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Local optimization of neuron arbors

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Abstract

How parsimoniously is brain wiring laid out, that is, how well does a neuron minimize costs of connections among its synapses? Neural optimization of dentritic and axonic arbors can be evaluated using a generalization of the Steiner tree concept from combinatorial network optimization theory. Local branch-junction geometry of neuronal connecting structures fits a volume minimization model well. In addition, volume of the arborizations at this neighborhood level is significantly more strongly minimized than their length, signal propagation speed, or surface area. The mechanism of this local volume optimization resembles those involved in formation of nonliving tree structures such as river junctions and electric-discharge patterns, and appears to govern initial nerve growth-cone behavior through vector-mechanical energy minimization.

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References

  • Banker G, Waxman A (1988) Hippocampal neurons generate natural shapes in cell culture. In: Lasek R, Black M (eds) Intrinsic determinants of neuronal form and function. Liss, New York

    Google Scholar 

  • Bern M, Graham R (1989) The shortest-network problem. Sci Am 260:84–89

    Google Scholar 

  • Berry M, Bradley P (1976) The growth of the dendritic trees of Purkinje cells in the cerebellum of the rat. Brain Res 112:1–35

    Google Scholar 

  • Bradley P, Berry M (1976) The effects of reduced climbing and parallel fibre input on Purkinje cell dendritic growth. Brain Res 109:133–151

    Google Scholar 

  • Bray D (1987) Growth cones: Do they pull or are they pushed? Trends Neurosci 10:431–434

    Google Scholar 

  • Cajal S, Ramon Y (1972) Histologie du systeme nerveux de l'homme et des vertebres, vols I & II. Consejo Superior de Investigaciones Cientificas, Madrid

    Google Scholar 

  • Cherniak C (1986) Minimal rationality. MIT Press, Cambridge, Mass

    Google Scholar 

  • Cherniak C (1988) Undebuggability and cognitive science. Commun Assoc Comput Machinery 31:402–412

    Google Scholar 

  • Cherniak C (1990) The bounded brain: Toward quantitative anatomy. J Cogn Neurosci 2:58–68

    Google Scholar 

  • Cherniak C (1991) Component placement optimization in the brain. University of Maryland Institute for Advanced Computer Study Technical Report 91–98

  • Cohen M (1970) A comparison of invertebrate and vertebrate central neurons. In: Schmitt F (eds) The neurosciences: second study program. MIT Press, Cambridge, Mass

    Google Scholar 

  • Collin S (1989) Topography and morphology of retinal ganglion cells in the coral trout Plectropomata leopardus (Serranidae): A retrograde cobaltous-lysine study. J Comp Neurol 281:143–158

    Google Scholar 

  • Courant R, Robbins H (1969) What is mathematics? Oxford University Press, New York

    Google Scholar 

  • Dann J, Buhl E, Peichl L (1988) Postnatal dendritic maturation of alpha and beta ganglion cells in cat retina. J Neurosci 8:1485–1499

    Google Scholar 

  • Fairen A, DeFelipe J, Regidor J (1984) Nonpyramidal neurons: General account. In: Peters A, Jones E (eds) Cerebral cortex, vol 1. Plenum Press, New York

    Google Scholar 

  • Garey M, Johnson D (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco

    Google Scholar 

  • Georgakopoulos G, Papadimitriou C (1987) The 1-Steiner tree problem. J Algorithms 8:122–130

    Google Scholar 

  • Hosokawa H, Mannen H (1963) Some aspects of the histology of neuroglia. In: Nakai J (eds) Morphology of neuroglia. Thomas, Springfield, Ill

    Google Scholar 

  • Kuhlenbeck H (1967) The central nervous sytem of vertebrates, vol 2. Academic Press, New York

    Google Scholar 

  • Lawler E, Lenstra J, Rinnooy Kan A, Shmoys D (eds) (1985) The travelling salesman problem. Wiley, New York

    Google Scholar 

  • Lorente de No R (1949) Cerebral cortex: architecture, intracortical connections, motor projections. In: Fulton J (eds) Physiology of the nervous system, 3rd edn. Oxford University Press, New York

    Google Scholar 

  • Murray C (1926) The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 9:835–841

    Google Scholar 

  • Murray C (1927) A relationship between circumference and weight in trees and its bearing on branching angles. J Gen Physiol 10:725–729

    Google Scholar 

  • Nevin R (1989) Morphological analysis of neurons in the cricket cereal system. Ph. D. dissertation. University of California, Berkeley

    Google Scholar 

  • Rall W (1959) Branching dendritic trees and motoneuron membrane resistivity. Exp Neurol 1:491–527

    Google Scholar 

  • Rodieck R (1973) The vertebrate retina. Freeman, San Francisco

    Google Scholar 

  • Roy A (1983) Optimal angular geometry models of river branching. Geograph Anal 15:87–96

    Google Scholar 

  • Sander L (1987) Fractal growth. Sci Am 256:94–100

    Google Scholar 

  • Shkol'nik-Yarros E (1971) Neurons and interneuronal connections of the central visual system. Plenum Press, New York

    Google Scholar 

  • Siegelman J, Ozanics V (1982) Retina. In: Jakobiec F (eds) Ocular anatomy, embryology, teratology. Harper and Row, Philadelphia

    Google Scholar 

  • Thompson D (1961) On growth and form. Cambridge University Press, New York

    Google Scholar 

  • Uylings H (1977) Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull Math Biol 39:509–520

    Google Scholar 

  • Uylings H, Smit G (1975) Three-dimensional branching structure of pyramidal cell dendrites. Brain Res 87:55–60

    Google Scholar 

  • Valverde F (1985) The organizing principles of the primary visual cortex in the monkey. In: Peters A, Jones E (eds) Cerebral cortex, vol 3. Plenum Press, New York

    Google Scholar 

  • White E (1981) Thalamocortical synaptic relations. In: Schmitt F, Worden F, Adelman G, Dennis S (eds) The organization of the cerebral cortex. MIT Press, Cambridge, Mass

    Google Scholar 

  • Winer J (1984a) The pyramidal neurons in layer III of cat primary auditory cortex. J Comp Neurol 229:476–496

    Google Scholar 

  • Winer J (1984b) The non-pyramidal cells in layer III of cat primary auditory cortex. J Comp Neurol 229:512–530

    Google Scholar 

  • Winer J, Morest D (1983) The neuronal architecture of the dorsal division of the medial geniculate body of the cat. J Comp Neurol 221:1–30

    Google Scholar 

  • Winer J, Morest D (1984) Axons of the dorsal diversion of the medial geniculate body of the cat. J Comp Neurol 224:344–370

    Google Scholar 

  • Woldenberg M, Horsfield K (1983) Finding the optimal lengths for three branches at a junction. J Theor Biol 104:301–318

    Google Scholar 

  • Zamir M (1976) Optimality principles in arterial branching. J Theor Biol 62:227–251

    Google Scholar 

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Cherniak, C. Local optimization of neuron arbors. Biol. Cybern. 66, 503–510 (1992). https://doi.org/10.1007/BF00204115

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  • DOI: https://doi.org/10.1007/BF00204115

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