Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

The reaction-diffusion system of the neuromuscular junction has been modeled in 3D using the finite element package FEtk. The numerical solution of the dynamics of acetylcholine with the detailed reaction processes of acetylcholinesterases and nicotinic acetylcholine receptors has been discussed with the reaction-determined boundary conditions. The simulation results describe the detailed acetylcholine hydrolysis process, and reveal the time-dependent interconversion of the closed and open states of the acetylcholine receptors as well as the percentages of unliganded/monoliganded/diliganded states during the neuro-transmission. The finite element method has demonstrated its flexibility and robustness in modeling large biological systems.     

Spatial distribution of acetylcholine receptors at developing chick neuromuscular junctions

Brain Cell Biology - The development of high-density clusters of acetylcholine receptors (AChRs) and the relationship of these clusters to nerve contacts on embryonic chick wing muscle fibres has...     

Regulation of turnover and number of acetylcholine receptors at neuromuscular junctions

The number and metabolic stability of acetylcholine receptors (AChRs) at neuromuscular junctions of rat tibialis anterior (TA) and soleus (SOL) muscles were examined after denervation, paralysis by continuous application of tetrodotoxin to the nerve, or denervation and direct stimulation of the muscle through implanted electrodes. After 18 days of denervation AChR half-life declined from about 10 days to 2.3 days (TA) or 3.6 days (SOL) and after 18 days of nerve conduction block to 3.1 days (TA). In contrast, the total number of AChRs per endplate was unaffected by these treatments. Denervation for 33 days had no further effect on AChR half-life but reduced the total number of AChRs to about 54% (SOL) or 38% (TA) of normal. Direct stimulation of the 33-day denervated SOL from day 18 restored normal AChR stability and counteracted muscle atrophy but had no effect on the decline in AChR number. The results indicate that motoneurons control the stability of junctional AChRs through evoked muscle activity and the number of junctional AChRs through trophic factors.     

Degradation rate of acetylcholine receptors inserted into denervated vertebrate neuromuscular junctions

Many studies exist on the effect of denervation on the degradation of acetylcholine receptors (AChRs) at the vertebrate neuromuscular junction (nmj). These studies have described the behavior of either the total population of junctional receptors at different times after denervation, or of the receptors present at the time of denervation (referred to as original receptors). No experimental studies yet exist on the degradation rate of the receptors newly inserted into denervated junctions. In the previous studies, the original receptors of mouse sternomastoid muscles were found to retain the slow degradation (t 1/2) of approximately 8-10 d of innervated junctional receptors for up to 10 d after denervation before accelerating to a t 1/2 of approximately 3 d. The total junctional receptors, on the other hand, showed a progressive increase in degradation rate from a t 1/2 of 8-10 d to a t 1/2 of 1 d. To reconcile these earlier observations, the present study examines the degradation of new receptors inserted into the nmj after denervation. To avoid possible contamination of the data with postdenervation extrajunctional receptors, we used transmission electron microscope autoradiography to study only receptors located at the postjunctional fold of the nmj. We established that the new receptors inserted into denervated junctions have a t 1/2 of approximately 1 d, considerably faster than that of the original receptors and equivalent to that of postdenervation extrajunctional receptors. Both original and new receptors are interspersed at the top of the junctional folds. Thus, until all the original receptors are degraded, the postjunctional membrane contains two populations of AChRs that maintain a total steady-state site density but degrade at different rates. The progressive increase in turnover rate of total AChRs therefore reflects the combined rates of the original and new receptors, as earlier postulated by Levitt and Salpeter (1981).     

Facilitation of spontaneous acetylcholine release induced by activation of cAMP in rat neuromuscular junctions

Regulation of neurotransmitter release is thought to involve modulation of the release probability by protein phosphorylation. Activation of the cAMP-protein kinase A (PKA) pathway has been shown to facilitate synaptic transmission in mammalian neuromuscular synapses, although the relevant phosphorylation targets are mostly unknown. We found that the inhibitor of the phosphodiesterase aminophylline (1 mM AMIN), the membrane-permeable analog of cAMP, 8-Br-cAMP (5 mM) and, the direct adenylate cyclase activator, forskolin (20 microM), induced an increase of miniature end-plate potentials (MEPPs) frequency in rat neuromuscular junctions. We investigated the possible involvement of the voltage-dependent calcium channels (VDCC), since these proteins are known to be phosphorylated by PKA. But this possibility was ruled out, since the increase in MEPPs frequency was not attenuated by the VDCC blocker Cd2+ (100 microM) and it was observed when AMIN was studied on hyperosmotic response, which is independent of [Ca2+]o and of Ca2+ influx through the VDCC. The lack of action of AMIN on MEPPs frequency when [Ca2+]i was diminished by exposing the preparations to zero Ca2+-EGTA solution (isotonic condition) or when nerve terminals were loaded with a permeant Ca2+ chelator (BAPTA-AM) (hypertonic condition), indicate that cAMP-mediated presynaptic facilitation is a function of nerve terminal Ca2+ concentration. We also found that AMIN exerted a comparable increase in MEPPs frequency in control and high K+ (10 and 15 mM), suggesting a single mechanism of action for spontaneous and K+-induced secretion.     

Influence of neostigmine treatment on embryonic development of acetylcholine receptors and neuromuscular junctions

The postulated role of the acetylcholine receptor in the formation of neuromuscular synapses during the course of embryonic development was investigated in the superior oblique muscle of white Peking duck embryos. The possibility that the number of receptors could be experimentally lowered by chronic injections of the anticholinesterase agent, neostigmine methylsulfate, was determined using 125I-alpha- bungarotoxin. The total number of acetylcholine receptors on incubation day 12, 2 d subsequent to the onset of treatment, was reducted 45% as compared to saline-treated controls. A similar reduction in total receptor content (49%) was also observed on day 19. Radioautographic preparations showed that clusters of acetylcholine receptors were rare and that the grain density of extrajunctional receptors was also reduced. Hence, chronic treatment with neostigimine during development was observed to exert an effect on both the number and distribution of receptors in the developing superior oblique muscle. These changes occurred in the absence of any apparent effect on muscle differentiation in general. Myoblasts and myotubes were present on day 14 and further differentiated into myofibers by day 18 in both neostigmine and saline-treated muscles. The cytology of the develop;ing muscle cells also appeared normal. This is in contradistinction to the striking morphological changes that take place in adult mammalian and avian muscle after anticholinesterase treatment. More significantly, the decreased total receptor content and sparsity of clusters had no apparent effect on the formation of developing neuromuscular junctions at the electron microscopic level. The frequency of neuromuscular junctions in neostigmine-treated muscles was similar to that of the controls. It is concluded that acetylcholine receptor clusters are not required for the events leading to the morphological formation of neuromuscular junctions during in vivo development.     

The clustering of acetylcholine receptors and formation of neuromuscular junctions in regenerating mammalian muscle grafts

The present investigation was undertaken to study the relationship between acetylcholine receptor (AchR) clustering and endplate formation within regenerating skeletal muscle grafts. Silver staining of nerves was combined with rhodamine-alpha-bungarotoxin labeling of AchR clusters in heterotopic grafts of the rat soleus muscle. Two major graft procedures were used: whole muscle grafts and grafts which lacked the zone of original motor endplates (MEP-less grafts). These categories were subdivided into standard grafts, where subsequent innervation was allowed, and noninnervated grafts, which were experimentally deprived of innervation. Grafting brought about the death and removal of muscle fibers, followed by regeneration of myotubes within surviving basal lamina sheaths. A transient population of small extra-junctional AchR clusters spontaneously appears shortly after myotube formation in all four muscle graft types. Early myotubes of whole muscle grafts (both innervated and standard grafts, prior to the time of innervation) also develop presumptive secondary synaptic clefts and large, organized aggregations of AchRs at original synaptic sites. At later times, nerves regenerating into standard whole muscle and MEP-less grafts lead to the formation of numerous ectopic endplates. In whole muscle grafts, endplates may also form at original synaptic sites. Functional graft innervation is achieved in whole muscle and MEP-less grafts as early as 20 days postgrafting. The results of this study support the existence of still-unknown factors associated with the original synaptic site which can direct postsynaptic differentiation independent of innervation. They also demonstrate that functional endplates may form in mammalian muscle grafts at both original synaptic sites and ectopic locations, thus indicating that the zone of original synaptic sites is not necessary for the establishment of numerous functional and morphologically well-differentiated endplates.     

Simulation of the diffusion of acetylcholine in the neuroeffector junctions of the sinus node

Traditionally, the diffusion of acetylcholine (ACh) from a neuron to cardiac muscle in a neuroeffector junction has been modeled as radial diffusion from a nerve ending into a spherical homogeneous medium. Various microscopic structures in the heart may or may not influence the spatial distribution of ACh within neuroeffector junctions. To determine the effect of microscopic anatomy on the diffusion of ACh in neuroeffector junctions, we simulated the diffusion of ACh in a two-dimensional inhomogeneous geometry that was based on micrographs of neuroeffector junctions in the sinus node. ACh was released at sites adjacent to a neuron. Simulations showed that the times of peak concentration after release and the peak concentrations per se were distributed symmetrically above and below and to the right and left of the neuron, but not radially about the neuron. We conclude that the diffusion of ACh in the neuroeffector junctions of the sinus node cannot be predicted well by a mathematical model that assumes radial diffusion in a spherical and homogeneous medium.     

Finite element simulations of a hip joint with femoroacetabular impingement

In this study, a three-dimensional finite element (FE) model based on the specific anatomy of a patient presenting a femoroacetabular impingement of the ‘cam’-type is developed. The FE meshes of the structures of interest are obtained from arthrographic magnetic resonance images. All soft tissues are considered linear elastic and isotropic, and the bones were assumed rigid. A compression of the femur on the acetabular cavity as well as flexural movements and internal rotations are applied. Stresses and contact pressures are evaluated in this patient-specific model in order to better interpret the mechanism of aggression of the femoral and acetabular cartilages. The corresponding results are presented and discussed. The values obtained for the contact pressures are similar to those reported by other models based on idealised geometries. An FE analysis of a non-cam hip is also performed for comparison with the pathological case.     

Agrin released by motor neurons induces the aggregation of acetylcholine receptors at neuromuscular junctions.

To test the hypothesis that agrin mediates motor neuron-induced aggregation of acetylcholine receptors (AChRs) in skeletal muscle fibers and to determine whether the agrin active in this process is released by motor neurons, we raised polyclonal antibodies to purified ray agrin that blocked its receptor aggregating activity. When the antibodies were applied to chick motor neuron--chick myotube cocultures, they inhibited the formation of AChR aggregates at and near neuromuscular contacts, demonstrating that agrin plays a role in the induction of the aggregates. Rat motor neurons, like chick motor neurons, induce AChR aggregates on chick myotubes. This effect was not inhibited by our antibodies, indicating that, although the antibodies inhibited the activity of chick agrin, they did not have a similar effect on rat agrin. We conclude that agrin released by rat motor neurons induced the chick myotubes to aggregate AChRs.     

Histochemistry of acetylcholine receptors and acetylcholinesterase during the formation of neuromuscular junctions in the urodele Hynobius nigrescens

The development and structure of neuromuscular junctions (n-m-js) in stylopodia of forelimbs of larvae and adults of Hynobius nigrescens were histochemically investigated for acetylcholine receptors (AChRs) and acetylcholinesterase (AChE) activity. In larvae, the tetramethyl rhodamine-labelled α-bungarotoxin (TMR-αBT) positive areas appeared either as small fluorescent spots or fluorescent plates of various sizes. The mature fluorescent plate was found to be formed by the successive addition of spots, and the plates thus established were arranged linearly parallel to the axes of muscle fibers. AChE activity occurred almost exactly at TMR-αBT-positive sites. In adults, plate assemblies were often seen as a single dotted line (type A form) for both AChR binding and AChE reaction, in contrast to larval n-m-js in which AChE activity appeared as a continuous line. By applying the TMR-αBT method, two other forms of adult n-m-js were observed: type B, a long dotted line several plates wide; and type C, with a cluster of plates randomly dispersed over the whole width of the muscle fiber. It seems that protoforms of the latter two forms of n-m-js appear in the muscles just before and after metamorphosis.     

Agrin and acetylcholine receptors are removed from abandoned synaptic sites at reinnervated frog neuromuscular junctions

Changes in the distribution of agrin and acetylcholine receptors (AChRs) were examined during reinnervation and following permanent denervation as a means of understanding mechanisms controlling the distribution of these molecules. Following nerve damage in the peripheral nervous system, regenerating nerve terminals preferentially return to previous synaptic sites leading to the restoration of synaptic activity. However, not all portions of original synaptic sites are reoccupied: Some of the synaptic sites are abandoned by both the nerve terminal and the Schwann cell. Abandoned synaptic sites contain agrin, AChRs, and acetylcholinesterase (AChE) without an overlying nerve terminal or Schwann cell providing a unique location to observe changes in the distribution of these synapse-specific molecules. The distribution of anti-agrin and AChR staining at abandoned synaptic sites was altered during the process of reinnervation, changing from a dense, wide distribution to a punctate, pale pattern, and finally becoming entirely absent. Agrin and AChRs were removed from abandoned synaptic sites in reinnervated frog neuromuscular junctions, while in contralateral muscles which were permanently denervated, anti-agrin and AChR staining remained at abandoned synaptic sites. Decreasing synaptic activity during reinnervation delayed the removal of agrin and AChRs from abandoned synaptic sites. Altogether, these results support the hypothesis that synaptic activity controls a cellular mechanism that directs the removal of agrin from synaptic basal lamina and the loss of agrin leads to the dispersal of AChRs. © 1997 John Wiley & Sons, Inc. J Neurobiol 33: 999–1018, 1997     

Trace postsynaptic reactions in neuromuscular junctions

Factors which control the duration of postsynaptic responses in neuromuscular junctions are discussed together with a possibility of origin of trace postsynaptic reactions (potentiation and desensitization). In experiments on nerve-muscle preparations of various vertebrates (lamprey, frog, chicken, rat), the key role of functional activity of acetylcholinesterase was revealed in regulation of the duration of both short- and long-living postsynaptic responses. The significance of sufficient activity of acetylcholinesterase for normal realization of neuromuscular transmission presumably increases in the course of evolution of vertebrates. An analysis of possible molecular nature of trace reactions on the postsynaptic membrane was carried out.     

Brain extract causes acetylcholine receptor redistribution which mimics some early events at developing neuromuscular junctions

We studied the effect of rat brain extract on rat muscle cells in vitro by light and electron microscope (EM) autoradiography after labeling acetylcholine receptors (AChR's) with 125I-alpha-bungarotoxin. We found that: (a) In the absence of brain extract, peak site densities within AChR clusters usually do not exceed 4,000 sites/micrometer2. (b) Within hours after exposure to brain extract, AChR's redistribute to form clusters in which the peak site densities are greater than 10,000 sites/micrometer2. Receptor concentration within extract-induced clusters is thus within a factor of 2 of that at the neuromuscular junction (nmj). (c) In the absence of extract, the AChR's and AChR clusters are predominantly on the bottom surface of the myotubes (facing the tissue culture dish). After extract treatment, they are predominantly at the top surface. (d) Plasma membrane in regions of high-density AChR clusters is enriched in membrane with enhanced electron density and surface basal lamina whether or not cells are treated with extract. Extract causes an increase in both these specializations on the top surface of the myotubes. (e) Brain extract does not produce an overall increase in AChR site density or a marked change in degradation rate of receptors in either clustered or nonclustered regions. By producing AChR clusters with junctional site densities and enhanced surface specialization, and by causing an overall shift in AChR's distribution, brain extract mimics early events reported at developing neuromuscular junctions.     

Development of neuromuscular junctions in rat embryos

Physiological properties of nerve-muscle junctions were studied in intercostal muscles of rat embryos of 13 to 21 days gestation and in neonates. Nerve bundles grew into the muscle region by Day 13 of gestation. Myotubes began to appear on Days 13–14. Myotubes were electrically coupled before birth, allowing the spread of depolarization laterally between fibers. The strength of coupling declined with embryonic age and disappeared after birth. At early times, some fibers of adjacent segments were also coupled, end to end. Resting potentials of myotubes were high (70–90mV) from the time of their appearance. Miniature end-plate potentials were recorded in some myotubes on Day 14 of gestation. At that time also, nerve stimulation could evoke an end-plate potential which was capable of triggering muscle contraction. The mean quantal content of transmitter released from individual terminals was small compared to that in adult muscle; it remained small through the first postnatal week. Individual myofibers had a single end-plate site near their center, which could receive as many as six distinct synaptic inputs. The number of inputs per fiber reached a peak at Day 17 of gestation, and then began to decline before birth, reaching its adult value of one input per fiber within the second postnatal week. The internal intercostal muscles contained about 30 motor units, each confined to a small zone in the muscle. The region occupied by a single motor unit was not obviously reduced in size as the number of synaptic inputs per fiber declined. At Day 17 of gestation 40% of the muscles contained one or more aberrant motor units, the parent axons of which projected out through the ventral roots of adjacent segments. Elimination of these units commenced at the same time as did the reduction in number of synaptic inputs to single myofibers, and 70% of the aberrant units were eliminated before birth.     

Facilitation at crayfish neuromuscular junctions

Electrophysical recordings from opener muscle fibers in the crayfishProcambarus clarkii (Fig. 1) show that pre-synaptic facilitation at terminals of the single excitatory axon usually decays in a dual-exponential fashion after a single pulse or after a train of pulses (Figs. 2, 3, 7, 9), as has been reported for frog neuromuscular junctions (Mallart and Martin, 1967) and squid giant synapses (Charlton and Bittner, 1974, 1976). Furthermore, the second component of decay at crayfish synapses is associated with a break in the monotonic decay of the first component, a result which suggests that the decay of facilitation is not due to the simple diffusion of some substance (such as calcium) from specialized release sites.The growth of facilitation at all opener synapses during trains of equalinterval stimuli could not be predicted by assuming that each pulse contributed an equal amount of facilitation which summed linearly with that remaining from all previous stimuli (Figs. 4, 6; Table 2), as reported for synapses in frog and squid. During high frequency stimulation (>40 Hz), those terminals which facilitate dramatically (highF _e synapses) show much greater amounts of facilitation than that predicted by the linear summation model (Figs. 4, 8), whereas other terminals (lowF _e synapses) show much less facilitation than predicted (Fig. 6). The rate of growth of facilitation was often very constant at various stimulus rates in highF _e or mixed type synapses (Figs. 4, 8, 10)-a result not predicted by the linear summation model. Finally, when highF _e synapses were stimulated at different frequencies, the rate of growth of facilitation changed dramatically in a fashion not predictable using linear summation (Mallert and Martin, 1967) or power law (Linder, 1974) models.     

Finite element modelling and simulations in dentistry: a bibliography 1990-2003

The paper gives a bibliographical review of the finite element modelling and simulations in dentistry from the theoretical as well as practical points of view. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1990 and 2003. At the end of this paper, more than 700 references are given dealing with subjects such as: dental materials; oral and maxillofacial mechanics and surgery; orthodontics, tooth movement, orthodontic appliances; root canals, filling and therapy; dental restorations and other topics.