Abstract
We designed four arborized neurons which are able to evaluate the exclusive-or (XOR) function from two inputs. The input neurons form exclusively excitatory synapses on a dendritic tree which is a patchwork of “passive” (ohmic) and “active” cable segments. The active segments are described by the Hodgkin-Huxley model. The dynamics of the neurons and their output are obtained by numerical integration of the cable equation. In neurons 1 and 2 the XOR function is based on the annihilation of colliding action potentials. In neuron No. 3 the design takes advantage of the refractory period of action potentials. In neuron No. 4 voltage inversion is used as it occurs for inactivated sodium conductance in the Hodgkin-Huxley model. In all cases the XOR function depends critically on an appropriate timing of the input signals and on delays of the voltage transients in different branches of the dendrite.
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References
Abeles M (1991) Corticonics, neural circuits of the cerebral cortex. Cambridge University Press, Cambridge
Bullock TH (1959) Neuron doctrine and electrophysiology, Science 129:997–1002
Claiborne BJ, Zador AM, Mainen ZF, Brown TH (1992) Computational models of hippocampal neurons. In: McKenna T, Davis J, Zornetzer SF (eds) Single neuron computation. Academic Press, Boston, pp 61–80
Dimitrova NA, Dimitrov GV (1991) Difference in excitability along geometrically inhomogeneous structures and occurrence of hot spots. Biol Cybern 66:185–189
Fromherz P, Vetter T (1992) Cable properties of arborized Retzius cells of the leech in culture as probed by a voltage-sensitive dye. Proc Natl Acad Sci USA 89:2041–2045
Hertz JH, Krogh A, Palmer RG (1991) Introduction to the theory of neural computation. Addison-Wesley, Redwood City, Calif
Hille B (1992) Ionic channels of excitable membranes, 2nd edn. Sinauer, Sunderland, Mass
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:500–544
Hounsgaard J, Midtgaard J (1989) Dendrite processing in more ways than one. Trends Neurosci 12:313–315
Jack JJB, Noble D, Tsien RW (1985) Electrical current flow in excitable, cells. Oxford University Press, Oxford
Kandel ER, Schwartz JH (1985) Principles of neural science, 2nd ed. Elsevier, New York
Koch C, Poggio T, Torre V (1982) Retinal ganglion cells: a functional interpretation of dendritic morphology. Philos Trans R Soc Lond [Biol.] 298:227–264
Llinas R, Sugimori M (1980) Electrophysiological properties of in vitro Purkinje cell dendrites in mammalian cerebellar slices. J Physiol (Lond) 305:197–213
Manor Y, Ganczarowski J, Segev O (1991) Propagation of action potentials along complex axonal trees. Biophys J 60:1411–1423
Mascagni MV (1989) Numerical methods for neuronal modeling. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge, Mass, pp 439–484
McCulloch WS, Pitts W (1943) A logical calculus of ideas immanent in nervous activity. Bull Math Biophys 5:115–133
Menzel R, Hammer M, Mauelshagen J (1990) Memory stages in the honey bee. In: Elsner N, Roth G (eds) Proc 18th Göttingen Neurobiology Conference. Thieme, Stuttgart, pp 111–119
Perkel DH, Perkel DJ (1985) Dendritic spines: role of active membrane in modulating synaptic efficiency. Brain Res 325:331–335
Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipes. Cambridge University Press, Cambridge
Rall W (1962) Theory of physiological properties of dendrites. Ann N Y Acad Sci 96:1071–1092
Rall W (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic inputs. J Neurophysiol 20:1138–1168
Ramon y Cajal S (1909) Histologie du systeme nerveux de l'homme et des vertebres. Maloine, Paris
Segev I, Fleshman JW, Burke RE (1989) Compartmental models of complex neurons. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge, Mass, pp 63–133
Shepherd GM, Brayton RK, Miller JP, Segev I, Rinzel J, Rall W (1985) Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines. Proc Natl Acad Sci USA 82:2192–2195
Traub RD, Wong RKS (1983) Synchronized burse discharge in the disinhibited hippocampal slice. II. Model of the cellular mechanism. J Neurophysiol 49:459–471
Wong RKS, Prince DA, Basbaum AI (1979) Intradendritic recording from hippocampal neurons. Proc Natl Acad Sci USA 76:986–990
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Fromherz, P., Gaede, V. Exclusive-OR function of single arborized neuron. Biol. Cybern. 69, 337–344 (1993). https://doi.org/10.1007/BF00203130
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DOI: https://doi.org/10.1007/BF00203130