Mathematics of Microswimming

Thursday, June 17 at 09:30am (PDT)
Thursday, June 17 at 05:30pm (BST)
Friday, June 18 01:30am (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS19" time block.
Note: this minisymposia has multiple sessions. The second session is MS18-MMPB (click here).

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Qixuan Wang (UC Riverside, United States), Bhargav Rallabandi (UC Riverside, United States), Mykhailo Potomkin (UC Riverside, United States)


Microorganisms are the most abundant in nature. Their ability to move autonomously and develop diverse strategies to survive in various environments is at the core of understanding life. Motility of numerous types of microorganisms, relevant for biological and medical applications, occurs in fluids. Such microorganisms, called microswimmers and exemplified by bacteria or spermatozoa, are relevant for many biological and medical applications. Recent advances in studies of biological microswimmers have inspired development of synthetic microrobots with potential medical applications such as drug delivery, decrease of biofluid viscosity or tissue repair. In this special session, we bring together experts in this area to discuss how the state-of-the-art techniques in modeling, theory and experiments can elucidate microwimming phenomena, develop new directions in this interdisciplinary research and provide new applications of microswimmers.

Rishabh V. More

(Mechanical Engineering, Purdue University, United States)
"Micro-swimmer dynamics in stratified fluids"
Understanding the motion of microorganisms in aquatic bodies like lakes and oceans has been an active area of research for decades with wide ecological and environmental impacts. Especially, the upper layer of oceans which sustains an intense biological activity, observes a vertical variation in the density (stratification) which can either be due to variations in water temperature or salinity, or both. From our fully resolved numerical simulations, we show that fluid stratification affects the locomotion of an individual, interactions between a pair, and the dynamics of suspensions of marine micro-swimmers in interesting and non-intuitive ways. At low Re, the vertical migration of small organisms is hydrodynamically affected due to the rapid velocity decay as well as higher energy expenditure in stratified fluids. At a finite Re, stratification even leads to striking differences in the swimming speeds and stability of swimmers as compared to their motion in a homogeneous fluid. The reduced flow signature of a swimming organism due to stratification can save them from getting detected by predators. Stratification increases the contact time of two colliding swimmers, thus, increasing the probability of successful reproduction. These results can explain the commonly observed accumulation of phytoplankton in oceans. Finally, collective motion microorganisms alter the temperature microstructure and lead to higher mixing with increasing stratification. Insights obtained from the investigations for an individual swimmer's motion and interactions between a pair of swimmers in a stratified fluid explain these observations.

Jeffrey L. Moran

(Department of Mechanical Engineering, George Mason University, United States)
"Chemokinesis-driven Accumulation of Artificial Microswimmers in Low-Motility Regions of Fuel Gradients"
Motile cells often detect and respond to changes in their local chemical environment by changing their speed or direction, which allows them to carry out important functions including finding nutrients, immune response, or predator evasion. Two common examples are chemotaxis (motion up or down a chemical concentration gradient) and chemokinesis (dependence of speed on chemical concentration). Chemokinesis is distinct from chemotaxis in that no directional sensing or reorientation capabilities are required. Over the past 15+ years, researchers have developed 'artificial microswimmers' or 'microrobots' that move at speeds that usually depend on the concentration of a chemical 'fuel' (chemokinesis). However, the behavior of artificial microswimmers in fuel gradients has not been thoroughly characterized and the extent to which they exhibit chemotaxis is not fully known. Here, we study the behavior of half-platinum half-gold self-propelled rods in steady state, antiparallel gradients of hydrogen peroxide fuel and potassium chloride salt, which tend to increase and decrease the rods' speed, respectively. Brownian Dynamics simulations, a Fokker-Planck theoretical model, and experiments demonstrate that at steady state, the chemokinetic self-propelled rods accumulate in low-speed (salt-rich, peroxide poor) regions not because of chemotaxis, but because of chemokinesis. The agreement between simulations, model, and experiments bolsters the role of chemokinesis in this system and validates previous theoretical findings [Popescu et al., Nano Lett. 18, 9 (2018)] that chemokinesis alone cannot lead to chemotaxis. This work suggests a novel strategy of exploiting chemokinesis to effect the accumulation of artificial microswimmers in desired areas, which could find application in environmental remediation, wound healing, and drug delivery for cancer treatment.

Eva Kanso

(University of Southern California, United States)
"Emergent Waves in Ciliary Carpets"
Motile cilia often line internal epithelial surfaces with thousands of multiciliated cells, each containing hundreds of cilia. Their coordinated motion drives flows with important biological functions in the respiratory, cerebrospinal, and reproductive systems in humans. Cilia coordination has been studied extensively at the level of pairs of cilia, and even in collections of cilia with metachronal waves. However, a general theory for investigating the hydrodynamics of cilia coordination in large systems remains lacking. Here, starting from discrete arrays of cilia, wherein each cilium is represented by a well-known oscillator model, we devise a fast numerical algorithm for investigating the dynamics of thousands of hydrodynamically-coupled cilia. We then develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter with classical Stokes flow methods. We analyze the stability of isotropic and synchronized states and show that they are unstable. Surprisingly, traveling wave patterns emerge in both the discrete and continuum theory regardless of initial conditions, indicating that these waves are global attractors.

David Saintillan

(Mechanical and Aerospace Engineering, University of California San Diego, United States)
"An Integrated Chemomechanical Model of Sperm Locomotion"
Mammalian sperm cells achieve locomotion by the spontaneous periodic oscillation of their flagellum. Dynein motors inside the flagellum consume energy from ATP to exert active sliding forces between microtubule doublets, thus creating bending waves along the flagellum and enabling the sperm cell to swim in a viscous medium. Using a sliding-control model of the axoneme that accounts for the coupling of motor kinetics with elastic deformations, we develop a chemomechanical model of a freely swimming sperm cell that accounts for the effect of non-local hydrodynamic interactions between the sperm head and flagellum. The model is shown to produce realistic beating patterns and swimming trajectories, which we analyze as a function of sperm number and motor activity. Remarkably, we find that the swimming velocity does not vary monotonically with motor activity, but instead displays two local maxima corresponding to distinct modes of swimming.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.