Equalization of Synaptic Efficacy by Synchronous Neural Activity

It is commonly believed that spike timings of a postsynaptic neuron tend to follow those of the presynaptic neuron. Such orthodromic firing may, however, cause a conflict with the functional integrity of complex neuronal networks due to asymmetric temporal Hebbian plasticity. We argue that reversed spike timing in a synapse is a typical phenomenon in the cortex, which has a stabilizing effect on the neuronal network structure. We further demonstrate how the firing causality in a synapse is perturbed by synchronous neural activity and how the equilibrium property of spike-timing dependent plasticity is determined principally by the degree of synchronization. Remarkably, even noise-induced activity and synchrony of neurons can result in equalization of synaptic efficacy.

Figure 1

Rate of change in the unidirectional synapse, $\Delta g_{12}/A$, in a globally coupled and synchronized network. (a) The synaptic strength $g_{ij}$ is set to be $2g_{\mathrm{syn}}$ for $(i,j)=(1,2)$, 0 for (2, 1), and $g_{\mathrm{syn}}$ otherwise, where $1\le i$, $j\le N$. (b) Rate of change versus ($V_{\mathrm{syn}}$, ${\tau }_d$) in the system of $N=3$, $g_{\mathrm{syn}}=0.3\mathrm{mS}/{\mathrm{cm}}^2$, and ${\tau }_a=2\mathrm{ms}$, for $I_{\mathrm{dc}}=15\mu \mathrm{A}/{\mathrm{cm}}^2$ and $D=0.01$. (c) Same as (b), except for $I_{\mathrm{dc}}=0\mu \mathrm{A}/{\mathrm{cm}}^2$ and $D=5$. Shown in (d) to (f) is the rate of change versus (${\tau }_a$, ${\tau }_d$) for $V_{\mathrm{syn}}=0\mathrm{mV}$, $I_{\mathrm{dc}}=0\mu \mathrm{A}/{\mathrm{cm}}^2$, and $D=5$ in systems of (d) $N=3$ and $g_{\mathrm{syn}}=0.3\mathrm{mS}/{\mathrm{cm}}^2$, (e) $N=3$ and $g_{\mathrm{syn}}=1.0\mathrm{mS}/{\mathrm{cm}}^2$, and (f) $N=6$ and $g_{\mathrm{syn}}=0.3\mathrm{mS}/\mathrm{cm}$.

Figure 2

Reverse of spike timings in a synapse after temporarily synchronized activities. (a) Spike timings of neurons for ${\tau }_d=0\mathrm{ms}$ and ${\tau }_a=2\mathrm{ms}$. (b) Same as (a), except for ${\tau }_d=2\mathrm{ms}$ and ${\tau }_a=8\mathrm{ms}$. (c) Firing probability ${\rho }_{*}^{(\ell )}$ of a neuron, receiving synchronized spikes from other $\ell$ neurons, versus the time delay. The interval between the second spikes of neurons 1 and 2 in (b) relates to the distance between the peaks of ${\rho }_{*}^{(N-1)}$ and ${\rho }_{*}^{(N-2)}$ (with $N=3$). Note that the time interval decreases with $N$.

Figure 3

Equilibrium conditions of STDP learning. (a) Coefficient deviation versus the network size. The data in red represent the case of global connection with $g_{\mathrm{syn}}=0.1\mathrm{mS}/{\mathrm{cm}}^2$, $V_{\mathrm{syn}}=0\mathrm{mV}$, and $({\tau }_d,{\tau }_a)=(0,2)$ (in ms). The latter parameters have been varied to (6, 2) (blue) and to (2, 8) (green) whereas the data for $g_{\mathrm{syn}}=0.01\mathrm{mS}/{\mathrm{cm}}^2$ with (${\tau }_d$, ${\tau }_a$) unchanged are plotted in black. On the other hand, the data in gray describe the case that only 25% of neuron pairs are randomly chosen and connected, still with the same parameters as the case plotted in red. (b) Average activity $f$ versus time at the early stage of evolution, corresponding to the data in red, with $N=64$ in the limit $A\to 0$. The average activity has been measured through the time window of 0.1 ms. (c) Same as (b), for the data in green.