Growth and elimination of nerve terminals at synaptic sites during polyneuronal innervation of muscle cells: a trophic hypothesis

Terminal Schwann cell and vacant site mediated synapse elimination at developing neuromuscular junctions

Synapses undergo transition from polyinnervation by multiple axons to single innervation a few weeks after birth. Synaptic activity of axons and interaxonal competition are thought to drive this developmental synapse elimination and tested as key parameters in quantitative models for further understanding. Recent studies of muscle synapses (endplates) show that there are also terminal Schwann cells (tSCs), glial cells associated with motor neurons and their functions, and vacant sites (or vacancies) devoid of tSCs and axons proposing tSCs as key effectors of synapse elimination. However, there is no quantitative model that considers roles of tSCs including vacancies. Here we develop a stochastic model of tSC and vacancy mediated synapse elimination. It employs their areas on individual endplates quantified by electron microscopy-based analyses assuming that vacancies form randomly and are taken over by adjacent axons or tSCs. The model reliably reproduced synapse elimination whereas equal or random probability models, similar to classical interaxonal competition models, did not. Furthermore, the model showed that synapse elimination is accelerated by enhanced synaptic activity of one axon and also by increased areas of vacancies and tSCs suggesting that the areas are important structural correlates of the rate of synapse elimination.

Dual constraints on synapse formation and regression in schizophrenia: neuregulin, neuroligin, dysbindin, DISC1, MuSK and agrin

During adolescence there is a loss of approximately 30% of the synapses formed in the cortex during childhood. Comprehensive studies of the visual cortex show that this loss of synapses does not occur as a consequence of less appropriate projections being eliminated in favour of more appropriate ones. Rather it seems that synapses with low efficacy for transmission are eliminated in favour of those with higher efficacy. The loss of low-efficacy synapses is known, on theoretical grounds, to enhance the function of neural networks, but large synapse losses lead to failure of network function. In the dorsolateral prefrontal cortex (DLPC) of those suffering from schizophrenia the number of synapses is relatively very low, approximately 60% lower than that observed in normal childhood. It is not known if this is due to an additional loss over that during normal adolescence or whether it results from a failure to form a normal complement of synapses during childhood. The first study of synapse loss in the mammalian nervous system was made on the neuromuscular junction at Sydney University in 1974. Since then this junction has provided principal insights into the molecular basis of synapse formation and regression, so providing a paradigm for investigations of these phenomena in the DLPC. For example the molecules muscle-specific receptor tyrosine kinase (MuSK), agrin and neuregulin have been identified and their critical roles in the formation and maintenance of synapses elucidated. Loss of function of MuSK or agrin leads to failure of neuromuscular synapse formation as well as a loss of approximately 30% of excitatory synapses in the cortex. Similar synapse loss occurs on failure of neuregulin in vitro and of neuroligin in vivo. It is suggested that three important questions need to be answered: first, over what development period are the synapse numbers in DLPC of subjects with schizophrenia lower than normal; second, what are the relative importance of MuSK/agrin, neuregulin/ErB and neurexin/neuroligin in synapse formation and regression in the DLPC; and third, to what extent have these molecules gone awry in schizophrenia.

Competition in neurite outgrowth and the development of nerve connections

During the development of the nervous system, neurons form their characteristic morphologies and become assembled into synaptically connected networks. In both neuronal morphogenesis and the development of nerve connections, competition plays an important role. Although the notion of competition is commonly used in neurobiology, there is little understanding of the nature of the competitive process and the underlying molecular and cellular mechanisms. In this chapter, we review a model of competition between outgrowing neurites, as well as various models of competition that have been proposed for the refinement of connections that takes place in the development of the neuromuscular and visual systems. We describe in detail a model that links competition in the development of nerve connections with the underlying actions and biochemistry of neurotrophic factors.

Mathematical analysis of competition between sensory ganglion cells for neurotrophic factor in the skin

A model is presented of competition between sensory axons for trophic molecules (e.g. a neurotrophin such as NGF), produced in a region of skin small enough to permit their free diffusion throughout it; e.g., a touch dome, or a vibrissal follicle hair sinus. The variables specified are the number of high affinity trophic factor receptors per axon terminal and the concentration of trophic factor in the extracellular space. Previous models of this class predicted the loss of all the axons innervating the region except the one requiring least trophic factor for its maintenance, even with high rates of trophic factor production. In the present model, we have imposed upper limits to axonal growth, thereby introducing new equilibria, and we show by a global analysis using LaSalle's theorem, and also by local analysis, that several axons can then coexist if the rate of production of trophic molecules is sufficiently high.

Neurophysiology of vocal fold paralysis

Although a tremendous volume of energy and literature has been devoted to laryngeal paralysis in the past decade, there are still substantial gaps in our understanding of fundamental issues. Oddly enough, controversy remains regarding the actual innervation pathways of the larynx and whether the paralyzed larynx is truly denervated or dysfunctionally reinnervated. An appreciation of these basic issues is prerequisite to making prudent decisions regarding the most appropriate type of intervention. The purpose of this article is to provide a brief overview of basic laryngeal anatomy and neurophysiology to prepare the reader for a subsequent discussion of futuristic research for treatment of laryngeal paralysis.A novel approach is described, which can induce selective reinnervation of individual laryngeal muscles by their original motor fibers within the recurrent laryngeal nerve.

Electrical stimulation of a denervated muscle promotes selective reinnervation by native over foreign motoneurons

The effect of electrical stimulation of the denervated posterior cricoarytenoid (PCA) muscle on its subsequent reinnervation was explored in the canine. Eight animals were implanted with a planar array of 36 electrodes for chronic stimulation and recording of spontaneous and evoked electromyographic (EMG) potentials across the entire fan-shaped surface of a muscle pair. Normative EMG data were recorded from each electrode site before unilateral nerve section, and from the innervated partner after nerve section. After randomizing the animals to experimental and control groups, the right recurrent laryngeal nerve innervating the PCA abductor muscle and its adductor antagonists was sectioned and reanastomosed. The PCA muscle in four experimental animals was continuously stimulated during the 11-mo experiment, using a 1-s, 30-pps, biphasic pulse train composed of 1-ms pulses 2-6 mA in amplitude and repeated every 10 s. The remaining four animals served as nonstimulated controls. Appropriate reinnervation by native inspiratory motoneurons was indexed behaviorally by the magnitude of vocal fold opening and electromyographically by the potential across all electrode sites. Inappropriate reinnervation by foreign adductor motoneurons was quantitated by recording EMG potentials evoked reflexly by stimulation of sensory afferents of the laryngeal mucosa. All four experimental animals showed a greater level of correct PCA muscle reinnervation (P < 0.0064) and a lesser level of incorrect reinnervation (P < 0.0084) than the controls. Direct muscle stimulation also appeared to enhance the overall magnitude of reinnervation, but the effect was not as strong (P < 0.113). These findings are consistent with a previous report and suggest that stimulation of a mammalian muscle may profoundly affect its receptivity to reinnervation by a particular motoneuron type.

Neuronal cell death, nerve growth factor and neurotrophic models: 50 years on

Viktor Hamburger has just died at the age of 100. It is 50 years since he and Rita Levi-Montalcini laid the foundations for the study of naturally occurring cell death and of neurotrophic factors in the nervous system. In a period of less than 10 years, from 1949 to 1958, Hamburger and Levi-Montalcini made the following seminal discoveries: that neuron cell death occurs in dorsal root ganglia, sympathetic ganglia and the cervical column of motoneurons; that the predictions arising from this observation, namely that survival is dependent on the supply of a trophic factor, could be substantiated by studying the effects of a sarcoma on the proliferation of ganglionic processes both in vivo and in vitro; and that the proliferation of these processes could be used as an assay system to isolate the factor. This work provides a short review mostly of the early history of this subject in the context of the Hamburger/Levi-Montalcini paradigm. This acts as an introduction to a consideration of models that have been proposed to account for how the different sources of growth factors provide for the survival of neurons during development. It is suggested that what has been called the 'social-control' model provides the most parsimonious quantitative description of the contribution of trophic factors to neuronal survival, a concept for which we are in debt to Viktor Hamburger and Rita Levi-Montalcini.

Development of nerve connections under the control of neurotrophic factors: parallels with consumer-resource systems in population biology

The development of connections between neurons and their target cells involves competition between axons for target-derived neurotrophic factors. Although the notion of competition is commonly used in neurobiology, the process is not well understood, and only a few formal models exist. In population biology, in contrast, the concept of competition is well developed and has been studied by means of many formal models of consumer-resource systems. Here we show that a recently formulated model of axonal competition can be rewritten as a general consumer-resource system. This allows neurobiological phenomena to be interpreted in population biological terms and, conversely, results from population biology to be applied to neurobiology. Using findings from population biology, we have studied two extensions of our axonal competition model. In the first extension, the spatial dimension of the target is explicitly taken into account. We show that distance between axons on their target mitigates competition and permits the coexistence of axons. The model can account for the fact that in many types of neurons a positive correlation exists between the size of the dendritic tree and the number of innervating axons surviving into adulthood. In the second extension, axons are allowed to respond to more than one neurotrophic factor. We show that this permits competitive exclusion among axons of one type, while at the same time there is coexistence with axons of another type innervating the same target. The model offers an explanation for the innervation pattern found on cerebellar Purkinje cells, where climbing fibres compete with each other until only a single one remains, which coexists with parallel fibre input to the same Purkinje cell.

Activity-driven synapse elimination leads paradoxically to domination by inactive neurons

In early postnatal life, multiple motor axons converge at individual neuromuscular junctions. However, during the first few weeks after birth, a competitive mechanism eliminates all the inputs but one. This phenomenon, known as synapse elimination, is thought to result from competition based on interaxonal differences in patterns or levels of activity (for review, see Lichtman,1995). Surprisingly, experimental data support two opposite views of the role of activity: that active axons have a competitive advantage (Ribchester and Taxt, 1983; Ridge and Betz, 1984; Balice-Gordon and Lichtman, 1994) and that inactive axons have a competitive advantage (Callaway et al., 1987, 1989). To understand this paradox, we have formulated a mathematical model of activity-mediated synapse elimination. We assume that the total amount of transmitter released, rather than the frequency of release, mediates synaptic competition. We further assume that the total synaptic area that a neuron can support is metabolically constrained by its activity level and size. This model resolves the paradox by showing that a competitive advantage of higher frequency axons early in development is overcome at later stages by greater synaptic efficacy of axons firing at a lower rate. This model both provides results consistent with experiments in which activity has been manipulated and an explanation for the origin of the size principle (Henneman, 1985).

Competition for neurotrophic factor in the development of nerve connections

The development of nerve connections is thought to involve competition among axons for survival promoting factors, or neurotrophins, which are released by the cells that are innervated by the axons. Although the notion of competition is widely used within neurobiology, there is little understanding of the nature of the competitive process and the underlying mechanisms. We present a new theoretical model to analyse competition in the development of nerve connections. According to the model, the precise manner in which neurotrophins regulate the growth of axons, in particular the growth of the amount of neurotrophin receptor, determines what patterns of target innervation can develop. The regulation of neurotrophin receptors is also involved in the degeneration and regeneration of connections. Competition in our model can be influenced by factors dependent on and independent of neuronal electrical activity. Our results point to the need to measure directly the specific form of the regulation by neurotrophins of their receptors.

Synapse formation molecules in muscle and autonomic ganglia: the dual constraint hypothesis

In 1970 it was thought that if the motor-nerve supply to a muscle was interrupted and then allowed to regenerate into the muscle, motor-synaptic terminals most often formed presynaptic specializations at random positions over the surface of the constituent muscle fibres, so that the original spatial pattern of synapses was not restored. However, in the early 1970s a systematic series of experiments were carried out showing that if injury to muscles was avoided then either reinnervation or cross-reinnervation reconstituted the pattern of synapses on the muscle fibres according to an analysis using the combined techniques of electrophysiology, electronmicroscopy and histology on the muscles. It was thus shown that motor-synaptic terminals are uniquely restored to their original synaptic positions. This led to the concept of the synaptic site, defined as that region on a muscle fibre that contains molecules for triggering synaptic terminal formation. However, nerves in developing muscles were found to form connections at random positions on the surface of the very short muscle cells, indicating that these molecules are not generated by the muscle but imprinted by the nerves themselves; growth in length of the cells on either side of the imprint creates the mature synaptic site in the approximate middle of the muscle fibres. This process is accompanied at first by the differentiation of an excess number of terminals at the synaptic site, and then the elimination of all but one of the terminals. In the succeeding 25 years, identification of the synaptic site molecules has been a major task of molecular neurobiology. This review presents an historical account of the developments this century of the idea that synaptic-site formation molecules exist in muscle. The properties that these molecules must possess if they are to guide the differentiation and elimination of synaptic terminals is considered in the context of a quantitative model of this process termed the dual-constraint hypothesis. It is suggested that the molecules agrin, ARIA, MuSK and S-laminin have suitable properties according to the dual-constraint hypothesis to subserve this purpose. The extent to which there is evidence for similar molecules at neuronal synapses such as those in autonomic ganglia is also considered.

Competition for neurotrophic factors: mathematical analysis

Neurotrophic factors, particularly the neurotrophin gene family of neurotrophic factors, are implicated in activity-dependent anatomical plasticity in the visual cortex and at the neuromuscular junction. Accumulating evidence implicates neurotrophic factors as possible mediators of activity-dependent competition between afferents, leading to the segregation of afferents' arbors on the target space. We present a biologically plausible mathematical model of competition for neurotrophic factors. We show that the model leads to anatomical segregation, provided that the levels of neurotrophic factors released in an activity-independent manner, or the levels available by exogenous infusion, are below a critical value, which we derive. Above this critical value, afferent segregation breaks down. We also show that the model segregates afferents even in the presence of very highly correlated patterns of afferent activity. The model is therefore ideally suited for application to the development of ocular dominance columns in the kitten visual cortex.

Marr's theory of the neocortex as a self-organizing neural network

Marr's proposal for the functioning of the neocortex (Marr, 1970) is the least known of his various theories for specific neural circuitries. He suggested that the neocortex learns by self-organization to extract the structure from the patterns of activity incident upon it. He proposed a feedforward neural network in which the connections to the output cells (identified with the pyramidal cells of the neocortex) are modified by a mechanism of competitive learning. It was intended that each output cell comes to be selective for the input patterns from a different class and is able to respond to new patterns from the same class that have not been seen before. The learning rule that Marr proposed was underspecified, but a logical extension of the basic idea results in a synaptic learning rule in which the total amount of synaptic strength of the connections from each input ("presynaptic") cell is kept at a constant level. In contrast, conventional competitive learning involves rules of the "postsynaptic" type. The network learns by exploiting the structure that Marr assumed to exist within the ensemble of input patterns. For this case, analysis is possible that extends that carried out by Marr, which was restricted to the binary classification task. This analysis is presented here, together with results from computer simulations of different types of competitive learning mechanisms. The presynaptic mechanism is best known in the computational neuroscience literature. In neural network applications, it may be a more suitable mechanism of competitive learning than those normally considered.

Presynaptic and postsynaptic competition in models for the development of neuromuscular connections

In the establishment of connections between nerve and muscle there is an initial stage when each muscle fibre is innervated by several different motor axons. Withdrawal of connections then takes place until each fibre has contact from just a single axon. The evidence suggests that the withdrawal process involves competition between nerve terminals. We examine in formal models several types of competitive mechanism that have been proposed for this phenomenon. We show that a model which combines competition for a presynaptic resource with competition for a postsynaptic resource is superior to others. This model accounts for many anatomical and physiological findings and has a biologically plausible implementation. Intrinsic withdrawal appears to be a side effect of the competitive mechanism rather than a separate non-competitive feature. The model's capabilities are confirmed by theoretical analysis and full scale computer simulations.

Development of calcitonin-gene-related peptide, chromogranin A, and synaptic vesicle markers in rat motor endplates, studied using immunofluorescence and confocal laser scanning

The presence of calcitonin-gene-related peptide (CGRP) and chromogranin A was investigated in the developing rat (E18-adult) motor system, using immunofluorescence and confocal laser scanning, and compared with synaptic vesicle markers, synaptophysin and synapsin I. In lumbar motor perikarya CGRP-LI and Chr A-LI were present in high intensities in E18 and P1 perikarya in the anterior horn. With increasing age immunoreactivity decreased. Chr A-LI was sparse in the adult. In peroneal endplates, p38-LI and SYN I-LI were present in all stages, including E18. Peptide-LI was very weak or absent in early stages (E18 and P1), but abundant in P8 and P18, especially CGRP-LI, and decreased again in P32 and adult animals. These observations indicate that the peptides have precise functions during certain developmental stages, possibly related to synapse maturation, receptor concentration, and reduction of supernumerary endplates. Both peptides are rapidly transported anterogradely in adult motor axons, and may serve physiological functions also in the adult.

Probabilistic secretion of quanta in the central nervous system: granule cell synaptic control of pattern separation and activity regulation

The implications of probabilistic secretion of quanta for the functioning of neural networks in the central nervous system have been explored. A model of stochastic secretion at synapses in simple networks, consisting of large numbers of granule cells and a relatively small number of inhibitory interneurons, has been analysed. Such networks occur in the input to the cerebellum Purkinje cells as well as to hippocampal CA3 pyramidal cells and to pyramidal cells in the visual cortex. In this model the input axons terminate on granule cells as well as on an inhibitory interneuron that projects to the granule cells. Stochastic secretion at these synapses involves both temporal variability in secretion at single synapses in the network as well as spatial variability in the secretion at different synapses. The role of this stochastic variability in controlling the size of the granule cell output to a level independent of the size of the input and in separating overlapping inputs has been determined analytically as well as by simulation. The regulation of granule-cell output activity to a reasonably constant value for different size inputs does not occur in the absence of an inhibitory interneuron when both spatial and temporal stochastic variability occurs at the remaining synapses; it is still very poor in the presence of such an interneuron but in the absence of stochastic variability. However, quite good regulation is achieved when the inhibitory interneuron is present with spatial and temporal stochastic variability of secretion at synapses in the network. Excellent regulation is achieved if, in addition, allowance is made for the nonlinear behaviour of the input-output characteristics of inhibitory interneurons. The capacity of granule-cell networks to separate overlapping patterns of activity on their inputs is adequate, with spatial variability in the secretion at synapses, but is improved if there is also temporal variability in the stochastic secretion at individual synapses, although this is at the expense of reliability in the network. Other factors which improve pattern separation are control of the output to very low activity levels, and a restriction on the cumulative size of the excitatory input terminals of each granule cell. Application of the theory to the input neural networks of the cerebellum and the hippocampus shows the role of stochastic variability in quantal transmission in determining the capacity of these networks for pattern separation and activity regulation.

Synaptic dynamics at the neuromuscular junction: mechanisms and models

During development, the neuromuscular junction passes through a stage of extensive polyinnervation followed by a period of wholesale synapse elimination. In this report we discuss mechanisms and interactions that could mediate many of the key aspects of these important developmental events. Our emphasis is on (1) establishing an overall conceptual framework within which the role of many distinct cellular interactions and molecular factors can be evaluated, and (2) generating computer simulations that systematically test the adequacy of different models in accounting for a wide range of biological data. Our analysis indicates that several relatively simple mechanisms are each capable of explaining a variety of experimental observations. On the other hand, no one mechanism can account for the full spectrum of experimental results. Thus, it is important to consider models that are based on interactions among multiple mechanisms. A potentially powerful combination is one based on (1) a scaffold within the basal lamina or in the postsynaptic membrane which is induced by nerve terminals and which serves to stabilize terminals by a positive feedback mechanism; (2) a sprouting factor whose release by muscle fibers is down-regulated by activity and perhaps other factors; and (3) an intrinsic tendency of motor neurons to withdraw some connections while allowing others to grow.