Transient synaptic redundancy in the developing cerebellum and isostatic random stacking of hard spheres

We propose an automaton for the simulation of the distribution of the number of climbing fibers (CF) making synapses on each Purkinje cell (PC) at the maximum of the synaptic redundancy that exists transiently in the newborn cerebellum. This automaton is based on the hypothesis that the synaptic maximum is limited by topological constraints and can be described by an isostatic random stacking of hard spheres. There is convincing agreement between the simulated distribution of the number of CF axons per Purkinje cell and the distribution experimentally obtained by electrophysiological techniques.

[1]  Growing tips of embryonic cerebellar axons in vivo , 1985, Journal of neuroscience research.

[2]  M. Bennett,et al.  The formation of synapses in striated muscle during development , 1974, The Journal of physiology.

[3]  Raoul Kopelman,et al.  Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm , 1976 .

[4]  J. Eccles,et al.  The excitatory synaptic action of climbing fibres on the Purkinje cells of the cerebellum , 1966, The Journal of physiology.

[5]  C. Sotelo,et al.  Postnatal development of the inferior olivary complex in the rat. II. Topographic organization of the immature olivocerebellar projection , 1984, The Journal of comparative neurology.

[6]  J. Mariani,et al.  Ontogenesis of olivocerebellar relationships. I. Studies by intracellular recordings of the multiple innervation of Purkinje cells by climbing fibers in the developing rat cerebellum , 1981, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[7]  J. Mariani,et al.  Ontogenesis of olivocerebellar relationships. II. Spontaneous activity of inferior olivary neurons and climbing fibermediated activity of cerebellar Purkinje cells in developing rats , 1981, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[8]  N. Lemkey-Johnston,et al.  Morphological characteristics of mouse stellate and basket cells and their neuroglial envelope: An electron microscopic study , 1968, The Journal of comparative neurology.

[9]  D. Purves,et al.  The elimination of redundant preganglionic innervation to hamster sympathetic ganglion cells in early post‐natal life. , 1980, The Journal of physiology.

[10]  N. Delhaye-bouchaud,et al.  Extent of multiple innervation of cerebellar Purkinje cells by climbing fibers in adult X-irradiated rats. Comparison of different schedules of irradiation during the first postnatal week. , 1990, Brain research. Developmental brain research.

[11]  C. Sotelo,et al.  Early Development of Olivocerebellar Projections in the Fetal Rat Using CGRP Immunocytochemistry , 1992, The European journal of neuroscience.

[12]  F. Crépel,et al.  Maturation of climbing fiber responses in the rat. , 1971, Brain research.

[13]  N. Delhaye-bouchaud,et al.  Enlargement of olivo-cerebellar microzones in the agranular cerebellum of adult rats , 1994, Brain Research.

[14]  J. Fawcett,et al.  Regressive events in neurogenesis. , 1984, Science.

[15]  D. Purves,et al.  Post‐natal reduction of neural unit size in the rabbit ciliary ganglion. , 1981, The Journal of physiology.

[16]  J. Lichtman.  The reorganization of synaptic connexions in the rat submandibular ganglion during post‐natal development. , 1977, The Journal of physiology.

[17]  K. Herrup,et al.  Role of the target in synapse elimination: studies in cerebellum of developing lurcher mutants and adult chimeric mice , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[18]  J. Mariani,et al.  Synapse Elimination in the Central Nervous System: Functional Significance and Cellular Mechanisms , 1996, Reviews in the neurosciences.

[19]  P. Redfern.  Neuromuscular transmission in new‐born rats , 1970, The Journal of physiology.

[20]  C. Sotelo,et al.  The 'creeper stage' in cerebellar climbing fiber synaptogenesis precedes the 'pericellular nest'--ultrastructural evidence with parvalbumin immunocytochemistry. , 1993, Brain research. Developmental brain research.

[21]  J. Mariani.  Elimination of synapses during the development of the central nervous system. , 1983, Progress in Brain Research.

[22]  J. Altman.  MORPHOLOGICAL DEVELOPMENT OF THE RAT CEREBELLUM AND SOME OF ITS MECHANISMS , 1982 .

[23]  S. Rabacchi,et al.  Involvement of the N-methyl D-aspartate (NMDA) receptor in synapse elimination during cerebellar development. , 1992, Science.

[24]  M. Dixmier,et al.  Une nouvelle description des empilements aléatoires et des fluides denses , 1978 .

[25]  Hisashi Yamamoto.  The Structure of Liquids , 1937, Nature.

[26]  N. Delhaye-bouchaud,et al.  Abnormal ipsilateral functional vibrissae projection onto Purkinje cells multiply innervated by climbing fibers in the rat. , 1995, Brain research. Developmental brain research.

[27]  F. Crépel,et al.  Evidence for a multiple innervation of Purkinje cells by climbing fibers in the immature rat cerebellum. , 1976, Journal of neurobiology.

[28]  F. Crépel,et al.  Fate of the multiple innervation of cerebellar Purkinje cells by climbing fibers in immature control, x-irradiated and hypothyroid rats. , 1981, Brain research.

[29]  A. Winfree,et al.  Postnatal development of the cerebellar cortex in the rat: V. Spatial organization of Purkinje cell perikarya , 1977, The Journal of comparative neurology.

[30]  M. Dennis,et al.  Development of neuromuscular junctions in rat embryos. , 1981, Developmental biology.

[31]  J. D. Bernal,et al.  The Bakerian Lecture, 1962 The structure of liquids , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.