Pulsing Polyps in Complex Colonies
Biologists have considerable interest in simple pieces that combine into
a greater whole. Ants form a sophisticated society. A school of fish
turns sharply in unison. Pacemaker cells synchronize to a heartbeat
while billions of neurons conjure a thought.
The aquatic colony Hydractiniid Hydroid is composed of connected polyps,
cylindrical organisms capable of absorbing food from the environment and
digesting it. Though a polyp responds only to its immediate surroundings
and can interact with others only through a connecting tube for sharing
fluid, a colony of hundreds of individual polyps is capable of
integrated environmental responses. Nutrients are distributed to the
polyps that need them the most. Colonies develop with dramatically
different structures depending on the availability of food. (See an animation of a contracting polyp.)
To more easily simulate colonies with large numbers of polyps, Professor
Leo Buss of Yale University wanted to know if each polyp could be
represented as a simple non-linear oscillator. To assist him, Rimas
Surna, a specialist in advanced imaging techniques, developed a process
to convert videos of individual polyps into a digital representation
that could be studied in three dimensions with the aid of
Mathematica.
Click for larger view.
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Captured image of a polyp...
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Imaging software creates a digital outline of the interior...
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...which allows scientists to measure the volume at different points along the
length.
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Using the graph below, the shape of the polyp at any time during its
oscillations can be seen in the cross sections at the tops of the
ridges, the bottoms of the valleys, or for time in between. While the
oscillations on the side connected to the communal fluid of the colony
vary considerably, the big oscillatory peaks in the middle of the polyp
remain remarkably stable despite the external influences. This behavior
suggests analogies to non-linear systems such as certain types of
neurons whose multiple firings depend only on initial conditions.
Click for larger view.
Mathematica-generated graph of expansions and contractions along the length of a polyp.
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Are comparisons between otherwise disparate phenomena useful, or are
their similarities merely superficial? With the aid of advanced
visualization software such as Mathematica, each new experiment has
the potential to provide convincing evidence or inspire unexpected
connections.
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