The effect of synaptic plasticity on orientation selectivity in a balanced model of primary visual cortex

Abstract

Orientation selectivity is ubiquitous in the primary visual cortex (V1) of mammals. In cats and monkeys, V1 displays spatially ordered maps of orientation preference. Instead, in mice, squirrels, and rats, orientation selective neurons in V1 are not spatially organized, giving rise to a seemingly random pattern usually referred to as a salt-and-pepper layout. The fact that such different organizations can sharpen orientation tuning leads to question the structural role of the intracortical connections; specifically the influence of plasticity and the generation of functional connectivity. In this work, we analyze the effect of plasticity processes on orientation selectivity for both scenarios. We study a computational model of layer 2/3 and a reduced one-dimensional model of orientation selective neurons, both in the balanced state. We analyze two plasticity mechanisms. The first one involves spike-timing dependent plasticity (STDP), while the second one considers the reconnection of the interactions according to the preferred orientations of the neurons. We find that under certain conditions STDP can indeed improve selectivity but it works in a somehow unexpected way, that is, effectively decreasing the modulated part of the intracortical connectivity as compared to the non-modulated part of it. For the reconnection mechanism we find that increasing functional connectivity leads, in fact, to a decrease in orientation selectivity if the network is in a stable balanced state. Both counterintuitive results are a consequence of the dynamics of the balanced state. We also find that selectivity can increase due to a reconnection process if the resulting connections give rise to an unstable balanced state. We compare these findings with recent experimental results.

Keywords: orientation map; orientation selectivity; plasticity; synaptic reconnection; visual cortex.

Figure 1

The network model. Each one of the cells of layer 2/3 (lower panels) receives a feed-forward input whose preferred orientation is shown in the corresponding position of the upper panel. The circle in layer 2/3 represents the width of the recurrent connectivity matrices. Left: orientation map; Right: salt-and-pepper layout.

Figure 2

STDP window: the relative changes of synaptic efficacy depend on the time difference between the post-synaptic (t_post) and the pre-synaptic (t_pre) spikes. Green indicates facilitation and red depression.

Figure 3

The excitatory and inhibitory inputs to one neuron tend to cancel even as they grow stronger with larger connectivity. (A) K = 250, (B) K = 1000. N_E = 16129, N_I = 4096. The rest of the parameters are set to default.

Figure 4

Distribution of orientation selectivity index for the neurons of the excitatory population. Systems with orientation maps (A) are less selective than networks with a salt-and-pepper organization (B). Parameters set to default values.

Figure 5

Spike-timing dependent plasticity increases selectivity. (A) Salt-and-pepper before synaptic modifications < OSI > = 0.57, (B) salt-and-pepper after synaptic modifications < OSI > = 0.63, (C) orientation map before synaptic modifications < OSI > = 0.27, (D) orientation map after synaptic modifications < OSI > = 0.36. In all the cases we show the distribution of orientation selectivity index for the neurons of the excitatory population. Parameters as in the previous figure.

Figure 6

Only for the system with salt-and-pepper organization STDP gives rise to a significant degree of functional connectivity. (A) Final value of the normalized synaptic efficacy w_{i, j} (see Equations 10 and 11) between neurons (i, E) and (j, E) as a function of the difference in the preferred orientations of the same neurons. (B) Average of the previous points in intervals of 10°. Green line: fit with the function $F(x)=a_0+2a_{1}cos(\pi x∕90^{°})$. The values of the fitted parameters are a₀ = 0.14, a₁ = 0.016. (C,D) As in (A,B) but for the orientation map. The values of the fitted parameters are now a₀ = 0.15, a₁ = −0.00084. All the rest of parameters as in the previous figure.

Figure 7

Preferred orientations of the neurons (PO_iA) are strongly correlated to preferred orientations of the feed-forward inputs (θ_iA) and they are conserved after reconnection. All the graphs correspond to the salt-and-pepper organization with default parameters. (A,C) Excitatory neurons. (B,D) Inhibitory neurons. In all the panels we show 2025 neurons. Parameters set as default.

Figure 8

When the balanced state is stable increasing functional connectivity in the excitatory interactions leads to a loss of selectivity in the excitatory population and an increase of selectivity in the inhibitory population. In contrast, increasing functional connectivity in the inhibitory interactions always leads to reduction of selectivity. (A) Average orientation selectivity index for the excitatory population (blue) and for the inhibitory population (red) as a function of the reconnection parameter ϵ_cE keeping ϵ_cI = 0.22. (B) The same averages as a function of ϵ_cI with ϵ_cE = 0.44.

Figure 9

When the balanced state is unstable for the first Fourier mode, increasing functional connectivity in the inhibitory interactions leads to reduction of selectivity. Average orientation selectivity index for the excitatory population (blue) and for the inhibitory population (red) as a function of ϵ_cI with ϵ_cE = 0.44.