The present work contains original research on the field of biophysics, specifically the study of swimming bacteria. Swimming microorganisms can be modeled as active particles moving at low Reynolds number (Re ≪ 1) and subject to different sources of noise. The term “active” means that they are self-propelled, while Re ≪ 1 implies that their motion is dominated by viscous stresses, therefore relying on non-reciprocal deformations in time, in order to achieve movement. Noise arises from thermal fluctuations and the inherent stochasticity of their propelling machinery, as a result, bacteria follow random trajectories. Nevertheless, bacteria have evolved to display a number of strategies to overcome randomness and achieve directed locomotion, known as “taxis”. Here, we explore the mechanisms involved in the propulsion and navigation of swimming bacteria, using low Reynolds number flow techniques and random walks.

First, we introduce the physical principles that govern the dynamics of a low Reynolds number swimmer. We pay special attention to the random walk model for the description of the swimming trajectories, since it allows to quantify motility in terms of statistical measures, such as diffusivity and drift velocity, which can be measured experimentally. After a general discussion of the model, we demonstrate its use by applying it to the dynamics of bacteria-driven microswimmers, which are active particles that use bacteria as a propulsion mechanism. We show in particular, that the diffusivity of such particles increases with the square of their size and that the microswimmers inherit the chemotactic capabilities from the bacteria that propel them. These results are in agreement with experiments and can be useful to improve the design of these artificial microswimmers.

Next, we investigate the motility properties of Spiroplasma melliferum, which is special among bacteria, as it can swim without flagella. Instead, Spiroplasma can switch the handedness of its helical body and in the process, the helical domains rotate generating propulsion. Based on experimental observations, we develop a hydrodynamic model to describe Spiroplasma motility. We obtain expressions for the total linear and angular displacements of the cell body per swimming stroke. Observing that the cell body does not reorient at the end of one period, we define an effective swimming speed and a hydrodynamic efficiency. Then, we show that the helical shape that maximises speed and efficiency has a pitch angle close to that of Spiroplasma, φ ≃ 35◦, in agreement with experimental observations and with previous numerical simulations.

Finally, we explore the dynamics of a low Reynolds number swimmer crossing a viscosity gradient. This is a work in collaboration with experimental groups in the National University of Mexico (UNAM) and Brown University. The experiments aim to shed light on the dynamics of the bacterium Helicobacter pylori, which inhabits the human gut and is capable of penetrating the mucus layer that protects the stomach. Experimentally, a magnetic swimmer is immersed in a stratified solution of miscible fluids with different viscosities. The swimmer consists of a helical tail and a cylindrical head that rotate at a fixed rate due to the action of an external magnetic field. As the swimmer advances, it accelerates or slows down, depending on its orientation with respect to the gradient. In general, the experimental results show that it is harder for a pusher-like swimmer to swim up the gradient, whereas for a puller-like swimmer it is the opposite. We rationalize this mathematically by assuming that the forces acting on the swimmer depend on the local viscosity that it experiences. This allows us to calculate the swimming speed as a function of the swimmer’s position along the gradient. The predictions of the model are in good agreement with the experimental observations. The results also suggest that viscotaxis is possible without viscoreceptors, and in fact governed solely by the motility pattern of the swimmer.

Together, the results presented in this thesis contribute to the understanding of bacterial motility and low Reynolds number swimmers in general. Furthermore, these results may be useful for future developments in biophysics, including applications to targeted drug delivery and microrobotics.