Randall K Powers, Adrienne Fairhall, & Marc D Binder
Department of Physiology & Biophysics, University of Washington School of Medicine, Seattle, WA 98195 USA

https://doi.org/10.36866/pn.61.40

Individual neurones respond to particular features of their synaptic inputs and encode these features in their spiking activity. Although feature selection is generally assumed to arise from the patterns of connectivity in a neural circuit, neurones driven with a repeated complex current input fire precisely at certain times (Bryant & Segundo, 1976; Mainen & Sejnowski, 1995), showing that feature selection also occurs at the single neurone level. What feature or features of a time­varying current input cause a neurone to fire? How are these features determined by the neurone’s biophysics?

The best estimate of the spike­triggering feature of the input to a neurone is found by applying a Gaussian white noise stimulus and using spike-triggered reverse correlation (de Boer & Kuyper, 1968) to compute the average stimulus trajectory preceding spikes (Bryant & Segundo 1976). This trajectory is known as the spike-triggered average, or STA. For many neurone types, STAs are characterized by a shallow hyperpolarizing trough followed by a more rapid depolarizing peak immediately preceding the spike (Aguera y Arcas et al. 2003; Powers et al. 2005). Examining this triggering process permits an understanding of the computation performed by the neurone. For example, the duration of the depolarizing peak in the STA may be a measure of the integration window for the detection of coincident synaptic inputs. Similarly, the hyperpolarizing trough in the STA may indicate that excitatory inputs are more likely to trigger spikes when excitation is preceded by inhibition.

The biophysical mechanisms governing feature selection in neurones can be difficult to disentangle. We and other investigators have proposed that the period of hyperpolarization in the STA may be required to decrease Na+ channel inactivation for a short time, increasing the spike-triggering efficacy of any subsequent depolarizing input (Poliakov et al. 1997; Powers et al. 2005; Svirkis et al. 2004). Our recent work (Aguera y Arcas et al. 2003; Powers et al. 2005) shows that the shape of the STA also reflects the dependence of firing on the occurrence of previous spikes; in the case of motoneurones, through the medium­duration afterhyperpolarization (mAHP) mediated by SK-type Ca2+ ­activated K+ channels. We quantify this effect using an autoregressive-moving average (ARMA) process, which provides separate estimates of the contribution of spiking history (AR) and stimulus history (MA) to the spike probability (Powers et al. 2005). We find that the STA is composed of two components, one due only to the stimulus, and one reflecting the influence of the mAHP produced by the preceding spikes. Figure 1 shows the effects of the specific SK-channel blocker, apamin, on the MA (upper traces) and AR (lower traces) kernels before (black) and after (red) applying apamin to a rat hypoglossal motoneurone. Selective block of the SK-channels leads to a reduction of the influence of spike history on spike probability, as reflected by the smaller AR component, without affecting the influence of stimulus history.

Recently developed analytical methods (cf. Aguera y Arcas et al. 2003) allow us to extract a more complete picture of the features that trigger a spike. Computing not just the mean but the second order moment (specifically, the eigenvectors of the covariance matrix) of the spike-triggered stimulus distribution allows one to find a set of stimulus features implicated in triggering a spike. The probability of spiking is then given by a decision function defined over that set of features (Fig. 2). The challenge is to determine how various aspects of this process are influenced by the biophysical features of different neurones. In particular, how does spike history determine the neurone’s sensitivity to different features of its input? The figure posits three ways to represent the effects of spike history on the subsequent probability of spiking: (1) as an additional input to the decision function, (2) as an influence on the shape of the spike-triggering stimulus features, and (3) as an influence on the shape of the decision function.

Several labs (Powers et al. 2005; Aguera y Arcas et al. 2003; Truccolo et al. 2005; Paninski et al. 2004) are currently investigating a variety of methods to account for spike history in models of neural coding. These efforts are leading to a better understanding of how a neurone’s own activity regulates its sensitivity to its inputs.

Acknowledgments

Work in our laboratories has been supported in part by grants from the National Science Foundation (IBN­9986167), the National Institutes of Health (NS-26840 and NS-31925), the Burroughs-Wellcome Trust and the Alfred P. Sloan Foundation.

References

Aguera y Arcas B, Fairhall AL & Bialek W (2003). Computation in a single neuron: Hodgkin-Huxley revisited. Neural Comput 15, 1715­1749.

Bryant HL & Segundo, JP (1976). Spike initiation by transmembrane current: a white-noise analysis. J Physiol 260, 279-314.

Mainen ZF & Sejnowski TJ (1995). Reliability of spike timing in neocortical neurons. Science 268, 1503-1506.
de Boer E & Kuyper, P (1968). Triggered correlation. IEEE Trans Biomed Engr 15, 169-179.

Poliakov AV, Powers RK & Binder MD (1997). Functional identification of the input-output transforms of motoneurones in the cat and rat. J Physiol 504, 401-424.

Powers RK, Dai, Y, Bell, BM, Percival, DB & Binder, MD (2005). Contributions of the input signal and prior activation history to the discharge behaviour of rat motoneurones. J Physiol 562, 707-724.

Paninski L, Pillow, JW & Simoncelli, E. (2004) Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model. Neural Comput 16, 2533-2561.

Svirkis G, Kotak V, Sanes D & Rinzel J (2004). Sodium along with low threshold potassium currents enhance coincidence detection of subthreshold noisy signals in MSO neurons. J Neurophysiol 91, 2465-2473.

Truccolo W, Eden, UT, Fellows, MR, Donoghue, JP and Brown, EN (2005). A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. J Neurophysiol 93, 1074-1089.