A spontaneous state of weakly correlated synaptic excitation and inhibition in visual cortex

Abstract

Cortical spontaneous activity reflects an animal's behavioral state and affects neural responses to sensory stimuli. The correlation between excitatory and inhibitory synaptic input to single neurons is a key parameter in models of cortical circuitry. Recent measurements demonstrated highly correlated synaptic excitation and inhibition during spontaneous "up-and-down" states, during which excitation accounted for approximately 80% of inhibitory variance (Shu et al., 2003; Haider et al., 2006). Here we report in vivo whole-cell estimates of the correlation between excitation and inhibition in the rat visual cortex under pentobarbital anesthesia, during which up-and-down states are absent. Excitation and inhibition are weakly correlated, relative to the up-and-down state: excitation accounts for less than 40% of inhibitory variance. Although these correlations are lower than when the circuit cycles between up-and-down states, both behaviors may arise from the same circuitry. Our observations provide evidence that different correlational patterns of excitation and inhibition underlie different cortical states.

Keywords: 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid; CI; HEPES; confidence interval; correlation; excitation; in vivo; inhibition; primary visual cortex; spontaneous activity.

Fig. 1

Correlated and uncorrelated excitation and inhibition can be distinguished by their sum. (A) Perfectly correlated excitation (blue) and inhibition (red) cancel perfectly in their sum (black). In the corresponding histograms on the right, the variances of excitation and inhibition are non-zero, but the variance of their sum is zero. (B) Uncorrelated excitation and inhibition do not cancel when summed. The variances of excitation, inhibition and their sum are non-zero.

Fig. 2

Single neuron excitatory–inhibitory correlation coefficients. (A) Synaptic currents at each of 3 membrane potentials; 30-s segments (left); 500 ms close-up from one repetition (right). (B) Histograms of current amplitudes. All horizontal axes represent the same relative range of currents. To conveniently display a highly skewed distribution, the −11 mV histogram represents currents greater than 250 pA by a single bar. (C) Plot of current variances versus membrane potential, and best fit quadratic. (D) Estimated single neuron excitatory–inhibitory correlation coefficients r_EI (error bars are 90% CI) for 7 neurons. The neuron in (A–C) is the 5th.

Fig. 3

Systematic uncertainties: membrane nonlinearity, reversal and junction potentials. (A) Time-averaged membrane current versus membrane potential for each of the seven neurons in Fig. 2D; current versus membrane potential data are well fit by a linear model in all seven neurons (r²>0.97).(B) Correlation coefficients r_EI for each of the seven neurons in Fig. 2D calculated with different assumed reversal and junction potentials within the experimentally plausible range: r_EI depended mainly on the excitatory reversal potential (V_E=−10 mV: black; V_E=0 mV: blue; V_E=+5 mV: red). For any given V_E, changing the inhibitory reversal potential (V_I) or the junction potential (V_J) did not significantly affect r_EI estimates, indicating that uncertainties in r_EI due to uncertainties in V_I and V_J are negligible compared to those due to uncertainties in V_E. Correlation coefficients in Fig. 2D were obtained with V_I and V_J fixed near their respective midpoints (V_I=−85 mV, V_J=10 mV), and with V_E=−10 mV chosen to minimize the non-systematic uncertainty indicated by the error bars (90% CI). Higher r_EI estimates are obtained with V_E=0 mV and V_E=+5 mV, suggesting that the estimates in Fig. 2D provide a reasonable lower bound, but only a weak upper bound on r_EI. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4

Using the ratio of excitatory to inhibitory rates to estimate an upper bound for the single neuron excitatory–inhibitory correlation. (A) Detected peaks (blue asterisks) in smoothed (sign-inverted) excitatory currents from one neuron (B) Logarithmically-scaled histogram of inter-event intervals for the neuron in (A). (C) Detected peaks (blue asterisks) in smoothed inhibitory currents from another neuron. (D) Logarithmically-scaled histogram of inter-event intervals for the neuron in (C). (E) Mean excitatory rate versus mean inhibitory rate across neurons. (F) Maximum cross-correlation versus ratio of the high rate to the low rate. Solid line is the analytic solution (y=x^−1/2) for Poisson processes; triangles are simulation results for filtered Poisson processes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5

Excitatory and inhibitory peaks at the intermediate membrane potential. (A) Mean-subtracted current at the intermediate membrane potential from an example neuron showing detected positive excitatory and negative inhibitory peaks (blue asterisks), and the pairing (red lines) of each inhibitory peak (bold red circles) with the nearest preceding excitatory peak (faint red circles). (B) Histograms of intervals between data inhibitory peaks and nearest preceding excitatory peaks (black squares); and randomized inhibitory peaks and nearest preceding excitatory peaks (gray circles) for the neuron in (A). (C) Median interval between randomized inhibitory peaks and nearest preceding excitatory peaks versus median interval between data inhibitory peaks and nearest preceding excitatory peaks (seven neurons). (D) Excitatory versus inhibitory peak amplitudes in excitatory–inhibitory peak pairs with interval less than 50 ms, from a different neuron than in (A). (E) Median interval for randomized peak pairs versus data peak pairs as in (C), but conditioned on pairs whose excitation lay in the largest (red upright triangles) or smallest (blue-inverted triangles) quartiles of excitatory peak amplitude (seven neurons).

Fig. 6

Single neuron excitatory–inhibitory correlations in different model network states. Note A–E, G, and H refer to the model, but (F) shows data. (A) The model consists of recurrently connected excitatory and inhibitory integrate-and-fire neurons which receive feedforward excitation from Poisson-spiking neuron groups. (B) Excitatory (blue) and inhibitory (red) conductances in a model parameter regime without up-and-down states. Conductances are normalized by the leak conductance. (C) Excitatory and inhibitory conductances in a model parameter regime with up-and-down states. (D) Unimodal current amplitude distributions for the model neuron in (B). All horizontal axes represent the same relative range of currents. To conveniently display a highly skewed distribution, the 0 mV histogram represents currents greater than 1.1 units by a single bar. (E) Bimodal current amplitude distributions for the model neuron in (C). All horizontal axes represent the same relative range of currents. (F) Cross-correlations between upper and (sign-inverted) lower halves of currents at the intermediate potential, for single neurons (gray), and mean across neurons (black). (G, H) Cross-correlations between upper and (sign-inverted) lower halves of currents at the intermediate potential for the respective model parameter regimes in (B, C), for randomly selected single model neurons (gray), and mean across neurons (black).