An approximation to the adaptive exponential integrate-and-fire neuron model allows fast and predictive fitting to physiological data

Frontiers in Computational Neuroscience

Volumn , Issue AUGUST, 2012, Pages

  Hertäg, Loreen ^a   Hass, Joachim ^a   Golovko, Tatiana ^a   Durstewitz, Daniel ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Adaptation; F i curve; Interneurons; Prefrontal cortex; Pyramidal cells; Spike timing; Temporal coding

Indexed keywords

ADAPTATION; F-I CURVE; INTERNEURONS; PREFRONTAL CORTEX; PYRAMIDAL CELL; SPIKE TIMING; TEMPORAL CODING;

CELLS; COMPUTER SIMULATION; CYTOLOGY; DIFFERENTIAL EQUATIONS; FACTOR ANALYSIS; LEARNING ALGORITHMS; NEURONS; PARAMETER ESTIMATION; PHYSIOLOGY;

PHYSIOLOGICAL MODELS;

ADAPTIVE BEHAVIOR; ANIMAL CELL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BRAIN CORTEX; IN VITRO STUDY; INTERNEURON; MATHEMATICAL MODEL; MOUSE; NERVE STIMULATION; NERVOUS SYSTEM ELECTROPHYSIOLOGY; NONHUMAN; PREDICTION; PREFRONTAL CORTEX; RAT; SPIKE WAVE; TASK PERFORMANCE;

EID: 84865959800     PISSN: 16625188     EISSN: None     Source Type: Journal    
DOI: 10.3389/fncom.2012.00062     Document Type: Article

References (92)

1. Bäck, T. and Schwefel, H. (1993). An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1(1):1-23.
2. Badel, L., Lefort, S., Berger, T. K., Petersen, C. C. H., Gerstner, W., and Richardson, M. J. E. (2008a). Extracting non-linear integrate-and-firemodels from experimental data using dynamic i-v curves. Biol Cybern, 99:361-370.
3. Badel, L., Lefort, S., Brette, R., Petersen, C., Gerstner, W., and Richardson, M. (2008b). Dynamic IV curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. Journal of Neurophysiology, 99(2):656-666.
4. Benda, J. and Herz, A. V. M. (2003). A universal model for Spike-Frequency adaptation. Neural Computation, 15(11):2523-2564.
5. Binzegger, T., Douglas, R. J., and Martin, K. A. C. (2004). A quantitative map of the circuit of cat primary visual cortex. The Journal of Neuroscience, 24(39):8441-8453.
6. Brette, R. and Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology, 94:3637-3642.
7. Brette, R. and Goodman, D. F. M. (2011). Vectorized algorithms for spiking neural network simulation. Neural Computation, 23(6):1503-1535.
8. Brette, R., Rudolph, M., Carnevale, T., Hines, M., Beeman, D., Bower, J., Diesmann, M., Morrison, A., Goodman, P., Harris, F., et al. (2007). Simulation of networks of spiking neurons: a review of tools and strategies. Journal of Computational Neuroscience, 23(3):349-398.
9. Chagnac-Amitai, Y., Luhmann, H. J., and Prince, D. A. (2004). Burst generating and regular spiking layer 5 pyramidal neurons of rat neocortex have different morphological features. The Journal of Comparative Neurology, 296(4):598-613.
10. Chance, F., Abbott, L., and Reyes, A. (2002). Gain modulation from background synaptic input. Neuron, 35(4):773-782.
11. Clopath, Jolivet, R., Rauch, A., Lüscher, H., and Gerstner, W. (2007). Predicting neuronal activity with simple models of the threshold type: Adaptive exponential Integrate-and-Fire model with two compartments. Neurocomputing, 70(10-12):1668-1673.
12. Connors, B.W. and Gutnick, M. J. (1990). Intrinsic firing patterns of diverse neocortical neurons. Trends in Neurosciences, 13(3):99-104.
13. Connors, B. W., Gutnick, M. J., and Prince, D. A. (1982). Electrophysiological properties of neocortical neurons in vitro. Journal of Neurophysiology, 48(6):1302-1320.
14. De Schutter, E., Bower, J.M., et al. (1994). An active membrane model of the cerebellar purkinje cell. II. simulation of synaptic responses. Journal of Neurophysiology, 71(1):401-419.
15. Destexhe, A. and Paré, D. (1999). Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. Journal of Neurophysiology, 81(4):1531-1547.
16. Destexhe, A., Rudolph, M., Fellous, J., and Sejnowski, T. (2001). Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons. Neuroscience, 107(1):13-24.
17. Destexhe, A., Rudolph, M., Paré, D., et al. (2003). The high-conductance state of neocortical neurons in vivo. Nature Reviews Neuroscience, 4(9):739-751.
18. Druckmann, S., Banitt, Y., Gidon, A., Schürmann, F., Markram, H., and Segev, I. (2007). A novel multiple objective optimization frame work for constraining Conductance-Based neuron models by experimental data. Frontiers in Neuroscience, 1(1):7-18.
19. Druckmann, S., Berger, T. K., Schürmann, F., Hill, S., Markram, H., and Segev, I. (2011). Effective stimuli for constructing reliable neuron models. PLoS Comput Biol, 7(8):e1002133.
20. Durstewitz, D. (2003). Self-Organizing neural integrator predicts interval times through climbing activity. The Journal of Neuroscience, 23(12):5342-5353.
21. Durstewitz, D. (2009). Implications of synaptic biophysics for recurrent network dynamics and active memory. Neural Networks, 22(8):1189-1200.
22. Durstewitz, D. and Gabriel, T. (2007). Dynamical basis of irregular spiking in NMDA-Driven prefrontal cortex neurons. Cerebral Cortex, 17(4):894-908.
23. Durstewitz, D., Vittoz, N. M., Floresco, S. B., and Seamans, J. K. (2010). Abrupt transitions between prefrontal neural ensemble states accompany behavioral transitions during rule learning. Neuron, 66(3):438-448.
24. Eberhart, R. and Shi, Y. (1998). Comparison between genetic algorithms and particle swarm optimization. In Porto, V., Saravanan, N., Waagen, D., and Eiben, A., editors, Evolutionary Programming 7, Lecture Notes in Computer Science, pages 611-616. Springer Berlin / Heidelberg.
25. Edman, A., Gestrelius, S., and Grampp, W. (1987). Analysis of gated membrane currents and mechanisms of firing control in the rapidly adapting lobster stretch receptor neurone. The Journal of Physiology, 384:649-669.
26. Ermentrout, G. B. and Kopell, N. (1986). Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM Journal on Applied Mathematics, 46(2):233-253.
27. Fourcaud-Trocmé, N., Hansel, D., van Vreeswijk, C., and Brunel, N. (2003). How spike generation mechanisms determine the neuronal response to fluctuating inputs. The Journal of Neuroscience, 23(37):11628-11640.
28. Gerstner, W. and Kistler, W. (2002). Spiking Neuron Models: Single Neurons, Populations, Plasticity. Cambridge University Press.
29. Gerstner, W. and Naud, R. (2009). How good are neuron models? Science, 326:379-380.
30. Gütig, R. and Sompolinsky, H. (2006). The tempotron: a neuron that learns spike timing-based decisions. Nat Neurosci, 9(3):420-428.
31. + current in prefrontal cortical cells. European Journal of Neuroscience, 4(11):1087-1092.
32. Hastie, T., Tibshirani, R., and Friedman, J. (2009). High-Dimensional problems: p n. In The Elements of Statistical Learning, Springer Series in Statistics, pages 1-50. Springer New York.
33. Hill, A. V. (1936). Excitation and accommodation in nerve. Proceedings of the Royal Society of London. Series B, Biological Sciences, 119(814):305-355.
34. Izhikevich, E. (2003). Simple model of spiking neurons. IEEE Trans Neural Networks, 14(6):1569-1572.
35. Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons? IEEE Trans Neural Networks, 15(5):1063-1070.
36. Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience. The MIT Press.
37. Izhikevich, E. M. and Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. PNAS, 105(9):3593-3598.
38. Izhikevitch, E. M. (2001). Resonate-and-fire neurons. Neural Networks, 14:883-894.
39. Jaeger, D., De Schutter, E., and Bower, J. M. (1997). The role of synaptic and voltage-gated currents in the control of purkinje cell spiking: Amodeling study. The Journal of Neuroscience, 17(1):91-106.
40. Jahr, C. E. and Stevens, C. F. (1990). Voltage dependence of NMDA-Activated macroscopic conductances predicted by Single-Channel kinetics. The Journal of Neuroscience, 10(9):3178-3182.
41. Jolivet, R., Kobayashi, R., Rauch, A., Naud, R., Shinomoto, S., and Gerstner, W. (2008). A benchmark test for a quantitative assessment of simple neuron models. Journal of Neuroscience Methods, 169:417-424.
42. Jolivet, R., Lewis, T., and Gerstner, W. (2004). Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. Journal of Neurophysiology, 92(2):959-976.
43. Jolivet, R., Rauch, A., Lüscher, H., and Gerstner, W. (2006). Predicting spike timing of neocortical pyramidal neurons by simple threshold models. Journal of Computational Neuroscience, 21(1):35-49.
44. Kistler, W., Gerstner, W., and Hemmen, J. (1997). Reduction of the Hodgkin-Huxley equations to a single-variable threshold model. Neural Computation, 9(5):1015-1045.
45. Kreiman, G., Krahe, R., Metzner, W., Koch, C., and Gabbiani, F. (2000). Robustness and variability of neuronal coding by Amplitude-Sensitive afferents in the weakly electric Fish Eigenmannia. Journal of Neurophysiology, 84(1):189-204.
46. Lansner, A. (2009). Associative memory models: from the cell-assembly theory to biophysically detailed cortex simulations. Trends in Neurosciences, 32(3):178-186.
47. Lansner, A., Fransén, E., and Sandberg, A. (2003). Cell assembly dynamics in detailed and abstract attractor models of cortical associative memory. Theory in Biosciences, 122(1):19-36.
48. Lapicque, L. (1907). Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarization. J. Physiol. Pathol. Gen, 9:620-635.
49. Lapish, C. C., Durstewitz, D., Chandler, L. J., and Seamans, J. K. (2008). Successful choice behavior is associated with distinct and coherent network states in anterior cingulate cortex. PNAS, 105(33):11963-11968.
50. Lee, A. K., Manns, I. D., Sakmann, B., and Brecht, M. (2006). Whole-Cell recordings in freely moving rats. Neuron, 51(4):399-407.
51. London, M., Roth, A., Beeren, L., Häusser, M., and Latham, P. E. (2010). Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature, 466(7302):123-127.
52. Lundqvist, M., Compte, A., and Lansner, A. (2010). Bistable, irregular firing and population oscillations in a modular attractor memory network. PLoS Comput Biol, 6(6):1-12.
53. Madison, D. V. and Nicoll, R. A. (1984). Control of the repetitive discharge of rat CA 1 pyramidal neurones in vitro. The Journal of Physiology, 354:319-331.
54. Mainen, Z. F. and Sejnowski, T. J. (1995). Reliability of spike timing in neocortical neurons. Science, 268:1503-1506.
55. Mainen, Z. F. and Sejnowski, T. J. (1996). Influence of dendritic structure on firing pattern in model neocortical neurons. Nature, 382:363-366.
56. Margrie, T., Brecht, M., and Sakmann, B. (2002). In vivo, low-resistance, whole-cell recordings from neurons in the anaesthetized and awake mammalian brain. Pflügers Archiv European Journal of Physiology, 444(4):491-498.
57. Markram, H. (2006). The blue brain project. Nat Rev Neurosci, 7(2):153-160.
58. Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., and Wu, C. (2004). Interneurons of the neocortical inhibitory system. Nat Rev Neurosci, 5(10):793-807.
59. Mason, A. and Larkman, A. (1990). Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. II. electrophysiology. The Journal of Neuroscience, 10(5):1415-1428.
60. Mason, A., Nicoll, A., and Stratford, K. (1991). Synaptic transmission between individual pyramidal neurons of the rat visual cortex in vitro. The Journal of Neuroscience, 11(1):72-84.
61. Moyer, J. T., Wolf, J. A., and Finkel, L. H. (2007). Effects of dopaminergic modulation on the integrative properties of the ventral striatal medium spiny neuron. Journal of Neurophysiology, 98(6):3731-3748.
62. Naud, R., Gerhard, F., Mensi, S., and Gerstner, W. (2011). Improved similarity measures for small sets of spike trains. Neural Computation, 23(12):3016-3069.
63. Naud, R., Marcille, N., Clopath, C., and Gerstner, W. (2008). Firing patterns in the adaptive exponential integrate-and-fire model. Biol Cybern, 99:335-347.
64. Owens, J. D., Luebke, D., Govindaraju, N., Harris, M., Krüger, J., Lefohn, A. E., and Purcell, T. J. (2007). A survey of General Purpose computation on graphics hardware. Computer Graphics Forum, 26(1):80-113.
65. Poirazi, P. and Mel, B. W. (2001). Impact of active dendrites and structural plasticity on the memory capacity of neural tissue. Neuron, 29(3):779-796.
66. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 3 edition.
67. Prinz, A. A., Billimoria, C. P., and Marder, E. (2003). Alternative to Hand-Tuning Conductance- Based models: Construction and analysis of databases of model neurons. Journal of Neurophysiology, 90(6):3998-4015.
68. Prinz, A. A., Bucher, D., and Marder, E. (2004). Similar network activity from disparate circuit parameters. Nat Neurosci, 7(12):1345-1352.
69. Rauch, A., La Camera, G., Lüscher, H., Senn, W., and Fusi, S. (2003). Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like input currents. Journal of Neurophysiology, 90(3):1598-1612.
70. Renart, A., Moreno-Bote, R., Wang, X., and Parga, N. (2006). Mean-Driven and Fluctuation- Driven persistent activity in recurrent networks. Neural Computation, 19(1):1-46.
71. Reyes, A., Lujan, R., Rozov, A., Burnashev, N., Somogyi, P., Sakmann, B., et al. (1998). Targetcell- specific facilitation and depression in neocortical circuits. Nat Neurosci, 1(4):279-285.
72. Richardson, M., Brunel, N., and Hakim, V. (2003). From subthreshold to firing-rate resonance. Journal of Neurophysiology, 89(5):2538-2554.
73. Rossant, C., Goodman, D. F. M., Fontaine, B., Platkiewicz, J., Magnusson, A. K., and Brette, R. (2011). Fitting neuron models to spike trains. Frontiers in Neuroscience, 5.
74. Rossant, C., Goodman, D. F. M., Platkiewicz, J., and Brette, R. (2010). Automatic fitting of spiking neuron models to electrophysiological recordings. Frontiers in Neuroinformatics, 4.
75. Rozov, A., Jerecic, J., Sakmann, B., and Burnashev, N. (2001). AMPA receptor channels with Long-Lasting desensitization in bipolar interneurons contribute to synaptic depression in a novel feedback circuit in layer 2/3 of rat neocortex. The Journal of Neuroscience, 21(20):8062-8071.
76. Schröder, R. and Luhmann, H. J. (1997). Morphology, electrophysiology and pathophysiology of supragranular neurons in rat primary somatosensory cortex. European Journal of Neuroscience, 9(1):163-176.
77. Shadlen, M. N. and Newsome, W. T. (1994). Noise, neural codes and cortical organization. Current Opinion in Neurobiology, 4(4):569-579.
78. Shu, Y., Hasenstaub, A., Duque, A., Yu, Y., and McCormick, D. A. (2006). Modulation of intracortical synaptic potentials by presynaptic somatic membrane potential. Nature, 441:761-765.
79. Steriade, M., Timofeev, I., and Grenier, F. (2001). Natural waking and sleep states: A view from inside neocortical neurons. Journal of Neurophysiology, 85(5):1969-1985.
80. + current in hippocampal pyramidal neurons. PNAS, 96(8):4662-4667.
81. Thomson, A. M. and Lamy, C. (2007). Functional maps of neocortical local circuitry. Frontiers in Neuroscience, 1(1):19-42.
82. Timofeev, I., Grenier, F., and Steriade, M. (2001). Disfacilitation and active inhibition in the neocortex during the natural Sleep-Wake cycle: An intracellular study. PNAS, 98(4):1924-1929.
83. Touboul, J. (2008). Bifurcation analysis of a general class of non-linear integrate and fire neurons. SIAM J Appl Math, 68(4):1045-1079.
84. Touboul, J. and Brette, R. (2008). Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biol Cybern, 99(4-5):319-334.
85. Traub, R. D., Contreras, D., Cunningham, M. O., Murray, H., LeBeau, F. E. N., Roopun, A., Bibbig, A., Wilent, W. B., Higley, M. J., and Whittington, M. A. (2005). Single-Column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. Journal of Neurophysiology, 93(4):2194-2232.
86. Traub, R. D., Miles, R., and Wong, R. K. (1988). Large scale simulations of the hippocampus. IEEE Engineering in Medicine and Biology Magazine, 7(4):31-38.
87. Traub, R. D., Wong, R. K., Miles, R., and Michelson, H. (1991). A model of a CA3 hippocampal pyramidal neuron incorporating Voltage-Clamp data on intrinsic conductances. Journal of Neurophysiology, 66(2):635-650.
88. Tseng, K. Y. and O'Donnell, P. (2005). Post-pubertal emergence of prefrontal cortical up states induced by d1-nmda co-activation. Cerebral Cortex, 15(1):49-57.
89. van Vreeswijk, C. and Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274(5293):1724-1726.
90. Victor, J. D. and Purpura, K. P. (1996). Nature and precision of temporal coding in visual cortex: A metric-space analysis. Journal of Neurophysiology, 76(2):1310-1326.
91. Wang, Y., Markram, H., Goodman, P. H., Berger, T. K., Ma, J., and Goldman-Rakic, P. S. (2006). Heterogeneity in the pyramidal network of the medial prefrontal cortex. Nat Neurosci, 9(4):534-542.
92. Whittington, M., Traub, R., Kopell, N., Ermentrout, B., and Buhl, E. (2000). Inhibition-based rhythms: experimental and mathematical observations on network dynamics. International Journal of Psychophysiology, 38(3):315-336.