A mathematical model of the eye lens epithelium of mammals that predicts cell density profiles in the ageing lens.

Quinlan, R.A.; Wu, J.J.; Wu, W.; Saunter, C.; Girkin, J.

Abstract

Purpose: To develop a mathematical model of the mammalian eye lens epithelium that is independent of the lens size and that accounts for the change in cell density from the anterior pole to the meridional rows at the lens equator. The model aims to predict the age dependent changes in cell density. Methods: Eye lenses were dissected, the epithelial flat mounted and then fixed and processed for immunofluoresence microscopy. Fluoresence signal were detected using either a Zeiss LSM 510 Meta or Leica SP5 scanning confocal microscope. Cell density measurements were made using DAPI and then bespoke software to segment images. Lenses from mice up to 2 years and from human donors from 20-90 years old were obtained with the required ethical, animal and human tissue authorisations. Results: The cellular distribution in the lens epithelium was measured in mouse, rat, rabbit, bovine and human lenses from the anterior pole of the lens to the meridional rows loacted at te lens equator. Measurements of cell proliferation (Ki67) and cell death (TUNEL) were also made. The epithelium was then modelled as a disk and an appropriate differential equation for the cell density distribution was solved. At any given time-point, this differential equation balances the pull-through due to fibre cell formation with net epithelial cell proliferation. Cell proliferation is concentrated in the peripheral region of the lens where the germinative zone is located, with only baseline proliferation rates observed in the central zone of the lens epithelium. The ratio of the per capita division rate for these two zones as predicted from the model was found to be equal to a recently measured gradient of matrix-bound FGF- 2 in the lens capsule. The model predicts that as the ratio of the proliferation parameter to the pull-through parameter declines, so the discrete peak in cell density found in the germinative zone will decay. Measurements of ageing mouse and human lens epithelial cell densities were used to affirm the predictive value of the model. Conclusions: We have developed a model of the mammalian lens epithelium that balances pull-through due to fibre cell formation with net cell proliferation. The model predicts the morphogen gradient that drives cell survival, cell proliferation and cell differentiation. It also successfully predicts the cell density changes that accompany ageing in the mouse lens. Commercial Relationships: Roy A. Quinlan, None; Junjie Wu, None; Weiju Wu, None; Chris Saunter, None; John Girkin, None Support: Fight for Sight (#1358) and Leverhulme Trust (RPG-2012- 554)

Citation

Quinlan, R., Wu, J., Wu, W., Saunter, C., & Girkin, J. (2015, May). A mathematical model of the eye lens epithelium of mammals that predicts cell density profiles in the ageing lens. Presented at ARVO 2015 Annual Meeting, Denver, Colorado

• Presentation Conference Type: Conference Paper (published)
• Conference Name: ARVO 2015 Annual Meeting
• Acceptance Date: Aug 30, 2015
• Publication Date: 2015-05
• Deposit Date: Mar 18, 2016
• Public URL: https://durham-repository.worktribe.com/output/1150794
• Publisher URL: http://www.arvo.org/webs/am2015/abstract/311.pdf