|Molecular Vision 2006;
Received 9 August 2005 | Accepted 14 March 2006 | Published 3 April 2006
Computer modeling of secondary fiber development and growth: I. Nonprimate lenses
Jer R. Kuszak,1,2 Mike
Mazurkiewicz,1,2 Rebecca Zoltoski3
Departments of 1Ophthalmology and 2Pathology, Rush University Medical Center, Chicago, IL; 3Department of Biological Sciences, Illinois College of Optometry, Chicago, IL
Correspondence to: Jer R. Kuszak, PhD, Department of Pathology, Rush University Medical Center, 1653 West Congress Parkway, Chicago, IL, 60612; Phone: (312) 942-5630; FAX: (312) 942-2371; email: firstname.lastname@example.org
Purpose: The purpose of this study was to use qualitative and quantitative structural data from nonprimate lenses with branched (Y and line) sutures to generate computer models (animations) of secondary fiber development and suture formation.
Methods: A minimum of 12-18 adult lenses/species (mice, cows, frogs, and rabbits) were used in this study. Lenses were analyzed by light (LM), transmission (TEM), and scanning electron microscopy (SEM). Fiber width, thickness, and length were ascertained from micrographs and by using formulations to calculate distances between degrees of latitude and longitude on asymmetrical oblate spheroids. This information was then used to create scale computer assisted drawings (CADs) of fibers at different stages of their development. The CADs were then placed on a timeline and animated to produce dynamic representations of secondary fiber development and growth.
Results: Animating secondary fiber development and suture formation with the inclusion of quantifiable differences in fiber dimensions at progressive stages of their differentiation revealed the following: first, there is the presumption that fibers migrate, rotate, and elongate until they reach their sutural destinations is not likely to be correct. When developing fibers reach approximatelty 60-65% of their eventual total length, their migration and rotation is complete. The remaining fiber elongation (the production of end segments) occurs without either concomitant cellular migration or rotation. Second, it is presumed that suture branches originate peripherally and are then constructed sequentially until all of the branches come to confluence at the poles is also not likely to be correct. While suture branches do originate peripherally, if the rate of elongation is constant in the anterior and posterior directions (intrafiber elongation speed) and between developing fibers within a forming growth shell (interfiber elongation speed), then only a part of their construction proceeds sequentially toward the poles. A second suture branch origin will be established at the poles resulting in a short distal portion of suture branches being formed sequentially in the reverse direction. Suture formation will conclude when a long proximal and a short distal portion of branches come to confluence within unequal anterior and posterior polar cap regions. This segmented suture formation scheme will be more pronounced in line suture lenses than in Y suture lenses. Third, because lenses with branched sutures have growth shells consisting of fibers of unequal length, fiber maturation is likely to be initiated in these lenses before a growth shell as well as suture formation is completed and would proceed in distinct patterns over a period of time. This is in marked contrast to avian lens fiber maturation which does not begin until growth shell and suture (branchless umbilical) formation is completed and then occurs rapidly and essentially simultaneously across the entire growth shell.
Conclusions: Animations of secondary fiber development and suture formation based on quantitative analysis of electron micrographs reveals important novel aspects of these processes that have not been apparent from the results of previous mechanistic studies. The more complex schemes of fiber differentiation and suture formation presented herein are consistent with the notion that lens function (dynamic focusing) is interdependent on lens structure and physiology. The animations confirm that while all vertebrate lenses have a similar structure, differences in the level of their structural complexity established early in development and maintained throughout life can account for the varying amount of optical quality known to exist between species.
Most people are familiar with the saying "a picture is worth a thousand words" and accept it at least pragmatically. Stated another way, to completely convey all of the information presented in a picture requires a lot of words. But for each individual that views a picture, the words used to describe or interpret it are often very different. Nevertheless, pictures are often considered a more effective means of conveying information than words because they transcend both literacy level and language preference whereas both the written and spoken word do not.
It is now possible to greatly extend the power of using imagery to present scientific information by using computers to create movies or animations of biological processes by "tweening". Tweening is the process whereby a computer is used to create transitional or "tweened" images from consistent elements in multiple images taken at defined times throughout a process. Then by placing all of the images on a timeline, this enables a movie to be produced that represents changes that had occurred during successive stages of that process. In this manner, it is reasonable to state that such movies should be worth hundreds of thousands of words.
Vertebrate crystalline lenses develop and grow in an inverted pattern [1,2]. As a result, unlike other stratified epithelia, lenses retain every cell formed throughout life. From the standpoint of development, growth, and aging, lenses contain a permanent record of all of the cells formed during these periods. Similarly, from the standpoint of function, dynamic focusing, malfunction, presbyopia, and cataract lenses contain all of the cells either involved in or affected by these pathologies. Thus, it should be possible to take micrographs of lens structure at different depths or age in a single lens (intralens analysis) or from a number of lenses (interlens analysis) and create movies representing aspects of lens development, growth, aging, function, and malfunction. In this manner, "reverse engineering," the process of analyzing an existing system to identify its components and their inter-relationships, and to create representations of the system in another form or at a higher level of abstraction, can be effectively incorporated into structural analysis of lenses. As an example, this approach has been used to elucidate the mechanism of accommodation at the level of lens fibers in primates .
Movies created as previously described, depicting lens development and growth may prove to be particularly useful for the following reason: The mechanism of lens growth, the peripheral addition of growth shells consisting of secondary fibers formed throughout life, is presumed to occur in the same manner in all vertebrate lenses. However, suture formation, a significant consequence of lens development and growth shell construction, is not identical in all lenses. There are four distinct types of lens sutures . In order of increasing complexity the suture types are the umbilical, line, Y, and star. Of the animal models commonly used in lens research, chickens have lenses with umbilical sutures while frogs and rabbits have line sutures. Mice, rats, cats, dogs, pigs, sheep, and cows all have lenses with Y sutures. Primate lenses have Y sutures throughout gestation, but then develop and grow progressively more complex iterations of star sutures during defined periods of life . It is not known how or why the different types of sutures are formed. But if lens development and growth are subject to the same controls in all vertebrates then it should be possible to determine how, when, and most important, why they are applied in order to produce the different suture types. This information is significant because sutures negatively affect lens optical quality (sharpness of focus), and this detrimental influence increases with age and with lens pathologies [6-13].
Therefore, we have used both qualitative and quantitative structural data derived from light and scanning electron micrographs of nonprimate lenses with line and Y sutures to create "scale" computer movies modeling secondary fiber development and suture formation. Animating these processes reveals information that is neither apparent in static or still images nor from "mechanistic" studies designed to identify the factor or factors that direct or control these processes.
This study is unusual in that many, but not all, of the micrographs of mouse, bovine, frog, and rabbit lenses used to create the scale computer-assisted drawings (CADs) and animations presented in this report were not taken from animals obtained exclusively for this study. Rather, new data obtained from specimens prepared specifically for this study was supplemented with archival material gathered from results obtained over the course of almost 30 years of lens research. In any event, in all cases, a minimum of 12-18 lenses/species (mice, cows, frogs, and rabbits) were collected from animals obtained from approved commercial sources and treated in accordance with the ARVO Resolution on the use of animals in research. Protocols describing how specimens were prepared for structural analysis (light microscopy [LM], transmission electron microscopy [TEM], and scanning electron microscopy [SEM]) and the microscopes and cameras that were used for taking the micrographs will only be described here briefly as this information has already been given in greater detail elsewhere . Fixed but nonosmicated lenses were either separated along the polar axis into radial cell column wedges defined by suture planes , or dissected in a manner that permitted the retrieval of complete, intact suture patterns at different ages or depths [7,15]. The specimens were then osmicated, washed, dehydrated, and either embedded in plastic for sectioning or critical point dried for SEM. After mounting on aluminum stubs with silver paste, specimens were sputter coated with gold and examined with a JEOL JSM 35c scanning electron microscope (Peabody, MA) at 10-10,000x magnification. Both conventional and stereo scanning electron micrographs were taken with a Polaroid camera system.
The creation of scale computer-assisted drawings and animations on the basis of quantitative analysis of micrographs
All of our CAD drawings are oriented on a Cartesian coordinate system as shown in Figure 1A. By convention, we draw lenses so that in the in situ position the equatorial and polar axes are aligned, respectively, along the x, y, and z axes as shown in Figure 1B. In this orientation, the most superior and inferior parts of a lens are positioned at the top and bottom of the x, y plane (the equatorial plane), and the lens poles are positioned on the z axis (the polar plane). Note that because lenses, like the earth, are asymmetrical oblate spheroids, the position and dimensions of lens fibers and sutures can be accurately described and measured by using degrees of latitude and longitude (Figure 1C) . Note also that each growth shell, the stratum of a lens, consists of fully elongated fibers of variable but related shapes and length arranged in distinct suture patterns (Figure 2A). As regards fiber shape, there are two types of fibers; straight or planar fibers, and opposite end curvature or nonplanar fibers (Figure 2B). A straight fiber has its entire length lying within a coincident plane passed through it and the polar axis of the lens (Figure 2C). Thus, in a two-dimensional micrograph, these fibers appear to be straight even though they are still characterized by crescent curvature. In contrast, an opposite end curvature fiber does not have its entire length lying within a coincident plane passed through it and the polar axis of the lens (Figure 2D). Thus, in a two-dimensional micrograph, these fibers appear to be S-shaped along their crescent curvature.
The knowledge of how lenses grow (by the progressive and continuous addition of new growth shells consisting of secondary fibers formed throughout life) was derived initially from histological sections of lenses at different stages of embryogenesis and at several ages (juvenile, adult, middle, and old age) [16-19]. A more complete picture of the structural changes that occur throughout lens development and growth (transformation of cuboidal cells into exceedingly long fibers that become arranged in highly ordered radial cell columns and growth shells with intricate suture patterns) has been ascertained from SEM analysis [1,14,19-24] and most recently by scanning confocal microscopy analysis . All of this information has frequently been represented in gross scale schematic drawings. That is to say, depictions that considered the quantifiable measures of lens width (equatorial axis) and thickness (anteroposterior axis) but rendered fiber shape, size, position, and orientation qualitatively are subject to the artist's interpretation. The reason for rendering fibers qualitatively rather than quantitatively is quite simple. Every vertebrate lens is composed of thousands of growth shells, each consisting of thousands of secondary fiber cells arranged in anterior and posterior suture patterns (Table 1). A normal adult mouse lens (equatorial diameter about 2.5 mm), has about 1,500 fibers in a growth shell formed 1,000 μm from the embryonic nucleus. Mouse lens growth shells typically feature six suture branches, three arranged in an anterior Y pattern, and three arranged in a posterior inverted Y pattern. Each branch is formed by the abutting and overlapping of the ends of about 250 enantiomeric pairs of fibers. By comparison, in the much larger normal adult bovine lens (equatorial diameter about 17 mm), has about 8,000 fibers in a proportionately, comparable growth shell formed 4,000 μm from the embryonic nucleus. Bovine lens growth shells also typically feature six suture branches arranged in an anterior Y and a posterior inverted Y pattern. But in the cow lens each branch is constructed by the abutting and overlapping of the ends of almost 1,500 enantiomeric pairs of fibers. Thus, it would be a formidable task, requiring an exceptional attention to detail and a powerful computer, to create a one to one scale model of secondary fiber development and suture formation in any vertebrate lens.
Therefore, we have devised the following method to produce dynamic models (animations) of secondary fiber development and suture formation from scale computer assisted drawings (CADs) of lenses.
Figure 3 is a simple demonstration of how we create scale CADs of suture patterns. Key frames from this animation are presented as static images in Figure 3. The initial frame of this animation is a small portion of a scanning electron micrograph photo montage from a complete, intact Y suture pattern in an adult mouse lens taken at 1,000x magnification (Figure 3A). As the animation continues, it can be seen how the boundaries of the straight fiber that defines the origin of this suture branch are delimited and then filled in yellow to facilitate this fiber from its sutural destination to the equator (Figure 3B). However, note that this is just the anterior portion, or segment, of this fiber. Similarly, the boundaries of the first through fifth, as well as the tenth and twentieth fibers positioned on either side of the straight fiber are delimited and then filled in green (Figure 3B). At this magnification, the shapes, orientations, sizes (length and width) and positions of the highlighted fibers are easily and accurately assessed. However, to analyze the fibers positioned farther away from a suture branch origin, or alternately closer to its termination, it is necessary to ratchet back-and-forth between higher and lower magnifications in order to accurately follow them from their sutural destinations to the equator. In this manner, it can be shown that difference in the shape, position, sizes and orientations of the fibers that make up a suture branch are miniscule and incremental. Therefore, the variable shape, position, size, and orientations of fibers along a suture branch can be accurately represented in groups of fibers contained in a defined span of longitudinal degrees (Figure 3C; 20 fibers/5° longitude). The final frames of this animation show how the above described scale CADs of the anterior portions of fibers are combined with the posterior portions of fibers to reconstruct a complete growth shell from a Y suture lens. It is important to note the animations are based on scale CADs derived from multiple quantitative measures of the lens parameters presented in Table 1 and Table 2. In this manner, neither the CADs, nor the subsequent animations are subject to artist's interpretation.
Similarly, Figure 4A shows a small portion from a scanning electron micrograph photo-montage showing the bow region in a radial cell column (RCC) face of an adult rat lens. At 750-1,000x magnification, the different shapes, orientation, and position of differentiating germinative and transitional zone epithelial cells as well as nascent fibers are readily assessed. The different shapes, orientation, and position of pregerminative and central zone epithelial cells, elongating and mature fibers are contained in other parts of the montage. However, at this magnification, the complete montage measures approximately 200 cm x 175 cm and thus cannot be because its size obviously greatly exceeds that of a page. Therefore, in order to accurately convey information on the changing size, shape, orientation, and position of lens cells as they differentiate, we again delimit the boundaries of defined groups of cells on small portions of the montage at different magnifications (Figure 4B,C). Then all of the portions of a montage are combined to produce the scale CADs Figure 5 and Figure 6 on which animations of secondary fiber development are based.
In addition, in all of the CADs presented herein we use color to indicate when certain landmarks are reached in the development of secondary fibers. As an example, in Figure 5 and Figure 6, the cuboidal cells in the germinative zone selected to become fibers are depicted in light blue. As these cells differentiate into exceedingly long fibers, this structural change is further dramatized by a gradual increase in their color value. In Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, and Figure 12, as nascent fibers elongate and form sutures, we depict their inner and outer broad faces of fibers in different hues. The inner and outer broad faces of opposite end curvature fibers are depicted in blue and green, while the inner and outer broad faces of straight fibers are rendered, respectively, in red and yellow. The anterior portion of fibers is also rendered semitransparent so that the posterior portion of fibers can be viewed simultaneously when examined at different orientations relative to the polar axes.
Secondary fiber development: Rotation, migration and elongation of developing fibers
Figure 5 is a flip book animation of the commonly held but likely erroneous interpretation of differentiating fibers simultaneously rotating, migrating and elongating until they reach their sutural destinations. Key frames from this animation are presented as static images in Figure 5. The animation begins with a CAD of a generic vertebrate lens radial cell column face. Since this is a generic CAD it cannot by definition be completely quantitative. However, this CAD does represent a reasonable averaged rendition of the height and width, shapes, position, size, and orientation of grouped central, pregerminative, germinative, and transitional zone epithelial cells. Similarly, in this view, the thickness, length, position, and orientation of developing fibers are also reasonably averaged (Figure 5A). Qualitatively, this type of image appears to show that an epithelial cell selected to differentiate into a fiber cell, progressively rotates about its polar axis while simultaneously migrating and elongating until their ends abut and overlap to form sutures [4,26]. Indeed, this premise would appear to be confirmed by creating a simple "flip book" animation of secondary fiber development from Figure 5A as follows: Multiple copies are made of Figure 5A. In the first copy (Figure 5B), a nascent fiber pair at the periphery of the transitional zone is highlighted (Figure 5B). In each successive copy (Figure 5C-O), the next more internalized developing fiber pair is highlighted until in the final copy (Figure 5P) the highlighted fiber pair not only have their ends abutted and overlapped to form a suture, but have already been internalized by the addition of more secondary fibers (Figure 5P). When all of the images (Figure 5B-O) are placed on a time line, and presented sequentially as in Figure 5, it certainly appears that the highlighted developing pair do indeed simultaneously rotate, migrate, and elongate until they reach their sutural destinations. However, this premise is incorrect because neither the static images nor the animation represent the change in lens size over time (the fourth dimension). Lenses grow throughout life by the addition of developing fibers at the periphery. Thus, lens width (equatorial diameter) and thickness (measure of the anteroposterior axis) increase over time.
Figure 6 shows how including changes in lens size due to growth, supports the premise that developing fiber rotation and migration end prior to the completion of fiber elongation. Key frames from this animation are presented as static images in Figure 6. The animation begins with a CAD of a developing lens having just completed formation of the primary fiber mass, or embryonic nucleus (Figure 6A). As the animation continues, simultaneous rotation about the long axis of these developing fibers, posterior migration and elongation of, respectively, the anterior ends of fibers insinuating themselves between the fiber mass and the epithelium and the posterior ends between the fiber mass and the posterior capsule is apparent (Figure 6B-E). Note the additional pairs of developing fibers (light to dark blue) that follow. When developing fibers have rotated about their long axis to become essentially parallel to the polar axis of the lens, cellular or fiber migration is complete (Figure 6F). That is to say, the position of the middle portion or segment of a fiber, remains unchanged from this point on (observe the constancy of the highlighted pairs position from 6F-P both down columns and across rows). Continued elongation involves only the ends of fibers culminating in the formation of suture branches. In point of fact, while this animation (Figure 6) correctly presents secondary fiber development in general, it fails to present suture branch formation at all. As regards to suture formation, animations 2 and 3 (Figure 5, Figure 6) are most representative of avian or reptilian lens secondary fiber formation producing umbilical or point suture formation.
Secondary fiber development and lens growth: Y and line suture formation
The suture patterns (number, position, and size of branches) that characterize the different lens suture types (umbilical [branchless], line, Y, simple star, star, and complex star) are seen to greatest advantage when viewed directly along the polar axis (Figure 7A) [5,27]. However, in such a view the three dimensionality of a lens, and in particular the recognition of the fact that secondary fibers interact with different fibers anteriorly and posteriorly to produce offset front and back suture branches is not apparent. This aspect of fiber organization within a growth shell is shown to partial advantage when a lens is rotated 90° about the y axis and then viewed along the equatorial axis (Figure 7B). Rotating a lens an additional 90° (for a total of 180°) about the y axis reveals the complete opposite suture pattern to best advantage (Figure 7C) but again the three dimensionality of anterior and posterior sutures is not apparent in this view. To better appreciate suture construction requires that lenses be viewed in several orientations.
Formation of suture patterns in each growth shell is an end point of secondary fiber development. Since this process occurs over time, the use of animations facilitate a better understanding of this seemingly simple, but in fact, remarkably complex process. From micrographs and qualitative schematic representations of Y and line sutures, the following inferences can be and have been made regarding non-primate branched suture formation. As secondary fiber formation occurs in both Y and line suture lenses, the entire length of nascent fibers is aligned directly along the polar axis until their anterior and posterior leading ends reach about 15-20° and -15-20° latitude, respectively. At this point, in Y suture lenses, the fibers positioned at about 60°, 180°, and 300° longitude cease elongating in the anterior direction (Figure 8A) while in line suture lenses, the fibers positioned at about 0° and 180° longitude cease elongating in the anterior direction. Similarly, at this point in Y suture lenses, fibers positioned at about 0°, 120°, and 240° longitude cease elongating in the posterior direction while in line suture lenses fibers positioned at about 90° and 270° cease elongating in the posterior direction. These fibers are referred to as straight fibers because although they are characterized by crescent curvature, when fully elongated, their entire length is still aligned with the polar axis. All of the other developing fibers are, by definition, positioned between the straight fibers described previously. As the fibers located closest to, but on either side of a straight fiber continue to elongate, their anterior and posterior ends curve toward each other, but away from the polar axis in opposite directions until they abut and overlap within the space created by the cessation of straight fiber elongation, thereby forming the peripheral ends or origins of suture branches (Figure 8B). Subsequently, as the developing fibers located next to these fibers, and thus, slightly farther away from the straight fibers, continue to elongate, their anterior and posterior ends follow the lead of the previous fibers curving toward each other, but again away from the polar axis in opposite directions, until they abut and overlap forming the next portion of evolving suture branches (Figure 8C). This process has been presumed to continue in sequence until all of the developing fibers positioned between any two straight fibers have contributed to the formation of a suture branch that extends to confluence at the poles (Figure 8D-H). To highlight the point at which fibers reach both of their sutural destinations (Figure 8D-H) and thus are fully elongated, their color value (darkness) is doubled.
While the above described interpretation of branched suture formation is, in general, conceptually correct, it is not likely to be entirely accurate because it fails to incorporate the influence of quantifiable solid geometry parameters of lenses and their component parts, the lens fibers. When these parameters, lens spheroidicity, variable fiber length, and number of suture branches in growth shells are considered, a much more intricate suture formation scheme becomes apparent.
All vertebrate lenses are asymmetrical oblate spheroids. During gestation, the anterior surface curvature is greater than the posterior surface curvature. However, after birth and throughout life, the anterior surface curvature is less than the posterior surface curvature. As a result, the distance that fibers traverse as they elongate to their sutural destination is always, by solid geometric definition, unequal in the anterior and posterior directions. Furthermore, fiber elongation is initiated posteriorly. Bidirectional fiber elongation occurs mostly after a nascent fiber has rotated essentially 180° about its long axis (Figure 3, Figure 6). The rate of fiber elongation or growth is likely to be the same in the anterior and posterior direction (intra-fiber speed of elongation) and between all of the developing fibers within any growth shell (inter-fiber speed of elongation). This is a reasonable presumption considering that in other epithelial cell systems the rate of cell growth does not vary during a defined period (e.g., gestation, infancy, adolescence, or adulthood) . It follows then, that the representation of anterior and posterior suture branches being constructed simultaneously and sequentially as shown in Figure 8 is "incorrect".
A representation of Y and line suture formation based on quantitative data on lenses and their component fibers are shown, respectively, in Figure 9 and Figure 10. Key frames from these animations are presented as still images in, respectively, Figure 9 and Figure 10. These animations begin with scale CADs of representative forming growth shells in the early stages of Y and line suture lenses as viewed directly along the polar axis. The anterior portions of fibers are rendered semi-transparent so that the posterior portion is more readily apparent. At this stage of their development, all of the fibers still have their entire length aligned with the polar axis. Note that the posterior ends of the fibers are closer to the posterior pole than the anterior ends to the anterior pole because the onset of posterior elongation precedes that of anterior elongation. However, as the animation proceeds, it can be seen that even though posterior fiber elongation has a slight (100-150 μm) head start over anterior elongation (Figure 3, Figure 6), suture formation is initiated anteriorly (Figure 9A,B, Figure 10A,B). The staggered start between anterior and posterior suture branch construction may simply be the result of anterior suture branches being longer than posterior suture branches and the anterior surface of lenses being flatter than the posterior surface. Therefore, the distance that fibers need to traverse anteriorly to reach their anterior suture destinations, is by solid geometric definition shorter than the distance that fibers need to traverse posteriorly to reach their posterior suture destinations Anterior suture branches typically measure approximately 75% of the lens' major radius while posterior suture branches only measure approximately 60% of a lens' major radius. Thus, an initially short peripheral segment (approximately 15% of a suture branches' length) of anterior suture branches is likely formed prior to initiation of posterior suture branch construction (Figure 9B, Figure 10B). The shortest fibers in a growth shell are the straight fibers that define the origin of anterior suture branches.
As the animations proceeds it can be seen that anterior and posterior suture branch formation continues concurrently but in offset segments as fibers of variable length, a consequence of the different amount and sharpness of end curvature, reach their sutural destinations at different times. The variation in length between fibers that make up either of the end segments of suture branches is greater than that of fibers that make up the mid-segment of suture branches (Table 2). As a result, fibers with acutely curved anterior ends already abutted and overlapped to make up the peripheral ends of anterior suture branches, have posterior ends that are still elongating on their way to making very gently curved distal ends of offset posterior suture branches (Figure 9C, Figure 10C). Conversely, fibers with acutely curved posterior ends already abutted and overlapped to make up the peripheral ends of posterior suture branches have anterior ends that are still elongating on their way to making very gently curved distal ends of offset anterior suture branches. In contrast, the fibers that make up the midpoint of suture branches, the longest fibers in any growth shell, have nearly equal broadly curved ends that reach both sutures almost simultaneously (Figure 9D, Figure 10D). These fibers will be at once the last fibers to reach their sutural destinations and the first to reach both of their sutural destinations. Stated another way, more than 50% of any suture branch will be formed before any one fiber has fully elongated.
After completing the peripheral or proximal half of suture branch formation, suture construction continues in a relatively sequential scheme as fibers of decreasing length, the result of less end curvature, form the distal segment. However, as the animations finish they clearly show that this sequential scheme does not continue until suture branches extend to confluence at the poles as has been presumed (Figure 9E-G, Figure 10E-G). Rather, a second, short suture branch segment will originate at the pole as the shorter straight fibers reach the poles prior to the arrival of the slightly longer, almost straight fibers that immediately surround them (those fibers positioned within ±5 longitudinal degrees of straight fibers; Table 2). As the ends of these surrounding fibers extend to their sutural destinations, a short distal end segment of a suture branch will form in the reverse direction to the still-forming suture branch as the straight fiber ends arrive at their polar sutural destinations ahead of their neighboring fibers arriving at their near-to-the-pole sutural destinations The formation of a distal end segment preceding the termination of suture branch construction is shown to greater advantage dynamically as seen in Figure 11. Key frames from this animation are presented in Figure 11. This short animation begins with a larger scale CAD of the inset area of Figure 9G. In this scale CAD, smaller groups of fibers are seen as they approach their near polar sutural destinations. As shown dynamically, suture branch formation is completed when the short secondary distal and the long primary proximal segment come to confluence a slight distance away from the poles (within the polar cap area circumscribed by about 10 latitudinal degrees).
In line suture lenses (four suture branches), a growth shell would be 64-75% complete when the formation of the anterior distal end segment began, whereas in Y suture lenses (six suture branches), a growth shell would be 88-96% complete when this process was initiated. These ranges are a function primarily of the number of suture branches and secondarily of spheroidicity because both of these parameters influence the range of intrashell fiber length (Table 1, Table 3, Figure 12). For example, in a mouse lens, an almost spherical lens, the distance that the forming proximal and distal portions of suture branches will traverse as they come to confluence is small. By comparison, in a bovine lens, a more oblate spheroidal lens, the distance that the forming proximal and distal portions of suture branches will traverse as they come to confluence is proportionately greater than in the mouse lens, though both are Y suture lenses. Similarly, the extent of suture branch segmentation will be proportionately greater in line suture lenses than in Y suture lenses of comparable spheroidicity (e.g., bovine compared to rabbit). This is because line suture lenses have fewer suture branches and, therefore, a broader range of intra growth shell fiber length.
As previously mentioned, in the scale CADs, color values of fibers are doubled when they have reached both of their sutural destinations. This landmark is important because fiber maturation, a process that results in the elimination of most cytoplasmic organelles, has been found to commence only after a fiber has reached both its sutural destinations . Thus, in avian lenses that feature growth shells consisting of meridian-like fibers (fibers of equal length that extend from pole to pole), fiber maturation occurs rapidly and literally simultaneously throughout a growth shell (Figure 13), as shown by another doubling of the fiber's color value. In marked contrast, in all other lenses fibers are not meridians. Typically, fibers within any growth are of unequal length, and not one fiber extends from pole to pole. Therefore, fiber maturation normally will occur gradually or in stages throughout a growth shell as suture branches are constructed segmentally. Some fibers within any growth shell will become mature even before the entire growth shell has been laid down and suture formation has been completed (Figure 9D-H,J, Figure 10D-H,J, Figure 13).
Thus, secondary fiber development likely involves the initial production of a straight middle segment (between 60 and 70% of a fiber's total length) followed by the production of curved anterior and posterior end segments (Table 2, Table 4, Figure 14). The length of end segments is a consequence of their equatorial location.
The computer modeling of secondary fiber development from scale CADs derived primarily from quantitative data in micrographs has revealed novel information as to how this lifelong process might occur and how it contributes to the establishment and maintenance of an interdependence of lens function and physiology on lens anatomy. Furthermore, this information may also explain, at least in part, how certain aspects of lens function are compromised with age and pathology. The scale CADs and animations can also be easily updated and revised as new information explaining specifics of fiber elongation (e.g., the onset and extent of end curvature) are determined.
In both line and Y suture lenses, sutures are likely to be made segmentally rather than sequentially as has been presumed. The extent of segmentation is a function of surface curvature, variability in fiber length and end curvature, and suture branch number. In all lenses, there are key fibers that define the primary origin of suture branches peripherally, the secondary origin of suture branches distally, and the midpoint of suture branches. In line and Y suture lenses there are four and six key straight fibers and four and six key opposite end curvature fibers required for normal suture formation (Figure 9, Figure 10, Figure 11, Figure 12). The straight fibers are key because they define both a primary, peripheral origin and a secondary, polar origin for suture branches. The longest fibers in a growth shell are key in that they define the midpoint of suture branches and are the first fibers to undergo the maturation process. This is likely to occur even before the complete growth shell has been laid down. The key fibers are important because the precise, nonradial, variation in intrashell fiber length and the variation in the amount of fiber opposite end curvature is contingent on their equatorial location.
It is important to note that the animations of segmented suture formation are theoretical and that they are predicated on the concept of intra- and interfiber speed of elongation being consistent. It is conceivable that intra- and interfiber speed of elongation is variable to compensate for the unequal distances that fibers need to travel to reach their anterior and posterior sutural destinations, owing to the unequal surface curvatures of lenses. This would appear to be a reasonable presumption, because the difference between the total length of the longest and shortest fiber from representative adult growth shells in the Y and line suture lenses examined for this study was, on average, about 20% (mouse, 3.31 and 2.88 mm; bovine, 22.5 and 19.43 mm; frog, 3.99 and 4.88 mm; and rabbit, 15.81 and 13.09 mm), as seen in Table 2. Thus, ostensibly, the difference in the interfiber speed of elongation need not be great to ensure that anterior and posterior suture formation, and fiber maturation, occurs closer to simultaneously as has been reported to be the case in avian lenses . Indeed, we have considered the afore mentioned and have animated Y and line suture formation with timing adjusted accordingly. However, irrespective of the rate or speed of elongation, suture formation involves the creation of a growth shell comprised of fibers with precisely controlled differences in length and shape that are organized into exact, offset suture patterns. The variation in fiber length and shape is influenced by unequal lens surface curvature. Thus, to determine what the range of fiber elongation speed would need to be for both sutures and fiber maturation to occur simultaneously, the difference in the lengths of anterior and posterior fiber segments must be calculated. The difference between the lengths of the longest and shortest anterior and longest and shortest posterior segments from representative adult growth shells in the Y and line suture lenses examined for this study was, on average, about 200% and 170%, respectively, as summarized in Table 5. Thus, the intrafiber speed of elongation speed would have to be as much as twice as fast in some fibers in order for suture formation and maturation to occur in a scheme comparable to avian lenses. Such a great disparity in the speed of fiber elongation as described and the fact that we are unaware of any other developing or growing epithelial tissue that has its component cells migrate and enlarge at such markedly different rates suggests that the segmental suture formation scheme described herein is the more likely scenario. Nevertheless, anatomically the two lens surfaces do exist in distinct environments of the eye. The anterior surface is bathed in aqueous while the posterior is surrounded by vitreous. It could be that the anterior and posterior ends of fibers are exposed to different signals directing the remarkably intricate organization of fibers into offset polar sutures. Further study will be necessary to fill in this void in our understanding of secondary fiber development and growth.
Though much information as to what factors are necessary to initiate secondary fiber development are known , specific details revealed by animating this process need to be addressed. For example: what directs a fiber to become a straight or opposite end curvature fiber? What determines the precise but nonradial variation in intrashell fiber length? What determines the exact curving of fiber ends in opposite directions? How is it determined which fibers will constitute enantiomeric pairs that are positioned as close as microns to one another and as far apart as millimeters? It should be possible to ascertain this information from animal studies, because irrespective of their disparate size, the key fibers in suture formation are positioned in comparable locations, and the measure of suture branches are proportionately equal in all lenses with Y sutures (e.g., mouse, rat, guinea pig, cat, dog, ovine, and bovine) and line sutures (frog and rabbit).
In order to migrate, or in the case of lens fibers, to elongate and form sutures, cells must be able to recognize and interact with specific extracellular matrix (ECM) components [31,32]. In lenses the capsule is the ECM . It has been proposed that posterior fiber elongation involves specific binding and detaching of membrane-spanning integrins with the capsule to form the posterior sutures . Interestingly, a unique feature of lenses is the presence of integrins on the apical membranes of epithelial cells . This atypical location of integrins might explain how anterior elongation can produce the anterior sutures. However, the scale CADs and animations of secondary fiber development presented herein show that fiber elongation is neither identical within nor between lenses. For example, elongating fibers located at 0 and 180° longitude in growth shells of line suture lenses define the origins of two anterior suture branches whereas in Y suture lenses the elongating fibers at the same locations define one posterior and one anterior suture branch. The situation in primate lenses is even more complex. In these lenses during gestation, elongating fibers located at 0° define a posterior suture branch, during infancy an anterior branch, during adolescence a fiber with opposite end curvature, and throughout adulthood, an anterior branch. Do these facts imply either that the expression of the factor or factors which direct and/or control fiber elongation is site specific or that not all fibers respond equally to a factor or factors during differentiation?
Unlike fibroblasts, epithelial cells can migrate in sheets . The scale CADs and animations presented herein show that the vast majority of fibers in any growth shell feature opposite end curvature and are arranged in groups between straight fibers. Fibers in any of these groups have progressive amounts and sharpness of end curvature. Fibers in any two neighboring groups consist of cells with comparable size and shape but opposite orientation. Thus, the suture branches are formed by the abutment and overlap of enantiomeric pairs of fibers from any two neighboring groups. Might the fibers with opposite end curvature constitute sheets or ribbons of fibers that elongate to form suture branch segments? If so then the number of fibers in each sheet would need to vary as a function of the number of suture branches that will be formed. A better understanding of the afore mentioned is important because proper suture formation is necessary for optimal lens optical quality [7-9,13,36] and improper suture formation results in quantifiable inferior lens optical quality [9,10,37].
In addition aged lenses are typically characterized by abnormal sub-branches formed at or near the sutural destinations of key fibers . This implies that with increased age, key fibers may either be defective or that the factor or factors that direct their formation may be lacking or improperly expressed. If organelles carry information important for proper fiber formation, that is to say when to stop elongating, how much and in what direction to curve away from the polar axis, then it could be that the age-related, abnormal subbranches are either a consequence of the wrong fibers receiving the message or the correct fibers misinterpreting the instructions.
Abnormal suture formation is also characteristic of certain diseases (e.g., diabetes, retinitis pigmentosa) [9,38], and as a side effect of some therapeutic treatments  and some ocular surgeries (e.g., vitrectomy and trabeulectomy; Figure 15) [10,39]. The latter is of particular interest since pharmacological agents have been developed that are effective in mediating post-surgical suture abnormalities in an animal model .
Although it is well established that fibers develop and grow from cuboidal cells into exceedingly long cells with opposite end curvature , questions remain as to why fibers are characterized by opposite end curvature and why fibers are arranged as enantiomeric pairs to form distinct suture patterns in concentric growth shells. A novel explanation for the mechanism of accommodation at the level of lens fibers based on the results of a correlative structure/function study of young and old primate (human and baboon) lenses  may provide the answers to these questions. In this study, an ex vivo mechanical device was utilized to stretch lenses into the unaccommodated state. Fiber morphology and dimensional parameters (length, width, and thickness) of these lenses, fixed in the unaccommodated state, were then compared to the same from the contralateral and age-matched lenses fixed in the accommodated state. The results of this study demonstrate that there is no variation in fiber morphology or dimensions during dynamic focusing. Accommodative lens shape changes are attributable to the end segments of fibers interfacing at the sutures. This mechanism of accommodation is made possible by opposite end curvature transforming fibers into simple coils or springs. As spring tension is released on the lens capsule, fibers in growth shells expand in unison to effect an increase in lens thickness while simultaneously reducing lens width as the diameter of the coils (fibers) decrease as fiber end segments interface at sutures. As spring tension is applied to the lens capsule, fibers in growth shells are compressed in unison to effect a decrease in lens thickness while simultaneously expanding lens width as the diameter of the coils (fibers) increase as fiber end segments only abut at sutures. Thus, animating secondary fiber development has elucidated how the coordinated transformation of cuboidal epithelial cells into simple coils or spring-like fibers can effect the synchronous interaction of fibers to produce accommodative lens shape changes.
The concept of fibers as springs accounting for accommodative lens shape changes is consistent with critical aspects of lens physiology. How lenses maintain fiber viability, especially in consideration of the fact that lifelong lens growth effectively displaces fibers farther away from their primary source of nutrition, the aqueous humor, is the subject of considerable study. Diffusion of nutrients into lenses is insufficient to maintain fiber viability because it is quite slow over long distances and thus would require several hours to move nutrients to the central fibers of an adult mammalian lens . Instead it has been proposed that vertebrate lenses develop an internal circulatory system consisting of intercellular communicating (gap) junctions and aquaporin water channels [41-47]. This unique circulatory system is predicated on fluid entering lenses at the poles, or at the confluens of suture branches, into the fibers via aquaporin water channels, being transported along the length of fibers, and then between fibers toward the equator via gap junctions. However, gap junctions primarily conjoin the middle segment of fibers [1,48]. Gap junctions are rare between the central zone epithelial cells and the underlying elongating fibers, the epithelial-fiber interface . In addition, lenses are characterized by cell-to-cell fusion of fibers [21,50-53]. Fiber fusion allows for transport between fibers above and beyond that which can pass through gap junctions. It has been proposed that fiber gap junctions, aquaporin water channels and fusion zones are so extensive, that lenses are "functional syncytiums" developed as the means to ensure that fibers remain viable throughout life. Animating secondary fiber development has revealed that developing fibers likely have a straight middle segment aligned parallel to the visual axis and end segments that curve in precisely defined amounts away from the polar axis. We propose that this secondary fiber development scheme has evolved to insure the following: End curvature of fibers is effected as a means of transforming fibers into simple coils or springs for accommodation; a middle segment of a fiber conjoined by intercellular junctions is effected as a means of maintaining fiber viability that can operate unimpeded as the ends of fibers interface during accommodation. In this manner, structural features of lens fibers necessary for lens function and physiology are mutually inclusive.
In summary, we have computer modeled nonprimate secondary fiber development and suture formation from micrographs taken at different depths of individual lenses (intralens analysis) and from lenses of different ages (interlens analysis). Animating these models reveals previously unrecognized aspects regarding the timing and specificity of these processes that relate to the establishment and maintenance of an interdependence of lens function and physiology on lens anatomy. First, the commonly held premise that developing fibers simultaneously rotate, migrate, and elongate until their ends abut and overlap to form sutures is incorrect. Fiber rotation and migration are completed early in the differentiation process, whereas most of fiber elongation occurs after a middle segment of a developing fiber becomes fixed in place. It could be argued that the afore described distinction between fiber migration and fiber elongation is merely semantics. Indeed, many consider fiber elongation to be fiber end migration  and the ends of fibers have features typical of migrating cells in other systems. But unlike typical migrating cells, developing secondary fibers have no trailing edge. Rather, it may be that developing secondary fibers have two leading edges and a fixed middle segment. Second, unless fibers elongate at variable rates as a function of their equatorial position, then line and Y sutures are formed in a more complex segmental scheme rather than sequentially, as was previously presumed. The extent of suture formation segmentation depends on the number of suture branches and the spheroidicity of the lens surface, which results in variable fiber length. This implies that in primate sutures, which feature more numerous branches as a function of development, growth, and aging, will involve the most complex segmentation scheme of all vertebrate lenses. It is important to confirm this premise because some naturally occurring human lens pathologies (cortical and diabetic cataracts) [5,54], surgically induced (vitrectomy and trabeculectomy) [10,39], and age-related lens changes are characterized by abnormal sutures.
The authors recognize the expert technical work of Layne Novak and Kurt Peterson. This work was supported by NIH NEI grant EY-06642 to JRK.
This paper is dedicated to my (JRK) father, Ray Kuszak, on the occasion of his 80th birthday. The ease with which I move about the third dimension is an inherited trait. Thanks Dad.
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