Fig. 3: Effect of distance dependence for excitatory current stability.
a,b, Schematics of the simulation. a, A single postsynaptic neuron receives 800 plastic excitatory (*) and 200 static inhibitory synapses. b, Top, all excitatory synapses are assumed to form a one-dimensional (1D) (line) connectivity pattern, with two consecutive synapses being separated by a unitary distance (normalized distance; Δx = 1). The effect of neighboring activation is weighted by a Gaussian curve centered at the synapse undergoing plasticity (black synapse) defined by a standard deviation, σ. Bottom, three examples for different σ values (σ = 1, 2 and 3). To compare different values of σ (c and d), the peak of the distance dependent interaction was normalized by the area under the curve. c,d, Average (c) and standard deviation (d) of the excitatory NMDA currents per synapse after learning as a function of the standard deviation, which defined the distance-dependent effect, σ. Gray dots represent simulations in which all presynaptic neuronsʼ firing rates are equal. Colored dots represent simulations in which individual excitatory presynaptic neuronsʼ firing rates are uniformly distributed between 0 Hz and 18 Hz. Each color indicates a different characteristic time for the excitatory current filter, E (equation (1)). All inhibitory neurons have a constant firing rate of 18 Hz. σth ≈ 0.6 defines the transition from effectively non-interacting (σ < σth) to interacting (σ > σth) synapses, whose steady-state distributions of synapse-specific NMDA currents differ (Extended Data Fig. 3). σfit ≈ 4.4 is the value fitted to the experimental curve (green curve in Fig. 2j; σ = 4.4 μm) assuming an average distance of 1 μm between neighboring synapses. e–g, Total excitatory NMDA current after learning as a function of the ratio between heterosynaptic and LTP learning rates (e), initial excitatory weights (f) and inhibitory weights (g). Continuous lines indicate a simplified analytical solution (Methods). The dashed line in e indicates the threshold for which the heterosynaptic plasticity term may induce vanishing of weights (shaded region; Methods).
