The Role of Activity in Synaptic 
Competition at the Neuromuscular 
Junction 
Samuel R. H. Joseph 
Centre for Cognitive Science 
Edinburgh University 
Edinburgh, U.K. 
email: sam@cns.ed.ac.uk 
David J. Willshaw 
Centre for Cognitive Science 
Edinburgh University 
Edinburgh, U.K. 
email: david@cns.ed.ac.uk 
Abstract 
An extended version of the dual constraint model of motor end- 
plate morphogenesis is presented that includes activity dependent 
and independent competition. It is supported by a wide range of 
recent neurophysiological evidence that indicates a strong relation- 
ship between synaptic efficacy and survival. The computational 
model is justified at the molecular level and its predictions match 
the developmental and regenerative behaviour of real synapses. 
I INTRODUCTION 
The neuromuscular junction (NMJ) of mammalian skeletal muscle is one of the 
most extensively studied areas of the nervous system. One aspect of its develop- 
ment that it shares with many other parts of the nervous system is its achievement 
of single innervation, one axon terminal connecting to one muscle fibre, after an 
initial state of polyinnervation. The presence of electrical activity is associated 
with this transition, but the exact relationship is far from clear. Understanding 
how activity interacts with the morphogenesis of neural systems could provide us 
with insights into methods for constructing artificial neural networks. With that in 
mind, this paper examines how some of the conflicting ideas about the development 
of neuromuscular connections can be resolved. 
The Role of Activity in Synaptic Competition at the Neuromuscular Junction 9 7 
2 EXPERIMENTAL FINDINGS 
The extent to which a muscle is innervated can be expressed in terms of the motor 
unit size - the number of fibres contacted by a given motor axon. Following removal 
of some motor axons at birth, the average size of the remaining motor units after 
withdrawal of polyinnervation is larger than normal (Fladby & Jansen, 1987). This 
strongly suggests that individual motor axons successfully innervate more fibres 
as a result of the absence of their neighbours. It is appealing to interpret this as 
a competitive process where terminals from different axons compete for the same 
muscle endplate. Since each terminal is made up of a number of synapses the 
process can be viewed as the co-existence of synapses from the same terminal and 
the elimination of synapses from different terminals on the same endplate. 
2.1 THE EFFECTS OF ELECTRICAL ACTIVITY 
There is a strong activity dependent component to synapse elimination. Paralysis 
or stimulation of selected motor units appears to favour the more active motor 
terminals (Colman  Lichtman, 1992), while inactive axon terminals tend to coexist. 
Recent work also shows that active synaptic sites can destabilise inactive synapses 
in their vicinity (Balice-Gordon  Lichtman, 1994). These findings support the 
idea that more active terminals have a competitive advantage over their inactive 
fellows, and that this competition takes place at a synaptic level. 
Activity independent competition has been demonstrated in the rat lumbrical mus- 
cle (Ribchester, 1993). This muscle is innervated by the sural and the lateral plantar 
nerves. If the sural nerve is damaged the lateral plantar nerve will expand its terri- 
tory to the extent that it innervates the entire muscle. On subsequent reinnervation 
the regenerating sural nerve may displace some of the lateral plantar nerve termi- 
nals. If the muscle is paralysed during reinnervation more lateral plantar nerve 
terminals are displaced than in the normal case, indicating that competition be- 
tween inactive terminals does take place, and that paralysis can give an advantage 
to some terminals. 
3 MODELS AND MECHANISMS 
If the nerve terminals are competing with each other for dominance of motor end- 
plates, what is the mechanism behind it? As mentioned above, activity is thought 
to play an important role in affecting the competitive chances of a terminal, but 
in most models the terminals compete for some kind of trophic resource (Gouze et 
al., 1983; Willshaw, 1981). It is possible to create models that use competition for 
either a postsynaptic (endplate) resource or a presynaptic (motor axon) resource. 
Both types of model have advantages and disadvantages, which leads naturally to 
the possibility of combining the two into a single model. 
3.1 BENNET AND ROBINSON'S DUAL CONSTRAINT MODEL 
The dual constraint model (DCM) (Bennet & Robinson, 1989), as extended by 
Rasmussen & Willshaw (1993), is based on a reversible reaction between molecules 
from a presynaptic resource A and a postsynaptic resource B. This reaction takes 
place in the synaptic cleft and produces a binding complex C which is essential for 
98 S.R.H. JOSEPH, D. J. WILLSHAW 
the terminal's survival. Each motor axon and muscle fibre has a limited amount of 
their particular resource and the size of each terminal is proportional to the amount 
of the binding complex at that terminal. The model achieves single innervation and 
a perturbation analysis performed by Rasmussen & Willshaw (1993) showed that 
this single innervation state is stable. However, for the DCM to function the forward 
rate of the reaction had to be made proportional to the size of the terminal, which 
was difficult to justify other than suggesting it was related to electrical activity. 
3.2 SELECTIVE MECHANISMS 
While the synapses in the surviving presynaptic terminal are allowed to coexist, 
synapses from other axons are eliminated. How do synapses make a distinction 
between synapses in their own terminal and those in others? There are two pos- 
sibilities: (i) Synchronous transmitter release in the synaptic boutons of a motor 
neuron could distinguish synapses, allowing them to compete as cartels rather than 
individuals (Colman  Lichtman, 1992). (ii) The synapses could be employing se- 
lective recognition mechanisms, e.g the 'induced-fit' model (Ribchester  Barry, 
1994). 
A selective mechanism implies that all the synapses of a given motor neuron can 
be identified by a molecular substrate. In the induced-fit model each motor neu- 
ron is associated with a specific isoform of a cellular adhesion molecule (CAM); 
the synapses compete by attempting to induce all the CAMs on the endplate into 
the conformation associated with their neuron. This kind of model can be used to 
account .for much of the developmental and regenerative processes of the NMJ. How- 
ever, it has difficulty explaining Balice-Gordon & Lichtman's (1994) focal blockade 
experiments which show competition between synapses distinguished only by the 
presence of activity. If, instead, activity is responsible for the distinction of friend 
from foe, how can competition take place at the terminal level when activity is not 
present? Could we resolve this dilemma by extending the dual constraint model? 
4 EXTENDING THE DUAL CONSTRAINT MODEL 
Tentative suggestions can be made for the identity of the 'mystery molecules' in 
the DCM. According to McMahan (1990) a protein called agrin is synthesised in 
the cell bodies of motor neurons and transported down their axons to the muscle. 
When this protein binds to the surface of the developing muscle, it causes acetyl- 
choline receptors (AChRs), and other components of the postsynaptic apparatus, 
to aggregate on the myotube surface in the vicinity of the activated agrin. 
Other work (Wallace, 1988) has provided insights into the mechanism used by agrin 
to cause the aggregation of the postsynaptic apparatus. Initially, AChR aggregates, 
or 'speckles', are free to diffuse laterally in the myotube plasma membrane (Axelrod 
et al., 1976). When agrin binds to an agrin-specific receptor, AChR speckles in the 
immediate vicinity of the agrin-receptor complex are immobilised. As more speckles 
are trapped larger patches are formed, until a steady state is reached. Such a patch 
will remain so long as agrin is bound to its receptor and Ca ++ and energy supplies 
are available. 
Following AChR activation by acetylcholine, Ca ++ enters the postsynaptic cell. 
Since Ca ++ is required for both the formation and maintenance of AChR aggregates, 
The Role of Activity in Synaptic Competition at the Neuromuscular Junction 99 
a feedback loop is possible whereby the bigger a patch is the more Ca ++ it will 
have available when the receptors are activated. Crucially, depolarisation of non- 
junctional regions blocks AChR expression (Andreose et al., 1995) and it is AChR 
activation at the NMJ that causes depolarisation of the postsynaptic cell. So it 
seems that agrin is a candidate for molecule A, but what about B or C?. It is 
tempting to posit AChR as molecule B since it is the critical postsynaptic resource. 
However, since agrin does not bind directly to the acetylcholine receptor, a different 
sort of reaction is required. 
4.1 A DIFFERENT SORT OF REACTION 
If AChR is molecule B, and one agrin molecule can attract at least 160 AChRs 
(Nitkin et al., 1987) the simple reversible reaction of the DCM is ruled out. Alter- 
natively, AChR could exist in either free, B f, or bound, Bb states, being converted 
through the mediation of A. Bb would now play the role of C in the DCM. It is 
possible to devise a rate equation for the change in the number of receptors at a 
nerve terminal over time: 
dB = aAB f - B (1) 
dt 
where a and  are rate constams. The increase in bound AChR over time is 
proportional to the amount of agrin at a junction and the number of free receptors 
in the endplate area, while the decrease is proportional to the amount of bound 
AChRs. The rate equation (1) can be used as the basis of an extended DCM if four 
other factors are considered: (i) Agrin stays active as receptors accumulate, so the 
conservation equations for A and B are: 
M 
Ao = An + ] Anj 
j=l 
N 
= + (2) 
i=1 
where the subscript 0 indicates the fixed resource available to each muscle or neuron, 
the lettered subscripts indicate the amount of that substance that is present in the 
neuron n, muscle fibre m and terminal nm, and there are N motor neurons and M 
muscle fibres. (ii) The size of a terminal is proportional to the number of bound 
AChRs, so if we assume the anterograde flow is evenly divided between the n 
terminals of neuron n, the transport equation for agrin is: 
dAn An An 
d = A-- - 6 (3) 
Yn Bnmb 
where A and 5 are transport rate constants and the retrograde flow is assumed 
proportional to the amount of agrin at the terminal and inversely proportional to 
the size of the terminal. (iii) AChRs are free to diffuse laterally across the surface 
of the muscle, so the forward reaction rate will be related to the probability of an 
AChR speckle intersecting a terminal, which is itself proportional to the terminal 
diameter. (iv) The influx of Ca ++ through AChRs on the surface of the endplate 
will also affect the forward reaction rate in proportion to the area of the terminal. 
Taking B0 to be proportional to the volume of the postsynaptic apparatus, these 
1/3 /2/3 respectively. This gives the final 
last two terms are proportional to B and b 
rate equation: 
r> D1/3 D2/3 
dBn, = aA,,,oiJnm,,,, _ Bn, = aAn,B,fBn,b - B,,,, (4) 
dt 
100 S.R.H. JOSEPH, D. J. WILLSHAW 
Equations (3) and (4) are similar to those in the original DCM, only now we have 
been able to justify the dependence of the forward reaction rate on the size of the 
terminal, Bn,0. We can also resolve the distinction paradox, as follows. 
4.2 RESOLVING THE DISTINCTION PARADOX 
In terms of distinguishing between synapses it seems plausible that concurrently 
active synapses (i.e. those belonging to the same neuron) will protect themselves 
from the negative effects of depolarisation. In paralysed systems, synapses will ben- 
efit from the AChR accumulating affects of the agrin molecules in those synapses 
nearby (i.e. those in the same terminal). It was suggested (Jennings, 1994) that 
competition between synapses of the same terminal was seen after focal blockade 
because active AChRs help stabilise the receptors around them and suppress those 
further away. This fits in with the stabilisation role of Ca ++ in this model and 
the suppressive effects of depolarisation, as well as the physical range of these ef- 
fects during 'heterosynaptic suppression' (Lo & Poo, 1991). It seems that Jenning's 
mechanism, although originally speculative, is actually quite a plausible explana- 
tion and one that fits in well with the extended DCM. The critical effect in the 
XDCM is that if the system is paralysed during development there is a change in 
the dependency of the forward reaction rate on the size of an individual terminal. 
This gives the reinnervating terminals a small initial advantage due to their more 
competitive diameter/volume ratios. As we shall see in the next section, this allows 
us to demonstrate activity independent competition. 
5 SIMULATING THE EXTENDED DCM 
In terms of achieving single innervation the extended DCM performs just as well 
as the original, and when subjected to the same perturbation analysis it has been 
demonstrated to be stable. Simulating a number of systems with as many muscle 
fibres and motor neurons as found in real muscles allowed a direct comparison of 
model findings with experimental data (figure 1). 
 Experimental 
+ Simulation 
Days after birth 
Figure 1: Elimination of Polyinnervation in Rat soleus muscle and Simulation 
Figure 2 shows nerve dominance histograms of reinnervation in both the rat lumbri- 
cal muscle and its extended DCM simulation. Both compare the results produced 
when the system is paralysed from the outset of reinnervation (removal of 
'- n 77t b 
The Role of Activity in Synaptic Competition at the Neuromuscular Junction 1 O1 
term from equation (4)) with the normal situation. Note that in both the simula- 
tion and the experiment the percentage of fibres singly innervated by the reinner- 
vating sural nerve is increased in the paralysis case. Inactive sural nerve terminals 
are displacing more inactive lateral plantar nerve terminals (activity independent 
competition). They can achieve this because during paralysis the terminals with 
the largest diameters capture more receptors, while the terminals with the largest 
volumes lose more agrin; so small reinnervating terminals do a little better. How- 
ever, if activity is present the receptors are captured in proportion to a terminal's 
volume, so there's no advantage to a small terminal's larger diameter/volume ratio. 
oo 
90 
80 
71) 
60 
50 
40 
I Nerve Dominance Histogram (Experimental) [ 
Paralysis 
Normal 
SingleLPN Multi SingleSN 
Nerve Dominance Histogram (Simulation) ] 
SingleLPN Mull 
SmgleSN 
Figure 2: Types of Innervation by Lateral Plantar and Sural Nerves 
6 DISCUSSION 
The extensions to the DCM outlined here demonstrate both activity dependent 
and independent competition and provide greater biochemical plausibility. How- 
ever this is still only a phenomenological demonstration and further experimental 
work is required to ascertain its validity. There is a need for illumination con- 
cerning the specific chemical mechanisms that underlie agrin's aggregational effects 
and the roles that both Ca ++ and depolarisation play in junctional dynamics. An 
important connection made here is one between synaptic efficiency and junctional 
survival. Ca ++ and NO have both been implicated in Hebbian mechanisms (Bliss 
&: Coilingridge, 1993) and perhaps some of the principles uncovered here may be 
applicable to neuroneuronic synapses. This work should be followed up with a direct 
model of synaptic interaction at the NMJ that includes the presynaptic effects of 
depolarisation, allowing the efficacy of the synapse to be related to its biochemistry; 
an important step forward in our understanding of nervous system plasticity. Re- 
lating changes in synaptic efficiency to neural morphogenesis may also give insights 
into the construction of artificial neural networks. 
Acknowledgements 
We are grateful to Michael Joseph and Bruce Graham for critical reading of the 
manuscript and to the M.R.C. for funding this work. 
102 S.R.H. JOSEPH, D. J. WILLSHAW 
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