Imprecise correlated activity in self-organizing maps of spiking neurons

Abstract

How neurons communicate with each other to form effective circuits providing support to functional features of the nervous system is currently under debate. While many experts argue the existence of sparse neural codes based either on oscillations, neural assemblies or synchronous fire chains, other studies defend the necessity of a precise inter-neural communication to arrange efficient neural codes. As it has been demonstrated in neurophysiological studies, in the visual pathway between the retina and the visual cortex of mammals, the correlated activity among neurons becomes less precise as a direct consequence of an increase in the variability of synaptic transmission latencies. Although it is difficult to measure the influence of this reduction of correlated firing precision on the self-organization of cortical maps, it does not preclude the emergence of receptive fields and orientation selectivity maps. This is in close agreement with authors who consider that codes for neural communication are sparse. In this article, integrate-and-fire neural networks are simulated to analyze how changes in the precision of correlated firing among neurons affect self-organization. We observe how by keeping these changes within biologically realistic ranges, orientation selectivity maps can emerge and the features of neuronal receptive fields are significantly affected.

Introduction

The pioneering work of Hubel and Wiesel (1962) on cortical activity in the primary visual cortex of cats showed that cortical neurons were more effectively activated when a certain receptive field on the retina was stimulated. They also demonstrated that the position of the receptive fields, the orientation selectivity and the ocular dominance present a global columnar organization in the cortex.

However, there is still some debate on how cortical orientation selectivity is set up (Ferster & Miller, 2000). While diverse physiological (Ferster et al., 1996, Reid and Alonso, 1995) and theoretical (Linsker, 1986, von der Malsburg, 1973) studies support the role of feed-forward connectivity for orientation selectivity (see Miller, Erwin, and Kayser (1999) and Swindale (1996) for revisions), other reputable works (Ben-Yishai et al., 1995, Martin, 2002, Somers, 1995) point to a greater influence of intracortical circuitry and inhibitory connections.

Another controversial issue is how the neurons communicate with each other to form the proper circuitry that will robustly support different features of the central nervous system. While many studies address the possibility of having a sparse neural code based on neural assemblies (Gerstein & Kirkland, 2001), synchronous fire chains (Gewaltig, Diesmann, & Aertsen, 2001), or oscillations (Ritz & Sejnowski, 1997), others claim the existence of neural codes that require a precise inter-neural communication to be arranged (Reich et al., 1997, Reinagel and Reid, 2000).

Neuronal response properties undergo several important transformations from the retina to the primary visual cortex. Receptive fields become more elaborated (Hubel & Wiesel, 1962), average firing rates are reduced and visual responses become more variable (Kara, Reinagel, & Reid, 2000). Studies of cross-correlation analysis suggest an additional transformation in which the correlated firing between presynaptic and postsynaptic neurons becomes less precise. While retinogeniculate connections generate very narrow correlograms with less than 1 ms width at half-amplitude (Usrey, Reppas, & Reid, 1999), the connections from the lateral geniculate nucleus (LGN) to cortical layer 4 and from layer 4 to layers 2 and 3 generate much wider correlograms (Alonso, Usrey, & Reid, 2001).

One of the main factors explaining this reduction of precision of the inter-neural correlated activity is synaptic jitter (Veredas, Vico, & Alonso, 2005). In the pathway between the retina and the visual cortex of mammals, neural synaptic jitter (i.e. the variability of synaptic transmission latencies) increases. For example, in the developing rat neocortex, Markram, Lubke, Frotscher, Roth, and Sakmann (1997) measured fluctuations in excitatory post-synaptic potential latency of 1.5 ms between layer 5 neurons, which is a very large value in comparison with the submillisecond produced by retinogeniculate connections (Cleland, Dubin, & Levick, 1971). Increasing transmission jitter significantly reduces the precision of the correlated firing (Veredas et al., 2005). The question that arises now is how this reduction of the time accuracy of spike transmissions could affect the organization of feature maps.

In this article we analyze the self-organization of receptive fields and orientation selectivity maps in feed-forward networks of integrate-and-fire (IAF) neurons with modifiable connections. Our results show how changes in the precision of the correlated firing among neurons do not prevent the emergence of orientation selectivity maps but affect the features of receptive fields. This means that reducing the exactness of inter-neural communication significantly influences the configuration of receptive fields in this sort of feed-forward network. We modified this accuracy of the correlated activity by introducing incremental and physiologically plausible changes in the synaptic transmission jitter, i.e. increasing the variability of synaptic transmission delays.

We address the problem using a spike-time dependent plasticity (STDP) (Panchev and Wermter, 2004, Rao and Sejnowski, 2001) approach, where modifiable excitatory synapses change during a learning process to converge into a self-organizing structure that presents orientation sensitive receptive fields.