How many neurons does it take to see?

How many neurons does it take to see?

A.C. HURLBERT AND A.M. DERRINGTON NEURAL CODING How many neurons does it take to see? Recent experimental results and model simulations shed light o...

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A.C. HURLBERT AND A.M. DERRINGTON

NEURAL CODING

How many neurons does it take to see? Recent experimental results and model simulations shed light on the contribution of individual neurons to coding in the brain, but leave some outstanding questions. That many brain cells are redundant is implied by basic facts of sensory system physiology and serves as a consoling truism for humans who suffer from ageing or indulge in the occasional neurotoxin. This neuronal redundancy raises the important question of what neurons with similar properties are doing when they are not compensating for their degenerated kin. This question is made more piquant by the recent demonstrations by Newsome, Movshon and colleagues [ 1 ] that the behaviour of single neurons can, on average, predict the performance of the whole animal in a certain visual task and, conversely, that by manipulating the activity of a small number of neurons the performance of the whole animal can be altered [2]. If a monkey can ‘see’ with just one neuron, what are the remaining billions doing? New simulations of neuronal behaviour [3] suggest an answer. The question usually appears in the obverse form ‘What do single neurons tell us about vision?‘, the topic of a recent workshop at Newcastle University. There are both historical and modern reasons for challenging the hegemony of the single neuron. In several past experiments, the sensitivity of a single neuron has seemed far less acute than that of the whole animal [4-6]. Furthermore, if each view of each detectable object had a single neuron devoted to it - the extreme implication of Barlow’s ‘single neuron doctrine’ [7] - the combinatorial consequences would overwhelm even the billions of neurons in the visual system. More recently, an enthusiasm has arisen for the notion that visual patterns are coded by the distribution of responses over large populations of less specific neurons. One seemingly potent argument against the suficiency of the single neuron is that the human observer is approximately 30. times more sensitive to luminance contrast than are parvocellular neurons (P cells) in the monkey thalamus, long accepted as a valid model of the human thalamus [S]. Some authors [9] have argued that this difference is so large that we should look to the more sensitive magnocellular cells (M cells) for the basis of contrast detection. Yet P cells are also about 30 times less sensitive to colour contrast than are humans [lo], and the P cell is the only one that relays colour signals to any significant extent. It now seems there are good reasons to discount this and other evidence suggesting single neurons give inadequate measures of a whole animal’s perceptual capabilities. One may simply argue that the whole animal improves on the capability of a single P cell by summing the signals from many of them. As Tolhurst et al. [4] and others have noted, summing many neuronal responses tends to cancel out the noise in each, making the total response more reliable than any of its parts. Yet how and where might 510

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the pooling occur? The neuron that pools, and whose sensitivity should therefore match that of the whole animal, might be difhcult to pinpoint as there need only be one such neuron for a given task. But we should probably look further ‘downstream’ from the thalamus, in cortical areas where neurons may exploit the labour of large ‘upstream’ populations. Indeed, Watson [ 111 suggests that to account for the observed contrast sensitivity of humans one need look no further than primary visual cortex (Vl >, the lirst stop after the thalamus. There, the sensitivies of neurons do approach those of humans, and Watson has shown that Vl neuronal responses could be created by pooling low-sensitivity P-cell inputs. Also, one may question whether the responses of neurons in the monkey thalamus ought really to be compared with human behaviour. Not only .are monkeys and humans different species, but in this example sensitivities were measured under very different conditions - the monkey under anaesthesia, the human alert. Furthermore, in these and other cases ([5], for example) the patterns used to stimulate the monkey’s neurons were not optimized for the preference or receptive field of the single neuron under study. Given these caveats, it is significant that in their work Newsome, Movshon and colleagues [ 11 matched the stimulus to the neuron’s receptive field, measured the behavioural and neuronal sensitivities in the same animal under the same conditions, and found the two measurements to agree almost perfectly. The measurements were made in visual area MT (or VS), an area even further downstream than Vl that is specialized for the analysis of visual motion [ 123. Each MT neuron responds preferentially to a particular speed and direction of visual motion; neurons with similar preferences are grouped together in columns perpendicular to the cortical surface [ 131. Newsome, Movshon and colleagues trained an alert monkey to discriminate the direction of motion of a cluster of moving dots, a difficult task as only a variable proportion of the dots moved coherently in the same direction, the remainder moving at random. In each session, an MT neuron was isolated with a microelectrode and the cluster of dots POsitioned exactly on its receptive field, their speed matched to the neuron’s preferred speed. The dots moved either in the neuron’s preferred direction or the opposite, and the monkey was required to signal which. The monkey’s performance improved as the proportion of dots moving coherently increased, reaching threshold reliability at between 5 % and 30 % coherence. Simultaneously, the neuron’s firing rate was recorded: this too increased in strength as the proportion of dots moving coherently in the neuron’s preferred direction increased. 1993, Vol

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For roughly half the neurons tested, the proportion coherence at which the neuron reliably signalled the correct direction closely matched the monkey’s threshold. Moreover, the neuron’s responses tended to match the monkey’s responses on each trial, so that if the monkey made a mistake by signalling ‘upward when the movement was actually ‘d6nward’, so too did the neuron, by inappropriately increasing its firing rate. Thus, the probability of correctly predicting the monkey’s response directly from the neuron’s firing rate (the SOC, or Sender Operating Characteristic probability) was fairly high - approximately 0.58 (Movshon, Newcastle workshop). Although these results help to restore the single neuron to a. useful role in explaining vision, they create a puzzle that is still unsolved. In one MT column there are probably in the order of 100 neurons [ 141. As all the neurons in the column have similar preferences, they should all be activated by the same stimulus - so why does the monkey seem to exploit the information from only one neuron? What function do the remaining 99 neurons serve? There are several possible answers. Perhaps the monkey does use only one neuron to guide its behavioural response, and the other 99 neurons send their information to other parts of the brain that do not directly influence performance on the task. Or perhaps fewer neurons than expected are sufficiently activated by the stimulus to contribute. Lastly, perhaps the monkey cannot read a single neuron’s signal as reliably as the calculations predict. This is a strong possibility, as the neuron’s threshold is calculated by assuming there is an ideal observer monitoring its signal. Perhaps there is no such observer in the monkey’s brain, and the monkey must monitor more than one neuron to reach a decision. A new model, sketched in [3] and reported by Movshon at the Newcastle workshop, suggests that the monkey might indeed exploit the responses of many neurons, but imperfectly. In their original computer simulation, B&ten et al. [ 1] showed that if the responses of neurons are summed in a perfectly linear way and with absolute precision, then a pool of only four neurons should lower the monkey’s

observed threshold by half (Fig. 1). This improvement is entirely expected because pooling neuronal responses cancels out noise in the individual signals, but only if that noise varies independently in each neuron. This is a key assumption, it is certainly wrong if the neurons in one column have similar properties because they are all driven by the same input. Then both the noise and neuronal responses would vary together, and pooling would not eliminate the shared noise. Indeed, when a correlation between neurons is introduced into the model, pooling is less effective. Yet Britten et al. [l] found that even with extremely high correlation levels (75 %>, pools of more than one neuron always outperformed the monkey. The model also assumes that an ideal observer counts and sums the number of action potentials fired by each neuron, without error. This is the second assumption that must be discarded, as it is unlikely that the pooling.process is perfect. When noise is added to the pooling stage itself, the performance of the simulated neuronal population begins to match the monkey’s But there exist many combinations of pooling noise and inter-neuron correlation that can make the model match the data, and a model with too many free parameters yields little insight into the working of the real brain. This is where the final constraint comes in - the SOC probability. Introducing correlation between neurons creates correlated noise that reduces the benefit of pooling. It also increases the amount of trial-to-trial variability that is the same for each neuron in the pool, and therefore increases the probability that the response of the pooling neuron vanes in the same way. In turn, this increases the SOC probability - that of correctly predicting the monkey’s response from the response of any one neuron contributing to the pool. It transpires that only a limited range of combined values of correlation, pooling noise and pool size can reproduce the monkey’s behaviour and match the observed SOC probability. The refined model [3] predicts a correlation value of roughly 15 %, which neatly matches the mean correlation value found when simultaneous responses of MT neuron pairs are analysed [15]. At I5 %

Stimulus I

Fig. 1. A model in which the pooling of responses of inherently noisy neurons gives a reliable signal. In the experiments of Newsome, Movshon and colleagues [II, a monkey observes a cluster of moving dots, some proportion of which are moving coherently in the upward direction. Upward directionselective MT neurons are activated, but each produces a noisy signal. If the responses of the upward-selective neurons are pooled, the noise averages out, so that the pooling neuron produces a regular signal of eight action potentials per interval. The pooled response of the downward-selective neurons is weaker, so the monkey decides in favour of the upward pool. As depicted, the noise is relatively large, but independent for each neuron. The results of Newsome, Movshon and colleagues suggest that the noise on individual neurons may be small but highly correlated, so that it does not entirely cancel out in the pooling stage.

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correlation, with the optimal amount of pooling noise, the model further predicts a pool size of 30 neurons or more - again a physiologically plausible numlber, as it is roughly the size of an MT column. But there is yet another twist. Three years ago, Newsome’s and Movshon’s group reported the dramatic result that a monkey’s performance on the motion discrimination task could be significantly altered by delivering a small electncal current to MT [ 161. Stimulating neurons that preferred an ‘upward direction of motion increased the monkey’s ‘upward responses, even when all dots moved at random. This effect increased for currents up to 40 micro-amps, but tended to reverse for larger currents [ 171. This suggests that larger currents activate neurons with opposing preferences, outside the targetted column, and thereby weaken the signal. Smaller currents presumably activate only a fraction of a column, as current spread is spherical and columns are long cylinders. And yet at 40 microamps stimulation the monkey performs even better than normal, reporting ‘upward movement on nearlly 100 % of stimuli that normally elicit only a threshold performance of 75 % ‘upward. This result implies that only a fraction of a column is necessary for maximum performance, and therefore suggests that under normal conditions far fewer neurons are active than their receptive field properties would indicate. Yet it is more likely that we have underestimated the number of relevant neurons responding to the task, as each neuron has far-reaching connections that activate others in more distant, but similarly responsive columns [ 181. Or perhaps the brain uses statistics that we don’t yet understand, and microstimulation {does more than simply add neurons to the pool. There is con&ct too over the amount of correlation between neurons. The value of 15 % implies a degree of redundancy that would seem to thwart the brain’s purpose of reliably encoding all the subtle variations in the visual world. Indeed, Gawne et al. [19] report that noise is correlated to a much smaller degree between neurons in the inferotemporal (IT) cortex, an area involved in object recognition. Perhaps this is because IT performs fundamentally different tasks from MT. Although IT cells have been found that respond to faces in general [ 201, no single IT cell has been found that responds exclusively to an individual face. Fujita and Tanaka [2l] estimate that to recognize any single object a monkey must rely on the responses of many simultaneously active IT columns. In Vl, where cells are highly selective for orientation, Foldiak [22] finds that the responses of at least eight differently-tuned cells are needed to predict the orientation of a light/dark edge, using real neuronal responses in a computer simulation. This number is conservative, as it assumes that the noise between neurons is entirely uncorrelated and that an ideal observer records their responses. It suggests that tasks demanding more than a binary response, such as ‘up’ or ‘down’, might require the responses of more than one neuron, combined in a more complicated way than pooling. Thus, it may be that single neurons in MT are peculiarly powerful in determining visual perception, particularly when stimulated by a natural stimuIus, which probably excites fewer neurons than a moving-dot cloud. Alternatively, MT neurons may indulge in a higher degree

of redundancy than other visual areas. Given the primitive importance of motion detection, the latter possibility is plausible. Either way, it is clear that electrophysiology of single neurons still holds answers to the puzzles it has created. References 1. 2.

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AC. Hurlbert and AM. Derrington, Department of Physiological Sciences, University of Newcastle upon Tyne, Framlington Place, Newcastle upon Tyne, NE2 4HH, UK.