This paper is dedicated to the memory of Antonie van Leeuwenhoek, who opened the eyes of humanity to the microcosmos with his pioneering observations and descriptions of protozoa.

Lin Qi Feng, Lin Yangchen (corresponding author) & Yeo Li Jia

Department of Statistics & Applied Probability
Department of Biological Sciences
National University of Singapore

Spring 2002

\begin{abstract} Motility confers upon flagellates several advantages over sedentary protists. Adaptations which boost motility would therefore be selected for in the course of evolution. The hypothesis was tested that exomorphologically symmetric unicellular marine phytoflagellates swim in the absence of turbulence at a speed different from that of their asymmetric counterparts. In addition, the mean swimming speeds of species engaging in different styles of flagellar propulsion were compared. 13 species representing Cryptophyceae, Dinophyceae, Prasinophyceae, Prymnesiophyceae and Raphidophyceae were studied including 3 dinoflagellates whose speeds and surface area:volume ratios (SA:V) are recorded but were not subject to comparison. Video footage of cultured plankters under bright-field microscopy was processed using a programme written in IDL 5.4 which enabled the locomotion tracks to be analysed at a resolution of 25 frames $\mathrm{s}^{-1}$. 10 species were categorised into 3 SA:V classes having ranges narrower than 0.10$\mu\mathrm{m}^{-1}$. Within each class, the mean swimming speed of the single symmetric species was compared with that of each asymmetric species by means of the {\it F}-test set at $\alpha=0.05$. The different styles of propulsion were compared in a similar fashion. In the SA:V range 0.24-0.31$\mu\mathrm{m^{-1}}$, the symmetric species was faster than all the asymmetric species while two helically propelled species were faster than one utilising a linear mode of locomotion in which the flagellum pulls the cell. However, there is no evidence in the other two SA:V classes that symmetry or style of propulsion are criteria for natural selection for speed. \end{abstract}


By virtue of its motility, the flagellate life-form has been highly successful in aquatic habitats (Sommer 1988). Dinophytes in particular are among the fastest of swimming plankton (Raven \& Richardson 1984) and, due to their large sizes and abundance along coasts, the best studied. Past investigations have correlated various physiological or environmental parameters to rate of locomotion, including energy expenditure of planktonic crustaceans (Klyashtorin \& Yarzhombek 1973), cell size of phytoflagellates (Kamykowski {\it et al}. 1992; Sommer 1988), equivalent spherical diameter of dinoflagellates (Kamykowski {\it et al}. 1992), gravitation (Machemer-Rohnisch {\it et al}. 1999), temperature (Glaser 1924, 1925; Hand {\it et al.} 1965; Kamykowski {\it et al}. 1988), light intensity (Kamykowski {\it et al}. 1988; Sineshchekov {\it et al}. 2000) and salinity (Hand {\it et al.} 1965; Tyler \& Seliger 1981). None, however, has examined the effect of morphological symmetry or style of propulsion. As speed engenders survival in competition for nutrients and escape from zooplanktonic predators or detrimental stimuli (Strickler 1977), symmetry if correlated to speed has the potential for being selected for or against in non-turbulent water bodies.

Gambierdiscus cf belizeanus fluorescing under a Zeiss laser scanning confocal microscope.

We hypothesise that exomorphologically symmetric unicellular marine phytoflagellates swim in the absence of turbulence at a speed different from that of asymmetric unicellular marine phytoflagellates. Although the speeds of several identified marine species have been conveniently summarized by Kamykowski {\it et al}. (1992) and Sournia (1982), the conditions in which they were observed lacked standardisation. The results, concerning mostly the vertical migration of dinoflagellates over relatively large distances and durations, furthermore involved the confounding factors of gravity and gradients of temperature, light intensity and nutrient concentration. Various other publications not only present similar obstacles but also are focused on Dinophyceae, Euglenophyceae or Copepoda. Our scope covers a wider taxonomic range and is restricted to horizontal motion.

Flagellates exhibit two general styles of propulsion. In linear propulsion, the flagellar wave is propagated either from the base to the tip or vice versa (Brennen \& Winet 1977). The direction of displacement is usually opposite to that of wave propagation by the flagellum (Brennen \& Winet 1977). Cells may be pulled or pushed through the medium; all members of a class employ the same polarity of locomotion. Helical propulsion, which is manifested to some extent in many species, is most significant in dinokont dinoflagellates. Unlike other flagellates, motility of dinokont dinoflagellates is powered by the transverse flagellum (Steidinger \& Tangen 1997). The helical wave propagated by the transverse flagellum gives rise to forward motion and rotation about the longitudinal axis (Jahn \& Votta 1972). Little work has been done on the relative speeds afforded by linear and helical propulsion. We project helical trajectories onto planes parallel to the helical axes for comparison of speed with two-dimensional linear paths.

A live culture of Tetraselmis suecica.

Sournia (1982) stated that the surface area:volume ratio (SA:V) of a planktonic cell is proportional to drag experienced during swimming. The large range of cell sizes encompassed in this study necessitates some degree of control over the effects of variation in the SA:V. A linear relationship between the SA:V and speed of dinokont dinoflagellates has been established by Kamykowski {\it et al}. (1992), but its applicability here is obviously limited. This paper compares speeds within reasonably narrow SA:V classes and speculates on the role of symmetry and style of propulsion in community ecology and macroevolutionary change.

\section{Materials and Methods}

\subsection{Strain culture and categorisation}

Strains (Table 1) were compiled from the collection of Dr Michael James Holmes, Department of Biological Sciences, National University of Singapore; Tropical Marine Science Institute (TMSI), Saint John's Island, Singapore; and Commonwealth Scientific and Industrial Research Organisation (CSIRO), Tasmania, Australia. Cultures from TMSI and CSIRO were supplied in $\mathrm{f_2}$ or GSe media (Table 1), those from CSIRO having been maintained at 20$\mathrm{^oC}$. All species were subcultured in 50ml Nunclon$\mathrm{^{TM}}$ plastic tissue flasks containing 5-7ml $\mathrm{f_{10k}}$ medium according to Holmes (2001) prior to observation. The strains were acclimatised and cloned at 25-29$\mathrm{^oC}$ and 30-34 psu salinity under 50-90$\mu\mathrm{mol}$ photons $\mathrm{m^{-2}s^{-1}}$ from Philips Daylight-54 fluorescent tubes with a 12:12 light-dark photoperiod.

Categorisation of species according to symmetry and style of flagellar propulsion (Table 2) is based on descriptions by Tomas (1997). As the locomotive flagellum of a dinokont dinoflagellate is housed in the cingulum, cingulum displacement as well as overall cell shape is an important criterion for the determination of symmetry. Except for {\it Scrippsiella} sp., which possesses a circular postmedian cingulum, the dinoflagellate species surveyed exhibit helical chirality of the cingulum (Table 2).

In order to calculate the SA:V, the cell shape of each species was represented by a sphere or prolate spheroid (Table 3). Samples were fixed in formaldehyde to a final concentration lower than 1\% w/v in culture medium and ten cells of each species measured at 200$\times$ or 400$\times$ by means of an ocular micrometer. The diameter readings of cells approximated to spheres were applied to

where {\it r} = radius, to obtain respectively the surface areas and volumes. For cells approximated to prolate spheroids, the measured polar and equatorial radii were applied to

where {\it a} = equatorial radius and {\it b} = polar radius, to obtain respectively the surface areas and volumes.


Special slides were constructed for the purpose of observation (Sow, personal communication). A circular opening approximately 8mm in diameter was drilled through the centre of an 80mm$\times$25mm piece cut from a perspex sheet approximately 1.8mm thick (Workshop, Department of Physics, National University of Singapore). By means of Norland Optical Adhesive (Norland Products Inc. Cranbury, NJ 08512, USA) cured under sunlight, the perspex was glued to a glass microscope slide. Chemotactic response of plankton to the cured adhesive is not known. The resulting slide with a cylindrical depression is similar in dimensions to the apparatus used by Hand {\it et al}. (1965). Concave-cavity slides, which encourage benthic species to follow curved trajectories with respect to the vertical plane, were avoided.

Enough culture was dispensed into the cavity to minimise spherical aberration concomitant with meniscus curvature. As shear forces can immotilise plankters (Tyler \& Seliger 1981), care was taken in drawing and expelling the fluid using Pasteur pipettes. The slide was immobilised horizontally without a cover glass (Davenport {\it et al}. 1962) under an Olympus BH2-UMA bright-field microscope at 50$\times$ or 100$\times$ (Table 1). Specimen temperature was maintained at 24$\pm$0.5$\mathrm{^oC}$ and light intensity was minimal. Footage was captured by a Hamamatsu C2847 video camera attached to the microscope through an MTV-3 fixture and fed into a Toshiba V-E27 recorder.

Calibrating the videomicroscope.

Detection, tracking and speed measurement of Coolia monotis in a digitized videomicrograph.

Trajectories of Chattonella sp.

Images were digitised in real time at 25 frames $\mathrm{s}^{-1}$ and 256 possible grey levels using a PCVision PCI video card in conjunction with the programme Image-Pro Plus 4.5. The field of view was calibrated with a stage micrometer (Davenport {\it et al}. 1962) placed on a microscope slide, the 100$\mu$m graduations being in the same position along the line of sight as that of the bottom of the cavity when the latter was under observation. From three separate measurements, the mean dimensions of each pixel were calculated to be 4.5$\mu$m$\times$4.5$\mu$m at 50$\times$ and 2.2$\mu$m$\times$2.2$\mu$m at 100$\times$. Of each species, ten tracks throughout which no collisions or stoppages occurred were chosen at random. The swimming speed in each frame of every track was determined by a programme written in IDL 5.4 (see Appendix below) and an average speed of each species was computed. Image analysis of a stationary point for 20s established the errors as $\pm21\mu\mathrm{ms}^{-1}$ at 50$\times$ and $\pm42\mu\mathrm{ms}^{-1}$ at 100$\times$.


The SA:V values of {\it Gymnodinium} sp. and {\it Scrippsiella} sp. (Table 3) are identical to those reported by Kamykowski {\it et al}. (1992) of {\it Gymnodinium sanguineum} and {\it Scrippsiella trochoidea}. The correlation coefficient was determined to be -0.565 by substituting the SA:V values and mean speeds of the 13 species into Pearson's product moment formula

where $S_x$ and $S_y$ are the standard deviations of the {\it x} and {\it y} variables.

Species were categorised into SA:V classes having ranges narrower than 0.10$\mu\mathrm{m}^{-1}$ (Table 4, 5). Within each class, the mean swimming speed of the single symmetric species was compared with that of each asymmetric species. The different styles of propulsion were compared in a similar fashion (Table 5). {\it G.} cf. {\it belizeanus}, {\it G. yasumotoi} and {\it G. catenatum} constituted an additional SA:V class (range 0.10-0.16$\mu\mathrm{m^{-1}}$) but were not considered because all three are asymmetric and share one style of propulsion.

Using the programme Minitab 13.2, one-way ANOVA was executed on each species. The null hypothesis and alternative hypothesis were given by

The sum of squares within samples and sum of squares between samples were calculated respectively from

where $n_1=n_2=10$ and $\bar{x}=$ pooled mean. {\it F}-statistics were computed from

where $N=n_1+n_2=20$ and $k=$ number of groups, and compared with the tabulated value of 4.41 at $\alpha=0.05$. The test is based on 3 assumptions (Johnson \& Kuby 2000):

1. The population has been randomly sampled.
2. The probability distribution of the swimming speeds of each species is normal.
3. The effects of chance and unknown factors are normally distributed and the variance caused by these effects is constant throughout the experiment.

Tables 4 and 5 summarise the results obtained. In the SA:V range 0.24-0.31$\mu\mathrm{m^{-1}}$, the symmetric species, {\it Scrippsiella} sp., was found to be faster than all the asymmetric species. The pulling mode of locomotion was slower than or as fast as the helical mode in this SA:V class. No significant difference existed between {\it T. suecica} and {\it S. microadriaticum}. In the SA:V range 1.09-1.18$\mu\mathrm{m^{-1}}$, the symmetric species engaging the pushing mode, {\it Nephroselmis} sp., was faster than one asymmetric species utilising the pulling mode but slower than the other.


Some limitations of the present study should be noted. Dinophyceae is relatively overrepresented (Table 1) while cultured members of Chlorophyceae, Chrysophyceae, Dictyochophyceae, Euglenophyceae, Eustigmatophyceae and Xanthophyceae could not be procured. By surveying more species in every class, a more reliable result could be obtained. Cells of {\it Prorocentrum} sp. (Dinophyceae) and {\it Amphidinium} cf. {\it operculatum} (Dinophyceae) from the collection of Dr Holmes were observed to be predominantly sedentary although motile (Holmes, personal communication). They were excluded from our investigation on the grounds of difficulty in generating speed data. The spectra of cell sizes and speeds observed in each clonal culture were due not to genetic variation but to different stages of the cell cycle (Holmes, personal communication). In the absence of multiple-strain data, the measurements from single cultures were considered the mean values of their respective species.

Maximum speed as the parameter for comparison has been suggested by Lim (personal communication). Under the controlled experimental environment, however, the sporadic maxima recorded from each organism are unlikely to be physiologically or ecologically meaningful. Moreover, the isolation of instances of maximum speed leaves endurance out of account. Our assessment of overall efficiency took endurance, acceleration, deceleration and turning into consideration. As the viscosity of water (Kamykowski {\it et al}. 1992) practically precludes displacement after the flagellum stops beating (Berg \& Purcell 1977), no part of the track was not due to active propulsion. By randomly selecting tracks, the potential for any correlation between cell age and speed to confound the results was reduced. Crenshaw {\it et al}. (2000) has introduced a procedure of analysing realistic, three-dimensional trajectories. This method, which accounts for gravitaxis, is nevertheless not suited to our purpose. The shallow depths of focus of the microscope objectives used here exclude large deviations from the horizontal but accommodate helical motion.

In {\it Gymnodinium catenatum}, the cingulum takes the form of a left-handed helix (Hallegraeff 1994). If cell morphology were associated with helical swimming (Levandowsky \& Kaneta 1987), cells of {\it G. catenatum} would be expected to rotate clockwise about the longitudinal axis when viewed from the apex. An analogy can be drawn with the movement of a turning screw. However, individual cells were observed to alternate between clockwise and counter-clockwise rotation. The rationale behind an apparently counterproductive direction of rotation remains to be seen.

Numerous variables, arising from interspecific differences in response to identical conditions, were impossible to control. Such variables include mucus secretion, chemotaxis and degree of shrinkage in formaldehyde. Mucus may respectively increase or reduce drag by increasing the viscosity of the surrounding fluid or by encapsulating the organism and creating a smooth interface with seawater. Shrinkage results in slight overestimation of the surface area:volume ratio, although this is unlikely to exceed the error incurred by approximating cell morphologies to geometric shapes. Except in a computer simulation (Uttamchandani, personal communication), a case of all things being equal cannot be realised (Sournia 1982). Kamykowski {\it et al}. (1992) doubted the utility of comparisons of the sort undertaken. Principal components analysis (Singh; Basu, personal communication) cannot address the problem before protocols are established for the measurement of all important variables and a database with a comprehensive inventory is set up. However, we argue that the absence of control over natural variability is consistent with our aim of discovering correlations between symmetry and speed or between style of propulsion and speed that apply {\it in vivo}.

The weak negative correlation found between SA:V and speed probably underestimates the effect on speed of SA:V per se. Although drag is proportional to SA:V given a constant cellular equivalent spherical diameter, it is inversely proportional to SA:V when variation in the latter is due largely to cell size. The increasing absolute drag experienced by cells of increasing size serves to negate the effects of decreasing SA:V. Moreover, the ultrastructure-mediated diameter of the flagellar apparatus remains constant while cell size changes, possibly resulting in smaller cells having disproportionately greater locomotive power.

Helical swimming in two species, {\it Gymnodinium} sp. and {\it Scrippsiella} sp., was observed to be faster than linear propulsion in {\it Chattonella} sp. As viscosity dominates the interactions between the microscopic organism and the medium (Kamykowski {\it et al}. 1992), helical propulsion may utilise energy more efficiently, being akin to a screw driven through wood rather than extracting a nail. The benefits of symmetry apparently outweigh those accorded by the resemblance between displaced transverse grooves and screw threads, as is demonstrated by the higher mean speed of {\it Scrippsiella} sp. compared to those of {\it C. monotis}, {\it Gymnodinium} sp. and {\it G. impudicum}. Drag may be increased through uneven water flow and eddy formation around asymmetric bodies. It is noted, however, that there is no evidence in two of the three SA:V classes that symmetry or style of propulsion has any general effect on swimming speed.


The small number of species tested qualifies this study only as preliminary. Further investigation involving an even broader taxonomic range, including freshwater species and the highly motile ciliates, is required for a fuller understanding of the relationship between symmetry and speed. Nevertheless, our results suggest that the swimming speed of unicellular marine phytoflagellates is not correlated to exomorphological symmetry or the style of propulsion. Even in lotic habitats where motility is significant in horizontal translocation, symmetry and the style of flagellar propulsion are unlikely criteria for natural selection for speed.


We are deeply indebted to Dr Michael James Holmes for his supervision and Dr Sow Chorng Haur for giving us the keys to his videomicroscopy lab so we could do research 24/7. The mentorship of Zeehan Jaafar and assistance by Dr Serena Teo, Dr Kuldip Singh, Dr Kanchan Mukherjee, Sasi Nayar, Lim Kim Yong, Rasvinder Kaur d/o Nund Singh, Ow Ping Yu, Abdul Latiff Zainal, Cathy Johnston, Uttamchandani Mahesh, Kamalesh Basu, Darwin Gosal and Leong Ji Hao are gratefully acknowledged. We also thank Connie Er, Soo Ka Jin, Lou Feng, Ng Foong Har, Lieutenant-Colonel Yeo Yew Hock and Patricia Netto for preliminary studies. This research was generously funded by the Special Programme in Science, National University of Singapore.\\

{\it Literature cited}

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Code in IDL 5.4 for measuring plankton swimming speed from digital videomicrographs
written by Lin Qi Feng

pro plankton_search, infiles, mcut, mgc,outfile

print, 'found ',nf,' files'

for i=1, nf do begin
print,'Processing ',i, ' out of ', nf, ' files'
if (i lt 10.) then begin
if (i ge 10. and i lt 100.) then begin
if (i ge 100. and i lt 1000.) then begin
if (i ge 1000.) then begin


w=where(ff(2,*) gt mcut, count)
if (count gt 0) then begin

nc=n_elements(g(*,0)) ; number of column in g
nr=n_elements(g(0,*)) ; number of row in g

if i ne 1 then list=[[list],[out]] else list = out

if i mod 20 eq 0 then begin
print,'file saved!'


pro plankton_speed_check, infile, n,datafile,speedfile



w=where(a(5,*) eq 2 )

for i=n, n do begin

for j=3, 499 do begin
ww=where(a(5,*) eq float(j))
w=where(abs(delx) lt 8.0 and abs(dely) lt 8.0, count)
if (count eq 1) then begin
cc=c(*,w) ; here this is the pos of the plankton in frame j


oplot,b(0,*),b(1,*),psym=5;, color=12



for k=0, nl-2 do begin
if (f2-f1 eq 1) then begin
r=sqrt( (x1-x2)^2 + (y1-y2)^2)

xtitle='Frame Number',$
ytitle='Plankton Speed (microns/second)'
print,' The average speed is ', avespeed,' microns/second'
print,' The max speed is ',z,' microns/second'

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