The penny pusher: a cellular model of lens growth

Abstract

Purpose: The mechanisms that regulate the number of cells in the lens and, therefore, its size and shape are unknown. We examined the dynamic relationship between proliferative behavior in the epithelial layer and macroscopic lens growth.

Methods: The distribution of S-phase cells across the epithelium was visualized by confocal microscopy and cell populations were determined from orthographic projections of the lens surface.

Results: The number of S-phase cells in the mouse lens epithelium fell exponentially, to an asymptotic value of approximately 200 cells by 6 months. Mitosis became increasingly restricted to a 300-μm-wide swath of equatorial epithelium, the germinative zone (GZ), within which two peaks in labeling index were detected. Postnatally, the cell population increased to approximately 50,000 cells at 4 weeks of age. Thereafter, the number of cells declined, despite continued growth in lens dimensions. This apparently paradoxical observation was explained by a time-dependent increase in the surface area of cells at all locations. The cell biological measurements were incorporated into a physical model, the Penny Pusher. In this simple model, cells were considered to be of a single type, the proliferative behavior of which depended solely on latitude. Simulations using the Penny Pusher predicted the emergence of cell clones and were in good agreement with data obtained from earlier lineage-tracing studies.

Conclusions: The Penny Pusher, a simple stochastic model, offers a useful conceptual framework for the investigation of lens growth mechanisms and provides a plausible alternative to growth models that postulate the existence of lens stem cells.

Keywords: epithelium; growth; model.

Figure 1

Growth of the mouse lens and distribution of proliferating cells. Maximum intensity orthographic projections of segments of the anterior lens hemisphere were used to produce this composite image. Note that lens growth is rapid during embryonic and early postnatal development but slows considerably at later time points. Proliferating cells (EdU-labeled; green) are numerous in young lenses, where they are distributed throughout the epithelium. At later stages, fewer proliferating cells are observed and these are increasingly restricted to the equatorial epithelium. The inset shows a higher-magnification view of the central epithelium. Note also that the cells are more densely packed in the epithelium of the younger lenses. Nuclei (red) are counterstained with Draq5. Scale bars: 250 μm and 100 μm (inset).

Figure 2

The number of S-phase cells per lens decays to an asymptotic value of approximately 200 labeled cells. Parameter values represent best fit to Y = Y₀ + ae^−bx. Data represent mean ± SD of three independent measurements at each time point.

Figure 3

Variation of EdU-labeling index with distance from the lens equator in 8-week-old mice. (A) The epithelial margin is demarcated by the appearance of MR. EdU-labeled cells (green) are most common in the GZ, although labeled cells are also detected, at lower frequency, in the PGZ. (B) Superimposition of six individual projections reveals two peaks (a and b) of labeling intensity within the GZ. (C) Quantitative analysis confirms the existence of two labeling maxima within the GZ. The EdU-labeling index falls to zero at approximately 800 μm from the equator. This marks the border between the PGZ and the CZ, the anterior cap of epithelial cells wherein S-phase cells are only rarely observed. Quantitative data represent mean and SD (n = 6).

Figure 4

Distribution of EdU-labeled cells as a function of age and distance from the lens equator. Data represent mean values of more than six determinations at each age. Error bars have been omitted for clarity but are similar in magnitude to those shown in Figure 3C. Within the GZ, two labeling peaks, a and b, are apparent. At later stages (>6 months), peak b is shifted anteriorly to position b*.

Figure 5

Migration of EdU-labeled cells. Immediately after EdU treatment (t = 0), labeled cells (green) are located exclusively in the GZ and PGZ. One week (t = 1w) after EdU treatment, pairs of labeled cells are observed, some of which have traversed the TZ and entered the MR. At later time points (t = 4w, 8w), labeled cell pairs persist in the PGZ but are not detected in the GZ. Scale bar: 200 μm.

Figure 6

Variation in the epithelial cell population (filled triangles) and area of the anterior lens epithelium (filled circles) with time. The maximum epithelial cell count (approximately 50,000 cells) is reached by 4 weeks of age, after which the population declines to approximately 40,000 cells, despite the continued expansion in the anterior lens surface area.

Figure 7

Change in cell surface area as a function of latitudinal position and age. Data represent mean ± SD (n ≥ 3). The TZ represents average cell area 0 to 100 μm from the equator, GZ represents average cell area 200 to 300 μm from the equator, PGZ represents average cell area 400 to 500 μm from the equator, and CZ is the average cell area within a 300 × 300-μm measurement quadrat positioned in the center of the epithelium.

Figure 8

Changes in the dimensions of individual epithelial cells over time. (A) Volume-rendered image of a living P7 epithelial cell (apical membrane is outlined) imaged in the intact epithelium. (B) Similar image of an optically isolated epithelial cell in a 6-month-old lens. Significant, age-related changes occur in apical membrane area (C), volume (D), and cell thickness (E). Data represent mean ± SD.

Figure 9

Incidence of apoptotic cell death in the lens epithelium is undetectably low. Lenses were cultured for 24 hours in the presence or absence of 1 μM staurosporine and then incubated with a fluorogenic caspase substrate to monitor DEVDase activity (green). Lens epithelial nuclei in staurosporine-treated samples were fluorescent, whereas those in untreated lenses were not. These data indicate that cell death rates in healthy lens epithelia are undetectably low.

Figure 10

Penny Pusher model. Three frames (days 0, 4.5, and 11) from an animated sequence (see Supplementary Video S1) are shown. This physical model covers approximately 10 degrees of longitude of the equatorial epithelium of the 8-week-old mouse lens. Individual cells are represented by pennies. “Cells” are allowed to divide at the rates shown (PGZ 0.5%, GZ 5.0%, TZ 0%). Cell division is simulated by inserting a penny directly adjacent to a randomly selected cell. Ten white cells are present at the beginning of the experiment. These cells have identical replicative behavior to nonwhite cells and are simply included to allow cell lineages to be followed. The addition of new cells results in migration from the PGZ, through the GZ and TZ. In living lenses, fiber cell differentiation commences at the bottom of the TZ region. Note the hexagonal packing of cells in the TZ at later stages. Cells migrate in the direction of the arrow and accelerate as they approach the equator. At the end of the model run (day 11), four of the original white cells have left the epithelium but some of the white cells remaining in the epithelium have formed clonal groupings.