Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2009 Apr;12(4):483-91.
doi: 10.1038/nn.2276. Epub 2009 Mar 22.

Gating multiple signals through detailed balance of excitation and inhibition in spiking networks

Tim P Vogels  1 , L F Abbott
Affiliations

Gating multiple signals through detailed balance of excitation and inhibition in spiking networks

Tim P Vogels et al. Nat Neurosci. 2009 Apr.

Abstract

Recent theoretical work has provided a basic understanding of signal propagation in networks of spiking neurons, but mechanisms for gating and controlling these signals have not been investigated previously. Here we introduce an idea for the gating of multiple signals in cortical networks that combines principles of signal propagation with aspects of balanced networks. Specifically, we studied networks in which incoming excitatory signals are normally cancelled by locally evoked inhibition, leaving the targeted layer unresponsive. Transmission can be gated 'on' by modulating excitatory and inhibitory gains to upset this detailed balance. We illustrate gating through detailed balance in large networks of integrate-and-fire neurons. We show successful gating of multiple signals and study failure modes that produce effects reminiscent of clinically observed pathologies. Provided that the individual signals are detectable, detailed balance has a large capacity for gating multiple signals.

PubMed Disclaimer

Conflict of interest statement

Conflict of Interest

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1. Network Connectivity and Properties
a) All excitatory and 65% of the inhibitory neurons are connected randomly with a connection probability of 2% (illustrated in red). The other 35% of the inhibitory neurons have local connectivity, targeting their nearest neighbors (illustrated in blue). b) An embedded signal pathway is created by selecting a group of sender neurons (in green) that target either excitatory or locally inhibitory neurons (in red and blue, respectively, throughout the figures) in a signal-receiving region (in red) of the network. C–f) Asynchronous background activity in the network model. Distributions for network neurons of: c) firing rates, d) average membrane potentials, e) ISIs plotted on a semi-log scale, and f) coefficients of variation for those ISIs. Arrows indicate the means of the distributions.
Figure 2
Figure 2. Detailed Balance in a Network
a) Average firing rate of the sender neurons responding to a sinusoidally varying input. b) Voltage trace of a randomly selected excitatory receiver neuron. Red trace: single trial. Black trace: the average subthreshold membrane potential over 100 trials. c) Average membrane currents of the excitatory receiver neurons. Excitatory and inhibitory currents are plotted in red and blue respectively, the net current, including voltage-dependent leak and constant background currents, is plotted in black. d) Blue trace: average firing rate of the inhibitory receiver neurons. Red histogram: average firing rate of the excitatory receiver neurons. e) Average firing rate of the entire network. f) Spike raster for 30 randomly chosen excitatory receiver neurons. Conditions shown are: No signal: All neurons fire at background rates. Balanced signal: Sender neurons fire in a correlated manner in response to oscillatory input and project the input firing pattern to both excitatory and inhibitory receiver neurons. Inhibitory receiver neurons reproduce the input pattern, preventing their excitatory neighbors from doing the same. Unbalanced signal: By decreasing the responsiveness of the inhibitory receiver neurons, the signal balance in the excitatory receiver neurons shifts in favor of excitation, and the signal is revealed in their firing pattern. All firing rates and averages are calculated in 5 ms bins.
Figure 3
Figure 3. Response Analysis
a) Firing rates of the excitatory receiver neurons as a function of different constant sender firing rates, in the balanced (solid trace) and unbalanced (dashed trace) states. b) Ratio of receiver to sender excitatory firing-rate oscillation amplitudes at different oscillation frequencies, in the balanced (solid trace) and unbalanced (dashed trace) states. c,d) Response to a random time filtered signal in the unbalanced (c) and balanced (d) states. Red trace: average firing rate of the excitatory receiver neurons. Black histogram: rates of the sender neurons. Deviations from the signal in c) and from the average background rate in d) are colored grey. e) Schematic of an input step. Step size (*) and step duration (**) are varied independently. f) Average responses of the excitatory receiver neurons in the balanced state to instantaneous steps of different sizes. g) Peak amplitude of the responses in these neurons to steps of different sizes (legend) and durations (horizontal axis).
Figure 4
Figure 4. Gain Properties
a) Maximum values of the cross-correlations (termed "similarity", see methods) between the sender region and the excitatory and inhibitory receiver cells (red and blue respectively) for different gains. Solid lines show similarity values for symmetric gain reduction, dashed lines show similarity for asymmetric gain reduction, when only the gain of the excitatory synapses onto the inhibitory receiver cells is changed. b) Similarity values between excitatory receiver activity and the signal in the balanced (gated-off) state as a function of increasing the variability (standard deviation σ) of the synaptic strengths of the excitatory (green trace) and inhibitory (blue trace) pathways. The arrows mark the variability limits beyond which the tails of the strength distributions get rectified to zero. c) Effect of reducing the number of inhibitory receiver neurons on the ability to gate signals off. Similarity values in the balanced state for decreasing numbers of inhibitory receiver cells, without and with synapse strength compensation (solid and dotted line, respectively). d) Operation of the gating mechanism with only 20 inhibitory receiver neurons by compensating synapse strength and shortened refractory times to allow for more rapid inhibitory firing. Similarity between the signal and the excitatory (red trace) and inhibitory (blue trace) receiver activity is plotted as a function of change in inhibitory gain.
Figure 5
Figure 5. Network Pathologies
(a) Average firing rate of the sender neurons without and with an oscillatory input. (b–d). Responses of excitatory (red histogram) and inhibitory (blue trace) receiver neurons with: b) Correct tuning. c) Weakened local inhibition, leading to a gating deficit. d) A hyperactive receiver region causing a response to the gating modulation. Conditions shown in the different columns are: No signal and no modulation. No signal but gated on. Signal on and gated on. Signal on but gated off. Firing rates are calculated in 5 ms bins.
Figure 6
Figure 6. Gating Two Signals in a Network
a,b) Average response of the excitatory receiver subnetwork to two simultaneously delivered signals ( S1 and S2). The colored bars indicate the difference between the average firing rate in the receiver region (plotted in red) and either S1 (purple bars in a) or S2 (green bars in b). First column: Both signal pathways are balanced, the signals are off. Second and third column: Signal pathways 2 and 1 are unbalanced, respectively, by shifting the gain of their respective inhibitory receiver populations to 15% of their control values. c,d) Similarity values between S1 and the excitatory receiver activity (c) and S2 and the same excitatory receiver activity (d) for all possible combinations of the two gain modulations. Both signals reach similarity values of above 85%. e) Similarity values for S1 and S2 for independent gain changes. To the left of the gray line only the gain for S1 is manipulated while the gain for S2 remains 100%, and vice versa on the right side. Black circles indicate the gain values used for panels a & b. f) Similarity values as in c & d) but measured for the combined signal S1+S2. g) Similarity values between S1+S2 and the excitatory receiver subnetwork activity as a function of combined (equal) inhibitory gains, taken from the results along the diagonal of f.
Figure 7
Figure 7. Multiple Signals into a Single Cell
a–c) Firing rates of the output signal (red), averaged over 200 runs, compared to the input signal (black). 1st row: 10 simultaneous signal paths. 2nd row: 25 simultaneous signals paths. 3rd row: 100 simultaneous signal paths. a) Each afferent to the model neuron carries only one signal. b) Each afferent carries 40 signals. c) Each afferent can carry 40 signals but only 5 signals are present at a given time. d–f) Similarity values as a function of the number of signals being gated in a–c). d) With one signal per afferent, gating is limited to less than about 20 signals. e) Overlapping several signals onto each afferent improves performance slightly. f) When only 5 signals are present at a given time, unlimited numbers of signals can be gated when 40 signals are carried on each afferent (solid trace), but performance is still limited if each afferent carries a single signal (dashed trace).
See this image and copyright information in PMC

Comment in

Similar articles

See all similar articles

Cited by

See all "Cited by" articles

References

    1. Shu Y, Hasenstaub A, McCormick DA. Turning on and off recurrent balanced cortical activity. Nature. 2003;423:288–293. - PubMed
    1. Haider B, Duque A, Hasenstaub AR, McCormick DA. Neocortical network activity in vivo is generated through a dynamic balance of excitation and inhibition. J. Neurosci. 2006;26:4535–4545. - PMC - PubMed
    1. Shadlen MN, Newsome WT. Noise, neural codes and cortical organization. Curr. Opin. Neurobiol. 1994;4:569–579. - PubMed
    1. Troyer TW, Miller KD. Physiological Gain Leads to High ISI Variability in a Simple Model of a Cortical Regular Spiking Cell. Neural Comput. 1997;9:971–983. - PubMed
    1. Amit DJ, Brunel N. Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex. 1997;7:237–252. - PubMed

Publication types

LinkOut - more resources