Abstract
This study is concerned with synaptic reorganization in local neuronal networks. Within networks of 30 neurons, an initial disequilibrium in connectivity has to be compensated by reorganization of synapses. Such plasticity is not a genetically determined process, but depends on results of neuronal interaction. Neurobiological experiments have lead to a model of the behavior of individual neurons during neuroplastic reorganization, formalized as a “synaptogenetic rule” that governs changes in the amount of synaptic elements on each neuron. — When this synaptogenetic rule is applied to a system of neurons, there is some freedom left to the choice of further conditions. In this study it is examined, which assumptions additional to the synaptogenetic rule are essential in order to obtain morphogenetic stability. By explicating these assumptions, their plausibility can be tested. It is analysed, in which respect these conditions are important, in which part of the model they exert their influence, and what kind of instability and degeneration happens if the assumptions are violated. —Our essentials for reaching morphogenetic stability are: (1) A network structure that guarantees the possibility of oscillations, (2) a compensation algorithm that guarantees a smooth morphogenesis, (3) kinetic parameters that guarantee convergence in the synaptic elements' change, and (4) a synaptic modification rule that prohibits Hebb-like as well as anti-Hebb-like synaptic changes. — It is concluded that many structural features of the mammalian cerebral cortex are in accordance with the requirements of the model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aghajanian GK, Bloom FE (1967) The formation of synaptic junctions in developing rat brain: quantitative electron microscopic study. Brain Res 6:716–727
Amari SI (1977) A mathematical approach to neural systems. In: Metzler J (ed) Systems neuroscience. Academic Press, New York, pp 67–117
Bähr S, Wolff JR (1985) Postnatal development of axosomatic synapses in the rat visual cortex. Morphogenesis and quantitative evaluation. J Comp Neurol 233:405–420
Barlow WB (1975) Visual experience and cortical development. Nature 258:199–204
Blue ME, Parnavelas JG (1983) The formation and maturation of synapses in the visual cortex of the rat. I. Quantitative analysis. J Neurocytol 12:599–616
Crain SM, Bronstein MB, Peterson ER (1968) Maturation of cultured embryonic CNS tissues during chronic exposures to agents which prevent bioelectric activity. Brain Res 8:363–372
Dammasch IE (1986) Morphogenesis and properties of neuronal model networks. In: Trappl R (ed) Cybernetics and systems '86. Reidel, Dordrecht, pp 327–334
Dammasch IE (1987) Reactive synaptogenesis in small neuronal circuits: Simulations based on the compensation algorithm. In: Proceedings of the 1st Annual International Conference on Neural Networks, San Diego (in press)
Dammasch IE, Wagner GP (1984) On the properties of randomly connected McCulloch-Pitts networks: differences between input-constant and input-variant networks. Cybern Syst 15:91–117
Dammasch IE, Wagner GP, Wolff JR (1986) Self-stabilization of neuronal networks. I. The compensation algorithm for synaptogenesis. Biol Cybern 54:211–222
Easton P, Gordon PE (1984) Stabilization of Hebbian neural nets by inhibitory learning. Biol Cybern 51:1–9
Eins S, Wolff JR (1976) Analysis of heterogeneous composition of central nervous tissue. In: Underwood EE (ed) Proceedings of the 4th International Congress Stereology, Gaithersburg USA. National Bureau of Standards, Washington, pp 327–331
Erdi P, Barna G (1984) Self-organizing mechanism for the formation of ordered neural mappings. Biol Cybern 51:93–101
Flohr H (1983) Control of plastic processes. In: Basar E, Flohr H, Haken H, Mandell AJ (eds) Synergetics of the brain. Springer, Berlin Heidelberg New York, pp 6–74
Griffith JS (1971) Mathematical neurobiology. Academic Press, London New York
Hebb DO (1949) The organization of behavior: a neurophysiological theory. Wiley, New York
Hinds JW, Hinds PL (1976) Synapse formation in the mouse olfactory bulb II. Morphogenesis. J Comp Neurol 169:41–62
Innocenti GM (1981) Transitory structures as a substrate for developmental plasticity of the brain. In: van Hof MW, Mohn G (eds) Functional recovery from damage. Elsevier, New York, pp 307–333
Jacobson M (1978) Developmental neurobiology. Plenum Press, New York
Kety SS (1970) The biogenic amines in the central nervous system: Their possible role in arousal, emotion, and learning. In: Schmidt FO (ed) The neurosciences, second study program. Rockefeller University Press, New York, pp 324–336
Malsburg von der C (1987) Synaptic plasticity as basis of brain organization. In: Changeux JP, Konishi M (eds) The neural and molecular bases of learning. Wiley, New York, pp 411–432
Palm G (1982) Rules for synaptic changes and their relevance for storage of information in the brain. In: Trappl R (ed) Cybernetics and Systems Research. North Holland, Amsterdam, pp 277–280
Rauschecker JP, Singer W (1981) The effects of early visual experience on the cat's visual cortex and their possible explanation by Hebb synapses. J Physiol 310:215–239
Schwartzkroin PA (1982) Development of rabbit hippocampus: physiology. Dev Brain Res 2:469–486
Singer W (1980) Central gating of developmental plasticity in rat striate cortex. Verh Dtsch Zool Ges 73:268–274
Szentagothai J (1978a) Specificity versus (quasi-)randomness in cortical connectivity. In: Brazier MAB, Petsche H (eds) Architectonics of the cerebral cortex. Raven Press, New York, pp 77–97
Szentagothai J (1978b) The neuron network of the cerebral cortex: a functional interpretation. Proc R Soc London Ser B 201:219–248
Wagner GP, Wolff JR (1987) A kinetic model of synaptogenesis based on morphogenetic consequences of excitation and inhibition (submitted)
Wiesel TN (1982) Postnatal development of the visual cortex and the influence of environment. Nature 299:583–591
Winfield DA (1981) The postnatal development of synapses in the visual cortex of the cat and the effect of eyelid closure. Brain Res 206:166–171
Wolff JR (1976) Stereological analysis of the heterogeneous composition of central nervous tissue: Synapses of the cerebral cortex. In: Underwood EE (ed) Proceedings of the 4th International Congress of Stereology, Gaithersburg USA. National Bureau of Standards, Washington, pp 331–335
Wolff JR (1978) Ontogenetic aspects of cortical architecture: Lamination. In: Brazier MAB, Petsche H (eds) Architectonics of the cerebral cortex. Raven Press, New York
Wolff JR (1981) Some morphogenetic aspects of the development of the central nervous system. In: Immelmann K, Barlow GW, Main M, Petrinovich L (eds) Behavioral development. The Bielefeld Interdisciplinary Project. Cambridge University Press, New York, pp 164–190
Wolff JR, Chronwall BM (1982) Axosomatic synapses in the visual cortex of adult rat. A comparison between GABA-accumulating and other neurons. J Neurocytol 11:409–425
Wolff JR, Wagner GP (1983) Selforganization in synaptogenesis: Interaction between the formation of excitatory and inhibitory synapses. In: Basar E, Flohr H, Haken H, Mandell AJ (eds) Synergetics of the brain. Springer, Berlin Heidelberg New York, pp 50–59
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dammasch, I.E., Wagner, G.P. & Wolff, J.R. Self-stabilization of neuronal networks. Biol. Cybern. 58, 149–158 (1988). https://doi.org/10.1007/BF00364134
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00364134