Acoustic tethering of microorganisms

Freely swimming microorganisms move as they please, and it requires patience to observe their appendage motions, swimming kinematics and the resulting flows. To make a well-focused video recording, the experimentalist has to wait until the microorganism is swimming with a suitable orientation in the focus plane of the microscope, and a successful recording is not guaranteed. Here, we demonstrate the possibility of using ultrasound to tether freely swimming flagellates in the focus plane and enable easy observation of the behavior of individual microorganisms with simple laboratory equipment and a standard light microscope.

Observations and models of flagellar motion and propulsion have a long history (Gray, 1955; Gray and Hancock, 1955), and the fluid dynamics of swimming and feeding at the micro-scale continues to be an active research field (Guasto et al., 2012; Lauga, 2020). Three-dimensional swimming motions have been tracked using multiple, synchronized cameras (Drescher et al., 2009) and microscopes with automatic feedback control to retain the individuals in focus (Berg, 1971; Darnige et al., 2017). Furthermore, observations of freely swimming flagellates have been carried out in three-dimensional chambers using standard microscopes (Drescher et al., 2010; Dölger et al., 2017), and detailed, time-resolved measurements have been made by confinement in quasi-two-dimensional water films (Guasto et al., 2010) and tethering using micropipettes (Brumley et al., 2014; Wei et al., 2019).

Contact-free, acoustic tethering is potentially an alternative to direct mechanical confinement and tethering. The use of ultrasound to manipulate small, suspended particles in a liquid is known as acoustofluidics, and it has over the past 20 years found widespread application to handle and separate particles and cells in microfluidic devices (Laurell et al., 2007). Acoustic tethering of micro-swimmers has been demonstrated for bacteria (Gutiérrez-Ramos et al., 2018), flagellates (Saito et al., 2002; Saito and Morita, 2006; Kim et al., 2019, 2021), ciliates (Saito et al., 1997, 2002), small multicellular worms (Baasch et al., 2018) and artificial, self-propelled particles (Takatori et al., 2016). These studies focused on tethering of populations of many individuals, e.g. to explore the properties of active suspensions (Takatori et al., 2016; Gutiérrez-Ramos et al., 2018), and as a tool to assess the swimming motility of Chlamydomonas reinhardtii by first confining and subsequently releasing a suspension of many flagellates (Kim et al., 2019).

Our aim in the following is to show how to construct and apply a simple setup to acoustically tether micro-swimmers and enable behavioral observations of individuals at high magnification. As far as we are aware, acoustic tethering has not been used previously for such observations, and the work on populations of many individuals by Gutiérrez-Ramos et al. (2018) is the only study in which ultrasound has been used to tether micro-swimmers in the focus plane of the microscope. In the principle design, standing ultrasound waves in the MHz regime are generated in the water sample by a piezoelectric actuator (Fig. 1A), and freely swimming microorganisms are pushed to the mid-plane of the sample chamber and tethered by the acoustic radiation force that results when the ultrasound impinges on the organisms (Fig. 1B,C). We first describe the basic theory of ultrasound resonance and the acoustic radiation force on a small particle. Guided by the theoretical constraints, we present a design made of simple components that are easy to mount in a standard microscope. We demonstrate the tethering capability of the setup using the dinoflagellate Alexandrium minutum, and we explore the effect of the ultrasound on its swimming and flagellar beat. We conclude by discussing the prospect of the method to explore other species of small aquatic organisms.

Standard seawater with salinity 35 g kg⁻¹ at atmospheric pressure and 20°C has ρ₀=1025 kg m⁻³, κ₀=4.28×10⁻¹⁰ Pa⁻¹ and c₀=1522 m s⁻¹ (Kaye and Laby, 1995). It follows from Eqn 7 that a piezoelectric actuator driven at the frequency f=2.0 MHz can excite the fundamental mode between two parallel plates with h=0.38 mm. For a typical cell with ρ_p=1100 kg m⁻³ and κ_p=4.00×10⁻¹⁰ Pa⁻¹ (Bruus, 2012c), we find Φ=0.135 using Eqn 13, and the positive acoustophoretic contrast factor suggests that the cell will be pushed towards the mid-plane and tethered as discussed above. A list of more precise values of the density and the compressibility of various cells can be found in Cushing et al. (2017).

We used the dinoflagellate Alexandrium minutum Halim 1960 as a representative microorganism to characterize the tethering capability of the setup (Fig. 1B). The phototrophic dinoflagellate swims using a transverse flagellum situated in a groove encircling the cell body and a longitudinal flagellum trailing the cell body (Fenchel, 2001; Lewis et al., 2006). The cell culture was maintained in filtered seawater with added B1 medium at 18°C (Hansen, 1989), and the culture was diluted once every month.

Furthermore, we worked with the ciliate Euplotes vannus (Müller 1786) to demonstrate the capability of the setup to tether relatively large microorganisms. The heterotrophic ciliate feeds on suspended food particles using a membranellar band that consists of rows of closely spaced cilia (Fenchel, 1980; Rode et al., 2022). The cell culture was grown in artificial seawater at 18°C and diluted 2–3 times per year with artificial seawater and autoclaved rice grains to serve as bacterial substrate (Rode et al., 2022).

The design of the experimental setup was aided by three-dimensional simulations building on Eqns 1, 2, 3, 8 and 9, and using models of the glass disks, spacer ring and piezoelectric actuator following the numerical method developed by Skov et al. (2019). The method was implemented in the finite-element software COMSOL using the mathematics-weakform-PDE module as exemplified by the scripts provided in the supplemental material of Muller and Bruus (2015). In the final design (Fig. 1D), the sample chamber was made of two disks and a spacer ring enclosing the water sample with suspended microorganisms (Fig. 1E). The two circular glass disks of thickness 1 mm and diameter 22 mm were made from standard microscope slides (soda-lime glass) using a water jet cutting machine. Preliminary experiments were performed using standard coverslips of thickness 0.170 and 0.300 mm, but the coverslips turned out to be too thin to allow efficient excitation of the fundamental mode, and the preliminary experiments were unsuccessful. The spacer ring was made from a rubber-like aerobic resistance band with a thickness of h=0.38 mm, and a Young's modulus and a Poisson's ratio of roughly 1 MPa and 0.5, respectively. The thickness of the spacer ring was selected to allow the fundamental mode at the frequency f=2.0 MHz as discussed above. The spacer ring was cut with a custom-made die with an inner diameter of 15 mm and an outer diameter of 19 mm. The smooth rubber-like surface provided strong and stable contact with the two glass disks, and it effectively sealed the sample chamber from the ambient air.

The piezoelectric actuator was attached on top of the upper glass disk by a thin layer of glycerol with a thickness of roughly 1 μm (Fig. 1E). Glycerol is commonly used as coupling layer in acoustofluidics (Hammarstrøm et al., 2010; Lenshof et al., 2012; Lickert et al., 2021), and it allows for the setup to be easily assembled and disassembled. The ring-shaped actuator with an inner diameter of 3.8 mm, an outer diameter of 20 mm and a thickness of 1 mm is a standard component made of the material Pz26, and it is designed to resonate at 2.0 MHz (Meggitt A/S, Kvistgård, Denmark). The geometry of the sample chamber and the central hole in the actuator made it easy to illuminate the water sample from above and observe it from below in the inverted microscope (Fig. 1D). The flat faces of the actuator were coated with silver electrodes, and a wire was soldered onto each face (Fig. 1E). The wires were placed close to the outer rim of the actuator, and the actuator was positioned slightly off center to establish a good coupling between its lower face and the upper glass disk. The function of the setup was robust and not sensitive to the details of the off-center placement of the actuator. The actuator was driven by a sinusoidal voltage signal from a function generator (Keysight Technologies 33522B Series Waveform Generator).

The sample chamber was assembled in each new experiment. First, the spacer ring was positioned directly on the lower glass disk, and the water sample with suspended microorganisms was placed centrally inside the spacer ring using a microliter pipette (LABSOLUTE, Th. Geyer GmbH & Co. KG). Subsequently, the upper glass disk was placed directly on top of the spacer ring (Fig. 1E). Depending on its volume, the sample either fills the sample chamber or forms a rotationally symmetric capillary bridge between the two glass plates (Fortes, 1982). Finally, the piezoelectric actuator was positioned on top of the upper glass disk with a thin coupling layer of glycerol. Throughout observations, we used a sample chamber holder (black) and an adapter (white) for the microscope stage table (Fig. 1D). The two components were 3D printed with the designs provided in Fig. S1. In the idealized, one-dimensional model, we have Eqn 7, and the gap height h=0.38 mm corresponds to the fundamental resonance frequency f=2.0 MHz. In practice, and as also studied in our numerical simulations, the modes are three-dimensional, and the resonance spectrum varies across sample chamber assemblies and contains around the fundamental resonance frequency a handful of modes with a nodal mid-plane. In each experiment, it is therefore necessary to search for a good resonance. This is done by observing the sample in the microscope while varying the frequency of the voltage signal around 2 MHz in steps of 10 kHz until a frequency is found at which the suspended organisms are pushed rapidly into focus in the mid-plane of the sample chamber. Alternatively, one can excite all resonances in a range around the fundamental resonance frequency by varying the frequency of the voltage signal, e.g. in the frequency range 1.95–2.05 MHz using a triangular sweep with repetition frequency 0.5 kHz (Manneberg et al., 2009).

We used an Olympus IX71 inverted microscope and a Phantom Miro LAB 320 high-speed video camera (1920×1200 pixels) at 10× magnification (Olympus UPlanFL, working distance 10 mm) and a frame rate of 25 frames s⁻¹ to observe the swimming trajectories of A. minutum, and 40× magnification (Olympus LCPlanFL, working distance 2.15–2.89 mm) and a frame rate of 1000 frames s⁻¹ to see the flagellar beat of A. minutum and the membranelle motion of E. vannus. The observations were made in a temperature-controlled room at 20°C. The dinoflagellates were tracked automatically using custom-written code. Our script in MATLAB and a series of video frames to illustrate the use of the code can be downloaded from the data repository DTU Data (https://doi.org/10.11583/DTU.21206291). To explore the effect of the acoustic tethering on the beat frequency of the longitudinal flagellum of A. minutum, we considered a data set with data for nine different individuals. For each individual, we visually inspected high-speed video of 15 uncorrelated beats before and 15 uncorrelated beats after the ultrasound was turned off, and determined the mean and the standard deviation of the mean of the beat frequencies f_on and f_off with and without ultrasound, respectively.

To illustrate the tethering capability of the setup, we present an experiment with three freely swimming individuals of A. minutum (Movie 1). The 1 μl water sample formed a capillary bridge with an inner diameter of 1.4 mm between the two glass disks, and the piezoelectric actuator was driven by a sinusoidal voltage signal with frequency 1.97 MHz and peak-to-peak amplitude 20 V (high-impedance output). We focus on one of the three individuals to explore the swimming motion and the tethering quantitatively (Fig. 2). Initially, the individual with diameter 18 μm was not swimming in the focus plane of the microscope (Fig. 2A). The ultrasound was turned on at time zero, and the organism was brought into focus in the mid-plane after 480–560 ms. Subsequently, the organism swam in the mid-plane, and it was ultimately confined to a small area of approximately 100×150 μm in the central part of the capillary bridge (Fig. 2B–D). The extent of the lateral confinement depends on the specific assembly of the setup and the details of the acoustic radiation force in the three-dimensional resonance.

After the ultrasound was turned off again, the individual swam freely with a helical trajectory with the central axis approximately in the mid-plane. Helical swimming trajectories are typical for dinoflagellates and many other microorganisms (Purcell, 1977; Fenchel, 2001). Assuming a simple helical trajectory with the central axis in the x–y plane (Crenshaw, 1993), we obtain a radius of 22 μm, a pitch of 110 μm and a frequency of 1.4 Hz. The parameters correspond to a swimming speed of 240 μm s⁻¹, which is normal for individuals of A. minutum (Lewis et al., 2006).

We expect the tethering capability to depend on the amplitude of the voltage signal driving the piezoelectric actuator as summarized in Eqns 12–14 and the subsequent discussion. We explored this effect in a sample with a few individuals of A. minutum subject to different voltage signals. In the experiment, the peak-to-peak amplitude, U, was reduced in a step-wise fashion as function of time (Fig. 3A), and we focused on a representative individual with cell diameter 20 μm (Fig. 3B–D). The cell was kept in focus and confined to a large, central area in the mid-plane at U=20 V and U=15 V, whereas it was swimming more freely and out of the mid-plane at and below U=10 V (Fig. 3B,C). In the experiment, the cell first moved significantly out of focus at U=10 V as shown in the selected video sequence (Fig. 3D).

The ultrasound allows us to tether the dinoflagellates, but it could potentially affect the organisms in unwanted ways, e.g. by altering their flagellar beat frequencies. As a test, we determined the beat frequency of the longitudinal flagellum for several different individuals when the actuation with peak-to-peak amplitude 20 V was on and off (Movie 2). The motion of the longitudinal flagellum is clearly observable, whereas the transverse flagellum and the rotation of the cell are difficult to follow. We therefore only report data for the beat frequency of the longitudinal flagellum. The individuals were released when the ultrasound was turned off, but they remained in focus for at least 30 consecutive beat periods, which allowed us to determine the beat frequency in the absence of ultrasound. There is large variability across individuals, but for each individual we find that f_off and f_on are similar (Fig. 3E). The frequency differences, Δf=f_on–f_off, are distributed around zero, and the average frequency difference of the nine individuals, ±0.8370 Hz, is not statistically different from zero (t-test, P=0.9996). (The uncertainty in is shown as one standard deviation of the mean.) The result suggests that the method is sufficiently gentle to allow tethering without influencing the natural beat pattern.

We have demonstrated that the setup allows us to tether and make behavioral observations of individual microorganisms using A. minutum as a study organism. Our result on the beat frequency of the longitudinal flagellum suggests that the flagellar apparatus is only weakly influenced by the ultrasound. We presume that the setup will work to confine other flagellates and ciliates. As a simple demonstration, we tethered the ciliate E. vannus with a cell length of roughly 90 μm (Movie 3), and we were able to observe the beating of the cilia in the membranellar band (Fenchel, 1980; Rode et al., 2022). Tethering of even larger organisms should be possible by choosing a piezoelectric actuator with a lower resonance frequency and increasing the gap height according to Eqn 7, as long as the observations are not constrained by the working distance of the microscope objective.

The swimming speed and the beat frequency of a typical microorganism are on the order of 100 μm s⁻¹ and 50 Hz, respectively, and if we assume that the thickness of the focus plane of the microscope (depth of field) is 40 μm at high magnification, we estimate that a typical, freely swimming individual will remain in focus for roughly 20 beat periods. A possible use of the method is therefore to bring the microorganism into the focus plane and subsequently release and observe it freely swimming. This approach allows observations of short swimming sequences, but it cannot replace microscopes designed specifically to follow long, three-dimensional swimming trajectories (Berg, 1971; Drescher et al., 2009; Darnige et al., 2017).

The acoustic radiation force is proportional to the cell radius cubed (Eqn 8), and the force might not be sufficient to tether micron-sized bacteria and small flagellates. Instead, the motion of micron-sized organisms may be dominated by acoustic streaming caused by motion in the viscous boundary layers at the walls of the sample chamber (Bruus, 2012c) and in the bulk liquid by the slight heating from the actuator (Joergensen and Bruus, 2021). Optical tethering provides an alternative to acoustic tethering (Thalhammer et al., 2011; Dholakia et al., 2020), and it is particularly advantageous for tethering of particles and cells of sizes less than 1 μm (Dholakia et al., 2020).

Acoustic tethering is not limited to spherical cells, as demonstrated for small multicellular worms (Baasch et al., 2018), but more work is needed to theoretically and experimentally understand the acoustic radiation force and torque on elongated cells and thin fibers such as flagella and cilia (Leão-Neto et al., 2021).

We are grateful to Meggitt A/S for providing piezoelectric actuators, Kirstine Berg-Sørensen, Anders Nielsen, Lars Pedersen, Fredrik Ryderheim, Ole Trinhammer and Willem van de Water for help and advice, and Erik Hansen for his careful work on design and construction of the experimental setup and for the technical drawings in Fig. S1. The results presented in Fig. 2 in this paper are reproduced from the PhD thesis of Mads Rode (Technical University of Denmark, 2021).