Feed-forward inhibition as a buffer of the neuronal input-output relation

Abstract

Neuronal processing depends on the input-output (I/O) relation between the frequency of synaptic stimulation and the resultant axonal firing rate. The all-or-none properties of spike generation and active membrane mechanisms can make the neuronal I/O relation very steep. The ensuing nearly bimodal behavior may severely limit information coding, as minimal input fluctuations within the expected natural variability could cause neuronal output to jump between quiescence and maximum firing rate. Here, using biophysically and anatomically realistic computational models of individual neurons, we demonstrate that feed-forward inhibition, a ubiquitous mechanism in which inhibitory interneurons and their target cells are activated by the same excitatory input, can change a steeply sigmoid I/O curve into a double-sigmoid typical of buffer systems. The addition of an intermediate plateau stabilizes the spiking response over a broad dynamic range of input frequency, ensuring robust integration of noisy synaptic signals. Both the buffered firing rate and its input firing range can be independently and extensively modulated by biologically plausible changes in the weight and number of excitatory synapses on the feed-forward interneuron. By providing a soft switch between essentially digital and analog rate-code, this continuous control of the circuit I/O could dramatically increase the computational power of neuronal integration.

Fig. 1.

Basic intrinsic properties of the modeled cells. (A) Schematic representation of the FFI model, including an interneuron (MOPP) and a principal (granule) cell. Red arrows identify the external excitatory input to both cells; n_M, w_M, n_g, and w_g represent number and weight of the synapses on the MOPP and granule cell, respectively. The blue line depicts the inhibitory output of the MOPP cell targeting the granule cell dendrites with n_f synapses of weight w_f. The granule cell output is illustrated without (red line) or with (purple line) the MOPP inhibitory input. (B) I-f curves of the model MOPP (Left, blue) and granule cell (Right, red) describing the firing rate response to somatic current injections. Experimental data (black) were replotted from published reports for MOPP cells (20) and for 3 independent studies of granule cells (exp1 (21), exp2 (22), and exp3 (23), respectively). Insets show somatic recordings for both experiments and models at specific current amplitudes.

Fig. 2.

The number and weight of synaptic inputs on the MOPP cell can modulate the buffering effect of FFI. (A) MOPP (blue) and granule cell (red) firing rates as a function of the frequency of excitatory synaptic input (without inhibition on the granule cell). The values for n_M and w_M were 200 and 0.05 nS, respectively. L^I and L^II are the lines used to fit the slope and saturation of the MOPP curve. Insets show sample traces for specific cases. (B) Granule cell firing rate under different conditions of MOPP activation and determination of R and F, by fitting the granule cell I/O curve with 4 lines (L1–L4). Error bars are standard deviations (n = 20 simulation sets).

Fig. 3.

The buffer range and frequency can be broadly and systematically controlled by the input to the inhibitory neuron. (A–D) Independent modulation of the granule cell firing rate F (Top) and range R (Bottom) as a function of the weight w_M (Left) and number n_M (Right) of the excitatory synapses on the MOPP cells. (E–F) Computed n_M and w_M values to obtain a target pair of F and R values. The quadratic equation has 2 solutions for each pair of F and R (high n_M and low w_M or vice versa), illustrated by corresponding color shades. Dots are fitted data.