Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores

  1. Quang D Tran  Is a corresponding author
  2. Eric Galiana
  3. Philippe Thomen
  4. Céline Cohen
  5. François Orange
  6. Fernando Peruani
  7. Xavier Noblin  Is a corresponding author
  1. Université Côte d’Azur, CNRS UMR 7010, Institut de Physique de Nice (INPHYNI), France
  2. Université Côte d’Azur, INRAE UMR 1355, CNRS UMR 7254, Institut Sophia Agrobiotech (ISA), France
  3. Université Côte d’Azur, Centre Commun de Microscopie Appliquée (CCMA), France
  4. Université Côte d’Azur, CNRS UMR 7351, Laboratoire J.A. Dieudonné (LJAD), France
  5. CY Cergy Paris Université, CNRS UMR 8089, Laboratoire de Physique Théorique et Modélisation, France

Abstract

Phytophthora species cause diseases in a large variety of plants and represent a serious agricultural threat, leading, every year, to multibillion dollar losses. Infection occurs when their biflagellated zoospores move across the soil at their characteristic high speed and reach the roots of a host plant. Despite the relevance of zoospore spreading in the epidemics of plant diseases, individual swimming of zoospores have not been fully investigated. It remains unknown about the characteristics of two opposite beating flagella during translation and turning, and the roles of each flagellum on zoospore swimming. Here, combining experiments and modeling, we show how these two flagella contribute to generate thrust when beating together, and identify the mastigonemes-attached anterior flagellum as the main source of thrust. Furthermore, we find that turning involves a complex active process, in which the posterior flagellum temporarily stops, while the anterior flagellum keeps on beating and changes its gait from sinusoidal waves to power and recovery strokes, similar to Chlamydomonas’s breaststroke, to reorient its body to a new direction. Our study is a fundamental step toward a better understanding of the spreading of plant pathogens’ motile forms, and shows that the motility pattern of these biflagellated zoospores represents a distinct eukaryotic version of the celebrated ‘run-and-tumble’ motility class exhibited by peritrichous bacteria.

Editor's evaluation

The authors present a study of the swimming behaviour of the zoospores of the water mold Phytophthora (Greek "Plant Destroyer"), which is responsible for significant crop damage worldwide. The motility of the zoospores is likely a significant contributor to the successful spread of the disease, and as such its study has potential wide impact. The authors suggest using a model that the anterior "hairy" (covered with mastigonemes) flagellum is the primary contributor to motility, and show with high-speed imaging that the microorganism is able to turn on the spot by stopping its posterior flagellum, and changing the beat-pattern of its anterior flagellum from "sperm-like" to "Chlamydomonas-like".

https://doi.org/10.7554/eLife.71227.sa0

eLife digest

Microorganisms of the Phytophthora genus are serious agricultural pests. They cause diseases in many crops, including potato, onion, tomato, tobacco, cotton, peppers, and citrus. These diseases cause billions of dollars in losses each year. Learning more about how the tiny creatures disseminate and reach host plants could help scientists develop new ways to prevent such crop damage.

The spore cells of Phytophthora, also known as zoospores, have two appendages called flagella on their bodies. A tinsel-shaped flagellum is near the front of the creature and a long smooth filament-like flagellum is near the posterior. Zoospores use their flagella to swim at high speeds through liquid toward potential plant hosts. Their complex swimming patterns change in response to different physical, chemical, and electrical signals in the environment. But exactly how they use their flagella to generate these movements is not clear.

Tran et al. reveal new details about zoospore locomotion. In the experiments, Tran et al. recorded the movements of zoospores in a tiny ‘swimming pool’ of fluid on top of a glass slide and analyzed the movements using statistical and mathematical models. The results uncovered coordinated actions of the flagella when zoospores swim in a straight line and when they turn. The tinsel-like front flagellum provides most of the force that propels the zoospore forward. To do this, it beats with an undulating wave pattern. It shifts the beating to a breast-stroke pattern to change direction. The posterior flagellum provides a smaller forward thrust and temporarily pauses during turns.

The study provides new details about zoospore’s movements that may help scientists develop new strategies to control these pests. It also offers more information about how flagella coordinate their actions to switch speeds or change directions that may be of interest to other scientists studying organisms that use flagella to move.

Introduction

Life of swimming microorganisms in viscosity-dominant world has been of great interest in biophysics research. The problems on microbial locomotion of those tiny individual flagellated swimmers are still far to be fully understood. There have been a multitude of theoretical and experimental models of microswimmers that study the hydrodynamics of the individual and collective motions of those cells (Ghanbari, 2020; Lauga and Goldstein, 2012). These swimming cells can be categorized into two groups: eukaryotes (having nuclei) and prokaryotes (no nuclei). Escherichia coli is one of the most studied prokaryotic swimmers, which possesses a bundle of passive helical flagella controlled by a rotary motor attached to the cell body (Turner et al., 2000). Eukaryotic microswimmers, such as green algae Chlamydomonas (Mitchell, 2001; Polin et al., 2009) and spermatozoa (Ishijima et al., 1986; Mortimer et al., 1997), have active and flexible flagella along which molecular motors are distributed. Here, we introduce a new type of microswimmer, named Phytophthora zoospores, which has two different flagella collaborating for unique swimming and turning mechanisms (Figure 1(A)).

Characteristics of P. parasitica zoospore.

(A) Swimming of zoospores in comparison with different prokaryotic and eukaryotic microswimmers. Black arrows indicate the swimming direction of the swimmers. (B) Scanning electron microscopy images of the zoospore. The insets show the enlarged images of the cell body and the two flagella. (C) Transmission electron microscopy images with negative staining. (1) Image of the zoospore showing the different structures of the two flagella. The anterior has multiple mastigonemes, while the posterior has a smooth straight structure. (2) Close zoom-in image of the anterior flagellum. It is noticed that there are two types of mastigonemes on this flagellum: one with straight tubular shape, the other with non-tubular shape but longer and bigger in size. (3) Close zoom-in image of the posterior flagellum. There are plenty of thin and short hairs wrapping along the flagellum and several non-tubular mastigonemes appearing near the cell body. (4) The non-tubular mastigonemes. (5) The tubular mastigonemes with tiny hairs at the tips.

Phytophthora is a genus of eukaryotic and filamentous microorganisms. They are classified as oomycetes and grouped in the kingdom of the Stramenopiles with the heterokont algae (such as diatoms and brown algae) (Burki, 2014; Derelle et al., 2016). A number of Phytophthora species are plant pathogens and cause tremendous damages to agro- and eco-systems (Derevnina et al., 2016; Kamoun et al., 2015). Nowadays, Phytophthora diseases are responsible for a big impact on economies with billions of dollars of damages each year and remain a threat to the food security worldwide (Drenth and Sendall, 2004; Judelson and Blanco, 2005; Strange and Scott, 2005). The diseases are pervasive as they release swimming biflagellated spores called ‘zoospores’ which initiates the spreading through water. These zoospores are able to achieve speed up to 250μms-1(Appiah et al., 2005) through thin water films, water droplets on leaves, or through pores within moist soils. To facilitate the spreading, their cell bodies store an amount of energy (mycolaminarin, lipid) allowing them to swim continuously for several hours (Judelson and Blanco, 2005). In natural ecosystems and even more in agro-systems, putative host plants are usually close. This proximity makes the distance to find a plant relatively short and it is compatible to the time-ability of zoospores to swim. When the zoospores reach plant roots, they stop swimming and release their flagella to produce a primary cell wall and become germinative cysts which are able to penetrate into the host tissue. Then, they start a hyphal growth inside the infected plant. In this study, we investigate the telluric species P. parasitica, a polyphagous pathogen attacking a wide range of hosts such as potato, onion, tomato, tobacco, ornamentals, cotton, pepper, citrus plants, and forest ecosystems (Panabieres et al., 2016).

Previous studies have shown that during the spreading and approaching the host, zoospores can have complicated swimming patterns and behaviors as they experience multiple interactions with environmental signals, both physical, electrical and chemical, in soil and host-root surface (Bassani et al., 2020a). Near the plant-root, zoospores can perceive various stimuli from the environment, such as ion exchange between soil particles and plant roots, the chemical gradients generated by root exudates, which activate cell responses. This results in coordinated behaviors of zoospores, allowing them to preferentially navigate to the water film at the interface between soil particles and plant roots. For instance, potassium, which is uptaken by roots in the soil, reduces zoospore swimming speed, causes immediate directional changes and also results in perpetual circle trajectories (Appiah et al., 2005; Galiana et al., 2019). Bassani et al. provide transcriptomic studies showing that potassium induces zoospore aggregation, which facilitates the advantages for zoospores to attack the host-root (Bassani et al., 2020b). Experimental evidence has demonstrated that zoospore-zoospore interaction can lead to ‘pattern swimming’, a microbial bioconvection happened without the appearance of chemical or electrical signals (Ochiai et al., 2011; Savory et al., 2014). These findings urge for a better understanding of the swimming physics of the individual zoospores and how the combination of their two heterogeneous flagella results in those complex swimming behaviors.

A zoospore is usually about 10 µm in size and has a kidney-like cell body (Mitchell et al., 2002; Walker and van West, 2007). At least two unique traits distinguish zoospores from other prokaryotic and eukaryotic microswimmers currently studied using physical approaches: (i) The two flagella beat longitudinally along the anterior-posterior axis of the cell body and not laterally as in the case of the green algae Chlamydomonas; (ii) two flagella distinguished from each other as the anterior flagellum has a tinsel-like structure, while the posterior flagellum has a smooth whiplash one, both beating periodically with wave propagation directions outwards the body. At first sight, these two flagella seem to be competing each other due to the opposite wave propagation directions. Contrarily, multiple mastigoneme structures on the anterior flagellum of zoospores are shown to have thrust reversal ability, which makes both flagella generate thrust in the same direction and propel the cell body forwards (Bassani et al., 2020b; Cahill et al., 1996). Although it has been known about how zoospores swim, characteristics of the swimming and the beating flagella have not been statistically reported. The effects of mastigonemes on zoospore swimming also need to be carefully investigated since the mechanical properties of mastigonemes such as size, rigidity, density, can affect the swimming differently (Namdeo et al., 2011). For instance, although mastigonemes are shown to generate thrust reversal in P. palmivora zoospores (Cahill et al., 1996), they do not contribute to enhance swimming of C. reinhardtii (Amador et al., 2020).

In other microswimmers, their flagella are often synchronized to perform a cooperative swimming when they are a few microns away from each other (Friedrich and Jülicher, 2012; Lauga and Goldstein, 2012). For examples, C. reinhardtii performs breaststroke swimming by two flagella drawing away and back to each other (Polin et al., 2009) or E. coli, B. subtilis bacteria’s flagella form a bundle and rotate together like a corkscrew to propel the cell body (Turner et al., 2000). The question that whether zoospores, as eukaryotic swimmers, possess the similar cooperative behaviors of their flagella is of good interest. It has been previously claimed that zoospore flagella are independent on each other and able to perform different tasks. Carlile, 1983 describes that the anterior flagellum is responsible for pulling the zoospore through water whereas the posterior flagellum acts as a rudder for steering the cell. However, Morris et al., 1995 observe P. palmivora zoospores stop momentarily and then self-orientate their bodies to a new direction relatively to the posterior flagellum. Nevertheless, the cooperative actions of the motor and rudder have not been carefully observed nor investigated, which remains unclear about how zoospores change direction either by random walks or in response to chemical and physical environment. This motivates us to unveil the physics behind individual swimming of zoospores.

In this article, we first investigate characteristics of zoospore trajectories at a global scale, then focus on the flagella scale’s swimming mechanisms. We observe that zoospores can perform long and stable straight runs, discontinued by active turning events. We obtain statistics of the trajectories and develop a numerical model to study and extrapolate the zoospore spreading characteristics solely by random walks. Then, we detail an in-depth study on the hydrodynamics of P. parasitica’s flagella and acquire a mathematical model to correlate the functions of two flagella on the motion of straight runs. Although theoretical models for microswimmers with single mastigonemes-attached flagella have been formulated (Brennen, 1975; Namdeo et al., 2011), models for microswimmers with two heterokont flagella have yet been considered as in case of zoospores. Here, we use Resistive Force Theory and further develop the model of a single flagellum with mastigonemes (Brennen, 1975; Namdeo et al., 2011) to adapt it with another smooth flagellum and a cell body, using a hypothesis of no interactions between two flagella. Moreover, we discover a unique active turning mechanism of zoospores including a body rotation then steering to a new direction, which results from the instantanous gait changing ability of their anterior flagellum. Our study reveals the mechanism and characteristics of zoospore spreading, which provides better insights on understanding and control of Phytophthora diseases.

Results and discussion

Characteristics of P. parasitica’s cell body and flagella

To understand the swimming, we first look at the cell body and flagellar structures of P. parasitica. By using Scanning Electron Microscopy (EM), we are able to observe the shape of the cell body and the positions of the flagellar base (Figure 1(B)). The cell in general has an ellipsoidal shape with tapered heads and a groove along the body. The size of the body is measured to be 8.8±0.4μm (SEM) in length, and 4.7±0.1μm (SEM) in width. The anterior flagellum attaches to the cell body in a narrow hole at one side of the groove, possessing an average length of 15.5±0.1μm (SEM). The posterior flagellum has the same diameter as the anterior’s (0.3μm) but it is longer (20.3±0.76μm (SEM)), and attaches directly to the surface of the groove. The roots of two flagella are apart from each other with a distance of 2.9±0.1μm (SEM). Some mastigoneme structures were observed on the anterior flagellum, but could only be distinguished with difficulty by Scanning EM technique.

Observing the zoospores with Transmission Electron Microscopy (TEM) after negative staining, we discover multiple mastigonemes on both flagella (Figure 1 (C1-3)). There are two different types of mastigonemes on the anterior flagellum: (type-1) straight and tubular shape, high density (∼ 13 per μm), 0.03μm diameter, 1.5μm long; (type-2) curved and irregular shape, longer and thicker in size (0.1μm diameter, 1.8μm long), and randomly distributed (Figure 1 (C2)). The posterior flagellum instead has a smooth whip shape with plenty of very fine hairs on the surface (Figure 1 (C3)). These hairs wrap around the flagellum to increase the contact surface, thus increasing the propulsion efficiency (Lee, 2018). We also see a few type-2 mastigonemes on the posterior flagellum but they only appear near the root. The function of type-2 mastigonemes (Figure 1 (C4)) is unknown, but their flexibility and random arrangement suggest that they might not contribute to generate drag. In contrary, the type-1 mastigonemes (Figure 1 (C5)) are tripartite hairs that occur in most of Stramenopiles kingdom. They are known to be able to generate increased drag and reverse thrust for the anterior flagellum (Cahill et al., 1996; Dodge, 2012).

Statistics of individual swimming patterns

We investigate the characteristics of zoospore swimming by analyzing their trajectories and behaviors in water. To facilitate that, we perform microscopic assays where a low concentration of individual zoospores are released to an open thin film of water with thickness of ∼100 µm on a glass slide. The setup of the water thin film can be visualized as a ‘swimming pool’ that is not covered as we want to avoid the unwanted physical interactions of zoospores with the top when they experience aerotaxis. The zoospore swimming is captured at 60 fps (interval time between two consecutive frames, Δt0.0167s). The images are processed by Fiji (Schindelin et al., 2012) and Trackmate plugin (Tinevez et al., 2017) to semi-automatically track the positions of zoospores during the experiment duration (see Video 1). Figure 2(A) illustrates the trajectories of zoospores captured from the microscopic assay. These trajectories indicate that zoospore can perform long and straight runs, some can even cross the whole observed region. The straight runs are separated by multiple turning events when zoospores randomly change directions. With this swimming strategy, zoospores can be categorized as run-and-tumble active particles (Khatami et al., 2016). From the position data of each zoospore over time, we achieve its movement characteristics defined by two parameters: magnitude of speed U and moving directions θ (Figure 2(B–C)), after applying moving average method with step length n=12 to improve the accuracy of moving direction and instantaneous speed of the zoospore. From U values, we can separate the movement of zoospores into 2 states: running state during straight runs and stopping state at turning events. While running, U and θ vary around a constant value. At turning events, U drops drastically, (occasionally close to 0) then quickly recovers, θ also rapidly changes to a new value. Uth is defined as the threshold speed that separates the two states of running and turning. With Uth, we determine two important parameters of zoospore swimming: (i) running time τr as the duration when UUth, deciding how long a zoospore is able to travel without turning; (ii) stopping time τs as the duration, when UUth, for a zoospore to perform a turn.d

Swimming trajectories of P. parasitica zoospores.

(A) Trajectories of zoospores swimming in water captured from the microscopic assay for 60 s. Sample size N=58. Note: not all trajectories are shown. Each position of the zoospores is captured every Δt=0.0167s. The trajectories are smoothed with moving average (step length n=12). (B) The progression of speed U and (C) moving directions θ over time of a single zoospore extracted from the population in the assay. (D) Distribution of zoospore speed p(U). (E) Polarity distribution of moving direction p(θ). (F) Survival curves p(τt) of the running time τr and stopping time τs. (G) Distribution of turning angle p(Δθ), with positive angle values indicating counter-clockwise, and negative as clockwise direction. (H) Schematics showing the strategy of the simulation model of zoospores swimming in water. (I) The estimated mean squared displacement (MSD) over time intervals t, constructed from the simulation data. The inset compares the experimental data and simulation of MSD at the experimental time-scale of 60 s. By simulation, at long time scale of 1 h, MSD of zoospores shows a diffusion of Brownian particles with the diffusion coefficient D=3.5×10-4cm2s-1.

Video 1
Zoospores swimming in thin water film.

The video was captured in the microscopic assay, with objectives 4×, 60 fps, duration 60 s. The trajectories of zoospores were tracked by combining TrackMate (in Fiji) and manual tracking.

We plot the distribution of U for all the trajectories of zoospores swimming in the observed region for duration of 60 s (total number of zoospores N=58) in Figure 2(D). The speed distribution p(U) exhibits a combination of two different normal distributions: f1(U)=0.082e-(U-μ1)2/2σ12 with μ1=176.6, σ1=22.3μms-1, and f2(U)=0.043e-(U-μ2)2/2σ22 with μ2=110, σ2=53μms-1. This bimodal distribution of U indicates that zoospore speed fluctuates around two speed values U=μ1 and U=μ2, corresponding to two behavioral states of running and turning. The distribution f1 is associated with the running state where zoospores experience stable moving speed, while f2 represents the speed at turning events where zoospores reduce their speed from a stable running speed to 0 then quickly recover. We achieve the fitting curve for p(U), resulting from the sum of two Gaussian fits f1+f2, and choose the speed at inflection point of the fitting curve where μsUμr as the speed threshold to separate two behavioral states, Uth=111.5μms1 at the inflection point determines a turning point for a significant change of the speed from running to turning state. The sensitivity of our Uth selection can be tolerated by ±10 % of the chosen value, ranging from 100 to 122.5 μms-1 (See Appendix 5). We also plot the polarity distribution of zoospores in Figure 2(E) based on the moving direction θ and acquire an equally distributed in all directions. With the defined Uth, we calculate and plot the distributions of τr and τs in form of survival curves p(τt) in Figure 2(F). Both survival curves show complex behaviors of zoospores during running and turning. The statistics p(τst) can be considered as sum of two exponential decays with average stopping time τ¯s=0.37s. Also, p(τrt) is in form of two exponential decays with average running time τ¯r=1.0s. We can estimate that zoospores stop and turn with the frequency 1/τ¯r greater than 1Hz (p(τr<1.0s)=0.82). Based on the moving direction over time, we calculate the average turning speed of zoospores at θ˙¯0.6πrads-1. At each stopping time they perform a turning angle Δθ=θi-θe, where θi and θe is the moving direction right before and after each turning event, respectively. The distribution of Δθ is shown in Figure 2(G), demonstrating the equal preference of turning directions. It is also shown that zoospores preferentially turn with the angle around 0°, which we speculate that it results from the failed out-of-plane movement when zoospores swim near the water/air interface during their aerotaxis (See Video 2).

Video 2
A zoospore swimming near water/air interface.

Since the motion of zoospore is characterized by the succession of straight runs and turning events, as illustrated in Figure 2(H), in order to quantify their large-scale transport properties, we assemble all previous measurements in the following way. Each straight run is characterized by a speed Ur>Uth and a duration τr drawn from the distributions in Figure 2(D), and (F), respectively. After a run phase, an idle phase of duration τs, drawn from Figure 2(F) follows. The moving direction of the r-th run phase is given by cos(θr)x^+sin(θr)y^, i.e. it is parameterized by an angle θr. Note that moving direction of two consecutive r-th and (r+1)-th run phases are correlated. Moreover, θr+1=θr+Δθ, where Δθ is a random angle drawn from the distribution in Figure 2(G). Mathematically, the position xm of the zoospore after m run phases is given by xm=r=1mUrτr[cos(θr)x^+sin(θr)y^], and its mean-square displacement is MSD(m)=(xmxm)2, where denotes average over realizations of the process. Our simulation results in a diffusive behavior of zoospores, with the MSD proportional to t (see Video 3). The diffusion coefficient is then obtained from D=limmMSD(m)4m(τr+τs). In the computation of MSD and D, we assume that the only random variable exhibiting correlations is θr, while Ur, τr, and τs are uncorrelated. This procedure allows us to obtain an estimate of D, with D=3.5×10-4cm2s-1, which is in the same order of magnitude as the diffusion coefficient of C. reinhardtii’s (Polin et al., 2009). We stress that direct measurements of D based on experimental MSD data are highly unreliable given the relatively small number of trajectories and their short duration. In our case, the data are enough to obtain reliable estimates on the distributions of Δθ, Ur, τr, and τs from which, as explained above, D can be reliably estimated from simulations. Similar methods of using a theoretical random walk model to estimate the macroscopic parameters from the microscopic experiment have been previously developed for C. reinhardtii (Hill and Hader, 1997; Vladimirov et al., 2004). We emphasize that D represents the estimation of diffusion coefficient of individual swimming of zoospores from random walks. This is more to show the intrinsic ability of individual zoospores to perform spatial exploration, rather than to quantify the bulk diffusivity where the collective swimming behaviors, which involve zoospore-zoospore interactions, play a major role.

Video 3
The result from our simulation with the strategy described in Figure 2(H).

The parameters of the simulation are extracted from the statistics of the swimming of zoospores, presented in Figure 2(D–G).

Role of two flagella in swimming motions of zoospores

Our statistics study on swimming trajectories of zoospores has delivered characteristics of their movement at large-scale, including the straight runs and turning events. These motions are controlled by two flagella oriented in opposite directions along the cell body’s anterior-posterior axis. In this section, we look in-depth to how these two flagella together generate speed and perform turning for zoospores by conducting microscopic assays at small length scale, of which the flagella are visible and in very short time scale.

Straight runs

We record movement of zoospores during their straight runs with visible flagella by conducting brightfield microscopy with 40× objective and a high-speed camera capturing at 2000 fps at exposure time 200 μs. In Figure 3(A), we show images of a P. parasitica zoospore swimming by two flagella beating in sinusoidal shapes with the wave propagation in opposite directions. While translating, the cell body gyrates around the moving direction simultaneously, which results in a helical swimming trajectory (see Video 4 for a long run of a zoospore swimming in water). We believe that this gyrational motion might result from the intrinsic chiral shape of the zoospore body and off-axis arrangement of their flagella (Figure 1(B)). Indeed, previous studies have shown that chirality of a microswimmer’s body induces spontaneous axial rotation resulting from the translational motion (Keaveny and Shelley, 2009; Löwen, 2016; Namdeo et al., 2014). From multiple observations, we obtain the pitch and radius of the helical trajectories at p=130±8μm (SEM) and R=4.0±0.2μm (SEM), respectively (data presented in Appendix). We then estimate the gyrational speed of the cell body ϕ˙=2π/Δtp, where Δtp is the duration the zoospore travels through a full turn of the helical path (Figure 3(B)). We obtain ϕ˙=(3.6±0.3)πrads-1 (SEM) (see Appendix). The observations of helical trajectories also confirm that each flagellum of zoospores beat as a flexible oar in a 2D plane as we notice the two flagella flattened into two straight lines during the gyration. Thus, zoospores are not expected to swim in circles when interacting with no-slip boundaries as seen in case of E. coli with a rotating flagellar bundle. The ‘curved straight runs’ of zoospores that we observed in Figure 2(A) might result from rotational diffusion and thermal fluctuations.

Theoretical model of swimming individual P. parasitica zoospore.

(A) Images of an individual zoospore swimming with two flagella beating in sinuisoidal waveform shapes and its cell body gyrating with rate ϕ˙ while moving forward with speed U. The combined motion results in a helical swimming trajectory with pitch p and radius R. (B) Schematics showing the gyration of the cell body. (C) Theoretical model of a zoospore translating in a 2D plane using Resistive Force Theory. (D) The dependence of translational speed UX on the type-1 mastigoneme density (Nm). The range of Nm with symbol (⋆) indicates the values measured by TEM. (E) The effects of beating frequencies of the two flagella, f1 and f2, on zoospore speed UX, (F) power consumption of each flagellum Pk, (G) total power consumption of two flagella (P1+P2), (H) power distributed to the anterior flagellum and (I) propelling efficiency of both flagella η. In these plots, Nm is set at 13 μm-1.

Video 4
An individual zoospore swimming in water.

First, it swims straight with the helical trajectory due to the spontaneous gyration of the cell body, then performs a 180° turning.

We retrieve the parameters of the beating flagella including beating frequencies f and wavelengths λ, by applying kymographs on the cross-sections within the two flagella and normal to the moving direction of the zoospore. We present more details of the parameter retrieval with kymographs in Appendix. Our data show that when swimming in straight runs, the anterior flagellum of zoospores usually beats at f170Hz while the posterior flagellum beats with the frequency f2120Hz that is approximately 1.7-fold faster than the anterior’s. We focus on a very short duration of less than 50 ms, which is equivalent to a translation of less than 10 µm. Compared with the rotation motion at time scale of 1 s, we neglect the effect of the cell body’s rotation in this short duration.

We then develop a mathematical model to study how the dynamics of beating flagella helps generating thrust for the cell to move forward. We assume that the gyration of the cell body does not affect the shapes and motions of the flagella since the beating frequencies of the two flagella are much higher than the gyrational speed. The gyration also does not contribute to the translation as we consider it as a passive motion resulting from the chirality of zoospores. Thus, the swimming zoospore can be considered as a 2D model (Figure 3(C)) in which the cell body is an ellipse defined as x2/a2+y2/b2=1 in its body-fixed frame (xOy), with the anterior and posterior flagellum having sine waveform shapes defined as

(1) y(x,t)=Aksin(ωkt+(1)k2π[x+(1)kc]λk)

as (-1)kx-c, where Ak is the amplitude, ωk is the angular speed, λk is the wavelength of the anterior (k=1) and the posterior flagellum (k=2). The two flagella are attached to the cell body at two points both lying on x-axis and distanced to the origin O a gap of c, and beating with the wave propagation vw having directions against each other. The anterior has length L1 and diameter d1 while those of the posterior are L2 and d2. Additionally, there are multiple tubular type-1 mastigonemes with length h and diameter dm attached to the surface of the anterior flagellum with density Nm indicating the number of mastigonemes attached on a unit length of the flagellum. It is important to determine the flexibility of these mastigonemes as it would impact the ability of the mastigonemes to produce drag. We estimate the flexibility by a dimensionless parameter, which has been carefully characterized in previous studies (Khaderi et al., 2009; Namdeo et al., 2011), Fm=12μKAωh3/(Edm3), where μ is the fluid viscosity, K=2π/λ is the wave number, E is the Young modulus of the mastigonemes. With this estimation, if Fm<0.1, mastigonemes are considered as fully rigid. In case of zoospores’ mastigonemes, we achieve Fm at order of 10-4, which is much lower than 0.1. Thus, we can assume that the mastigonemes of zoospores are non-deformable and rigidly attached to the anterior flagellum. As a result, hydrodynamic interactions between neighboring mastigonemes can also be neglected. Additionally, we ignore the effects of the type-2 mastigonemes in producing drag due to their non-tubular and random structures.

Zoospores swim in water with very low Reynolds number (Re<<1), resulting in negligible inertia, dominant viscous force and the kinetic reversibility (Purcell, 1977; Qiu et al., 2014). Microswimmers with flexible flagella generate thrust from drag force acted by fluid on the flagellum segments. In our model, we use Resistive Force Theory (RFT) to deal with the calculation of fluid’s drag force on the two flagella of the zoospore. RFT has proven to be an effective and accurate method to predict the propulsive force and velocity of microswimmers regardless of the interactions of flagellum-flagellum or flagellum-body (Gray and Hancock, 1955; Lauga and Powers, 2009; Marcos et al., 2014). In case of zoospores where two flagella are in opposite directions, and the flagellum-body interaction is insignificant, RFT is a suitable solution to apply. Following this method, each flagellum is divided into an infinite numbers of very small segments with length dsk, and each segment is located in the body-fixed frame (xOy) by a position vector rk=xki+ykj, where i, j are the unit vectors in x- and y-direction, respectively; xk and yk satisfy the shape equation (Equation 1).

RFT states that the drag force by fluid acting on an infinitesimal segment ds of the flagellum is proportional to the relative velocity of fluid to the flagellum segment (Gray and Hancock, 1955; Hancock, 1953; Koh and Shen, 2016), as follows

(2) dFds=KNVNn^+KLVLl^,

where VN and VL are two components of relative velocity of fluid in normal and tangent direction to the flagellum segment, KN and KL are drag coefficients of the flagellum in normal and tangent to the flagellum segment, n^ and l^ are the unit vectors normal and tangent to the flagellum segment, respectively. The drag coefficients KN and KL are estimated by Brennen and Winet, 1977, which depends on fluid viscosity, the wavelength and diameter of a flagellum.

We then apply RFT on each flagellum of the zoospore to calculate the total drag force acting on it. For the posterior flagellum, each segment ds2 is a simple smooth and slender filament (see inset ds2 in Figure 3(C)), having drag coefficients KN2 and KL2. For the anterior flagellum, each segment ds1 contains additional Nmds1 mastigonemes. Using a strategy from previous models for flagella with mastigonemes (Brennen, 1975; Namdeo et al., 2011), we consider these mastigonemes stay perpendicular to the segment itself (see inset ds1 of Figure 3(C)) and also act as slender filaments experienced drag from water. Interestingly, due to the direction arrangement, the relative velocity normal to the flagellum segment results in drag force in tangent direction to the mastigonemes, and subsequently, the relative velocity tangent to the flagellum segment results in drag force in normal direction to the mastigonemes. In another perspective, we can consider the anterior flagellum receives additional drag from the mastigonemes, which is presented by two increased drag coefficients in normal and tangent direction, defined as

(3) KN1=(KNf1+NmhKLm1)

and

(4) KL1=(KLf1+NmhKNm1),

respectively. Here, KNf1 and KLf1 are the drag coefficients in normal and tangent direction of the flagellum filament, respectively; KNm1 and KLm1 are the drag coefficients in normal and tangent direction of the mastigonemes, respectively.

In low Reynolds number condition, total forces equate to zero due to approximately zero inertia. Thus, we derive translational velocity UX of the zoospore as shown in Equation 5

(5) UX=2π2KN1L1vw1(γ11)β121+2π2β122π2KN2L2vw2(γ21)β221+2π2β22KN1L1(γ111+2π2β12+1)+KN2L2(γ211+2π2β22+1)+6πμbξe,

where vwk=λkfk is the wave propagation velocity of the flagellum, γk=KLk/KNk is the drag coefficient ratio, βk=Ak/λk is the flagellar shape coefficient, and ξe is the shape coefficient of the ellipse cell body (see Appendix for the detailed derivatives).

We first study the effects of mastigonemes on zoospore speed by ploting the value of UX with different density of the mastigonemes, and varying the beating frequency of the posterior flagellum f2 while the anterior flagellum beats with a usual f1=70Hz in Figure 3(D). The dimensions and physical parameters of the zoospore’s cell body and two flagella are shown in Appendix. The plot shows that the appearance of mastigonemes results in a reversed thrust from the anterior flagellum. To illustrate this, when there are no mastigonemes on the front flagellum (Nm=0) and the posterior flagellum is excluded (f2=0, L2=0), the anterior flagellum generates a thrust in negative X-direction (UX<0). This agrees well with previous studies modeling a smooth reciprocal beating flagellum (Gray and Hancock, 1955; Hancock, 1953; Lauga and Powers, 2009). But since Nm>2, the velocity of the zoospore is reversed to positive X-direction due to the extra drag from the mastigonemes. This phenomenon was also described in hydrodynamics by Namdeo et al., 2011, and observed in experiment of Cahill et al., 1996. Interestingly, when changing directions, zoospores are observed to swim with the solely beating anterior flagellum to pull the body forwards while the posterior flagellum is immobile (Figure 4(A)) and Video 5, which confirms the thrust reversal ability of the mastigonemes. The beating frequency of the anterior flagellum in this case increases to f1110Hz. This finding also reassures the importance of mastigonemes on zoospore swimming, which is not similar to those of C. reinhardtii (Amador et al., 2020). The front flagellum of zoospores has fibrillar mastigonemes, similar to Chlamydomonas, but at higher density with tubular shape and larger in size, that could render into account of the different beating properties from the smooth posterior flagellum. However, high mastigoneme density (more than 20 per 1 µm flagellum length) shows mild effect on speed. From TEM images taken at the anterior flagellum, we estimate the mastigoneme density by averaging the number of mastigonemes manually counted over a flagellum length (See Appendix). We obtain Nm=13.0±0.8μm-1 (SD), which falls between the optimum range to generate speed (Figure 3(D)).

Active turning of individual P. parasitica zoospores in water.

(A) Images of a zoospore changing direction. The two flagella cooperate to help the cell body rotate and steer to a new direction achieving a turning angle Δθ. (B) Trajectory of the zoospore during the turning event. Three red arrows represent 3 back and forth stroke-like motions. (C) The speed U of the zoospore during the turning event. The turning starts when the speed begins to fluctuate with large magnitude and lower frequency, and lasts for a duration of τs with a rotation of the cell body followed by steering to the new direction. (D) The moving directions θ and the body orientation ψ of the zoospore during the turning event. (E) Images of the anterior flagellum of a zoospore beats with power and recovery stroke, similar to C. reinhardtii’s in a temporal zoom corresponding to the "Rotate" step of the turning event (but not from the same video as (A)). (F) Schematic to describe the gait of the flagella during a turning event. (1-2) Power stroke 1, (2-3) recovery stroke 1, (3-4) power stroke 2.

Video 5
A zoospore performing a turning event, which involves reducing speed, body rotation and steering resulting from active beating of anterior flagellum.

The posterior flagellum is immobile during the turning event.

To understand how the coordination of two flagella influences zoospore speed, we vary the beating frequency of one flagellum while the other’s remains constant and obtain the resultant speed (Figure 3(E)). We find that although both flagella contribute to zoospore speed, the anterior flagellum has larger impact on speed than the posterior does. For instance, the anterior flagellum can singly generate a speed threefold higher than the posterior flagellum can do at the same beating frequency. Moreover, the additional speed contributed by the anterior flagellum remains almost the same regardless of the varation of frequency of the posterior flagellum, while the speed contribution of the posterior flagellum decreases as the anterior flagellum increases its frequency. Since the contribution to zoospore speed is different between two flagella, we ask whether the energy consumption of each flagellum might also be different or equally distributed. In our model, each flagellar segment consumes a power deriving from the dot product between the drag force of water acting on the segment and the relative velocity of water to the segment, which can be written as Pvw/fdF (see Appendix for detailed derivatives). We achieve that, the power consumption of each flagellum depends on both flagella at low frequencies (f ≤ 40 Hz), and becomes solely dependent on its own beating at high frequencies (f ≥ 40 Hz) (Figure 3(F)). At high frequencies, the anterior flagellum consumes approximately fivefold more power than the posterior, given the same beating frequency. As a result, the total power consumed for both flagella becomes less dependent on the posterior flagellum as the anterior flagellum beats faster (Figure 3(G)). In Figure 3(H), we show the fraction of power consumed by the anterior flagellum over the total power consumption of the zoospore. We notice that, at the same beating frequency with the posterior flagellum, the anterior flagellum accounts for ∼80 % of the total power. Interestingly, when the frequency of the posterior flagellum is ∼1.7-fold higher than that of the anterior flagellum, both flagella consume the same amount of power. Indeed, this result agrees well with our experimental data, in which we obtain the anterior flagellum normally beats at 70 Hz and the posterior flagellum at 120 Hz. Thus, we can speculate that the energy is equally distributed for both flagella. In addition, we also estimate the propelling efficiency of the zoospore η=P0P1+P2, with P0 as required power to move the cell body forward at speed UX (see Appendix for derivatives). We achieve that η is higher as the anterior flagellum increases its frequency (Figure 3(I)). The efficiency reaches its maximum value at ∼1.2 % when the beating frequency of the posterior is ∼1.7-fold higher than that of the anterior flagellum. Overall, we show that the energy is shared in comparable manner between two flagella, but the anterior flagellum has more influence on zoospore speed, power consumption and propelling efficiency. On the other hand, the posterior flagellum provides a modest contribution to zoospore speed despite beating at higher frequency and consuming half of the energy. Taking the fact that the anterior flagellum can beat singly with the posterior flagellum staying on pause during turning events, we speculate that the anterior flagellum is the main motor of zoospores. Nevertheless, the function of the posterior flagellum remains cryptic and we investigate more on its role during turning events.

Turning events

We capture zoospores changing their directions by a unique active turning mechanism and an interesting coordination between two flagella. The videos of zoospore turning are recorded at 2000 fps with the same setup as the microscopic assay (Figure 4(A) and Video 5). Using Fiji and Trackmate, we track the positions of the zoospore and plot the trajectory, smoothed by moving average with step length n=40, during its turning event (Figure 4(B)). We then compute the zoospore speed U (Figure 4(C)), and the moving directions θ from the trajectory while manually measure body orientation ψ over time (Figure 4(D)). We observe that at first, to prepare for the turn, the zoospore reduces its speed as both flagella beat with smaller amplitudes. Then, the posterior flagellum instantaneously stops beating, which marks the beginning of a turning event (Figure 4 (A1-2)). The anterior flagellum now takes full control of zoospore motion during turning. The zoospore then perform two distinct sequences of motions right after the posterior stops beating: (i) rotation of the cell body out of the old direction resulting from a few repetitive stroke-like beating of the anterior flagellum (Figure 4 (A3)), then (ii) steering towards a new direction as the anterior flagellum switches back to normal beating with sinusoidal waveform to propel the body (Figure 4 (A4-5)). These two sequences of turning can be distinguished by two different patterns of trajectory during turning. While the rotation is indicated by multiple circular curves, in which each of them corresponds to a stroke-like back and forth beating motions, the steering results in straight line (Figure 4(B)). Additionally, the zoospore speed U during this period also consists of two different patterns of fluctuations (Figure 4(C)), while the moving direction θ changes from large fluctuations (for rotation) to stable direction (for steering) (Figure 4(C)). The turning event ends when the cell body stably moves in the new direction, which is indicated by the recovery of speed and the overlap of the moving direction and body orientation. The anterior flagellum continues to propel the cell body out of the location of the turning event (∼5 µm away), which we call ‘stabilize’ step (Figure 4 (A6)). We notice that in this step, the anterior flagellum beats at a higher frequency than usual (∼110 Hz, compared to normally at ∼70 Hz) and achieves a high-speed of ∼250 µm s-1. Finally, the posterior flagellum resumes its beating and the zoospore returns to the normal straight run state.

It is striking that the anterior flagellum is able to completely change its gait from sinusoidal traveling wave to stroke-like beating during the rotation step of the turning event. Thus, we need to have experimental evidence from direct observation of the shape of the anterior flagellum during this gait changing period, which is sometimes hidden underneath the cell body due to the off-axis postion of the flagellar base, to extend our understanding on this turning behavior. We capture new videos of zoospore turning events, but the focus plane is slightly offset from the focus plane of the cell body (Figure 4(E) and Video 6). We observe that the anterior flagellum instantaneously perform continuous power and recovery strokes, similar to the breast-stroke beating of Chlamydomonas’s flagella. As a result, the cell body can rotate quickly about a fixed point, which helps the zoospore make a sharp turn. We summarize the turning of zoospores by a schematic in Figure 4(F). Indeed, this rotation motion is similar to that of uniflagellate C. reinhardtii (Bayly et al., 2011), which strengthens the evidence for the actively switchable beating pattern of zoospores’ anterior flagellum. While the anterior flagellum plays a major role in turning events on top of straight runs, the posterior flagellum only stays immobile throughout the process. Here, we can confirm that the posterior flagellum does not act as a rudder to steer the direction. Instead, it is fully stretched during turning events and might contribute to increase drag at one end of the cell body. The function of the posterior flagellum is not completely clear regarding thrust production during translation or turning. Thus, we speculate that it might contribute to other non-physical activities such as chemical and electrical sensing. The advantage of zoospore turning mechanism is that it allows them to actively and quickly achieve a new direction, which is not the case of other microswimmers such as the tumbling of E. coli’s (Darnton et al., 2007; Perez Ipiña et al., 2019) or Chlamydomonas’s (Bennett and Golestanian, 2015; Polin et al., 2009).

Video 6
A zoospore during a turning event changes gait of its anterior flagellum from sinuisoidal wave to power and recovery stroke, similar to C. reinhardtii’s.

Conclusion

We have performed the first systematic study of the swimming pattern and spreading features of P. parasitica zoospores, a plant pathogen, which is considered a major agricultural threat. Combining high-speed imaging and Resistive Force Theory, we show how the two opposite flagella are coordinated in producing thrust by beating together, allowing the microorganism to achieve high-speed swimming during straight runs. Furthermore, we find that turning is a coordinated process, in which the the posterior flagellum stops beating, while the anterior flagellum actively moves causing the cell body to rotate. Finally, we explain how fast-swimming periods and active turning events combine to produce a diffusion coefficient of D=3.5×10-4cm2s-1, a quantity that characterizes spatio-temporal spreading of this pathogen during plant epidemics.

It is worth stressing the motility pattern exhibited by the zoospores represents an Eukaryotic version of the ‘run-and-tumble’ motility class exhibited by bacteria peritrichous bacteria. Several eukaryotic swimmers, for example spermatozoa, do not exhibit such kind of motility pattern, but C. reinhardtii have been reported to also fall into this category (Polin et al., 2009). There are, however, important differences. Chlamydomonas possess two identical flagella located at one tip of the cell. Reorientation events occur during asynchronous beating periods of the two identical flagella, while straight runs require synchronous beating. In sharp contrast to this picture, we show that in zoospores while straight runs also involve a coordinated beating of the opposite and different flagella, turning involves temporary halting of posterior flagellum, while the anterior flagellum continues beating. This strongly suggests that P. parasitica navigates using a fundamentally different internal regulation mechanism to control swimming, than C. reinhardtii, a mechanism that is likely to be present in other Eukaryotic swimmers with two opposite and different flagella.

We believe our findings on the coordination of two flagella bring more insights on zoospore swimming dynamics. It was also not known from the literature about the role of each flagellum on the straight runs, and on turning events in particular. We show that although the energy is shared in comparable manner between both flagella, the anterior flagellum contributes more to zoospore speed. Zoospores actively change directions thanks to the sole beating of the anterior flagellum. We believe that anterior flagellum could be the main motor of zoospores that is in charge of generating speed, changing beating patterns from sinusoidal wave to power and recover stroke to quickly rotate the body, while the posterior flagellum might play a role in chemical/electrical sensing and providing an anchor-like turning point for zoospores, instead of acting like a rudder as previously hypothesized. These findings pave new ways for controlling the disease since now we can have different strategies on targeting one of the flagella.

Materials and methods

P. parasitica mycelium culture and zoospore release

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We culture mycelium of Phytophthora parasitica (isolate 310, Phytophthora INRAE collection, Sophia-Antipolis, France) (Bassani et al., 2020b; Galiana et al., 2019) routinely on malt agar at 24 °C in the dark. To produce zoospores, we prepare the mycelium which is grown for one week in V8 liquid medium at 24 °C under continuous light. The material is then drained, macerated and incubated for a further four days on water agar (2 %) to induce sporangiogenesis. Zoospores are released from sporangia by a heat shock procedure. We place a petri-dish of mycelium inside a refrigerator at 4 °C for 30 min, then pour 10 mL of 37 °C distilled water on top of the mycelium and continue to incubate it at room temperature (25 °C) for another 30 min. Zoospores then escape from sporangia and swim up to the water. The zoospore suspension is then collected for further experiments.

Scanning electron microscopy and transmission electron microscopy with negative staining

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For Scanning Electron Microscopy and Transmission Electron Microscopy, cell pellets are fixed in a 2.5 % glutaraldehyde solution in 0.1 M sodium cacodylate buffer (pH 7.4) at room temperature (∼25 °C) for 1 h and then stored at 4 °C. For Scanning EM observations, after three rinsing in distilled water, protists are filtered on a 0.2 µm isopore filter. Samples on filters are subsequently dehydrated in a series of ethanol baths (70 %, 96 %, 100 % three times, 15 min each). After a final bath in hexamethyldisilazane (HMDS, 5 min), samples are left to dry overnight. Samples on filters are mounted on Scanning EM stubs with silver paint and coated with platinum (3 nm) prior to observing. The Scanning EM observations are performed with a Jeol JSM-6700F scanning electron microscope at an accelerating voltage of 3 kV.

For TEM observations, samples are prepared using the negative staining method. After three rinsing in distilled water, a drop of cells suspension (∼10 µL) is left for 5 min on a TEM copper grid (400 mesh) with a carbon support film. The excess liquid is removed with a filter paper. Subsequently, staining is done by adding a drop of 0.5 % (w/v) aqueous solution of uranyl acetate on the grid for 1.5 min, followed by removal of excess solution. The TEM observations are carried out with a JEOL JEM-1400 transmission electron microscope equipped with a Morada camera at 100 kV.

Microscopic assays of zoospores

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We pipette a droplet of 10 µL water containing zoospores onto a microscopic glass slide and spread the droplet to thoroughly cover the marked area of 1 × 1 cm. We then achieve a thin water film of approximately 100 µm thickness. We do not put coverslips on the water film to prevent the unwanted interactions between the zoospores and rigid surface of coverslips. We observe the swimming of individual zoospores inside the water film under a bright field transmission microscope (Nikon Eclipse Ti2, Minato, Tokyo, Japan) at 40× objective with the high-speed camera Phantom v711 (Vision Research, NJ, USA). For the experiment to observe the swimming trajectories of the zoospores, we use 4× objective to capture a large swimming region of 5000 × 4000 µm. The captured images are processed by Fiji with Trackmate plugin.

Estimation of trajectory parameters

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Positions of an individual zoospore are captured at each time frame Δt. At each tj=jΔt (j=1,2,3,), the zoospore has a position zj=(x(tj),y(tj)). First, we smooth the trajectory by moving average with step n. The smoothed positions Zj,n are calculated as,

Zj,n=1njn+j-1zj.

Each new position Zj,n possesses a velocity vector with speed,

Uj,n=1Δtzj+n-zj,

and moving direction (angle between velocity vector and x-axis).

θj=atan(yj+n-yjxj+n-xj).

Appendix 1

Obtaining characteristics of beating flagella by kymograph

We first use Fiji with StackReg plugin to fix the position of the cell body in the swimming videos, and only the two flagella remain beating.

We retrieve the parameters of the beating flagella by applying kymographs on multiple cross-sections which are along to or normal to the moving direction at the positions shown in the figure below. These kymographs help converting the complex time-dependent 2D image data of the flagella from (X,Y,t) to separate signals (X,t) and (Y,t). As a result, the kymographs at cross-section (1) and (2) give us the average amplitudes A of the waveform shapes of the two flagella, and the ones at (3) and (4) provide us with information of beating frequencies f and wavelengths λ.

Appendix 1—figure 1
Strategy to apply kymograph to obtain characteristics of beating zoospore flagella.

Appendix 2

Variation of Uth

To verify if the way we chose the value of Uth will affect the result of turning angles and other swimming parameters, we vary the Uth value by ±10 % of the chosen value, which ranges from 100 to 122.5 µm s-1. We plot the running time τr, stopping time τs and turning angles Δθ according to the varied Uth. Data are shown in the figure below. We see that the changes do not affect the results of τr, τs and Δθ estimation. Thus, we believe the sensitivity of Uth selection can be tolerated by ±10%.

Appendix 2—figure 1
Estimation of τr, τs and Δθ for different variation of Uth.

(A) τr, τs and (B) Δθ for Uth-10% (C), τr τs and (D) Δθ for Uth+10%.

Appendix 3

Characteristics of helical trajectories

From the microscopic assays with high-speed camera and 40× objective, we observe zoospores swimming in helical trajectories. We manually measure the characteristics of these helical trajectories and present the data in the table below.

Appendix 3—table 1
Characteristics of helical trajectories of zoospores during straight runs.
SamplePitch p (μm)Radius R (μm)Gyrational speedϕ˙ (rads1)
11223.2503.64 π
21234.4354.00 π
31454.1292.86 π
41643.3902.5 π
51784.8502.1 π
61123.0104.44 π
71204.3004.44 π
8964.2445 π
91274.0903.33 π
101064.7444 π

Appendix 4

Estimation of mastigoneme density

Mastigoneme density is an important parameter, which determines the thrust reversal effect of the anterior flagellum and generates speed for zoospores. Using TEM, we capture images of anterior flagellum containing the mastigonemes. We first select a longitudinal flagellum length and manually count the total number of mastigonemes attached along that distance (See figure below). The mastigoneme density Nm is calculated as the ratio between the number of counted mastigonemes and the selected flagellum length.

Appendix 4—table 1
Measurement data of mastigonemes in TEM images.
SampleNo. of mastigonemesFlagellum length (μm)Density (μm-1)
115211.84212.8357
216811.59714.4865
31138.62713.0984
418113.59013.3186
519815.19513.0306
617713.99412.6483
7887.49911.7349
Appendix 4—figure 1
Strategy to estimate mastigoneme density.

Appendix 5

Hydrodynamics of two flagella in a swimming zoospore using Resistive Force Theory

Following the schematics of Figure 3(a) in the main text, we consider a parameter sk as the distance along the flagellum from the root to the segment dsk, then we define dimensionless constants αk as the ratios of the wavelength to the arc length of the anterior (k=1) and posterior flagellum (k=2), respectively. Whereas

(6) α1=λ1L1=x1-cs1

and

(7) α2=λ2L2=-(x2+c)s2.

Thus, we can express the segment position rk in terms of sk, as follows

(8) r1=(α1s1+c)i+A1sin(ω1t-2πs1L1)j,

and

(9) r2=(-α2s2-c)i+A2sin(ω2t-2πs2L2)j.

We achieve the velocity of the flagella relative to the cell body as

(10) vf/b=drk/dt=ωkAkcos(ωkt-2πskLk)j.

The beating of flagella results in the movement of the cell body relative to water, with a velocity:

(11) vb/w=UXi.

We neglect the velocity of the cell body in Y-direction with the assumption that the zoospore swimming is very directional and UX>>UY.

Resistive Force Theory (RFT) states that the drag force by fluid acting on an infinitesimal segment d s of the flagellum is proportional to the relative velocity of fluid to the flagellum segment, as follows

(12) dFds=KNVNn+KLVLl,

where VN and VL are two components of relative velocity of fluid in normal and tangent direction to the flagellum segment, KN and KL are the drag coefficients of the flagellum in normal and tangent to the flagellum segment, n^ and l^ are the unit vectors normal and tangent to the flagellum segment, respectively.

Equation (12) can be expressed as:

(13) dFds=KN(vw/fn)n+KL(vw/fl)l=KN(vw/f(vw/fl)l)+KL(vw/fl)l=KN[(vw/fl)(KLKN1)l+vw/f],

where vw/f is the relative velocity of water to the flagellum, which is achieved as

(14) vw/f=vb/wvf/b,

and the tangent unit vector l^ is expressed as

(15) l=1|rs|rs.

During the derivative, we use an assumption that the flagella have small amplitude deflection (A<<L). Thus, we can approximate that cos2(2πskLk-ωkt)0.5. This helps to simplify the term |rs|=αk2+4π2Ak2Lk2cos2(2πskLk-ωkt)=αk2+2π2Ak2Lk2.

The drag coefficients KN and KL is estimated by Brennen and Winet, as follows:

(16) KN=4πμln(4λd)-2.90,
(17) KL=2πμln(4λd)-1.90,

where μ=8.9×10-4Pas is the water viscosity at 25C, λ is the wavelength and d is the diameter of the flagellum. With UY being neglected, we also consider that the two flagella do not generate force in Y-direction, but only induce thrust in X-direction. Hence,

(18) dFdFXi=(dFi)i.

We then apply RFT on each flagellum of the zoospore to calculate the total drag force acting on it. For the posterior flagellum, each segment ds2 is a simple smooth and slender filament, having drag coefficients KN2 and KL2. following equation (16) and (17). From equation (13) and (18), we derive the drag force of water acting on posterior flagellum as

(19) FX,2=KN2L2[-2π2vw2(γ2-1)β22-(γ2-1)UX1+2π2β22-UX],

where vw2=λ2f2 is the wave propagation velocity, γ2=KL2/KN2, β2=A2/λ2. For the anterior flagellum, each segment ds1 contains additional Nds1 mastigonemes which are considered perpendicular to the segment itself. These mastigonemes also act as slender filaments experienced drag from water. Interestingly, due to the direction arrangement, the relative velocity normal to the flagellum segment results in drag force in tangent direction to the mastigonemes, and subsequently, the relative velocity tangent to the flagellum segment results in drag force in normal direction to the mastigonemes. Hence, the total drag force acting on a segment of the anterior flagellum is derived as:

(20) dF1ds1=(KNf1+NhKLm1)VN1n1+(KLf1+NhKNm1)VL1l1,

where N is the density of mastigonemes, h is the length of each mastigoneme, VN1 and VL1 are two components of relative velocity of fluid in normal and tangent direction to the segment ds1, KNf1 and KLf1 are the drag coefficients in normal and tangent direction of the flagellum filament, respectively; KNm1 and KLm1 are the drag coefficients in normal and tangent direction of the mastigonemes, respectively. KNf1, KLf1, KNm1 and KLm1 are also calculated from equation (16) and (17). In another perspective, we can consider the anterior flagellum receives additional drag from the mastigonemes, which is presented by two increased drag coefficients in normal and tangent direction defined as

(21) KN1=(KNf1+NmhKLm1)

and

(22) KL1=(KLf1+NmhKNm1),

respectively. Here, Nm is the density of mastigonemes; h is the length of each mastigoneme; KNf1 and KLf1 are the drag coefficients in normal and tangent direction of the flagellum filament, respectively; KNm1 and KLm1 are the drag coefficients in normal and tangent direction of the mastigonemes, respectively. KNf1, KLf1, KNm1 and KLm1 are also calculated from equation (16) and (17). The total fluid drag force acting on the anterior flagellum is also derived from equation 13 and 18:

(23) FX,1=KN1L1[2π2vw1(γ1-1)β12-(γ1-1)UX1+2π2β12-UX],

where vw1=λ1f1 is the wave propagation velocity of the anterior flagellum, γ1=KL1/KN1, β1=A1/λ1.

At the same time, the ellipsoidal cell body moving with velocity UX also experiences a drag force from water (following Happel and Brenner)

(24) Fd,cell=-6πμbξeUXi,

where μ is water viscosity, ξe is the shape coefficient of the ellipse cell body in 2D. ξe is estimated as

(25) ξe=4/3(κ2-1)2κ2-1κ2-1ln(κ+κ2-1)-κ,

with κ=a/b being the ellipse body ratio. In low Reynolds number condition, total forces equate to zero due to approximately zero inertia. Thus,

(26) ΣF=F1+F2+Fd,cell=0.

Combine equation (19), (23) and (24), we achieve translational velocity UX of the zoospore as shown in Equation 5.

Appendix 6

Power and efficiency of two flagella during in zoospore swimming

We derive the power that each flagellum generates during zoospore swimming to investigate how the two flagella cooperate and contribute to the swimming. The power generated by the anterior flagellum P1 is calculated as

(27) P1=s1=0L1v1dF1,

where v1=vw/f(1) is the relative velocity vector of water to each flagellar segment, and dF1 is the drag force of water acting on each flagellar segment. From (13), we have

(28) v1dF1=KN1[(γ11)(v1l^1)2+v12]ds1.

Then, we can derive P1 from (14), (15) and (28) as

(29) P1=KN1L1[(γ1-1)(2π2vw1β12-UX)21+2π2β12+UX2+2π2vw12β12].

Similarly, we can also derive P2 as

(30) P2=KN2L2[(γ2-1)(2π2vw2β22+UX)21+2π2β22+UX2+2π2vw22β22].

The useful power P0 required to propel the cell body with a speed UX can be derived as

(31) P0=Fd,cellUX=6πμbξeUX2.

The efficiency of the two flagella in propelling the cell body is estimated as

(32) η=P0P1+P2.

Appendix 7

Dimensions and physical parameters of zoospore’s flagella

With the characteristics of beating flagella obtained by kymograph, we calculate the values of drag coefficients KN, KL, flagellum shape ratio β, and drag coefficient ratio γ. The results are presented in the table below.

Appendix 7—table 1
Physical parameters of beating flagella of P parasitica zoospores in normal conditions.
StructuresParametersDenotesValue
AnteriorAmplitude (μm)A11.6
flagellumWavelength (μm)λ17.5
Length (μm)L123.4
Beating freq. (Hz)f174
Drag coeff. of filamentsKNf16.558910-15
(Nsμm-2)
KLf12.06710-15
Drag coeff. of mastigonemesKNm2.790610-15
(Nsμm-2)
KLm1.116710-15
Mastigoneme length (μm)h1.5
Mastigoneme density (μm-1)Nm13
(A1/λ1)ratioβ10.21
Drag coeff. ratio (KL1/KN1)γ12.047
PosteriorAmplitude (μm)A22.9
flagellumWavelength (μm)λ215.17
Beating freq. (Hz)f2128
Length (μm)L225.8
Drag coefficientsKN24.641510-15
(Nsμm-2)
KL21.640110-15
(A2/λ2)ratioβ20.19
Drag coeff. ratio (KL2/KN2)γ20.3534

Appendix 8

Data publication

Our experimental data are accessible via Zenodo (https://doi.org/10.5281/zenodo.4710633).

In the data, we include

  1. Datasets of all zoospore positions along multiple trajectories in the experiment of Figure 2,

  2. A MATLAB file to compute all the statistical results in Figure 2(D–G),

  3. A MATLAB file containing the simulation model presented in Figure 2(H),

  4. Datasets of zoospore positions, speed, moving directions, body orientations during the turning, presented in Figure 4(A–D).

Data availability

All data generated and simulation files are available via Zenodo using this URL: https://doi.org/10.5281/zenodo.4710633https://doi.org/10.5281/zenodo.4710633. In the data, we include: (1) datasets of all zoospore positions along multiple trajectories in the experiment of Figure 2, (2) a MATLAB file to compute all the statistical results in Figure 2(D-G), (3) a MATLAB file containing the simulation model presented in Figure 2(H), (4) datasets of zoospore positions, speed, moving directions, body orientations during the turning, presented in Figure 4(A-D).

The following data sets were generated
    1. Tran QD
    2. Galiana E
    3. Thomen P
    4. Cohen C
    5. Orange F
    6. Peruani F
    7. Noblin X
    (2021) Zenodo
    Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores.
    https://doi.org/10.5281/zenodo.4710633

References

    1. Brennen C
    (1975)
    Locomotion of flagellates with mastigonemes
    Journal of Mechanochemistry & Cell Motility 3:207–217.
    1. Carlile M
    (1983)
    Motility, taxis and tropism in phytophthora
    Phytophthora: Its Biology, Taxonomy, Ecology and Pathology 1:95–107.
    1. Drenth A
    2. Sendall B
    (2004)
    Economic Impact of Phytophthora Diseases in Southeast Asia
    Diversity and Management of Phytophthora in Southeast Asia ACIAR Monograph 114:10–28.
    1. Keaveny EE
    2. Shelley MJ
    (2009) Hydrodynamic mobility of chiral colloidal aggregates
    Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 79:051405.
    https://doi.org/10.1103/PhysRevE.79.051405

Decision letter

  1. Raymond E Goldstein
    Reviewing Editor; University of Cambridge, United Kingdom
  2. Aleksandra M Walczak
    Senior Editor; CNRS LPENS, France

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Decision letter after peer review:

Thank you for sending your article entitled "Cooperation of two opposite flagella allows high-speed swimming and active turning in zoospores" for peer review at eLife. Your article is being evaluated by 2 peer reviewers, and the evaluation is being overseen by a Reviewing Editor and Aleksandra Walczak as the Senior Editor.

While the reviewers and editor are supportive of the paper, it was our consensus opinion that a substantial amount of revision to the manuscript is needed to clarify the points below. Furthermore, since active turning and steering feature prominently in the title and abstract, it would be crucial to further investigate the flagellar motion and gait changes during turns. Without this, we believe that the conclusions of the paper are overstated.

Reviewer #2:

The capacity for swimming microorganisms to efficiently explore their environment can be essential for their survival and proliferation. This manuscript by Galiana et al., examines the swimming characteristics of P. parasitica, a plant pathogen known for causing widespread disease and economic loss. The authors present high-speed video recordings which reveal how individual cells execute turning events during their swimming motion. There is considerable experimental data, which in combination with a mathematical model for flagellar motion, sheds light on how the two flagella collectively produce locomotion and turning events.

The turning events are largely portrayed as being due to temporary arresting of the posterior flagellar beating. E.g., "turning requires the posterior flagellum to halt, while the anterior one continue beating". However, while stopping the posterior beating is necessary, it is not sufficient. What is lacking is a detailed explanation of precisely how the cells turn. From Video 4, it appears that the anterior flagellum changes its gait completely from a sinusoidal travelling wave to something more reminiscent of Chlamydomonas, with distinct power and recovery strokes (but with mastigonemes). The oscillations of angle of Figure 4d indeed suggest that a distinct gait is employed to turn the cell. The authors mention this on line 389, but this is not investigated further, citing imaging capabilities. Cell turning events seem to require coordinating the stop/start motion of one flagellum and distinct gait changes in the other, but the mechanism(s) behind this remain unclear.

From the trajectories presented in Figure 2, numerous quantities are extracted, including swimming speed, turning angle, run times, etc. The swimming speed threshold is essential for delineating turns events from 'runs', and one method for extracting Uth is presented. This leads to the conclusion that the most likely reorientation angle (Δθ, see Figure 2g) is actually 0 degrees. i.e. the cell stops and then continues in the same direction. It could be that this is an artefact of a relatively high value of Uth, which misclassifies one run into two smaller ones. This sensitivity is further shown in Figure 2b – increasing Uth to just ~125 microns/second would result in one single turning event (taus) instead of three distinct ones. It is not clear from the data how the results would change if Uth were varied in a sensitivity analysis, or defined in another way.

The authors have presented an experimental system which is capable of recording reasonably long trajectories of swimming P. parasitica cells, and an analysis pipeline which can extract statistical distributions of various swimming properties. The overarching assumption is that the 2D measurements can be extrapolated to three dimensions. Given the displayed trajectories are quite long (several millimetres), it seems that there are very few issues with the cells swimming out of focus. It is likely that the shallow chamber (100 microns) helps to maintain the cells within the focal plane and helps to minimise biases in the run time measurement. However, if that is the case, it's hard to know the effect that confinement has on the motility characteristics. It could be that the stop-start motion with Δθ=0 actually represents failed out-of-plane turning events.

The authors utilised microscopic parameters from the swimming motion to predict the bulk diffusivity. It was mentioned that the direct measurement of D is unreliable given the small number of trajectories and their short duration. However, this seems to be inconsistent with the supplementary videos, which show cells in focus for extended periods of time and allow collection of trajectory data. Even if individual MSD measurements cannot be collected in large sets, perhaps a bulk diffusivity could be measured at lower magnification. At the moment, there is no strong quantitative link between the simulated diffusivity and the actual spreading of cells.

A simplified mathematical model is developed in which resistive force theory (RFT) applied to the two flagella calculates the propulsive force on the cell body. This is then used to derive a closed form expression for the swimming speed (Equation 5), which predicts values commensurate with the observed swimming speeds (Figure 3). It is an interesting finding that the mastigonemes modify the sign of the propulsive force (also noted in previous works), enabling the anterior flagellum to pull the cell through the fluid. The planar motion of the flagellum in the model seems reasonable given the dynamics presented in Video 3. However, it is unclear by what mechanism the cells rotate as they swim. Perhaps this has something to do with the off-axis position of the flagellar base. Since the helical motion of the cells features prominently in the paper and is likely important for overall dispersal, it would be great if the model could account for viscous torques, calculate the cell body rotation rate and characteristics of the helical path.

The observed dynamics have been classified into straight runs and turning events. However, many of the 'runs' are certainly not straight (see Figure 2). It is not clear whether these curved trajectories are due to rotational diffusion, or perhaps from hydrodynamic interactions with the boundaries (bacteria are known to swim in circles near no-slip walls). This could have significant implications for the dispersal calculations, and for classification of events within the trajectories.

In order to calculate a cell's 'run time', it is necessary to visualise two successive turning events which bookend a single run. However, for cells swimming in three dimensions, the probability of observing a given run length depends on the value of the run length. Can the authors please provide information about any biases in their data collection, and the extent of any biases in the presented distributions? This could include discussion of depth of field, chamber height, and whether any cells were excluded.

The motility strategy examined in this paper is described as "steering" and is presented as a possible method for pathogenic cells to target the plant host. However, the dynamics are all spatially isotropic, and it is not clear how cells could navigate towards specific chemical cues (e.g. potassium, physical cues, electrical signals).

The motor efficiency is determined in terms of the swimming speed to wave propagation. There are many ways of calculating efficiency in low Reynolds number hydrodynamics, many of which include power/energy calculations. The authors allude to a link between power and drag due to mastigonemes, but it's hard to determine from the presented results how much energy the cell needs to swim. I think it would be very helpful to expand the section on efficiency, connecting with other established methods, and results for other organisms.

Quantifying the microscale trajectory features and predicting the collective cell diffusivity requires a threshold value of Uth. It would be very important to examine the sensitivity of the measurements to the value of Uth, and explore the implications if another definition was chosen.

Figure 2. Some of the time-dependent processes are plotted in terms of frame number (t/dt), and others in absolute time (t). It would be best to include all processes in terms of t, so that conclusions are independent of frame rate.

Line 38 mentions that E. coli possess "a passive helical flagellum", but they possess a bundle of these. Please correct the numbers.

There is a need to better distinguish between axial rotation and cell "rotation" during turns. Perhaps it would be better not to use the same word.

Line 58. The organisms can apparently swim for several hours. However, this may be very short compared to the timescales required to find a plant. Can the authors please elaborate on how motility can be sustained in a typical environment, and how long it might take for a cell to reach its target (assuming no active navigation)?

The article should be carefully read by a native English speaker. For example, "underwhelming knowledge" is not an appropriate way of describing open questions. "Flimsy" also refers to an object's structural integrity and not its shape. The word "accumulating" is used extensively throughout the paper but is not appropriate since it implies temporal integrating. i.e drag and velocity don't 'accumulate' along the flagellum.

Reviewer #3 (Recommendations for the authors):

The authors present a study of the swimming behaviour of the zoospores of the water mold Phytopthora, which combines experimental imaging of fixed cells (to examine structure), image capture and analysis of multiple swimming cells to examine bulk swimming behaviour, high-speed imaging to characterise on the spot turning behaviour, and an analytical mathematical model of the straight "run" swimming behaviour that incorporates the mastigonemes on the anterior flagellum.

In terms of what is already known about these systems, it is already known that Phytophora zoospores swim with two flagella at the high speeds shown herein, and that the anterior flagellum is covered with mastigonemes (see for instance the authors' previous work DOI: 10.1016/j.csbj.2020.10.045). It has also been known for some time that mastigonemes reverse the expected direction of propulsion for a flagellum beating with a sperm-like (travelling wave) waveform, so this behaviour is expected, and indeed commented on in the authors' previous work. The model provided is based upon previous models (see eg https://doi.org/10.1063/1.3608240), which should be made clearer in the text, with the adaptation being that there are 2 flagella and a body here.

The main novel components are (1) the discussion that the anterior flagellum accounts for the majority of the propulsion, and (2) the characterisation of the on-the-spot turning (as far as I know). The first point is based on analysis from the analytical model. My concerns with this conclusion are three-fold. Firstly, it relies on mastigonemes remaining rigid and normal to the tangent of the main flagellum, whereas some bending with the flow is to be expected (reducing their impact). Secondly, the resistive force theory model, while qualitatively powerful, does not include hydrodynamic interactions between neighbouring mastigonemes, which may also reduce their impact. Thirdly, it is quite sensitive to the mastigoneme density once this drops to around 10 per micron (the way in which the mastigoneme density was estimated, and the data, should be made clear in the manuscript), and fourthly, the posterior flagellum naturally beats at around twice the frequency (probably because they are expending the same amount of energy), so I do not feel that the conclusion "we consider the anterior flagellum as the main motor of zoospores because it has the ability to immensely increase or decrease speed with a small adjustment of its beating frequency" is justified.

The characterisation of the on-the spot turning from high speed image microscopy is very nice, to the best of my knowledge novel, and the analogues to peritrichous bacteria and Chlamydomonas well drawn up. This section is well described (though not modelled), but would probably benefit from a schematic in addition to the set of experimental images.

The paper would benefit from a clearer exposition of what the novel components are in relation to previous work, and a link back to the motivation of crop damage and how this understanding of motility may be used in future pest control strategies.

While I enjoyed reading the article, the authors should endeavour to make it clearer in certain places what has come before, and what is the novel component. For instance, the modelling seems to follow the arguments of https://doi.org/10.1063/1.3608240, and while this is cited elsewhere, I believe this should be stated very clearer in the model section. Secondly, there are a few sentences which mislead with respect to aspects of the novelty, for instance:

1. "Despite the relevance of zoospore spreading in the epidemics of plant diseases, it is not known how these zoospores swim and steer with two opposite beating flagella." For the swimming this is clearly known, as the authors commented on in their previous work, it is the turning I believe that was not well characterised.

2. "Here, we introduce a new type of microswimmer, named Phytophthora zoospores, which has two different flagella collaborating for unique swimming and turning mechanisms (Figure 1(a))." – you have presented work previously on the swimming of this organism.

I believe the data on mastigoneme density is critical to one of your conclusions, and should be presented carefully, and I believe this conclusion about the anterior flagellum being the main driver for motility is probably not correct, more broadly – it certainly needs more careful treatment.

https://doi.org/10.7554/eLife.71227.sa1

Author response

While the reviewers and editor are supportive of the paper, it was our consensus opinion that a substantial amount of revision to the manuscript is needed to clarify the points below. Furthermore, since active turning and steering feature prominently in the title and abstract, it would be crucial to further investigate the flagellar motion and gait changes during turns. Without this, we believe that the conclusions of the paper are overstated.

We have performed additional experiments to observe the shape of the zoospore flagella during turning. Indeed, as the Reviewer 2 predicted, the anterior flagellum is shown to perform power and recovery strokes, similarly to Chlamydomonas’s. It also shows that the anterior flagellum of zoospores can completely change its gait from sinusoidal beating to distinct power and recovery strokes during turning events. We believe the experimental evidence is more convincing than the simulation as we planned in our Action plan. So, we instead just performed this experiment and did not add the simulation into our article. The details of the new experiment are presented in the question below of Reviewer 2. Additionally, we have changed the title of the paper into “Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores”, as we think coordination is a more suitable word than “cooperation” to describe the functions of the two flagella. Also, in the conclusion, line 466, we have changed the term “turning requires halting of posterior flagellum…” into “ turning involves temporary halting of posterior flagellum…” The word “requires” might be misleading since it is probably not a condition for the turning.

Reviewer #2 (Recommendations for the authors):

The capacity for swimming microorganisms to efficiently explore their environment can be essential for their survival and proliferation. This manuscript by Galiana et al., examines the swimming characteristics of P. parasitica, a plant pathogen known for causing widespread disease and economic loss. The authors present high-speed video recordings which reveal how individual cells execute turning events during their swimming motion. There is considerable experimental data, which in combination with a mathematical model for flagellar motion, sheds light on how the two flagella collectively produce locomotion and turning events.

The turning events are largely portrayed as being due to temporary arresting of the posterior flagellar beating. E.g., "turning requires the posterior flagellum to halt, while the anterior one continue beating". However, while stopping the posterior beating is necessary, it is not sufficient. What is lacking is a detailed explanation of precisely how the cells turn. From Video 4, it appears that the anterior flagellum changes its gait completely from a sinusoidal travelling wave to something more reminiscent of Chlamydomonas, with distinct power and recovery strokes (but with mastigonemes). The oscillations of angle of Figure 4d indeed suggest that a distinct gait is employed to turn the cell. The authors mention this on line 389, but this is not investigated further, citing imaging capabilities. Cell turning events seem to require coordinating the stop/start motion of one flagellum and distinct gait changes in the other, but the mechanism(s) behind this remain unclear.

We thank the Reviewer for a very important suggestion that the turning mechanism of zoospores shares similarities with the behavior observed in Chlamydomonas. Indeed, Figure 4D suggests that turning in zoospores occurs via power and recovery strokes. Despite lacking of 3D observations of the flagella during turning, we observe the zoospore turning at different 2D view angles and notice that the turning happens on a same focus plane. This suggests that the anterior flagellum has changed its swimming pattern but its beating is still a planar motion. Importantly, we observe that during turning the dynamics of the anterior flagellum is fundamentally different from the sinusoidal waveform observed during run phases. Moreover, we find that the anterior flagellum of zoospores, which possesses mastigonemes, performs power and recovery strokes, similarly to the flagellum beating of Chlamydomonas. We also observed that while the anterior flagellum takes control of the zoospores during turning, the posterior flagellum completely stops beating. We speculate that the posterior flagellum contributes to chemical/electrical sensing.

Though a full fluid mechanics understanding of the turning – which is beyond the scope of the current manuscript – is missing, our study identifies key distinct elements of the turning of zoospores: beyond providing a statistical characterization of the duration and turning angles of these events, we observe that during turning the posterior flagellum does not beat, while the anterior one does it, and its gait is different from the sinusoidal travelling wave that characterizes run phases. These observations suggest that turning in zoospore is different from turning observed in Chlamydomonas and other microorganisms. We stress that to the best of our knowledge, this is the first systematic quantitative study of the swimming pattern of Phytophthora. A detailed fluid mechanics understanding of the turning is beyond the scope of the current study and represents an experimental and theoretical challenge.

We have added Figure 4E and Supp. Video 6 to show the gait changing of the anterior flagellum during turning, and Figure 4F to show the schematics summarizing the turning event of zoospores. We have rewritten the whole sub-section “Turning events” (from line 399 to 447) to better describe this gait changing mechanism. We also include the gait changing finding in the abstract (line 2427):

“Furthermore, we find that turning involves a complex active process, in which the posterior flagellum temporarily stops, while the anterior flagellum keeps on beating and changes its pattern from sinusoidal waves to power and recovery strokes, similar to Chlamydomonas’s breaststroke, to reorient its body to a new direction”

From the trajectories presented in Figure 2, numerous quantities are extracted, including swimming speed, turning angle, run times, etc. The swimming speed threshold is essential for delineating turns events from 'runs', and one method for extracting Uth is presented. This leads to the conclusion that the most likely reorientation angle (Δθ, see Figure 2g) is actually 0 degrees. i.e. the cell stops and then continues in the same direction. It could be that this is an artefact of a relatively high value of Uth, which misclassifies one run into two smaller ones. This sensitivity is further shown in Figure 2b – increasing Uth to just ~125 microns/second would result in one single turning event (taus) instead of three distinct ones. It is not clear from the data how the results would change if Uth were varied in a sensitivity analysis, or defined in another way.

To verify if the way we chose the value of Uth will affect results of turning angles, run and turning events durations, we have varied the Uth value by ±10% of the chosen value, ranging from 100 to 122.5 μm s-1. We plot the running time, stopping time and turning angles according to the varied Uth and add the data in the Appendix 2. We see that the changes do not affect much the estimations of average taus and taur or the statistics of Δθ. Thus, we believe the sensitivity of Uth selection can be tolerated by 10%.

We have added a description for this sensitivity of Uth from line 192-194 (Section “Statistics of individual swimming patterns”):

“The sensitivity of our Uth selection can be tolerated by ±10 % of the chosen value, ranging from 100 to 122.5 μm s-1 (See Appendix)”

The authors have presented an experimental system which is capable of recording reasonably long trajectories of swimming P. parasitica cells, and an analysis pipeline which can extract statistical distributions of various swimming properties. The overarching assumption is that the 2D measurements can be extrapolated to three dimensions. Given the displayed trajectories are quite long (several millimetres), it seems that there are very few issues with the cells swimming out of focus. It is likely that the shallow chamber (100 microns) helps to maintain the cells within the focal plane and helps to minimise biases in the run time measurement. However, if that is the case, it's hard to know the effect that confinement has on the motility characteristics. It could be that the stop-start motion with Δθ=0 actually represents failed out-of-plane turning events.

As zoospores experience aerotaxis, they naturally swim close to the water surface. Thus, we design our experimental system as a swimming pool, instead of a chamber, because we do not cover the top of the sample droplet to avoid unwanted physical interaction between zoospores and the cover. To produce this “swimming pool”, we first draw a square of 1cm × 1cm on a glass slide, then pipette a droplet of 10μl of solution with zoospores into that square. After that, we gently spread the droplet to cover all the surface area of the square and achieved a thin layer of liquid with height of ~100μm. Though we have introduced this method in the experimental section at the end of the manuscript, we think that the setup needs to be described more clearly in the main texts. We have added a few sentences to better introduce this setup (line 160-162, section “Statistics of individual swimming patterns”):

“The setup of the water thin film can be visualized as a “swimming pool” that is not covered as we want to avoid the unwanted physical interactions of zoospores with the top when they experience aerotaxis…”

Moreover, we agree with the Reviewer that the dominant Δθ = 0 could result from the failed out-of-plane movement close to the water surface. We also observe this behavior experimentally. Thus we have added Video 2 and implemented this speculation into the discussion of the Δθ result, as follows (line 206-208):

“It is also shown that zoospores preferentially turn with the angle around 0o, which we speculate that it results from the failed out-of-plane movement when zoospores swim near the water surface during their aerotaxis (see Video 2).”

The authors utilised microscopic parameters from the swimming motion to predict the bulk diffusivity. It was mentioned that the direct measurement of D is unreliable given the small number of trajectories and their short duration. However, this seems to be inconsistent with the supplementary videos, which show cells in focus for extended periods of time and allow collection of trajectory data. Even if individual MSD measurements cannot be collected in large sets, perhaps a bulk diffusivity could be measured at lower magnification. At the moment, there is no strong quantitative link between the simulated diffusivity and the actual spreading of cells.

This was indeed done as can be seen in the inset of Figure 2I (for the MSD, from which D can be extracted): D = 3.5 × 10-4 cm2 s-1. However, we note that the average duration of runs is 5 seconds and the observed trajectories are typically less than 40 seconds in length, and so involving not more than 8 runs on average. Furthermore, the directions of motion of consecutive run phases are correlated (see Figure 2G). Estimations of the diffusion coefficient based on direct measurements of individual trajectories are highly unreliable (in general, and particularly for the experimental limitations of the experiment). However, the collected data allows a reliable estimate of the statistics of run phases and of the correlations between consecutive run phases. These quantities fully determine the large-scale properties of the diffusive process and provide the most reliable way to estimate the diffusion coefficient even when a much larger number of longer trajectories is available. As a proof of this, see the dispersion in MSD in simulations where we used 1h trajectories. Reliable estimations on MSD measurements require a large number of long trajectories, which are typically out of reach experimentally (for instance, direct measurements of MSD has repeatedly lead to wrongly report anomalous transport, etc).

Low magnification experiments that track the expansion of an initial high concentration drop of microorganisms provide an alternative reliable method, but here again, there is no direct measurement of the MSD of individuals, but based on the assumption of an underlying diffusion process where the diffusion coefficient D is a fitting parameter. In an initial high concentration, however, interactions among microorganisms can lead to a series of collective mechanisms that impact the behavior of the microorganisms and estimation of the diffusion process.

In summary, we are convinced that the performed analysis is the most reliable method to estimate the diffusion coefficient of individual zoospores and insist that the diffusion coefficient is fully determined – as in any random walk process – by the properties and correlations of run phases (as well as duration of turning angle).

We have added a few sentences to further discuss this point (line 230-234):

“We emphasize that D represents the estimation of diffusion coefficient of individual swimming of zoospores from random walk process. This is more to show the intrinsic ability of individual zoospores to perform spatial exploration, rather than to quantify the bulk diffusivity where the collective swimming behaviors, which involve zoospore-zoospore interactions, play a major role.”

A simplified mathematical model is developed in which resistive force theory (RFT) applied to the two flagella calculates the propulsive force on the cell body. This is then used to derive a closed form expression for the swimming speed (Equation 5), which predicts values commensurate with the observed swimming speeds (Figure 3). It is an interesting finding that the mastigonemes modify the sign of the propulsive force (also noted in previous works), enabling the anterior flagellum to pull the cell through the fluid. The planar motion of the flagellum in the model seems reasonable given the dynamics presented in Video 3. However, it is unclear by what mechanism the cells rotate as they swim. Perhaps this has something to do with the off-axis position of the flagellar base. Since the helical motion of the cells features prominently in the paper and is likely important for overall dispersal, it would be great if the model could account for viscous torques, calculate the cell body rotation rate and characteristics of the helical path.

We agree with the reviewer that the body self-rotation might result from the off-axis position of the flagellar base. However, we believe positions of the flagella and the kidney-shaped cell body might contribute to the chirality of zoospores, which causes the spontaneous self-rotation together with the translation and results in a helical trajectory (10.1140/epjst/e2016-60054-6). Although we have implemented this explanation in the section “Straight runs”, it was not very clearly stated and the estimation of the body rotation rate and characteristics of the helical path were not well-presented. We have revised this part, as follows (line 248-256):

“While translating, the cell body gyrates around the moving direction simultaneously, which results in a helical swimming trajectory (see Supp. Video 4 for a long run of a zoospore swimming in water). We believe that this gyrational motion might result from the intrinsic chiral shape of the zoospore body and off-axis arrangement of their flagella (Figure 1(B)). Indeed, previous studies have shown that chirality of a microswimmer’s body induces spontaneous axial rotation resulting from the translational motion (Keaveny and Shelley, 2009; Namdeo et al., 2014; Löwen, 2016). From multiple observations, we obtained the pitch and radius of the helical trajectories at p = 130 ± 8 µm (SEM) and R = 4.0 ± 0.2 µm (SEM), respectively (data presented in Appendix). We then estimate the gyrational speed of the cell body ϕ = 2π /Δt, where Δt is the duration the zoospore travels through a full turn of the helical path (Figure 3(B)). We obtain ϕ = (3.6 ± 0.3)π rad s-1 (SEM) (see Appendix).”

The reviewer suggested revising the model to account the viscous torques. However, we believe this body self-rotation (or we call “gyration” to distinguish with the rotation during turning) does not contribute to the translational motion. The two flagella, during reciprocal beating, can generate small vibrations in axial direction of the cell body, but not the directional axial rotation. Thus, the gyration of the cell body solely depends on the chirality of the zoospores, which can be considered as a passive motion resulting from the translation. Integrating the chirality of the zoospores into the model to describe the gyration is out of scope of the paper since we are focusing on the thrust generation of the two flagella. However, we have instead obtained the gyration rate and characteristics of the helical paths from experimental observations.

We have added some explanation, as follows (line 272-275):

“We assume that the gyration of the cell body does not affect the shapes and motions of the flagella since the beating frequencies of the two flagella are much higher than the gyrational speed. The gyration also does not contribute to the translation as we consider it as a passive motion resulting from the chirality of zoospores. Thus, the swimming zoospore can be considered as a 2D model…”

The observed dynamics have been classified into straight runs and turning events. However, many of the 'runs' are certainly not straight (see Figure 2). It is not clear whether these curved trajectories are due to rotational diffusion, or perhaps from hydrodynamic interactions with the boundaries (bacteria are known to swim in circles near no-slip walls). This could have significant implications for the dispersal calculations, and for classification of events within the trajectories.

Certainly, bacteria as well as zoospores are subject to thermal fluctuations, and thus mathematical straight trajectories do not exist. Abrupt changes in trajectories are systematically related to a turning event. We used the term “straight” to indicate that run phases do not display neither abrupt changes of direction neither a finite curvature (as when motion is chiral). Note that the anterior and posterior flagellum do not rotates as the flagellar bundle of E. coli does, see Figure 3. Thus, there is no reason to expect that a no-slip wall will induce a hydrodynamic torque as occurs in E. coli. Furthermore, we do not observe chiral motion near the bottom surface. Furthermore, note that for bacteria, oriented curvature associated to trajectories (on a given surface), exhibits the same sign: i.e., it is expected that bacteria on the surface turn in the same direction. It is evident that this does not occur for zoospores.

We have added some sentences to discuss this point (line 256-261):

“The observations of helical trajectories also confirm that each flagellum of zoospores beat as a flexible oar in a 2D plane as we observe the two flagella flattened into two straight lines during the gyration. Thus, zoospores are not expected to swim in circles when interacting with no-slip boundaries as seen in case of E. coli with a rotating flagellar bundle. The “curved straight runs” of zoospores that we observed in Figure 2(A) might result from rotational diffusion and thermal fluctuations.”

In order to calculate a cell's 'run time', it is necessary to visualise two successive turning events which bookend a single run. However, for cells swimming in three dimensions, the probability of observing a given run length depends on the value of the run length. Can the authors please provide information about any biases in their data collection, and the extent of any biases in the presented distributions? This could include discussion of depth of field, chamber height, and whether any cells were excluded.

The height of the thin film of water containing zoospores is ~100μm, while the speed of zoospores is averaged at 150μm/s, we assume the swimming of zoospores in our “swimming pool” is straight as interactions with substrate will result in disruption of the straight runs. We believe the zoospores can swim straight in a long time due to their aerotaxis, which makes them tend to stay close to the water surface. We have discussed this aerotaxis in the section of “Statistics of individual swimming”.

We used survival curves to obtain the statistics of running time and stopping time because we were aware of that there were situations the swimmers cross the observation region without making a turn. Thus, we obtained the probability that the running time or stopping time is greater than a time period.

Except for the dead cells that keep fluctuating around certain positions during the whole video, we did not exclude any swimmers from the data.

The motility strategy examined in this paper is described as "steering" and is presented as a possible method for pathogenic cells to target the plant host. However, the dynamics are all spatially isotropic, and it is not clear how cells could navigate towards specific chemical cues (e.g. potassium, physical cues, electrical signals).

It is known that zoospore can perform chemotaxis (see https://doi.org/10.1016/j.fbr.2007.02.001, https://doi.org/10.1038/nrmicro1064 or in our recent review https://10.1016/j.csbj.2020.10.045). In shorts, near the plant-root, zoospores can perceive diverse stimuli at multiple levels. The ion exchange dynamics between soil particles and plant roots, together with the chemical gradients generated by root exudates, can activate cell responses. This results in biased motion towards a preferential localization at the interface between soil particles and plant roots. However, it is not known how zoospore steer towards a desired direction, or how flagella dynamics is affected in the presence of chemical gradients.

We have added this description in the introduction part, as follows (line 66-73):

“Previous studies have shown that during the spreading and approaching the host, zoospores can have complicated swimming patterns and behaviors as they experience multiple interactions with environmental signals, both physical, electrical and chemical, in soil and host-root surface (Bassani et al., 2020a). Near the plant-root, zoospores can perceive various stimuli from the environment, such as ion exchange between soil particles and plant roots, the chemical gradients generated by root exudates, which activate cell responses. This results in coordinated behaviors of zoospores, allowing them to preferentially navigate to the water film at the interface between soil particles and plant roots.”

The motor efficiency is determined in terms of the swimming speed to wave propagation. There are many ways of calculating efficiency in low Reynolds number hydrodynamics, many of which include power/energy calculations. The authors allude to a link between power and drag due to mastigonemes, but it's hard to determine from the presented results how much energy the cell needs to swim. I think it would be very helpful to expand the section on efficiency, connecting with other established methods, and results for other organisms.

We thank the Reviewer for this suggestion. We have calculated the power consumption of each flagellum as well as the propelling efficiency of the zoospore. This question is similar to the question of Reviewer 3. Please find the detail answer in the response below for Reviewer 3.

Quantifying the microscale trajectory features and predicting the collective cell diffusivity requires a threshold value of Uth. It would be very important to examine the sensitivity of the measurements to the value of Uth, and explore the implications if another definition was chosen.

We have varied the Uth value and show that 10% or slightly higher variation of its value does not affect results. See our reply to this point above.

Figure 2. Some of the time-dependent processes are plotted in terms of frame number (t/dt), and others in absolute time (t). It would be best to include all processes in terms of t, so that conclusions are independent of frame rate.

We have already fixed the Figure 2 according to reviewer’s suggestion.

Line 38 mentions that E. coli possess "a passive helical flagellum", but they possess a bundle of these. Please correct the numbers.

We have fixed the number. The new sentence is now:

Escherichia coli is one of the most studied prokaryotic swimmers, which possesses a bundle of passive helical flagella…”

There is a need to better distinguish between axial rotation and cell "rotation" during turns. Perhaps it would be better not to use the same word.

We name this axial rotation as “gyration”. The cell rotation during turning is remained as “rotation”. We have revised the texts accordingly.

Line 58. The organisms can apparently swim for several hours. However, this may be very short compared to the timescales required to find a plant. Can the authors please elaborate on how motility can be sustained in a typical environment, and how long it might take for a cell to reach its target (assuming no active navigation)?

In natural ecosystems and even more in agro-systems, putative host plants are close.

This “proximity’ makes the distance to find a plant relatively short and it is compatible to timeability of zoospore to swim. Moreover, zoospores can sense the electrical and chemical signals released from the plant roots, which helps them navigate the direction towards the target.

We have added a few sentences to elaborate this point (line 57-60):

“To facilitate the spreading, their cell bodies store an amount of energy (mycolaminarin, lipid) allowing them to swim continuously for several hours (Judelson and Blanco, 2005). In natural ecosystems and even more in agro-systems, putative host plants are usually close. This proximity makes the distance to find a plant relatively short and it is compatible to the time-ability of zoospores to swim”

The article should be carefully read by a native English speaker. For example, "underwhelming knowledge" is not an appropriate way of describing open questions. "Flimsy" also refers to an object's structural integrity and not its shape. The word "accumulating" is used extensively throughout the paper but is not appropriate since it implies temporal integrating. i.e drag and velocity don't 'accumulate' along the flagellum.

We have rewritten the whole sentence with the term “underwhelming knowledge”.

The word “flimsy” has been removed, and the word “accumulating” has been replaced by suitable words.

Reviewer #3 (Recommendations for the authors):

The authors present a study of the swimming behaviour of the zoospores of the water mold Phytopthora, which combines experimental imaging of fixed cells (to examine structure), image capture and analysis of multiple swimming cells to examine bulk swimming behaviour, high-speed imaging to characterise on the spot turning behaviour, and an analytical mathematical model of the straight "run" swimming behaviour that incorporates the mastigonemes on the anterior flagellum.

In terms of what is already known about these systems, it is already known that Phytophora zoospores swim with two flagella at the high speeds shown herein, and that the anterior flagellum is covered with mastigonemes (see for instance the authors' previous work DOI: 10.1016/j.csbj.2020.10.045). It has also been known for some time that mastigonemes reverse the expected direction of propulsion for a flagellum beating with a sperm-like (travelling wave) waveform, so this behaviour is expected, and indeed commented on in the authors' previous work. The model provided is based upon previous models (see eg https://doi.org/10.1063/1.3608240), which should be made clearer in the text, with the adaptation being that there are 2 flagella and a body here.

We thank Reviewer 3 for the comment. As the Reviewer stated, it is already known that Phytophthora zoospores swim with two sinusoidal waveform flagella, and the mastigonemes reverse the thrust. In our previous review (DOI: 10.1016/j.csbj.2020.10.045), we have recapped the current knowledge about zoospore swimming, which involves the anterior flagellum with mastigonemes and smooth posterior flagellum both beating to propel the body forwards. However, the characteristics of the beating flagella during swimming such as beating frequencies, amplitudes, wavelengths (for example, the posterior flagellum beats with frequency 1.7-fold higher than the anterior flagellum), together with characteristics of the zoospore swimming trajectories such as body lateral rotation speed, turning angles, running time, turning time, are not known.

Moreover, our work also looks at individual contribution of each flagellum on zoospore swimming, and how the two flagella are coordinated during swimming and turning. We develop a model based on Resistive Force Theory (RFT), consisting of both flagella and a cell body, to better understand that cooperation. To construct this model, we have consulted from many previous studies using RFT, including the paper from Namdeo et al., as the Reviewer has mentioned (https://doi.org/10.1063/1.3608240). Though we have cited the paper when confirming the thrust reversal effect in zoospores, we agree with the Reviewer that it needs to be stated more clearly. Following the Reviewer’s recommendations, we have made the reference of the previous model from Namdeo et al., clearer and emphasize our scopes better. Below are the changes made:

Abstract, line 19-21:

“Despite the relevance of zoospore spreading in the epidemics of plant diseases, characteristics of individual swimming of zoospores have not been fully investigated. It remains unknown about the characteristics of two opposite beating flagella during translation and turning, and the roles of each flagellum on zoospore swimming…”

Introduction section, line 93-99:

“Although it has been known about how zoospores swim, characteristics of the swimming and the beating flagella have not been statistically reported. The effects of mastigonemes on zoospore swimming also need to be carefully investigated since the mechanical properties of mastigonemes such as size, rigidity, density, can affect the swimming differently (Namdeo et al., 2011). For instance, while mastigonemes are shown to generate thrust reversal in P. palmivora zoospores (Cahill et al., 1996), they do not contribute to enhance swimming of C. reinhardtii (Amador et al., 2020).”

Introduction section, line 117-126:

“ We obtain statistics of the trajectories and develop a numerical model to study and extrapolate the zoospore spreading characteristics solely by random walks. Then, we detail an in-depth study on the hydrodynamics of P. parasitica’s flagella and acquire a mathematical model to correlate the functions of two flagella on the motion of straight runs. Although theoretical models for microswimmers with single mastigonemes-attached flagella have been formulated (Brennen, 1975; Namdeo et al., 2011), models for microswimmers with two heterokont flagella have yet been considered as in case of zoospores. Here, we use Resistive Force Theory and further develop the model of a single flagellum with mastigonemes (Brennen, 1975; Namdeo et al., 2011) to adapt it with another smooth flagellum and a cell body, using a hypothesis of no interactions between two flagella…”

The main novel components are (1) the discussion that the anterior flagellum accounts for the majority of the propulsion, and (2) the characterisation of the on-the-spot turning (as far as I know). The first point is based on analysis from the analytical model. My concerns with this conclusion are three-fold. Firstly, it relies on mastigonemes remaining rigid and normal to the tangent of the main flagellum, whereas some bending with the flow is to be expected (reducing their impact).

We agree with the Reviewer that the thrust reversal effect of the mastigonemes depends on their flexibility. In fact, this flexibility has been carefully characterized in the paper of Namdeo et al., (https://doi.org/10.1063/1.3608240) and Khaderi et al.,

(https://doi.org/10.1103/PhysRevE.79.046304). The flexibility of mastigonemes can be defined by a dimensionless parameter Fm = 12µKAωh3/(Edm3) where µ is the fluid viscosity, K = 2π/λ, A is the amplitude of the beating flagellum, ω = 2πf, h is the height of mastigonemes, dm is the diameter of mastigonemes, and E is the Young modulus of mastigonemes. Fm is the ratio between viscous force and elastic force on mastigonemes, thus can be used to characterize the flexibility of the mastigonemes. With Fm < 0.1, mastigonemes are considered as rigid and the thrust reversal effect is preserved.

In our case, the zoospores’ mastigonemes have Fm at order of 10-4, which is much lower than 0.1. Thus, we can assume that the mastigonemes of zoospores are rigid and non-deformable. We realize that we did not clarify our assumption well enough.

Thus, we have added the following information for the flexibility of the mastigonemes (subsection Straight runs, line 283-294):

“Additionally, there are multiple tubular type-1 mastigonemes with length h and diameter dm attached to the surface of the anterior flagellum with density Nm indicating the number of mastigonemes attached on a unit length of the flagellum. It is important to determine the flexibility of these mastigonemes as it would impact the ability of the mastigonemes to produce drag. We estimate the flexibility by a dimensionless parameter, which were carefully characterized in previous studies (Namdeo et al., 2011; Khaderi et al., 2009), Fm = 12µKAωh3/(Edm3), where µ is the fluid viscosity, K = 2π/λ is the wave number, E is the Young modulus of the mastigonemes. With this estimation, if Fm < 0.1, mastigonemes are considered as fully rigid. In case of zoospores’ mastigonemes, we achieve Fm at order of 10-4, which is much lower than 0.1. Thus, we can assume that the mastigonemes of zoospores are non-deformable and rigidly attached to the anterior flagellum. As a result, hydrodynamic interactions between neighboring mastigonemes can also be neglected.”

Secondly, the resistive force theory model, while qualitatively powerful, does not include hydrodynamic interactions between neighbouring mastigonemes, which may also reduce their impact.

Since we now have the flexibility parameter Fm defined, our zoospore mastigonemes can be treated as fully rigid and non-deformable. Thus, we can neglect the effect of hydrodynamic interactions between neighboring mastigonemes.

Thirdly, it is quite sensitive to the mastigoneme density once this drops to around 10 per micron (the way in which the mastigoneme density was estimated, and the data, should be made clear in the manuscript),

We have re-analyze the mastigoneme density following the Reviewer’s suggestion. We have also introduced the method and experimental data to estimate the mastigoneme density in the Appendix 4. In short, the mastigoneme density Nm is defined as the number of mastigonemes attached to a unit length of the anterior flagellum. The number of mastigonemes were manually counted, then divided by the flagellum length that contains all those counted mastigonemes. The measurement data show that Nm = 13.0 ± 0.8 µm-1 (SD).

and fourthly, the posterior flagellum naturally beats at around twice the frequency (probably because they are expending the same amount of energy), so I do not feel that the conclusion "we consider the anterior flagellum as the main motor of zoospores because it has the ability to immensely increase or decrease speed with a small adjustment of its beating frequency" is justified.

The Reviewer has raised a very interesting point that both flagella might expend the same amount of energy, which leads to the posterior flagellum beats at twice the frequency as that of the anterior flagellum. The conclusion we made about the anterior flagellum as the main motor indeed needs a better explanation. To further investigate this, we have calculated the power generated by each beating flagellum to propel the cell body forward. In our model, each flagellar segment moves in water and received a drag force from water. Hence, the power produced by a flagellar segment results from the dot product between the drag force of water acting on the segment and the relative velocity of water to the segment, which can be written as dPvw/fdF. From this equation, we can derive the power generated by each flagellum P1 and P2, and estimate the propelling efficiency of the two flagella as η = P0/(P1 + P2), where P0 = Fd . Ux is the useful power required to propel the cell body forward with a speed Ux. The detail derivative is added to the Appendix 6. Then, we plotted 4 new figures, 3F, G, H, I to show the correlation of the power of each flagellum, the propelling efficiency of two flagella according to different beating frequencies of the two flagella.

We have re-written the whole paragraph to correctly conclude about the cooperation of the two flagella, from line 362 to 398 of subsection “Straight runs”.

The characterisation of the on-the spot turning from high speed image microscopy is very nice, to the best of my knowledge novel, and the analogues to peritrichous bacteria and Chlamydomonas well drawn up. This section is well described (though not modelled), but would probably benefit from a schematic in addition to the set of experimental images.

We thank the reviewer for the compliment. We have added the schematics showing the shape of the two flagella during the turning event in Figure 4F.

The paper would benefit from a clearer exposition of what the novel components are in relation to previous work, and a link back to the motivation of crop damage and how this understanding of motility may be used in future pest control strategies.

We have added a discussion to explain clearer the novel components in our study and link back to the motivation of crop damage to emphasize the importance of this study which can be used in pest control strategies. The new discussion is as follows (line 470-480):

“We believe our findings on the cooperation of two flagella bring more insights on zoospore swimming dynamics. It was also not from the literature about the role of each flagellum on the straight runs and on turning events, in particular. We show that although the energy is shared in comparable manner between both flagella, the anterior flagellum contributes more to zoospore speed. Zoospores actively change direction thanks to the sole beating of the anterior flagellum. We believe that anterior flagellum could be the main motor of zoospores that is in charge of generating speed, changing beating patterns from sinusoidal wave to power and recover stroke to quickly rotate the body, while the posterior flagellum might play a role in chemical/electrical sensing and providing an anchor-like turning point for zoospores, instead of acting like a rudder as previously hypothesized. These findings pave new ways for controlling the disease since now we can have different strategies on targeting one of the flagella.”

While I enjoyed reading the article, the authors should endeavour to make it clearer in certain places what has come before, and what is the novel component. For instance, the modelling seems to follow the arguments of https://doi.org/10.1063/1.3608240, and while this is cited elsewhere, I believe this should be stated very clearer in the model section. Secondly, there are a few sentences which mislead with respect to aspects of the novelty, for instance:

1. "Despite the relevance of zoospore spreading in the epidemics of plant diseases, it is not known how these zoospores swim and steer with two opposite beating flagella." For the swimming this is clearly known, as the authors commented on in their previous work, it is the turning I believe that was not well characterised.

2. "Here, we introduce a new type of microswimmer, named Phytophthora zoospores, which has two different flagella collaborating for unique swimming and turning mechanisms (Figure 1(a))." – you have presented work previously on the swimming of this organism.

I believe the data on mastigoneme density is critical to one of your conclusions, and should be presented carefully, and I believe this conclusion about the anterior flagellum being the main driver for motility is probably not correct, more broadly – it certainly needs more careful treatment.

We thank the Reviewer for these recommendations. We have followed them and revised the manuscript accordingly. The Reviewer can find the answers to these recommendations in the previous questions.

https://doi.org/10.7554/eLife.71227.sa2

Article and author information

Author details

  1. Quang D Tran

    Université Côte d’Azur, CNRS UMR 7010, Institut de Physique de Nice (INPHYNI), Nice, France
    Present address
    Université Paris Cité, CNRS, Institut Jacques Monod, Paris, France
    Contribution
    Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Validation, Visualization, Writing – original draft, Writing – review and editing
    For correspondence
    duc-quang.tran@ijm.fr
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5637-0647
  2. Eric Galiana

    Université Côte d’Azur, INRAE UMR 1355, CNRS UMR 7254, Institut Sophia Agrobiotech (ISA), Sophia Antipolis, France
    Contribution
    Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Writing – review and editing
    Competing interests
    No competing interests declared
  3. Philippe Thomen

    Université Côte d’Azur, CNRS UMR 7010, Institut de Physique de Nice (INPHYNI), Nice, France
    Contribution
    Conceptualization, Investigation, Methodology, Writing – review and editing
    Competing interests
    No competing interests declared
  4. Céline Cohen

    Université Côte d’Azur, CNRS UMR 7010, Institut de Physique de Nice (INPHYNI), Nice, France
    Contribution
    Conceptualization, Investigation, Writing – review and editing
    Competing interests
    No competing interests declared
  5. François Orange

    Université Côte d’Azur, Centre Commun de Microscopie Appliquée (CCMA), Nice, France
    Contribution
    Investigation, Methodology, Writing – review and editing
    Competing interests
    No competing interests declared
  6. Fernando Peruani

    1. Université Côte d’Azur, CNRS UMR 7351, Laboratoire J.A. Dieudonné (LJAD), Nice, France
    2. CY Cergy Paris Université, CNRS UMR 8089, Laboratoire de Physique Théorique et Modélisation, Cergy-Pontoise, France
    Contribution
    Formal analysis, Methodology, Software, Validation, Writing – review and editing
    Competing interests
    No competing interests declared
  7. Xavier Noblin

    Université Côte d’Azur, CNRS UMR 7010, Institut de Physique de Nice (INPHYNI), Nice, France
    Contribution
    Conceptualization, Data curation, Funding acquisition, Project administration, Supervision, Validation, Writing – review and editing
    For correspondence
    xavier.noblin@univ-cotedazur.fr
    Competing interests
    No competing interests declared

Funding

French Government - Investissements d'Avenir - ANR (UCAJEDI ANR-15-IDEX-01)

  • Eric Galiana
  • Xavier Noblin

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work has been supported by the French Government, managed by the National Research Agency under the Project UCAJEDI "Investissements d'Avenir Investments" bearing the reference n° ANR-15-IDEX-01. CCMA electron microscopy equipments have been funded by the Région Sud - Provence-Alpes-Côte d’Azur, the Conseil Général des Alpes Maritimes, and the GIS-IBiSA. We thank Ilaria Bassani, Nicolas Bruot, Xinhui Shen and Ngoc-Phu Tran for fruitful discussions, as well as Marcos, David Gonzalez-Rodriguez and the three reviewers for their careful reading and giving valuable feedback to improve the manuscript.

Senior Editor

  1. Aleksandra M Walczak, CNRS LPENS, France

Reviewing Editor

  1. Raymond E Goldstein, University of Cambridge, United Kingdom

Publication history

  1. Preprint posted: April 23, 2021 (view preprint)
  2. Received: June 12, 2021
  3. Accepted: March 25, 2022
  4. Accepted Manuscript published: March 28, 2022 (version 1)
  5. Accepted Manuscript updated: April 4, 2022 (version 2)
  6. Version of Record published: May 3, 2022 (version 3)

Copyright

© 2022, Tran et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Quang D Tran
  2. Eric Galiana
  3. Philippe Thomen
  4. Céline Cohen
  5. François Orange
  6. Fernando Peruani
  7. Xavier Noblin
(2022)
Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores
eLife 11:e71227.
https://doi.org/10.7554/eLife.71227
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