Rate dynamics of leaky integrate-and-fire neurons with strong synapses

Frontiers in Computational Neuroscience

Volumn 4, Issue , 2010, Pages

  Nordlie, Eilen ^a   Tetzlaff, Tom ^a   Einevoll, Gaute T ^a  

^a NORWEGIAN UNIVERSITY OF LIFE SCIENCES   (Norway)

Author keywords

Diffusion limit; Finite synaptic weights; Firing rate model; Leaky integrate and fire neuron; Linear response; Linear nonlinear model; Spiking neuron model; Transfer function

Indexed keywords

DIFFUSION LIMITS; INTEGRATE-AND-FIRE NEURONS; LINEAR RESPONSE; LINEAR-NONLINEAR MODELS; SPIKING NEURON MODELS; SYNAPTIC WEIGHT;

CUTOFF FREQUENCY; DYNAMICS; MODULATION; NONLINEAR SYSTEMS; TRANSFER FUNCTIONS;

NEURONS;

ACCURACY; AMPLITUDE MODULATION; ARTICLE; CELL POPULATION; EXCITATORY POSTSYNAPTIC POTENTIAL; FREQUENCY MODULATION; LINEAR SYSTEM; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; NERVE CELL; NONLINEAR SYSTEM; PREDICTION; SIGNAL DETECTION; SPIKE WAVE; STATISTICAL DISTRIBUTION; STIMULUS RESPONSE; SYNAPTIC POTENTIAL; SYNAPTIC TRANSMISSION;

EID: 80052031291     PISSN: 16625188     EISSN: None     Source Type: Journal    
DOI: 10.3389/fncom.2010.00149     Document Type: Article

References (46)

1. Arsiero, M., Luscher, H.-R., Lundstrom, B. N., and Giugliano, M. (2007). The impact of input fluctuations on the frequency-current relationships of layer 5 pyramidal neurons in the rat medial prefrontal cortex. J. Neurosci. 27, 3274-3284.
2. Bannister, A. P., and Thomson, A. M. (2007). Dynamic properties of excitatory synaptic connections involving layer 4 pyramidal cells in adult rat and cat neocortex. Cerebr. Cortex 17, 2190-2203.
3. Blomquist, P., Devor, A., Indahl, U. G., Ulbert, I., Einevoll, G. T., and Dale, A. M. (2009). Estimation of thalamocortical and intracortical network models from joint thalamic single-electrode and cortical laminar-electrode recordings in the rat barrel system. PLoS Comput. Biol. 5(3), e1000328. doi: 10.1371/journal.pcbi.1000328.
4. Boucsein, C., Nawrot, M. P., Rotter, S., Aertsen, A., and Heck, D. (2005). Controlling synaptic input patterns in vitro by dynamic photo stimulation. J. Neurophysiol. 94, 2948-2958.
5. Boucsein, C., Tetzlaff, T., Meier, R., Aertsen, A., and Naundorf, B. (2009). Dynamical response properties of neocortical neuron ensembles: multiplicative versus additive noise. J. Neurosci. 29, 1006-1010.
6. Brown, E. N., Barbieri, R., Ventura, V., Kaas, R. E., and Frank, L. M. (2001). The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput. 14, 325-346.
7. Brunel, N., Chance, F. S., Fourcaud, N., and Abbott, L. F. (2001). Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys. Rev. Lett. 86, 2186-2189.
8. Bruno, R. M., and Sakmann, B. (2006). Cortex is driven by weak but synchronously active thalamocortical synapses. Science 312, 1622-1627.
9. Cardanobile, S., and Rotter, S. (2010). "Simulation of stochastic point processes with defined properties," in Analysis of Parallel Spike Trains, eds S. Rotter and S. Grun (Berlin: Springer), 343-382.
10. Cleland, B., Dubin, M., and Levick, W. (1971). Simultaneous recording of input and output of lateral geniculate neurones. Nat. New Biol. 231, 191-192.
11. Destexhe, A., and Sejnowski, T. J. (2009). The Wilson-Cowan model, 36 years later. Biol. Cybern. 101, 1-2.
12. Devroye, L. (1986). Non-Uniform Random Variate Generation. New York: Springer-Verlag.
13. DeWeese, M. R., and Zador, A. M. (2006). Non-gaussian membrane potential dynamics imply sparse, synchronous activity in auditory cortex. J. Neurosci. 26, 12206-12218.
14. Fetz, E., Toyama, K., and Smith, W. (1991). "Synaptic interactions between cortical neurons," In Cerebral Cortex, Vol. 9, Chapter 1, ed. A. Peters (New York and London: Plenum Press), 1-47.
15. Fourcaud, N., and Brunel, N. (2002). Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput. 14, 2057-2110.
16. Fourcaud-Trocme, N., Hansel, D., van Vreeswijk, C., and Brunel, N. (2003). How spike generation mechanisms determine the neuronal response to fluctuating inputs. J. Neurosci. 23, 11628-11640.
17. Gerstner, W. (2000). Population dynamics of spiking neurons: fast transients, asynchronous states, and locking. Neural Comput. 12, 43-89.
18. Gewaltig, M.-O., and Diesmann, M. (2007). NEST (neural simulation tool). Scholarpedia 2, 1430.
19. Helias, M., Deger, M., Rotter, S., and Diesmann, M. (2010). Instantaneous non-linear processing by pulse-coupled threshold units. PLoS Comput. Biol. 6(9), e1000929. doi: 10.1371/journal.pcbi.1000929.
20. Johannesma, P. I. M. (1968). "Diffusion models for the stochastic activity of neurons," in Neural Networks: Proceedings of the School on Neural Networks Ravello, June 1967, ed E. R. Caianiello (Berlin: Springer-Verlag), 116-144.
21. Knight, B. W. (1972a). Dynamics of encoding in a population of neurons. J. General Physiol. 59, 734-766.
22. Knight, B. W. (1972b). The relationship between the firing rate of a single neuron and the level of activity in a population of neurons. J. General Physiol. 59, 767-778.
23. Kondgen, H., Geisler, C., Fusi, S., Wang, X.-J., Luscher, H.-R., and Giugliano, M. (2008). The dynamical response properties of neocortical neurons to temporally modulated noisy inputs in vitro. Cerebr. Cortex 18, 2086-2097.
24. Kuhn, A., Aertsen, A., and Rotter, S. (2004). Neuronal integration of synaptic input in the fluctuation-driven regime. J. Neurosci. 24, 2345-2356.
25. Lapicque, L. (1907). Recherches quantitative sur l'excitation electrique des nerfs traitee comme une polarization. J. Physiol. Pathol. Gen. 9, 620-635.
26. Lee, A., Manns, I., Sakmann, B., and Brecht, M. (2006). Whole-cell recordings in freely moving rats. Neuron 51, 399-407.
27. Lefort, S., Tomm, C., Sarria, J. F., and Petersen, C. C. (2009). The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61, 301-316.
28. Lindner, B., and Schimansky-Geier, L. (2001). Transmission of noise coded versus additive signals through a neuronal ensemble. Phys. Rev. Lett. 86, 2934-2937.
29. Mattia, M., and Del Giudice, P. (2002). Population dynamics of interacting spiking neurons. Phys. Rev. E. 66, 051917.
30. Naundorf, B., Geisel, T., and Wolf, F. (2005). Action potential onset dynamics and the response speed of neuronal populations. J. Comput. Neurosci. 18, 297-309.
31. Nawrot, M. P., Boucsein, C., Rodriguez Molina, V., Riehle, A., Aertsen, A., and Rotter, S. (2008). Measurement of variability dynamics in cortical spike trains. J. Neurosci. Methods 169, 374-390.
32. Nordbo, O., Wyller, J., and Einevoll, G. T. (2007). Neural network firing-rate models on integral form: Effects of temporal coupling kernels on equilibrium- state stability. Biol. Cybern. 97, 195-209.
33. Nordlie, E., Gewaltig, M.-O., and Plesser, H. E. (2009). Towards reproducible descriptions of neuronal network models. PLoS Comput. Biol. 5(8), e1000456. doi: 10.1371/journal.pcbi.1000456.
34. Papoulis, A., and Pillai, S. U. (2002). Probability, Random Variables, and Stochastic Processes, 4th Edn. Boston: McGraw-Hill.
35. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes in C, 2nd Edn. Cambridge: Cambridge University Press.
36. Pressley, J., and Troyer, T. (2009). Complementary responses to mean and variance modulations in the perfect integrate-and-fire model. Biol. Cybern. 101, 63-70.
37. Richardson, M. J. E. (2007). Firing-rate response of linear and nonlinear integrate- and-fire neurons to modulated current-based and conductance-based synaptic drive. Phys. Rev. E. 76, 1-15.
38. Rotter, S., and Diesmann, M. (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling. Biol. Cybern. 81, 381-402.
39. Sakai, H. M. (1992). White-noise analysis in neurophysiology. Physiol. Rev. 72, 491-505.
40. Silberberg, G., Bethge, M., Markram, H., Pawelzik, K., and Tsodyks, M. (2004). Dynamics of population codes in ensembles of neocortical neurons. J. Neurophysiol. 91, 704-709.
41. Sirovich, L. (2008). Populations of tightly coupled neurons: The RGC/LGN system. Neural Comput. 20, 1179-1210.
42. Song, S., Per, S., Reigl, M., Nelson, S., and Chklovskii, D. (2005). Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 3, 0507-0519. doi: 10.1371/journal.pbio.0030068.
43. Tsodyks, M., Pawelzik, K., and Markram, H. (1998). Neural networks with dynamic synapses. Neural Comput. 10, 821-835.
44. Tuckwell, H. C. (1988). Introduction to Theoretical Neurobiology, Vol. 1. Cambridge: Cambridge University Press.
45. Usrey, W. M., Reppas, J. B., and Reid, R. C. (1998). Paired-spike interactions and synaptic efficacy of retinal inputs to the thalamus. Nature 395, 384-387.
46. Wilson, H. R., and Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1-24.