SIAM News Blog

The Math of Dinoflagellate Predation

By Karthika Swamy Cohen

Single-celled algae called dinoflagellates form the second largest group of phytoplankton. 

They can be auto-, hetero-, or mixotrophic, meaning some can self-nourish with inorganic materials, others can only use organic carbon for growth, and still others can utilize both organic and inorganic sources of carbon.

Marine dinoflagellates are known to produce a diverse variety of complex toxins, utilized to enhance predation. Observations have revealed that toxin production by mixotrophic dinoflagellates may facilitate predation by immobilization of prey.

Dinoflagellates exhibit complex swimming dynamics. They use two flagella, a transverse flagellum and a longitudinal flagellum, the combination of motion of the two resulting in a helical swimming pattern. This type of movement allows the cell to orient itself based on chemical gradients and the presence of prey. Predatory dinoflagellates significantly alter their swimming behavior in the presence of prey. 

Dinoflagellates can cause harmful algal blooms. The picture shows an algal bloom off the southern coast of Devon and Cornwall in England, in 1999. Image credit: Wikipedia
The mixotrophic dinoflagellate, Karlodinium veneficum is found globally, and produces a potent toxin, karlotoxin, which kills fish and causes harmful algal bloom formation. It has been previously observed that, in addition to slowing down and immobilizing prey, K. veneficum also dramatically alters its own swimming behavior in the presence of prey. 

Michael Mazzoleni’s group at Duke University investigates how K. veneficum uses toxins to immobilize prey and thus increase feeding rate. At a minisymposium on mathematics of plankton at the SIAM Conference on Mathematics of Planet Earth, Mazzoleni described the use of numerical simulations to analyze predator-prey dynamics of dinoflagellates.

Using the knowledge of swimming properties of phytoplankton and fundamental physical laws, his team characterized the predation rate of dinoflagellates and derived a mathematical model for predation. This is the first mechanistic model advanced to describe predation rates of K. veneficum.

The simple model mechanics used to study these interactions are derived from chemical kinetics. The researchers calculate relative velocity and contact angle based on predator density and encounter rates between predator and prey.

Scanning electron microscope image of a dinoflagellate. Image credit: Wikipedia

Assuming perfectly efficient predation, this method offers a simple model for predator-prey interactions, which is a function of experimentally-measurable parameters. The model is then modified to account for inefficient predation. This is calculated by exploring situations in which the prey is able to escape, such as, high velocity when predator and prey bump into each other, leading them to bounce off each other, quick predator movement which may alert prey of its arrival, and so on. 

Experimental studies were shown to closely match model predictions. Based on experimental observations of predatory dinoflagellate behavior, additional simulations were run to account for more complex dynamics. 

Results from these computational simulations were seen to closely match the experimentally observed behavior of K. veneficum during predation. These studies reinforce the hypothesis that predatory dinoflagellates use toxins to increase their feeding rate. Numerical simulations of predator-prey interactions were seen to align with experimentally observed predatory behavior.

Using this model, the researchers demonstrated that toxin-induced changes in swimming behavior of K. veneficum as well as its prey augment predation by impacting the frequency of predator-prey encounters and making these encounters more productive for predation.

  Karthika Swamy Cohen is the managing editor of SIAM News. 
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