Common bacterial species such as E. coli and B. subtilis swim through fluids at low Reynolds numbers propelled from behind by a flagella bundle. The flagella bundle unravels at times leading to cell tumbling. This run and tumble motion becomes biased in the presence of a chemical attractant gradient such as a nutrient or a chemical signal released by other cells. The cells tumble less frequently when swimming up the chemical gradient leading to a mean chemotactic cell velocity. This biased motion also leads to a net orientation of the cells and an anisotropy of the active stresses the cells exert on the fluid as they swim. Thus, a bacterial suspension viewed as a continuum living fluid has the unusual feature of developing anisotropic stresses due to chemical gradients. This project explores the ways in which these chemically induced hydrodynamic stresses and the resulting hydrodynamic flows aid or hinder suspensions of bacteria as they use chemotaxis to seek nutrients or respond to cell-cell chemical signaling.
Intellectual Merit: Linear stability analyses and computational solutions of the nonlinear behavior of ensemble averaged equations of motion for bacteria suspensions are used to predict the macroscopic hydrodynamic flows induced by chemotactic bacteria. Complementary experiments include visualization of the motion of fluorescent bacterial cells and tracer colloidal beads and measurement of the bacteria cell concentration. A bacteria suspension in a microfluidic well subjected to a linear chemo-attractant gradient provides a simple case with a time-independent base state. In this system a dilute bacteria suspension develops a steady concentration that is an exponential function of position in the chemo-gradient direction due to the competition of the chemotactic velocity and the diffusion due to their run-and-tumble motion. However, the chemical-gradient induced active stresses are expected to induce convection above a critical bacteria concentration. Experimental measurements will test the critical concentration predicted by linear stability analysis and the convective patterns obtained from numerical solutions. The dispersal of bacteria into a chemical attractant is studied for two parallel fluid streams which carry bacteria and attractant in a microchannel. A quasi-steady stability analysis and a dynamic solution of the equations of motion will be used to predict the conditions leading to formation of waves at the bacteria-attractant interface in both the presence and absence of an imposed pressure-driven flow. When bacteria release chemical signals that attract other bacteria, they form patterns including rings and spherical clusters with high cell concentrations. Similarity solutions have been developed based on chemotaxis and diffusion that predict the development of singularities in the concentration field. This project considers the role of active hydrodynamic stresses in this clustering phenomenon.
Broader Impacts: The possibility that collective hydrodynamic motions alter important bacteria behaviors involving search for nutrients and assembly due to chemical signals could have a broad impact in the field of microbiology. This topic also provides a good setting in which to introduce students to the nonlinear dynamics of coupled reaction-convection-diffusion in an interesting biological setting. A web site and summer research opportunity targeted toward high school students will be developed to explore pattern formation due to chemical signaling among bacteria.
