Parameters of the diffusion leaky integrate-and-fire neuronal model for a slowly fluctuating signal

Neural Computation

Volumn 20, Issue 11, 2008, Pages 2696-2714

  Picchini, Umberto ^a,b   Ditlevsen, Susanne ^a   De Gaetano, Andrea ^b   Lansky, Petr ^c  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b CATHOLIC UNIVERSITY   (Italy)

^c INSTITUTE OF PHYSIOLOGY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL MEMBRANE POTENTIAL; GUINEA PIG; NERVE CELL; NONLINEAR SYSTEM; PHYSIOLOGY; SIGNAL TRANSDUCTION; STATISTICS; TIME;

ACTION POTENTIALS; ANIMALS; GUINEA PIGS; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEURONS; NONLINEAR DYNAMICS; SIGNAL TRANSDUCTION; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 55749107079     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2008.11-07-653     Document Type: Article

References (48)

1. Abramowitz, M., & Stegun, I. A. (1964). Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover.
2. Barrowes, B. (2007). Multiple precision toolbox for Matlab. Available online at http://www.mathworks.com/matlabcentral/fileexchange/ loadFile.do?objectId=6446&objectType=File.
3. Brunel, N., & van Rossum, M. C. W. (2007). Lapicque's 1907 paper: From frogs to integrate-and-fire. Biol. Cybern., 97, 337-339.
4. Burkitt, A. N. (2006). A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol. Cybern., 95, 1-19.
5. Cecchi, G. A., Sigman, M., Alonso, J. M., Martinez, L., Chialvo, D. R., & Magnasco, M. (2000). Noise in neurons is message-dependent. Proceedings of the National Academy of Sciences, 97, 5557-5561.
6. Clopath, C., Jolivet, R., Rauch, A., Lüscher, H.-R., & Gerstner, W. (2007). Predicting neuronal activity with simple models of the threshold type: Adaptive exponential integrate-and-fire model with two compartments. Neurocomput., 70, 1668-1673.
7. Davidian, M., & Giltinan, D. M. (1995). Nonlinear models for repeated measurement data. London: Chapman and Hall.
8. Dayan, P., & Abbott, L. F. (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge, MA: MIT Press.
9. Diggle, P. J., Heagerty, P., Liang, K. Y., & Zeger, S. L. (2002). Analysis of longitudinal data. New York: Oxford University Press.
10. Ditlevsen, S., & De Gaetano, A. (2005). Mixed effects in stochastic differential equations models. REVSTAT - Statistical Journal, 3(2), 137-153.
11. Ditlevsen, S., & Ditlevsen, O. (2008). Parameter estimation from observations of first-passage times of the Ornstein-Uhlenbeck process and the Feller process. Prob. Eng. Mech., 23, 170-179.
12. Ditlevsen, S., & Lansky, P. (2005). Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. Phys. Rev. E, 71, 011907.
13. Ditlevsen, S., & Lansky, P. (2006). Estimation of the input parameters in the Feller neuronal model. Phys. Rev. E, 73, 061910.
14. Ditlevsen, S., & Lansky, P. (2007). Parameters of stochastic diffusion processes estimated from observations of first hitting-times: Application to the leaky integrate-and-fire neuronal model. Phys. Rev. E, 76, 041906.
15. Donnet, S., & Samson, A. (2008). Parametric inference for mixed models defined by stochastic differential equations. ESAIM: Probability and Statistics, 12, 196-218.
16. Fröberg, C. E. (1985). Numerical mathematics. Upper Saddle River, NJ: Benjamin/Cummings.
17. Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Cambridge: Cambridge University Press.
18. Habib, M. K., & Thavaneswaran, A. (1990). Inference for stochastic neuronal models. Applied Math. Comput., 38, 51-73.
19. Höpfner, R. (2007). On a set of data for the membrane potential in a neuron. Math. Biosci., 207, 275-301.
20. Huys, Q. J. M., Ahrens, M. B., & Paninski, L. (2006). Efficient estimation of detailed single-neuron models. J. Neurophysiol., 96, 872-890.
21. Inoue, J., Sato, S., & Ricciardi, L. M. (1995). On the parameter estimation for diffusion models of single neurons' activity. Biol. Cybern., 73, 209-221.
22. Jolivet, R., Lewis, T. J., & Gerstner, W. (2004). Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J. Neurophysiol., 92, 959-976.
23. Jolivet, R., Rauch, A., Lüscher, H.-R., & Gerstner, W. (2006). Predicting spike timing of neocortical pyramidal neurons by simple threshold models. J. Comput. Neurosci., 21, 35-49.
24. Kloeden, P. E., & Platen, E. (1992). Numerical solution of stochastic differential equations. New York: Springer.
25. Krommer, A. R., & Ueberhuber, C. W. (1998). Computational Integration. Philadelphia: Society for Industrial and Applied Mathematics.
26. La Camera, G., Rauch, A., Lüscher, H.-R., Senn, W., & Fusi, S. (2004). Minimal models of adapted neuronal response to in vivo-like input currents. Neural Comput., 16, 2101-2124.
27. Lanska, V., & Lansky, P. (1998). Input parameters in a one-dimensional neuronal model with reversal potentials. Biosystems, 48, 123-129.
28. Lansky, P. (1983). Inference for diffusion models of neuronal activity. Math. Biosci., 67, 247-260.
29. Lansky, P., & Sacerdote, L. (2001). The Ornstein-Uhlenbeck neuronal model with signal-dependent noise. Physics Letters A, 285, 132-140.
30. Lansky, P., Sanda, P., & He, J. (2006). The parameters of the stochastic leaky integrate-and-fire neuronal model. J. Comput. Neurosci., 21, 211-223.
31. Lavielle, M., Mesa, H., & Monolix Group. (2007). MONOLIX (MOdèles NOn LInéaires à effets miXtes). Available online at http://www.monolix.org.
32. McCulloch, C. E., & Searle, S. R. (2001). Generalized, linear and mixed models. New York: Wiley.
33. Mortensen, S. B., Klim, S., Dammann, B., Kristensen, N. R., Madsen, H., & Overgaard, R. (2007). A Matlab framework for estimation of NLME models using stochastic differential equations: Applications for estimation of insulin secretion rates. J. Pharmacokinet. Pharmacodyn., 34(5), 623-642.
34. Overgaard, R. V., Jonsson, N., Tornøe, C. W., & Madsen, H. (2005). Non-linear mixed effects models with stochastic differential equations: Implementation of an estimation algorithm. J. Pharmacokinet. Pharmacodyn., 32, 85-107.
35. Paninski, L., Pillow, J. W., & Simoncelli, E. P. (2004). Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model. Neural Comput., 16, 2533-2561.
36. Paninski, L., Pillow, J., & Simoncelli, E. (2005). Comparing integrate-and-fire-models estimated using intracellular and extracellular data. Neurocomputing, 65-66, 379-385.
37. Picchini, U., De Gaetano, A., & Ditlevsen, S. (2006). Parameter estimation in stochastic differential mixed-effects models (Tech. Rep. 06/12). Copenhagen: Department of Biostatistics, University of Copenhagen.
38. Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. New York: Springer-Verlag.
39. Pinheiro, J. C., Bates, D. M., DebRoy, S., Sarkar, D., & R Core Team. (2007). nlme: Linear and nonlinear mixed effects models. The R Foundation for Statistical Computing. R package version 3.1-86 available online at http://www.r-project.org/.
40. Powers, R. K., & Binder, M. D. (1996). Experimental evaluation of input-output models of motoneuron discharge. J. Neurophysiol., 75, 367-379.
41. Rauch, A., La Camera, G., Lüscher, H.-R., Senn, W., & Fusi, S. (2003). Neocortical pyramidal cells respond as integrate-and fire neurons in vivo-like input currents. J. Neurophysiol., 90, 1598-1612.
42. Ricciardi, L. M. (1977). Diffusion processes and related topics in biology. Berlin: Springer.
43. Salzer, H. E., Zucker, R., & Capuano, R. (1952). Table of the zeros and weight factors of the first twenty Hermite polynomials. Journal of Research of the National Bureau of Standards, 48, 111-116. Available online at http://nvl.nist.gov/pub/nistpubs/jres/048/2/V48.N02.A04.pdf.
44. Shinomoto, S., Sakai, Y., & Funahashi, S. (1999). The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex. Neural Comput., 11, 935-951.
45. Tornøe, C. W., Overgaard, R. V., Agersø, H., Nielsen, H. A., Madsen, H., & Jonsson, E. N. (2005). Stochastic differential equations in NONMEM: Implementation, application, and comparison with ordinary differential equations. Pharmaceutical Research, 22(8), 1247-1258.
46. Tuckwell, H. C. (1988). Introduction to theoretical neurobiology, Vol. 2: Nonlinear and stochastic theories. Cambridge: Cambridge University Press.
47. Tuckwell, H. C., & Richter, W. (1978). Neuronal interspike time distributions and the estimation of neurophysiological and neuroanatomical parameters. J. Theor. Biol., 71, 167-180.
48. Yu, Y. Q., Xiong, Y., Chan, Y. S., & He, J. F. (2004). Corticofugal gating of auditory information in the thalamus: An in vivo intracellular recording study. J. Neurosci., 24, 3060-3069.