Stimulus-Dependent Correlations in Threshold-Crossing Spiking Neurons

Neural Computation

Volumn 21, Issue 8, 2009, Pages 2269-2308

  Burak, Yoram ^a   Lewallen, Sam ^b   Sompolinsky, Haim ^a,c  

^a HARVARD UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALDEHYDES; FIRES;

CORRELATION FUNCTION; CROSS-CORRELATIONS; GAUSSIAN STATISTICS; INTEGRATE-AND-FIRE MODEL; LOW THRESHOLDS; SIMPLE MODELING; SPIKE TRAIN; SPIKING NEURONES; THRESHOLD CROSSING MODELS; THRESHOLD-CROSSING;

NEURONS;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; DIFFERENTIAL THRESHOLD; HUMAN; NERVE CELL; NONLINEAR SYSTEM; PHYSIOLOGY; STATISTICS;

ACTION POTENTIALS; ANIMALS; DIFFERENTIAL THRESHOLD; HUMANS; MODELS, NEUROLOGICAL; NEURONS; NONLINEAR DYNAMICS; STATISTICS AS TOPIC;

EID: 70249141329     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2009.07-08-830     Document Type: Article

References (42)

1. Baccus, S. A., & Meister, M. (2002). Fast and slow contrast adaptation in retinal circuitry. Neuron, 36, 909–919.
2. Badel, L., Gerstner, W., & Richardson, M. J. (2006). Dependence of the spike-triggered average voltage on membrane response properties. Neurocomputing, 69, 1062– 1065.
3. Berry, M. J., & Meister, M. (1998a). Refractoriness and neural precision. Journal of Neuroscience, 18, 2200–2211.
4. Berry, M. J., & Meister, M. (1998b). Refractoriness and neural prediction. Journal of Neuroscience, 18, 2200–2211.
5. Berry, M. J., Warland, D. K., & Meister, M. (1997). The structure and precision of retinal spike trains. Proceedings of the National Academy of Sciences of the USA, 94, 5411–5416.
6. Brunel, N., & Sergi, S. (1998). Firing frequency of leaky integrate-and-firing neurons with synaptic current dynamics. Journal of Theoretical Biology, 195, 87–95.
7. Burkitt, A. N. (2006). A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biological Cybernetics, 95, 1–19.
8. Chichilnisky, E. (2001). A simple white noise analysis of neuronal light responses. Network: Computation in Neural Systems, 12, 199–213.
9. Chichilnisky, E. J., & Kalmar, R. S. (2002). Functional asymmetries in on and off ganglion cells of primate retina. Journal of Neuroscience, 22, 2737–2747.
10. Dayan, P., & Abbott, L. (2001). Theoretical neuroscience. Cambridge, MA: MIT Press.
11. de Ruyter van Steveninck, R., & Bialek, W. (1988). Coding and information transfer in short spike sequences. Proceedings of the Royal Society of London B, 234, 379–414.
12. de Ruyter van Steveninck, R. R., Lewen, G. D., Strong, S. P., Koberle, R., & Bialek, W. (1997). Reproducibility and variability in neural spike trains. Science, 275, 1805–1808.
13. Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Cambridge: Cambridge University Press.
14. Ginzburg, I., & Sompolinsky, H. (1994). Theory of correlations in stochastic neural networks. Physical Review E, 50, 3171–3191.
15. Gollisch, T., & Meister, M. (2008). Rapid neural coding in the retina with relative spike latencies. Science, 319, 1108–1111.
16. Hopfield, J. J. (1995). Pattern recognition computation using action potential timing for stimulus representation. Nature, 376, 33–36.
17. Hosoya, T., Baccus, S. A., & Meister, M. (2005). Dynamic predictive coding by the retina. Nature, 436, 71–77.
18. Jung, P. (1994). Threshold devices: Fractal noise and neural talk. Physical Review E, 50, 2513–2522.
19. Kanev, J., Wenning, G., & Obermayer, K. (2003). Approximating the response stimulus correlation for the integrate-and-fire neuron. Neurocomputing, 58, 47–52.
20. Keat, J., Reinagel, P., Reid, R. C., & Meister, M. (2001). Predicting every spike: A model for the responses of visual neurons. Neuron, 30, 803–817.
21. Korenberg, M. J., & Hunter, I. W. (1986). The identification of nonlinear biological systems: LNl cascade models. Biological Cybernetics, 55, 125–134.
22. Kuhn, A., Aertsen, A., & Rotter, S. (2003). Higher-order statistics of input ensembles and the response of simple model neurons. Neural Computation, 15, 67–101.
23. Mainen, Z. F., & Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268, 1503–1506.
24. Markowitz, D. A., Collman, F., Brody, C. D., & Hopfield, J. J., & Tank, D. W. (2008). Rate-specific synchrony: Using noisy oscillations to detect equally active neurons. Proceedings of the National Academy of Sciences of the USA, 105, 8422–8427.
25. Meister, M., & Berry, M. J. (1999). The neural code of the retina. Neuron, 22, 435–450.
26. Moreno, R., de la Rocha, J., Renart, A., & Parga, N. (2002). Response of spiking neurons to correlated inputs. Physical Review Letters, 89, 288101.
27. Moreno-Bote, R., & Parga, N. (2006). Auto-and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses. Physical Review Letters, 96, 028101.
28. Paninski, L. (2003). Convergence properties of three spike-triggered analysis techniques. Network: Computing in Neural Systems, 14, 437–464.
29. Paninski, L. (2006). The spike-triggered average of the integrate-and-fire cell driven by gaussian white noise. Neural Computation, 18, 2592–2616.
30. Rice, S. O. (1954). Mathematical analysis of random noise. In N. Wax (Ed.), Selected papers on noise and stochastic processes (pp. 133–294). New York: Dover.
31. Rieke, F. (2001). Temporal contrast adaptation in salamander bipolar cells. Journal of Neuroscience, 21, 9445–9454.
32. Rieke, F., Warland, D., de Ruyter van Steveninck, R., & Bialek, W. (1996). Spikes: Exploring the neural code. Cambridge, MA: MIT Press.
33. Rust, N. C., Schwartz, O., Movshon, J. A., & Simoncelli, E. P. (2005). Spatiotemporal elements of macaque V1 receptive fields. Neuron, 46, 945–956.
34. Salinas, E., & Sejnowski, T. J. (2000). Impact of correlated synaptic input on output firing rate and variability in simple neuronal models. Journal of Neuroscience, 20, 6193–6209.
35. Salinas, E., & Sejnowski, T. (2002). Integrate-and-fire neurons driven by correlated stochastic input. Neural Computation, 14, 2111–2155.
36. Schwalger, T., & Schimansky-Geier, L. (2008). Interspike interval statistics of a leaky integrate-and-fire neuron driven by gaussian noise with large correlation times. Physical Review E, 77, 031914.
37. Schwartz, O. (2006). Spike-triggered neural characterization. Journal of Vision, 6, 484– 507.
38. Stroeve, S., & Gielen, S. (2001). Correlation between uncoupled conductance based integrate-and-fire neurons due to common and synchronous presynaptic firing. Neural Computation, 13, 2005–2029.
39. Tchumatchenko, T., Malyshev, A., Geisel, T., Volgushev, M., & Wolf, F. (2008). Correlations and synchrony in threshold neuron models. Available online at http://arxiv.org/abs/0810.2901v2.
40. Tuckwell, H. (1988a). Introduction to theoretical neurobiology: Vol. 1. Linear cable theory and dendritic structure. Cambridge: Cambridge University Press.
41. Tuckwell, H. (1988b). Introduction to theoretical neurobiology: Vol. 2. Nonlinear and stochastic theories. Cambridge: Cambridge University Press.
42. Uzzell, V., & Chichilnisky, E. (2004). Precision of spike trains in primate retinal ganglion cells. Journal of Neurophysiology, 92, 780–789.