We produced a simple physical model (called the
Penny Pusher, after an arcade game in which players add pennies to the proximal edge of a preexisting sheet of coins with the aim of dislodging, and thereby pocketing, any coins that fall from the distal edge of the sheet) of the lens epithelium based on morphometric and labeling data obtained from 2-month-old mouse lenses (see
Figs. 3C,
6). The Penny Pusher was used to model cell production and movement in a sector of the peripheral lens epithelium over an 11-day period (
Fig. 10). The assumptions underlying the model were merely that the total number of cells in the epithelium is constant (
Fig. 6), cell death is absent (
Fig. 9), and S-phase lasts 12 hours.
19 Under these circumstances, introduction of supernumerary cells by mitosis in the GZ or PGZ must result in the displacement of an equal number of TZ cells into the fiber cell compartment. For simplicity, we considered the cell proliferation rate within the GZ (5%) to be uniform, whereas a bimodal distribution of S-phase cells is actually observed (see
Figs. 3B,
3C). The proliferative rate in the PGZ was set at 0.5%. To simulate cell division, an appropriate number of new cells (pennies) was introduced randomly into the proliferative compartments (PGZ and GZ) per day. As expected, the introduction of new cells at higher latitudes caused cells at lower latitudes to be displaced toward the edge of the epithelium. The model revealed that cells may accelerate as they approach the equator (see the animated sequence in
Supplementary Video S1). Acceleration occurred because of the cumulative displacement effect of mitoses occurring at higher latitudes, which imparted a greater “push” to cells as they approached the equator. Another interesting aspect of the model was that hexagonal packing of the “cells” was evident in the postmitotic TZ but not in the proliferative GZ and PGZ. In the model, the introduction of new cells into the proliferative regions of the epithelium served to continuously destabilize the hexagonal lattice that would otherwise have formed. Although the pennies in our model bore little physical resemblance to living lens epithelial cells (see
Fig. 8A or 8B, for example), it is possible that the need to avoid continuous destabilization of the lattice could be one reason why living lens epithelial cells pass through a postmitotic region (the TZ) before adopting the regular hexagonal packing that characterizes the rest of the fiber cell mass.