Background synaptic input modulates the visuospatial working memory

It is generally thought that persistent firing of neurons in the prefrontal cortex underlies working memory. Previous studies have focused on the influence of recurrent synaptic connectivity in local circuits on memory storage. Given neurons in the neocortex are extensively connected, individual neural circuits should receive synaptic inputs from other areas. Here we explore how background synaptic inputs (BSIs) modulate the visuospatial working memory in an oculomotor delayed response task. In a local recurrent network composed of pyramidal cells and interneurons, a bump attractor persists across the delay period, encoding the cue location. Under independent BSIs, the spontaneous network state before the cue presentation can be classified as inactive, active, or overactive, occurring successively with increasing the BSI strength, and the active state facilitates the memory storage. Under spatially correlated BSIs, optimal scenarios, in terms of accuracy of representation and resistance to distraction, involve the BSIs with intermediate strength and low correlation or high strength and moderate correlation. Our results demonstrate how the memory storage is regulated via tuning the balance between local excitation and global inhibition in the network. The current work reveals the functional importance of background input and suggests that robust memory storage could be accomplished over a variety of network states.

Figure 1

Schematics of network model and background synaptic inputs (BSIs). (a) Shown is synaptic connectivity in the network composed of pyramidal cells (P) and interneurons (I). (b) For independent BSIs, each neuron (either pyramidal cell or interneuron) receives $N_0$ Poisson spike trains at $f_0$ and $f_{\mathrm{BSI}}=N_0$ $f_0$. (c) For spatially correlated BSIs, each neuron receives $N_{\mathrm{u}}$ independent Poisson spike trains at $f_0$ and $N_{\mathrm{c}}$ Poisson spike trains that are common to all neurons, with $f_{\mathrm{BSI}}=\left(N_{\mathrm{u}}+N_{\mathrm{c}}\right)$ $f_0$.

Figure 2

Different types of spontaneous state under independent BSIs. (a) A raster plot for pyramidal cells in a spontaneous state at $f_{\mathrm{BSI}}=1.0\mathrm{kHz}$. (b) The membrane potential $V_m$ (diamond) and firing rate $f_{\mathrm{SP}}$ (circle) averaged over all pyramidal cells and over a time interval of 2 s vs $f_{\mathrm{BSI}}$. The inset shows the results for interneurons. (c) Various sources of currents to pyramidal cells. Shown are the average excitatory (circle), inhibitory (up triangle), and total recurrent (down triangle) current, together with the total current (square), under the same condition as in (b). The inset shows the results for interneurons. All the mean values are obtained by averaging over 100 trials.

Figure 3

Persistent firing activity underlying memory storage under independent BSIs. (a) A raster plot for pyramidal cells at $f_{\mathrm{BSI}}=1.0\mathrm{kHz}$. A cue is presented at 180° between 750 and 1000 ms with $I_{\mathrm{cue}}=120\mathrm{pA}$, while a response is evoked after 4.75 s. (b) Occurrence probability of bump attractor vs the cue strength at $f_{\mathrm{BSI}}=1.0\mathrm{kHz}$. An average over 100 trials is taken for each $I_{\mathrm{cue}}$. $P_{\mathrm{ba}}\ge 0.95$ for $I_{\mathrm{cue}}\ge I_{\min }$. (c) $I_{\min }$ vs $f_{\mathrm{BSI}}$.

Figure 4

Population firing profile (PFP) of pyramidal cells under independent BSIs. (a)–(c) The PFP (a), total recurrent current (b), and total current (c) for different values of $f_{\mathrm{BSI}}$ (in kHz). Each data point is obtained by averaging over the interval from 250 to 1250 ms after the cue is removed and over 100 trials. The cue is always presented at 180°. (d),(e) The relative height (d) and sharpness (e) of the PFP vs $f_{\mathrm{BSI}}$ under the same condition as in (a).

Figure 5

Random drift of the bump attractor under independent BSIs. (a)–(c) Time courses of the angle of population vector on 100 trials for $f_{\mathrm{BSI}}=0.3$, 1.2, or 1.8 kHz. The red lines in (c) mark the trials where the attractor vanishes before 4 s and the corresponding timing is labeled with a dot. (d) Temporal evolution of the standard deviation of ${\theta }_P$, σ, for different values of $f_{\mathrm{BSI}}$ (in kHz). Note that $t=0$ in (a)–(d) corresponds to 200 ms after the cue disappearance; this is to eliminate the influence of firing activities during the cue period on population vector (population vector is calculated based on firing rates averaged over 400 ms). (e) The value of σ at 4 s vs $f_{\mathrm{BSI}}$. An averaging over 100 trials is made for each σ.

Figure 6

Resistance of memory storage to a distractor under independent BSIs. (a),(b) Raster plots for $f_{\mathrm{BSI}}=0.8\mathrm{kHz}$ (a) and 1.6 kHz (b). Both the cue and distractor are presented for 250 ms, and both the input currents are 500 pA. The distractor appears at 1.5 s after the cue is removed. (c) Shown is R vs the angular difference between the cue and distractor directions for different values of $f_{\mathrm{BSI}}$ (in kHz). (d) R vs $f_{\mathrm{BSI}}$ for different angular differences. An averaging over 100 trials is performed for each R.

Figure 7

Profile of total recurrent currents to pyramidal cells and histogram of R. (a),(c) Examples of the profile of total recurrent current to each neuron at three time points, i.e., before, during and after the distraction, at $f_{\mathrm{BSI}}=1.2$ kHz; the current is averaged over a time window of 250 ms and smoothed using a Gaussian kernel of 3°. The angular difference between the cue and distractor is $\mathrm{\Delta }\theta ={45}^{\circ }$ (a) or 180° (c). (b),(d) Histograms of R for $f_{\mathrm{BSI}}=0.3$, 1.2, and 1.8 kHz; 100 trials are taken for each case. $\mathrm{\Delta }\theta ={45}^{\circ }$ (b) or 180° (d).

Figure 8

Spontaneous state under correlated BSIs. (a) A raster plot for pyramidal cells where a bump attractor is generated (upper panel), and temporal evolution of the length of the corresponding population vector (lower panel). (b) Histograms of the occurrence time of the attractor for $\rho =0.1$, 0.4, and 0.7 at $f_{\mathrm{BSI}}=1.2\mathrm{kHz}$. (c) Average occurrence time vs ρ for different values of $f_{\mathrm{BSI}}$ (in kHz).

Figure 9

The PFP of pyramidal cells with correlated BSIs. (a)–(c) Shown are the PFP (a), total recurrent current (b), and total current (c) of pyramidal cells for different levels of spatial correlation at $f_{\mathrm{BSI}}=1.2\mathrm{kHz}$. Each data point is obtained by averaging over the period of 1 s and over 100 trials. (d),(e) The relative height (d) and sharpness (e) of the PFP vs ρ for $f_{\mathrm{BSI}}=0.3$, 1.2, and 1.8 kHz.

Figure 10

Stability of memory storage under correlated BSIs. (a) Time courses of the standard deviation of ${\theta }_P$ for different ρ at $f_{\mathrm{BSI}}=2\mathrm{kHz}$. (b) σ vs $f_{\mathrm{BSI}}$ for different ρ. (c)–(e) R vs Δθ for different ρ at $f_{\mathrm{BSI}}=0.3$, 1.2, or 1.8 kHz. (f)–(i) R vs ρ for different $f_{\mathrm{BSI}}$ (in kHz) at $\mathrm{\Delta }\theta ={45}^{\circ }$, 90°, 135°, or 180°. The input current from the distractor is fixed at 500 pA in all cases. Each data point is obtained by averaging over 100 trials.