Quantitative assessment of computational models for retinotopic map formation

Abstract

Molecular and activity-based cues acting together are thought to guide retinal axons to their terminal sites in vertebrate optic tectum or superior colliculus (SC) to form an ordered map of connections. The details of mechanisms involved, and the degree to which they might interact, are still not well understood. We have developed a framework within which existing computational models can be assessed in an unbiased and quantitative manner against a set of experimental data curated from the mouse retinocollicular system. Our framework facilitates comparison between models, testing new models against known phenotypes and simulating new phenotypes in existing models. We have used this framework to assess four representative models that combine Eph/ephrin gradients and/or activity-based mechanisms and competition. Two of the models were updated from their original form to fit into our framework. The models were tested against five different phenotypes: wild type, Isl2-EphA3ki/ki, Isl2-EphA3ki/+, ephrin-A2,A3,A5 triple knock-out (TKO), and Math5−/− (Atoh7). Two models successfully reproduced the extent of the Math5−/− anteromedial projection, but only one of those could account for the collapse point in Isl2-EphA3ki/+. The models needed a weak anteroposterior gradient in the SC to reproduce the residual order in the ephrin-A2,A3,A5 TKO phenotype, suggesting either an incomplete knock-out or the presence of another guidance molecule. Our article demonstrates the importance of testing retinotopic models against as full a range of phenotypes as possible, and we have made available MATLAB software, we wrote to facilitate this process.

Novel Models of Visual Topographic Map Alignment in the Superior Colliculus

“…To model the development of corticocollicular connections, we extended a stochastical model [22] that was developed to model the establishment of retinocollicular topography and showed best qualitative assessment against experimental data [4]. As in the original approach, the model minimizes total energy E in the V1-SC system, which is a function of connectivity.…”

“…In the visual system, image-forming regions are organized into topographics maps, such that neighboring neurons monitor adjacent regions of visual space [1, 2]. The development of topographic connections in the visual system has been the focus of intense study, both experimentally and theoretically, elucidating general principles underlying neural circuit wiring [3, 4]. However, these studies have focused primarily on the mechanisms by which topographic connectivity is established for a single projection.…”

“…Indeed, several mathematical models have been developed to describe topographic mapping of retinocollicular projections [27–32]. However, each of the current models has weaknesses and cannot replicate the full complement of empirical data obtained from in vivo studies of mutant mice [4]. Further, no theoretical models of visual map alignment have been developed, hindering our ability to probe potential mechanisms of this critical developmental event.…”

In vivo imaging of the zebrafish retinotectal map

“…Models and experiments together have debated the various roles of the ephrin gradients and chemospecificity [74,125,129,229], competition [130,183,339,340] and axon-axon interactions [25,264,307].…”

“…Topographic wiring of the retinotectal connection in zebrafish from zebrafish is also likely to be useful to help constrain theoretical models of retinotectal map development [105,125].…”