The development of retinotectal maps: A review of models based on molecular gradients

Geoffrey J. Goodhill, Jun Xu
2005 Network  
Information about the world is often represented in the brain in the form of topographic maps. A paradigm example is the topographic representation of the visual world in the optic tectum/superior colliculus. This map initially forms during neural development using activity-independent molecular cues, most notably some type of chemospecific matching between molecular gradients in the retina and corresponding gradients in the tectum/superior colliculus. Exactly how this process might work has
more » ... s might work has been studied both experimentally and theoretically for several decades. This review discusses the experimental data briefly, and then in more detail the theoretical models proposed. The principal conclusions are that (1) theoretical models have helped clarify several important ideas in the field, (2) earlier models were often more sophisticated than more recent models, and (3) substantial revisions to current modelling approaches are probably required to account for more than isolated subsets of the experimental data. two-dimensional input structure and two-dimensional output structure such that neighbouring points in the input structure map to neighbouring points in the output structure and vice versa. ("Topographic map" is also sometimes used to describe a one or two-dimensional representation of a space of input features which has more than two dimensions (see Swindale 1996; Chklovskii & Koulakov 2004 for reviews). Topographic maps are an extremely common method used in the brain to represent information about the world. Such representations are probably crucial for efficient information processing, though exactly why is not definitively known (for some suggestions, see Cowey 1979; Linsker 1989; Durbin & Mitchison 1990) . The paradigm example of topographic map formation in the brain is the projection from the eye to the optic tectum, or superior colliculus (SC) in mammals. This is often referred to as the "retinotectal map", and in this context, "topography" is sometimes referred to as "retinotopy". Experimentally, this is the best studied and most completely characterized of all topographic projections. The mechanisms underlying retinotectal map formation may also be important in establishing connections in the retinogeniculocortical pathway, along which all the visual information we are consciously aware of enters our brain. Similar mechanisms are probably also crucial for establishing topography in other sensory pathways (Feldheim et al. 1998; Vanderhaeghen et al. 2000; Ellsworth et al. 2005) , and between more central brain structures (e.g., Gao et al. 1996) . Deciphering retinotectal map formation is therefore likely to increase our understanding of topographic map formation in the brain more generally, and thus our understanding of the basic information processing strategies used by nervous systems. This review focuses on theoretical models of retinotectal map formation. By a theoretical model, we mean one or more hypothesized principles underlying map formation stated as mathematical equations, usually accompanied by an analytical and/or computational demonstration of the consequences of these principles. These types of models offer several advantages over the "qualitative" models that are more common in biology in general. First, they force underlying assumptions to be made explicit rather than merely implied. Second, such models reveal which ranges of parameters are consistent with the desired outcome. Third, such models allow richer predictions for future experiments than are obtainable from qualitative models. These can include behaviours that do not appear to follow intuitively from the original idea, subtle quantitative effects not predictable from a purely qualitative model, and suggestions for new types of experiments that had not been inspired by purely qualitative reasoning. Theoretical models of this type are ubiquitous, and extremely successful, in physics (e.g., Greene 2004) but as yet have made fewer inroads in biology (for a sociological discussion of models in developmental biology, see Keller 2003). However, retinotectal map formation is an area where an unusually large and varied set of theoretical models were proposed in the 1970s and 1980s. The last 10 years have seen rapid progress in the experimental data and some new models, but the way in which these data and models relate to earlier theoretical proposals has not been much discussed. It is thus timely to do so now. We begin by reviewing the relevant experimental data. Retinotectal map development depends on both guidance of axons by molecular cues and refinement of synaptic strengths by neural activity. Conventionally, these have been regarded as two sequential phases of development, though they may also act in concert (Ruthazer & Cline 2004) . To maintain a manageable scope, this review focuses entirely on activity-independent processes; for reviews of relating modelling focusing more on activity-dependent development, see Swindale (1996) and van Ooyen (2001) . We then review the most significant theoretical models that have attempted to address subsets of this data (no model has yet attempted to address it all). Finally, we summarize the key ideas underlying modelling in this area and how these relate to experimental data, and make some suggestions for future modelling. Development of retinotectal maps 7 Experimental data Mapping in the adult In vertebrates, including fish, amphibians, and birds, the main visual centre in the brain is the optic tectum, part of the midbrain, which receives projections from the axons of retinal ganglion cells. In these species, retinal projections are mostly crossed (decussated) at the optic chiasm, meaning that left eye axons project mostly to the right (contralateral) tectum, with no fibres projecting to the left (ipsilateral) tectum, and vice versa for the right eye. In mammals, the retinal projection is split between the SC (the equivalent of the optic tectum) and the lateral geniculate nucleus of the thalamus. In addition, there is only a partial decussation of projections at the optic chiasm. The degree of decussation roughly correlates with the degree of binocular vision, i.e., the extent to which information from different eyes represents the same part of the world. For simplicity, we will sometimes use "tectum" to also mean the SC. The optic tectum and SC are layered structures. Within the layer to which retinal ganglion cell axons project, there is a topographic map of the visual world. This is oriented such that the nasal-temporal and dorsal-ventral axes of each retina map to the caudal-rostral and ventral-dorsal axes of each tectum, respectively (see Figure 1 ). This topographic map is crucial for visual function. For instance, in a classic body of work from the 1940s, Sperry showed that rewiring the projection so that it was inverted caused frogs to misplace visual targets by 180 • (reviewed in Sperry 1963). In mammals, the retinogeniculocortical pathway is more important for behaviour, and in humans it is the route for our conscious awareness of visual information. However, the projection to the SC is significant for the coordination of eye movements, which relies on a topographic representation of visual space aligned with maps of auditory and somatosensory space in other layers (reviewed in King 2004). Normal development of the pathway We do not discuss the development of retinal ganglion cells, or the guidance of ganglion cell axons out of the eye, along the optic nerve, across the optic chiasm, into the tectum, and into a specific tectal layer. Each of these stages of development relies on distinct molecular
doi:10.1080/09548980500254654 pmid:16353341 fatcat:g3shciassvchvlfd4b5opa5jfe