Spike-triggered average

The spike-triggered averaging (STA) is a tool for characterizing the response properties of a neuron using the spikes emitted in response to a time-varying stimulus. The STA provides an estimate of a neuron's linear receptive field. It is a useful technique for the analysis of electrophysiological data.

Diagram showing how the STA is calculated. A stimulus (consisting here of a checkerboard with random pixels) is presented, and spikes from the neuron are recorded. The stimuli in some time window preceding each spike (here consisting of 3 time bins) are selected (color boxes) and then averaged (here just summed for clarity) to obtain the STA. The STA indicates that this neuron is selective for a bright spot of light just before the spike, located in the top left corner of the checkerboard.

Mathematically, the STA is the average stimulus preceding a spike.[1][2][3][4] To compute the STA, the stimulus in the time window preceding each spike is extracted, and the resulting (spike-triggered) stimuli are averaged (see diagram). The STA provides an unbiased estimate of a neuron's receptive field only if the stimulus distribution is spherically symmetric (e.g., Gaussian white noise).[3][5][6]

The STA has been used to characterize retinal ganglion cells,[7][8] neurons in the lateral geniculate nucleus and simple cells in the striate cortex (V1) .[9][10] It can be used to estimate the linear stage of the linear-nonlinear-Poisson (LNP) cascade model.[4] The approach has also been used to analyze how transcription factor dynamics control gene regulation within individual cells.[11]

Spike-triggered averaging is also commonly referred to as reverse correlation or white-noise analysis. The STA is well known as the first term in the Volterra kernel or Wiener kernel series expansion.[12] It is closely related to linear regression, and identical to it in common circumstances.

  1. ^ de Boer and Kuyper (1968) Triggered Correlation. IEEE Transact. Biomed. Eng., 15:169-179
  2. ^ Marmarelis, P. Z. and Naka, K. (1972). White-noise analysis of a neuron chain: an application of the Wiener theory. Science, 175:1276-1278
  3. ^ a b Chichilnisky, E. J. (2001). A simple white noise analysis of neuronal light responses. Network: Computation in Neural Systems, 12:199-213
  4. ^ a b Simoncelli, E. P., Paninski, L., Pillow, J. & Swartz, O. (2004). "Characterization of neural responses with stochastic stimuli". In M. Gazzaniga (Ed.) The Cognitive Neurosciences, III (pp. 327-338). MIT press.
  5. ^ Paninski, L. (2003). Convergence properties of some spike-triggered analysis techniques. Network: Computation in Neural Systems 14:437-464
  6. ^ Sharpee, T.O., Rust, N.C., & Bialek, W. (2004). Analyzing neural responses to natural signals: Maximally informative dimensions. Neural Computation 16:223-250
  7. ^ Sakai and Naka (1987).
  8. ^ Meister, Pine, and Baylor (1994).
  9. ^ Jones and Palmer (1987).
  10. ^ McLean and Palmer (1989).
  11. ^ Lin, Yihan (2015). "Combinatorial gene regulation by modulation of relative pulse timing". Nature. 527 (7576): 54–58. Bibcode:2015Natur.527...54L. doi:10.1038/nature15710. PMC 4870307. PMID 26466562.
  12. ^ Lee and Schetzen (1965). Measurement of the Wiener kernels of a non- linear system by cross-correlation. International Journal of Control, First Series, 2:237-254