Reliability of Neuronal Responses
Authors: J.Anthony Movshon
Journal: Neuron (2000)

Woody Allen once observed that "80% of success is showing up." In other words, reliability matters, and nowhere more than in the nervous system. But neuronal responses vary from moment to moment. Identical stimuli delivered to sensory neurons never elicit identical responses on repeated trials, and the signals carried by single neurons are therefore imperfect representations of the input signals that give rise to them. The performance of the nervous system is ultimately limited by the fidelity with which signals can be relayed from one neuron to the next, so understanding the nature and causes of this variability is crucial to understanding neural computation. Response variability is a property of synaptic connections, not of neurons themselves: neurons stimulated directly by current injection in the absence of synaptic input give highly stereotyped and precise responses (8Mainen Z.F. Sejnowski T.J Science. 1995; 268: 1503-1506Crossref PubMed Scopus (1388) Google Scholar). Variability must therefore arise as a result of the variability of the postsynaptic current elicited by stereotyped firing in a presynaptic neuron, which may be substantial (2Bekkers J.M. Stevens C.F Proc. Natl. Acad. Sci. USA. 1991; 88: 7834-7838Crossref PubMed Scopus (422) Google Scholar). Neural circuits interconnected by unreliable synapses will naturally produce spikes whose timing and frequency vary, even if driven by unvarying signals. Neuronal variability and its importance for signaling has been most extensively studied in the mammalian visual system, first by Barlow and his colleagues in the retina (1Barlow H.B. Levick W.R J. Physiol. Lond. 1969; 200: 1-24Google Scholar), and later by others in visual cortex (e.g.6Heggelund P. Albus K Exp. Brain Res. 1978; 32: 197-211Crossref PubMed Scopus (98) Google Scholar, 12Tolhurst D.J. Movshon J.A. Thompson I.D Exp. Brain Res. 1981; 41: 414-419PubMed Google Scholar). Comparisons of variability in these different visual structures show that the responses of retinal ganglion cells are rather reliable, while those of cortical cells are much more variable. This increase in variability has important implications for cortical computation (10Shadlen M.N. Newsome W.T J. Neurosci. 1998; 18: 3870-3896PubMed Google Scholar), but its exact nature and origins are imperfectly understood. The variability of neuronal spike trains is often characterized with reference to the variability expected of a Poisson process, in which each event occurs with a fixed probability that is independent of the occurrence of other events. For a Poisson process, the variance of the number of events counted in a set of equal time intervals is equal to the mean count across the intervals. For neuronal responses, the variance of this counting distribution is usually proportional to the mean count, but typically not equal to it—the constant of proportionality is known as the Fano factorF, and is exactly 1 for a train of Poisson events. If F is smaller than 1, the variance of the counting distribution is low and reliability is high, compared to the Poisson benchmark. In this issue of Neuron, Kara and his colleagues (7Kara P. Reinagel P. Reid R.C Neuron. 2000; 27 (this issue,): 635-646Abstract Full Text Full Text PDF PubMed Scopus (254) Google Scholar) report the first direct comparison of response variability in neurons simultaneously recorded from retina, lateral geniculate nucleus (LGN), and layer IV of primary visual cortex. In a technical tour de force, they placed electrodes in all three structures and measured responses simultaneously while activating the neurons with a drifting sinusoidal grating target chosen to drive all the recorded neurons well. Their measurements confirm earlier impressions that response variability increases from retina to cortex. F is very small for retinal ganglion cells and approximately doubles at each successive processing stage. Despite this increase, Kara et al. report values of F for cortical neurons to be substantially less than 1, suggesting that the variability of cortical responses can be substantially less than previously reported. This result probably reflects the fact that the cortical recordings in their study were made from simple cells in layer IV. It is reasonable to suppose that these neurons, which receive strong and direct input from the LGN through synapses of unusual strength and reliability, would be less variable in their discharge than other cortical neurons primarily driven by intracortical circuits (10Shadlen M.N. Newsome W.T J. Neurosci. 1998; 18: 3870-3896PubMed Google Scholar). Only one other previous study has reported such low variability for visual cortical responses (5Gur M. Beylin A. Snodderly D.M J. Neurosci. 1997; 17: 2914-2920PubMed Google Scholar); much of the data from that study probably also came from layer IV. Other studies in which neurons were recorded from all layers usually show values of F in the range of 1–2; the values are typically somewhat higher in anesthetized animals (like those of Kara et al.) than in awake, behaving animals (e.g.13Vogels R. Spileers W. Orban G.A Exp. Brain Res. 1989; 77: 432-436Crossref PubMed Scopus (185) Google Scholar, 4Britten K.H. Shadlen M.N. Newsome W.T. Movshon J.A Vis. Neurosci. 1993; 10: 1157-1169Crossref PubMed Scopus (438) Google Scholar, 5Gur M. Beylin A. Snodderly D.M J. Neurosci. 1997; 17: 2914-2920PubMed Google Scholar). Kara and his colleagues conducted simulations to try to understand the reason for their findings, and the explanation they offer is based on the relationship between the distributions of spike counts and the distribution of interspike intervals in neuronal spike trains (see 9Rieke F. Warland D. de Ruyter van Steveninck R. Bialek W Spikes. MIT Press, Cambridge, MA1997Google Scholar, for a comprehensive account). In a Poisson event train, the time intervals between successive events are exponentially distributed; the irregularity of the distribution of counts in a particular time interval derives directly from the irregularity of spike timing. The interspike interval distribution for many neurons is approximately exponential, but the absolute and relative refractoriness of neuronal spiking reduce the frequency of short intervals below the value expected from an exponential distribution (11Teich M.C. Matin L. Cantor B.I J. Opt. Soc. Am. 1978; 68: 386-402Crossref PubMed Scopus (42) Google Scholar). By forbidding these short intervals, neuronal refractoriness increases the regularity of interspike interval distributions, and this decreases the variability of spike count distributions, especially when neuronal firing rates are high and the average interspike interval is brief. The simulations conducted by Kara et al. suggest that the differences in variability they observe can be explained simply by changes in the refractoriness of the neurons and by changes in the average discharge rates elicited by visual stimuli (cf. 3Berry M.J.I. Meister M J. Neurosci. 1998; 18: 2200-2211PubMed Google Scholar). In this model, responses in retinal ganglion cells are very regular because these cells have relatively long refractory periods that force spikes to be spaced more evenly; variability is further reduced because these cells give vigorous visual responses in which the average interspike interval is small compared to the refractory period. Responses in cortical cells are irregular because their refractory periods are shorter, and their lower firing rates mean that interspike intervals are on average rather long compared to refractory periods. The quantitative fits to this model are impressively good, but the interpreting these fits is not as simple as it might seem. It is difficult to understand why refractoriness in cortical neurons should be briefer than in retinal neurons, and it is well to bear in mind an interpretive caution raised by Kara et al.: the refractory period in their model may reflect refractoriness at any stage in the cortical circuit and need not directly reflect the refractoriness of spike generation in the cell being recorded. The results of Kara et al. show that central neuronal responses to sensory stimuli are more variable than those of neurons in the periphery. They also show that the responses of at least some cortical neurons are quite reliable, though one may doubt that such high reliability will be found for most neurons lying outside thalamic recipient layers in cortex. Their simulations offer an appealingly simple descriptive account of the differences in firing pattern between retina and cortex, although the relationship between these simulations and the machinery of neuronal circuits is unclear. Whatever the mechanisms involved, it is worth noting that the trend for response variability to increase from peripheral to central structures is abruptly arrested when signals reach the cerebral cortex. Response variability in "higher" cortical areas is probably not different from variability in primary sensory areas; rather, a roughly constant—and substantial—level of response variability is observed throughout the cerebral cortex (see 10Shadlen M.N. Newsome W.T J. Neurosci. 1998; 18: 3870-3896PubMed Google Scholar).