spatial variability of ion concentrations and the electrical potential along the cleft gap between two adjacent cells, which osmotically drives the flow across the lateral membranes. This flow is directed from the sub-retinal space to the choroid and has a magnitude close to measured values. Electroosmosis is subdominant by three orders of magnitude to osmosis and has an opposite direction, suggesting that local osmosis is the main driving mechanism for water transport across the RPE.

A Mathematical Model of Aqueous Humor Production and Composition.

Purpose: We develop a mathematical model that predicts aqueous humor (AH) production rate by the ciliary processes and aqueous composition in the posterior chamber (PC), with the aim of estimating how the aqueous production rate depends on the controlling parameters and how it can be manipulated. Methods: We propose a compartmental mathematical model that considers the stromal region, ciliary epithelium, and PC. All domains contain an aqueous solution with different chemical species. We impose the concentration of all species on the stromal side and exploit the various ion channels present on the cell membrane to compute the water flux produced by osmosis, the solute concentrations in the AH and the transepithelial potential difference. Results: With a feasible set of parameters, the model predictions of water flux from the stroma to the PC and of the solute concentrations in the AH are in good agreement with measurements. Key parameters which impact the aqueous production rate are identified. A relevant role is predicted to be played by cell membrane permeability to \(\text{K}^+\) and \(\text{Cl}^-\), by the level of transport due to the Na+-H+ exchanger and to the co-transporter of Na+/K+/2Cl-; and by carbonic anhydrase. Conclusions: The mathematical model predicts the formation and composition of AH, based on the structure of the ciliary epithelium. The model provides insight into the physical processes underlying the functioning of drugs that are adopted to regulate the aqueous production. It also suggests ion channels and cell membrane properties that may be targeted to manipulate the aqueous production rate.

Hydrodynamics and direction change of tumbling bacteria.

The bacterium Escherichia coli (E. coli) swims in viscous fluids by rotating several helical flagellar filaments, which are gathered in a bundle behind the cell during 'runs' wherein the cell moves steadily forward. In between runs, the cell undergoes quick 'tumble' events, during which at least one flagellum reverses its rotation direction and separates from the bundle, resulting in erratic motion in place and a random reorientation of the cell. Alternating between runs and tumbles allows cells to sample space by stochastically changing their propulsion direction after each tumble. The change of direction during a tumble is not uniformly distributed but is skewed towards smaller angles with an average of about 62°-68°, as first measured by Berg and Brown (1972). Here we develop a theoretical approach to model the angular distribution of swimming E. coli cells during tumbles. We first use past experimental imaging results to construct a kinematic description of the dynamics of the flagellar filaments during a tumble. We then employ low-Reynolds number hydrodynamics to compute the consequences of the kinematic model on the force and torque balance of the cell and to deduce the overall change in orientation. The results of our model are in good agreement with experimental observations. We find that the main change of direction occurs during the 'bundling' part of the process wherein, at the end of a tumble, the dispersed flagellar filaments are brought back together in the helical bundle, which we confirm using a simplified forced-sphere model.

Fluid and solute transport across the retinal pigment epithelium: a theoretical model.

The retina is composed of two main layers-the neuroretina and the retinal pigment epithelium (RPE)-that are separated by a potential gap termed the sub-retinal space (SRS). Accumulation of fluid in the SRS may result in a retinal detachment. A key function of the RPE is to prevent fluid accumulation in the SRS by actively pumping fluid from this space to the choroid. We have developed a mathematical model of this process that incorporates the transport of seven chemical species: Na+, K+, Cl-, HCO3-, H+, CO2 and H2CO3. This allows us to estimate solute and water fluxes and to understand the role of the different membrane ion channels. We have performed a global sensitivity analysis using the extended Fourier amplitude sensitivity test to investigate the relative importance of parameters in generating the model outputs. The model predicts that flow across the RPE is driven by an osmotic gradient in the cleft gap between adjacent cells. Moreover, the model estimates how water flux is modified in response to inhibition of membrane ion channels and carbonic anhydrase (CA). It provides a possible explanation for how CA inhibitors, which are used clinically to prevent fluid accumulation in the SRS, may be acting.