Exact neural mass model for synaptic-based working memory

TL;DR

A neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity consisting of hundreds of thousands neurons in terms of a few macroscopic variables is developed.

Abstract

A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to get insight on Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are associated to stimulus-locked transient oscillations followed by a steady-state activity in the $β-γ$ band, thus resembling what observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the $γ$ power increases with the number of loaded items, as reported in many experiments, while $θ$ and $β$ power reveal non monotonic behaviours.

Figures (13)

• Figure 1: Comparison among neural mass and network models The results of the neural mass model (solid line) are compared with the network simulations (shaded lines) for a single excitatory population with $\upmu$-STP (column A) and with m-STP (column B). The corresponding raster plots for a subset of 2000 neurons are reported in ( A1-B1), the profiles of the stimulation current $I_\mathrm{S}(t)$ in ( A2-B2), the instantaneous population firing rates $r(t)$ in ( A3-B3), the available synaptic resources $x(t)$ in ( A4-B4), and the utilization factors $u(t)$ in ( A5-B5). Simulation parameters are $\tau_\mathrm{m}^e=15$ ms, $H=0$, $\Delta=0.25$, $J=15$, $I_\mathrm{B}=-1$ and network size $N=\mathrm{200,000}$.
• Figure 2: Two-item architecture The reported network is composed of two identical and mutually coupled excitatory populations and an inhibitory one: this architecture can at most store two WM items, one for each excitatory population.
• Figure 3: Memory loading, maintenance and rehearsal The results of three experiments are reported here for different background currents: selective reactivation of the target population ($I_\mathrm{B}=1.2$, A); WM maintenance via spontaneous reactivation of the target population ($I_\mathrm{B}=1.532$, B) and via a persistent asynchronous activity ($I_\mathrm{B}=2$, C). Raster plots of the network activity for the first (blue, A1-C1) and second (orange, A3-C3) excitatory population; here the activity of only 400 neurons over 200,000 ones is shown for each population. Profiles of the stimulation current $I_\mathrm{S}^{(k)}(t)$ for the first ( A2-C2) (second ( A4-C4)) excitatory population. Population firing rates $r_k$(t) ( A5-C5), normalized available resources ${\tilde{x}}_k(t)$ ( A6-C6) and normalized utilization factors ${\tilde{u}}_k(t)$ ( A7-C7) of the excitatory populations calculated from the simulations of the neural mass model (solid line) and of the network (shading). Spectrograms of the mean membrane potentials $v_1(t)$ ( A8-C8), $v_2(t)$ ( A9-C9), and $v_0(t)$ ( A10-C10) obtained from the neural mass model; for clarity the frequencies in these three cases have been denoted as $f_1$,$f_2$ and $f_0$, respectively. Red arrows in columns (B) and (C) indicate the time $t=2.15$ s at which the background current is set to the value $I_\mathrm{B}=1.2$ employed in column (A). The network simulations have been obtained by considering three populations of $N=\mathrm{200,000}$ neurons each (for a total of 600,000 neurons) arranged with the architecture displayed in Fig. \ref{['fig:topology']}. Other parameters: $H^{(i)}=H^{(e)}=0$, $\Delta^{(i)}=\Delta^{(e)}=0.1$, $J_\mathrm{ee}^\mathrm{(c)}=5 \sqrt{a}$, $J_\mathrm{ee}^\mathrm{(s)}=35 \sqrt{a}$, $J_\mathrm{ie}=13 \sqrt{a}$, $J_\mathrm{ei}=-16 \sqrt{a}$, $J_\mathrm{ii}=-14 \sqrt{a}$ with $a=0.4$.
• Figure 4: WM operations for a heuristic firing rate model The results of two experiments are reported here for different background currents: WM maintenance via spontaneous reactivation of the target population ($I_\mathrm{B}=1.520$, A) and via a persistent asynchronous activity ($I_\mathrm{B}=2.05$, B). Profiles of the stimulation current $I_\mathrm{S}^{(k)}(t)$ for the excitatory populations ( A1-B1). Population firing rates $r_k$(t) ( A2-B2), local field potentials $\mathrm{LFP}_k$ defined in Eqs. \ref{['LFP']} ( A3-B3), normalized available resources ${\tilde{x}}_k(t)$ ( A4-C4) and normalized utilization factors ${\tilde{u}}_k(t)$ ( A5-C6) of the excitatory populations calculated from simulations of the firing rate model \ref{['eq:wc1']},\ref{['eq:sfi2']}. Spectrograms of the local field potentials: $\mathrm{LFP}_1(t)$ ( A6-B6), $\mathrm{LFP}_2(t)$ ( A7-B7), and $\mathrm{LFP}_0(t)$ ( A8-B8). All the other parameter values as in Fig. \ref{['fig0']}.
• Figure 5: Juggling between two memory items The memory juggling is obtained in two experiments with different background currents: in presence of a periodic unspecific stimulation ($I_\mathrm{B}=1.2$, A) and in the case of spontaneous WM reactivation ($I_\mathrm{B}=1.532$, B). Raster plots of the network activity for the first (blue, A1-B1) and second (orange, A3-B3) excitatory population. Profiles of the stimulation current $I_\mathrm{S}^{(k)}(t)$ for the first ( A2-B2) (second ( A4-B4))) excitatory population. Population firing rates $r_k$(t) ( A5-B5), normalized available resources ${\tilde{x}}_k(t)$ ( A6-B6) and normalized utilization factors ${\tilde{u}}_k(t)$ ( A7-B7) of the excitatory populations calculated from the simulations of the neural mass model (solid line) and of the network (shading). Spectrograms of the mean membrane potentials $v_1(t)$ ( A8-B8), $v_2(t)$ ( A9-B9), and $v_0(t)$ ( A10-B10) obtained from the neural mass model. All the other parameter values as in Fig. \ref{['fig0']}.