Scientific Understanding of Consciousness
Rate Coding in Cortex
Nature 466, 123–127 (01 July 2010)
Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex
Michael London,1 Arnd Roth,1 Lisa Beeren,1 Michael Häusser1 & Peter E. Latham2
1Wolfson Institute for Biomedical Research and Department of Neuroscience, Physiology and Pharmacology, University College London, Gower Street, London WC1E 6BT, UK
2Gatsby Computational Neuroscience Unit, University College London, Queen Square, London WC1N 3AR, UK
It is well known that neural activity exhibits variability, in the sense that identical sensory stimuli produce different responses, but it has been difficult to determine what this variability means. Is it noise, or does it carry important information—about, for example, the internal state of the organism? Here we address this issue from the bottom up, by asking whether small perturbations to activity in cortical networks are amplified. Based on in vivo whole-cell patch-clamp recordings in rat barrel cortex, we find that a perturbation consisting of a single extra spike in one neuron produces approximately 28 additional spikes in its postsynaptic targets. We also show, using simultaneous intra- and extracellular recordings, that a single spike in a neuron produces a detectable increase in firing rate in the local network. Theoretical analysis indicates that this amplification leads to intrinsic, stimulus-independent variations in membrane potential of the order of ±2.2–4.5 mV—variations that are pure noise, and so carry no information at all. Therefore, for the brain to perform reliable computations, it must either use a rate code, or generate very large, fast depolarizing events, such as those proposed by the theory of synfire chains. However, in our in vivo recordings, we found that such events were very rare. Our findings are thus consistent with the idea that cortex is likely to use primarily a rate code.
The brain, like all physical devices, operates in the presence of noise. Nevertheless, it performs complex computations with amazing speed and accuracy, in some cases reaching fundamental physical limits set by its sensors. Clearly, the brain has devised computational strategies, and a neural code, that are robust to noise. Understanding the structure of that noise should shed light on both.
The traditional experimental approach to studying noise in cortical sensory areas is to present the same stimulus repeatedly to an organism while recording neuronal responses. Such recordings always show substantial trial-to-trial variability. However, interpreting that variability has been difficult, as there are two possible sources for it. One is the variability associated with truly random events, such as ion channel noise and stochastic synaptic release. This is intrinsic noise: intrinsic because it cannot be eliminated, and noise because it contributes to the neuronal variability but carries no information whatsoever. The other source of variability is activity from other brain areas. That activity might provide information about, say, the degree of arousal or some other internal state, but it would not be related to the stimulus. This variability is signal, even though it would look like noise to an observer trying to relate the neural activity to the stimulus.
Here we determine a lower bound on the level of intrinsic noise in cortical networks. The lower bound we consider is the trial-to-trial variability that would be observed in a deterministic network that received identical input, down to the last spike, on multiple trials, except for one very brief random event. If the dynamics of the network is such that small differences in activity associated with the single random event lead to very large differences in patterns of neuronal activity, then trial-to-trial variability would, necessarily, be high. If, on the other hand, small differences in activity lead to even smaller differences in patterns of neuronal activity, then trial-to-trial variability can be low.
In our analysis and experiments, the random event is a single extra spike added to a randomly chosen excitatory neuron. This one extra spike can produce other extra spikes in its postsynaptic targets. If it produces more than one, on average, then perturbations would be amplified, and noise would be high. If, on the other hand, one extra spike produces less than one extra spike, on average, then perturbations would decay, and noise could be small.
To determine the average number of extra postsynaptic spikes produced by a single extra presynaptic spike, we note that it is the product of two numbers: the average number of connections made by each neuron, and the average probability that a unitary synaptic event produces an extra spike.
The first number is known from anatomical studies to be between 1,000 and 2,000 (a synaptic connection that gives rise to a unitary excitatory postsynaptic potential (EPSP) can consist of multiple synaptic contacts; here we assume that a neuron makes five synaptic contacts per connection). Thus, one extra spike produces, on average, 1,500 ± 500 extra EPSPs in the network.
The second number, the probability that a unitary synaptic input produces an extra spike, was determined experimentally. We made whole-cell patch-clamp recordings from layer 5 pyramidal neurons in the barrel cortex of anaesthetized rats while injecting current pulses to generate postsynaptic currents (injected PSCs) of various amplitudes. For each amplitude we constructed a post-stimulus time histogram (PSTH) triggered on the time of the injected current pulses, and used it to deduce the probability of an extra spike. In a single trial it is very difficult to tell whether an individual injected PSC has an effect on the probability of an extra spike. The PSTHs, however, reveal a clear signal. Integrating the PSTH over a time window of 5 ms, we find that a single input with an amplitude of +25 pA causes the probability of observing a spike to increase by 0.004, and an input with an amplitude of −25 pA causes the probability to decrease by 0.001.
Neuronal Networks are Chaotic (Complexity and Self-Organization)
Our study is in line with previous theoretical work that suggests neuronal networks are chaotic. However, it is, to our knowledge, the first experimental demonstration of the sensitivity of an intact network to perturbations in vivo. We are also the first to explore the consequences of these results for the level of noise in the cortex and its likely effect on the precision of spike timing.
What do our results imply for neural coding? Superficially, it seems natural to conclude that if every spike has a large effect on network activity, then every spike should count, and the brain must be using a very sophisticated neural code in which the time and identity of every spike carries meaningful information. In fact, our results imply just the opposite. This is because network activity is bounded, so growth of perturbations in some dimensions (for example, as measured by trial-to-trial difference in membrane potential) necessarily implies contraction in others. It is this contraction that causes networks to rapidly forget their past. Thus, although an extra spike can radically modify patterns of activity, patterns of activity cannot encode which extra spike caused the modification. The implication, then, is not that rat barrel cortex (and, we suspect, other areas of cortex and other species) must be using a very sophisticated spike timing code, but that it is likely to be using a code that is robust to perturbations, such as a rate code in which it is the average firing rate over large populations of neurons that carries information.
Finally, the fact that studies have found millisecond timing both in anaesthetized and awake animals in the rat barrel cortex as well as in other cortical regions is not inconsistent with our results. The precise timing in those studies is associated with a feedforward sweep of activity caused by a rapidly time-varying stimulus. Our results, on the other hand, apply to slowly varying stimuli and higher-order computations, and suggest that in those cases the cortex does not rely on precise spike timing.
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