Abstract
Pannychia moseleyi exhibits waves of bioluminescence under
neural control. The mean speed of propagation of the luminescent
waves is 16.8 +- 8.8 cm/s. Excitation propagates both in the radial
nerves and in the nerve net, with respective conduction velocities of
31.9 cm/s and 7.1 cm/s. The bioluminescence acts as an excitable
medium; however, the dispersion relation predicted by excitable
media theory between conduction velocity and period is not
observed. Pacemakers controlling the bioluminescence have periods
between 0.33 and 0.69 s. The activity of these pacemakers may be
controlled by an inward calcium current because the period of the
pacemaker increases in high concentrations of magnesium.
Introduction
Pannychia moseleyi is a benthic holothurian that lives between
500 and 3000 meters of depth. Complex waves of bioluminescence
propagate swiftly across the organism's dorsal surface. The simplest
patterns within these waves were studied using excitable media
theory. An excitable medium is a refractory system with spatial
dimension in which adjacent sections are coupled so that a wave of
excitation can propagate (Winfree, 1986). Excitable media theory
successfully explains oscillations in chemical media, but extension of
the theory to inhomogeneous biological systems such as
bioluminescence in Pannychia may strengthen the possible
applications to cardiac contractions and nervous systems.
The easily-detected bioluminescence serves as a useful
reflection of neural activity that controls the luminescent waves. The
non-invasive studies, although limited, may give important insights
into neural activity as a naturally occurring process rather than as a
result of experimental manipulation. The pacemaker neurons
mediating the repetitive waves of stimulation may eventually be
isolated by examining the innervation of the light-producing cells;
however, for now, intact animals provide initial insights into the
properties of the pacemaker neuron.
Materials and Methods
Pannychia were collected by the remotely operated vehicle
Ventana aboard the ship Point Lobos in the Monterey Bay from 550
to 900 meters in depth. The organisms were transferred to
Rubbermaid containers along with the mud that was grasped in the
collection process. We stored the containers in holding tanks
maintained at 5 C for the duration of the experiments. At least once
a week we replaced the sea water in the containers. We fed the
Pannychia nothing and exposed them only to red-filtered light.
Approximately once every three days, we filmed each animal.
We transferred the Pannychia to butter dishes full of sea water at
least 1/2 hour before filming. We used a Cohu Silicon Intensified
Tube (SIT) camera to capture both images illuminated obliquely with
an unfiltered flashlight and images of luminescence with no
background lighting. We stimulated the animals mechanically with a
glass rod.
We transferred images from videotape to optical disk using an
OMDR. We then analyzed the images using Megavision. Images
included in this paper were captured by scanning single frames from
optical disk or overlaying and averaging up to 20 frames. We
measured speed of propagation, space constant, and period of the
waves.
In some experiments, we altered the concentration of
magnesium chloride in the environment by mixing ratios of normal
sea water and isotonic magnesium chloride in the butter dish. We
ran experiments at 1 to 2, 1 to 5, and 1 to 7 isotonic magnesium
chloride to normal sea water ratios. We let the animal acclimate in
the high magnesium for 45 minutes before filming.
In other experiments, we transected the radial nerve in living
Pannychia. Using scissors, we snipped through the outer layer of the
animal about five centimeters from the caudal tip. In cutting the
nerve cord, we also cut epithelial layers around the nerve. In one
animal, we made two transections in a single radial nerve spaced one
centimeter apart.
Results
General appearance of bioluminescence
When prodded gently with a glass rod, Pannychia display a
complex pattern of luminescence. I use the word wave to describe
the propagation of a patch of light on the body surface. An area of
excitation consists of a section of the body that contains any number
of waves of luminescence. One response refers to all the excitations
caused by a single prodding.
Only the dorsal surface of the animal luminesces. The caudal
end of the animal responds more frequently regardless of stimulus
location. The papillae on the dorsal surface have no light-producing
capabilities (Fig 1). Animals show three distinct classes of response.
The most common class is defined waves of light moving across
darkness. Often, one portion a few square centimeters in area
remains excited for several seconds before this excitation migrates
gradually, saltates to another area, or ceases entirely. However, in
some animals, excited areas luminesce continuously with waves of
greater intensity moving within the glowing area. One Pannychia has
primarily small spots flashing rather than patches of light.
Wave front shapes
Whatever the class of response, the wave fronts form
characteristic shapes as well as complex patterns (Fig. 2). One shape
appears in the same location up to 15 times before the excitation
evolves and the pattern disrupts. In general, the direction of
propagation remains constant during repetitive waves; however, on
one occasion we observed a reversal of wave direction while the
wave shape and location remained unchanged. All wave shapes
annihilate upon collision (Fig. 3). Annihilation is the abrupt loss of
the intensity that occurs when two wave fronts approach each
other's refractory region.
Circular waves spread out from a single pulsing point. Circular
waves sometimes evolve into spiral waves with period 0.42 +- 0.04
s. Propagating waves consist of wave fronts moving in a defined
direction. These waves move most often along the radial nerve cords
and have curved or straight wave front shapes. Propagating waves
occasionally jump from one nerve cord to the other. Some waves
display dark bands perpendicular to the direction of propagation.
These dark bands consist of dark spots located at the base of the
papillae as well as patches connecting these spots. In some waves
with dark bands, a colorized frame from optical disk shows that
patches connecting the dark papillae spots are in fact faintly
illuminated (Fig 4).
Some propagating waves are what I term decomposable. In
decomposable waves, the overall direction of propagation appears to
be longitudinal; however, the excitation is actually a series of small
waves transverse to the radial nerve (Fig 5).
Quantitative analysis of propagating waves
The mean conduction velocity is 16.8 + 8.8 cm/s.
Measurements of the conduction velocity of individual waves range
from 5.18 to 40.3 cm/s. Even within a single animal, the velocity
typically varies 10 cm/s or more between different locations on the
body. For each measurement, we print a line on the monitor and
watch the waves in slow motion until both observers agree that the
line accurately reflects the direction of propagation of the wave. If
the line is not acceptable, either we correct the line and re-run the
analysis or we find alternate waves to measure. The image processor
plots the intensity at points along the line through time. We also
reject any readings whose scans through time do not have a definite
slope of maximum intensity. We aim for a total of ten or more
velocity readings along at least four different wave fronts for each
stimulation transferred to optical disk, but sometimes only one or
two velocity readings are acceptable.
Velocities from decomposable waves are not included in
averages and other analysis because their direction of wave
propagation is not clearly defined. For one such excitation, the radial
portion has speed 26.8 +10.7 cm/s. The transverse wavelets have
a mean conduction velocity of 7.06 +2.1 cm/s.
The period between repetitive waves ranges from 0.33 to 0.69
s with a mean of 0.50 + 0.09 s. Figure 6 shows the dispersion
relation, defined as the dependence of conduction velocity on period.
The points consist of averages of all the velocity and period readings
from a single stimulation. Waves that do not repeat at least three
times are not included in this analysis.
The space constant l, defined as the distance between the
maximum intensity and the leading edge of the wave front, averages
0.037 + 0.016 cm. The space constant is greater when the wave
front is curved rather than straight (Fig. 7). The curved and straight
velocities are statistically different (Mann-Whitney U-test, p«0.01).
Magnesium chloride vs. normal sea water experiments
Adding magnesium chloride at a ratio of 1/3 isotonic
magnesium chloride to 2/3 normal sea water to the Pannychia's
environment blocks all luminescence. Lower ratios increase the
threshold of the organism so that only stimuli of greater magnitudes
cause luminescence. The conduction velocity is not conclusively
altered by magnesium chloride (Fig. 8). The period between waves
increases in the high magnesium chloride experiments (Fig. 9). The
normal and magnesium periods are significantly different (Mann¬
Whitney U-test, p«0.05).
Trends and velocities in transection studies
Transection of the radial nerve can block the spread of
luminescence (Fig. 10). When a nerve cord is cut once and the
animal is stimulated ipsilateral and rostral to the cut, most of the
luminescence remains rostral to the cut, often with a marked wall at
the site of the lesion. Large responses can sneak around the cut, but
do not usually propagate far. A double transection of the same nerve
cord effectively blocks all transmission of luminescence caudal to the
lesion. The response to an ipsilateral stimulus in the tail does move
rostral to the double cut. Contralateral rostral stimuli do propagate
caudal to the single and double transections. The mean velocity of
responses in transected animals is 15.5 +1.3 cm/s.
Discussion
The patterns of response in Pannychia suggest control by nerve
nets as well as signaling by radial nerves. The average diffusion
constant Dç=vA for the Pannychia luminescence was 5.8E+9 u2/s.
Molecules diffuse at a maximum rate of 1000 u2/s in aqueous
solutions (Meyer, 1991); hence, the luminescent waves cannot be
account for by molecular diffusion. Modeling neural activity as the
diffusion of charge, Meyer calculated a diffusion coefficient of
6.7E+10 u2/s for a giant squid axon (1991). Because long-distance
voltage diffusion occurs only in the nervous system, the quickly
diffusing bioluminescence in Pannychia must be under neural
control. The tendency of the caudal end to luminesce more readily
also suggest neural control, for molecular diffusion generally would
not display such polarity. The tail of the Ptychodera flava (Baxter
and Pickens, 1964), a luminescent system controlled by nerve nets, is
also more sensitive to stimulation than the rest of the body.
The decomposable waves along the radial nerve involve
transmission of an impulse along the nerve cord that excites the
nerve net locally. Hence the signal has an overall longitudinal
direction as the radial nerve triggers sequential impulses to spread
transversely through the nerve net. This hypothesis is supported by
the relative velocities of the longitudinal and transverse parts. The
26.8 cm/s speed measured for the longitudinal part approaches the
conduction velocity of 55 cm/s in an ophiuroid radial nerve (Yee et
al., 1987). However, the 7.06 cm/s velocity of the transverse waves
is similar to nerve net conduction speeds in other organisms. Pantin
reported velocities of 10-20 cm/s for lateral conduction in
coelenterate nerve nets (1935).
The complexity of bioluminescent waves is based on the
interplay between pattern and randomness. Studying intensity in an
excitation area through time often shows that each point retraces the
same pattern of intensity with each repetition of the wave. However,
one cannot predict whether a pattern will repeat twice or twenty
times or where the excitation will migrate next. Waves tend to
retrace their predecessor's paths because of facilitation. Facilitation
occurs in nerve nets when each impulse eases the passage of
subsequent impulses. The radial nerve is most likely responsible for
the saltation of an excitation area, whereas migration of excitation
areas suggests facilitation. Facilitation enables migration because
impulses travel slightly farther than previous impulses, leading to an
overall extension or movement in the direction of wave propagation.
The transection experiments support the idea that radial and
nerve nets mediate different modes of evolution of excitation. When
excitation cannot travel through the radial nerve, luminescence
migrates rather than saltates. A double cut presents a greater block
to luminescence than a single cut by forcing the waves to travel
through greater lengths of the decremental facilitated nerve net. The
radial nerves work independently of each other to respond to local
stimuli, since ipsilateral and contralateral stimulation had different
effects. The nerve cords can communicate, however, for excitation in
non-transected animals can jump from one nerve cord to the other.
Using bioluminescence as a monitor of neural activity, we can
describe some properties of the Pannychia nerve net. The range of
conduction velocities between 5 and 40 cm/s is consistent with
neural conduction speeds. The wide range of velocities is due to two
main experimental errors: the decrease in normal speed for a curved
wave front and the difference in conduction speeds in waves
controlled by radial nerves and by nerve nets. Even so, Brehm
reported a range of 10 to 85 cm/s for bioluminescent propagation in
an ophiuroid (1977). An area of nerve net characterized more by
interneural facilitation than by through-conduction should have a
lower velocity (Pantin, 1935). Different paths of spread might
involve more synapses; hence, synaptic delay may decrease velocity.
Therefore, even if the two experimental errors limiting appropriate
comparison were avoided, we would see a range of velocities.
Because nerve nets act as excitable media, I thought the
neurally controlled bioluminescence might also be an excitable
medium. The existence of spiral waves and annihilation proves the
luminescence has a refractory period. Spiral waves exist because a
regular wave front such as a circular wave hits a region with
variable refractory periods, breaking the circle into a regular spiral
wave whose period depends on the refractory period. Waves
annihilate rather than pass through each other only in refractory
media. The absolute refractory period of the nerve net is necessarily
less than the minimum period observed between bioluminescent
pulses. Our maximum limit on the refractory period is 0.33 s, much
greater than the estimates for refractory periods in nerve nets of 40
to 65 ms (Pantin, 1935). The diffusion constant relationship often
applied to excitable media, De = vA, explains why A increases with
curvature, for normal velocity decrease for a curved wave front.
The dispersion relationship is a central equation describing
excitable media. Excitable media generally display an increase in
velocity with increasing period, for the medium is still in a relative
refractory period if the new wave is initiated too soon. The opposite
trend observed in this experiment suggest that the refractory period
is short enough that such slowing is not seen. The absolute
refractory period calculated by one model for calcium stores was 4.7
s, two orders of magnitude greater than the nerve net refractory
period (Lechleiter et al., 1991). Hence, this dispersion relation
predicted by theory (Gerhart et al., 1990) and verified
experimentally using the Belousov-Zhabotinskii reaction (Foerster et
al., 1989) may apply only to media excited by molecular diffusion.
10
At extremely short periods, the conduction velocity of Pannychia
bioluminescence should decrease with decreasing period; however,
the theory is not sufficient to describe the dispersion relation at
naturally-occurring periods.
The regularity of the impulses suggest control by a pacemaker
neuron. Bullock proposes two theoretical mechanisms for
endogenous rhythms, oscillating circuits and pacemaker neurons, but
states that no rhythmic oscillatory circuits have been described in
invertebrates; therefore, the neural rhythm is probably set by
pacemaker neurons (1965). Most pacemakers have, when excited, an
inward current that gradually depolarizes the cell to threshold. At
threshold, the action potential is generated, followed by quick
repolarization. The repolarization returns the cell to its initial state
in which the inward current causes the cycle to recur. Because the
pulsing points that initiate bioluminescence can be located anywhere
on the dorsal surface of the animal and because several points may
be pulsing independently at the same time, the pacemaker neurons
are most likely diffusely spread throughout the nerve net.
The period of the pacemaker depends on the magnitude of the
inward current, the threshold voltage, and properties of the cell
membrane. A nerve cell with a constant current can be modeled as a
simple RC circuit (Jack et al., 1983). The equation V = IR(I-etR
describes the voltage during the charging of a capacitor. The time
required to reach threshold is therefore t =-RC*In(1 - Vth/IR).
Increasing the threshold voltage will therefore increase the period as
it takes longer for the cell to reach threshold voltage.
11
The conduction velocity in a nerve net is also related to the
threshold voltage for action potentials. If the threshold voltage is
higher, accumulating enough charge for the post-synaptic potential to
reach the threshold voltage will take longer. This increase in
synaptic delay will slow conduction through the nerve net. Since an
increase in threshold corresponds to both a larger period and a
slower speed, the dispersion relation determined experimentally
agrees with the properties of the pacemaker neurons.
The increase in period under high magnesium conditions
suggests that the pacemaker neuron is depolarized by a current
carried at least in part by calcium ions. Most pacemaker neurons
studied in invertebrates have currents carried by calcium ions. Most
pacemaker neurons studied in Aplysia (Gorman et al., 1982), Helix
(Gerschenfeldet al., 1986), Tritonia (Smith and Thompson, 1985), and
calf Purkinje cells (Kass, et al., 1978) all have calcium-dependent
pacemakers. In Aplysia, the channels are permeable to magnesium,
but the mean open time is shorter when magnesium replaces calcium
in the environment. Other calcium channels are impermeable to
magnesium. Since magnesium blocks or alters calcium channels, the
change in period at high magnesium concentrations indicates that
calcium channels are involved in the oscillation of the pacemaker
neuron.
12
Acknowledgments
Thank you
to Edge, for studying the silent scream with me, for
measuring my kneecaps, and for making all those long nights fun.
to Stuart, for both giving advice and holding back so I could
think for myself.
to Sam, for teaching me those things a real physics major
should know.
to Molly, for advice, friendship, and good luck head-rubs.
to Chuck, for the Pannychia and the wise words.
to Chris, for all-around help and for good advice on my
presentation.
to Erin, Jay, Ildiko, and Adawia, for making me feel welcome
whenever I actually appeared during the day.
to Michelle and Ravi, for our silly, eccentric, amazing home.
Works Cited
Baxter, Charles H. and Pickens, Peter E. (1964). Control of
luminescence in hemichordates and some properties of a nerve
net system. Journal of Experimental Biology 41.
Brehm, Paul (1977). Electrophysiology and luminecence of an
ophioid radial nerve. Journal of Experimental Biology 71, 215.
Bullock, T.H., Mechanisms of integration. In Bullock, T.H. and
Horridge, G.A. Structure and Function in the Nervous system of
Invertebrates. (W.H. Freeman and Company, San Francisco,
1965) 314 - 322.
Foerster, P., Muller, S. C., and Hess, B. (1989). Critical size and
curvature of wave formation in an excitable chemical medium.
Proceedings of the National Academy of the Sciences of the USA
86, 6831-6834.
Gerhart, M., Schuster, H., and Tyson, John J. (1990). A cellular
automaton model of excitable media including curvature and
dispersion. Science 247, 1563-1566.
Gerschenfeld, H.M., Hammond, C., and Paupardin-Tritsch, D. (1986).
Modulation of the calcium current of molluscan neurones by
neurotransmitters. Journal of Experimental Biology 124, 73-91
Gorman, A.L.F., Hermann, A., and Thomas, M.V. (1982). Ionic
requirements fo rmembrane oscillations and their dependence
on the calcium concentration in a molluscan pace-maker
neurone. Journal of Physiology 327, 185-217.
Jack, J.J.B., Noble, D., and Tsien, R.W. Electrical current flow in
excitable cells (Clarendon Press, Oxford, 1983).
Kass, R.s., Lederer, W.J., Tsien, R.W., and Weingart, R. (1978). Journal
of Physiology 281, 187-208.
Lechleiter, J., Girard, S., Peralta, E., and Clapham, D. (1991) Science
252, 123-126.
14
Meyer, Tobias (1991). Cell signaling by second messenger waves.
Cell 64, 675-678.
Pantin, C.F.A. (1935). The nerve net of the Actinizoa. Journal of
Experimental Biology 12.
Smith, S., and Thompson, Stuart H. (1987) Slow membrane currents
in bursting pace-maker neurones of Tritonia. Journal of
Physiology 382, 425-448.
Winfree, Arthur T. When Time Breaks Down. (Princeton University
Press, Princeton NJ, 1986).
Yee, A., Burkhardt, J., and Gilly, W.F. (1987). Mobilization of a
coordinated escape response by giant axons in the ophiuroid
Ophiopteris papillosa. Journal of Experimental Biology 128.
15
Figure Captions
Figure 1: The waves have dark spots because the papillae do not
luminesce.
Figure 2: Common shapes of waves.
a) A circular wave on the left-hand side of the luminescence,
single frame.
b) A spiral wave, single frame.
c) A propagating wave, accumulation of 20 frames.
Figure 3: Annihilation
a) The wave fronts in the upper right approach each other,
single frame.
b) Three frames later, the wave fronts are just about to collide.
c) Four frames later, the intensity of hte colliding wave fronts
has almost disappeared.
Figure 4: Dark bands, accumulation of 20 frames. Patches between
papillae sometimes show faint lighting (purple dots).
Figure 5: The large arrow represents the overall direction of
decomposable waves. The small arrows represent the
individual wavelets that create the decomposable effect.
Wavelet 1 fires just before wavelet 2, followed by 3 then 4 as
the excitation propagates in the direction of the large arrow.
Figure 6: The dependence of speed of propagation on period. Each
point represents the average speed and average period for a
single bioluminescent response.
Figure 7: Comparison of the space constant X for curved and straight
wave fronts.
Figure 8: Comparison of the speed of propagation of bioluminescence
in normal sea water and in high magnesium chloride.
Figure 9: Comparison of the period between waves in normal sea
water and in high magnesium chloride.
Figure 10: Luminescence stops abruptly at the first cut in a double
transection of the radial nerve, single frame.
16








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