Abstract
A mathematical model for the formation and maintenance of synaptic contacts at the motor endplate is proposed. It is based on diffusion between sarcoplasmic nuclei of limiting amounts of a morphogen substance. The morphogen is postulated to act on genetic switch-like intranuclear units and to regulate positively both the transcription of its own gene and that of acetylcholine receptor (AChR) subunit genes. The efficacy of autoregulation is assumed to be depressed by electrical activity; while AChR genes transcription is enhanced by anterograde neural factors. Thus the model involves Turing's classical ingredients: autocatalysis and short range activation by the morphogen, and long range inhibition by electrical activity. Our predictions include: the stabilization of a single, transcriptionally active nucleus located in the central region of the developing muscle fiber (or myotube); the frequent occurrence of transcriptional activity in nuclei at the tendinous ends; and the onset, upon denervation of adult muscle, of transcription waves, starting from both the central site and the tendinous nuclei. In noninnervated fibers, the calculations show that spontaneous, irregular electrical activity leads to a variety of near-periodic spatial patterns of transcription; these are also predicted in innervated fibers when the depressing effect of electrical activity is weak, giving rise to the stabilization of multiple endplates as occurs in muscles with distributed innervation.