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Review
Biology Department, Emory University, Atlanta, Georgia 30322
Submitted 7 April 2003; accepted in final form 22 April 2003
INTRODUCTION
The study of the neural basis of motor patterns that underlie wavelike
behaviors such as undulatory swimming has contributed to our general
understanding of coordination in the nervous system. Numerous studies have
shown that the isolated nervous system is capable of producing rhythmic motor
output in the absence of sensory feedback
(Marder and Calabrese 1996
).
In addition, in many cases these rhythmic motor patterns are similar to those
required for specific behaviors in the intact animal. For example, in the
lamprey forward swimming is accomplished by means of side-to-side undulations
that travel from anterior to posterior along the length of the body
(Wallén and Williams
1984
). In the lamprey, as in many other animals, wavelike motor
patterns arise from a network of neurons that is distributed longitudinally
along the neural axis. This type of neural network consists of a chain of
coupled segmental oscillators, local neural networks that are capable of
independently generating rhythmic output
(Skinner and Mulloney 1998a
).
The appropriate phase relationships between these segmental oscillators arise
as an emergent property of the segmental oscillators and the coupling between
them. Although this distributed organization is found in many different
animals, there are large differences in terms of the properties of the
segmental oscillators, the strength and symmetry of coupling, and the
importance of sensory feedback. In this review, we will discuss some of the
variations in design found in three animals: the lamprey, leech, and
crayfish.
PHASE CONSTANCY IS NECESSARY FOR UNDULATORY SWIMMING
The leech and the lamprey both swim in an undulatory fashion with the body
forming approximately one full wave at any given time during swimming. To
maintain this mode of swimming as an animal changes its swim cycle period, the
phase between the muscle contractions in different segments must remain
constant. In the leech, there are 18 body segments that are actively used for
swimming. Thus the phase lag between consecutive body segments is about
20° in the swimming animal (Kristan et
al. 1974
). Intersegmental phase lags that are nearly independent
of cycle period are also observed in isolated chains of the leech nerve cord
consisting of as few as two ganglia
(Pearce and Friesen 1985
).
However, in contrast to the intact animal, the phase lag per segment within a
long chain of ganglia in vitro is only about 8°.
In the leech swim network, the segmental oscillators are not uniform in
their ability to generate rhythmic output. Isolated ganglia from the anterior
end to the midpoint of the ventral nerve cord are capable of generating
swim-like oscillations, but not individual posterior ganglia
(Hocker et al. 2000
; cf.
Tunstall et al. 2002
). In
addition, there is a U-shaped gradient of cycle period. Isolated mid-cord
ganglia produce oscillations with a shorter cycle period than either
individual anterior ganglia or short chains of posterior ganglia.
A segmental oscillator of the leech swim network consists of motor neurons
and oscillator interneurons within a single ganglion that are organized into
two bilaterally symmetric hemisegmental circuits. Oscillations originate
within a single ganglion from the local circuit formed by these oscillator
interneurons, which are connected almost exclusively by inhibitory synapses
(Friesen and Pearce 1993
). The
hemisegments within a single ganglion oscillate synchronously based on strong
electrical and chemical coupling across the midline
(Friesen and Hocker 2001
).
This activity pattern is appropriate since the leech swims by dorsoventral
undulations, which require synchronous activation of muscles on the left and
right sides of the body. Because the two hemisegments are equivalent, in
studying intersegmental coordination it is justified to consider only the
circuitry on one side of the animal. The segmental oscillators are coupled by
ascending and descending projections of the oscillator interneurons, which
synapse directly with oscillator interneurons in other ganglia
(Fig. 1).
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In principle, the generation of phase lags appropriate for forward swimming
can be explained by a system consisting of a chain of coupled oscillators in
which the anterior oscillators have shorter inherent periods than the
posterior oscillators (Ikeda and Wiersma
1964
; Matsushima and Grillner
1992
). When a system such as this is coupled, all segmental
oscillators of the network share the same period, but the faster oscillators
will lead in phase. In the case of the leech swimming, this explanation is not
sufficient to explain forward swimming because the segmental oscillators with
the shortest cycle period lie at the mid point of the ventral nerve cord.
Experimental and modeling work has provided evidence that forward swimming
most likely arises from asymmetries in the coupling between the segmental
oscillators (Cang and Friesen
2002
).
Intersegmental coupling, which spans six segments in both the ascending and
the descending directions, is approximately equal in functional strength in
either direction (Friesen and Hocker
2001
; Pierce and Friesen 1985). However, at the level of specific
interconnections there are many asymmetries. The oscillator interneurons are
active at three different phases separated by 120°
(Fig. 1). The interneurons in
the 0° phase group all project their axons in the descending direction,
whereas the interneurons of the 120° and 240° groups only project in
the ascending direction (Friesen
1989
). In addition, the sole excitatory interneuron projects in
the descending direction, whereas inhibitory interneurons project in both
directions (Brodfuehrer et al.
1995
). Finally, the synaptic targets are asymmetric; ascending and
descending projection neurons project to targets with different activity
phases (Friesen 1989
). A
computer model that incorporates these asymmetries but not the inherent period
differences produced a 810° phase lag similar to that seen in long
chains of isolated nerve cords as well as phase constancy with changing cycle
period (Cang and Friesen
2002
).
Although the model replicated the behavior of the isolated nerve cord, the
8° phase lag between segments is clearly too small to produce a traveling
wave of one wavelength along the body. To test the idea that sensory feedback
from stretch receptors embedded in the body wall and mechanical coupling
between muscles in neighboring segments may contribute to the phase lag
observed in the intact animal, these mechanisms were added to the computer
model (Cang and Friesen 2000
;
Yu et al. 1999
). The resulting
computer model produced a phase lag of 17° per segment, which is similar
to the value in the intact animal (20°), suggesting that sensory feedback
and mechanical coupling are indeed important for appropriate coordination
(Cang and Friesen 2002
;
Friesen and Cang 2001
).
Experiments in which the nervous system was transected
(Wallén 1982
;
Yu et al. 1999
) have shown
that mechanical coupling and sensory feedback are more important for
intersegmental coordination in the leech than in the lamprey, which is
discussed in the following text. Perhaps a high degree of peripheral feedback
is necessary in an animal such as the leech, which has a hydrostatic
skeleton.
In the lamprey as in the leech, forward swimming results from a traveling
wave of one body length that begins at the anterior end of the animal. The
lamprey has about 100 body segments; therefore, the phase difference between
body segments is about 1% in the intact animal. An identical phase difference
occurs in the isolated spinal cord when rhythmic activity is induced with the
NMDA receptor agonist, D-glutamate
(Wallén and Williams
1984
).
Although it is not possible to identify individual interneurons as in the
leech swim network, two classes of interneurons, excitatory (E) and inhibitory
(C), appear to be essential for burst generation
(Grillner et al. 1995
). The E
interneurons synapse ipsilaterally with other E interneurons and with C
interneurons (Fig. 2). The
mutual excitation between E interneurons appears to support the generation of
bursts in hemisegments (Hellgren-Kotaleski
et al. 1999b
). The C interneurons project contralaterally and
inhibit other C interneurons as well as E interneurons
(Buchanan 1982
). These
interneurons are responsible for producing alternating activity between the
right and left sides of the spinal cord, which is necessary for side-to-side
undulatory swimming (Hellgren-Kotaleski et
al. 1999a
).
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In the first model of a segmental oscillator in this system, burst
termination was governed by reciprocal inhibition and the hemisegments were
incapable of independent bursting. This network generated oscillations with a
duty cycle (burst duration divided by cycle period) of 50%, a characteristic
property of a half-center oscillator
(Skinner et al. 1994
;
Wallén et al. 1992
). In
contrast, in the biological system, the duty cycle is 3040% and when
inhibitory synapses are pharmacologically blocked, the hemisegments burst
endogenously (Hagevik and McClellan
1994
; Wallén and
Williams 1984
).
Recent work has confirmed that reciprocal inhibition is not the primary
factor that terminates bursts, but rather the activation of two types of
Ca2+-dependent K+ channels (KCa).
One type, activated by Ca2+ that enters during action
potentials, causes postspike afterhyperpolarizations that lead to spike
frequency adaptation (Tegnér et al.
1998
). The other type, activated by Ca2+
that enters through open NMDA channels during each burst, produces a more
gradual hyperpolarization (Brodin et al.
1991
). The incorporation of these mechanisms into a model of a
segmental oscillator results in hemisegments that can oscillate independently
and a duty cycle similar to that of the biological system
(Hellgren-Kotaleski et al.
1999b
). The addition of a mechanism in which the amount of
adaptation (based loosely on KCa activation) increases as the cycle
frequency increases resulted in a model that was capable of oscillating with a
constant duty cycle over roughly a 10-fold frequency range, which would be
necessary for the animal to swim at different speeds
(Ullström et al.
1998
).
Important early theoretical work
(Kopell and Ermentrout 1988
)
indicated that appropriate phase lags for lamprey swimming may be generated by
two mechanisms: asymmetries in the coupling between segmental oscillators and
differences in inherent segmental periods. Evidence for coupling asymmetries
comes from a variety of experiments. Movements imposed on the isolated spinal
cord can entrain the activity of the entire swim network by activating
intra-spinal stretch receptors, which provide sensory feedback to the
interneurons (Fig. 2)
(Grillner et al. 1981
).
Interestingly, movement applied to the caudal end of the spinal cord can
entrain the system to a greater range of frequencies than movements applied to
the rostral end (Williams et al.
1990
). Additionally, split-bath experiments in which the rostral
and caudal halves of the spinal cord were bathed in pools with different
concentrations of D-glutamate demonstrated that the rostral spinal
cord dominates the frequency of the coupled network
(Sigvardt and Williams 1996
).
In another study, physiological and computer modeling results suggested that
longitudinal coupling is due primarily to ipsilateral excitatory coupling that
is stronger in the descending direction than in the ascending direction
(Hagevik and McClellan 1994
).
There is also evidence of anatomical coupling asymmetries. For example,
whereas the E interneurons project symmetrically over a few segments both
rostrally and caudally, the C interneurons project 1420 segments
caudally but have only short rostral projections
(Buchanan 1982
;
Dale 1986
).
Evidence for, or against, the existence of a gradient of segmental
oscillator frequency is more limited than for asymmetric coupling.
Pharmacologically induced frequency gradients can alter and even reverse the
normal rostrocaudal phase lags in the isolated spinal cord
(Matsushima and Grillner 1992
;
Tegnér et al. 1993
).
Although such experiments cannot demonstrate that such a gradient exists
naturally, they show that at least in principle a gradient could produce the
appropriate phase lags. Presumably in the intact system a gradient of
oscillator frequencies could be produced by a corresponding gradient of
descending synaptic drive as has been found in the swim network of
Xenopus embryos (Tunstall and
Roberts 1994
). In contrast to these results, surgically isolated
sections of the spinal cord do not vary in frequency in a systematic way
(Cohen 1987
). One problem with
this study, however, is that the rhythm was induced pharmacologically rather
than by normal descending spinal pathways. To address this problem, a study
was conducted in which fictive swimming was induced by pharmacological
microstimulation of the brain. By blocking local rhythmic activity in either
the rostral or the caudal half of the spinal cord with a low
Ca2+ saline, it was possible to measure the activity of
independent sections of the spinal cord
(Hagevik and McClellan 1999
).
This study revealed faster oscillations in the rostral spinal cord than in the
caudal spinal cord.
The extent of longitudinal coupling between segmental oscillators in the
lamprey is doubtless another important factor for determining phase lags.
Functional coupling that determines phase appears to extend over a much more
limited range than the full projection range of 3050 segmental reported
for some interneurons (Rovainen
1974
). In one study, the lamprey spinal cord was placed in a
chamber with partitions allowing the rostral, middle, and caudal sections to
be bathed in different solutions (Miller
and Sigvardt 2000
). Local synaptic activity was blocked in the
middle section with a solution containing low-Ca2+ and
high-Mg2+ without affecting spike conduction in axons
spanning the middle compartment. The results indicated that although the
maximal functional length of proprio-spinal coupling is 1620 segments,
phase was controlled by short-range coupling that spans only 46
segments (see also McClellan and Hagevik
1999
). It has been proposed that the interneurons that comprise a
segmental oscillator act not only to generate the local rhythm but also
project to, and influence, rhythm generation in other segments. The
feasibility of this idea, which has been termed "synaptic spread,"
has been demonstrated in modeling studies in which the synaptic contacts made
locally by an interneuron are also made with similar targets in neighboring
segments but with lower synaptic strengths
(Buchanan 1992
;
Ekeberg 1993
;
Wadden et al. 1997
;
Williams 1992
). Recent models
incorporating cellular and synaptic properties of the swim network can
replicate many of the observed properties of the swimming animal such as a
reversal of phase lag necessary for backward swimming
(Ullström et al.
1998
).
At first glance, sensory feedback appears to be less important for swimming
in the lamprey than in the leech since the motor output of the isolated spinal
cord closely resembles the pattern of the intact animal
(Wallén and Williams
1984
). To assess the contribution of sensory feedback, a model was
created that included the swim network, muscle activation, body mechanics,
counteracting water forces, and sensory feedback
(Ekeberg 1993
; Ekeberg et al.
1999). In this model, stretch receptors had very little effect on swimming
movements in still water. However, when the virtual lamprey swam in a cross
current, a model incorporating stretch receptors performed much better than a
model lacking them. In the latter, transversely flowing water forced the head
to one side, eventually resulting in a complete change of direction. In the
model with stretch receptors, the sensory feedback counteracted the perturbing
effects of the current and allowed the simulated lamprey to swim straight.
Therefore although sensory feedback does not contribute strongly to phase lag
as in the leech, it is necessary to counteract environmental
perturbations.
PHASE FLEXIBILITY IN THE LEECH HEARTBEAT NETWORK
The timing network that paces the leech heartbeat differs in many ways from
the two systems discussed so far. In this system, the interaction between
segmental oscillators is characterized by phase flexibility rather than phase
constancy. The heartbeat network contains two segmental oscillators located in
the 3rd and 4th ganglia of the ventral nerve cord
(Fig. 3A) (Peterson
1983a
,b
).
The output of these two segmental oscillators paces and coordinates the
activity of a network of interneurons and motor neurons that control the
peristaltic contractions of two lateral heart tubes that run the length of the
body (Calabrese et al.
1995
).
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The phase between these oscillators in isolated nerve cords is stable for
the duration of an experiment but varies between preparations from about
12 to +20% (the median phase difference is 6%; a positive phase lag
indicates that the G4 segmental oscillator leads in phase)
(Masino and Calabrese 2002a
).
A combination of physiological and modeling work has demonstrated that this
wide phase range can be accounted for by the specific network configuration
combined with intrinsic period differences between the segmental
oscillators.
At the core of each segmental oscillator is a pair of heart interneurons
(HN cells) that form reciprocally inhibitory synapses across the ganglion
midline and constitute a half-center oscillator
(Fig. 3A). For
example, the heart interneuron on the left side of the 3rd ganglion [HN(L,3)]
is reciprocally inhibitory with its contralateral homologue. Similar to the
hemisegments in the lamprey spinal cord, these interneurons are capable of
endogenous oscillations when inhibitory synapses are blocked
(Cymbalyuk et al. 2002
).
However, physiological and modeling data show that although the individual
oscillator interneurons are capable of endogenous bursting, the half-center
configuration makes the oscillations more robust, ensures bilateral
alternation of bursting, alters period substantially from the inherent period,
and fixes duty cycle near 50% (Cymbalyuk
et al. 2002
). The two segmental oscillators are coupled by
coordinating interneurons that have cell bodies in the first and second
ganglia but have spike initiation sites and form reciprocally inhibitory
synapses with ipsilateral oscillator interneurons in the 3rd and 4th ganglia
(Fig. 3A)
(Masino and Calabrese 2002a
;
Peterson 1983b
).
To understand how phase and cycle period are controlled in this system,
alternative models that incorporated different assumptions about the system
were created (Hill et al.
2002
). Based on anatomical and physiological data, one possible
configuration of the network is a "symmetric" model in which the
oscillator neurons of both segmental oscillators equally inhibit the
ipsilateral coordinating interneurons (Fig.
3B). This model assumes that the G3 spike initiation
sites of the coordinating interneurons are silent and that all spikes
originate at the G4 sites (Fig.
3A). In this model, the activity of a coordinating
interneuron is completely inhibited when either the G3 or the G4 oscillator
interneuron on the same side of the body is active. Therefore a coordinating
interneuron only fires in the window of time when neither the ipsilateral G3
nor the G4 interneuron is active (yellow rectangles in
Fig. 3C).
In a model in which the two segmental oscillators had the same intrinsic
period, the phase difference was zero and the duty cycle of the coordinating
interneurons was large (40%, not shown). Under conditions where the intrinsic
period of one segmental oscillator was shorter than the other, the faster
segmental oscillator led in phase and the duty cycle of the coordinating
interneurons was reduced (30%, Fig.
3C). In the symmetric model, either segmental oscillator
can lead in phase and the period of the system is equal to the period of the
faster segmental oscillator (Hill et al.
2002
). The range of phase values (20 to +20%) is greater in
the negative direction than in the biological system (12 to +20%),
perhaps reflecting a tendency of the real G4 oscillator to be inherently
faster than the G3 oscillator (Masino and
Calabrese 2002b
).
How are stable phase lags created in this system and why is the range of
stable phase lags so great? On a cycle-by-cycle basis the faster segmental
oscillator will lead in phase due to its shorter intrinsic period. As a
result, the oscillator interneurons of the faster segmental oscillator will
terminate the bursts of the ipsilateral coordinating interneurons. Thus during
each cycle there is a brief interval in which an interneuron of the slower
segmental oscillator only receives inhibition from its contralateral partner.
The faster oscillator interneuron "removes" inhibition that would
normally fall late during the inhibited phase of the slower oscillator
interneuron's cycle. In this way, the faster segmental oscillator speeds the
slower segmental oscillator to its own period. The greater the phase
difference, the greater the removal of inhibition and the stronger the
speeding effect on the slower segmental oscillator. At the limit the faster
segmental oscillator can accelerate the coupled system to the slower
oscillator's half-center oscillator periodthe period that it expresses
in the absence of inhibition from the coordinating interneurons. Beyond this
point, the two oscillators do not share the same period
(Hill et al. 2002
).
The properties of this symmetric network depend not only on the details of
the network configuration, but also on the intrinsic properties of the
interneurons themselves. For this reason many voltage-dependent currents have
been incorporated in the model oscillator interneurons
(Hill et al. 2001
). For
example, the bursts are supported by several currents including a
low-threshold, slowly inactivating Ca2+ current
(ICaS). ICaS is important because it
inactivates during a burst, causing a slow decline in the membrane potential.
This decline leads to a reduction in spike frequency, which helps to release
the contralateral interneuron from synaptic inhibition. Simultaneously,
Ih becomes activated in the contralateral interneuron,
helping it to escape from inhibition and begin to burst. Late in the inhibited
phase, small changes in the amount of inhibition can have large effects on the
timing of the next burst (Hill et al.
2002
). Therefore the removal of inhibition can effectively speed
an oscillator interneuron that lags in phase. Similar results, showing that
inhibitory input can cause either phase advances or delays depending on its
timing, have been found in a modeling study of intersegmental coordination in
the tadpole swim network (Tunstall et al.
2002
).
The predictions of this simple symmetric model are largely in agreement
with physiological data (Masino and Calabrese
2002a
,b
).
In mutual entrainment experiments in which the two segmental oscillators were
reversibly uncoupled by blocking spike conduction in the connective between
the 3rd and 4th ganglia, the period of the coupled system was equal to that of
the faster oscillator regardless of which oscillator was faster (G3 or G4). In
addition, in split-bath experiments the application of pharmacological agents
that accelerated or slowed the period of a segmental oscillator allowed for a
reversal in the phase relationships between the oscillators
(Masino and Calabrese 2002b
).
For example, in a preparation in which the G4 oscillator originally led in
phase, a decrease in the intrinsic period of the G3 segmental oscillator
allowed the latter to lead in phase.
The agreement between the model and the biological data breaks down,
however, in experiments in which repetitive pulses of current were used to
drive one of the segmental oscillators to periods faster or slower than that
of the mutually entrained system (analogous to the forcing experiments
described in the lamprey) (Masino and
Calabrese 2002c
). The symmetric model predicts that the driven
oscillator cannot slow the follower segmental oscillator by lagging in phase
because there is no mechanism to add inhibition to the follower oscillator. In
contrast, in the biological system the driven segmental oscillator may lag in
phase and consequently slow the system. A new generation of the model, which
incorporates details such as spike frequency adaptation of the coordinating
interneurons, has been able to account for this property
(Jezzini et al. 2000
).
In addition, contrary to the assumptions of the symmetric model, the
driving experiments have revealed that the system can behave asymmetrically.
The driven G3 oscillator can entrain the network over a broader range of cycle
periods than the G4 oscillator (Masino and
Calabrese 2002c
). This result shows that the leech heartbeat
network changes dynamically depending on the experimental conditions. The
network behaves symmetrically under conditions of mutual entrainment but
asymmetrically when driven by external input. The ability of the system to
switch between these two modes has been explored in a new model in which
coordinating interneurons have two spike initiation zones
(Jezzini et al. 2000
).
The functional role of the large variations in phase observed in the
mutually entrained system is not known. The experiments and modeling to date
have been concerned with short isolated chains of ganglia. In experiments in
which phase was measured between segmental motor neurons in long,
de-afferented chains, intersegmental phase differences were consistent between
preparations and were independent of cycle period
(Wenning et al. 2000
). The
study of semi-intact preparations in which afferent input is preserved may
yield further information about the normal phase relations in this system.
A LARGE AND CONSTANT PHASE LAG IS NECESSARY FOR THE BEATING OF CRAYFISH SWIMMERETS
Intersegmental coordination has also been studied in the crayfish swimmeret
system (Mulloney et al. 1993
,
1998
). The crayfish swims
forward by beating four pairs of swimmerets located ventrally on the abdomen.
Normally the two swimmerets located on a single abdominal segment beat
synchronously in a cycle consisting of a power-stroke followed by a
return-stroke (Hughes and Wiersma
1960
). Together the swimmerets beat in a wavelike pattern that
begins with the posterior-most pair and then spreads anteriorly with a phase
lag of 25% between neighboring abdominal segments. As in the leech and lamprey
swim networks, the phase lag between segments is independent of cycle
frequency (Braun and Mulloney
1993
).
The isolated abdominal nerve cord of the crayfish can produce a rhythm that
is nearly identical to that in the intact animal (Braun and Mulloney
1993
,
1995
;
Ikeda and Wiersma 1964
). In
addition, a single isolated ganglion can produce a normal and robust motor
pattern (Murchison et al.
1993
). Similar to the lamprey swim network, a segmental oscillator
consists of two hemisegmental pattern-generating circuits that are capable of
independent oscillation, although in the crayfish the hemisegments are active
in phase as would be necessary for synchronous beating of swimmeret pairs
(Murchison et al. 1993
).
Each hemisegment contains all the circuitry necessary to control a single
swimmeret (Murchison et al.
1993
). In addition to two groups of antagonistic motor neurons and
a set of primary afferent neurons, each hemisegment contains four local,
nonspiking interneurons. Two of these interneurons (1A and 1B) depolarize
during the return-stroke portion of each cycle while the other two
interneurons (2), which are identical, depolarize during the power-stroke
phase (Fig. 4) (Paul and
Mulloney
1985a
,b
).
Alternating oscillations between these two groups of interneurons may be based
on reciprocal inhibition (Fig.
4) (Skinner and Mulloney
1998b
).
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It was originally proposed that the wavelike activation of the swimmerets
arises from a gradient of intrinsic segmental oscillator periods
(Ikeda and Wiersma 1964
).
However, no systematic difference in segmental oscillator periods was
subsequently found between isolated ganglia
(Mulloney 1997
). In contrast,
the pattern of intersegmental connectivity is asymmetric. Three types of
coordinating interneurons have been identified that are necessary and
sufficient for intersegmental coordination
(Namba and Mulloney 1999
). In
each hemisegment, there are two interneurons that project in the ascending
direction (ASCL and ASCE), and one interneuron that
projects in the descending direction (DSC)
(Fig. 4). The ASCL
and ASCE interneurons fire bursts in phase with the power-stroke in
their home ganglion, whereas the DSC interneuron fires bursts in phase with
return-stroke. These coordinating interneurons have little direct effect on
activity in their home ganglion but affect the timing of motor output in their
target ganglia where they make spike-mediated synapses with local, nonspiking
commissural interneurons, which in turn entrain hemisegmental activity
(Mulloney and Hall 2002
;
Namba and Mulloney 1999
).
Chains of only two ganglia exhibited normal phase relationships, leading to
the original assumption that intersegmental coordinating interneurons project
only to neighboring ganglia (Skinner and
Mulloney 1998b
). However, when the rhythmic activity of an
individual ganglion of a chain was blocked with a
low-Ca2+, high-Mg2+ saline, the
segmental oscillators on either side maintained their normal phase difference,
demonstrating that coordinating interneurons project to targets at least two
ganglia away (Tschuluun et al.
2001
). In agreement with the synaptic spread model proposed for
lamprey swimming these distant connections are weaker than those between
neighboring ganglia. In contrast, the appropriate phase lag of about 50% is
maintained between the two ganglia on either side of the inactive ganglion,
suggesting that the connections in distant ganglia are not identical to those
made in neighboring ganglia.
A variety of models have been used to help understand how intersegmental
coordination is accomplished in the crayfish swimmeret system. In one model,
the swimmeret network was represented as a system of phase-coupled oscillators
(Skinner et al. 1997
). Fitting
this model to the experimental data resulted in a number of predictions:
coupling is asymmetric; ascending and descending coupling are about equal in
strength, and either ascending or descending coupling alone can generate a
phase difference of 25%. To understand what these asymmetries mean in synaptic
terms, a cellular model was created in which the segmental oscillators were
modeled using MorrisLecar-type equations to represent the nonspiking
interneurons (Skinner and Mulloney
1998b
). A number of alternative circuits, constrained by
experimental results and the predictions of the phase-coupled model, were
tested. One circuit exhibited at constant phase of 25% over a range of
oscillation frequencies. As predicted by the phase-coupled oscillator model,
either the ascending or the descending coordinating interneurons alone could
produce a 25% phase lag. However, only the full circuit model showed phase
constancy. This cellular-based model shows that the asymmetric coupling may be
embodied in differences in phases of coordinating interneuron activity,
choices of intersegmental targets, and signs of intersegmental
connections.
The cellular model predicts that certain network configurations produce
appropriate phase lags but cannot explain why these phase lags are stable. In
a study based on the assumptions of weakly coupled oscillator theory, coupling
functions were calculated for individual intersegmental connections in the
cellular model (Jones et al.
2003
). These coupling functions are curves that predict stable
phase lags for individual connections and when added together can predict
stable phase lags within a full network. For example, in the cellular model a
stable phase lag of 25% was found with a specific pair of ascending excitatory
and inhibitory connections. By examining the coupling functions of these two
connections, it was possible to see that although neither connection on its
own produces an appropriate phase, together they yield a stable phase lag of
25%. Furthermore, this analysis explained why bidirectional connections are
required for phase constancy. With only either ascending or descending
connections, the predicted phase lags shifted systematically with oscillation
frequency. In a model with bidirectional coupling, however, these phase shifts
cancelled out, resulting in a constant phase lag over a range of
frequencies.
CONCLUSIONS
This review has focused on intersegmental coordination in a few
well-studied preparations. Discovering how motor patterns are coordinated in
these model systems may help us to understand how coordination is accomplished
in more complicated networks such as those responsible for terrestrial limbed
locomotion (Bem et al. 2003
;
Butt et al. 2002
). At the most
fundamental level of rhythm generation there are clear similarities between
the model systems we have discussed. For example, in the lamprey swim network
and in the leech heartbeat system, hemisegments are capable of endogenous
bursting even though they are embedded in a half-center oscillator circuit.
However, at the network level, the differences are perhaps more striking than
the similarities. For example, the swimming behaviors of leech and lamprey are
very similar yet the two underlying neural circuits are very different in
terms of their architecture and the role of sensory feedback.
A further complexity is that a given network may operate differently
depending on experimental conditions. For example, the leech heartbeat network
behaves nearly symmetrically under conditions of mutual entrainment but
asymmetrically during driving experiments, demonstrating an ability to change
dynamically that is similar to network reconfiguration in the crustacean
stomatogastric nervous system (Marder and
Calabrese 1996
; Masino and Calabrese
2002b
,c
).
The future of this field will clearly continue to involve modeling work because the dynamic nature of these oscillatory networks makes comprehension based on static circuit diagrams impossible. The use of models with different levels of detail, as in the study of the crayfish swimmeret system, may be the best approach. Abstract models provide a general indication of the important features of a system, while more detailed models allow for a direct comparison with the biological system.
FOOTNOTES
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Address for reprint requests: R. L. Calabrese (E-mail: RCalabre{at}Biology.EMORY.EDU).
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