Digital holographic microscopy reveals prey-induced
changes in swimming behavior of
Jian Sheng*, Edwin Malkiel*, Joseph Katz*†, Jason Adolf‡, Robert Belas‡, and Allen R. Place‡
*Department of Mechanical Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218; and‡Center of Marine
Biotechnology, University of Maryland Biotechnology Institute, 701 East Pratt Street, Baltimore, MD 21202
Edited by J. Woodland Hastings, Harvard University, Cambridge, MA, and approved September 6, 2007 (received for review May 17, 2007)
The shallow depth of field of conventional microscopy hampers
analyses of 3D swimming behavior of fast dinoflagellates, whose
motility influences macroassemblages of these cells into often-
holographic microscopy data enables simultaneous tracking and
characterization of swimming of thousands of cells within dense
suspensions. We focus on Karlodinium veneficum and Pfiesteria
piscicida, mixotrophic and heterotrophic dinoflagellates, respec-
tively, and their preys. Nearest-neighbor distance analysis shows
that predator and prey cells are randomly distributed relative to
themselves, but, in mixed culture, each predator clusters around its
respective prey. Both dinoflagellate species exhibit complex highly
helical swimming trajectories and by translational and angular
velocity. K. veneficum moves in both left- and right-hand helices,
whereas P. piscicida swims only in right-hand helices. When pre-
sented with its prey (Storeatula major), the slower K. veneficum
reduces its velocity, radius, and pitch but increases its angular
scanning its environment as ‘‘a spinning antenna.’’ Conversely, the
faster P. piscicida increases its speed, radius, and angular velocity
but slightly reduces its pitch when exposed to prey (Rhodomonas
sp.), suggesting the preferred predation tactics of an ‘‘active
blooms or ‘‘red tides’’ (1), is vital to their success in aquatic
ecosystems (2). Predation, which involves complex microbial inter-
actions, is an important facet of the behavior of heterotrophic and
mixotrophic (combining phototrophic and heterotrophic nutrition)
dinoflagellates (3). Dinoflagellates typically move in helical trajec-
tories (4, 5), which may help them in detecting nutrient gradients
(6), although little is known about how differences in species or
environment (i.e., resource availability) affect their swimming
characteristics. However, evidence suggests that certain dinoflagel-
lates adapt swimming strategy that increases their encounter rate
with prey as the quarry concentration decreases (7).
Being limited by the shallow depth of field of conventional
microscopy, most studies of dinoflagellates’ swimming have been
performed in thin containers, where ‘‘wall effects’’ are likely to
affect behavior. Triggering of imaging systems as subjects cross
in-focus planes or 3D traversing systems that follow organisms
provide only limited solutions to this problem. The tendency of
dinoflagellates to cluster together in dense suspensions further
complicates measurements of behavior of individuals in their
natural setting. In this study, we use high-speed cinematic digital
holographic microscopy, as described in Materials and Methods, to
data on 3D swimming behavior of thousands of organisms in space
and time within dense suspensions of 50,000–100,000 cells per ml
that have substantial depth (3 mm, ?300 cell lengths). Obtaining
lates alone and comparing its statistics to those occurring in mixed
he swimming behavior of dinoflagellates, biflagellated plank-
tonic protists that are sometimes associated with harmful algal
cultures of dinoflagellate predators and their cryptophytes prey
enables us to quantify the substantial species-dependent change in
behavior of predatory dinoflagellates in the presence of prey.
As a representative for heterotrophic dinoflagellates, we mea-
sure the swimming characteristics of Pfiesteria piscicida, a relatively
fast (8) 5- to 20-?m voracious grazer (9) that is widely distributed
in temperate-subtropical estuarine waters (10, 11) and has been
linked to major fish kills, fish lesions, and adverse human health
impacts (12–15). As a representative of mixotrophic dinoflagellates
(i.e., those that graze prey and perform photosynthesis), we exam-
cell with a worldwide distribution (16, 17) that has been associated
with fish kills (18–20). P. piscicida can consume algal prey (9) two
to three times faster than K. veneficum (21). Although P. piscicida
depends on prey consumption for survival, K. veneficum does not.
The response to prey is examined for both species by introducing
cryptophytes (unicellular flagellated algae) into the media. We
show that both dinoflagellates regularly perform complex swim-
ming maneuvers, but their responses to introduction of prey are
Results and Discussion
Gallery of Motion of Individual Cells. In this section, we present
samples of the characteristic trajectories of the dinoflagellates
demonstrating the variability in raw data and the ability of digital
holographic microscopy to capture the shape and 3D motions of
multiple particles simultaneously in densely populated samples.
Spatial resolution is 0.975 ?m in directions parallel to the imaging
plane and 2 ?m in depth direction. Temporal resolution, as
determined by acquisition rate, is 120 Hz. Fig. 1a is a typical 3D
trajectory of a K. veneficum with velocity magnitude color-coded,
shown along with selected (1 in 20) in-focus images of the cell. In
particle. Additional K. veneficum tracks are presented in Fig. 1b.
The complexity of movement is self-evident, displaying varying
pitch and radius of helices, as defined in Fig. 1a, and velocity
magnitudes, which are typically in the 20–90 ?m/s range. Although
most helices are right-handed, this organism frequently switches to
left-handed helices. Fig. 1c shows a sample trajectory of K. venefi-
cum (red) moving in unison with its prey, Storeatula major (blue),
the latter being distinguished from predator by its smaller size (6–8
?m) and ellipsoidal shape. Selected images of predator and prey
Author contributions: J.S., E.M., and J.K. designed research; J.S. performed research; E.M.,
J.A., R.B., and A.R.P. contributed new reagents/analytic tools; J.S., J.K., J.A., R.B., and A.R.P.
analyzed data; and J.S., J.K., J.A., R.B., and A.R.P. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Abbreviations: NND, nearest-neighbor distance; PDF, probability distribution function.
†To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2007 by The National Academy of Sciences of the USA
October 30, 2007 ?
vol. 104 ?
the timing of each image. To provide clearer details, some images
are magnified ?4 and shown to the left of the trajectories.
Fig. 1d presents an overall view of an entire 0.8 ? 0.8 ? 3.0 mm
volume (the latter is depth), this time containing P. piscicida alone,
along with a magnified section of this sample. All four raw
databases of this study have similar ‘‘spaghetti’’-like patterns with
varying directions, scales, and velocity. Selected characteristic tra-
jectories of individuals, from this sample and from the one with
prey, are presented in Fig. 1e. Clearly, the velocity of P. piscicida is
higher than that of K. veneficum, reaching 380 ?m/s, and it varies
substantially over short distances. Essentially, all of the P. piscicida
trajectories are right-handed, but pitch and radius change signifi-
cantly along the same trajectory. Clearly, helical motion with
pitch of helices are species-dependent and altered by presence of
Statistics and Analysis of Swimming Behavior of Dinoflagellates.
Dynamics of dinoflagellate swimming can be characterized by
translational velocity (V), pitch (P), and radius (R) of helices and
angular velocity, ? ? 2?/? ? V/(R2? P2)1/2. Any three of these
Joint probability distribution functions (PDFs) involving these
parameters, highlighting swimming behavior of K. veneficum alone
for P. piscicida alone are shown in Fig. 2 c and g. Here, a negative
radius indicates a left-handed helical trajectory. Mean values and
sampled at every 40 time steps (0.33 s). (Insets) SEM and reconstructed image of K. veneficum. (b) Sample characteristic trajectories of K. veneficum cells. (Scale
bars: 50 ?m.) (c) Sample trajectories of K. veneficum and S. major moving in unison. To the right of trajectories are shown selected in-focus images of predator
and prey cells, with arrows indicating timing of image. To the left of the trajectories are shown some of the images magnified ?4 with arrows indicating
corresponding timing. (d) The 3-mm-deep sample volume showing trajectories of P. piscicida before introduction of prey. (Upper Inset) Close-up of part of the
?m.) (Inset) SEM of P. piscicida. [SEMs reproduced with permission (Copyright 1995, Florida Wildlife Conservation Commission).]
Gallery of dinoflagellate motion. (a) A 3D trajectory of K. veneficum, color-coded with cell swimming velocity, superimposed with in-focus images
Sheng et al.
October 30, 2007 ?
vol. 104 ?
no. 44 ?
standard deviations are provided in Table 1. Both dinoflagellates
move in helical trajectories, in agreement with prior observations
(5–9), with wide ranges of velocity, pitch, and radius. Although
PDFs of velocity vs. radius are broad (Fig. 2 a and c), in both cases,
velocity increases with radius. However, the mean velocity of the
slower K. veneficum is ?50% that of P. piscicida. The variability in
K. veneficum velocity is also much lower, as evidenced by corre-
sponding ?V(Table 1). The range of radii is similar (0–15 ?m), but
those of the P. piscicida helices are larger and always right-handed,
whereas K. veneficum swim in left-handed trajectories 25% of the
time. The mean pitch of K. veneficum’s helix and its standard
velocity magnitude of P. piscicida and its variability are 25% higher
than those of K. veneficum.
Substantial changes in all PDFs of swimming parameters of both
dinoflagellates occur in response to prey but trends differ. In the
presence of S. major (Fig. 2 b and f and Table 1), the mean and
variance of velocity, radius, and pitch of K. veneficum decrease.
Furthermore, the skewed radius–velocity joint PDF without prey
(Fig. 2a), which indicates preferred right-handed helices and ve-
locity increasing with radius, becomes symmetric in the presence of
prey (Fig. 2b), with smaller radii and almost equal chances of being
right or left-handed helices. The bimodal diverging PDF with
positive and negative radii indicates that velocity still increases with
radius. The radius–pitch PDF also becomes more symmetric (Fig.
2f) with branches extending to small positive and negative radii.
changes in velocity, radius, and pitch of P. piscicida movement. The
single-mode in joint PDFs of the organism alone (Fig. 2 c and g)
changes to bimodal distributions (Fig. 2 d and h). However, ?80%
of the population significantly increases its velocity and radius but
decreases its pitch. Although the overall mean velocity increases
only by 38% (Table 1), in part because of low speed contribution,
no prey to 320 ?m/s (Fig. 2 c and d). Similarly, the mean radius
increases by 20%, but the most probable value increases from 10 to
15 ?m. Even after introducing prey, essentially all P. piscicida cells
25% (Fig. 2 g and h).
PDFs of angular velocities for both organisms are shown in Fig.
3. In the case of P. piscicida, introduction of prey substantially
expands the distribution of ?, resulting in 67% increase in mean
value and 75% increase in standard deviation (Table 1). Clearly, in
the presence of prey, P. piscicida moves faster in a larger radius and
with a higher and more variable angular velocity. Unlike the
reduction in translational velocity of K. veneficum in the presence
of prey, the angular velocity increases. However, the PDFs (Fig. 3)
slightly since the distribution broadens, causing a 40% increase in
??(Table 1). In an attempt to elucidate this trend, we performed
conditional sampling of radius and pitch based on angular velocity.
A sample, conditioned on ? ? 7, is shown as an inset in Fig. 3. The
Table 1. Mean statistics of velocity, radius, pitch, angular velocity, and acceleration of the organisms
?V? ? ?V, ?m/s
?R? ? ?R, ?m
Pitch of a helix,
?P? ? ?P, ?m
??? ? ??, rad/s
?a? ? ?a, mm/s2
K. veneficum (control)
K. veneficum (with prey)
P. piscicida (control)
P. piscicida (with prey)
S. major (with predator)
Rhodomonas sp. (with predator)
80.9 ? 38.9
37.8 ? 40.1
173.8 ? 83.0
240.4 ? 112.6
61.3 ? 44.9
84.5 ? 26.6
4.3 ? 8.4
0.0 ? 6.2
9.6 ? 8.7
11.4 ? 9.0
?0.7 ? 5.5
0.0 ? 2.3
61.6 ? 52.8
35.2 ? 45.2
80.4 ? 70.4
60.9 ? 60.9
37.4 ? 49.0
44.6 ? 56.5
5.0 ? 2.7
6.8 ? 3.8
7.0 ? 3.5
11.7 ? 6.1
7.2 ? 4.0
3.0 ? 2.2
(0.66 ? 0.72) ? 104
(0.02 ? 0.0197) ? 104
(0.68 ? 0.66) ? 104
(1.25 ? 1.83) ? 104
(1.76 ? 1.66) ? 104
(2.24 ? 2.29) ? 104
?? Indicates ensemble mean, and ? indicates the standard deviation.
P. Each column represents a different experimental condition. (a and e) K. veneficum alone. (b and f) K. veneficum–S. major mixture. (c and g) P. piscicida alone.
(d and h) P. piscicida–Rhodomonas sp. mixture.
Joint PDFs of swimming behavior characterized by velocity (V), radius (R), and pitch (P) of helices. (a–d) Joint PDFs of V and R. (e–h) Joint pdfs of R and
www.pnas.org?cgi?doi?10.1073?pnas.0704658104Sheng et al.
peak is located at a radius of ?1 ?m and pitch of ?12 ?m,
significantly lower than the corresponding overall values, indicating
that elevated angular velocity is associated with small radius and
pitch. K. veneficum seems to slow down while increasing the
scanning frequency of its surrounding. Changes to the mean
motion, also demonstrate the different responses to prey. In sus-
pensions with predators alone, the mean accelerations of both
predators are very similar. After introducing prey, the acceleration
of P. piscicida increases by 83%, whereas the acceleration of K.
veneficum diminishes, indicating a slow nonvarying translation.
The very different responses of dinoflagellate predators of
similar sizes to introduction of prey indicate distinctly different
‘‘predation strategies.’’ The slower, less motile K. veneficum, when
exposed to prey that swim at a comparable velocity (Table 1),
Conversely, P. piscicida, which is faster than its prey, greatly
increases its linear motion and rotation rate. These dissimilar
behaviors are most likely associated with physiological differences
between organisms. P. piscicida uses a peduncle, an extensible
mouth-like feeding appendage, to capture prey directly, and seems
to adopt an ‘‘active hunter’s’’ tactics of chasing prey (10, 22).
Conversely, K. veneficum seems to use ‘‘ambush tactics’’ and then
(21, 23). The higher velocity and radius in the absence of food may
represent a ‘‘search mode,’’ aimed at increasing the volume being
scanned. By slowing down, K. veneficum reduces its own hydrody-
namic signature, possibly to camouflage its presence and decrease
the likelihood of being detected by prey. However, in the Stokes
flow low-Reynolds world (Re ? 0.001) for self-propelled bodies
(i.e., ignoring effect of gravity), the flow, induced by swimming, is
proportional to velocity but decays faster than the distance squared
(24, 25); i.e., the hydrodynamic signature of such motion is quite
local. One may also speculate that increasing its angular velocity
when the radius is small helps the K. veneficum detect prey by
operating as a ‘‘fast spinning antenna.’’
Structure of a Suspension: Nearest-Neighbor Distance (NND). Thecell
suspension structure and location of an organism relative to others
can be characterized based on the NND among individuals of the
same species and between predator and prey (26). The NNDs are
calculated from 3D loci of all dinoflagellates and prey at each given
moment. PDFs of ensemble averaged NNDs with and without prey
are presented in Fig. 4, each compared with a random distribution
(dash-dot lines) at the same concentration. Deviation from a
random distribution shows whether the likely position of an organ-
ism within a suspension is affected by presence of other particles.
Fig. 4 a and c compare NNDs of control samples, i.e., those
without prey, to those for all particles in samples with prey. Data
indicate that both control populations have random distributions
(null hypothesis) with confidence levels ?94% (z-scores of ?0.87
for K. veneficum and ?0.91 for P. piscicida). At a concentration of
50,000–100,000 cells per ml, both K. veneficum and P. piscicida
appear to be oblivious to other cells of the same species. A likely
contributor to this trend is the rapid decay of swimming induced
flow with distance (24, 25). This does not imply that there is no
momentary reaction to contact or proximity between cells, e.g., a
brief increase in K. veneficum velocity when it comes close to
another cell (Fig. 1a). However, such interactions have little effect
on NND statistics, suggesting that cell–cell interactions seem to be
short-lived and localized, e.g., altering trajectories to prevent col-
lision. They have little effect on how cells are arranged in a
in the presence of prey, conditioned on ? ? 7 rad/s.
concentrations. (a) Overall NND of K. veneficum alone and K. veneficum–S. major mixture. (b) Overall NNDs of P. piscicida alone and of P. piscicida–Rhodomonas sp.
mixture. (c) Cross-NND between predator and prey cells in K. veneficum–S. major mixture. (Inset) PDFs of auto-NNDs between predator and prey cells themselves. (d)
Cross-NND between predator and prey cells in the P. piscicida–Rhodomonas mixture. (Inset) Auto-NNDs between predator and prey cells themselves.
Probability density functions of NND (solid lines) superimposed with those obtained for random distributions (dash-dot lines) at the corresponding cell
Sheng et al.
October 30, 2007 ?
vol. 104 ?
no. 44 ?
suspension. Conditional samplings of velocity, acceleration, and
direction of swimming as a function of distance between cells (data
not shown) do not display significant trends, showing no evidence
that local interactions affect the statistics of motion.
In the K. veneficum data (Fig. 4a), a higher prey concentration
(Table 2) decreases the mean NND between particles. In the P.
piscicida case (Fig. 4c), prey and predator cultures have the same
concentration, i.e., the mean NND does not change when predator
cease to be random, showing clear evidence of clustering with
confidence level ?99% (z-scores of ?1.87 for the K. veneficum–S.
major mixture and ?2.98 for the Pfiesteria–Rhodomonas mixture).
Further understanding comes from measuring the auto-NNDs,
i.e., the distances among predator and prey themselves, and cross-
NNDs, the distance from predator to prey (Fig. 4 b and d). All four
auto-NNDs are nearly randomly distributed, i.e., there is no evi-
dence of clustering among organisms of the same species (z-scores
of 0.67 and ?0.51, respectively). Conversely, the cross-NNDs
deviate substantially from random distributions. Two-tailed testing
(27) shows 99.1% confidence in claiming clustering for the K.
veneficum–S. major cross-NND and 99.99% in the P. piscicida–
Rhodomonas case. Cleary, clustering in overall NNDs is caused by
predators preferentially locating themselves near their prey.
In the K. veneficum–S. major mixture (Fig. 4b), clustering is
manifested by a shift in the peak of the NND PDF from 115 to 95
?m, i.e., by approximately one cell length. Furthermore, there is a
considerable increase in the number of predator cells that are
located less than one body length (NND less than ?15 ?m) from
their prey. As noted before, we have seen seven cases of K.
veneficum and S. major moving in unison over the entire 13-s test
period, in trajectories that do not involve helical motion. The
distance between predator and prey remains almost constant, but
their relative orientation varies (Fig. 1c). Because K. veneficum
extends a capture filament to capture and haul in its prey in a
process lasting ?3 min (21, 23), it is possible we are observing part
of the predation process.
The PDF peak of the P. piscicida–Rhodomonas mixture remains
at the same distance, and clustering is manifested as a deficit
and augmentation at NND ? 30 ?m, i.e., approximately four body
lengths. Clustering causes a selective change in length scale, not a
broad-spectrum reduction in the NND that would characterize the
clustering of nonmotile particles in, e.g., turbulent flow (28).
Namely, a significant fraction of the P. piscicida cells, originally
located 15–25 cell lengths away from their prey, preferentially
reduction also appears in the NND PDF of K. veneficum–S. major
mixture, but it is less pronounced.
Holographic microscopy provides an unprecedented ability to
measure cellular behavior and interactions among microorganisms
in dense suspensions and analyze behavior in response to various
stimuli, e.g., characterization of helical motion, showing that K.
veneficum swims in both right and left-hand helices. Using detailed
statistics obtained in dense suspensions, we demonstrate that
dinoflagellates of similar size but with different swimming charac-
teristics, speed in comparison to prey, and feeding strategies
(peduncle vs. tow line) have substantially different responses to
introduction of prey. The distance between organisms of the same
species in dense suspensions, with or without prey, has a random
distribution, but predators clearly cluster around prey.
The present analysis should extend further, e.g., to search for
Levy Walk search strategy by following the procedures of Bar-
tumeus et al. (7). On first glance, the present frequency spectra of
time series of velocity components (data not shown) do not reveal
a range with power law decay with increasing frequency. It seems
that unlike the behavior of the dinoflagellate in (7) (Oxyrrhis
marina), the scales of directed motion and those of helical trajec-
motion. However, using the velocity component aligned with the
helix axis to estimate directed motion, the spectral slopes of this
component steepen (negative magnitude increases) when prey is
introduced for both K. veneficum and P. piscicida, clearly in agree-
ment with the study in ref. 7. Also, the previously mentioned
conditional sampling was based solely on the distance between
organisms, which does not reveal repeatable trends and appears to
oversimplify the causes of the changes in behavior. For example, (i)
even in Stokes flow, the induced motion by an organism is axisym-
metric and not circumferentially uniform, i.e., it depends on direc-
tion and (ii) for Peclet numbers of 1–2.5 (VL/D; D is molecular
diffusivity), the fore-aft chemical traces are not symmetric. Thus,
of motion, which is clearly achievable with the holographic micros-
Materials and Methods
Rhodomonas sp. (CCMP 768), and K. veneficum (CCMP 2064) and
it prey, S. major, in mid-log growth. P. piscicida and Rhodomonas
S. major were grown and maintained in f/2 growth medium (36), 15
parts per thousand salinity, based on water from the Indian River
Inlet, DE. Details on concentration and dimensions are summa-
rized in Table 2. Measurements are performed at water tempera-
Experimental setup of a digital holographic microscope and sample
Table 2. Experimental conditions and characteristics of organisms
cells per ml
K. veneficum (alone)
K. veneficum ? S. major
P. piscicida (alone)
P. piscicida ? Rhodomonas sp.
www.pnas.org?cgi?doi?10.1073?pnas.0704658104Sheng et al.
Setup and Data Acquisition. The optical setup is illustrated in Fig. 5.
Samples are placed in a glass cuvette with inner dimensions of 3 ?
3 ? 40 mm. Large dimensions in comparison to organism size
ensure that cells are less likely to be influenced by boundaries in
comparison with microscopic slides. Behavior is studied by using
in-line cinematic digital holographic microscopy, which enables
a dense volume (30). Other approaches to digital holographic
microscopy are described in refs. 31 and 32. Our process consists of
illuminating the cuvette with a collimated, spatially filtered, pulsed
ND:YLF laser beam (660-nm wavelength) and recording the
wall of the cuvette. Using a 20? objective lens, the hologram is
magnified and recorded for 13 s at 120 frames per second by a
CMOS camera with 1,024 ? 1,024 pixels, with a maximum acqui-
sition rate of 2,000 frames per second at full frame and 19 ? 19 ?m
pixels. Resolution is 0.975 ?m per pixel in planes parallel to the
hologram plane and ?2 ?m in depth. Image enhancement before
reconstruction includes removal of time-invariant defects, e.g.,
scratches on windows, equalization to correct for laser intensity
up-sampling to improve resolution. Numerical reconstruction (30,
33) performed at depth intervals of 10 ?m over the 3-mm sample
provides in-focus images of particles in each plane. Further details
are provided in supporting information (SI) Appendix.
Data Analysis. Information on cell locations is extracted by using a
hybrid, two-step autofocusing routine. First, 3D segmentation (30)
is used to construct the 3D shape of each cell, followed by edge
In-focus images of cells are stored along with the 3D location of
their centroid and their cross-section areas and volumes. Depth
resolution smaller than the distance between reconstructed planes
is achieved by fitting a Gaussian curves to surface integrals of
Laplacian derivatives in each plane (34). Tracking of cells in time
utilizes size, shape, location, 3D correlations, velocity, and accel-
eration as criteria (see SI Appendix). Using differential geometry
(35), helix parameters (Fig. 1) are calculated from the particle
position vector, r ?(t), using
V?t? ? ?r ?˙?t??; R ??e ?r ˙? ?e ?r ¨? e ?˙r ¨??e ?˙r ¨???
P ?e ?r ˙??e ?r ¨? e ?˙r ¨??e ?˙r ¨??
; ??? ? V?t??k2? ?2;
k ? ?r ?˙? r ????r ?˙3; ? ? r ?˙??r ?¨? r ?????r ?˙? r ???2,
where e ?(t) is a unit vector aligned with the vector indicated in
subscript, the number of dots indicates order of time derivatives, k
(as defined above) is the radius of curvature, and ? represents
torsion. Associated uncertainties are ?2.5% for 3D velocity and
?5% for radius and pitch.
During analysis, predators are distinguished from prey based on
shape and size. Besides automatic analysis based on measured
confirmed by manual examination of all in-focused images. The
mean fluid velocity in the test section is calculated based on motion
of particles moving in trajectories with zero radius, presumably
immotile cells or other particles. It varies spatially because of
existence of weak circulation, with maximum value of 25 ?m/s,
which varies little during each 13-s experiment. Local values are
subtracted from velocity of each particle. Results do not show
significant correlation between background fluid velocity and cell
velocity relative to the fluid.
The Johns Hopkins University group was funded by National Science
Foundation (NSF) Ecology and Oceanography of Harmful Algal Blooms
CTS 0625571. Instrumentation was funded by NSF Major Research Instru-
mentation Grant CTS0079674. The Center of Marine Biotechnology group
was supported by National Oceanic and Atmospheric Administration
Disease Control and Prevention Grant U50/CCU 323376, the Maryland
Department of Health and Mental Hygiene, and NSF Grant MCB-0446001
(to R.B.). This is contribution no. 07-175 of the Center of Marine Biotech-
nology and no. 243 from the Ecology and Oceanography of Harmful Algal
1. Ramsdellm JS, Anderson DM, Glibert PM (2005) in HARRNESS 2005,
Harmful Algal Research and Response: A National Environmental Science
Strategy 2005-2015 (Ecological Society of America, Washington, DC).
2. Kamykowski D (1995) J Phycol 31:200–208.
3. Graneli E, Carlsson P (1998) in Physiological Ecology of Harmful Algal Blooms,
eds Anderson DM, Cembella AD, Hallegraeff GM (Springer, Berlin), pp
4. Crenshaw HC, Ciampaglio CN, McHenry M (2000) J Exp Biol 203:961–982.
5. Fenchel T (2001) Protist 152:329–338.
6. Crenshaw HC (1996) Amer Zool 36:608–618.
7. Bartumeus F, Peters F, Pueyo S, Marrase C, Catalan J (2003) Proc Natl Acad
Sci USA 100:12771–12775.
8. Burkholder JM, Glasgow HB (1997) Limn Oceanogr 42:1052–1075.
9. Lin SJ, Mulholland MR, Zhang H, Feinstein TN, Jochem FJ, Carpenter EJ
(2004) J Phycol 40:1062–1073.
10. Parrow MW, Burkholder JM (2003) J Phycol 39:697–711.
11. Litaker RW, Steidinger KA, Mason PL, Landsberg JH, Shields JD, Reece KS,
Haas LW, Vogelbein WK, Vandersea MW, Kibler SR, Tester PA (2005) J
12. Burkholder JM, Glasgow HB, Hobbs CW (1995) Mar Ecol Prog Ser 124:43–61.
13. Grattan LM (1998) MD Med J 47:148–151.
14. Fleming LE, Easom J, Baden D, Rowan A, Levin B (1999) Toxicol Pathol
15. Burkholder JM, Glasgow HB (2001) Bioscience 51:827–841.
16. Li AS, Stoecker DK, Coats DW (2000) J Plank Res 22:2105–2124.
17. Marshall HG (1999) VA J Mar Sci 50:281–285.
18. Terlizzi DE, Stoecker DK, Glibert PM (2000) in AQUA 2000, eds Flos R,
Ressell L (European Aquaculture Society, Nice, France).
19. Kempton JW, Lewitus AJ, Deeds JR, Law JM, Wilde SB, Place AR (2002)
Harmful Algae 1:233–241.
21. Li AS, Stoecker DK, Adolf JE (1999) Aquat Microbial Ecol 19:163–176.
22. Cancellieri PJ, Burkholder JM, Deamer-Melia NJ, Glasgow HB (2001) J Exper
Marine Biol Ecol 264:29–45.
23. Adolf JE, Krupatkina D, Bachvaroff T, Place AR (2007) Harmful Algae
24. Stone HA, Samuel ADT (1996) Phys Rev Lett 77:4102–4104.
25. Childress S, Koehl MAR, Miksis M (1987) J Fluid Mech 177:407–436.
26. Malkiel E, Abras JN, Widder EA, Katz J (2006) J Plank Res 28:149–170.
27. Walpole RE, Myers RH (1985) Probability and Statistics for Engineers and
Scientists (Macmillan, New York).
28. Eaton JK, Fessler JR (1994) Int J Multiph Flow 20:169–209.
29. Alavi M, Miller T, Erlandson K, Schneider R, Belas R (2001) Environ Microbiol
30. Sheng J, Malkiel E, Katz J (2006) Appl Opt 45:3893–3901.
31. Colomb T, Durr F, Cuche E, Marquet P, Limberger HG, Salathe RP,
Depeursinge C (2005) Appl Opt 44:4461–4469.
32. Xu WB, Jericho MH, Meinertzhagen IA, Kreuzer HJ (2001) Proc Natl Acad
33. Malkiel E, Sheng J, Katz J, Strickler JR (2003) J Exp Biol 206:3657–3666.
34. Russ JC (2007) The Image Processing Handbook (CRC, Boca Raton, FL).
35. Berger M (1988) Differential Geometry: Manifolds, Curves, and Surfaces
(Springer, New York).
36. Guillard RRL (1975) in Culture of Marine Invertebrate Animals, eds Smith WL,
Chanley MH (Plenum, New York).
Sheng et al.
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