The lens growth process.

The factors that regulate the size of organs to ensure that they fit within an organism are not well understood. A simple organ, the ocular lens serves as a useful model with which to tackle this problem. In many systems, considerable variance in the organ growth process is tolerable. This is almost certainly not the case in the lens, which in addition to fitting comfortably within the eyeball, must also be of the correct size and shape to focus light sharply onto the retina. Furthermore, the lens does not perform its optical function in isolation. Its growth, which continues throughout life, must therefore be coordinated with that of other tissues in the optical train. Here, we review the lens growth process in detail, from pioneering clinical investigations in the late nineteenth century to insights gleaned more recently in the course of cell and molecular studies. During embryonic development, the lens forms from an invagination of surface ectoderm. Consequently, the progenitor cell population is located at its surface and differentiated cells are confined to the interior. The interactions that regulate cell fate thus occur within the obligate ellipsoidal geometry of the lens. In this context, mathematical models are particularly appropriate tools with which to examine the growth process. In addition to identifying key growth determinants, such models constitute a framework for integrating cell biological and optical data, helping clarify the relationship between gene expression in the lens and image quality at the retinal plane.

A full lifespan model of vertebrate lens growth.

The mathematical determinants of vertebrate organ growth have yet to be elucidated fully. Here, we utilized empirical measurements and a dynamic branching process-based model to examine the growth of a simple organ system, the mouse lens, from E14.5 until the end of life. Our stochastic model used difference equations to model immigration and emigration between zones of the lens epithelium and included some deterministic elements, such as cellular footprint area. We found that the epithelial cell cycle was shortened significantly in the embryo, facilitating the rapid growth that marks early lens development. As development progressed, epithelial cell division becomes non-uniform and four zones, each with a characteristic proliferation rate, could be discerned. Adjustment of two model parameters, proliferation rate and rate of change in cellular footprint area, was sufficient to specify all growth trajectories. Modelling suggested that the direction of cellular migration across zonal boundaries was sensitive to footprint area, a phenomenon that may isolate specific cell populations. Model runs consisted of more than 1000 iterations, in each of which the stochastic behaviour of thousands of cells was followed. Nevertheless, sequential runs were almost superimposable. This remarkable degree of precision was attributed, in part, to the presence of non-mitotic flanking regions, which constituted a path by which epithelial cells could escape the growth process. Spatial modelling suggested that clonal clusters of about 50 cells are produced during migration and that transit times lengthen significantly at later stages, findings with implications for the formation of certain types of cataract.

A stochastic model of eye lens growth.

The size and shape of the ocular lens must be controlled with precision if light is to be focused sharply on the retina. The lifelong growth of the lens depends on the production of cells in the anterior epithelium. At the lens equator, epithelial cells differentiate into fiber cells, which are added to the surface of the existing fiber cell mass, increasing its volume and area. We developed a stochastic model relating the rates of cell proliferation and death in various regions of the lens epithelium to deposition of fiber cells and radial lens growth. Epithelial population dynamics were modeled as a branching process with emigration and immigration between proliferative zones. Numerical simulations were in agreement with empirical measurements and demonstrated that, operating within the strict confines of lens geometry, a stochastic growth engine can produce the smooth and precise growth necessary for lens function.

The penny pusher: a cellular model of lens growth.

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.