Download Vibration Sensitivity and a Computational Theory for Prey

AMER. ZOOL., 41:1229–1240 (2001)
Vibration Sensitivity and a Computational Theory for Prey-Localizing
Behavior in Sand Scorpions1
PHILIP H. BROWNELL2,*
AND
J. LEO
VAN
HEMMEN†
*Department of Zoology, Oregon State University, Corvallis, Oregon 97331
†Physik Department, TU München, D-85747 Garching bei München, Germany
SYNOPSIS. As burrowing, nocturnal predators of small arthropods, sand scorpions have evolved exquisite sensitivity to vibrational information that comes to them
through the substrate they live on, dry sand. Over distances of a few decimeters,
sand conducts low velocity (;50 m/sec) surface (Rayleigh) waves of sufficient amplitude and bandwidth (200, f ,500 Hz) to be biologically detectable. Eight acceleration-sensitive receptors (slit sensilla) at the tips of the scorpion’s circularly arranged legs detect surface waves generated by prey movements or ‘‘juddering’’
signals from other scorpions. From this input alone, direction of the disturbance
source is calculated up to 20 cm distance. By ablating slit sensilla in various combinations on the eight legs, the contribution each makes in computing target location can be assessed. Other behavioral experiments show that differential timing
of surface wave arrival at each sensor is most likely the cue that determines target
location. Given the simplicity of this sensory system, a computational theory to
account for wave source localization has been developed using a population of
second-order neurons, each receiving excitatory input from one vibration receptor
and inhibition from the triad of receptors opposite to it in the eight-element array.
Input from a passing surface wave opens and closes a time widow, the width of
which determines the firing probability of second-order neurons. Target direction
is encoded as the relative excitation of these neurons, and stochastic optimization
tunes the relative strengths of excitatory and inhibitory inputs for accuracy of
response. The excellent agreement between predictions of the model and observed
behavior of sand scorpions confirms a simple theory for computational mapping
of surface vibration space.
VIBRATIONAL COMMUNICATION AND PREY
LOCALIZING BEHAVIOR OF SAND SCORPIONS
Beyond direct contact, vibrational communication implies the existence of a medium capable of conducting mechanical
waves between a message sender and a
message receiver. Judging from the steady
growth of literature on vibration sensitivity
in psammophilous animals (Salmon and
Horsch, 1972; Brownell, 1977, 1984; Aicher and Tautz, 1990; Henschel, 1997; Brownell and Polis, 2001; Mason and Narins,
2001), sand appears be a particularly favorable substrate for conduction of mechanical
information. In this paper we describe the
prey localizing behavior of the Mojave
1 From the Symposium Vibration as a Communication Channel presented at the Annual Meeting of the
Society for Integrative and Comparative Biology, 3–7
January 2001, at Chicago, Illinois.
2 E-mail: [email protected]
Desert sand scorpion, Paruroctonus mesaensis, and some of the physical properties
of loose sand that make it a good conductor
of surface waves. The exquisite sensitivity
of Paruroctonus to vibrational information
is certainly not limited to signals emanating
from prey alone, however, and likely mediates intraspecific vibrational communication in the form of ‘‘juddering’’ movements
(sudden strong lurches of the body forward), tail thumping and tail wiping behaviors commonly observed in psammophilic
scorpions (Tallarovic et al., 2000; Brownell
and Polis, 2001). In this way an evolutionary connection may be drawn between passive detection of vibrational information for
purposes of orientation to food and the
more evolved process of active signal generation for purposes of communication between conspecifics.
Sand scorpions make excellent models
for analysis of surface vibrational infor-
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AND
mation, as much for the physical simplicity
of the substrate they inhabit as for the elegant simplicity of the predatory behavior
they display. In many respects the scorpion’s orientation to prey disturbing the flat,
featureless surface of a sand dune is the
same sensory problem that orb spiders face
in orienting to prey caught up in a web, or
that water striders encounter in locating
prey struggling at the surface of a pond.
With these similarities in mind, we expect
the study of predatory behavior in sand
scorpions to transcend vibrational media
and address the more general question of
how animals make sense of mechanical information propagating through space. For
this we present a computational model conceived for the specific circumstances and
behaviors of sand scorpions but simple
enough to apply as a general theory for perception of vibrational information conducted along free surfaces.
Vibration-source localizing behavior
quantified
Paruroctonus mesaensis is an ambush
predator of insects and other scorpions, always hunting at night from a motionless
rest position outside its burrow on the sand
surface. When prospective prey approach
within 20 cm, the sand scorpion first assumes an alert posture with its body slightly
elevated from the substrate and the pedipalps (organs of prey capture) extended and
open forward. Subsequent disturbances of
the sand by the prey evoke a sequence of
quick rotations with forward movements toward the target until the pedipalps can grasp
and immobilize the prey for stinging. Scorpions are naturally fluorescent under portable blacklights (Fig. 1) so that images of
this predatory orientation response (POR)
can be captured on film at night and subsequently measured for accuracy in the laboratory. The two components of the POR—
the angle of turning and the distance moved
toward the prey—were both shown to be
highly accurate within 10 cm distance
(Brownell and Farley, 1979a), confirming
the impressions from field observations that
prey within this radius are nearly always
captured in a single orientation response.
A second orientation behavior of Paru-
J. L.
VAN
HEMMEN
FIG. 1. The Mojave sand scorpion, Paruroctonus mesaensis, in its hunting stance with tarsi resting on sand
in a circular array. Photo taken under ultraviolet illumination shows natural fluorescence of the cuticle.
roctonus, the defensive orientation response (DOR), has more utility for experimental analysis of vibration sensing behavior because it is easily and repeatably
evoked in the laboratory when animals are
agitated into defensive posture. The DOR
is characterized by the same accurate rotation of the body to align the pedipalps
toward a vibrational disturbance but there
is no forward movement. Figure 2 shows
an example of the accuracy of DOR for
stimuli presented at 8–10 cm distance.
With this angular component of vibration
source localization assayable under controlled conditions, we have a means of
demonstrating that the signals used by the
scorpion to determine stimulus location are
mechanical waves propagating along the
surface of sand (Brownell, 1977, 1984).
Wave propagation in sand
When considering the prospects for vibrational communication between animals,
our attention is drawn immediately to the
solid substrates through which the signal
must pass. From a physical perspective,
most natural substrates are massive, rigid
and highly inelastic to conduction of mechanical waves when compared to air and
water. Unlike air and water which, by com-
VIBRATION SENSORY SYSTEM
FIG. 2. Accuracy of orientation to vibrational stimuli
presented to Paruroctonus. A. The angle of the turning
response (ordinate) to target stimuli presented at various angles (abscissa) 8–10 cm away is accurate (●)
compared to perfect response (dashed line). B. When
vibration receptors on the left legs (BCSS L1–L4, darts
in inset) were inactivated by puncture with a pin, turning behavior was biased toward 908 right, indicating
the ablated animal’s perception of stimulus direction
was calculated from the remaining (R1–R4) receptors.
D, O; responses of two animals, both with L1–L4 sensors ablated.
parison, are excellent conductors of sound,
light and volatile chemical substances, solid
media are difficult to move and absorbent
to mechanical waves. But dry sand, like
that found in desert dunes is a surprisingly
good conductor of the wave type that carries most of the energy away from surface
disturbances—the Rayleigh wave.
The physical characteristics of sand
waves are summarized in Figure 3. ‘‘Substrate vibration’’ is an imprecise term used
to describe mechanical movements of a solid substrate. Beyond a short distance from
the source of disturbance, mechanical motions in solids propagate as one of four elastic waves (White, 1965; Graff, 1975). Two
of these are body waves—the compressional and shear waves, and two conduct along
the surface—the Rayleigh and Love waves
(Fig. 3A). The properties of these waves
and the proportion of source energy transported by each depends on physical properties of the substrate and the disturbance.
These values for dry, loose sand have been
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measured (Brownell, 1977; Aicher and
Tautz, 1990) as summarized in Figure 3a.
Over distances of a few decimeters, loose
sand is a surprisingly good conductor of
low velocity (;50 m/sec) surface (mostly
Rayleigh) waves, the wave type that conducts more than 70% of the mechanical energy away from the source. Furthermore,
regardless of the disturbance that creates vibrational energy at the source, most of the
surface wave component propagating beyond a few centimeters is contained within
a bandwidth of 300–400 Hz (Fig. 3B). At
these frequencies frictional loss of energy,
measured as the coefficient of absorption,
a10, and expressed in units of decibels attenuation per centimeter distance, is sufficiently low that nearly all of the signal loss
with distance is attributable to geometric
spreading of the wave front (Fig. 3c). These
are effectively the same factors of attenuation existing at the surface of water.
Vibration sensing
In sand scorpions, vibrational stimuli are
sensed by slit sensilla embedded in the cuticle (Brownell and Farley, 1979b). As in
other arachnids, slit sensilla are typically located near joints in the exoskeleton where
they monitor changes in tension during locomotion (Barth, 1985). In sand scorpions
the 6 to 7 slits just proximal to the basitarsal–tarsal joint of each leg (Fig. 4) are particularly large and responsive to small amplitude accelerations of the tarsi resting on
the substrate (e.g., vibrational stimuli). Together, the eight sense organs act as an array
of accelerometers, arranged around the circle of contact points the scorpion’s legs
(tarsi) make with the substrate (Fig. 1). Behavioral experiments show this simple field
of receptors generates the input from which
target direction is accurately calculated
(Brownell and Farley, 1979c).
Morphological and physiological analysis of the basitarsal slit sensilla (BCSS)
show them to be of typical arachnid structure, with two neurons innervating each slit.
One BCSS with six slits contains 12 afferent neurons, but only one or a few of these
respond reliably to threshold levels of stimulation. This can be shown electrophysiologically by accelerating the tarsus at small
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P. H. BROWNELL
AND
J. L.
VAN
HEMMEN
FIG. 3. Wave propagation in dry sand. A. Diagram and table summarizing physical properties of surface and
body waves propagating away from a source disturbance in dry sand. B. Left panel: Surface wave recordings
from two accelerometers placed at 21 cm (upper trace) and 81.5 cm (lower trace) from an episodic surface
disturbance. Right panel: Fast Fourier transform spectra for the recordings to the left, showing most energy of
the wave is contained in a narrow band centered at about 350 Hz (from Aicher and Tautz, 1990, with permission).
C. A comparison of factors contributing to attenuation of the surface wave (i.e., geometric spreading, and
absorbance at a10 5 0.23 db/cm) shows most of the loss is due to simple spreading of the wave front. Threshold
acceleration for BCSS stimulation is below 0.01 m/sec2 (ref. Fig. 4).
amplitudes and variable frequency (Fig. 4).
At low frequencies (;100 Hz) the receptor
cells in one slit respond with phase-locked
regularity relative to periodic motions of
the stimulus. At higher frequencies (.500
Hz), unit responses (‘‘spikes’’) from the
BCSS appear to remain phase-locked even
though failing to respond to every cycle of
oscillation. This apparent phase-locking of
the sensory response to peaks in the acceleration stimulus is the first indication that
highly accurate timing of the stimulus arrival at each leg may be important to sensory processing in this system. By varying
the frequency of the vibrating stimulus and
measuring the threshold amplitude necessary to evoke a sensory response, it is possible to show that acceleration sensitivity
over the bandwidth of 200 to 500 Hz, the
same bandwidth containing most of the vibrational energy of sand (Fig. 3b), is below
1 cm/sec2. Such sensitivity accounts for the
animal’s ability to detect strong signals
from prey (i.e., sand burrowing cockroaches) beyond 30 cm distance (cf. Fig. 3c).
Mechanisms of source localization
If the eight BCSS are the only source of
sensory input required for accurate determination of vibration source location, then
it should be possible to ‘‘blind’’ sand scorpions to vibrational stimuli by ablating just
these receptors. Furthermore, since there
are only eight of them, selective elimination
of part of the sensory field should preserve
some level of sensitivity to vibrational stimuli while compromising accuracy of the
turning response in a predictable pattern. As
predicted, animals with all eight of their
BCSS ablated are unresponsive to local disturbance of the substrate, and those with
two or more sensilla intact continue to respond to stimulation but with systematic
patterns of inaccuracy. An example of the
latter is shown in Figure 2, for animals
missing the left half of their sensory field
VIBRATION SENSORY SYSTEM
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FIG. 4. Vibration receptors and sensory response. A. Diagram of the tarsus (T) in P. mesaensis showing location
(SS) of the BCSS just above a terminal leg joint. (M, C, MC, LC, PS; hairs and claws aiding support of the
tarsus on sand). B. Photomicrograph of slit sensilla (ss) with their mechanosensory neurons (m) labeled by
neuronal tracer dye. C. Electrophysiological response, Ve, recorded from a single BCSS slit. Sensory units
respond at fixed phase intervals relative to vibrational accelerations, Vd, applied in realistic bursts to the tarsus.
Calibrations: upper traces, 1 mV; lower traces, 1 cm/sec2.
(i.e., all receptors on the left legs ablated).
The manipulated animals still respond vigorously to stimuli presented at all angles,
but the turning response is, itself, unilateral
(toward the intact right side). Moreover,
even for targets presented toward the intact
side of the animal, the accuracy of turning
is biased toward the mean direction of the
remaining legs, that is, about 908 right. Various combinations of sensory ablation similar to this one (Brownell and Farley,
1979c; cf. Fig. 7) give clear indication that
input from all sensors is integrated during
the assessment of target location, not just
those few sensors closest to the source.
Thus, the BCSS are both necessary and sufficient input for directing the sand scorpion’s turning response and some form of
central integration of their combined input
will specify direction.
Another way to access the mechanism of
source localization is to alter the pattern of
sensory stimulation by placing fully intact
animals on manipulated substrates. One approach is to introduce a thin (;1 mm) gap
of air into the substrate beneath a scorpion
so that its left and right legs rest on separate
and vibrationally uncoupled half-spaces
(Brownell and Farley, 1979a, c). Under
these circumstances the animal behaves as
though only half its legs are receiving input,
the left legs or the right legs, depending on
which side of the gap the target is presented.
A variation of this experimental manipulation uses piezoelectric crystals to vibrate
the two half-spaces independently, thus
gaining control over the amplitude and timing of substrate movements beneath the
right and left legs (Fig. 5). These investigations show that either relative amplitude
or timing of stimulus presentation can be
used independently as a cue for source localization (Brownell and Farley, 1979c).
However, when amplitude and timing cues
are presented in opposition to each other
(e.g., a dichotomous stimulus where amplitude predicts turns in one direction and timing in the opposite direction), scorpions
demonstrate preference for the timing cue
by turning in the direction of the platform
that moves first rather than at greatest amplitude. This experiment also shows that
sand scorpions can detect time intervals between stimulation of the legs as small as 0.2
msec, well below the transit time required
for a Rayleigh wave to cross the expanse
of the sensory field (diameter/VR ø 1 msec).
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P. H. BROWNELL
AND
J. L.
VAN
HEMMEN
computational analysis. The success or failure of such a model, as judged by how well
it predicts observed behavior, will direct our
attention to what needs further clarification
through neurobiological analysis.
FIG. 5. Experiment demonstrating the importance of
stimulus timing as the cue for source localization.
When right and left legs of a scorpion are placed on
separate platforms separated by a narrow gap, the two
halves of the sensory field can be stimulated independently at different times and amplitudes relative to
each other using pulse trains from two piezoelectric
transducers (TR, TL). Plotted points show mean angle
of turn (6SE) for variable time intervals (Dt) between
movements of the left and right platforms. The inset
shows time-shifted (Dt) pulse trains (125 Hz, 1 sec
duration) applied to left (TL) and right (TR) platforms.
(After Brownell and Farley, 1979c).
Thus, the temporal responsiveness of the
sensory system appears to be well within
sufficiency for resolving which legs are
closest to the wave source. With these essential facts in hand, we can begin to construct a neural model for perception of vibrational space around the sand scorpion.
A COMPUTATIONAL MODEL OF VIBRATION
SOURCE LOCALIZATION
If timing of vibrational stimulation to a
field of eight vibration sensors is sufficient
information for the sand scorpion to determine source direction, how might neuronal
circuitry in the animal’s brain transform information in the temporal domain (time of
stimulus arrival at each receptor) into information in a spatial domain (the angle of
the turn to be made)? The mapping of time
into space is a characteristic feature of auditory processing networks for which there
is a considerable literature (Carr and Konishi, 1990; Buonomano and Merzenich,
1995; Grothe, 2000), but little has been
done to illuminate the mechanisms for perception of mechanical waves propagating
along free surfaces. It is instructive to begin
such analysis by constructing a theory of
how localization might work, one simple
enough to be expressed mathematically for
Formulation of the model
We begin formulation of the model
(Stürzl et al., 2000) by representing the spatial structure of the scorpion’s vibrational
sensory field in mathematical terms, then
calculating the temporal information available to the animal during the passage of a
simulated natural signal, the Rayleigh
wave. The tarsi of adult Paruroctonus and
their vibration sensors are arranged in a circle (Fig. 1) of radius R ø 2.5 cm in adults.
Furthermore, in their hunting stance, each
tarsus is held at relatively fixed positions
given by angles gk 5 6188, 6548, 6908,
61408, where 08 is directly anterior (see inset Fig. 2). We label these inputs individually as 1 # k # 8 moving clockwise from
the right front leg. The Rayleigh wave generated by a stimulus at angle wS and distance r from the leg-circle center approximates a plane wave when r $ 8 cm. For a
given stimulus angle, wS, the time difference Dt (gk, glzwS) between the arrival of a
wave at two BCSS on tarsi at angles gk and
gl is then
Dt(gk , gl z wS )
5 {R/vR}[cos(wS 2 gl ) 2 cos(wS 2 gk )]
(1)
so that Dt ∈ [2Dt0, Dt0] with Dt0 5 2R/vR.
A quick inspection of Eq. 1 shows that for
opposed legs (gk 5 gl 1 1808) the cosine
term is 2cos(wS 2 gl, giving 2R (circumference of the leg circle) divided by propagation velocity of the Raleigh wave (vR) as
the maximal time interval the scorpion can
experience. That is, Dt ;1 msec.
The next step in model formulation is to
make an informed guess at the neuronal
mechanism that could transform time information into patterned neuronal activity in
the scorpion’s brain. While we know comparatively little about the neuroanatomy of
scorpion central nervous systems, we have
fairly detailed studies of spiders showing
ring-shaped integrative neurons in the sub-
VIBRATION SENSORY SYSTEM
OF
SAND SCORPIONS
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FIG. 6. Inhibitory triad model to account for vibration source localization in sand scorpions. The circular array
of BCSS receptors (outer circles), at fixed angles g relative to the sensory field center, innervate eight command
neurons (inner circles). Two of the eight associated inhibitory neurons (grey) are shown (for clarity, only those
corresponding to R3 and L2). Inhibitory and excitatory synapses are represented as open or darkened circles,
respectively. This arrangement of neurons and interactions is hypothetical but consistent with other time-measuring circuits in vertebrates (Carr and Konishi, 1990). (After Stürzl et al., 2000).
oesophageal ganglion (SOG) where fiber
tracts from the eight legs converge (Babu
and Barth, 1984; Babu, 1985; Gronenberg,
1989, 1990; Anton and Barth, 1993). Similarly, we know from behavioral observations of sand scorpions that vibration source
localization requires integrative input from
multiple receptors within the ring of eight,
with receptors nearest and farthest away
from the target having the greatest impact
on accuracy (Brownell and Farley, 1979c).
Figure 6 shows a diagrammatic representation of interneuronal circuitry that meets
these requirements using conventional synaptic connectivity between a small set of
interneurons. Central to its construction are
eight excitatory command neurons and inhibitory partners which will evaluate the
sensory input and calculate an appropriate
motor output for rotation toward the target.
Each BCSS, representing a direction gk,
with 1 # k # 8, excites its corresponding
command neuron and the associated inhibitory interneuron k. The latter also receives
excitation from BCSS gk21 and gk11 adjacent
to gk, thus forming an inhibitory triad that
will act with synaptic delay (DtI 5 0.7
msec) to block the action of the command
neuron coding for direction gḱ opposite gk
in the sensory field. Thus, for each command neuron encoding for turns in one direction (gk), the inhibitory triad antagonistic
to it is centered and represented by k̄ 5 [(k
1 3), mod 8] 1 1.
The circuitry of Figure 6 and Eq. 1 provides a foundation for computing differences in rate of firing for the command neurons
from the differences in timing of sensory
input they receive from the BCSS. For this
computation the concept of a time window
is introduced as the physical parameter that
will control excitability of the command
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P. H. BROWNELL
AND
neurons in our model. For convenience of
discussion, let us assume that R3 is closest
to a wave source and that M sensory neurons associated with this BCSS can, but
need not3, fire first as the Rayleigh wave
passes beneath. Excitatory input from R3
opens a time window of increased excitability for its corresponding command neuron, and simultaneously activates the inhibitory triad that will suppress (after synaptic
delay DtI 5 0.7 msec) activity of the command neuron for L2, opposite R3 in the array. As the Rayleigh wave passes through
the sensory field, other BCSS are excited
probabilistically as well, and these, in turn,
excite their corresponding command neurons and associated inhibitory partners.
Thus, in the general terms of our model, as
the stimulus angle wS varies, the width of
each command neuron’s time window is the
order of 2Dt 1 DI where Dt is given by Eq.
14, DI 5 a7ms, and a negative width indicates that inhibition comes before excitation. For command neuron k opposite direction wS of the stimulus, inhibition will
arrive before the excitation from its corresponding BCSS and there is low probability
of that cell firing. On the other hand, if wS
ø gk, excitatory input may trigger a spike
before its opposing inhibitory triad can suppress it. Eventually, all time windows for
increased rate of firing in the interneurons
are reliably closed by action of the inhibitory triads.
Representing time as a population vector
code
Since the currency of information transfer to motorneurons is a rate of spike discharge, the neural circuitry controlling the
angle of turn must produce a rate code
specifying target location. Conversion of
time information to a rate code in our model is performed by means of a population
vector, a representation commonly used in
other motor system modeling applications
3 Two neurons behind each slit respond probabilistically to the passing Rayleigh wave. Thus, angles of
turn computed by the model will be expressed as a
probability density (see Fig. 7).
4 We take conduction delays from the slit sensilla to
the SOG to be equal for all legs.
J. L.
VAN
HEMMEN
(Georgopoulos et al., 1986; Salinas and Abbott, 1994; Lewis, 1999). The N 5 8 command neurons constitute the population that
decides the direction of turn by taking the
sum of the eight vectors corresponding to
the directions of the eight legs, weighted by
their relative rates of firing. For each command neuron k there is a spike rate nk
roughly determined by Dt, the time window
each passing Rayleigh wave opens and
closes as it passes beneath BCSS k and k’s
inhibitory triad, respectively. Using the
complex number exp(igk) to represent directions on a two-dimensional surface, we
define the population vector n exp(if) by
One
N
ne if 5
k51
k
igk
⇒ f 5 arg
One
N
k51
k
igk
(2)
with its argument f being the direction the
animal perceives as the desired angle of
turn. Since the nk are stochastic variables so
too will be the population vector’s argument
f 5 f(wS). Given the stimulus angle wS, its
probability density P(f) is to be computed
(Lamperti, 1998).
Testing the model
In constructing a realistic stimulus to present to our model, we are fortunate that the
physical characteristics of Rayleigh waves
in sand are known (Fig. 3; Aicher and Tautz
1990) and relatively simple to reconstruct
in mathematical terms. Natural vibrational
stimuli in sand vary in duration but even
those of short duration, say TS 5 100 msec,
are capable of generating accurate turning
responses. We can synthesize a reasonable
approximation of the natural signal by assuming a discrete Gaussian distribution of
cosine waves with a mean of 300 Hz and a
standard deviation of 50 Hz. Thus we have
used y(t)/y0 5 100 [SkD(fk)cos(2pfkt 1 xk)]/
[SkD(fk)], fk 5 300 1 (k 2 150) Hz, where
D(.) is a Gaussian with ^ f & 5 300 Hz, the
standard deviation is 50 Hz, and the xk, 0
# k # 300, are independent equidistributed
random variables.
The sensory response of the BCSS is
computed by applying the stimulus y(t) to
each organ with the assumption that each
VIBRATION SENSORY SYSTEM
slit responds independently5. Spike generation is then governed by an inhomogeneous
Poisson process (Kempter et al., 1998) with
density
pF (t) 5
5
0
A ln[1 1 y(t)/y0 ]
for y(t) , 0
for y(t) $ 0
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model of Hodgkin and Huxley6 (Koch,
1999). Depending on neuronal potential V
at time t, the resulting excitatory and inhibitory postsynaptic currents (E/IPSCs) give
rise to the total input current
I(V, t) 5
O [g a(t 2 t ; t )(V 2 V)
E
t
E
E
E
f
(3)
where A 5 250 s interjects phase locking
around 300 Hz. The logarithmic function
follows from Weber’s law governing the generic relationship between stimulus intensity and sensory excitation (Dusenbery,
1992). An ‘‘inhomogeneous Poisson Process’’ with density pF means that (i) the
probability of an event in an interval of duration Dt at time t equals pF(t)Dt, the inhomogeneity stemming from an explicit dependence of pF(t) upon the time t, (ii) the
probability of two or more events during Dt
is o(Dt), thus negligible as Dt becomes
small, and (iii) events in disjoint intervals
are independent.
Finally, the input from the entire field of
receptors, as stimulated by our ‘‘natural’’
signal, is applied to the model of interneuron circuitry proposed in Figure 6. In quantitative terms, the spikes generated by
BCSS gk are ‘‘fed’’ to its command neuron
as those of the triad centered at k̄ opposite
gk inhibit the command neuron with synaptic delay DI (50.7 msec). We thus generate two independent Poisson processes of
spikes labeled by f arriving at times tfE from
gk and tfI from gk̄ with densities pF,E(t) 5 pF(t)
and pF,I(t) 5u pF(t 1 Dt 2 DI). As before,
Dt 5 Dt (gk, gl̄zwS) is given by (1) and l̄ is
taken to be the member of the inhibitory
triad of gk that fires first.
These independent excitatory and inhibitory inputs are applied to command neurons using the well-known excitability
21
5 The sensory response is a train of stimulus-locked
action potentials (cf. Fig. 4). BCSS spikes triggered by
different amplitude maxima in the Rayleigh waves
train are assumed to be phase-locked to the stimulus.
They are taken to be independent and non-interacting
events because of the sharp peak near 300 Hz for the
vibrational power spectrum of sand (Brownell, 1979;
Aicher and Tautz, 1990); cf. Fig. 3B).
1 gI a(t 2 t If ; tI )(VI 2 V)]
(4)
where VE 5 40 mV, VI 5 25 mV, while gE
and gI are synaptic conductances. The postsynaptic potential a(t; tsyn) :5 (t/tsyn) exp[1
2 t/tsyn] vanishes for t , 0. Using time constants characteristic of arthropod neurons,
we have tsyn 5 tE 5 tI 5 1 ms, sufficiently
less than the oscillation period of ;3 ms
for Rayleigh waves at 300–350 Hz. These
computed currents are applied to the command neurons controlling angle of turn and
the sum of their activities (Eq. 2) yields the
computed angle of turn f(wS).
Figure 7 presents a graphical display of
the probability density P(f) computed from
our theoretical model superimposed on experimental data obtained from scorpions. In
addition to predicting the turning behavior
of normal animals with intact sensory field,
the model accounts rather well for the altered behavior of animals with partially ablated sensory fields (Brownell and Farley,
1979a; Brownell, 1984). The dark shadings
of Figure 7 also encompass the intrinsic
scatter observed in behavioral data. Moreover, the importance of incorporating a triad
of receptors for the antagonistic inhibitory
input of our model, rather than a singlet,
can be seen in the inadequacy of the latter
to predict the observed behavior (see, e.g.,
Fig. 7e, f).
Optimizing model performance
Throughout development of this model,
care has been taken to incorporate the probabilistic nature of ‘‘real world’’ sensory
processing (e.g., stimulus waveform variance, probabilistic nature of sensory spike
generation) and to minimize complexity of
6 The parameters are the canonical values, with T 5
188C. Given the E/IPSCs chosen, it was found that a
command neuron did not fire as long as 20.517 msec
, tE 2 tI , 1.107 msec where tE and tI are the arrival
times of the ‘‘excitatory’’ and ‘‘inhibitory’’ spike.
1238
P. H. BROWNELL
AND
J. L.
VAN
HEMMEN
FIG. 7. Comparison of model predictions with observed turning behavior of Paruroctonus. In each panel, the
response angle f of turn (ordinate) is plotted as a function of the stimulus angle wS (abscissa). (A) the response
of an animal with fully intact sensory field shows fairly accurate orientation (6158) at all angles of target
presentation. (B)–(F) Animals with BCSS ablated on some legs (dots) show systematic errors in turning accuracy.
Both the probability density P(f) (dark shadings) and experimental points (dots or triangles, taken from Brownell
and Farley, 1979c) are indicated. When the inhibitory triad is replaced by a single inhibitory neuron in the
model, the mean response (dashed line) gives less satisfying fit to the observed behavior. (From Stürzl et al.,
2000).
the circuitry required to account for the observed behavior. We now assess the impact
of some of our assumptions on model performance.
The influence that the number N of command neurons has on precision of the computed angle of turn can be seen in the standard
deviation of response, sN, expressed as
sf2 ø
8sk2
N(^n k &max 2 ^nk &min ) 2
(5)
Here 1nk,max and 1nk,min are the maximum
and minimum number of spikes computed
for command neurons as a function of Dt,
and s2k 5 Var (nk) (Stürzl et al., 2000). Figure 8 shows that for M 5 2 sensory neu-
VIBRATION SENSORY SYSTEM
OF
SAND SCORPIONS
1239
FIG. 8. Standard deviation sf of the turning angle f as a function of the conductance gE appearing in Eq. 4
for fixed ratios x 5 gI/gE. For 1 # x # 3 the mean error sf shows a broad minimum with center near the dashed
line. Stochastic optimization is realized through tuning the synaptic efficacies gI and gE. The values of sF near
the minima agree with the scatter of the behavioral data shown in Figure 7. (From Stürzl et al., 2000).
rons/command neurons and N 5 8 a precision of turning within 13–15 degrees error
is easily obtained. This is within range of
the observed natural behavior (Fig. 2) indicating that the number of sensory and interneuronal elements required to execute
the behavior can be minimized.
Likewise, noise is inherent in the integrated response of command neurons assessing target direction since BCSS sensory
neurons are excited probabilistically by a
variable waveform, and the firing times,
though phase-locked to the Rayleigh wave,
are not precisely predictable. Under these
circumstances it is natural to ask if plasticity of synaptic processing within the model
can be tuned to minimize the effects of
noise on accuracy, i.e., by ‘‘Stochastic Optimization,’’ a reinterpretation (Stürzl et al.,
2000) of stochastic resonance (Wiesenfeld
and Moss, 1995). To answer this question
we have varied the synaptic conductance gE
in (5) for various fixed ratios of inhibitory
vs. excitatory synaptic effectiveness (gI/gE).
The broad minima seen in Figure 8 for the
standard deviation of targeting accuracy
(sN) at intermediate values of gI/gE strongly
suggest that the system is optimized for precision, presumably through evolutionary
adaptation (Grothe, 2000; Jaramillo and
Wiesenfeld, 1998).
CONCLUSIONS
The results summarized here from behavioral, sensory, and computational analysis
of vibration source localizing behavior of
sand scorpions all point to an underlying
simplicity in the mechanisms animals may
use for perception of vibrational space. Perhaps these mechanisms were particularly
evident in sand scorpions because of the
economy of sensory structure and function
involved, the clean nature of the vibrational
signals detected, and the accessibility of
orientational behaviors for experimental
analysis. Consistent with this biology, the
computational theory presented here uses a
few-neuron model and conventional synaptic interactions to generate one of the
simplest neuronal maps yet described for
processing of spatio-temporal information
from the outside world (van Hemmen,
2001). Moreover, the excellent agreement
between predictions of theory and behavioral observations suggest that the neuronal
mechanisms for perception of vibrational
space will to some extent be similar to those
used for localization in auditory space. Finally, we have shown that stochastic optimization can be a driving force for evolution of ever more accurate perception of
source location, simply by tuning the relative effectiveness of excitatory and inhibi-
1240
P. H. BROWNELL
AND
tory synaptic connections within a neural
circuit. For a group of animals whose paleontological record stretches back to the
beginnings of terrestrial life on earth, it
seems a safe bet that natural selection
would have done so by now.
ACKNOWLEDGMENTS
The authors thank Wolfgang Stürzl for
his central role in development of the computational model, and Prof. F. Barth for
stimulating discussions. These investigations were supported in part by an NSF
grant (BNS8709890) to PHB and DFG (FG
Hörobjekte) funding to JLvH.
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