Koulakov, A. A., Tsigankov, D. N. (August 2004) A stochastic model for retinocollicular map development. BMC Neurosci, 5. p. 30. ISSN 1471-2202 (Electronic)
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Abstract
BACKGROUND: We examine results of gain-of-function experiments on retinocollicular maps in knock-in mice [Brown et al. (2000) Cell 102:77]. In wild-type mice the temporal-nasal axis of retina is mapped to the rostral-caudal axis of superior colliculus. The established map is single-valued, which implies that each point in retina maps to a unique termination zone in superior colliculus. In homozygous Isl2/EphA3 knock-in mice the map is double-valued, which means that each point on retina maps to two termination zones in superior colliculus. This is because about 50 percent of cells in retina express Isl2, and two types of projections, wild-type and Isl2/EphA3 positive, form two branches of the map. In heterozygous Isl2/EphA3 knock-ins the map is intermediate between the homozygous and wild-type: it is single-valued in temporal and double-valued in the nasal parts of retina. In this study we address possible reasons for such a bifurcation of the map. RESULTS: We study the map formation using stochastic model based on Markov chains. In our model the map undergoes a series of reconstructions with probabilities dependent upon a set of chemical cues. Our model suggests that the map in heterozygotes is single-valued in temporal region of retina for two reasons. First, the inhomogeneous gradient of endogenous receptor in retina makes the impact of exogenous receptor less significant in temporal retina. Second, the gradient of ephrin in the corresponding region of superior colliculus is smaller, which reduces the chemical signal-to-noise ratio. We predict that if gradient of ephrin is reduced by a genetic manipulation, the single-valued region of the map should extend to a larger portion of temporal retina, i.e. the point of transition between single-and double-valued maps should move to a more nasal position in Isl2-EphA3 heterozygotes. CONCLUSIONS: We present a theoretical model for retinocollicular map development, which can account for intriguing behaviors observed in gain-of-function experiments by Brown et al., including bifurcation in heterozygous Isl2/EphA3 knock-ins. The model is based on known chemical labels, axonal repulsion/competition, and stochasticity. Possible mapping in Isl2/EphB knock-ins is also discussed.
| Item Type: | Paper |
|---|---|
| Uncontrolled Keywords: | Animals Axons physiology Ephrin-B2 metabolism Ephrin-B3 metabolism Ephrins metabolism Heterozygote Homeodomain Proteins biosynthesis genetics Homozygote Ligands Markov Chains Mice Mice Transgenic Models Neurological Receptor, EphA3 biosynthesis genetics Retina anatomy & histology growth & development metabolism Retinal Ganglion Cells cytology metabolism Stochastic Processes Superior Colliculus anatomy & histology growth & development metabolism Transcription Factors biosynthesis genetics |
| Subjects: | bioinformatics > genomics and proteomics > annotation > map annotation organs, tissues, organelles, cell types and functions > tissues types and functions > retina organs, tissues, organelles, cell types and functions > tissues types and functions > superior colliculus |
| CSHL Authors: | |
| Communities: | CSHL labs > Koulakov lab |
| Depositing User: | CSHL Librarian |
| Date: | 31 August 2004 |
| Date Deposited: | 01 Feb 2012 18:11 |
| Last Modified: | 18 Jan 2017 19:48 |
| PMCID: | PMC520742 |
| Related URLs: | |
| URI: | https://repository.cshl.edu/id/eprint/22416 |
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