Instantaneous non-linear processing by pulse-coupled threshold units

PLoS Computational Biology

Volumn 6, Issue 9, 2010, Pages

  Helias, Moritz ^a   Deger, Moritz ^b   Rotter, Stefan ^b   Diesmann, Markus ^a,b,c  

^a RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

^b UNIVERSITY OF FREIBURG   (Germany)

^c RIKEN   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

NEURAL NETWORKS; NEURONS;

BACKGROUND NOISE; CHARACTERISTICS LEVELS; DIFFUSION LIMITS; INTEGRATE-AND-FIRE NEURONS; LINEAR RESPONSE; LOW-PASS; NEURON MODELING; NONLINEAR PROCESSING; SPIKING NEURONAL NETWORKS; SYNAPTIC WEIGHT;

PROBABILITY DENSITY FUNCTION;

ARTICLE; EXCITATORY POSTSYNAPTIC POTENTIAL; INFORMATION PROCESSING; KERNEL METHOD; MEMBRANE POTENTIAL; NERVE CELL NETWORK; NERVE CELL PLASTICITY; NERVE POTENTIAL; NOISE; POSTSYNAPTIC POTENTIAL; PULSE COUPLING; QUALITATIVE ANALYSIS; SPIKE; STEADY STATE; STOCHASTIC MODEL;

EID: 78049437495     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1000929     Document Type: Article

References (65)

1. Stein RB (1965) A theoretical analysis of neuronal variability. Biophys J 5: 173-194.
2. Rotter S, Diesmann M (1999) Exact digital simulation of time-invariant linear systems with applications to neuronal modeling. Biol Cybern 81: 381-402.
3. Gewaltig MO, Diesmann M (2007) NEST (Neural Simulation Tool). Scholarpedia J 2: 1430.
4. Rauch A, La Camera G, Lüscher H, Senn W, Fusi S (2003) Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo like input currents. J Neurophysiol 90: 1598-1612.
5. La Camera G, Rauch A, Luscher H, Senn W, Fusi S (2004) Minimal models of adapted neuronal response to in vivo-like input currents. Neural Comput 10: 2101-2124.
6. Jovilet R, Kobayashi R, Rauch A, Naud R, Shinomoto S, et al. (2008) A benchmark test for a quantitative assessment of simple neuron models. J Neurosci Methods 169: 417-424.
7. Izhikevich E (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 5: 1063-1070.
8. Ricciardi LM, Sacerdote L (1979) The Ornstein-Uhlenbeck process as a model for neuronal activity. Biol Cybern 35: 1-9.
9. Risken H (1996) The Fokker-Planck Equation Springer Verlag Berlin Heidelberg.
10. Siegert AJ (1951) On the first passage time probability problem. Phys Rev 81: 617-623.
11. Johannesma PIM (1968) Diffusion models for the stochastic activity of neurons. In: Caianiello ER, ed. Neural Networks: Proceedings of the School on Neural Networks Ravello, June 1967 Springer-Verlag Verlag. pp 116-144.
12. Brunel N, Chance FS, Fourcaud N, Abbott LF (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86: 2186-2189.
13. Fourcaud N, Brunel N (2002) Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput 14: 2057-2110.
14. Moreno-Bote R, Parga N (2006) Auto- and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses. Phys Rev Lett 96: 028101.
15. Chizhov AV, Graham LJ (2008) Efficient evaluation of neuron populations receiving colored-noise current based on a refractory density method. Phys Rev E 77: 011910.
16. Sirovich L, Omurtag A, Knight BW (2000) Dynamics of neuronal populations: The equilibrium solution. SIAM J Appl Math 60: 2009-2028.
17. Sirovich L (2003) Dynamics of neuronal populations: eigenfunction theory; some solvable cases. Network: Comput Neural Systems 14: 249-272.
18. Omurtag A, Knight BW, Sirovich L (2000) On the simulation of large populations of neurons. J Comput Neurosci 8: 51-63.
19. Hohn N, Burkitt AN (2001) Shot noise in the leaky integrate-and-fire neuron. Phys Rev E 63: 1-11.
20. Wolff L, Lindner B (2008) Method to calculate the moments of the membrane voltage in a model neuron driven by multiplicative filtered shot noise. Phys Rev E 77.
21. Jacobsen M, Jensen AT (2007) Exit times for a class of piecewise exponential markov processes with two-sided jumps. Stoch Proc Appl 117: 1330-1356.
22. Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-andfire neurons with low firing rates. Neural Comput 11: 1621-1671.
23. Lindner B, Schimansky-Geier L (2001) Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett 86: 2934-2937.
24. Gerstner W (2000) Population dynamics of spiking neurons: fast transients, asynchronous states, and locking. Neural Comput 12: 43-89.
25. Douglass JK, Wilkens L, Pantazelou E, Moss F (1993) Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365: 337-340.
26. Levin JE, Miller JP (1996) Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance. Nature 380: 165-168.
27. Cordo P, Inglis JT, Sabine V, Collins JJ, Merfeld DM, et al. (1996) Noise in human muscle spindles. Nature 383: 769-770.
28. McDonnell MD, Abbott D (2009) What is stochastic resonance? definitions, misconceptions, debates, and its relevance to biology. PLoS Comput Biol 5: e1000348. doi:10.1371/journal.pcbi.1000348.
29. Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8: 183-208.
30. Tetzlaff T, Buschermöhle M, Geisel T, Diesmann M (2003) The spread of rate and correlation in stationary cortical networks. Neurocomputing 52-54: 949-954.
31. De la Rocha J, Doiron B, Shea-Brown E, Kresimir J, Reyes A (2007) Correlation between neural spike trains increases with firing rate. Nature 448: 802-807.
32. Kempter R, Gerstner W, van Hemmen JL (1999) Hebbian learning and spiking neurons. Phys Rev E 59: 4498-4514.
33. Morrison A, Diesmann M, Gerstner W (2008) Phenomenological models of synaptic plasticity based on spike-timing. Biol Cybern 98: 459-478.
34. Helias M, Rotter S, Gewaltig M, Diesmann M (2008) Structural plasticity controlled by calcium based correlation detection. Front Comput Neurosci 2: doi:10.3389/neuro.10.007.2008.
35. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity - strengthening correlated input pathways. Biol Cybern 101: 81-102.
36. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity - symmetry breaking. Biol Cybern 101: 103-114.
37. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III. Partially connected neurons driven by spontaneous activity. Biol Cybern 101: 411-426.
38. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL (2009) Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV. Structuring synaptic pathways among recurrent connections. Biol Cybern 101: 427-444.
39. Richardson MJE (2007) Firing-rate response of linear and nonlinear integrateand- fire neurons to modulated current-based and conductance-based synaptic drive. Phys Rev E 76: 1-15.
40. Richardson MJE (2008) Spike-train spectra and network response functions for non-linear integrate-and-fire neurons. Biol Cybern 99: 381-392.
41. De Kamps M (2003) A simple and stable numerical solution for the population density equation. Neural Comput 15: 2129-2146.
42. Poulet J, Petersen C (2008) Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice. Nature 454: 881-5.
43. Goedeke S, Diesmann M (2008) The mechanism of synchronization in feedforward neuronal networks. New J Phys 10: 015007.
44. Morrison A, Straube S, Plesser HE, Diesmann M (2007) Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Comput 19: 47-79.
45. Hanuschkin A, Kunkel S, Helias M, Morrison A, Diesmann M (2010) A general and efficient method for incorporating precise spike times in globally time-driven simulations. Submitted.
46. Ricciardi LM, Di Crescenzo A, Giorno V, Nobile AG (1999) An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. MathJaponica 50: 247-322.
47. Van den Broeck C, Hänggi P (1984) Activation rates for nonlinear stochastic flows driven by non-gaussian noise. Phys Rev A 30: 2730-2736.
48. Hanggi P, Talkner P (1985) First-passage time problems for non-Markovian processes. Phys Rev A 32: 1934-1937.
49. Helias M, Deger M, Diesmann M, Rotter S (2010) Equilibrium and response properties of the integrate-and-fire neuron in discrete time. Front Comput Neurosci 3: doi:10.3389/neuro.10.029.2009.
50. van Vreeswijk C, Sompolinsky H (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274: 1724-1726.
51. Risken H (1989) The Fokker-Planck Equation Springer, 2nd edition.
52. Collins JJ, Chow CC, Capela AC, Imhoff TT (1996) Aperiodic stochastic resonance. Phys Rev E 54: 5575-5584.
53. Fetz E, Gustafsson B (1983) Relation between shapes of postsynaptic potentials and changes in firing probability of cat motoneurones. J Physiol (Lond) 341: 387-410.
54. Knox CK, Poppele RE (1977) Correlation analysis of stimulus-evoked changes in excitability of spontaneously firing neurons. J Neurophysiol 40: 616-625.
55. Silberberg G, Bethge M, Markram H, Pawelzik K, Tsodyks M (2004) Dynamics of population codes in ensembles of neocortical neurons. J Neurophysiol 91: 704-709.
56. DeWeese MR, Zador AM (2006) Non-gaussian membrane potential dynamics imply sparse, synchronous activity in auditory cortex. J Neurosci 26: 12206-12218.
57. Herz AVM, Gollisch T, Machens CK, Jaeger D (2006) Modeling single-neuron dynamics and computations: A balance of detail and abstraction. Science 314: 80-84.
58. Poirazi P, Mel BW (2001) Impact of active dendrites and structural plasticity on the memory capacity of neural tissue. Neuron 29: 779-796.
59. Renart A, De La Rocha J, Bartho P, Hollender L, Parga N, et al. (2010) The asynchronous state in cortical cicuits. Science 327: 587-590.
60. Bi Gq, Poo Mm (1998) Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18: 10464-10472.
61. Hebb DO (1949) The organization of behavior: A neuropsychological theory. New York: John Wiley & Sons.
62. Morrison A, Aertsen A, Diesmann M (2007) Spike-timing dependent plasticity in balanced random networks. Neural Comput 19: 1437-1467.
63. Fourcaud-Trocmé N, Hansel D, van Vreeswijk C, Brunel (2003) How spike generation mechanisms determine the neuronal response to fluctuating inputs. J Neurosci 23: 11628-11640.
64. Naundorf B, Geisel T, Wolf F (2005) Action potential onset dynamics and the response speed of neuronal populations. J Comput Neurosci 18: 297-309.
65. Kuhn A, Aertsen A, Rotter S (2003) Higher-order statistics of input ensembles and the response of simple model neurons. Neural Comput 15: 67-101.