encounter is best considered as effective diffusion with the diffusion coefficient Deff = u2τ/3 depending on u the
prey speed and τ the run time41. This process is considerably faster than Brownian diffusion of passive particles
with D = kBT/(6πμap), where kBT is the Boltzmann energy at 16 °C. For both diffusive processes the haptonema
is treated as a slender spheroid resulting in the clearance rate Q = 2πDlh/ln(lh/ap) (Table 2)42. Our estimates of
advective, diffusive, and ballistic clearance rates of P. polylepis show that all contributions are considerably lower
than the estimated guideline daily amount for heterotrophs. For micrometer-sized prey Brownian diffusion is
negligible. Encounters of motile prey, both ballistic and effective diffusive, give the highest estimated clearance
rates, however, still ten times lower than the GDA (Table 2).
We have shown that our analytical model can be used to represent near cell flows around freely swimming biflagellates
with different flagellar arrangements. With the model we identified trade-offs between equatorial flagellar
arrangements that favour fast and quiet swimming as opposed to puller arrangements that favour feeding. The
optimal force distance is far away to swim fast and close to the cell body in order to create the least flow disturbance.
The clearance rate estimates for the example of P. polylepis result in values which are too low to ensure survival
in the pelagic realm, and we therefore argue that photosynthesis and nutrient uptake are likely to be essential
for the survival of this species and potentially other mixotrophic biflagellates.
The time-averaged thrust force magnitudes per unit flagellum length in the two biflagellates were found to be
approximately equal (Table 1). Prymnesium parvum was shown to have a favourable equatorial beat pattern and
intermediate force distances that appear to make a compromise between fast and quiet swimming. Prymnesium
polylepis, in contrast, was, based on its time-averaged force arrangement, not found to be particularly optimal,
neither for swimming nor for advective feeding even though this species is dependent on encountering small
prey. The low advective contribution to prey capture is one possible reason why the flagellar arrangement in P.
polylepis is not defined by the optimum for steady advective feeding. Furthermore, the flagella and the highly
time-varying flows around them could hinder prey capture, if the flagella were in a puller arrangement positioned
close to the haptonema.
Another aspect of prey capture in P. polylepis is the design of the haptonema that is optimized as a long slender
structure favourable for prey encounter, but with physical limitations given by the cost of production, stability,
flow resistance, and the ability to reach the ingestion site at the back end of the cell. The created feeding flow does
not only support the motion of prey towards but also along the haptonema towards the aggregation point close to
the cell body (Fig. 1c). The Stokes drag on particles of 1 μm radius moving with the local flow velocity decreases to
around 0.4 pN at the distance of 5 μm from the cell body, reported as the typical location of the aggregation point8.
The transport of captured prey along the haptonema towards the aggregation point can therefore be purely due
to the flow created by the flagellar beat if the friction on the haptonema is not larger than this drag. We speculate
that the positioning of the prey at the aggregation point allows the haptophyte to hold on to the prey with the least
effort without blocking the capture of additional prey.
Some of the above predictions can readily be applied to other biflagellates. For example the 2–3 times speed
difference between the two swimming modes of C. reinhardtii could, according to our model analysis, be due to
the difference in angular force arrangements between the ciliary puller beat and the undulatory pusher beat22.
Furthermore the time-varying biflagellate model with moving point forces implies that an approximately four
times larger force is needed to propel the unsteady swimmer P. parvum, than the time-averaged model suggests.
A similar numerical factor has earlier been found by comparison of power dissipation in time-resolved and
time-averaged flows around C. reinhardtii26. As an outlook the model can be generalized to fit other microswimmers
with different numbers and arrangements of appendages, further taking into account body rotation using
the torque balance. It will in particular be relevant to examine how purely heterotrophic flagellates acquire sufficient
Cultures and observations. Cultures were grown in B1-medium (non-axenic) with a salinity of 32 at 20 °C.
They were subjected to 100 μmol photons m−2 s−1 on a 12:12 h light:dark cycle. Observations of swimming haptophyte
cells were made using an Olympus IX71 inverted microscope equipped with a 100 × DIC objective, and in
some cases an additional 2 × magnifying lens. Recordings were made using a Phantom V210 high-speed (1000 fps
for P. polylepis, 500 fps for P. parvum), high-resolution (1280 × 800 pixels) digital video camera. Fields of
view were 0.26 mm × 0.16 mm for P. polylepis and 0.13 mm × 0.08 mm for P. parvum. The organisms swam in
10 mm × 10 mm × 0.5 mm chambers mounted on a microscope slide with silicone grease. The microscope was
focused at the full working distance of the lens (150 μm) from the cover glass to limit wall effects. Observations
were made in an air-conditioned room set to 16 °C.
Flow measurements. Flow fields were measured with micro particle image velocimetry. The medium was
seeded with neutrally buoyant, polymer spheres with diameter d = 300 nm. The focal depth of the objective of
approximately 1 μm defined the thickness of the observation plane. Organisms were masked using ImageJ 1.46r
prior to analysis. We used a multi-pass algorithm in DaVis PIV software 8.0.6 (Lavision GmbH, Göttingen,
Germany) with decreasing size of the interrogation windows, with a final window size of 32 × 32 pixels with 75%
overlap. There were on average Np = 16 and Np = 4 particles in each interrogation window for P. polylepis and
P. parvum, respectively. The flow speed resolution limit due to Brownian motion of seeding particles was estimated
as vB = 2 D/(NpNft) with D = kBT/(3πμd), the time resolution Δt, and Nf the number of averaged
frames43. For the time-resolved flow fields we calculated vB = 8.8 μm s−1 for P. polylepis with Nf = 4 and
vB = 14.4 μm s−1 for P. parvum with Nf = 3.
Scientific Reports | 7:39892 | DOI: 10.1038/srep39892 8