Department of Physiology and Biophysics and Fishberg Research Center for Neurobiology, Mount Sinai School of Medicine, New York, New York 10029
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ABSTRACT |
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Brezina, Vladimir, Irina V. Orekhova, and Klaudiusz R. Weiss. Optimization of Rhythmic Behaviors by Modulation of the Neuromuscular Transform. J. Neurophysiol. 83: 260-279, 2000. We conclude our study of the properties and the functional role of the neuromuscular transform (NMT). The NMT is an input-output relation that formalizes the processes by which patterns of motor neuron firing are transformed to muscle contractions. Because the NMT acts as a dynamic, nonlinear, and modifiable filter, the transformation is complex. In the two preceding papers we developed a framework for analysis of the NMT and identified with it principles by which the NMT transforms different firing patterns to contractions. We then saw that, with fixed properties, the NMT significantly constrains the production of functional behavior. Many desirable behaviors are not possible with any firing pattern. Here we examine, theoretically as well as experimentally in the accessory radula closer (ARC) neuromuscular system of Aplysia, how this constraint is alleviated by making the properties of the NMT variable by neuromuscular plasticity and modulation. These processes dynamically tune the properties of the NMT to match the desired behavior, expanding the range of behaviors that can be produced. For specific illustration, we continue to focus on the relation between the speed of the NMT and the speed of cyclical, rhythmic behavior. Our analytic framework emphasizes the functional distinction between intrinsic plasticity or modulation of the NMT, dependent, like the contraction itself, on the motor neuron firing pattern, and extrinsic modulation, independent of it. The former is well suited to automatically optimizing the performance of a single behavior; the latter, to multiplying contraction shapes for multiple behaviors. In any case, to alleviate the constraint of the NMT, the plasticity and modulation must be peripheral. Such processes are likely to play a critical role wherever the nervous system must command, through the constraint of the NMT, a broad range of functional behaviors.
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INTRODUCTION |
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In the first of these papers (Brezina et al.
2000, henceforth referred to as Paper I), we studied the
complex way in which motor neuron firing patterns are transformed to
muscle contractions by the neuromuscular transform (NMT). In the second
paper (Brezina and Weiss 2000
, referred to as Paper II),
we extended our analysis to functional movements and behavior. In
sending the firing patterns through the NMT, the nervous system is
attempting to command behavior. But the filter of the NMT constrains
which firing patterns produce functional and efficient behavior, and,
even more importantly, the range of behavior that can be produced. Such
constraints are particularly clear in cyclical, rhythmic behaviors.
With fixed properties of the NMT, the constraints are severe. But the
properties of real NMTs are not fixed. Rather, they are variable by
virtue of the fact that most NMTs incorporate or are subject to various kinds of plasticity and modulation (reviewed by Bittner
1989
; Calabrese 1989
; Fisher et al.
1997
; Hooper et al. 1999
; Hoyle 1983
; Worden 1998
; Zucker 1989
;
further references in RESULTS and DISCUSSION).
In this paper we examine how such mechanisms tune the properties of the
NMT to match the desired behavior, alleviating the constraints imposed
by the NMT to expand the range and optimize the production of
functional rhythmic behaviors.
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METHODS |
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We continue with the approach described in detail in Papers I and II. We briefly review it here.
Input firing patterns and parameters
The firing pattern is taken to be synonymous with the waveform
f(t) of firing frequency f as a
function of time t. (For a summary list of symbols, see
Table 1 of Paper I.) We consider a canonical set of bursting patterns
completely definable by the alternative parameter triplets
(dintra, dinter,
fintra), (P, F, fintra), and (P, F,
f
). Here dintra
is the burst duration, dinter the interburst
interval, fintra the intraburst firing
frequency, P the cycle period, F the duty cycle,
and
f
the mean (period-averaged) firing
frequency. These parameters, and so the alternative triplets, are
related by the equations
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(1a) |
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(1b) |
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(1c) |
NMTs
The NMT is an input-output relation that converts the input waveform f(t) to an output waveform c(t), of contraction amplitude c as a function of time. We focus on two NMTs, the real B15-ARC NMT of Aplysia and a model NMT that has similar but completely known properties.
The model NMT is implicitly defined by the kinetic schema
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(2) |
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(3) |
The B15-ARC NMT was studied experimentally as in Paper I. Motor neuron B15 was intracellularly stimulated to fire in the desired pattern; the resulting contractions of the accessory radula closer (ARC) muscle were measured under isotonic, lightly loaded conditions.
Output contractions and parameters
We consider the whole output waveform c(t)
or its parameters, in particular its period-wise maximum
, minimum c, and mean
c
. In the dynamical steady state of the system,
c(t) settles to the steady-state output waveform
[c(t)]
, and
,
c, and
c
settle to its
corresponding parameters
,
c
, and
c
.
Functional movement and performance
We consider a further output parameter, the functional movement
m, or, in the steady state, m. By
itself or in the normalized forms
m
/P and
m
/P
c
,
this parameter provides a measure of performance and efficiency in
different behavioral tasks.
Geometric and graphical representation
The operation of the NMT can be represented as a dynamical
structure in a multidimensional input-output space. Here we focus on
the structure of the steady state m (or one
of its normalized forms) primarily in the (P, F,
fintra, m), and to some extent in the
(P, F,
f
,
m), spaces, or simply on the functions
m
(P, F,
fintra) and
m
(P, F,
f
). These spaces are four-dimensional, with the function m
occupying a
three-dimensional volume. (A more complex neuromuscular system, such as
the antagonistic muscle pair in Figs. 5 and 6, requires, strictly,
additional input dimensions.) For graphical manageability, we show
representative three-dimensional sections, obtained by setting one of
the input parameters to a constant value, in which
m
appears as a two-dimensional surface (Figs.
2-6).
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RESULTS |
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Strategy
We continue with the same analytic framework, essentially an elementary dynamical systems approach, with the same set of canonical firing patterns, and the same two illustrative NMTs, a model NMT and the real B15-ARC NMT of Aplysia, as in Papers I and II. A brief review of the mechanics of our approach is provided in METHODS. A summary list of symbols was given in Table 1 of Paper I.
In Paper I, we studied how the NMT transforms different input firing
patterns or waveforms f(t) to output
contraction waveforms c(t), and the relationships
it thus establishes between different parameters of the former and of
the latter. We focused on such elementary output parameters as the
maximum contraction , minimum contraction
c, and mean contraction
c
. We
studied primarily the dynamical steady state of the system, which, as
we saw, is the key element in the dynamical structure of the NMT and
its physiological operation. In the steady state,
c(t) settles to the steady-state output waveform
[c(t)]
, and
,
c, and
c
settle correspondingly
to
,
c
, and
c
. In Paper II, we then extended the
scope of the NMT from contractions to functional movement and behavior.
For a series of representative behavioral tasks, we computed from the
contraction waveform a new output parameter, the functional movement
m, or in the steady state m
, a
measure of performance in the task.
Throughout, we have observed and analyzed how the input-output space is critically structured by the properties of the NMT. We have stressed, in particular, how the speed of the NMT limits the speed of functional behavior. So far, the properties of the NMT have been fixed, indeed, with our two NMTs, fixed in a very restricted way (Paper I). Here, working first with our mathematical model NMT, we will vary or modulate the properties of the NMT in certain ways that are common in real systems (see below and DISCUSSION). For example, we will modulate the NMT so as to alter the size of contractions, or alter their kinetics. We will examine how this alters the functional performance of the NMT in some of the tasks from Paper II, again particularly as the behavior accelerates.
We will then describe results of an experimental examination of such modulation of NMT properties in the real ARC muscle of Aplysia. As will be seen, modulation of the B15-ARC NMT by a number of endogenous modulators, very much like the modulation of the model NMT, is such as to significantly expand the range of speeds of functional behavior.
Effects of NMT modulation on contractions
In real systems, modulation of the NMT is usually described in terms of the effects that it has on contraction shape. The ARC and other buccal muscles of Aplysia present a typical case. Their numerous modulators can be classified, broadly, as 1) changing (increasing or decreasing) contraction amplitude, 2) accelerating the rate of contraction, and 3) accelerating the rate of relaxation (see further Modulation of the B15-ARC NMT below). In detail these can be complex, and usually not pure, effects in the real system.
Our model NMT, however, allows us to implement each of these three
effects in pure form, and then, as desired, in combination. Our work in
Paper I gives us equations (APPENDIX A, 1) for
the whole contraction waveform
[c(t)] and parameters such as
and
c
explicitly in terms of
contr and
relax, time constants
underlying the kinetics of contraction and relaxation, respectively
(see APPENDIX A, 2). These time constants, as
well as the amplitude of the contraction, can then be independently
varied (APPENDIX A, 1). In this paper, we will
restrict ourselves to just three illustrative manipulations (and their
combinations): 1) we will increase contraction amplitude twofold (to decrease contraction amplitude, we can simply interchange the unmodulated and modulated contractions); 2) to
accelerate the kinetics of contraction, we will decrease
contr fivefold; 3) to accelerate the kinetics
of relaxation, we will decrease
relax fivefold. The
magnitude of these changes is entirely physiological in the ARC muscle,
for instance (e.g., Brezina et al. 1995
).
How these three manipulations affect contraction shape can be seen in Fig. 1.
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Increasing contraction amplitude (Fig. 1A) simply scales up
the contraction waveform [c(t)]
and its parameters
, c
, and
c
, to the same extent for all firing
patterns. Although this modulation does not alter kinetics, we note
that over any absolute amplitude interval the contraction can rise
faster than before. Even pure amplitude modulation, therefore, potentially affects the functional speed of the NMT.
The effect of decreasing contr and
relax
(Fig. 1B) is immediately understandable from our analysis in
Paper I, where we saw how the period-wise shape of
[c(t)]
depends on the point-wise
kinetics of contraction and relaxation described by
contr and
relax. During each burst of
firing, when f = fintra, the muscle
contracts toward the true steady state
c
(fintra) with
a time course reflecting
contr; during each interburst
interval, when f = 0, it relaxes toward the true steady
state c
(0) = 0 with a time course
reflecting
relax. The amplitude of
[c(t)]
and its parameters such
as
and
c
then reflects the balance of
the progress in the two directions. Consequently, favoring the
contraction by decreasing
contr raises
[c(t)]
,
, and (to a lesser extent)
c
closer to c
(fintra);
favoring the relaxation by decreasing
relax lowers
[c(t)]
,
c
, and
closer to
c
(0) = 0. Decreasing both
contr and
relax
accelerating the overall
kinetics of the NMT
spreads
[c(t)]
in both directions,
raising
and lowering
c
. Thus, in general, altering the
kinetics of contraction inevitably changes its amplitude too.
As Fig. 1C shows, such effects of altered kinetics are
especially large for firing patterns of intermediate speed, comparable to the speed of the NMT, where the contraction makes significant progress toward but does not actually reach either true steady state in
each cycle: where the contraction is partly phasic and partly tonic.
With very slow patterns, which produce a phasic contraction oscillating
quasi-instantaneously from one steady state to the other, altering
contr and
relax has little effect because
it (exactly converse to the modulation in Fig. 1A) alters selectively just the approach to the steady state, not the steady state
itself. Similarly for very fast patterns, which produce a tonic
contraction. The contraction remains tonic, although, as we can see in
Fig. 1, C1 and C2, its amplitude can change as a
result of pattern dependence of the sort discussed in Paper I. [Essentially, altering in an uncompensated way just one parameter such
as
contr or
relax gives equations that
are no longer solutions of the simple differential equation (Eq. 3 in METHODS) that becomes linear for fast patterns
(APPENDIX G, 1 of Paper I).]
In sum, different kinds of modulation change the input-output structure of the NMT in different and sometimes quite complex ways in different parts of the space, to greater or lesser effect (revealing, in other words, greater or lesser sensitivity of the NMT to that kind of modulation) depending on the firing pattern and the contraction parameter being considered. With respect to what we found in Paper II to be important for functional performance as rhythmic behavior accelerates, we can broadly summarize by saying that these different kinds of modulation, to different degrees, speed up the NMT in such a way that, especially over the intermediate, physiological range of firing pattern speeds, they produce larger phasic contractions for a particular pattern, or, conversely, extend phasic contractions to faster patterns. We will express this more precisely later, after we have seen how it affects performance.
Effects of NMT modulation on functional performance
We can now observe how these effects on contraction shape translate into effects on performance in some of our behavioral tasks from Paper II.
Figures 2-4 show how our three
illustrative manipulations of the NMT and their combinations affect the
performance measure m/P
the total
functional movement over time
in a typical task, Task III. We recall
from Paper II that this task requires a single neuromuscular unit to
produce rhythmic movement beyond distinct upper and lower thresholds.
Column 1 in each figure recapitulates the unmodulated performance from Paper II. We recall our main conclusions: only a
subset of firing patterns gives functional performance; to obtain that
performance, the nervous system must send a pattern with parameters so
matched that it is within the bounds of the subset. Performance
increases as the period P of the pattern decreases
as the
pattern and the behavior accelerates
provided that its other parameters, here the duty cycle F and the intraburst firing
frequency fintra, are matched within ever
narrower bounds. But eventually, as the pattern becomes too fast
relative to the speed of the NMT, performance fails, essentially as the
contraction becomes too tonic, or insufficiently phasic, for the task.
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Because performance is just another output parameter, we find that our summary picture of how modulation of the NMT appears at the level of contractions (end of the preceding section) is valid also for performance. In Fig. 2 we see, for instance, that increase of contraction amplitude increases performance for some firing patterns, but decreases it for others. Roughly, the former are those where the contraction was too small for the task, and now is more optimal (for example, with smaller than optimal fintra: bottom pair of plots); the latter those where it was optimal, but now is too large (for example, with larger than optimal fintra and large F: front of top pair of plots). The subset of functional firing patterns does not obviously expand or contract, but it shifts its bounds. The nervous system must alter the parameters of the pattern that it sends correspondingly. This becomes increasingly critical as P decreases and the bounds of the functional subset narrow. To maintain performance at a particular small P, with a particular fintra, Fig. 2 shows that increased amplitude modulation must be accompanied by a matching decrease in F.
But is the highest performance achievable through the NMT, with any pattern, increased by the modulation? With pure modulation of contraction amplitude, this does not obviously happen. Performance increases as P decreases, and substantial increase in performance is achieved, we saw in Paper II, primarily by extending the range of functional, sufficiently phasic contractions to substantially smaller P. Because this range is limited by the speed of the NMT, that speed must be increased correspondingly. But a pure increase of contraction amplitude speeds up the NMT too little to extend phasic contractions to much smaller P. Because the contraction can rise over an absolute amplitude interval faster than before, provided the smaller P is matched with other alterations in the firing pattern, some parts of the NMT can become functionally faster, but the effect of increased amplitude modulation, alone, is small.
Phenomena of the same kind as in Fig. 2 can be seen in Fig.
3, where the kinetics of contraction have
been accelerated by decreasing contr (column
2), the kinetics of relaxation accelerated by decreasing
relax (column 3), or both (column
4). In some of these cases, however, we do see significant
increases in the highest performance achievable through the NMT,
because these manipulations do speed up the NMT so as to extend phasic
contractions to substantially smaller P.
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Decreasing contr, alone, increases performance
relatively little. Indeed, the effect is not very different from that
of increasing contraction amplitude (compare Fig. 2 and Fig. 3,
columns 1 and 2). A much larger increase in
performance is obtained by decreasing
relax. This
reflects an interesting asymmetry in the importance of the two time
constants, and more generally of the processes of contraction and
relaxation, for functional phasic contractions (APPENDIX B,
and next section). In particular, it reflects the fact that while
decreasing
contr, just like increasing contraction amplitude, can give contractions whose phasic component is absolutely larger, their tonic component is also correspondingly larger: the
contractions are not more phasic than before. Only
decreasing
relax, alone or as part of a more complex
modulation, can give contractions that are relatively more phasic
(compare Fig. 1, B1 and B2, C1 and C2;
see next section).
The largest increase in performance, furthermore without complex shifts
in the subset of functional patterns, is obtained by decreasing both
contr and
relax: by speeding up the
overall kinetics of the NMT (Fig. 3, column 4). Intuitively,
this reflects the fact that here the two component effects balance to
leave a relatively pure, large enhancement of the phasic nature of
contractions without much change in their overall amplitude (Fig. 1,
B3 and C3).
As Fig. 4 shows, combining the modulation
increasing contraction amplitude with that decreasing
relax (a combination common, for instance, in the
Aplysia ARC system: see Modulation of the B15-ARC
NMT) also brings about a large increase in the highest performance
that can be achieved. Intuitively, again, the increase and the decrease
in contraction amplitude (Fig. 1, A and B2)
balance to leave, simply, a more phasic contraction.
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Very similar phenomena can be seen in other tasks from Paper II. Figure
5, for instance, shows performance in
Task IV, in which the combined contraction of two antagonistic muscles,
here of unequal size or strength, is required to rhythmically cross a
given movement axis. The kinetics of the stronger muscle, the weaker
muscle, or both, have been accelerated by decreasing both contr and
relax. All three manipulations,
but especially the modulation of both muscles, extend the subset of
functional patterns to smaller P and increase the
performance achievable through the NMT.
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Finally, in Paper II we normalized the performance
m/P by the mean contraction
amplitude
c
to arrive at a measure of
the relative efficiency of different firing patterns in producing the
behavior. In Fig. 6 we see that speeding
up of the NMT (in this case acceleration of the kinetics of both
muscles in Task IV, as in the last panel of Fig. 5) increases, even
more than the performance, the highest efficiency that can be achieved through the NMT. Examination of a representative set of contraction waveforms (top) shows that the faster NMT not only enables
more phasic contractions to perform the task where they could not
before, but at the same time decreases the mean contraction amplitude, a measure of the energy expended in the process (cf. Fig.
1C3). As we discussed in Paper II, the faster NMT changes
the shape of the contraction so as to direct its energy more
productively into rhythmic movement and behavior.
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Phasic fraction of the contraction as a simple indicator of NMT speed
The key to extending the range of functional rhythmic behavior to faster speeds and increasing its performance and efficiency is the speed of the NMT. The aspect of "speed" is difficult to extract from the overall structure of the NMT; it is not exactly expressible by a single number even for our simple model NMT (APPENDIX A, 2) and certainly not for a real NMT such as the Aplysia B15-ARC NMT (Paper I). But, as we saw in Papers I and II and in our discussion above, the speed is broadly reflected, in a way that is immediately relevant to functional rhythmic behavior, in the extent to which the contraction is phasic, or tonic.
A single number that expresses this is the phasic fraction of the
contraction, (
c
)/
[or its complement, the tonic fraction of the contraction,
c
/
= 1
(
c
)/
].
Because this single output parameter lumps together the whole
contraction waveform [c(t)]
, and
by normalizing by
gives up knowledge of absolute amplitude, it cannot be a precise quantitative measure of
performance in the way that m
is. It does,
however, provide a good qualitative idea of the possibility of rhythmic behavior: the larger the phasic fraction, the better the performance of
a rhythmic task can be. It is especially useful in dealing with a real
NMT (in the next section, for instance, the B15-ARC NMT) where the
quantitative requirements of the task may not be completely certain in
any case, and where the normalization helps reconcile measurements from
different preparations that may vary greatly in absolute amplitude.
Figure 7, an extension of Fig. 1, shows
explicitly how acceleration of the overall kinetics of the model NMT,
the fivefold decrease of both contr and
relax, affects contractions produced by firing patterns
of different speeds (Fig. 7A), raising
, lowering
c
(Fig. 7B), and so
increasing the phasic fraction of the contraction at any particular
P, or, conversely, shifting a particular phasic fraction to
smaller P (Fig. 7C). The phasic fraction changes
most at intermediate pattern speeds, comparable to the speed of the
NMT.
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Interestingly, with the model NMT, the phasic fraction depends, of the
two time constants, only on relax, and not at all on
contr. Likewise with a real NMT that has similar
properties, such as the B15-ARC NMT, relaxation kinetics are likely to
be the primary, and contraction kinetics only a secondary, determinant of the phasic fraction (APPENDIX B, 1). Because
functional performance, too, is affected much more by modulation of
relax (Fig. 3, columns 3 and 4, and Fig. 4) than of
contr (Fig. 3, column 2),
this further validates the phasic fraction as a functionally relevant
indicator of NMT speed. Pure modulation of contraction amplitude has,
with the model NMT, no effect at all on the phasic fraction.
Modulation of the B15-ARC NMT
Contractions of the ARC muscle, as well as those of its
antagonist, the radula opener, and other buccal muscles of
Aplysia, are shaped by numerous endogenous modulators. Well
studied modulators are serotonin (5-HT) and neuropeptides of the small
cardioactive peptide (SCP), myomodulin (MM), buccalin (BUC), and
FRF/FMRFamide families (e.g., Brezina et al. 1995;
Church et al. 1993
; Cropper et al. 1987
,
1988
, 1994
; Evans et al. 1999
; Fox
and Lloyd 1997
, 1998
;
Lloyd et al. 1984
; Weiss et al. 1978
;
Whim and Lloyd 1990
; reviewed by Kupfermann et
al. 1997
; Weiss et al. 1992
,
1993
).
The effect of each of these modulators is likely to be complex. Where
investigated, the modulators have been found to act through multiple
cellular mechanisms (e.g., Brezina et al.
1994a,b
; Probst et al. 1994
; Scott et al. 1997
)
that then underlie multiple, distinguishable components of the
modulation of contraction shape (Brezina et al. 1995
,
1996
, and see below).
The standard practice, however, is to demonstrate the effects on
contraction shape using single contractions, elicited by single, brief
bursts of motor neuron firing. These, too, are part of the NMT
that
with short burst duration and very long interburst interval, or very
large P and small F, as input
but a part that,
functionally, is not very significant. In our experiments here, we have
examined a more functionally relevant part of the B15-ARC NMT,
contractions produced by more physiological firing patterns, focusing
on how the modulation affects the phasic fraction of the contraction, our indicator of the speed of the NMT and the possibility of functional rhythmic behavior.
Figures 8-11 show the results for four representative modulators of the B15-ARC NMT. In each figure, A shows the typical effect on a single contraction, known from previous work. B then shows the effect on the steady-state contraction waveforms produced by physiological, repetitive firing patterns of different speeds. The parameters used were F = 0.4-0.5, fintra = 10-12 Hz (both fixed in any particular experiment) and P ranging from 0.5 to 10 s; these values well cover the physiological range (Paper II). C compares the unmodulated and modulated phasic fraction, plotted as a function of P.
Buccalin (BUCA; Fig. 8) is usually described as simply decreasing contraction amplitude (Fig. 8A). On the patterned contractions, however, its effect was clearly more complex. Contraction amplitude decreased (Fig. 8B), but at the same time the phasic fraction increased (Fig. 8C). This is inconsistent with a pure modulation of contraction amplitude of the kind that we studied with the model NMT. The BUC effect was largest for patterns of intermediate speed, where the contraction was partly phasic and partly tonic. Furthermore, with very slow patterns BUC appeared to have relatively little effect even on contraction amplitude. All this suggests that a significant component of BUC action amounts to an acceleration of the kinetics (perhaps primarily of the relaxation kinetics) of the NMT (compare Figs. 8B and 7A, 8C and 7C).
|
Myomodulin C (MMC; Fig. 9)
was included in these experiments because, like BUC, it can appear to
have a relatively simple effect on single contractions. Through
distinct mechanisms, MMs, and other modulators such as SCP and 5-HT,
exert three simultaneous effects on contractions that have been
described as increasing and decreasing their amplitude and accelerating
their relaxation rate (Brezina et al. 1995,
1996
). With MMC,
at some relatively high concentration, the effects on amplitude balance
out, leaving just a net acceleration of the relaxation rate of single
contractions (Fig. 9A). As expected with such acceleration,
MMC increased the phasic fraction of the patterned
contractions (Fig. 9C), indeed very much as BUC did.
|
Small cardioactive peptide (SCPB; Fig. 10) exerts the three effects just mentioned, but decreases contractions only weakly: the net effect is to increase the amplitude and accelerate the relaxation rate of single contractions (Fig. 10A). With the patterned contractions, the phasic fraction increased (Fig. 10C) as with BUC and MMC. Similar effects were seen with 5-HT.
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Finally, myomodulin A (MMA; Fig. 11) exerts the three effects, but decreases contractions strongly: at moderately high concentrations of MMA, the net effect is to decrease the amplitude and accelerate the relaxation rate of single contractions (Fig. 11A). Again, the phasic fraction of the patterned contractions increased (Fig. 11C) as with the other modulators.
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Not all manipulations of the B15-ARC NMT increase the phasic fraction,
however. Figure 12 shows the effect of
decreased temperature, which increases contractions (cf. Vilim
et al. 1996a) and slows their relaxation rate (Fig.
12A). In this case the phasic fraction of the patterned
contractions decreased (Fig. 12C).
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Several points can be made with regard to these findings. Extrapolation of the effects of modulation from one part of the NMT to another, in particular from single contractions to more physiological, patterned contractions, can be very misleading. The manifestations of the modulation are likely to be quantitatively, perhaps even qualitatively, different. With BUC, for example, the simple decrease of the amplitude of single contractions would not have predicted the increased phasic fraction of the patterned contractions. Similarly in Fig. 9, where we titrated the MMC concentration so as to leave the amplitude of single contractions unchanged (Fig. 9A), yet there were significant changes in the amplitude of the patterned contractions (Fig. 9B). Such quantitative differences were a consistent finding with all of the modulators.
Such differences can be expected for three reasons. First, we saw
with the model NMT that even a pure modulatory effect will manifest
itself differently in different parts of the NMT: a pure modulation of
kinetics will change the amplitude and the phasic fraction of
contractions produced by firing patterns of intermediate speed, but not
of those produced by very slow patterns. Second, the outward
manifestations of the modulation, especially on just a limited set of
contractions produced by a real NMT, often leave ambiguous what
variable is primarily being modulated, of the kind that we had a priori
knowledge of with our model NMT and that we would need to identify for
successful extrapolation to other parts of the NMT. Modulation of
kinetics also appears as change in amplitude, and vice versa (Fig. 1).
Because, over a fixed time interval, faster rise and larger amplitude
are necessarily coupled, does the effect of, for example, SCP on single
ARC contractions (Fig. 10A) reflect (in addition to a
modulation of relaxation kinetics) a primary modulation of amplitude,
or of contraction kinetics? (See further below.) Third, as we
see already in the ARC system, real modulators are unlikely to modulate
just one such variable. This is because they actually modulate some
underlying physiological process (and probably several of these) such
as Ca2+ entry and handling in the presynaptic terminal or
in the muscle (cf. Brezina et al.
1994a,b
). Such a
process will inevitably influence, very likely in a complex
pattern-dependent manner, both amplitude and kinetics.
In some cases, of course, there is a correlation between the modulation of the single and the patterned contractions. Thus the accelerated relaxation rate of single contractions with the MMs and SCP correlates, qualitatively, with the increased phasic fraction of the patterned contractions. (And similarly for the opposite changes with decreased temperature.) The problem is that, with a complex real NMT, it is difficult to predict when the correlation will hold.
Functionally, the most striking finding in these experiments is the increase in phasic fraction brought about by the modulators. In different cases, this may be coupled with different other effects, such as increased or decreased contraction amplitude, but it is clear that a significant component of the action of all of the modulators, even an unsuspected one such as BUC, is to increase the phasic fraction of contractions: to speed up the NMT.
In view of this and the ambiguity of interpretation of the modulation
of single contractions noted above, it may be more correct to think of
SCP, for instance, as primarily modulating, in addition to relaxation
kinetics, not contraction amplitude but rather contraction kinetics: as
accelerating the overall kinetics of the NMT. The increased amplitude
of single contractions (Fig. 10A) would then simply reflect
the faster contraction rate operating over the same fixed time
interval. Acceleration of contraction kinetics by SCP and other
modulators has indeed been emphasized in studies of other buccal
muscles of Aplysia (e.g., Evans et al. 1999;
Fox and Lloyd 1997
, 1998
). This interpretation would also explain why SCP had
little effect on contraction amplitude with very slow patterns (Fig.
10B, right). (These contractions were large, but this was
not limiting because much larger contractions could be produced by
increasing fintra.)
Speeding up the NMT should extend the range of functional rhythmic
behavior to faster speeds. Does this in fact happen? In Fig.
13 we have used the unmodulated and
modulated contraction waveforms from one of the experiments just
described (that with BUC in Fig. 8) to reconstruct the activity of the
antagonistic ARC-opener neuromuscular system and its performance in
Task VI, our realistic task from Paper II. Figure 13, A and
B, shows examples at two values of P; Fig.
13C then compares the unmodulated and modulated performance
m/P as a function of P.
Indeed, speeding up of the NMT by BUC extends opening and closing of
the radula (crossing of the movement axis) to very small
P (Fig. 13A, P = 1 s). And at only
slightly larger P, it enables good performance of the full
Task VI
opening and closing of the radula timed correctly relative to
its protraction and retraction
where there was none before (Fig. 13,
B and C, P = 2 s). At the same time,
the mean amplitude of the contractions decreases (Fig. 13, A
and B), increasing the efficiency of the behavior. The
extension of performance occurs over those intermediate values of
P where the largest shift of the phasic fraction occurred
(cf. Fig. 8C). At large P, where performance was
good before, it may conversely decrease (Fig. 13C, P = 10 s).
|
We see in this example how we might work toward an eventual full quantitative accounting of the effects and the functional roles of all of the diverse modulators in the ARC-opener system. It would be premature to consider further details here, however, for three reasons, which apply also to many other neuromuscular systems (see the DISCUSSION).
First, as discussed in Paper II, the task requirements and the NMTs involved will need to be better understood.
Second, because many of the modulators are intrinsic modulators,
released from the motor neurons themselves by the same firing patterns
that produce the contractions, it is difficult to dissociate the
modulation from the basic operation of the NMT. Indeed, although our
"unmodulated" ARC contractions, here and in Paper I, were recorded
in such a way as to keep modulation to a minimum (for example, we
worked at room temperature, where modulator release is low;
Vilim et al. 1996a), they may already be modulated to some degree. For further dissection, selective blockers of the release
or effects of the modulators will be needed.
And third, the system is in reality modulated, not by fixed
concentrations of single modulators, but by dynamically changing mixtures of multiple modulators. Somewhat different complements of
modulators act on different buccal muscles. Indeed, even the simple
assumption implicit in Fig. 13 that the ARC and opener muscles are both
modulated similarly by BUC is not strictly correct. The two muscles do
share modulators with similar effects, including the MMs, but BUC is
apparently present just in the ARC, not in the opener muscle
(Evans et al. 1999).
![]() |
DISCUSSION |
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All motor commands of the nervous system pass through the filter of the NMT, whose properties significantly constrain the behaviors that can be produced. For optimal performance of a particular behavior, we saw in Paper II that the properties of the NMT must match the behavior, so that some set of motor neuron firing patterns exists that can produce the behavior, and produce it efficiently. The speed of the NMT, in particular, must match the speed of the desired behavior. But if the speed of the NMT is fixed, in a rigid way such as we studied with our two NMTs in Paper I, it will correctly match and allow behavior over only a narrow range of speeds. A slow NMT will allow slow behavior, but not fast behavior as well; a fast NMT will not allow slow behavior with any efficiency. It will not be possible to vary much the speed of a behavior, or to perform behaviors of different speeds with the same neuromuscular plant. However, as we discussed in Paper II, real systems do this routinely. They are able to do it because the speed and other properties of their NMTs are not fixed, but variable. In particular, real NMTs incorporate or are subject to various kinds of neuromuscular plasticity and modulation that dynamically tune their properties to match varying behavior.
Diversity of neuromuscular plasticity and modulation
At neuromuscular junctions of both vertebrates and
invertebrates, presynaptic transmitter release exhibits multiple
components of plasticityfacilitation, augmentation, potentiation,
depression
on a wide range of time scales (Atwood 1976
;
Atwood and Cooper 1996
; Atwood et al.
1989
; Bittner 1989
; Fisher et al.
1997
; Magleby and Zengel 1982
; Zucker
1989
). Once released, the transmitter can feed back to modulate
its own release (Bowman et al. 1988
; Parnas et
al. 1994
; Wessler 1989
). In addition to these
effects intrinsically involving the contraction-mediating transmitter itself, many, perhaps most, neuromuscular junctions and muscles are
modulated by a variety of other transmitters and peptides (reviewed by
Adams et al. 1989
; Calabrese 1989
;
Evans and Myers 1986
; Hooper et al. 1999
;
Muneoka and Kobayashi 1992
; Muneoka et al.
1991
; Worden 1998
; further references below).
Such modulation is especially prominent in invertebrates, but is found
even in fast vertebrate skeletal muscles (Bowman and Nott
1969
; Williams and Barnes 1989
). The modulators
may be "intrinsic," released as cotransmitters from the motor
neurons themselves, or "extrinsic," released from additional
modulatory neurons or arriving as hormones (cf. Katz
1995
; Kupfermann 1991
). The site of modulation
may be any of the steps comprising the NMT, including the release of the mediating transmitter (e.g., Atwood et al. 1989
;
Bittner 1989
; Cropper et al. 1988
;
Meriney and Grinnell 1991
), the response of the
postsynaptic receptors (Jorge-Rivera and Marder 1997
;
Mulle et al. 1988
), and the electrical and contractile
events in the muscle (Brezina et al.
1994a
,b
;
Erxleben et al. 1995
; Probst et al.
1994
). The modulation may interact with the plasticity of transmitter release (Jorge-Rivera et al. 1998
;
Qian and Delaney 1997
) as well as, very likely in a
pattern-dependent manner, with the basic properties of the NMT. Such
plasticity and modulation may account for many of the complexities of
the neuromuscular response, for instance neuromuscular "warm-up"
(cf. Fig. 4C of Paper I), that are seen in practically all
neuromuscular systems (Hoyle 1983
). In
RESULTS, we have already noted a number of these phenomena
in our representative system, the ARC and other buccal muscles of
Aplysia. These muscles exhibit both multiple components of
synaptic plasticity (Cohen et al. 1978
; Jordan et
al. 1993
) and extensive networks of intrinsic as well as
extrinsic modulatory actions.
Formal framework for analysis of NMT variability
The overview above includes both the classic phenomena of pure synaptic plasticity as well as perhaps completely extrasynaptic modulation. In RESULTS, we focused on the latter, in part because it naturally led us to the simplest picture of NMT variability, as alteration imposed on a basic, unmodulated NMT by the action of an external modulator, as mimicked by its exogenous application. Synaptic plasticity, in contrast, seems to be embedded, in a much less separable way, within the structure of the NMT. But synaptic plasticity, too, can be conceptually separated from the basic structure. And conversely, our dynamical systems approach allows us to expand our representation of the NMT so that it incorporates within it the different states of modulation as well as synaptic plasticity. This more general view then shows the two types of variability as formally equivalent. Both appear as quantitative, region-specific alterations or added dimensions of the dynamical structure of a single, general NMT. If the formal alterations of the structure are similar with synaptic plasticity and modulation, their functional consequences will also be similar. Furthermore, as will be seen below, incorporation of the modulation within the structure of the NMT is not just a convenient formal device, but reflects physiological reality when the modulation, like the synaptic plasticity, depends on the motor neuron firing pattern.
We can expand the NMT along the lines discussed in Paper I. We recall that, with the dynamical systems approach, we are seeking a representation of the system in terms of a set of variables whose present values are sufficient to completely summarize its history, and predict its future.
Most generally, we add one or more dimensions orthogonal to those of
the basic dynamical structure of the NMT. In Fig.
14, for example, we have added to our
usual four-dimensional input-output structure one such dimension, for
the modulation factor M (see APPENDIX A,
1), representing in this case the degree of acceleration of
the overall kinetics of the NMT by decrease of both
contr and
relax. For the purposes of our
later discussion, the output here is already performance in our
standard Task III, but we could equally well have plotted the
underlying contraction. The extra M dimension allows us to
represent within the NMT itself all possible states of this modulation,
including all those in Fig. 3. (With an extra dimension, of course, the
section we can show is even more restricted: see Fig. 14 legend.)
|
When there are multiple independent sources of variability, multiple modulators for instance, each requires its own set of orthogonal dimensions.
The most general representation is necessary if the added variability, while interacting with the original structure of the NMT, is not in turn restricted by it: most importantly, if it is independent of the motor neuron firing pattern. This is the case with extrinsic modulation by a hormone or a modulator released from an independent modulatory neuron. Such extrinsic modulation behaves, formally, as extra input to the NMT.
But often the variability does depend on the motor neuron firing
pattern, just as the contraction itself does. This is the case with
intrinsic modulation and synaptic plasticity, the sources of
variability that, for that very reason, seem to be more deeply embedded
in the NMT. Each such source exhibits a relationship to the firing
pattern that has all the properties that we studied in Paper I for the
contraction itself, because the transforms from the firing pattern to
the contraction and to the variability share the relevant formal
properties (cf. Brezina et al. 1997). When the
variability is incorporated in the expanded NMT, its pattern dependence
appears in the NMT along with that of the contraction, as well as
interactions between the two. (We saw a relatively simple case of such
interaction in RESULTS, where some contraction shapes
expressed modulation of kinetics more than others.) Quantitatively, of
course, the pattern dependence of the contraction and the variability can be very different. Different physiological processes, with different dose-response shapes and time constants, are involved, allowing them to react differentially to, and be differentially controlled by, different patterns (Paper I; Brezina et al.
1997
). Thus, for instance, different patterns of motor neuron
firing are optimal for release of the contraction-mediating transmitter and intrinsic modulatory cotransmitters (Bartfai et al.
1988
; Kupfermann 1991
; Vilim et al.
1996a
; Whim and Lloyd 1989
, 1990
). As a result of such differences in pattern
dependence, some firing patterns may, for example, produce contractions
without inducing long-term plasticity of the neuromuscular junction;
others just the opposite (Atwood et al. 1989
;
Baxter and Byrne 1993
; Bittner 1989
).
As with the contraction itself, the pattern-dependent dynamics of
the variability (and so indeed of the NMT as a whole) are likely to
tend toward a point steady state. In that steady state, the variability
will still alter the contraction, but in just one way. It will no
longer contribute true variability, in the sense of expanding the range
that the contraction can occupy. The important question is on what time
scale the variability relaxes to the steady state relative to the time
scale of the input patterns and contractions of interest. The faster
this happens, the smaller will be the range of true variability around
the basic contraction shape. In the steady state, and so, if the
variability relaxes essentially instantaneously on the time scale of
interest, always, the contraction will be altered in just one fixed
way. In this case the NMT needs no extra dimensions at all to
incorporate the variability: it is already implicit in the contraction
shape itself. This is likely to be true, for example, for the faster
components of synaptic plasticity (Fisher et al. 1997)
on the relatively slow time scale of the patterns that we have used
here with the B15-ARC NMT.
Formally, then, the different kinds of variability alter the structure of the NMT in two basic ways, distinguished not so much by the physiological mechanism but by the source of the variability: is it intrinsic to the motor neuron and so, like the contraction itself, dependent on its firing pattern, or extrinsic, independent of it? Intrinsic variability alters the shape of the contraction, but does not expand the range of shapes that can be produced by each pattern, except transiently. A steady-state surface within the structure of the NMT, of the sort we have plotted in many of our figures, is altered in shape, but remains a surface. Extrinsic variability, by contrast, does bring about such expansion, in the steady state as well as transiently, on any time scale. This is because it acts as extra input to the NMT (see APPENDIX L of Paper I.) For the same reason, expansion also occurs when there are multiple independent sources of intrinsic variability, such as multiple modulators released from separate motor neurons (see Again, issues of predictability and controllability).
Functionally, when the contraction shapes are then translated to performance, the fundamental point is that the structure of the NMT has been so altered that it can produce, and produce efficiently, a broader range of behaviors.
Modulation of the speed of the NMT
Throughout, we have focused on the illustrative aspect of speed.
For optimal performance and efficiency, the speed of the NMT must match
the speed of the behavior. The speed of a rhythmic behavior is set by
the period of the firing pattern, P. Thus a particular speed
of the NMT is optimal for a particular P. But it is not
optimal for others. In particular, the performance and efficiency of
rhythmic behavior falls dramatically as P decreasesas the
nervous system attempts to accelerate the behavior
if the speed of the
NMT remains fixed. If the NMT is accelerated correspondingly, however,
functional behavior is maintained. If the NMT is accelerated in a
correctly balanced way (with our model NMT, for example, by decreasing
both
contr and
relax by the same amount),
the behavior may indeed unfold much as before, just compressed in time
(cf. Fig. 1 of Paper I). And, as we saw in Paper II, this compression
may well bring higher performance and efficiency, not just at a
particular speed, but overall.
There is good reason to believe that such modulation of speed is
ubiquitous in NMTs. In the Aplysia ARC muscle, we found a significant component of kinetic acceleration in the action of every
modulator that we tested, even an unsuspected one such as BUC. Similar
modulation is seen in the antagonist radula opener and in other buccal
muscles (Church et al. 1993; Evans et al. 1999
; Fox and Lloyd 1997
, 1998
). In a variety of other neuromuscular systems,
too, a frequent theme in the action of modulators is simultaneous
acceleration of contraction kinetics (or increase of the amplitude of
single contractions, which, as we saw, may well be a reflection of it)
and relaxation kinetics (e.g., Evans and Myers 1986
;
Evans and Siegler 1982
; Jorge-Rivera et al.
1998
; Lingle 1981
; Lloyd 1980
;
McPherson and Blankenship 1991
; Whim and Evans
1988
). These two simultaneous actions will balance out changes
in amplitude and emphasize the component of kinetic acceleration (Figs.
1, B3 and C3, and 7). In nonspiking muscles,
modulators often bring in spikes, which will accelerate the NMT
(Erxleben et al. 1995
; Jorge-Rivera and Marder
1996
; Kravitz et al. 1985
; Meyrand and
Marder 1991
; Satterlie and Norekian 1996
).
Virtually all neuromuscular systems exhibit components of synaptic
plasticity, such as facilitation, with the right properties to
accelerate the NMT. Such phenomena have prompted previous discussion of
the importance of the speed of muscle contraction and relaxation for the performance of rhythmic behavior, by, for example, Evans and Siegler (1982)
, Whim and Evans (1988)
,
Weiss et al. (1992
, 1993
), and Satterlie and Norekian (1996)
.
Very similar modulation is observed in the hearts of many species,
including myogenic hearts that strictly are beyond the scope of this
work (Buckett et al. 1990; Calabrese and Maranto 1984
; Greenberg and Price 1980
; Watson
and Groome 1989
). In the vertebrate heart, of course, the
kinetics of relaxation are well-known to be critical for functional
performance and are modulated to match changes in heart rate
(Katz 1992
; Morad and Rolett 1972
).
Again, issues of predictability and controllability
We now return to some of the fundamental questions of Paper I. When the nervous system sends firing patterns through the NMT, to what extent can it predict the contractions and performance that will result? To what extent can it, through those patterns, control various desired behaviors? In Paper I we saw that the answers to these questions have to do with the size and structure of the NMT. Because variability, in general, makes the NMT larger and more complex, it complicates predictability, but at the same time expands the possibilities for control. More particularly, because the intrinsic and extrinsic variabilities alter the NMT in qualitatively different ways, they have different consequences in these respects.
As before, the problems as well as possibilities are greatest in non-steady-state situations, for instance during transitions between different behaviors. This is true even with intrinsic variability, to the extent that it expands the structure of the NMT.
Thus, in the Aplysia ARC system, the SCPs, MMs, and BUCs are
all intrinsic cotransmitters of the motor neurons B15 and B16, and each
motor neuron releases a different mixture of these peptides, with
multiple effects on different time scales (Brezina et al. 1996; Brezina and Weiss 1998
; Vilim et
al. 1996b
). After a few cycles of each of the firing patterns
that drive the system's several distinct behaviors, such as biting,
swallowing, and rejection, the whole NMT, the contraction itself as
well as the modulatory effects, will reach a point steady state. But it
will be a different steady state in each behavior, and, when the firing
pattern then switches to a new behavior, the different variables of the
NMT will relax to the new steady state on different time scales, most of them, experiments show, as slow as or slower than the time scale of
the firing pattern (Brezina and Weiss 1998
). During this period of transient expansion of the NMT, the nervous system will be
able to predict the contractions and performance, strictly, only if it
knows the values of those variables. And for smooth control of the
transition, it may have to make transient adjustments to the firing
pattern: relax the firing pattern more slowly, too, in coordination
with the relaxation of the modulatory effects.
But eventually, with intrinsic variability, the dynamics of the NMT do collapse to a simple point steady state, just as those of the NMT without any variability do. Qualitatively, the structure of the NMT is just the same. Then the contractions and performance are, just as before, completely predictable: for each firing pattern, there is a single steady-state contraction waveform and performance value. But if it is not expanded, how can the NMT produce a broader range of functional behavior? It is able to do so because, quantitatively, it is so altered that it produces functional contractions, with high performance and efficiency, over a broader range of patterns. The nervous system controls, through the NMT, no more contraction shapes than before, but more of those that it does control are functional.
With respect to speed, we can see how this happens in Fig. 14. In this
section, the general expansion of the NMT is represented by the
two-dimensional base of the plot, P × M: for each
value of the period P, any strength of the modulation
M is possible. But if M represents intrinsic
modulation, it depends on P, and in the steady state, only
one value of M is possible for each P. The system
cannot access the whole two-dimensional surface based on P × M, but is restricted to a one-dimensional curve through it. As
P changes, so, in a fixed way, does M. Starting
at point A, for example, as the nervous system decreases P
to accelerate the behavior, M may depend on P in
such a way that M coordinately increases. Then the system
may follow some trajectory such as A C. Along this trajectory, at
every P, M is automatically adjusted so as to
give the highest performance possible for that P. The speed
of the NMT, in other words, does not remain fixed and optimal for just
one value of P, but varies so that it is always optimally tuned to the current value of P. And we see again in Fig. 14
how this tuning extends the range of the functional behavior to smaller P, and so to much higher overall performance, than would be
possible without the modulation (trajectory A
B).
Of course, M must have the correct dependence on
P. A different dependence would give a different, less
optimal, trajectory across the surface in Fig. 14. Increasing
M too little as P decreases would give, in the
extreme, the trajectory A B; increasing M too much, the
trajectory A
D. Like accelerating the NMT too little, accelerating
it too much
more than is optimal for the current value of
P
decreases performance and efficiency (Fig. 13C; Paper II). Intrinsic variability in real systems does
indeed seem to have the correct sort of pattern dependence. For
example, neuromuscular facilitation (Atwood 1976
;
Fisher et al. 1997
; Magleby and Zengel
1982
; Zucker 1989
), release of intrinsic
modulators (Vilim et al. 1996a
; Whim and Lloyd
1989
, 1990
), and in
some cases their actions (Jorge-Rivera et al. 1998
) all
tend to increase as motor neurons fire at higher frequency and in more
frequent bursts.
Thus intrinsic variability builds into the structure of the NMT a tight coupling of contraction and variability so that the same motor neuron firing pattern that commands the muscle to contract simultaneously optimizes the contraction for the performance of a behavioral task. No additional input is needed. This automatic mechanism is well suited to extending the functional range of a single behavior.
But, because the coupling is tight, the system produces a set of
contraction shapes that is no less restricted than before (Paper I)in
the steady state, just a single shape for each pattern. And if this
shape has been optimized for one behavior, it may not be optimal for a
different behavior that the nervous system may ask the system to
perform. Sometimes it may even be desirable to suppress the contraction
completely, freeing the motor neuron to fire in other peripheral or
central tasks (Hooper et al. 1999
). For multiple
behaviors, what is needed is true variability that will provide
independent control over
that will uncouple
multiple parameters of
the contraction shape. Such expansion of the NMT is possible only with
additional input.
Within limits, such expansion can occur with multiple sources of
intrinsic variability, such as modulators from different motor neurons.
In the Aplysia ARC system, we have previously described how
the SCPs from motor neuron B15 and the MMs from motor neuron B16
uncouple, over a certain range, the size and the relaxation rate of
contractions (Brezina et al. 1996; Brezina and
Weiss 1997
).
The fullest expansion occurs with extrinsic variability, input that can
be completely independent of the motor neuron firing pattern. If
M in Fig. 14 represents extrinsic modulation, the system can
access the whole surface P × M. In the ARC system,
such modulation is provided by 5-HT, with effects similar to SCP (Fig.
10), released from the purely modulatory metacerebral neurons
(Weiss et al. 1978). Some of the benefits of the
independence of the mediating and modulating inputs are well
illustrated in this case, such as the fact that the latter can prepare
the system before the former begin the actual behavior
(Kupfermann and Weiss 1982
). Extrinsic variability, much
more readily than intrinsic variability, can preconfigure the system
for a behavior, or for a class of related behaviors, without yet
committing it to a specific behavior through a specific pattern of
motor neuron firing.
Full expansion of the NMT, however, introduces the converse problem.
Whereas intrinsic variability allowed too few contraction shapes,
extrinsic variability allows too many. No mechanism prevents the system
from reaching many parts of the input-output space that are not
functional. In Fig. 14, the trajectory A D, for example, can now be
achieved, but it still is probably not desirable. In other words, some
of the restrictive coupling that intrinsic variability built into the
structure of the NMT, but which is absent with extrinsic variability,
must be reintroduced. This can be done centrally, by coupling the
inputs. Thus we find in some systems that the firing pattern of
extrinsic modulatory neurons is closely coupled to that of the
mediating motor neurons (Baudoux et al. 1998
;
Burrows and Pflüger 1995
). In many systems,
extrinsic modulators simultaneously modify, and so potentially couple,
the central patterns and the peripheral NMT (e.g.,
Harris-Warrick et al. 1989
,
1992
; Kravitz
et al. 1985
; Satterlie and Norekian 1996
;
Weimann et al. 1997
). They may modulate, too, sensory
neurons that feed peripheral information back to the CNS. Indeed, the sensory neurons themselves may release central as well as peripheral modulators. The last three mechanisms may all be present in
Aplysia buccal neuromuscular systems (Alexeeva et al.
1998
; Cropper et al. 1996
; Kupfermann et
al. 1997
; Weiss et al. 1978
).
All these are the same fundamental issues of central-peripheral
coordination and control that we discussed in Papers I and II, but now
in a more complex NMT. A broader range of behavior is possible,
provided that the nervous system can select the correct firing
patterns. And it would seem to be correspondingly more difficult to
compute these; they must, for instance, vary with the degree of
modulation of the NMT (Figs. 2-5). But the patterns are not actually
computed by the nervous system on the basis of complete
knowledge of the structure of the NMT (Paper I). Rather, they are
generated by an automatic mechanism that uses the information "hard-wired" in the structure of the NMTthe kinds of coupling that we have discussed
to send the system along just a few desirable trajectories through the input-output space.
Concluding remarks
Faced with evidence for peripheral neuromuscular modulation,
a frequently asked question (for instance, with respect to the Aplysia ARC system, by Hoyle 1983, p. 468)
is, why is the additional layer of modulation necessary? Why could not
the basic contraction mechanisms, and the central motor neuron firing
patterns, be configured so as to suffice? The answer emerges from our
work here. The properties of the basic NMT are inherently so
constraining that, through it, many desirable behaviors cannot be
produced with any firing pattern. And because the constraints of the
NMT are peripheral, they can only be alleviated by
peripheral modulation.
The Aplysia ARC neuromuscular system is a particularly
well studied but probably by no means atypical example. In this paper we have given some idea of the complex network of intrinsic as well as
extrinsic modulation that allows this single muscle to perform with
increasing speed and efficiency in food-induced arousal (Susswein et al. 1978), in multiple behaviors such as
biting, swallowing, and rejection (Kupfermann 1974
), and
when dealing with food of varying quality (Hurwitz and Susswein
1992
). As the ARC must integrate its contractions with those of
the antagonist radula opener as well as other buccal muscles, very
similar kinds of modulation occur in those muscles. (For example, the
speed of both antagonist muscles must be modulated for optimal results: Fig. 5.) Most if not all buccal motor neurons contain intrinsic modulatory cotransmitters (Church and Lloyd 1991
), and
the metacerebral neurons provide widespread extrinsic modulation. In
this way not just a single muscle, but the whole feeding musculature is
modulated coordinately. Similar complexities of NMT modulation are
being described in other neuromuscular systems (e.g., Evans and
Myers 1986
; Jorge-Rivera and Marder, 1996
, 1997
;
Jorge-Rivera et al. 1998
; Muneoka et al.
1991
). Such modulation is likely to be found wherever the
nervous system commands, through the constraints of the NMT, a broad
range of functional behaviors.
![]() |
APPENDIX A |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Modulation of the model NMT
1 | We use as our basis the equations in APPENDIX F of Paper I. Specifically, for the dynamical steady state of the system, by making
again the substitutions
![]() ![]() ![]() ![]() ![]() ![]()
|
||||||||||||||
Equations A1-A5 describe the original, unmodulated NMT. We can then apply different kinds of modulation. | |||||||||||||||
To modulate contraction amplitude, we scale the original waveform
[c(t')]![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
|||||||||||||||
To modulate the kinetics of contraction, we make the substitution
![]() ![]() |
|||||||||||||||
To modulate the kinetics of relaxation, we make the substitution
![]() ![]() |
|||||||||||||||
Modulating both ![]() ![]() ![]() ![]() ![]() ![]() |
2 | ![]() ![]() ![]() ![]() |
![]() |
APPENDIX B |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Special importance of relaxation kinetics and their modulation
2 | From the broader perspective of neuromuscular control, we expect
modulation of ![]() ![]() ![]() ![]() ![]() |
![]() |
ACKNOWLEDGMENTS |
---|
This work was supported by National Institutes of Health Grants MH-36730 and K05 MH-01427 to K. R. Weiss and by funds from the Whitehall Foundation to V. Brezina. Some Aplysia were provided by the National Center for Research Resources National Resource for Aplysia at the University of Miami under NIH Grant RR-10294.
![]() |
FOOTNOTES |
---|
Address for reprint requests: V. Brezina, Dept. of Physiology and Biophysics, Box 1218, Mt. Sinai School of Medicine, 1 Gustave L. Levy Place, New York, NY 10029.
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.
Received 26 April 1999; accepted in final form 31 August 1999.
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REFERENCES |
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