Energetics and Dynamics of Self-Propelled Microorganisms

C.A. CONDAT

Botucatu

Congreso; SOLABIMA 2015; 2015

Sociedad Latinoamericana de Biología Matemática

In their classical work, Berg and Purcell [Biophys. J. 20, 193 (1977)] concluded that the motion of a small microorganism would not significantly increase its nutrient uptake rate, if the nutrient consisted of high diffusivity particles. As a result, it has been generally assumed that nutrient transport to small microorganisms such as bacteria is dominated by molecular diffusion and that swimming and feeding currents play a negligible role. I describe a model to investigate the hypothesis that fast-moving microbes may enhance their swimming speed by taking advantage of advection to increase nutrient absorption. Surprisingly, even modest increases in nutrient absorption may lead to a significant increase of the microbial speed. Optimally, the rate of effective energy transfer to the microbial propulsion system should be proportional to the speed for slow motion, while it should be proportional to a power of the speed close to two for fast motion. Self-propelled microorganisms are also attracted to surfaces. This makes their dynamic behavior in restricted geometries very different from that observed in the bulk. We have investigated the nature of sperm cell trajectories in shallow chambers and their accumulation near the side boundaries. In particular, observed cell trajectories are composed of a succession of quasi-circular and quasi-linear segments. This suggests that the cells follow a path of intermittent trappings near the top and down surfaces separated by stretches of quasi-free motion near the center of the gap. Use of microstructured petal-shaped edges limits accumulation near the borders and contributes to increase the concentration in the chamber interior. System stabilization occurs over times of the order of minutes, which agrees with a theoretical estimate that assumes that the cell mean-square displacement is largely due to the quasi-linear segments. Our estimates also indicate that stabilization proceeds 2.5 times faster in the rosette geometries than in the smooth-edged chambers, which is another reason to prefer the former.