Figure 1.

Schematic diagram of the model architecture. A, Excitatory pyramidal cells (bottom pyramids) receive input [“(external/feedforward) input to the memory circuit”] from neurons in the input layer (top circles) via the feedforward excitatory connections (red arrows). These feedforward connections are assumed to be topographically organized in a functional sense, but not necessarily in a physical sense, such that a pyramidal cell and an input layer neuron with similar location/angle preference (or memory/response field: black small arrows in the top circles and the bottom pyramids) are strongly connected (as indicated by the width of the red arrows). This feedforward excitation comprises the following two parts: axons of the input layer neurons (yellow-backed region) and dendrites of the pyramidal cells (green-backed region), between which there are feedforward synapses (small black-filled circles). B, The pyramidal cells are connected by recurrent excitatory connections (red arrows), which are assumed to be organized such that the strength of synaptic coupling between two pyramidal cells decreases with the difference in their preferred angles (represented by the width of the red arrows). This recurrent excitation is assumed to be added to each dendritic branch, rather than to the soma, of the pyramidal cells, as illustrated schematically. C, The soma-targeting inhibitory interneurons (bottom left ellipse) are activated by the pooled activity of all the pyramidal cells; in turn, these interneurons give inhibition onto the somata of the pyramidal cells [inhibitory interneurons are not explicitly modeled but instead represented by negative signs preceding the connection strengths (see Materials and Methods)]. D, Similarly, the dendrite-targeting inhibitory interneurons (bottom right ellipse) are activated by the pooled activity of all the pyramidal cells (global inhibition) or of nearby cells (local inhibition) and these interneurons give inhibition onto individual dendritic branch of the pyramidal cells. Although soma-targeting and dendrite-targeting interneurons are schematically illustrated as separate cell populations in those figures, it might be more likely that a single cell population could implement both of them (for details, see Results, On the nature of recurrent inhibition; and Materials and Methods, Network architecture). E, The neural circuit for spatial working memory was assumed to consist of topographically organized feedforward excitatory connections from neurons in the preceding visual cortices (top circles) to the pyramidal cells in the memory circuit (bottom pyramid), recurrent excitation between pyramidal cells, and either somatically or dendritically mediated recurrent inhibition. Nonlinear input integration was assumed to be imposed on each dendritic branch of the pyramidal cells (black square; see H). For more details, see Materials and Methods. F, Schematic view of the assumption regarding the distribution of the feedforward excitatory inputs onto the dendritic branches of pyramidal cells. The external space was assumed to be mapped, not only onto a population of neurons constituting the circuit (“topographic organization of the feedforward inputs”; left), but also onto a dendritic tree of individual component neurons (right), by virtue of the dendritic branch-specific plasticity rules (for details, see Results and Materials and Methods). The morphology of the pyramidal cell was taken from a layer 2/3 neocortical pyramidal cell model (Mainen et al., 1995) in the NEURON computational neuroscience model archive. G, The number of input layer neurons and that of dendritic branches of every pyramidal cell are assumed to be the same, for simplicity, and each single dendritic branch of a given pyramidal cell receives feedforward input from a different single input layer neuron. The feedforward excitatory connection strength between each dendritic branch and the input layer neuron connected to the branch is assumed to have a bell-shaped distribution (indicated by the orange line) peaked at the input layer neuron with the same angle preference as the pyramidal cell (0° in this figure). Note that, because of this assumption, dendritic branches connected to the input layer neurons with the angle preferences of −45 ∼45° receive almost all the feedforward inputs, whereas other branches mainly receive recurrent inputs. In most of the simulations, recurrent excitation was assumed to be uniformly distributed over the branches (red solid line), although nonuniformly distributed recurrent excitation (red dashed line) was also examined in some simulations (Fig. 13D–F and the corresponding text). Note that the relative strength of the feedforward and recurrent excitation shown in the graph does not represent the actual value (for the values, see Materials and Methods). Ha, The nonlinearity of the input integration in the dendritic branches was modeled as a piecewise linear function, characterized by threshold, slope, and upper bound (saturation). I considered two different cases as follows. Hb, The case of moderately nonlinear dendrite. This could represent the situation of a short passive dendritic branch, in which input integration is nearly linear except for the saturation and branch restrictiveness of shunting inhibition, which was modeled by rectification (threshold at 0). The effect of inhibition applied onto the branch, when it was considered, was modeled as a subtraction (blue arrow). Hc, The case of highly nonlinear dendrite. This could represent the situation of a long active dendritic branch, in which the branch can contribute to somatic firing almost only when the excitation applied onto the branch exceeds a certain amount (represented as a positive threshold in the function) so that dendritic spikes are generated. The effect of inhibition applied onto the branch was modeled as a division on the input, resulting in a combination of division and subtraction on the output firing rate, as indicated by the reduction in the slope and the rightward shift (blue arrows), respectively.