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The Molecular Genetics and Evolution of Red and Green Color Vision in Vertebrates
Shozo Yokoyamaa and F. Bernhard Radlwimmeraa Department of Biology, Syracuse University, Syracuse, New York 13244
Corresponding author: Shozo Yokoyama, Biological Research Laboratories, Department of Biology, Syracuse University, 130 College Pl., Syracuse, NY 13244., syokoyam{at}mailbox.syr.edu (E-mail)
Communicating editor: S. W. SCHAEFFER
| ABSTRACT |
|---|
To better understand the evolution of red-green color vision in vertebrates, we inferred the amino acid sequences of the ancestral pigments of 11 selected visual pigments: the LWS pigments of cave fish (Astyanax fasciatus), frog (Xenopus laevis), chicken (Gallus gallus), chameleon (Anolis carolinensis), goat (Capra hircus), and human (Homo sapiens); and the MWS pigments of cave fish, gecko (Gekko gekko), mouse (Mus musculus), squirrel (Sciurus carolinensis), and human. We constructed these ancestral pigments by introducing the necessary mutations into contemporary pigments and evaluated their absorption spectra using an in vitro assay. The results show that the common ancestor of vertebrates and most other ancestors had LWS pigments. Multiple regression analyses of ancestral and contemporary MWS and LWS pigments show that single mutations S180A, H197Y, Y277F, T285A, A308S, and double mutations S180A/H197Y shift the
max of the pigments by -7, -28, -8, -15, -27, and 11 nm, respectively. It is most likely that this "five-sites" rule is the molecular basis of spectral tuning in the MWS and LWS pigments during vertebrate evolution.
HUMAN color vision is achieved through three types of photosensitive molecules: short wavelength- (or blue-) sensitive (SWS), middle wavelength- (or green-) sensitive (MWS), and long wavelength- (or red-) sensitive (LWS) visual pigments, which absorb light maximally (
max) at
420,
530, and
560 nm, respectively (![]()
8% of males (![]()
max of most LWS pigments ranges from 550 to 560 nm, while the MWS pigments detect a wider range of light with
max at
510540 nm (![]()
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Each visual pigment consists of a chromophore, 11-cis-retinal, and a transmembrane protein, opsin, which is encoded by a specific opsin gene. The SWS, MWS, and LWS opsin genes were cloned for the first time from human (![]()
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A at site 180), H197Y, Y277F, T285A, and A308S shift the
max of the LWS/MWS pigments toward green by 7, 28, 7, 15, and 16 nm, respectively, and the reverse changes toward red by the same amounts (![]()
max of virtually all LWS/MWS pigments of vertebrates. The MWS pigment of bottlenose dolphin (Tursiops truncatus) is an exception, where the observed
max is 13 nm lower than the expected value from this five-sites rule (![]()
The evolution of red-green color vision was also studied by inferring the amino acid sequences at the five critical sites of the ancestral pigments. Comparing the MWS and LWS pigments from human and fish (Astyanax fasciatus), it was suggested that the LWS pigments in these species evolved from the ancestral MWS pigment independently (![]()
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max of such ancestral visual pigments are determined, we can study not only the evolutionary processes of LWS/MWS pigments directly but also the molecular bases of red-green color vision through time.
Here, we infer the amino acid sequences of ancestral pigments from contemporary sequences, construct the ancestral pigments, evaluate their
max, and test the validity of the five-sites rule during vertebrate evolution. To accomplish the first three goals, we consider 11 pigments: the LWS pigments of human, goat (Capra hircus), American chameleon (Anolis carolinensis), chicken (Gallus gallus), clawed frog (Xenopus laevis), and cave fish (A. fasciatus) and the MWS pigments of human, squirrel (Sciurus carolinensis), mouse (M. musculus), gecko (Gekko gekko), and cave fish (A. fasciatus). The results suggest that virtually all ancestral pigments had amino acids SHYTA (amino acids S, H, Y, T, and A at sites 180, 197, 277, 285, and 308, respectively) and were red sensitive. Statistical and mutagenesis analyses show that the five-sites rule, now including the synergistic effect of amino acid sites 180 and 197, fully explains the variation in the spectral sensitivity of all ancestral and currently known LWS/MWS pigments in vertebrates, including the dolphin MWS pigment.
| MATERIALS AND METHODS |
|---|
cDNA cloning and DNA sequencing:
Total retinal RNAs of chicken (Gallus gallus) and frog (Xenopus laevis) are gifts from Dr. Mary Pierce at the SUNY Upstate Medical University at Syracuse, and that of cave fish (A. fasciatus) was isolated using the procedure of ![]()
|
For each set of primers, cDNA was reverse transcribed at 42° for 1 hr and at 95° for 5 min, and then PCR was carried out for 30 cycles at 94° for 45 sec, 55° for 1.5 min, and 72° for 2 min. PCR products were gel isolated and subcloned into the T-tailed EcoRV-digested Bluescript plasmid vector with T-overhang attached to 3' ends (![]()
Expression and spectral analyses of pigments:
The PCR-amplified opsin cDNAs were subcloned into the EcoRI and SalI restriction sites of the expression vector pMT5 (![]()
![]()
Mutants were generated by using the QuickChange site-directed mutagenesis kit (Stratagene, La Jolla, CA). All DNA fragments that were subjected to mutagenesis were sequenced to rule out spurious mutations. UV-visible spectra were recorded at 20° using a Hitachi U-3000 dual beam spectrophotometer. Visual pigments were bleached for 3 min using a 60-W standard light bulb equipped with a Kodak Wratten #3 filter at a distance of 20 cm. Data were analyzed using Sigmaplot software (Jandel Scientific, San Rafael, CA).
Sequence data analyses:
The sources of the amino acid sequences of the MWS and LWS pigments of different vertebrate species are given in Table 1, where both of their amino acid sequences and
max are known. So far, with the exception of the chicken, frog, and cave fish pigments, their
max's have been evaluated using in vitro assay.
|
We selected two fish, two frog, two reptile, and one bird LWS/MWS pigments (Table 1). The numbers of mammalian pigments with
max at
510,
530, and
560 nm are 4, 7, and 6, respectively (Table 1), from which we selected 1, 2, and 2 pigments, respectively. Thus, with respect to the phylogenetic and spectral diversities, these 11 pigments represent every segment of currently known LWS/MWS pigments in vertebrates. The phylogenetic relationship of fish, frog, reptiles, and mammals is well established (e.g., see ![]()
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To study the spectral sensitivities of ancestral mammalian pigments further, we consider yet another phylogenetic tree of LWS/MWS pigments: [(((human (P560), human (P530)), (marmoset (P562), marmoset (P553), marmoset (P540))), rabbit (P509), (goat (P553), deer (P531))), guinea pig (P516), (squirrel (P532), mouse (P508))]. This tree topology of the mammalian pigments is basically the same as that in ![]()
| RESULTS |
|---|
Absorption spectra of the chicken, frog, and cave fish LWS/MWS pigments:
To study the mechanisms of spectral tuning of visual pigments, we applied the in vitro assay (![]()
280 nm and another at 530561 nm (Fig 2). When these pigments are exposed to light, the second peak shifts to
380 nm (results not shown), indicating the cis-trans isomerization of the chromophore (![]()
max at 558 ± 2, 557 ± 2, and 561 ± 2 nm, respectively, while the MWS pigment of cave fish has a
max at 530 ± 2 nm (Fig 2, Table 1). The respective dark-light difference spectra are given by 557, 557, 561, and 531 nm, all of which are also precise to within ±2 nm (Fig 2, insets) and are very close to the corresponding dark spectra.
|
Previously, using a 3-[(3-cholamidopropyl) dimethylammonio]-1-propanesulfonate-phosphatidylcholine (CHAPS-PC) mixture and microspectrophotometry (MSP) methods, the
max of the chicken LWS pigment were estimated to be 571 (![]()
![]()
10 nm lower than these values. The cause of this difference is not immediately clear. However, in the CHAPS-PC method, the sample used for the evaluation of the
max is not pure and contains
92% of the LWS pigments, while the MSP analyses are often subject to sampling errors. Compared with these methods, the visual pigments regenerated using an in vitro assay are identical and are expected to provide a more reliable
max of each specific pigment.
The two previous estimates of the
max of frog (P557) pigment are very different: 611 nm by MSP (![]()
![]()
max's. MSP estimates for the cave fish MWS and LWS pigments regenerated with 11-cis-retinal showed
max's at 533 ± 3 and 563 ± 4 nm, respectively (F. I. HAROSI and J. KLEINSCHMIDT, personal communication; see also ![]()
max of the chicken, frog, and cave fish pigments (Table 1).
Amino acid sequences of the ancestral LWS/MWS pigments:
Given the tree topology of the vertebrate pigments in Fig 3, the amino acid sequences of the ancestral pigments at nodes ai (pigments ai, respectively) were inferred by using the JTT model of amino acid replacements (![]()
![]()
|
|
Using the contemporary pigments, we suggested that the spectral sensitivities of the LWS/MWS pigments are controlled mainly by the amino acids at 180, 197, 277, 285, and 308 (![]()
![]()
Absorption spectra of the ancestral pigments:
Many inferred amino acids of the ancestral pigments are identical to those of the contemporary pigments (Fig 4), showing that pigments ai can be constructed by introducing necessary mutations into some extant pigments. Indeed, pigments df were constructed by introducing six mutations into human (P560) pigment, nine mutations into pigment d, and nine mutations into squirrel (P532) pigment, respectively (Fig 5A). The amino acid sequences of pigments ac, g (= h), and i are similar to that of chameleon (P560) pigment, which can be divided into segments IIV by three restriction sites (Fig 4 and Fig 5B). Thus, by introducing necessary mutations into these segments, we constructed I1I4, II1II4, III1III4, and IV1IV2, respectively (Fig 5C). The pigments ac, g (= h), and i were then obtained by recombining these four segments at the three restriction sites (Fig 5C). In this way, we constructed one ancestral pigment at each node, each amino acid having the highest posterior probability.
|
When measured in the dark, the
max of pigments af, g (= h), and i are 563 ± 2, 563 ± 2, 561 ± 2, 558 ± 2, 558 ± 2, 536 ± 1, 561 ± 2, and 564 ± 2 nm, respectively (Fig 6). The respective dark-light difference spectra are given by 564, 563, 561, 558, 558, 536, 561, and 564 nm, all of which are precise to within ±2 nm (Fig 6, insets). They are virtually identical to the corresponding dark spectra. Thus, pigment f with SYYTA at the five critical sites has a
max at 536 nm, while the other ancestral pigments with SHYTA have
max at 558564 nm (Fig 3 and Fig 6). These results suggest that the pigment of the common ancestor was red sensitive and the contemporary LWS/MWS pigments evolved from the LWS pigment. As noted earlier, for pigments df, S180 and A180 are predicted with probabilities 0.7 and 0.3, respectively. As we see below, changes S180A and A180S should shift the
max for no more than 7 nm and, therefore, the uncertain inference of amino acids at site 180 does not change the red and green sensitivities of the ancestral pigments.
|
Now, what do the spectral sensitivity data in Fig 3 tell us about the mechanisms of spectral tuning in the LWS and MWS pigments? Following ![]()
180,
197,
277,
285,
308, and Z be the magnitudes of the
max shifts caused by S180A, H197Y, Y277F, T285A, A308S, and the absorption spectrum of a pigment with SHYTA. Note that the amino acid compositions for all contemporary and ancestral pigments are either Y277/T285 (Y277 and T285) or F277/A285 (Fig 4) and, therefore, two parameters,
277 and
285, cannot be estimated separately. When multiple linear regression analysis is applied to the
max of the 11 contemporary and 9 ancestral pigments,
180 = -7 ± 2 nm,
197 = -26 ± 2 nm,
= -24 ± 3 nm,
308 = -19 ± 4 nm, and Z = 560 ± 1 nm. When the regression analysis is applied to only the 11 contemporary pigments,
180 = -6 ± 2 nm,
197 = -27 ± 2 nm,
= -24 ± 2 nm,
308 = -18 ± 3 nm, and Z = 559 ± 1 nm. Thus, the two sets of estimates are practically identical. Using the former set of estimates, we can predict the expected
max for the contemporary and ancestral pigments (Table 2). Table 2 shows that the observed
max of frog (P557) and cave fish (P558) pigments and ancestral pigments a, b, d, e, and i fall outside of the 95% confidence interval. However, considering the standard errors associated with the estimation of the
max, the expected and corresponding observed
max's are in reasonably good agreement.
|
Table 2 clearly shows that the spectral tuning of the LWS/MWS pigments is determined mainly by the amino acids at 180, 197, 277, 285, and 308. It is also true that, despite having the same amino acid composition SHYTA at the five critical sites, pigments ae, g (= h), and i have somewhat different
max, ranging from 558 to 564 nm (Fig 3 and Fig 6). Among these, the
max of pigments d and e (both with
max = 558 nm) and that of pigment i (
max = 564 nm) are significantly different (P < 0.05). Where does this variation in the
max values come from? As noted earlier, the spectral sensitivities of human (P530) and human (P560) pigments are determined mainly by the three-sites rule. However, additional amino acid differences at sites 116, 230, 233, and 309 are known to have some minor influence on the differentiation of the two pigments (![]()
max between pigments d and e and pigment i is caused most probably by the slightly decreased
max in the former two pigments due to S116Y/A233S. It should be stressed, however, that the minor variation in
max is found only in certain mammalian pigments. Thus, this minor adjustment in the mechanisms of spectral tuning seems to be a local phenomenon.
Five-sites rule:
Using the contemporary and ancestral pigments in Fig 3, we could not infer
277 and
285 separately. However, if we consider the amino acid sequences of all 26 pigments in Table 1, we can evaluate
277 and
285 separately and also determine interactions between sites 180 and 197 (
180x197); 180 and 285 (
180x285); 197 and 285 (
197x285); 197 and 308 (
197x308); 277 and 285 (
277x285); and 180, 277, and 285 (
180x277x285; Appendix).
When the interaction terms are neglected, Z = 559 nm,
180 = -5 nm,
197 = -22 nm,
277 = -8 nm,
285 = -17 nm, and
308 = -25 nm (Table 3, model a). When the
max for the 26 pigments are estimated by using these
values, they agree reasonably well with the corresponding observed values (Table 4, column a). However, the
max of dolphin (P524) and squirrel (P532) pigments deviate from the corresponding expected values by 5 and 4 nm, respectively (see also ![]()
max values of dolphin (P524) and squirrel (P532) pigments are 526532 nm and 533539 nm, respectively. The corresponding observed
max fall outside of these intervals. Thus, some improvement in the estimation procedure is desirable. It turns out that such an improvement can be made by considering interactions among the five critical sites. The improvement in the estimation procedures with and without a specific interaction term can be tested by

where SSE1 and SSE2 indicate the SSE values (see Appendix) for the models with and without a specific interaction term, respectively. When interaction terms
180x197,
180x285,
197x285,
197x308,
277x285, and
180x277x285 are considered separately, the F20, 19 values are 3.4 (P < 0.001), 1.2 (P = 0.250.5), 1.2 (P = 0.250.5), 1.6 (P = 0.10.25), 1.0 (P
0.5), and 1.0 (P
0.5), respectively. These tests show that only the estimation procedure with
180x197 should significantly improve the estimates.
|
|
If we include an interaction term
180x197, then Z = 559 nm,
180 = -7 nm,
197 = -28 nm,
277 = -8 nm,
285 = -15 nm,
308 = -27 nm, and
180x197 = 11 nm (Table 3, model b). Thus, Z,
180,
277,
285, and
308 are similar to those of model a, but
197 decreases and, at the same time,
180x197 causes a significant red shift in the
max. When the expected
max of the 26 pigments are inferred using these estimates, the differences between the expected and observed
max are significantly reduced (Table 4, column b). The 95% confidence intervals for the
max of dolphin (P524) and squirrel (P532) pigments are now 523528 nm and 529534 nm, respectively, and contain the observed
max.
These analyses show that the five-sites rule, now including the synergistic effect of sites 180 and 197, explains the
max of all contemporary pigments. According to the five-sites rule, the ancestral pigments with SHYTA and SYYTA should have
max at 559 and 536 nm, respectively. The corresponding observed values are 558564 and 536 nm (Fig 3). Thus, this rule explains the spectral tunings of the LWS/MWS pigments during the entire history of vertebrate evolution. Sites 180, 277, 285, and 308 are located near the chromophore (![]()
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![]()
![]()
![]()
max shift, it suggests an intimate relationship between the chloride binding site at 197 and the spectral tuning residue at 180.
Ancestral mammalian pigments:
By applying the JTT model of amino acid replacements to another tree topology of the mammalian pigments (Fig 7), we also inferred the amino acid sequences of the common ancestors of the 11 mammalian pigments (pigment x), of human (P560) and human (P530) pigments (pigment y), and of squirrel (P532) and mouse (P508) pigments (pigment z). Pigments xz roughly correspond to pigments df in Fig 3, respectively. Most amino acids inferred have posterior probabilities of >0.9 and pigments xz have only four, two, and five sites, where the posterior probabilities are <0.9 (Fig 4).
|
Using site-directed mutagenesis and recombinant DNA techniques, we then reconstructed these three ancestral pigments. Again, using an in vitro assay, the
max of pigments xz are determined to be 533 ± 1, 553 ± 1, and 533 ± 2 nm, respectively (Fig 7 and Fig 8). These results are consistent with those of ![]()
max of pigments df are given by 558, 558, and 536 nm, respectively (see Fig 3). Thus, the
max of pigment x is 25 nm lower than that of pigment d.
|
Pigments xz have AYYTA, AHYTA, and AYYTA at the five critical sites, respectively, whereas pigments df have SHYTA, SHYTA, and SYYTA, respectively. Thus, the difference between the
max of pigments x and d must have been caused by the amino acid differences at sites 180 and 197. Slightly lower
max of pigments y and z than those of pigments e and f can be explained by the amino acid differences at site 180. These results clearly show that the inference of the ancestral pigments depends not only on the phylogenetic relationship of extant pigments but also on the types of pigments used for constructing the phylogenetic tree. As noted earlier, however, the phylogenetic relationship of mammalian species has not been resolved. Thus, until the issue is resolved, it is premature to discuss whether the mammalian ancestor had MWS or LWS pigment.
Compared with the variability in the spectral sensitivities of those of the mammalian pigments, the
max of LWS/MWS pigments of nonmammalian vertebrates are more uniform. The currently available data show that all fish, amphibian, reptile, and avian lineages have LWS pigments but not necessarily MWS pigments (Table 1). Similarly, the orthologous pigment in marine lamprey (Lamptera marinus) has P180, Y277, and T285, showing the LWS pigment-specific feature (H. ZHANG and S. YOKOYAMA, unpublished data). It seems that the divergence between chameleon (P560) and gecko (P527) pigments (Fig 3, node h) and between cave fish (P558) and cave fish (P530) pigments (node i) occurred
150190 million years (MY) ago (![]()
190320 MY ago (![]()
30 MY ago (![]()
| DISCUSSION |
|---|
It is highly likely that the vertebrate ancestor possessed the LWS pigment with SHYTA at the five critical amino acid sites and that the contemporary LWS/MWS pigments evolved from the ancestral LWS pigment. We have also seen that the five-sites rule, now including the synergistic effect between amino acid sites 180 and 197, fully explains the variation in the
max of the LWS/MWS pigments during the entire history of vertebrate evolution. The first conclusion was based on a single amino acid sequence at each ancestral node, while the second conclusion was derived using a purely statistical argument. Here, we address these points in more detail.
Uncertain inference of amino acids and spectral sensitivity:
As noted earlier, ancestral mammalian pigments xz have 4, 2, and 5 amino acid sites where the posterior probabilities are <0.9. We replaced these amino acids by those with the second highest posterior probabilities and determined the
max of the mutant pigments. The results clearly show that the
max of the regenerated mutant pigments are virtually identical to those without such mutations, showing that the amino acid differences at these 11 sites have little effect on the
max shift (Table 5).
|
Interestingly, amino acid changes A180S introduced into pigments x and z do not shift the
max either. Considering
180 of -7 nm (Table 3, model b), this observation may be surprising. These results need to be understood, however, by considering the interaction between sites 180 and 197. Note that squirrel (P532) and mole rat (P534) pigments have AYYTA and SYYTA at the five critical sites, respectively, but their
max values are 532 and 534 nm and are virtually identical (Table 4). On the other hand, human (P552), marmoset (P553), goat (P553), and cat (P553) pigments have AHYTA, whereas human (P560), marmoset (P561), chicken (P561), pigeon (P560), zebra finch (P560), chameleon (P560), frog (P557), cave fish (P558), and goldfish (P559) pigments all have SHYTA (Table 4). The
max of the two groups of pigments differ by 49 nm (Table 4). Thus, the
max shift caused by A108S is very small, if there is any, for pigments with Y197, but it is
7 nm for pigments with H197. From these observations, it is expected that since both pigments x and z have AYYTA, A180S should not cause any significant
max shift.
More on the five-sites rule:
The statistical inferences strongly suggest that the five-sites rule explains the variation in the
max of all contemporary and ancestral LWS/MWS pigments. When the five critical sites are considered, the contemporary LWS/MWS pigments are classified into nine different groups (Table 6). To test the validity of the statistical result further, we reconstructed the nine types of pigments by modifying the amino acid compositions at the five critical sites of pigment x. Using the in vitro assay, the
max of these mutant pigments are measured. Table 6 clearly shows that, as long as the amino acid compositions at the five critical sites are the same, the
max of the mutants are virtually identical to those of the corresponding contemporary pigments.
|
It should be stressed that these mutant pigments with the background of pigment x and the corresponding contemporary LWS/MWS pigments can have very different amino acid compositions at sites other than the 5 critical sites. For example, reflecting dynamic evolutionary processes of amino acid replacements during vertebrate evolution, pigment x differs from human (P560) pigment at 27 amino acid sites, whereas it differs from cave fish (P558) pigment at 91 sites. Thus, the majority of these amino acid replacements have contributed very little to the spectral tuning in the LWS/MWS pigments and may be considered as "neutral" changes. The mutagenesis analyses using the mammalian ancestral pigment strengthen the argument that the "five-sites" rule has been the molecular mechanism of spectral tuning in the LWS/MWS pigments throughout vertebrate evolution.
Red-green color vision:
To study the structure-function relationships of the LWS/MWS pigments, we considered only the visual pigments with 11-cis-retinal (also known as vitamin A1 aldehyde). In nature, however, the
max of these visual pigments can be modified further at the visual pigment level as well as at the photoreceptor cell level. It turns out that many fishes, amphibians, and reptiles can use 11-cis-3, 4-dehydroretinal (or vitamin A2 aldehyde) as the chromophore, which causes a red shift in the
max (![]()
![]()
max value at
620 nm (![]()
![]()
![]()
max at
560620 nm depending upon the composition of the chromophore. Cone photoreceptor cells in many amphibians, reptiles, and birds use different devices, colored oil droplets. Although their exact functions have not been fully elucidated, the oil droplets often contain a high concentration of carotenoids and are likely to serve as cutoff filters (![]()
![]()
max at 600620 nm (![]()
max at
560 nm (see ![]()
When the actual
max of visual pigments are red shifted, how do animals achieve
max at
530 nm? It turns out that many species use an evolutionarily distantly related group of RH2 pigments for their green color detection (![]()
![]()
![]()
max from
510 nm to 530540 nm (![]()
![]()
max at
510 nm actually achieves a
max at 533 nm due to the presence of a green oil droplet in the cell (![]()
Vitamin A1 aldehyde is used by both vertebrates and invertebrates, but a vitamin A2 aldehyde-based pigment has not been found in invertebrates (![]()
![]()
![]()
Purifying selection and adaptive evolution:
For visual pigments, the numbers of amino acid replacements (K) can differ considerably between comparable branches. In Fig 3, for example, compared with the K for branch b-frog (P557) pigment (29), those for b-gecko (P527), b-mouse (P508), b-squirrel (P532), b-goat (P553), b-human (P530), and b-human (P560) pigments are 64, 99, 72, 80, 75, and 70, respectively. These values are all >>29 (P < 0.01). This difference is largely due to the accelerated evolution in the mammalian ancestor, represented by branch cd. Similarly, the K for branches f-mouse (P508) pigment and h-gecko (P527) pigment are significantly larger than those for f-squirrel (P532) pigment and h-chameleon (P560) pigment, respectively (both with P < 0.01; Fig 3).
These results seem to show that the accelerated evolutionary rate of amino acid replacement leads to the acquisition of new functions. More specifically, the K tend to be larger for branches where amino acid replacements occur at the functionally important five sites 180, 197, 277, 285, and 308 than those without such changes. Furthermore, the gecko pigment has pure rod-retinas (![]()
![]()
max shift from 558 nm to either 536 nm in the ancestral rodent pigment or 553 nm of the goat pigment (Fig 3). If it turns out that the rodents are most distantly related to the other groups of mammals, then the K associated with H197Y in the ancestral rodent pigment will be >8. On the other hand, if the goat pigment is most distantly related, then the K associated with S180A can be >26. Thus, there is a positive correlation between the evolutionary rate of amino acid replacement and the level of the divergence in the
max. Such correlation has also been detected for various evolutionary groups of visual pigments in the gecko (![]()
![]()
| ACKNOWLEDGMENTS |
|---|
Comments by Ruth Yokoyama, Stephen Schaeffer, and two anonymous reviewers are greatly appreciated. This work was supported by National Institutes of Health grant GM-42379.
Manuscript received March 19, 2001; Accepted for publication May 29, 2001.
| APPENDIX |
|---|
Consider the relationships

where ei's (i = 1, 2, ... , 26) denote random errors.
This is represented in a matrix form as

where

and

If we assume that the random term, e, has a normal distribution with mean 0 and
2I, then the mean (
) and standard error (
) of
' = [
180
197
277
285
308
180x197
180x285
197x308
277x285
180x277x285 Z] are estimated from

where

and n and p denote the number of samples and parameters, respectively (![]()
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|---|
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