Experimental Brain Research

, Volume 8, Issue 3, pp 269–283 | Cite as

Dendritic spines in the visual cortex of the mouse: Introduction to a mathematical model

  • F. Valverde
  • A. Ruiz-Marcos


The spines of apical dendrites of the layer V pyramidal cells of the area striata in the mouse represent a sequence of post-synaptic structures receiving a variety of contacts from terminal fibers derived fundamentally from short axon cells and superficial pyramidal cells. The study of Golgi preparations of mice 180 days old shows the existence of the most complicated terminal structures over portions of apical dendrites at the levels of layers III and IV. Observations on young mice reveals the terminations of the specific afferent fibers on the dendrites of short axon cells. A mathematical model which defines the distribution of spines along the apical dendrites is introduced. The principal equation of the model has been adjusted from the data processing of microscope countings through a series of programs written for an IBM 7070. The equation defines satisfactorily the different distributions of dendritic spines in mice 10–180 days old raised in normal conditions and in complete darkness. The equation defines also the distribution of dendritic spines in the visual cortex of mice enucleated at birth on one side, and the distribution along the apical dendrites of various cortical areas of the hamster, cat and man. The number of dendritic spines increases with the age of the subject and their distribution varies significantly according to the values of the parameters of the model.

Key words

Visual cortex Dendritic spines Specific afferents Model of spine distribution 


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  1. Cajal, S.R.: Sur la structure de l'écorce cérébrale de quelques mammifères. Cellule 7, 1–54 (1891).Google Scholar
  2. —: Les preuves objectives de l'unité anatomique des cellules nerveuses. Trav. Lab. Rech. Biol., Univ. Madrid 29, 1–137 (1934).Google Scholar
  3. —: Histologie du système nerveux de l'homme et des vertébrés. Vol. II. Paris: A. Maloine 1911. Reimpress. Madrid: Instituto Cajal 1955.Google Scholar
  4. Chang, H.-T.: Cortical neurons with particular reference to the apical dendrites. Cold Spr. Harb. Symp. quant, Biol. 17, 189–202 (1952).Google Scholar
  5. Colonnier, M.: The structural design of the neocortex. In: Study week on brain and conscious experience, pp. 1–23. Ed. by J.C. Eccles. Berlin-Heidelberg-New York: Springer 1966.Google Scholar
  6. —: Synaptic patterns on different cell types in the different laminae of the cat visual cortex. An electron microscope study. Brain Res. 9, 268–287 (1968).Google Scholar
  7. Conel, J.L.: The postnatal development of the human cerebral cortex. Vol. 3. The cortex of the three-month infant. Cambridge/Mass.: Harvard University Press 1947.Google Scholar
  8. —: The postnatal development of the human cerebral cortex. Vol.4. The cortex of the six-month infant. Cambridge/Mass.: Harvard University Press 1951.Google Scholar
  9. Fox, C.A., and J.W. Barnard: A quantitative study of Purkinje cell dendritic branchlets and their relationship to efferent fibers. J. Anat. (Lond.) 91, 299–313 (1957).Google Scholar
  10. Globus, A., and A.B. Scheibel: Synaptic loci on parietal cortical neurons: terminations of corpus callosum fibers. Science 156, 1127–1129 (1967a).Google Scholar
  11. —: Synaptic loci on visual cortical neurons of the rabbit: the specific afferent radiation. Exp. Neurol. 18, 116–131 (1967b).Google Scholar
  12. Gray, E.G.: Electron microscopy of synaptic contacts on dendrite spines of the cerebral cortex. Nature (Lond.) 183, 1592–1593 (1959a).Google Scholar
  13. —: Axo-somatic and axo-dendritic synapses of the cerebral cortex. An electron microscope study. J. Anat. (Lond.) 93, 420–433 (1959b).Google Scholar
  14. —, and R.W. Guillery: A note on the dendritic spine apparatus. J. Anat. (Lond.) 97, 389–392 (1963).Google Scholar
  15. Hamlyn, L.H.: Electron microscopy of mossy fibre endings in Ammon's horn. Nature (Lond.) 190, 645–646 (1961).Google Scholar
  16. —: An electron microscope study of pyramidal neurons in the Ammon's horn of the rabbit. J. Anat. (Lond.) 97, 189–201 (1963).Google Scholar
  17. Hámori, J., and J. Szentagothai: The “crossing over” synapse. An electron microscope study of the molecular layer in the cerebellar cortex. Acta Biol. Hung. 15, 95–117 (1964).Google Scholar
  18. Lison, L.: Les méthodes de reconstruction graphique en technique microscopique. In: A. Policard, eds Actualités Scientifiques et Industrielles, 553, VI, Histophysiologie, pp. 28–44. Paris: Herman et Cie. 1937.Google Scholar
  19. Lorente de Nó, R.: La corteza cerebral del ratón (Primera contributión. — La corteza acústica). Trab. Lab. Invest. Biol., Univ. Madrid 20, 41–78 (1922).Google Scholar
  20. —: Cerebral cortex: architecture, intracortical connections, motor projections. In: Fulton's Physiology of the Nervous System, pp. 288–330. London: Oxford University Press 1949.Google Scholar
  21. Marin-Padilla, M.: Number and distribution of the apical dendritic spines of the layer V pyramidal cells in man. J. comp. Neurol. 131, 475–489 (1967).Google Scholar
  22. —: Cortical axo-spinodendritic synapses in man. A Golgi study. Brain Res. 8, 196–200 (1968).Google Scholar
  23. —, and G. R. Stibitz: Distribution of the apical dendritic spines of the layer V pyramidal cells of the hamster neocortex. Brain Res. 11, 580–592 (1968).Google Scholar
  24. O'Leary, J.L.: Structure of the area striata of the cat. J. comp. Neurol. 75, 131–164 (1941).Google Scholar
  25. —, and G.H. Bishop: The optically excitable cortex of the rabbit. J. comp. Neurol. 68, 423–478 (1938).Google Scholar
  26. Palay, S.L.: The structural basis for neural action. In: Brain Function, vol. 2, pp. 69–108. Ed. by M.A.B. Brazier. Berkeley and Los Angeles: University of California Press 1964.Google Scholar
  27. Pappas, G.D., and D.P. Purpura: Fine structure of dendrites in the superficial neocortical neuropil. Exp. Neurol. 4, 507–530 (1961).Google Scholar
  28. Polyak, S.: The vertebrate visual system. Ed. by H. Klüver. Chicago: University of Chicago Press 1957.Google Scholar
  29. Scheibel, M.E., and A.B. Scheibel: On the nature of dendritic spines. Report of a workshop. Comm. behav. Biol., A 1, 231–265 (1968).Google Scholar
  30. Shkolnik-Yarros, E.G.: Neurons and interneuronal connections. The visual analyzer. Leningrad: Academy of Medical Sciences, USSR 1965 (Russian edition).Google Scholar
  31. Valverde, F.: Studies on the piriform lobe. Cambridge: Harvard University Press 1965.Google Scholar
  32. —: Apical dendritic spines of the visual cortex and light deprivation in the mouse. Exp. Brain Res. 3, 337–352 (1967).Google Scholar
  33. —: Structural changes in the area striata of the mouse after enucleation. Exp. Brain Res. 5, 274–292 (1968).Google Scholar
  34. —, and M.E. Esteban: Peristriate cortex of mouse: location and the effects of enucleation on the number of dendritic spines. Brain Res. 9, 145–148 (1968).Google Scholar
  35. —, and A. Ruiz-Marcos: Light deprivation and the spines of apical dendrites in the visual cortex of the mouse. Anat. Rec. (Abstr.) 157, 392 (1967).Google Scholar
  36. Whittaker, V.P., and E.G. Gray: The synapse: biology and morphology. Brit. med. Bull 18, 223–228 (1962).Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • F. Valverde
    • 1
  • A. Ruiz-Marcos
    • 1
  1. 1.Secoión de Neuroanatomía Comparada and Departamento de BiofísicaInstitute CajalMadridSpain

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