From early paired recordings of connected neurons, it has often been noted that the typical spike sequence changes from one neuron to the next, suggesting that a change in feature representation also occurs (Hubel and Wiesel, 1961
; Bishop et al., 1962
; Hamamoto et al., 1994
; Benardete and Kaplan, 1997
; Ruksenas et al., 2000
). There has been considerable progress in elucidating how stimuli are represented in spike trains, especially in the visual system (Bialek et al., 1991
; Meister and Berry, 1999
). By comparison, there has been far less effort aimed at understanding how or why stimulus representations change from one neuron to the next. One reason is the technical difficulty of recording from two cells simultaneously for the length of time it takes to characterize firing behavior. Another reason is that synaptic convergence is quite high in most neural systems. Instances where a neuron receives input from only one or a few presynaptic cells are uncommon. Such an arrangement, though not necessary, makes the analysis of spike coding more tractable. The calyx of Held in the brainstem is an ideal example (von Gersdorff and Borst, 2002
), but access to the pre- and postsynaptic cells is difficult, except in vitro
. In neocortex, where cells are multiply innervated, some insights about coding have been obtained from connected cell pairs (Thomson et al., 2002
), but the generally hyperpolarized state of neurons in vitro
precludes expression of the normal activity pattern expected in vivo
. Since neural coding is likely to be typical only in vivo
, it is worthwhile to find an intact system where the inputs and outputs of a neuron can be readily recorded and realistic stimuli can be used. The macaque LGN comes close to fulfilling these criteria.
We have shown that the relevant stimulus features are more efficiently coded by LGN neurons than by retinal ganglion cells, based on the finding that each LGN spike conveys more information than is carried by each retinal spike. This boost in information per spike helps to compensate for a potentially large loss of information, as it has been recognized that many retinal EPSPs do not lead to LGN spikes (Hubel and Wiesel, 1961
). In our population of neurons, mean EPSP efficacy was 53% during the unique stimulus sequences. In the presence of synaptic noise, one might have expected the information transfer efficacy to end up at or below 53%, as it did when retinal spikes were dropped through random failures in synaptic transmission (). Instead, information transfer efficacy averaged 72% (). Notably, EPSP efficacy never reached 100% in any cell, yet a third of the population achieved lossless information transfer rates. In these cases, the increase in information per spike was the maximum allowed by the laws of information transmission (Cover and Thomas, 1991
). This result indicates that LGN neurons alter the incoming representations of the visual stimulus, and that a reliable mechanism determines which EPSPs elicit LGN spikes (Carandini et al., 2007
; Casti et al., 2008
The search for relevant stimulus dimensions revealed two distinct temporal filters for retinal ganglion cells as well as LGN neurons. Multiple filters have been reported in salamander retinal ganglion cells (Fairhall et al., 2006
). However, the filters in the macaque LGN were not simply inherited from the retina. By recording the EPSPs as well as the LGN spikes, we could demonstrate that the retinal and LGN filters were genuinely different. The higher information content of LGN spikes suggests that the altered filters represent the statistics of the naturalistic stimuli better than ganglion cells. Although pre- and postsynaptic cells have not been recorded simultaneously in V1, it is clear that the receptive fields of both simple and complex cells are also best described by multiple filters (Touryan et al., 2002
; Rust et al., 2005
; Chen et al., 2007
). Thus neural responses at every major stage of the early visual system—retina, V1, and now LGN—appear to be influenced by multiple stimulus combinations, with signal transformations at every step of the pathway. Spike-triggered averaging methods have proved insufficient for revealing the full complexity of neural responses. When used with non-Gaussian stimuli, these methods are inherently biased, leading to features that are shifted away from relevant dimensions by a finite vector that does not disappear even in the limit of infinite data (Paninski, 2003
; Sharpee et al., 2004
). This finite bias is large enough to obscure differences between the relevant stimulus features of retinal and LGN neurons ().
The increased information per spike means a greater modulation of the average firing rate in response to different stimuli relative to the average rate for all stimuli (Eq. 1
. There are multiple ways to increase firing rate modulation. Previous in vitro
studies showed that ganglion cell activity consists of separate “events” of high firing separated by epochs with no spikes (Berry et al., 1997
; Fairhall et al., 2006
). In this case, information per spike can be increased by reducing the duration of the firing events, or by dropping some events altogether. Given fewer events, when they do occur they signal stimuli from a smaller subset, reducing the uncertainty of which stimulus was presented and thus leading to more information. Alternatively, shortening the average duration of firing events allows one to distinguish a greater number of stimuli. Under our stimulus conditions, the number of firing events was similar for connected neural pairs (p = 0.1, Wilcoxon paired test), and the firing events (as defined by Berry et al. 1997
) had similar duration between minima (p = 0.3, Wilcoxon paired test). Therefore, neither of these mechanisms explain the information capacity differences between ganglion cells and LGN neurons. Instead, the firing events in vivo
appeared better “defined” by clear temporal sharpening of the firing peaks rather than the absence of firing (), reflecting the importance of changes in spike rate gain as a means of increasing information capacity in single spikes.
To understand how the LGN neurons could achieve greater reliability in reporting different stimuli, we analyzed segments of the retinal spike trains that were most effective in eliciting LGN spikes. This analysis showed that inputs arriving within a ~30 ms period determine LGN firing. This is the same period during which nearly all EPSPs summate to reach spike threshold (Carandini et al., 2007
; Sincich et al., 2007
). Over this time scale, such summation is mediated mostly by NMDA current, with the effect being more pronounced at more depolarized membrane potentials (Sillito et al., 1990
; Blitz and Regehr, 2003
; Augustinaite and Heggelund, 2007
). Very closely arriving EPSPs yield the most reliable LGN responses, and consequently if one computed retinal filters from such EPSPs they would be nearly identical to LGN filters. However, as the temporal jitter between EPSP pairs begins to increase, the first “priming” EPSP is shifted in time and would begin to introduce noise into the retinal filters that would lower their information capacity. A second source of noise for the retinal spikes would be the EPSPs occurring at intervals longer than 30 ms and not associated with LGN spikes (several examples appear in ). These unsuccessful EPSPs occur throughout the stimulus ensemble, bringing irrelevant stimuli into the filter computation. The requirement for EPSP summation constrains the relevant stimuli to those that generate EPSP sequences which are more effective for reaching an LGN neuron’s threshold, thereby refining the stimulus representations transmitted to cortex. Consequently, reliability is increased and LGN neurons can transmit more information with fewer spikes.
EPSP summation may not be the only way to raise information content per spike. In the cat inferior colliculus of the auditory system, it was found that more information was carried by single spikes when spike trains were sparser (Escabi et al., 2005
). It was proposed that the cells with a lower firing rate had a higher spike threshold, and that this higher threshold could account for the increased information capacity (Goldman, 2004
; Escabi et al., 2005
). When the information in bits per spike was multiplied by the spike rate, this produced an information transmission rate that was always lower for spike trains with lower average firing rates. In contrast, when retinal ganglion cells or LGN neurons are considered alone, we found no relationship between spike rate and bit rate (RGC, p > 0.5; LGN, p > 0.1; Fisher Z transform test). As shown in , in one third of the LGN cells information rate did not decrease despite the decrease in the firing rate. Instead, the re-encoding that occurs in LGN neurons allowed some of them to maintain their information transmission rates, despite a firing rate that was lower than retinal ganglion cells. This suggests that a difference in spike threshold is unlikely to be a sufficient mechanism for the preserved information transfer in the LGN.
Computations by neurons are usually cast in terms of an operation performed on multiple convergent inputs to yield an output. Our analysis of a major synaptic relay in the vertebrate visual system shows that even when neurons are driven by only one input they can perform a time-dependent operation having biological utility. The temporal receptive field is altered rather than faithfully relayed, information is well conserved, and the spike rate is reduced, implying a sparser representation at a lower metabolic cost (Laughlin, 2001
; Olshausen and Field, 2004
). If the information content per spike continues to increase along the visual pathways, it would help explain how higher cortical areas can represent complex stimuli with so few spikes.