Computation in a single neuron: Hodgkin and Huxley revisited

Neural Computation

Volumn 15, Issue 8, 2003, Pages 1715-1749

  Agüera y Arcas, Blaise ^a   Fairhall, Adrienne L ^a,b   Bialek, William ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b NEC LABORATORIES AMERICA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; BIOLOGICAL MODEL; NERVE CELL; PHYSIOLOGY; REVIEW;

ACTION POTENTIALS; MODELS, NEUROLOGICAL; NEURONS;

EID: 0043180466     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/08997660360675017     Document Type: Review

References (52)

1. Abbott, L. F., & Kepler, T. (1990). Model neurons: From Hodgkin-Huxley to Hopfield. In L. Garrido (Ed.), Statistical mechanisms of neural networks (pp. 5-18). Berlin: Springer-Verlag.
2. Agüera y Arcas, B. (1998). Reducing the neuron: A computational approach. Unpublished master's thesis, Princeton University.
3. Agüera y Areas, B., Bialek, W., & Fairhall, A. L. (2001). What can a single neuron compute? In T. Leen, T. Dietterich, & V. Tresp (Eds.), Advances in neural information processing systems, 13 (pp. 75-81). Cambridge, MA: MIT Press.
4. Agüera y Areas, B., & Fairhall, A. (2003). What causes a neuron to spike? Neural Computation, 15, 1789-1807.
5. Barlow, H. B. (1953). Summation and inhibition in the frog's retina. J. Physiol., 119, 69-88.
6. Barlow, H. B., Hill, R. M., & Levick, W. R. (1964). Retinal ganglion cells responding selectively to direction and speed of image motion in the rabbit. J. Physiol., 173, 377-407.
7. Berry, M. J. II, & Meister, M. (1999). The neural code of the retina. Neuron, 22, 435-450.
8. Berry, M. J. II, Warland, D., & Meister, M. (1997). The structure and precision of retinal spike trains. Proc. Natl. Acad. Sci. U.S.A., 94, 5411-5416.
9. Bialek, W., & de Ruyter van Steveninck, R. R. (2003). Features and dimensions: Motion estimation in fly vision. Unpublished manuscript.
10. Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992). A training algorithm for optimal margin classifiers. In D. Haussler (Ed.), 5th Annual ACM Workshop on COLT (pp. 144-152). Pittsburgh, PA: ACM Press.
11. Bray, D. (1995). Protein molecules as computational elements in living cells. Nature, 376, 307-312.
12. Brenner, N., Agam, O., Bialek, W., & de Ruyter van Steveninck, R. R. (1998). Universal statistical behavior of neural spike trains. Phys. Rev. Lett., 81, 4000-4003.
13. Brenner, N., Bialek, W., & de Ruyter van Steveninck, R. R. (2000). Adaptive rescaling maximizes information transmission. Neuron, 26, 695-702.
14. Brenner, N., Strong, S., Koberle, R., Bialek, W., & de Ruyter van Steveninck, R. R. (2000). Synergy in a neural code. Neural Comp., 12, 1531-1552. Available on-line: http://xxx.lanl.gov/abs/physics/9902067.
15. Cottrell, G. W., Munro, P., & Zipser, D. (1988). Image compression by back propagation: A demonstration of extensional programming. In N. Sharkey (Ed.), Models of cognition: A review of cognitive science (Vol. 2, pp. 208-240). Norwood, NJ: Ablex.
16. Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York: Wiley.
17. de Boer, E., & Kuyper, P. (1968). Triggered correlation. IEEE Trans. Biomed. Eng., 15, 169-179.
18. de Ruyter van Steveninck, R. R., & Bialek, W. (1988). Real-time performance of a movement sensitive in the blowfly visual system: Information transfer in short spike sequences. Proc. Roy. Soc. Lond. B, 234, 379-414.
19. de Ruyter van Steveninck, R., Lewen, G. D., Strong, S. P., Koberle, R., & Bialek, W. (1997). Reproducibility and variability in neural spike trains. Science, 275, 1805-1808.
20. Dear, S. P., Simmons, J. A., & Fritz, J. (1993). A possible neuronal basis for representation of acoustic scenes in auditory cortex of the big brown bat. Nature, 364, 620-623.
21. Fairhall, A., Lewen, G., Bialek, W., & de Ruyter van Steveninck, R. R. (2001). Efficiency and ambiguity in an adaptive neural code. Nature, 412, 787-792.
22. Fitzhugh, R. (1961). Impulse and physiological states in models of nerve membrane. Biophysics J., 1, 445-466.
23. Guyon, I. M., Boser, B. E., & Vapnik, V. N. (1993). Automatic capacity tuning of very large VC-dimension classifiers. In S. J. Hanson, J. D. Cowan, & C. Giles (Eds.), Advances in neural information processing systems, 5 (pp. 147-155). San Mateo, CA: Morgan Kaufmann.
24. Hartline, H. K. (1940). The receptive fields of optic nerve fibres. Amer. J. Physiol., 130, 690-699.
25. Hille, B. (1992). Ionic channels of excitable membranes. Sunderland, MA: Sinauer.
26. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., 463, 391-407.
27. Hubel, D. H., & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J. Physiol. (Lond.), 160, 106-154.
28. Iverson, L., & Zucker, S. W. (1995). Logical/linear operators for image curves. IEEE Trans. Pattern Analysis and Machine Intelligence, 17, 982-996.
29. Keat, J., Reinagel, P., Reid, R. C., & Meister, M. (2001). Predicting every spike: A model for the responses of visual neurons. Neuron, 30(3), 803-817.
30. Kepler, T., Abbott, L. F., & Marder, E. (1992). Reduction of conductance-based neuron models. Biological Cybernetics, 66, 381-387.
31. Kistler, W., Gerstner, W., & van Hemmen, J. L. (1997). Reduction of the Hodgkin-Huxley equations to a single-variable threshold model. Neural Computation, 9, 1015-1045.
32. Koch, C. (1999). Biophysics of computation: Information processing in single neurons. New York: Oxford University Press.
33. Kuffler, S. W. (1953). Discharge patterns and functional organization of mammalian retina. J. Neurophysiol., 16, 37-68.
34. Lewen, G. D., Bialek, W., & de Ruyter van Steveninck, R. R. (2001). Neural coding of naturalistic motion stimuli. Network, 12, 317-329.
35. Mainen, Z. F., & Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268, 1503-1506.
36. Nagumo, J., Arimoto, S., & Yoshikawa, Z. (1962). An active pulse transmission line simulating nerve axon. Proc. IRE, 50, 2061-2071.
37. Oja, E., & Karhunen, J. (1995). Signal separation by nonlinear Hebbian learning. In M. Palaniswami, Y. Attikiouzel, R. J. Marks II, D. Fogel, & T. Fukuda (Eds.), Computational intelligence - a dynamic system perspective (pp. 83-97). New York: IEEE Press.
38. Panzeri, S., Petersen, R., Schultz, S., Lebedev, M., & Diamond, M. (2001). The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron, 29, 769-777.
39. Reinagel, P., Godwin, D., Sherman, S. M., & Koch, C. (1999). Encoding of visual information by LGN bursts. J. Neurophys., 81, 2558-2569.
40. Reinagel, P., & Reid, R. C. (2000). Temporal coding of visual information in the thalamus. J. Neuroscience, 20(14), 5392-5400.
41. Rieke, F., Warland, D., Bialek, W., & de Ruyter van Steveninck, R. R. (1997). Spikes: Exploring the neural code. Cambridge, MA: MIT Press.
42. Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review, 65, 386-408.
43. Rosenblatt, F. (1962). Principles of neurodynamics. New York: Spartan Books.
44. Roweis, S., & Saul, L. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290, 2323-2326.
45. Schneidman, E., Freedman, B., & Segev, I. (1998). Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comp., 10, 1679-1703.
46. Shannon, C. E. (1948). A mathematical theory of communication. Bell Sys. Tech. Journal, 27, 379-423, 623-656.
47. Sharpee, T., Rust, N. C., & Bialek, W. (in press). Maximally informative dimensions: analysing neural responses to natural signals. Neural Information Processing Systems 2002. Available on-line: http://xxx.lanl.gov/abs/physics/0208057.
48. Sharpee, T., Rust, N. C., & Bialek, W. (2003). Maximally informative dimensions: Analysing neural responses to natural signals. Unpublished manuscript.
49. Stanley, G. B., Lei, F. F., & Dan, Y. (1999). Reconstruction of natural scenes from ensemble responses in the lateral geniculate nucleus. J. Neurosci., 19(18), 8036-8042.
50. Theunissen, F., Sen, K., & Doupe, A. (2000). Spectral-temporal receptive fields of nonlinear auditory neurons obtained using natural sounds. J. Neurosci., 20, 2315-2331.
51. Tiesinga, P. H. E., José, J., & Sejnowski, T. (2000). Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels. Physical Review E, 62, 8413-8419.
52. Tishby, N., Pereira, F., & Bialek, W. (1999). The information bottleneck method. In B. Hajek & R. S. Sreenivas (Eds.), Proceedings of the 37th Annual Allerton Conference on Communication, Control and Computing (pp. 368-377). Champaign, IL. Available on-line: http://xxx.lanl.gov/abs/physics/0004057.