An equivalent cable model for neuronal trees with active membrane

Biological Cybernetics

Volumn 78, Issue 3, 1998, Pages 227-243

  Ohme, M ^a   Schierwagen, A ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Active membrane; Dendritic information processing; Dendritic profile; Non uniform equivalent cable; Reduced neuron model

Indexed keywords

ION CHANNEL;

ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; COMPUTER SIMULATION; CYBERNETICS; DENDRITE; METABOLISM; NERVE CELL; ULTRASTRUCTURE;

COMPUTER SIMULATION; CYBERNETICS; DENDRITES; ION CHANNELS; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NEURONS;

EID: 0032018258     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004220050429     Document Type: Article

References (33)

1. Agmon-Snir H, Segev I (1993) Signal delay and input synchronization in passive dendritic structures. J Neurophysiol 70:2066-2085
2. Bunow B, Segev I, Fleshman JW (1985) Modeling the electrical behavior of anatomically complex neurons using a network analysis program: excitable membrane. Biol Cybern 53:41-56
3. Bush PC, Sejnowski TJ (1993) Reduced compartment models of neocortical pyramidal cells. J Neurosci Methods 46:159-166
4. Clements JD, Redman SJ (1989) Cable properties of cat spinal motoneurones measured by combining voltage clamp, current clamp and intracellular staining. J Physiol (Lond) 409:63-87
5. FitzHugh R (1969) Mathematical models of excitation and propagation in nerve. In: Schwan HP (ed) Biological Engineering. McGraw-Hill, New York, pp 1-85
6. Fleshman JW, Segev I, Burke RB (1988) Electrotonic architecture of type-identified alpha-motoneurons in the cat spinal cord. J Neurophysiol 60:60-85
7. 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
8. Holmes WR, Rail W 1992) Estimating the electrotonic structure of neurons with compartmental models. J Neurophysiol 68:1438-1452
9. Jack JJB, Noble D, Tsien RW (1983) Electric current flow in excitable cells. Oxford University Press, Oxford
10. König P, Engel AK, Singer W (1996) Integrator or coincidence detector? The role of the cortical neuron revisited. Trends Neurosci 19:130-137
11. Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382:363-366
12. Mainen ZF, Joerges J, Huguenard JR, Sejnowski TJ (1995) A model of spike initiation in neocortical pyramidal neurons. Neuron 15:1427-1439
13. Mainen ZF, Carnevale NT, Zador AM, Claiborne BJ, Brown TH (1996) Electrotonic architecture of hippocampal cal pyramidal neurons based on three-dimensional reconstructions. J Neurophysiol, 76:1904-1923
14. Mel BW (1994) Information processing in dendritic trees. Neural Comput 6:1031-1085
15. Ohme M (1996) Modellierung der neuronalen Signalverarbeitung mittels kontinuierlicher Kabelmodelle. Dissertation, University of Leipzig, Department of Computer Science
16. Ohme M, Schierwagen AK (1993) Influence of geometry on velocity and frequency of action potential propagation in excitable neural fibres. In: Elsner N, Heisenberg M (eds) Gen - Gehirn -Verhalten: Proceedings of the 21th Göttingen neurobiology conference, Thieme, Stuttgart
17. Ohme M, Schierwagen AK (1994) Heterosynaptic inputs in dendritic trees. In: Elsner N, Heisenberg M (eds) Sensorische Transduktion: Proceedings of the 22th Göttingen neurobiology conference, Thieme, Stuttgart
18. Ohme M, Schierwagen AK (1996a) A method for analysing transients in dendritic trees with nonuniform segments. In: Trappl R (ed) Cybernetics and systems '96. Austrian Society for Cybernetic Studies, Vienna pp 542-547
19. Ohme M, Schierwagen AK (1996b) A reduced model for dendritic trees with active membrane. In: von der Malsburg C, von Seelen W, Vorbrüggen JC, Sendhoff B (eds) Artificial neural networks - ICANN 96. Springer, Berlin Heidelberg New York pp 691-696
20. Ohme M, Schierwagen AK (1997) Modelling dendritic trees with active membrane. In: ELsner N, Ẅssle H (eds) From membrane to mind: Proceedings of the 25th Göttingen neurobiology conference. Thieme, Stuttgart
21. Rail W (1962) Theory of physiological properties of dendrites. Ann N Y Acad Sci 96:1071-1092
22. Rapp M, Segev I, Yarom Y (1994) Physiology, morphology and detailed passive models of guinea-pig cerebellar Purkinje cells. J Physiol (Lond) 474:101-118
23. Rinzel J, Terman D (1982) Propagation phenomena in a bistable reaction-diffusion system. SIAM J Appl Math, 42:1111-1136
24. Schierwagen AK (1989) A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree. J Theor Biol 141:159-179
25. Schierwagen AK (1991) Travelling wave solutions of a simple nerve conduction equation for inhomogeneous axons. In: Holden AV, Markus M, Othmer H (eds) Nonlinear wave processes in excitable media, Manchester University Press, Manchester, pp 107-114
26. Schierwagen AK (1994) Exploring the computational capabilities of single neurons by continuous cable modelling. In: van Pelt J, Corner MA, Uylings HBM, Lopes da Silva FH (eds) The selforganizing brain - from growth cones to functional networks. (Progress in brain research, vol 102) Elsevier, Amsterdam, pp 151-167
27. Schierwagen AK, Grantyn R (1986) Quantitative morphological analysis of deep superior colliculus neurons stained intracellularly with HRP in the cat. J Hirnforsch 27:611-623
28. Segev I, Fleshman JW, Miller JP, Bunow B (1995) Modeling the electrical behavior of anatomically complex neurons using a network analysis program: passive membrane. Biol Cybern 53:27-40
29. Segev I (1995) Dendritic processing. In: Arbib MA (ed) The handbook of brain theory and neural networks, MIT Press, Cambridge, Mass, pp 282-289
30. Softky W (1994) Sub-millisecond coincidence detection in active dendritic trees. Neuroscience, 58:13-41
31. Stratford K, Mason A, Larkman A, Major G, Jack JJB (1989) The modelling of pyramidal neurons in the visual cortex. In: Durbin R, Miall C, Mitchison G (eds) The computing neuron, Addison-Wesley, London, pp 296-321
32. Stuart G, Spruston N, Sakmann B, Hausser M (1997) Action potential initiation and backpropagation in neurons of the mammalian CNS. Trends Neurosci 3:125-131
33. van Pelt J (1992) A simple vector implementation of the Laplace-transformed cable equations in passive dendritic trees. Biol Cybern 68:15-21