Skip to main content
PMC home page
Biophysical Journal logoLink to Biophysical Journal
. 1974 Aug;14(8):567–582. doi: 10.1016/S0006-3495(74)85936-9

Cross-Correlation Functions for a Neuronal Model

C K Knox
PMCID: PMC1334553  PMID: 4851214

Abstract

Cross-correlation functions, RXY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, RXY(t,τ) = fU [θ-h(τ), t + τ] {h′(τ) + EU [u′(t + τ)]} for positive values of this quantity, where fU(u,t) is the probability density function of U(t) and EU [u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in RXY(t,τ) for a neuron subjected only to excitation. (3) For large τ, RXY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) RXY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time.

Full text

PDF
569

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bryant H. L., Jr, Marcos A. R., Segundo J. P. Correlations of neuronal spike discharges produced by monosynaptic connections and by common inputs. J Neurophysiol. 1973 Mar;36(2):205–225. doi: 10.1152/jn.1973.36.2.205. [DOI] [PubMed] [Google Scholar]
  2. COOMBS J. S., CURTIS D. R., ECCLES J. C. The electrical constants of the motoneurone membrane. J Physiol. 1959 Mar 12;145(3):505–528. doi: 10.1113/jphysiol.1959.sp006158. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Knight B. W. Dynamics of encoding in a population of neurons. J Gen Physiol. 1972 Jun;59(6):734–766. doi: 10.1085/jgp.59.6.734. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Knox C. K., Poppele R. E. A neuronal circuit modeling program. Comput Biomed Res. 1973 Oct;6(5):487–497. doi: 10.1016/0010-4809(73)90081-5. [DOI] [PubMed] [Google Scholar]
  5. Marmarelis P. Z., Naka K. I. Nonlinear analysis and synthesis of receptive-field responses in the catfish retina. I. Horizontal cell leads to ganglion cell chain. J Neurophysiol. 1973 Jul;36(4):605–618. doi: 10.1152/jn.1973.36.4.605. [DOI] [PubMed] [Google Scholar]
  6. Moore G. P., Segundo J. P., Perkel D. H., Levitan H. Statistical signs of synaptic interaction in neurons. Biophys J. 1970 Sep;10(9):876–900. doi: 10.1016/S0006-3495(70)86341-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. RALL W. Membrane time constant of motoneurons. Science. 1957 Sep 6;126(3271):454–454. doi: 10.1126/science.126.3271.454. [DOI] [PubMed] [Google Scholar]
  8. Rall W. Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. J Neurophysiol. 1967 Sep;30(5):1138–1168. doi: 10.1152/jn.1967.30.5.1138. [DOI] [PubMed] [Google Scholar]
  9. Stein R. B., French A. S., Holden A. V. The frequency response, coherence, and information capacity of two neuronal models. Biophys J. 1972 Mar;12(3):295–322. doi: 10.1016/S0006-3495(72)86087-9. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES