How can squint change the spacing of ocular dominance columns?

Abstract

The pattern of ocular dominance columns in primary visual cortex of mammals such as cats and macaque monkeys arises during development by the activity-dependent refinement of thalamocortical connections. Manipulating visual experience in kittens by the induction of squint leads to the emergence of ocular dominance columns with a larger size and larger column-to-column spacing than in normally raised animals. The mechanism underlying this phenomenon is presently unknown. Theory suggests that experience cannot influence the spacing of columns if the development proceeds through purely Hebbian mechanisms. Here we study a developmental model in which Hebbian mechanisms are complemented by activity-dependent regulation of the total strength of afferent synapses converging onto a cortical neurone. We show that this model implies an influence of visual experience on the spacing of ocular dominance columns and provides a conceptually simple explanation for the emergence of larger sized columns in squinting animals. Assuming that during development cortical neurones become active in local groups, which we call co-activated cortical domains (CCDs), ocular dominance segregation is controlled by the size of these groups: (1) Size and spacing of ocular dominance columns are proportional to the size σ of CCDs. (2) There is a critical size σ* of CCDs such that ocular dominance columns form if σ<σ* but do not form spontaneously if σ>σ*. This critical size of CCDs is determined by the correlation functions of activity patterns in the two eyes and specifies the influence of experience on ocular dominance segregation. We show that σ* is larger with squint than with normal visual experience. Since experimental evidence indicates that the size of CCDs decreases during development, ocular dominance columns are predicted to form earlier and with a larger spacing in squinters compared to normal animals.

Introduction

In layer IV of primary visual cortex, afferents from the left and right eye are segregated into spatially distinct domains called ocular dominance columns (ODCs) [30], [48]. Neurones in individual domains preferentially respond to stimulation of either the left or the right eye [23], [24]. In the primary visual cortex of cats, ODCs form a roughly repetitive pattern [1], [33], [48], [49]. During development the initially overlapping thalamocortical afferents of the two eyes gradually segregate into alternating patches between the third and sixth postnatal week [31], [49]. Functionally, however, ocular dominance columns can be visualized already between the second and third postnatal week [10], [44]. Many lines of evidence indicate that ocular dominance segregation is driven by activity-dependent competition for cortical territory between the geniculocortical afferents serving the two eyes [9], [20], [52]. At the level of individual neurones and synapses this competition presumably results from an activity-dependent refinement of synaptic connections whereby ‘improper’ connections are removed and ‘appropriate’ connections are elaborated [8], [26], [51]. It was shown previously that the spacing of ODCs in squinting cats was significantly larger than in normally raised animals [32] (figure 1). This dependence of ODC spacing on visual experience has also been suggested from model simulations [19] and similar observations have meanwhile been reported from cats that were raised with alternating monocular occlusion [56].

Because a global change in columnar spacing cannot be easily produced by shifting ocular dominance borders in a pre-existing grid these experimental observations rather indicate that the initially emerging pattern of ODCs forms spontaneously and is not determined by a yet unobserved pre-pattern.

The actual mechanism by which squint leads to a larger spacing of ODCs is presently unknown. Indeed the phenomenon that ODC spacing changes in response to a manipulation of visual experience seems to be at odds with a basic principle governing pattern formation in mathematical models of visual development. In a large class of models for the formation of ocular dominance patterns, it has been demonstrated mathematically that the spacing of ODCs is (1) determined by the range of lateral interactions within the cortical layer and (2) is independent of the degree of correlation among afferent activity patterns from the two eyes [39], [40], [54]. In particular, Miller has shown that (1) and (2) hold if activity-dependent rearrangement of synaptic connections follows a generalized Hebbian rule, i.e. is driven by the correlation of arbitrary functions of pre- and post-synaptic activity [34]. Because manipulating visual experience must be assumed to primarily affect the correlations among afferent activity patterns, the above observations [32], [56] appear rather surprising from a theoretical point of view. For reasons that are either mathematically or biologically not well understood some models for the formation of ocular dominance patterns appear to exhibit a dependence of column spacing on afferent activity patterns [4], [13], [19], [47].

In this paper we argue that the observed experience-dependence of the spacing of ODCs is readily explicable if the occurrence of ODC segregation is controlled by the range of intracortical interactions. Our mathematical analysis indicates that the range of intracortical interactions may not only determine the spacing of the emerging ODCs but also control ODC segregation in the sense that segregation can only occur if this range is below a threshold value.

Two assumptions appear essential for such a qualitative dependence of ODC segregation on intracortical interactions. (A1) Cortical activity patterns take the shape of locally co-activated domains. (A2) The total strength of synaptic connections is dynamically regulated by an activity-dependent mechanism.

In order to investigate how a changing range of intracortical interactions influences the segregation of afferent connections, we analysed a simple phenomenological model equation for ODC development which idealizes assumptions (A1) and (A2). In the following, we will first discuss the behaviour of this model assuming that the cortical response to an afferent activity pattern consists of a single co-activated domain. We will then show that the basic properties of this simple model persist when cortical activity patterns are a general nonlinear functional of afferent input. Our results demonstrate that the size σ of CCDs is a decisive parameter in the considered model. We show that under a wide range of conditions there exists a critical size σ* of CCDs such that ODCs can only form if σ is smaller than σ*. Furthermore, if ODCs do form their spacing is proportional to σ. Since evidence suggests that the size of CCDs decreases during development [2], [6], [12], [14], [17], [53], this implies that (1) ODCs arise by a symmetry breaking bifurcation that takes place as σ decreases below the critical value σ* (see also [21]) and (2) the spacing of ODCs is proportional to the size of CCDs when symmetry is broken. We show that the critical size σ* depends on the correlations between activity patterns in the two eyes and should be larger in squinting compared to normally raised animals. This dependency of the bifurcation threshold on afferent activity patterns yields a conceptually simple and experimentally testable mechanism for the development of larger sized columns in squinters.

ODCs are predicted to form earlier in squinting animals, i.e. at a time when co-activated domains are still of a larger size. As a consequence they exhibit a larger spacing in these animals. This should however only be the case if squint is induced before the emergence of ODCs. Ways to experimentally test the validity of the proposed mechanism are suggested.