Universidad Autónoma Madrid

Dept. Ingeniería Informática

28049 Madrid (SPAIN)

{manuel,corbacho,siguenza}@ii.uam.es

Tel.: +34-1-397-4319 Fax: +34-1-397-5277

The behavior of the cortical structures in the striate cortex is typically explained by the selectivity of neurons to different aspects of the incoming information (e.g., orientation, direction, or color of the stimulus). Existing models of how this selectivity is achieved in the striate cortex can be clustered into three groups. In the first group of models it can be the result of selective neurons existing as early as in the retina (e.g. Barlow & Levick, 1965), in a second group of models it can be obtained by specific connectivity patterns coming from the LGN (Hubel & Wiesel, 1962), and in a third type of models it can be a phenomena emerging from the given cortical area under investigation. In the case of directional selectivity it is known that the input coming from the LGN is not directionally selective (Hubel & Wiesel, 1959). Therefore models based on retinal directional selectivity e.g. (Koch et al., 1986; Borg-Graham & Grzywacz, 1992) are not applicable. According to the dominant theories, strong postsynaptic inhibitory processes shunt the ample non directional excitation coming from LGN when movement in the non-preferred direction occurs, whereas this inhibition does not emerge in case of movement in the preferred direction (Goodwin et al., 1975; Orban, 1984; Koch and Poggio, 1985). However, careful intracellular recordings have not revealed such a strong inhibition in response to non-preferred stimuli (Douglas et al., 1991). Moreover, the strongest inhibitory signal was recorded when preferred stimuli were projected to the retina (Berman et al., 1991).

Douglas and Martin (1991) proposed a model of microcircuits in the cat visual cortex which potentially resolves the aforementioned puzzle. Our point of departure is precisely the canonical microcircuit developed by Douglas and Martin (1991). The smooth cell is modeled by three compartments consisting of one spherical soma, and two cylindrical compartments representinf the dendritic tree. The spiny neurons are modeled by four compartments consisting of one soma and three cylindrical dendritic compartments. Although all compartments are modeled with passive membranes, the soma compartments are assumed to have an active component that generates a string of pulses to be output along the axon (the average firing rate being a function of the membrane potential). The geometrical parameters of these compartments were derived from data provided by (Douglas and Martin, 1991) using typical cells from the three populations. Figure X shows the principal structure of the canonical microcircuit. The three boxes represent three populations in the cat striate cortex:

1. the pyramidal cells in the superficial layers (layer 2 and 3), and the spiny stellate cells in layer 4,
2. the pyramidal cells in the deep layers (layers 5 and 6),
3. the smooth cells in all these layers.

The formulation of these 3 clusters of cells is based on responses to electrical stimuli, which revealed no differences in responses within these groups and strong differences between them. This explains why the population of smooth cells compromises all superficial and deep basket cells and all the other types of known interneurons in one single cluster. The delicate tandem formed by the inhibitory and excitatory signals explains well why it is so difficult to detect inhibition with non-preferred stimuli. The less the intracortical excitation, the less input activates the smooth population, which in turn, exhibits less inhibition.

In this paper we present a theoretical analysis complemented with a computational model on some of the mechanisms that impart specificity to the developing nervous system. In particular we pay special emphasize on activity-dependent synaptic remodeling in the striate cortex. In particular we have included mechanisms specific to the development of local circuits in mammalian visual cortex (Katz & Callaway, 1992) to account for the development of activity-dependent neural specificity giving rise to directional selectivity.

Modeling synaptic plasticity can be carried out at different levels of abstraction. In this paper we elaborate on the work of von der Malsburg and Singer (1988) on how a set of cells may differentiate during development into a set of feature detectors that cover the perceptual feature space. Key to this work is the fact that no global control is induced upon the developing system. It is only through distributed and local control that the system attains a global organization, implementing the philosophy outlined by von der Malsburg and Singer (1988). The main feature of the organizing scheme is the cooperation and competition amongst neighboring groups of cells. In general, very local groups of cells positively support one another, while cells further away contribute inhibitory signals. Learning reinforces the connections of those cells that ultimately achieve a higher level of activity. This is implemented as a Hebbian learning rule, with a normalizing term that enforces a competition between incoming synapses. Thus, after learning, the field of cells will respond to a particular stimulus with a set of islands of activity, with each island consisting of several cells. Small shifts in the input stimulus are reflected by small shifts in the position of the islands.

One important drawback of von der Malsburg´s algorithm is its reliance upon a normalizing term that requires direct knowledge of all incoming synapses to update a single synapse. Other forms of normalization with a more distributed flavor have stronger biological support. In particular the temporal competition mechanism for weight update (Cooper et al., 1979) is one possible alternative to the normalizing term. According to this scheme, when an incidence between an incoming signal and the firing of a cell is detected, a weight update occurs. As opposed to the stantard Hebbian (LTP) update, however, the weights may also be decreased in response to an incidence. The decision to increase or decrease the weights is determined by whether or not the cell´s activity has reached above some threshold. Below the threshold anti-Hebbian (LTD) update (decrease of efficacy) occurs, above it the update is a Hebbian learning (increase of efficacy). An improved model was suggested by Bienenstock et al. (1982). According to their scheme, the activity of the cell is kept in check by allowing the LTD-LTP threshold to change over time. In general, this threshold is controlled by the overall activity of the cell (taken over a long period of time). Thus, when a cell is overly active, the threshold will increase, causing responses to most inputs to fall below the threshold into the LTD range, resulting in a decrease of the weights. Similarly, when the cell´s activity is very low, the threshold will decrease resulting in a general increase in weights and activity. In this paper we have exemplified how this style of computation may be utilized to develop an array of directional-specific cells.

We have achieved the following stages: first we have implemented a compartmental model of the cat striate cortex which reproduces the responses of the real cortex for electrical excitation with considerable fidelity. Second we have created a stimulus which represents LGN inputs to the striate cortex. Next we wire up the cells in the cortical area with biologically plausible synapses in a locally random fashion that corresponds to the pre-developmental state of the given cortical area. Finally we have implemented a local Hebbian-antiHebbian learning mechanism that develops a distribution of directionally selective cells similar to what has been observed in cats striate cortex.