A dimensionless ordered pull-through model of the mammalian lens epithelium evidences scaling across species and explains the age-dependent changes in cell density in the human lens |
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Authors: | Jun Jie Wu Weiju Wu Frederique M Tholozan Christopher D Saunter John M Girkin Roy A Quinlan |
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Affiliation: | 1Biophysical Sciences Institute and School of Engineering and Computing Sciences, Durham University, Durham DH1 3LE, UK;2Biophysical Sciences Institute and School of Biological and Biomedical Sciences, Durham University, Durham DH1 3LE, UK;3Biophysical Sciences Institute and Department of Physics, Durham University, Durham DH1 3LE, UK |
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Abstract: | We present a mathematical (ordered pull-through; OPT) model of the cell-density profile for the mammalian lens epithelium together with new experimental data. The model is based upon dimensionless parameters, an important criterion for inter-species comparisons where lens sizes can vary greatly (e.g. bovine (approx. 18 mm); mouse (approx. 2 mm)) and confirms that mammalian lenses scale with size. The validated model includes two parameters: β/α, which is the ratio of the proliferation rate in the peripheral and in the central region of the lens; and γGZ, a dimensionless pull-through parameter that accounts for the cell transition and exit from the epithelium into the lens body. Best-fit values were determined for mouse, rat, rabbit, bovine and human lens epithelia. The OPT model accounts for the peak in cell density at the periphery of the lens epithelium, a region where cell proliferation is concentrated and reaches a maximum coincident with the germinative zone. The β/α ratio correlates with the measured FGF-2 gradient, a morphogen critical to lens cell survival, proliferation and differentiation. As proliferation declines with age, the OPT model predicted age-dependent changes in cell-density profiles, which we observed in mouse and human lenses. |
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Keywords: | eye lens cell proliferation ageing cataract mathematical model scaling |
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