Bistability and hysteresis of sodium channels at neuromuscular junction

All voluntary movements in mammals are accomplished by muscles which are controlled by the brain through a specialized synapse called neuromuscular junction (NMJ). To have full control over the movement disorders caused due to dysfunctions of neuromuscular junction (e.g., Myasthenia Gravis, Lambert-Eaton Myasthenic Syndrome) and for the engineering of rehabilitation neuroprosthetic devices, a clear knowledge about the neuromuscular junction transmission mechanism during the communication between the neuron and the muscle is essential. The NMJ is the place where the axon terminal of a motor neuron and the motor endplate of a muscle fiber meet creating a synapse. The pulse carried by the presynaptic neuron when reaches the synapse causes release of Acetylcholine (ACh) into the synaptic cleft which binds to the AChR at the motor end plate causing the sodium ions to flow in and potassium ions to flow out of the muscle's cytosol producing a local depolarization of the motor end plate called end-plate synaptic potential. The extracellular potential in the narrow extracellular space between nerve cell and muscle fiber (cleft) is affected by the current flow generated by the opening of sodium channels; consequently, voltage-dependent processes may be affected in the adjacent membranes. This phenomenon of current passing through weakly opened sodium channels and decreasing the potential of the extracellular space by boosting channels activation and by a positive feedback is termed “self-gating”. According to this hypothesis applied to NMJ, the extracellular voltage drop in the cleft may modify the voltages across the muscle fiber membrane, thus increasing the probability of opening the voltage-gated ion channels. In the last few decades some mathematical models of NMJ have been derived considering different aspects. But in the existing models the effect of voltage in the cleft is left unnoticed. The proposed model incorporates the voltage of the synaptic cleft and self-gating effect of the sodium channel at the NMJ to study for the NMJ properties of rat and frog. In modeling the NMJ a barrel shaped muscle is considered (50 µm diameter × 500 µm long). To form a synapse, an axon terminal is connected to the highly-excitable muscle fiber with a synaptic cleft (distance: 50 nm). The potential at the cleft (Vj) is calculated using the sodium conductance of the endplate motoneuron (global conductance) and the resistance of the cleft. The Acetylcholine Receptor current (AChR) together with the endplate sodium current (EPINa) act as stimulus current for the Hodgkin-Huxley based membrane potential (Vm) calculation at the muscle fiber. The conductance associated to the voltage-gated sodium channels depends on the voltage drop between the potentials of the junction and the membrane. The junction potential calculated for different membrane potentials shows that the voltage-dependent sodium conductance at the NMJ demonstrates self-gating behavior. This is mainly due to the drop of junction potential in the synaptic cleft caused by depolarization of the muscle membrane. We have studied the activation, inactivation, voltage and time dependency of recovery from inactivation of sodium channel and voltage and time dependent Hodgkin-Huxley model parameters under voltage clamp condition for both self-gating and non-self-gating states to check out the effect of junction potential drop in the muscle membrane. Some action potential generation based performance i.e., Overshoot, Maximum Rate of Rise have been evaluated. Implications for the firing frequency have been addressed. A Radius-Conductance factor has been proposed to get a clear idea about the relation among the size of the radius of the motorneuron, maximum sodium conductance and the AChR based stimulus current. The proposed transmission model considering the contribution of sodium channels at the muscle membrane infolds and extracellular voltages in the cleft detect the ability of neuromuscular transmission to remain effective under various physiological conditions and stresses (safety-factor) of the NMJ around 15%. During the self-gating condition a switching behavior was noticed in the sodium channels conductance: from low to high during depolarization and from high to low during repolarization of membrane potential. At this time bistability and hysteresis of sodium channels occurred which explains the transmission efficiency of the NMJ under self-gating condition. The remedies of several NMJ diseases (i. e., Myasthenia Gravis, Lembert-Eaton Myasthenic Syndrome) are also hampered by limited understanding of the transmission process at the NMJ. The proposed model explores the transmission mechanism at the NMJ and may be used to plan therapy for such diseases. However, more experimental validations have to be performed before implementing it at clinical level. Also, the model may contribute to the engineering of bio-inspired neuroprosthetic devices for rehabilitation and therapy in patients with motor impairments.