Growth of the eye lens: I. Weight accumulation in multiple species

Wet weight accumulation

Changes in lens wet weight over a substantial part of the life span were available for 39 species. Lens wet weights measured in the author’s laboratory ranged from a low of 0.2 mg for a newborn dunnart to 7,500 mg for an adult bluefin trevally. Six examples of the growth curves obtained are shown in Figure 1. These were selected to demonstrate the range in quantity and quality of the available data.

Although there is scatter in some of the plots, it is clear from these figures that wet weight accumulation, i.e., lens growth, is continuous throughout life in all species, rapid early in life and gradually slowing toward an apparent asymptotic maximum. Similar curves were obtained for the other 33 species.

Dry weight accumulation

Data on the relationship between lens dry weight and age were obtained for 121 species. Measured dry weights ranged from a low of 0.15 mg for a newborn mouse lens to over 5,000 mg for the bluefin trevally. Examples of the dry weight growth curves are presented in Figure 2.

As with the wet weights, the data indicate growth is continuous throughout life and slows toward an apparent asymptotic maximum. Similar curves were obtained for all but 6 of the data sets.

Growth analysis

For both wet and dry weights, differences are seen in the shapes of the lens weight versus age curves (Figure 1 and Figure 2) suggesting that the growth rates may vary in different species. Thus, the dry weight appears to increase more rapidly for the dingo than it does for the wild boar and others. However, the apparent shape of the plots is dependent on the time frame for which data were available, relative to the life expectancy. The wild boar data represent only 15% of the animal’s possible life span while those for the dingo encompass over 60%. A more reliable assessment of the growth rates requires fitting of growth algorithms to the data.

To identify the most appropriate way to describe lens growth, several growth functions, including various versions of the logistic, Bertalanffy, Gompertz, Janoschek and Richards relationships were tested. The following version of the two parameter logistic-type equation, used previously for analysis of kangaroo and rabbit lens growth [6,9], was selected because of its simplicity and because it yielded best fits of the data for most species.

W = W m ∗ e − ( k / ( A p + 1 / c )

Where W is lens weight, W_m is the maximum asymptotic weight, A_p is the postnatal age, k is the logistic slope and c is an age constant. This equation is very similar to that first used by Lord [13]. In studies where the Lord relationship was used, 1/c was allowed to vary to obtain the best statistical fit of the data [13-17]. However, as discussed previously [9], the term 1/c represents the prenatal time from lens formation to birth and cannot be greater than the gestational period. It is appreciated that lens growth does not commence until well after conception, but the precise time is not known for most of the species examined in the present study. Therefore, the gestational period (G) was used for 1/c, so that the total age (A=A_p+G) of a lens corresponds to the time since conception. For the 12 species where the time of lens placode formation was known, regression analysis indicated that the age since conception generally gave a slightly better fit of the data than the time since placode formation. Thus, Equation 1 reduces to

W = W m ∗ e − ( k / ( A ) )

Logistic analysis

Data were plotted according to the transformed version of the two parameter logistic equation

ln ( W ) = ln ( W m ) − ( k / A )

The logistic plots for the wet weights shown in Figure 1 are presented in Figure 3 while the dry weight plots, corresponding to Figure 2 data, are shown in Figure 4. Each of the data sets shown yields a single straight line for the whole of the available time frame, indicative of self-limiting monophasic growth toward an asymptote. With the exception of those discussed below, all other species also yielded reasonable to good linear logistic plots (R², 0.60–0.99) but substantial differences were evident, in both the slopes and intercepts.

The logistic slope, k, and the maximum asymptotic weight, W_m (=exp^{(y-axis intercept)}), were determined from these plots. They are presented in The Appendix 1. For species with short gestation times, using the time since lens placode formation, rather than the gestation period, generated plots with lower slopes but this had little effect on W_m. The slopes and intercepts of species with long gestation periods were unaffected.

Possible exceptions

Red squirrel data [18], on first analysis, yielded a curved logistic plot. However, it was found that the authors had estimated ages for the 4 oldest animals based on the assumption that lens growth was linear. After elimination of these points, leaving only the actually known-age data, a monophasic growth plot (single straight line) was obtained.

Initial analysis of the smooth dogfish data also yielded a curved plot. It was noted that the ages cited in the report [19] were estimated from body lengths by comparison with those of the spiny dogfish since no other information was available at the time. However, the growth characteristics and life cycles of these two species are quite different. Recently obtained body length/age data for the smooth dogfish [20] have indicated that the previous age estimates were almost double the true ages. Adjustment of the ages generated a single straight line for the logistic plot.

Six of the data sets did not yield single straight lines on logistic analysis. For one of these, human, it has previously been shown that the lens grows in a biphasic manner [5]. The other exceptions, all from the literature, were the African elephant [10,11], American mink [21], hippopotamus [22], Spanish ibex [23] and woodchuck [24,25]. The growth curves and corresponding logistic plots for two examples, the elephant and the woodchuck, are presented in Figure 5.

The logistic plots show distinct upward curvatures at low 1/A (i.e., high ages), consistent with a change in growth mode. Curve fitting indicated that both sets of data can be described with an asymptotic growth phase early in life followed by linear growth, as has been observed for the human lens. A similar conclusion was made for the hippopotamus. The transitions seem to occur around 6–8 years for the elephant, 3–4 years for the hippopotamus and 500–600 days for the woodchuck, respectively. Insufficient data are available to permit more precise estimations. The slopes of the linear phases for the elephant, hippopotamus, human and woodchuck were estimated to be 10.5, 5.3, 0.54, 0.44 years, respectively.

The American mink [21] and Spanish ibex [23] data also yielded biphasic logistic plots. However, the weights of young lenses were very high, relative to the adult lenses. Young male mink lenses were reported to be over 30% heavier than those from females of the same age. In view of observations on 71 other species (see below), this is unlikely to be correct. No adult gender data were presented. Lens weights for young ibexes also appeared to be high but this might be due to inaccurate age estimates. Adult lens data only were used for analyses of these two species.

Some of the other data sets showed a small amount of upward curvature in the dry weight logistic plots at low 1/A values. This curvature was not considered significant as it was generally associated with inadequate drying procedures, such as 24 h at 55 °C. Since the time required for lens drying varies with lens size as well as temperature [9], the larger older lenses may not have dried completely when mild drying conditions were used. For example, it was reported that giraffe lenses had not reached constant dry weight after 120 h at 80 °C [26].

Gender

The gender of the lens donors was known for 73 sets of data, permitting an assessment of possible gender differences. Two examples, the guano bat [27] and the black tailed Columbian deer [28,29] are presented in Figure 6. It is clear that lens weights in males and females of the same age are indistinguishable. The same conclusion was reached for a total of 66 species.

For the remaining seven species (American mink [21], beagle dog [30], corn mouse [31], European common vole [32-34], northern fur seal [35], pheasant [36,37] and Wistar rat [38]) male and female lenses have been reported to differ. However, it is probable that some of the apparent differences are not real. As mentioned earlier, there appear to be problems with the young American mink data. With the beagle dog [30], it was not really possible to make any definitive conclusion since the data were highly scattered and there was also substantial overlap between the genders. By comparison, no suggestion of a difference was observed with the closely related dingo or with other carnivores. Male Wistar rat lenses were reported to be larger than those from females in one study [38] but this was not observed in another [39] or in the author's laboratory. Furthermore, several other species of rats show no difference between males and females.

Janova and colleagues concluded that lens dry weight is not reliable for estimating age in the vole, Microtus arvalis, because lens growth is different between males and females and between reproducing and non-reproducing females [34,40]. However, such differences have not been observed by others in M arvalis [32,33] or in other voles. Although male and female corn mice, older than 11 weeks, were reported to differ [31], the comparison was based on the average weights for 4 broad age groups. It was not possible to assess whether the age distributions within the male and female groups were comparable. Lens weights have been found to be the same in numerous other small rodents. It is concluded that male and female lenses in beagle dogs, corn mice and Wistar rats are probably not different and, therefore, the male and female data were combined for further analyses.

Insufficient information is available to assess the reported gender differences in the pheasant and fur seal. The separate male and female analyses for these are included in Appendix I. The logistic slopes (growth rates) for the genders are the same but the maximum asymptotic weights differ. The female weights were used in subsequent data analyses.

Thus, for 71 out of 73 species examined, there appear to be no differences between male and female lenses. There is no a priori reason for male and female lenses to be the same or different but, intuitively, one would expect them to be the same since lens function would be unrelated to gender. If, like many other organs, lens size scales with body size, and since male body size is frequently greater than that of females, it might be expected that male lenses would also be larger. However, male body size is not always larger, sometimes females are larger, and for many species, there is no difference or the difference is subtle and does not manifest until sexual maturation. By then, the lens has generally reached 80% of its maximum asymptotic value and subsequent differences in lens growth would have no obvious benefit to either gender. On the basis of these considerations, it is concluded that for most, if not all species, there is no difference between male and female lens weights.

The growth constant

The rate at which lens weight approaches the asymptotic maximum, i.e., the growth constant, is indicated by the slope of the logistic plot. For warm-blooded animals, exhibiting monophasic growth, the slopes range from 20 to 600 days for dry weights and from 27 to 485 days for wet weights. Where data are available for both wet and dry weights, logistic slopes are usually 10%–20% higher for dry weights. The only exceptions are crocodile and chicken where the slopes are identical. Very high slopes are found with the ectothermal species, fish, amphibians and reptiles (The Appendix 1). Insufficient data are available to permit meaningful comparisons of these since some are ovuliparous (ova fertilized externally) and others are viviparous (young develop in mother). In addition, animal growth rate and gestational time (as well as gender of the newborn) are dependent on the temperature of the external environment. Therefore, only warm blooded animal data will be analyzed and compared in the following discussions but reliable ectothermal animal data will still be presented.

Within groups of closely related species, the logistic slopes are generally similar, with the lowest slopes found in the birds and the highest among the ungulates (The Appendix 1). Nevertheless, some members in the groups differ, suggesting that the slopes may reflect some parameter other than taxonomic relationship. To determine what parameters may contribute, the slopes were compared with several other properties using allometric analyses. This included the asymptotic maximum lens size, normal maximum bodyweight, maximum possible life span and gestation period. The comparisons for lens dry weight in warm-blooded animals with monophasic lens growth are presented in Figure 7. Similar relationships were observed with the wet weights, but fewer data were available.

Low slopes (30–100 days) are associated with small lenses, low bodyweights, short life spans and short gestation periods. The slope increases as each of these parameters increases, not only between the taxonomic groups but also within them (Figure 7A-D). In all species, the lens reached 50% of its maximum dry weight at around 3 times the length of the gestation period, corresponding to around 5% of the maximum life span. At the time of sexual maturation, dry weight was around 80% of the maximum.

It might have been expected that the closest relationship of the growth constant would be observed with gestational time since it can be shown, by rearrangement of Equation 1, that the logistic slope is related to the term describing the gestational lens growth period (1/c). However, primates have lower slopes and marsupials, higher slopes than other animals with the same gestational times. For the 83 species remaining after excluding the marsupials and primates, the relationship was

k = 7 ∗ G 0.75 ( R 2 = 0.89 )

Bodyweight (BW) also yielded a good fit with birds and marsupials appearing to differ from the others. Excluding these two groups,

k = 25 ∗ B W 0.22 ( R 2 = 0.87 )

Although quite good fits of the data were obtained for each of the analyses, especially when apparently outlying groups were excluded, it is concluded that parameters, other than those tested here, are responsible for regulating the rate of lens growth. However, it is still possible that the rate is determined by bodyweight or gestation time and that the species which do not fit the general trend represent adaptations for a specific lifestyle.

Five of the species examined- the chipmunk, garden dormouse, ground squirrel, hamster and woodchuck - undergo ‘true’ hibernation (lowered body temperature with low metabolic, breathing and heart rates) in winter. None of these exhibit variations in lens growth rate which can be attributed to the periods of hibernation. As mentioned above, there appears to be a transition in woodchuck lens growth at around 1.5 years but this is well past the time of the first hibernation. Thus, it would appear that lens growth continues unabated during hibernation.

Age determination

The continuous growth of the lens throughout life offers the possibility of using lens weight for determining animal ages. This was realized by Lord [13] who applied the method to cotton tail rabbits and derived an algorithm for the rabbit which is essentially identical to the logistic type equation used here. The only difference is in the age term. Lord used (postnatal Age + c) where c is a constant determined from the best fit of the data. This should correspond to the time of prenatal lens growth. Several authors have since collected data on lens weights to develop relationships for estimating ages for animals culled in the wild. Many of these used the Lord approach. Unfortunately, because of the variability in data collected in the wild and imprecise estimates of age, the best fit approach frequently yields values of c, well in excess of the gestation period. As discussed previously [9], this can lead to erroneous conclusions regarding factors affecting lens growth. The data from the published studies have been used in the current analyses but were reinterpreted using the gestation time instead of the Lord age constant (c).

Several other approaches have been used for analyzing lens growth data. A frequently used one is to regress known postnatal age on lens weight and fit a linear function. This has been used for predicting ages. As can be seen in Figure 8, a good linear fit was observed for the black rat data using this approach (R²=0.90) [41]. (Note that log₁₀ is used for this regression, as in the data source [41] rather than the ln used in the present study.) However, for the rabbit [9] the relationship is clearly sigmoidal. Re-analysis of the rat data indicates that a sigmoidal fit is slightly better (R²=0.93) than the linear. The apparent linearity of the relationships, also reported for several other species [42-47], reflects the limited age ranges examined. Samples from early and late in life are required to reveal the sigmoidal relationship. Use of this apparently linear relationship for determining ages will result in overestimates for the old animals and underestimates for the young. A better fit of the data are obtained if age since conception is used for the regression.

Several attempts have been made to use lens wet weight or fixed wet weight (but not dried) for age determination. This is unsatisfactory since lens hydration, and hence the weight, varies with post-mortem and/or fixation time. Fixed dried lens weight is best but care must be taken that drying is complete. It was noted, during compilation of the data for this study, that, in studies where short drying times at low temperatures were used, the data were variable, especially for large lenses.

It is concluded that the logistic type equation used in the present study provides a satisfactory algorithm for age determination using dried lenses. As described previously, lenses must be fixed for at least 2 weeks and dried at >80 °C until the weight is constant, a process which will take over 2 weeks for large lenses.

Compaction

Both wet and dry weights were available for 32 species, permitting an assessment of the change in the average concentration of lens solids with increasing age and the maximum concentration reached, i.e., the amount of compaction possible in different species. Limited adult data were available for another 9 species.

The logistic plots for wet and dry weight accumulation in the chicken, Norwegian rat and sheep are shown in Figure 9. These reveal interesting differences.

For the rat and sheep (Figure 9A,B) the logistic slopes are different indicating that wet and dry weights accumulate at different rates, with the dry weight accumulation being the more rapid. This is also evident in the plots showing the ratios of dry weight/wet weight (Figure 9D,E). With increasing age, this ratio increases toward the asymptotic maximum which can be calculated from the logistic intercepts, 0.40 for the sheep and 0.45 for the rat. These ratios correspond to maximum dry weight concentrations of around 45 and 50% (w/v) respectively. Similar increases were observed for most of the other species.

By contrast, the logistic plot slopes for the dry and wet weights in the chicken are the same (Figure 9C), indicating that wet and dry weights increase at the same rate. Consequently, as can be seen from Figure 9F, the dry weight/wet weight ratio remains constant at near 0.27 throughout life. The crocodile was similar but with a lower constant ratio of around 0.20. These observations indicate there is no compaction with age in the chicken and crocodile lens and, hence, probably no refractive index gradient. Low ratios were also observed with adult lenses from the little penguin (0.26), mallard (0.27) and Jackson’s chameleon (0.25). However, the numbers of lenses available were too small to determine if these ratios are constant with age. The low ratios of the chicken, little penguin and mallard lenses are consistent with the conclusion that these have monofocal optical systems [48] while the higher ratio of the boobook owl lens (0.31) is consistent with its multifocal system [48].

The very low concentration of solids in these lenses indicates that they are very soft and flexible, as was been observed during processing, and capable of large accommodative changes. This would be especially so in the crocodile lens, probably reflecting the need for large lens shape changes when vision switches between air and water.

The asymptotic ratios of dry weight/wet weight and the calculated densities, for the species where data were available, are presented in Appendix 2, together with values calculated from adult lenses where lens numbers were low. The ratios range from 0.2 in the crocodile to >0.6 for several rodents and the corresponding densities from 1.05 to 1.22. It should be noted that these are average values for the whole lens. In most lenses the dry mass is distributed along a concentration gradient with the highest concentration in the center. This generates the refractive index gradient necessary for reducing eye length. The density in the center would be considerably higher than the average.

Allometric analysis (log Dry weight versus log Wet weight) also shows that dry weight increases more rapidly than wet weight in most species, indicative of compaction. Examples are included in Figure 9G,H,I for the chicken, rat and sheep. The allometric compaction constants determined from the slopes of the allometric plot range from 1.00, in birds and reptiles, to 1.33 in mammals.

Concluding remarks

The availability of the above detailed information on lens growth in so many species makes it possible to make several conclusions. Lens growth in most species is monophasic, continuous throughout life, slowing toward an asymptotic maximum. For species with low bodyweights and short gestation periods, growth in adults is so slow as to appear to have stopped. This slow growth makes it difficult to use lens size as a criterion for determining age in older animals, especially in small-bodied species. However, determining annual growth classes from dry weight in small animals and actual ages for large-bodied animals is feasible and convenient provided care is taken in the handling/drying of the lens.

Treton and Courtois [49], using 16 of the data sets used in the current study, concluded that lens growth took place through two linear growth phases; early rapid growth in a ‘lens development stage’ (LDS) followed by slow growth in the ‘resting lifespan (adult stage)’. The intersection of the extrapolated two linear fits to plots of lens weight against age was taken to be length of the LDS. However, for many of the species studied, insufficient data were available to fit straight lines with any certainty. The present observations indicate that the concept of two growth phases is not applicable to most of species. As discussed earlier, only human lenses and possibly those from the elephant, hippopotamus and woodchuck exhibit biphasic growth.

For most, if not all species, lens growth is independent of gender and unaffected by external influences such as environment and diet [1,7]. Although only three examples were available, it is probable that hibernation also does not affect the rate of lens growth. These and other observations suggest that the lens is genetically programmed to achieve a certain size at a certain rate for each animal and normal internal as well as external influences are unable to alter this, except, perhaps, the abnormal stresses which can lead to cataract formation. The lack of direct connections to the cardiovascular and nervous systems ensures that the lens is isolated from signals which affect the rest of the body. Taken together with the immune response by the host to leaked lens proteins [50], these various observations suggest that the lens may be considered as a separate organism, which relies on the host eye for a stable environment and its miniscule nutritional requirements, but is otherwise independent.

This conclusion appears at odds with the elegant demonstration by McAvoy and others that the various stages of lens morphogenesis in the chick and rat– epithelial cell proliferation, cell migration and differentiation – are dependent on Fibroblast Growth Factor (FGF) and other growth factors present in the vitreous and aqueous humors [2]. It has been demonstrated that retinal factors can alter lens polarity, promote zonule attachment and support growth of lenses implanted in 6 day old mice [51] but less is known of the possible influence of external growth factors on the older lens. An antero-posterior FGF gradient (low-high) is thought to regulate lens growth, suggesting that the slowing of lens growth with increasing age could be attributed to a decrease in the growth factors being delivered by the aqueous. Flattening of morphogen gradients has been invoked to govern other organ shapes and sizes [52,53]. Alternatively, the reduced responses of epithelial cells to FGF with increasing age may be responsible [54]. This does not appear to be the case in humans, elephants, hippopotami and woodchucks since lens growth does not slow with age.

The unique growth of the lens, in which epithelial cells proliferate and differentiate into fiber cells in the equatorial region, provides the necessary building blocks for constructing a refractive index gradient by packing mature fiber cells into the central (nuclear) regions and compacting these through the removal of water. The refractive index gradient thus generated varies with species and presumably is determined by life style [1,3]. However, these processes do not cease when the desired gradient has been established but continue at different rates in different species. They are also continuous in species which do not form a gradient. By contrast, the eye and other ocular structures stop growing very early in life [55].

This raises the question, “Why doesn’t the lens stop growing in adulthood, like the rest of the eye and so many other organs”? There does not appear to be an obvious answer. Perhaps it does not matter: perhaps there are no untoward effects.

Turnover of the epithelium is not required for maintenance of the tissue. Although the cells are capable of undergoing apoptosis and division [56,57], for the most part, the central epithelium is quiescent and the cells are very old. Yet, they continue to function in maintaining lens homeostasis and protection against stress, at least until late in life. Significant mitosis seems to take place only in the equatorial region and leads to fiber cell production. Interestingly, this can be stimulated by increased oxygen levels in mice [58].

The increasing size of the lens is unlikely to create problems in most species since any increase in weight results in much smaller changes in dimensions. In most warmblooded species, lens dry weight has reached 80% of its maximum around the time of sexual maturation when optimum visual function would be required. For the remaining 20%, the dimensions increase by an average of only ~6% over the rest of life. Furthermore, any visual defects arising from growth in the post-reproductive years may not be targets of evolutionary selection pressures.

The foregoing data analyses and discussion have concentrated on the rate of lens growth. More information can be gleaned from a consideration of the actual weights of the lenses. This will be addressed in the following paper.