Dynamic force patterns of an undulatory microswimmer

Methods and Measures for Investigating Microscale Motility

Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks, and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we summarize the main mechanisms of microscale motility and give an overview of different experimental, analytical, and mathematical methods used to study them across different scales encompassing the molecular-, individual-, to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.

Dynamic force measurements on swimming Chlamydomonas cells using micropipette force sensors

Flagella and cilia are cellular appendages that inherit essential functions of microbial life including sensing and navigating the environment. In order to propel a swimming microorganism they displace the surrounding fluid by means of periodic motions, while precisely timed modulations of their beating patterns enable the cell to steer towards or away from specific locations. Characterizing the dynamic forces, however, is challenging and typically relies on indirect experimental approaches. Here, we present direct in vivo measurements of the dynamic forces of motile Chlamydomonas reinhardtii cells in controlled environments. The experiments are based on partially aspirating a living microorganism at the tip of a micropipette force sensor and optically recording the micropipette's position fluctuations with high temporal and sub-pixel spatial resolution. Spectral signal analysis allows for isolating the cell-generated dynamic forces caused by the periodic motion of the flagella from background noise. We provide an analytic, elasto-hydrodynamic model for the micropipette force sensor and describe how to obtain the micropipette's full frequency response function from a dynamic force calibration. Using this approach, we measure the amplitude of the oscillatory forces during the swimming activity of individual Chlamydomonas reinhardtii cells of 26 ± 5 pN, resulting from the coordinated flagellar beating with a frequency of 49 ± 5 Hz. This dynamic micropipette force sensor technique generalizes the applicability of micropipettes as force sensors from static to dynamic force measurements, yielding a force sensitivity in the piconewton range. In addition to measurements in bulk liquid environment, we study the dynamic forces of the biflagellated microswimmer in the vicinity of a solid/liquid interface. As we gradually decrease the distance of the swimming microbe to the interface, we measure a significantly enhanced force transduction at distances larger than the maximum extent of the beating flagella, highlighting the importance of hydrodynamic interactions for scenarios in which flagellated microorganisms encounter surfaces.

Micropipette force sensors for in vivo force measurements on single cells and multicellular microorganisms

Measuring forces from the piconewton to millinewton range is of great importance for the study of living systems from a biophysical perspective. The use of flexible micropipettes as highly sensitive force probes has become established in the biophysical community, advancing our understanding of cellular processes and microbial behavior. The micropipette force sensor (MFS) technique relies on measurement of the forces acting on a force-calibrated, hollow glass micropipette by optically detecting its deflections. The MFS technique covers a wide micro- and mesoscopic regime of detectable forces (tens of piconewtons to millinewtons) and sample sizes (micrometers to millimeters), does not require gluing of the sample to the cantilever, and allows simultaneous optical imaging of the sample throughout the experiment. Here, we provide a detailed protocol describing how to manufacture and calibrate the micropipettes, as well as how to successfully design, perform, and troubleshoot MFS experiments. We exemplify our approach using the model nematode Caenorhabditis elegans, but by following this protocol, a wide variety of living samples, ranging from single cells to multicellular aggregates and millimeter-sized organisms, can be studied in vivo, with a force resolution as low as 10 pN. A skilled (under)graduate student can master the technique in ~1-2 months. The whole protocol takes ~1-2 d to finish.

Direct measurements of drag forces in C. elegans crawling locomotion

With a simple and versatile microcantilever-based force measurement technique, we have probed the drag forces involved in Caenorhabditis elegans locomotion. As a worm crawls on an agar surface, we found that substrate viscoelasticity introduces nonlinearities in the force-velocity relationships, yielding nonconstant drag coefficients that are not captured by original resistive force theory. A major contributing factor to these nonlinearities is the formation of a shallow groove on the agar surface. We measured both the adhesion forces that cause the worm's body to settle into the agar and the resulting dynamics of groove formation. Furthermore, we quantified the locomotive forces produced by C. elegans undulatory motions on a wet viscoelastic agar surface. We show that an extension of resistive force theory is able to use the dynamics of a nematode's body shape along with the measured drag coefficients to predict the forces generated by a crawling nematode.

The nematode C. elegans as a complex viscoelastic fluid

The viscoelastic material properties of the model organism C. elegans were probed with a micropipette deflection technique and modelled with the standard linear solid model. Dynamic relaxation measurements were performed on the millimetric nematode to investigate its viscous characteristics in detail. We show that the internal properties of C. elegans can not be fully described by a simple Newtonian fluid. Instead, a power-law fluid model was implemented and shown to be in excellent agreement with experimental results. The nematode exhibits shear thinning properties and its complex fluid characteristics were quantified. The bending-rate dependence of the internal damping coefficient of C. elegans could affect its gait modulation in different external environments.

Tangling of tethered swimmers: interactions between two nematodes

The tangling of two tethered microswimming worms serving as the ends of "active strings" is investigated experimentally and modeled analytically. C. elegans nematodes of similar size are caught by their tails using micropipettes and left to swim and interact at different separations over long times. The worms are found to tangle in a reproducible and statistically predictable manner, which is modeled based on the relative motion of the worm heads. Our results provide insight into the intricate tangling interactions present in active biological systems.