Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex

Abstract

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.

Figure 1. The effect of an extra spike

(a) Schematic showing the propagation of missed and extra spikes in a recurrent network. Each two-column block represents a snapshot of the activity of a population of excitatory and inhibitory neurons on two different trials. Filled neurons are spiking. The trials are identical until time t=0, at which point an extra spike is added to a neuron in trial 2 (point 1). The extra spike has no effect on the majority of its postsynaptic targets (dashed arrows and 2,3; omitted subsequently for clarity), but it triggers an extra spike in a fraction of them (magenta arrows and 4,5). These extra spikes cause a cascade of extra and, as soon as inhibitory neurons are recruited, missed spikes (6-8). Extra inhibitory spikes (5) and missed excitatory spikes (6,7) are indicated with cyan arrows. The perturbation amplification rate decreases when collisions occur (9,10), and eventually missed and extra spikes occur at the same rate, resulting in a steady state (rightmost column). (b) Membrane potential of the bottom neuron (*) on the two trials. The membrane potential is identical until an extra presynaptic spike causes a slight divergence (3). As missed and extra spikes accumulate the difference grows (7), until it eventually reaches steady state.

Figure 2. Small perturbations affect spiking probability

(a) Positive and negative current pulses (upper trace) were injected via a whole-cell patch-clamp electrode into a neuron, and the accompanying membrane potential was recorded (lower trace). (b) PSTHs triggered on the +25 pA (top) and -25 pA (bottom) current pulses, binned at 1 ms; the green line shows the average firing rate. For this neuron the probability of an extra spike is 0.004 for +25 pA and the probability of a missed spike is 0.001 for -25 pA.

Figure 3. Determining the sensitivity of neurons to small perturbations

(a) Top: injected PSCs. Center: combined PSTHs from 40 experiments, triggered on the current pulses (t=0) and binned at 1 ms. Cyan: missed spikes; magenta: extra spikes; green lines: mean firing rate. Bottom: cumulative probability of an extra spike; yellow indicates one standard deviation. (b) Probability of an extra spike within 5 ms of the current pulse versus total injected charge. Magenta and cyan lines: least squares fit to the data; dashed lines: 95% confidence intervals; error bars: standard error of the mean. Positive charge: slope=0.061±0.010 probability/pC (p=5×10⁻⁹); negative charge: slope=-0.018±0.0049 probability/pC (p=4×10⁻⁴). (c) Same as B but from simulations of a layer 5 pyramidal neuron (Supplementary Information, Sec. 4 and Fig. S3). Black: current injected at the soma; green: current injected at the distal dendrites, 403 μm from the soma.

Figure 4. The effect of one extra spike on network activity

(a) The recording configuration. The extracellular silicon probe (red) contained 16 recording sites spaced 50 μm apart. The patch electrode (blue) was used to trigger spikes via brief depolarizing current pulses. (b) Extracellular spikes (top) and intracellular membrane potential (bottom). (c) PSTH triggered on the stimulus and binned at 5 ms; includes all extracellular spikes on all electrodes from 10 experiments. Error bars are one standard deviation. Inset: change in firing rate per neuron, assuming an average firing rate of 1 Hz (ref. 30). (d) Cumulative probability of an extra spike, averaged over all recorded neurons, again assuming an average firing rate of 1 Hz. Dash lines indicate one standard deviation, obtained using bootstrap sampling. Left scale: probability of an extra spike in a randomly chosen neuron. Right scale: probability of an extra spike between connected pairs, found by dividing the left side by 0.04, corresponding to the 4% connectivity observed in somatosensory cortex.

Figure 5. Precisely timed events are rare

(a) Top: example membrane potential recording. A steady current between -250 and -450 pA was applied to reduce the frequency of action potentials. Bottom: expanded view of an up state. The coloured line segments indicate events of various amplitudes and rise times. Green: amplitude 3 mV, rise time 12 ms; cyan: 6 mV, 20 ms; magenta: 6 mV, 5 ms. (b) The rate of events with precision δτ (events for which the voltage change by at least 2σ_V mV in time δτ, averaged over our uncertainty in σ_V , the latter given in Supplementary Figure S7). Data from nine cells recorded in vivo, with events counted only during up states (boxed regions in panel a). Three of the cells received, on alternate trials, stimulation via a slowly rotating (1 Hz) drum of sandpaper. There was no statistically significant difference between event rates with and without whisker stimulation.