On the Importance of Countergradients for the Development of Retinotopy: Insights from a Generalised Gierer Model

• Published in: PloS one Vol. 8; no. 6; p. e67096
• Main Author: Sterratt, David C
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 27-06-2013; Public Library of Science (PLoS)
• Subjects: Animals; Basic Helix-Loop-Helix Transcription Factors - genetics; Basic Helix-Loop-Helix Transcription Factors - metabolism; Biology; Brain architecture; Colliculus; Compensation; Computer Simulation; Eph protein; Gene Knock-In Techniques; Gene Knockout Techniques; Ligands; Mapping; Matching; Mice, Transgenic; Models, Neurological; Nerve Tissue Proteins - genetics; Nerve Tissue Proteins - metabolism; Neuronal Plasticity - physiology; Neurons - cytology; Neurons - physiology; Phenotype; Receptor, EphA3 - genetics; Receptor, EphA3 - metabolism; Receptors; Receptors, Eph Family - genetics; Receptors, Eph Family - metabolism; Retina; Retina - cytology; Retina - growth & development; Retina - physiology; Superior Colliculi - cytology; Superior Colliculi - growth & development; Superior Colliculi - physiology; Superior colliculus; Topographic mapping; Topographic maps; Topography; Visual pathways; Visual Pathways - cytology; Visual Pathways - growth & development; Visual Pathways - physiology
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0067096

During the development of the topographic map from vertebrate retina to superior colliculus (SC), EphA receptors are expressed in a gradient along the nasotemporal retinal axis. Their ligands, ephrin-As, are expressed in a gradient along the rostrocaudal axis of the SC. Countergradients of ephrin-As in the retina and EphAs in the SC are also expressed. Disruption of any of these gradients leads to mapping errors. Gierer's (1981) model, which uses well-matched pairs of gradients and countergradients to establish the mapping, can account for the formation of wild type maps, but not the double maps found in EphA knock-in experiments. I show that these maps can be explained by models, such as Gierer's (1983), which have gradients and no countergradients, together with a powerful compensatory mechanism that helps to distribute connections evenly over the target region. However, this type of model cannot explain mapping errors found when the countergradients are knocked out partially. I examine the relative importance of countergradients as against compensatory mechanisms by generalising Gierer's (1983) model so that the strength of compensation is adjustable. Either matching gradients and countergradients alone or poorly matching gradients and countergradients together with a strong compensatory mechanism are sufficient to establish an ordered mapping. With a weaker compensatory mechanism, gradients without countergradients lead to a poorer map, but the addition of countergradients improves the mapping. This model produces the double maps in simulated EphA knock-in experiments and a map consistent with the Math5 knock-out phenotype. Simulations of a set of phenotypes from the literature substantiate the finding that countergradients and compensation can be traded off against each other to give similar maps. I conclude that a successful model of retinotopy should contain countergradients and some form of compensation mechanism, but not in the strong form put forward by Gierer.