Supralinear increase of recurrent inhibition during sparse activity in the somatosensory cortex

Abstract

The balance between excitation and inhibition in the cortex is crucial in determining sensory processing. Because the amount of excitation varies, maintaining this balance is a dynamic process; yet the underlying mechanisms are poorly understood. We show here that the activity of even a single layer 2/3 pyramidal cell in the somatosensory cortex of the rat generates widespread inhibition that increases disproportionately with the number of active pyramidal neurons. This supralinear increase of inhibition results from the incremental recruitment of somatostatin-expressing inhibitory interneurons located in layers 2/3 and 5. The recruitment of these interneurons increases tenfold when they are excited by two pyramidal cells. A simple model demonstrates that the distribution of excitatory input amplitudes onto inhibitory neurons influences the sensitivity and dynamic range of the recurrent circuit. These data show that through a highly sensitive recurrent inhibitory circuit, cortical excitability can be modulated by one pyramidal cell.

Figure 1

Unitary recurrent inhibitory circuits. (a) The spiking (ten action potentials at 100 Hz) of a layer 2/3 pyramidal cell (black trace) evokes outward currents in a simultaneously recorded target layer 2/3 pyramidal cell (blue traces; V_H, −40 mV). The top trace is the average of 15 sweeps, 3 of which are shown superimposed in the middle. Upper left, schematic of the recording configuration. Vclamp, voltage clamp; Iclamp, current clamp. (b) Summary current, averaged over all experiments (n = 38), recorded in layer 2/3 pyramidal cells in response to a train of action potential in a neighboring pyramidal cell (the dots indicate the time of the spikes). Individual currents were normalized by their peak amplitudes. Inset, peak current for each recurrent IPSC (n = 38; open symbols) and the averaged peak of all experiments (solid symbol). (c) Same configuration illustrated in a (different pair), except that target pyramidal cell is recorded in current clamp (blue traces; V_m = −52 mV). Inset, peak hyperpolarization for nine similar experiments (open symbols) and the average of all experiments (solid symbol). (d) Same recording configuration illustrated in a (different pair). Application of the AMPA/kainate receptor antagonist NBQX (10 μM) completely abolishes the outward current. (e) Simultaneous recording from three layer 2/3 pyramidal cells. The spiking of one of the cells (black trace) evokes outward current in the two other pyramidal cells (blue and green traces; V_H, −40 mV). The top traces are the average of 23 sweeps. Lower traces show four individual sweeps recorded simultaneously in the green and blue pyramidal cells. Black–blue pair same as in d.

Figure 2

Supralinear increase of inhibition. (a) Simultaneous recording from three layer 2/3 pyramidal cells (PC1, blue; PC2, black; PC3, green). Left, a train of action potentials in PC2 elicits no current in PC1 nor PC3 (V_H, −40 mV). Middle, a train of action potentials in PC3 elicits no current in PC1 or PC2 (V_H, −40 mV). Right, simultaneous trains of action potentials in PC2 and PC3 elicit an outward current in PC1. All current traces are averages of multiple sweeps. (b) Same recording configuration as in a (different cells). Left, the spiking of either PC2 or PC3 alone elicits outward currents in PC1. Note the earlier onset of inhibition in PC1 (blue trace) when PC2 and PC3 are spiking simultaneously (the PC2-PC1 pair is the same one as in Fig. 1a). Right top, gray trace: algebraic sum of the currents elicited in PC1 in response to the spiking of PC2 and PC3 alone. Blue trace, outward current elicited in response to the simultaneous spiking of PC2 and PC3. Right bottom, running integral of the two currents illustrated on top. Note that the inhibitory charge in response to the simultaneous spiking of PC2 and PC3 is larger than the inhibitory charge of the algebraic sum of the responses of PC1 to the spiking of PC2 and PC3 alone. All current traces are averages of multiple sweeps. (c) Cumulative distribution of the nonlinearity index (see Results for details) for 38 similar experiments. Note that most values are larger than 0, indicating supralinear increase in recurrent inhibition when PC2 and PC3 are spiking simultaneously.

Figure 3

Intra- and translaminar recurrent inhibitory circuits. (a) Reciprocal connection between a layer 2/3 pyramidal cell (black traces) and a layer 2/3 fast-spiking (FS) cell (blue traces) receiving depressing inputs. Upper, a train of action potentials in the pyramidal cell elicits depressing unitary EPSCs or EPSPs in the FS interneuron recorded in the voltage- or current-clamp mode, respectively. Inset, spiking response of the interneuron to a 2-s-long square current pulse. Lower, same pair: a train of action potentials in the interneuron elicits unitary IPSCs in the pyramidal cell (V_H, −40 mV). (b) Reciprocal connection between a layer 2/3 pyramidal cell (black traces) and a layer 2/3 regular spiking interneuron receiving depressing inputs (dRS cell; blue traces). Protocols same as in a. (c) Reciprocal connection between a layer 2/3 pyramidal cell (black traces) and a layer 2/3 interneuron (blue traces) receiving facilitating inputs (fRS cell). Protocols same as in a. Note the summation of consecutive EPSPs. (d) Reciprocal connection between a layer 2/3 pyramidal cell (black traces) and a layer 5 fRS cell (blue traces). Protocols same as in a. (e) Summary graph of unitary EPSC amplitudes normalized by the amplitude of the largest EPSC in the train and plotted against presynaptic action potential number. Closed circles, fRS cells (n = 36); open circles, FS and dRS cells (n = 21 and 13, respectively, pooled). (f) Summary graph of the time course of membrane depolarization plotted against presynaptic action potential number. The peak depolarization achieved after each action potential is normalized by the maximum depolarization achieved during the train. Closed circles, fRS cells (n = 31); open circles, FS and dRS cells (n = 12 and 6, respectively, pooled). (g) z projection of a confocal stack showing a biocytin-filled fRS interneuron (streptavidin–Alexa 488, green; left), anti-SOM immunostaining of the same field (Alexa 594, red; middle) and their superimposition (right). Scale bar, 20 μm. Pial surface is to the top.

Figure 4

Spike timing of somatostatin-positive interneurons determines the time course of recurrent inhibition. (a) A train of spikes at 100 Hz in a layer 2/3 pyramidal cell (black trace) elicits action potentials in an SOM interneuron (threshold for action potential generation was achieved in some (blue races; 12 superimposed sweeps) but not all (gray traces, 14 superimposed sweeps) trials (V_m interneuron, −63 mV)). Inset, the interneuron was reciprocally connected with the pyramidal cell: spiking of the interneuron (blue trace) triggered outward currents in the pyramidal cell (black trace). (b) Summary graph of the distribution of spike times in SOM interneurons in response to trains of action potentials at 100Hz in the presynaptic pyramidal cells (n = 12). (c) The blue trace illustrates the result of the convolution of the spike time distribution (in b) with a fit to an average unitary IPSC (sum of two exponential functions; τ_rise, 1.7 ms; τ_decay, 11 ms). The convolution is superimposed onto the time course, averaged over all experiments, of the outward current elicited by the spiking of a single pyramidal cell onto a neighboring pyramidal cell (gray trace, from Fig. 1b). Note the similarity of the rising and decaying phase of the two currents. Inset: gray trace, standard IPSC; black trace, unitary IPSC from a. (d) Summary graph of the distribution of spike times in interneurons receiving depressing inputs in response to trains of action potentials at 100 Hz in the presynaptic pyramidal cells (n = 2). Inset, a train of spikes at 100 Hz in a layer 2/3 pyramidal cell (black trace) elicits action potentials in an interneuron receiving depressing inputs (blue traces; five superimposed sweeps where threshold for action potential generation was achieved (V_m interneuron, −63 mV)). (e) Convolution (blue trace) of the spike distribution (in d) with the fit of an average IPSC (sum of two exponential functions; τ_rise, 0.8 ms; τ_decay, 9.4 ms). The convolution is superimposed onto the time course, averaged over all experiments, of the outward current elicited by the spiking of a single pyramidal cell onto a neighboring pyramidal cell (gray trace, from Fig. 1b). Note the very different rising and decaying phases of the two currents. (f) Simultaneous recording from three layer 2/3 pyramidal cells (blue, PC1; black, PC2; green, PC3). A train of spikes in PC2 alone leads to inhibition with late onset in PC1 (V_H, −40 mV; black traces), similar to that illustrated in Figures 1 and 2. A train of spikes in PC3 alone leads to no inhibition in PC1 (green traces). A simultaneous train of spikes in PC2 and PC3 leads to the appearance of an early component of inhibition (open arrow) followed by the late component (black arrow) in PC1 (blue trace).

Figure 5

Increase in the recruitment of somatostatin-expressing interneurons. (a) Schematic of the projection of two pyramidal cells onto SOM interneurons. N is the total population of SOM interneurons; P_PI is the probability of a pyramidal cell contacting a SOM interneuron; N × P_PI is the population of SOM interneurons contacted by one layer 2/3 pyramidal cell; and N × (P_PI)² is the population of interneurons targeted by both pyramidal cells. The number of interneurons assigned to each population is for illustration purpose only. (b) Top, when only one of the two pyramidal cells is spiking, the N₁ SOM interneurons are recruited (filled red circles). Bottom, when two pyramidal cells are spiking, almost five times more interneurons (N₂) are recruited. (c) Within the population of interneurons receiving convergent input from two pyramidal cells (N × (P_PI)²), the fraction that is recruited in response to the activity of two pyramidal cells (bottom) is 11.8 times larger than the one that is recruited by one pyramidal cell only (top; see Methods).

Figure 6

Model describing range and sensitivity of recurrent inhibition. (a) Left, mean EPSP amplitude recorded in SOM interneurons after the tenth action potential evoked in the presynaptic pyramidal cell, plotted against the standard deviation (s.d.) of the EPSP, for each of the 31 unitary connections. Middle, distribution of EPSP amplitudes (blue bars) and alpha function (black curve) that fits the distribution. Right, cumulative distribution of EPSP amplitudes (blue line) and alpha function (black line). (b) Left, distribution of EPSP amplitudes evoked by one pyramidal cell (D₁: black line) or two pyramidal cells (D₂: gray line) in the interneuron populations contacted by one pyramidal cell or by either of two pyramidal cells, respectively. Values at zero represent the fraction of unconnected interneurons (black: 1 − P_PI, gray: 1 − (1 − P_PI)²). The threshold for action potential generation (11.3 mV above resting potential) is shown by a dashed line. Right, prediction of the fraction of recruited SOM interneurons (INs) plotted against the number of active pyramidal cells (interneuron activation curve). The blue dotted lines illustrate half activation. (c) Left: black line, D₁ (same as in b; values at zero have been cut; mean 4.6 mV, s.d. ± 2.8 mV); continuous gray line, EPSP distribution with same mean but small s.d. (mean 4.6 mV; s.d. ± 0.5 mV); dotted gray line, EPSP distribution with large mean (mean 10.3 mV, s.d. ± 0.5 mV), yet same fraction of EPSPs above threshold as D₁. Right: interneuron activation curves for the three EPSP distributions shown on the left (black trace same as in b). Note the faster saturation of the activation curve for the EPSP distribution with a large mean (dotted gray trace) and the right-shifted onset for the EPSP distribution with a small s.d. (continuous gray trace). The blue dotted lines illustrate half activation. Inset, the minimum number of pyramidal cells required to activate inhibitory circuit for experimental EPSP distribution is 1, as compared to 3 for the normal distribution of the same mean with a smaller s.d.