THE STEPWISE MUTATION MODEL: AN EXPERIMENTAL EVALUATION UTILIZING HEMOGLOBIN VARIANTS PAUL A. FUERST .~ND ROBERT E. FERRELL Center for Demographic and Population Genetics, University of Texas Health Science Center, P. 0. Box 20334, Houston Texas 77025 Manuscript received March 1, 1979 Revised copy received June 6, 1979 ABSTRACT The stepwise mutation model of OHTA and KIMURA (1973) was proposed to explain patterns of genetic variability revealed by means of electrophoresis. The assumption that electrophoretic mobility was principally determined by unit changes in net molecular charge has been criticized by JOHNSON (1974, 1977). This assumption has been tested directly using hemoglobin. Twenty- seven human hemoglobin variants with known amino acid substitutions, and 26 nonhuman hemoglobins with known sequences were studied by starch gel electrophoresis. Of these hemoglobin% 60 to 70% had electrophoretic mobilities that could be predicted solely on the basis of net charge calculated from the amino acid composition alone, ignoring tertiary structure. Only four hemo- globins showed a mobility that was clearly different from an expected mobility calculated using only the net charge of the molecule. For the remaining 30% of hemoglobins studied, mobility was determined by a combination. of net charge and other unidentified components, probably reflecting changes in ioni- zation of some amino acid residues as a result of small alterations in tertiary structure due to the amino acid substitution in the variant. For the nonhuman hemoglobins, the deviation of a sample from its expected mobility increased with increasing amino acid divergence from human hemoglobin A.-It is concluded that the net electrostatic charge of a molecule is the principal deter- minant of electrophoretic mobility under the conditions studied. However, because of the significant deviation from strict stepwise mobility detected for 30 to 40% of the variants studied, it is further concluded that the infinite-allele model of KIMURA and CROW (1964) or a “mixed model” such as that proposed by LI (1976) may be more appropriate than the stepwise mutation model for the analysis of much of the available electrophoretic data from natural populations. HE stepwise mutation model was proposed by OHTA and KIMURA (1973) to study gene frequency data that has been obtained using electrophoresis. In this model all alleles at a locus are assumed to belong to discrete classes called electromorphs, which are determined solely by the net electrostatic charge of the protein. The model assumed additionally that this net charge was a function solely of the amino acid composition of the molecule and was not affected by tertiary structure. Amino acid substitutions that result in an alteration in net Genetics 94: 185-201 January, 1980.
Transcript
THE STEPWISE MUTATION MODEL: AN EXPERIMENTAL EVALUATION UTILIZING
HEMOGLOBIN VARIANTS
PAUL A. FUERST . ~ N D ROBERT E. FERRELL
Center for Demographic and Population Genetics, University of Texas Health Science Center, P. 0. Box 20334, Houston Texas 77025
Manuscript received March 1, 1979 Revised copy received June 6, 1979
ABSTRACT
The stepwise mutation model of OHTA and KIMURA (1973) was proposed to explain patterns of genetic variability revealed by means of electrophoresis. The assumption that electrophoretic mobility was principally determined by unit changes in net molecular charge has been criticized by JOHNSON (1974, 1977). This assumption has been tested directly using hemoglobin. Twenty- seven human hemoglobin variants with known amino acid substitutions, and 26 nonhuman hemoglobins with known sequences were studied by starch gel electrophoresis. Of these hemoglobin% 60 to 70% had electrophoretic mobilities that could be predicted solely on the basis of net charge calculated from the amino acid composition alone, ignoring tertiary structure. Only four hemo- globins showed a mobility that was clearly different from an expected mobility calculated using only the net charge of the molecule. For the remaining 30% of hemoglobins studied, mobility was determined by a combination. of net charge and other unidentified components, probably reflecting changes in ioni- zation of some amino acid residues as a result of small alterations in tertiary structure due to the amino acid substitution in the variant. For the nonhuman hemoglobins, the deviation of a sample from its expected mobility increased with increasing amino acid divergence from human hemoglobin A.-It is concluded that the net electrostatic charge of a molecule is the principal deter- minant of electrophoretic mobility under the conditions studied. However, because of the significant deviation from strict stepwise mobility detected for 30 to 40% of the variants studied, it is further concluded that the infinite-allele model of KIMURA and CROW (1964) or a “mixed model” such as that proposed by LI (1976) may be more appropriate than the stepwise mutation model for the analysis of much of the available electrophoretic data from natural populations.
HE stepwise mutation model was proposed by OHTA and KIMURA (1973) to study gene frequency data that has been obtained using electrophoresis. In
this model all alleles at a locus are assumed to belong to discrete classes called electromorphs, which are determined solely by the net electrostatic charge of the protein. The model assumed additionally that this net charge was a function solely of the amino acid composition of the molecule and was not affected by tertiary structure. Amino acid substitutions that result in an alteration in net Genetics 94: 185-201 January, 1980.
186 P. A. FUERST AND R. E. FERRELL
charge would cause an allele to move to one of the two adjacent electromorph classes (or rarely to the second class in either direction). The direction of the shift in mobility would depend upon the direction of the shift in net charge. A second amino acid substitution with an opposite shift in charge, but not neces- sarily occurring at the same amino acid site, would exactly cancel the original shift in electrophoretic mobility. The new protein would be indistinguishable from the original allele on an electrophoretic gel.
The model has proven useful for describing some patterns of genetic variability in natural populations. I t was clear, however, even before the stepwise mutation model was proposed, that electrophoresis was capable o€ distinguishing molecules that in theory have identical net charges. HENNING and YANOFSKY (1963) noted that several double mutants in the A protein of tryptophan synthetase of E. coli had mobilities inconsistent with a simple combination of the mobilities of the single mutants. They attributed these differences to either gross structural altera- tions in the molecule o r alteration in the irue net charge of the morecule because of exposure er masking of charged amino acid side chains. It appeared therefore that the tertiary position or an amino acid affected the residue’s contribution to the true net charge of the molecule and to the subsequent electrophoretic behavior of the molecule. Similar findings were reported €or some human hemo- globin variants (HUEHNS and SHOOTER 1965) and most recently in a study of five alleles at the alcohol dehydrogenase locus of Drosophila melanogaster (RETZIOS and THATCHER, in preparation). The most serious criticisms of the stepwise mutation model have therefore focused upon the underlying biochemi- cal assumptions (JOHNSON 1974, 1977). While some investigators suggested that assumptions concerning the proportion of charge changes were generally robust (MARSHALL and BROWN 1975), JOHNSON (1974) criticized the model as being totally unrealistic. The problems inherent in predicting electrophoretic charge when tertiary and quarternary structure are considered have also been discussed theoretically by KOEHN and FANES (1978). JOHNSON (1977) suggested that protein conformation, not molecular charge, was the over-riding determinant of electrophoretic mobility. He concluded that the electromorph classes of the Est-5 locus in Drosophila pseudoobscura were heterogeneous assemblages of differ- ently charged molecules and that interpretation of mobility “steps” on the basis of charge was not valid. Other authors (COBBS and PRAK~SH 1977), using John- son’s methodology and studying the same locus, came to opposite conclusions, however. Conclusions suggesting that charge heterogeneity was not particularly important were also reached when charge classes were defined by isoelectric focusing, rather than by Johnson’s gel sieving methods (RAMSHAW and EANES 1978). None o€ these studies, however. involved the comparison of molecules in which allelic differences had a known structural basis.
Here we shall present the results of a study of the hemoglobin molecule. Hemoglobin was chosen because of the availability of numerous variants with known structural changes. We have determined the correspondence between the observed electrophoretic mobility obtained using a standard electrophoretic screening method and the expected mobility predicted by relative charge cal-
STEPWISE MUTATION MODEL 187
culated solely from the amino acid composition of the variant. In particular, we are interested in determining whether mobility is not predictable by a knowledge of net charge, as suggested by JOHNSON (1977). If net charge is the over-riding determinant of mobility, and most similarly charged alleles are indistinguishable, then the stepwise mutation model would clearly be appropriate for interpreting electrophoretic data from natural populations. If electrophoretic mobility is largely (but not completely) predictable, then observations from nature can be bracketed between expectations of the infinite-allele model of WRIGHT (1949) and KIMURA and CROW (1964), and of the step-mutation model of OHTA and KIMURA (1973). For instance, a mixed model such as that suggested by LI (1976) may be appropriate. Note, however, that if factors other than charge cause most, or all, allelic variants to be distinguishable, even though their mobili- ties are reasonably predictable using charge alone, the infinite-allele model would certainly be the preferred model for comparison with data. If migration is un- predictable, as suggested by JOHNSON (1977) ~ however, no model currently iormulated can be applied validly to the study o i available electrophoretic survey data.
MATEKIALS A N D METHODS
Hemoglcbin samples were obtained, either in whole blood or as red cell hemolysates, from a number of different investigators. Each sample studied was either a human variant with known single amino acid substitution, or a hemoglobin from a species for which the complete sequences of both the alpha and beta chains have been reported. These two groups will subsequently be referred to as “human” and “interspecific” variants, even though, for the purpose of analysis, the latter group contains human Hb-A, and Hb-F. The samples studied in this investigation are listed in Tables 1 and 2. The net charge of each variant, given in Tables I and 2, is expressed relative to human Hb-A. The net charge is calculated only from the balance of basic (arginine and lysine) and acidic (glutamic acid and aspartic acid) residues. For all interspecific variants except savannah monkey, capuchin monkey and slow loris, samples from several differ- ent individuals were obtained. No intraspecific variability was detected, but the number of individuals tested was not large. Amino acid sequences for the interspecific variants were derived from DAYHOFF (1972) LIN, KIM and CHERNOFF (1976) and STENZEL and BRIMHALL (1977).
Electrophoresis was performed using a standard hemoglobin screening procedure that has been extensively utilized by many laboratories in population surveys of genetic variability (UEDA et al. 1977; NEEL 1978; FERRELL et al. 1978). Results obtained should thus be applicable to data obtained during standard population screening. Such would not necessarily be the case if a more sensitive method such as isoelectric focusing, which is not normally applied for p o p - lation surveys, had been used for this study. Red cell hemolysates were diluted and the hemo- globin converted to cyanmethemoglobin prior to electrophoresis. Horizontal starch gel electro- phoresis was carried out in 12% starch gels (Electrostarch Lot No. 307) in 0.045 M Tris/0.025 M
boric acid, 0.001 M (ethylene dinitri1o)-tetraacetic acid, p H 8.6. Samples were applied to the gel using filter paper wicks and electrophoresed for 18 hr at 4.5 volts per cm gel (24 mAmps). Gels were stained using the benzidine staining method of OWEN, SILBERMAN and GOT (1958).
Following staining, migrational distance from the origin to the leading edge of each band was measured to the nearest millimeter by three different observers. Far each gel X observer combination, the absolute migration of each band was then expressed relative to the average migration of all human Hb-A bands on that gel. The number of Hb-A bands per gel varied from three to eight depending upon the variants being studied. This variation arises because most of the human variant samples studied were obtained in heterozygous form. The stan-
188 P,. A. FUERST AND R. E. FERRELL
TABLE 1
Human variants studied, listed with the substitution involved
Number Variant Site
I Russ G-Philadelphia Matsu-Oki Tarrant Cubujuqui S C G-San Jose J-Baltimore E Athens-Ga Austin G-Galveston N-Seattle Korle Bu Mobile Baylor N-Bal timore Kempsey Hi jiyama D-Punjab 0-Arab Camden Hope Andrew-Minneapolis Hiroshima
dardized value of a band was averaged over observers to obtain the final value for a particular observation that is used for further analysis. Ten slots were run per gel, including two samples that were a mixture of hemoglobin A: S and C, and a third, an AS sample. These samples were used to determine if any gel gave inconsistent results. No such gel was detected in this study. The samples being studied were randomized over gels. Each sample was measured on at least six replicate gels, to permit intergel variability to be evaluated.
Variants are classified according to expected relative charge. Six separate charge classes are represented in the data. One of these (+6) cmtains only a single sample. Tu analyze deviations from the model, the expected mobility for each charge class must be defined. Only the 0 class has an obvious standard, human hemoglobin A, with average mobility defined as 1.00. We begin by considering the mobility of all variants within a charge class. A comparison of the mobilities of each class suggested that some variants should be considered as outliers for the purpose of calculated class mobilities. These are indicated in Tables 1 and 2. After excluding these outliers, the average mobility of all remaining variants (human and interspecific) was calculated. TVe consider these averages to be the best available estimate of the expected mobility of each charge class. The results are given in Table 3.
The procedure that we used results in apparent clustering around the expected value. It also acts to minimize deviations from the expected mobility. To measure the magnitude of this
STEPWISE M U T A T I O N MODEL 189
TABLE 2
Multiple substitution of nonhuman sample studied with total number of amino acid differences reported for both chains as compared to human hemoglobin A
Net Expected Average No. substitutions charge mobilitJr
* Expected mobility for the +6 class was calculated by assuming that the ratio of the width of the “step” between the 4-4 and +6 classes and the width of the step between +2 and 4-4 was the same as the average ratio for each adjacent step for the other four steps. By this reasoning, the 4 -64-6 step would be 1.2 times as large as the +%+4 step.
190 P. A. FUERST AND R. E. FERRELL
potential bias, we have examined the zero charge class, which contains the natural standard human hemoglobin A. From Table 3 we can obtain the difference between the defined standard and the calculated aberage mobility, which was used to estimate expected mobility for the other charge classes. The difference (0.007) represents a shift of approximately one-half standard deviation in mobility (as defined below). If one uses the calculated average mobility of the class as a standard, the average deviation of the 11 variants, excluding human Hb-A is 0.033. When the natural standard 1.00, the migration of human Hb-A, is used, the calculated deviation in- creases only to 0.034. This result suggests that our use of the average mobility as a n estimator of the expected class mobility is not unreasonable and that the effect on our estimates d relative deviation is probably small.
RESULTS
Figures 1 and 2 present the observed electrophoretic mobility of all the variants. The average mobilities of each charge class are given in Table 3. Note
-4
-2
0
m x -U
m n
+2 --I , g
% 0 I
h m
+4
+6
CHARGE CLASS
FIGURE 1.-Observed migration of human variants. Numbers refer to those given in Table 1. The central bar for each variant i s the average relative mobility for the variant estimated from at least six different gels. Outer bars delimit the 95% confidence interval of the estimated mean. Dashed lines give estimated location of each charge “step”; for details see text. Variants are grouped according to charge as given at the bottom of the figure, and within each charge class by increasing observed mobility. Relative mobility expressed compared to human Hb-A (1.00).
STEPWISE MUTATION MODEL 191
FIGURE 2.-Observed migration of interspecific hemoglobins. Numbers refer to those given in Table 2. The central bar for each variant is the average relative mobility for the variant estimated from at least six different gels. Outer bars delimit the 95% confidence interval of the estimated mean. Dashed lines give estimated location of each charge “step”; for details see text. Variants are grouped according to charge as given at the bottom of the figure, and within charge by increasing observed mobility. Relative mobility expressed compared to human Hb-A (1.00).
that the distance between classes is not constant, but tends to decline when moving from the more positively charged variants (which migrate cathodically to Hb-A) towards the more negatively charged variants (which migrate anodi- cally to Hb-A) . Considering the differences between the four steps that are well represented in the data, we estimate an average step to be 0.224, relative to the migration of human Hb-A.
Examination of the mobility of each variant in Figures 1 and 2 reveals the following: (1) Highly discrete groups exist for the +4 and -4 charge classes (and for the $6 class if we accept the migration of chicken as being representa- tive of that class). The only discrepancy arises from rabbit hemoglobin which has a $4 charge, but migrates as a 4-2 sample. (2) The +2, 0 and -2 classes for the human variants form an almost continuous set of migration values. The groups are more discrete in the interspecific material. Closer examination re- veals, however, that there is very little true overlap between charge groups. The only variants whose mobilities would place them into a charge class different
192 P. A. FUERST AND R. E. FERRELL
from their expected class are Hb-Austin and the two cat hemoglobins, each of which migrates more cathodically than their expected charge class, and the rabbit, which migrates more anodically. As a first approximation, the results indicate that mobility is generally predictable by considering only expected charge.
Since each variant was studied on a minimum of six different gels, confidence limits for the migration of each variant can be obtained. These limits can be used to determine whether the mobility of a variant is significantly different from its charge class by comparing the observed mobility with the expected mobility given in Table 3.
To show the magnitude of inter-run variability that was encountered, results €or the human hemoglobins A, S, C and A, are given in Figure 3. It can be seen that a replicate may deviate by as much as 0.06 units from the average migra- tion of the particular variant. Note that the standard deviation is remarkably constant over this group of lour variants with an average value of about u=0.0153. The average standard deviation for all variants was U = 0.0152. There was no tendency for the amount of migrational “error” due to intergel vari- ability to be dependent upon the migration distance. (Inter-observer variation was estimated to be half as large as the observed between-gel variation, sobs = 0.0081. This source of error had been removed beIore calculating confidence limits. Removing the inter-observer variability should yield results similar to automated methods, such as scanning densitometry, which would apply a com- pletely objective definition of mobility.)
Since we define mobility relative to the auerage Hb-A mobility on a gel, there is the possibility that our results underestimate the true intergel variability in electrophoretic mobility. To evaluate the potential bias, we re-examined the variation in migration for Hb-S, Hb-C and Hb-A, using two alternative defini- tions of mobility. In the first, mobility is defined as the ratio of the migration distance of the variant to the migration distance of a Hb-A band in the same gel slot. This would account most directly for within-gel variability. The standard deviation of mobility for the three variants was reduced by an average of 5.5%, which was not a significant reduction for any of the three variants. The second definition of mobility uses the ratio of a variant band’s migration distance to the migration distance of one randomly selected Hb-A band from the same gel. This resulted in an increase in the standard deviation of mobility by 14.3%, which was significant for Hb-S, but not for Hb-C or Hb-A,.
The 95% confidence limits for each variant are shown in Figures 1 and 2. To determine significant deviation, the limits were compared with the expected class mobility values obtained previously, which are shown as the dashed hori- zontal lines in Figures 1 and 2. The results are summarized in Table 4. Thirty- six percent of the hemoglobins studied show significant deviation from their expected class mobilities. Given the small number of observations in each class, there was no detectable heterogeneity among charge classes for the proportion of deviant samples. Neither were there any differences between human variants and the interspecific chains. Tf we include both nonallelic duplicate chains for
STEPWISE MUTATION MODEL 193
50
40
30
20
10
0
LL W
P z 2 0
f 0.015
1 .bo - - - L - -
Hb-S
Z = 0 . 7 4 L
c m = 1 3 7 1 f 0 . 0 1 5
0 . 7 4
lo 1 , .
:;:58 f 0.017
0 0 . 4 5
1
= 0 . 4 7 9 f 0 . 0 1 5
m = 5 6
0
0 . 4 8
MOBILITY ( I N 0 . 0 1 RELATIVE U N I T S )
FIGURE 3.Abserved variation, over all gels, of relative mobility for four hemoglobin vari- ants. Histograms show absolute number of replicates with a particular relative mobility.
the dog (which contain different noncharged substitutions, but which did not resolve from each other as clear bands) nine of 26 of the interspecific hemo- globins had significant migrational differences from their expected class values. There were 11 of 27 human variants that showed significant deviations. In con- clusion, slightly more than one-third of all variants tested showed a significant
194 P. A. FUERST AND R. E. FERRELL
TABLE 4
Distribution of significant deviations from expected class mobility
* Because of the uncertainty of the expected migration for the $6 class, the single value was not considered to differ significantly.
deviation from a strict stepwise pattern of migration, but only four of the 53 total variants examined (Hb-Austifi, rabbit and two cats) showed a mobility that fell totally outside the normal range of their mobility class.
If we use alternative values of the 95% confidence limits, determined using the two alternative de€initions of mobility given above, these results are only slightly altered. By decreasing the 95% limits by 5.5%, equivalent to matching to a standard Hb-A in the same slot, one additional variant would be judged to deviate significantly from its expected mobility. If the additional 14.3% varia- tion resulting from randomly matching Hb-A’s with variants were included, three variants considered significant by our original criteria would be judged not different from their expected mobilities.
Finally, we will consider the effect of amino acid sequence divergence on deviations from the step-nature of mobility. It is possible that amino acid sub- stitutions have a small effect on mobility that occurs independently of any alteration in charge. These would likely be small conformational changes that may affect mobility. The changes, however, may often be too small to be norm- ally detected when only a single amino acid substitution is involved. If this is true, deviations from the expected mobility will increase with increasing amino acid sequence divergence from the standard. The definition of departure from the step-nature of mobility will then depend upon the sequence used as a stan- dard. Since human hemoglobin A is the standard for sequence divergence, it is important that the determination of expected mobility 01 each charge class be highly dependent upon sequences with relatively little amino acid divergence from this standard. The data are dominated by, first, the 27 human variants and, second, the 14 primate sequences (including human Hb-A and the four Hb-A, chains). Therefore, such standardization does appear to be the case. Examination of Table 2 suggests that, with respect to amount of amino acid divergence, the data consist largely of two groups. First, there are the primate Hb-A and Hb-A, sequences, with amino acid differences ranging from zero (for chimpanzee) to 20, compared to Hb-A. If we confine ourselves to those sequences with nine to 20 differences from Hb-A, the average number of amino acid differences in the two chains is 12.4 for 11 sequences (note that the actual number of differences in the intact tetramer is double this value, 24.8), and the average deviation from the expected class mobilities is 7% of a step. As previously noted, an average mobility step was estimated to be 0.224 on the relative scale by considering dif- ferences between +4 and -4 classes as being equivalent to four steps. The
SI'EPWISE MUTATION MODEL 195
second group of sequences consists of nonprimate mammal hemoglobins and hemoglobin F, with amino acid differences about four times as great (averaging 41 .I for 11 sequences, 82.2 in the intact tetramer, including both hemoglobin species from dog, horse and cat). These sequences show an average deviation of 54% of an average step. Note that only the two cat sequences, the rabbit and Hb-F show deviations greater than 25%, however. The results are summarized in Figure 4.
Clearly, a relationship between accumulation of amino acid differences and departure from the strict stepwise nature of migration exists. Loosely, mobility deviations increase by 5 to 10% of a step for every 20 amino acid differences from human Hb-A in the intact hemoglobin tetramer. This is further substan- tiated by considering the regression of the percent deviation from expected migra- tion upon the number of amino acid differences from €33-A. An estimate can be obtained of the amount of amino acid differentiation beyond which significant migrational deviation will be expected as a rule. Significant deviation is defined as a relative deviation of 0.03, about two times the average standard deviations. This corresponds to 13% of the average step. We excluded the four sequences shown in Figure 4 that have unusually large deviations from their expected mobility (Hb-F', the two cat hemoglobins and rabbit) because these differences appear to arise from mechanisms other than the gradual accumulation of small structural changes. Regression analysis indicates that significant deviation will
W W
W 2 150- z z - v
w 100- s
W 0 a w > P - w 50- W a I- * z w ** U E * * *
e * w a
I I I 1 I I 1 0 40 80 120 160
AMINO ACID DIFFERENCES FROM HUMAN Hb-A
FIGURE 4.--Relationship between the deviation from strict stepwise migration (expressed as a percentage of the average step) and the degree of sequence divergence from human hemo- globin A. Human variants are not considered. Amino acid differences are measured for the intact tetramer. Consequently, the values given are twice those appearing in Table 2. Analysis of the regression of mobility divergence (as a percent of average step distance, 0.224) upon number of amino acid differences from Hb-A leads to the following regression equation: Y = 0.0018X $- 0.032. The regression coefficient b = 0.0018 is highly significant.
196 P. A. FUERST A N D R. E. FERRELL
accompany the accumulation of 53.1 amino acid differences in the intact tetramer. Examining the data, we find that only one of the 13 sequences with deviations less than this value are significantly deviant from expected migration, while five of eight sequences with greater amino acid divergence are significantly deviant. Including the four most divergent species increases this last figure to nine of 12 species.
DISCUSSION
The results presented here differ markedly from those reported for the Est-5 locus of Drosophila pseudoobscura by JOHNSON ( 1977). JOHNSON concluded ihat interpretation of mobility classes as homogeneous charge classes was not warranted. Our results yield an opposite conclusion; very few variant hemo- globins with similar mobilities have dissimilar charge.
The results indicate clearly, however, that the stepwise mutation model is only a crude approximation of the analytic power of standard electrophoretic methods. Variants that do not differ by charge can be distinguished in a signifi- cant proportion of cases, despite the fact that their mobilities do not differ significantly.
Our studies were not designed to answer questions such as the correct identifi- cation of alleles, amount of variability hidden within an electromorph or the proportion of alleles that can be unambiguously separated. Only a first approach to these problems can be made using the data we collected. By examining gels used to obtain the data presented above, we have tallied all cases in which a pair of alleles from the same charge class were run on the same gel. If we assume ihat the ranking of the mobilities obtained from Tables 1 and 2 is accurate, we can classify each comparison as being either correct, ambiguous or incorrect. Table 5 presents the results of these comparisons as a function of the difference between the average mobilities o€ the pair of variants being compared. It can be seen that the correct identification increases rapidly with increasing distance
TABLE 5
Proportion of pairwise comparisons between variants within a charge class which resulted in correct, ambiguous or incorrect ranking of variants as judged b y the average
One standard deviation equals 0.0152 units of migration relative to the mobility of Hb-A.
STEPWISE MUTATION MODEL 197
between variants. On average, one standard deviation corresponded to 1.3 mm absolute distance. Differences between the average mobility of variants of less than one standard deviation resulted in considerable ambiguity. These variants were not unambiguously distinguishable on single comparisons and would prob- ably have been classified together if the study had been a population screening in which structural variants were not known prior to analysis. As such, the groups would have constituted elec tromorphs harboring hidden variation. Vir- tually no misclassification was observed if variants differed by more than 1.5 standard deviations of mobility. Readers worried about the problem of classifica- tion of hemoglobin variants on the basis of electrophoretic mobilities are referred to the work of SCHNEIDER and BARWICK (1978, 1979). I t is clear that when attempts are made to differentiate alleles using a combination of screening sys- tems, much more than 30 to 40% of the alleles can be identified. The work of SCHNEIDER over the last decade has clearly shown that sequential use of differ- ent electrophoretic conditions will provide an essentially unique classification of hemoglobin variants (summarized in SCHNEIDER and BARWICK 1979).
Caution must be exercised in extrapolating from our results. As shown by Figure 4, deviations from stepwise migration increase with amino acid divergence from the standard. Sequences with amino acid divergence less than 10% (i.e., less than about 50 amino acid differences among the 574 amino acids in the intact hemoglobin tetramer) show very little deviation from stepwise mobility. In fact, only one of these sequences differs significantly from its expected mobility. Nevertheless, 11 out of 27 humen variants, each of which carry only two amino acid differences in the intact molecule, show significant deviation from stepwise mobility. This may be due to potential differences in the nature of the two types of variants being studied. A significant proportion of the human variants studied were discovered because of some clinical abnormality observed in heterozygous carriers. In these cases, the amino acid substitutions involved impair the function of the hemoglobin. As a consequence, many of these mutations may have delete- rious fitness effects. Substitutions accumulated in the interspecific sequences, however, must have had an effect too small to disrupt normal function of the molecule. Otherwise, it is unlikely that complete substitution would have oc- curred. The four human variants we have studied that attain polymorphic fre- quencies in some populations (S, C, E and D-Punjab) have an average deviation only half as large as the other 23 variants (average deviation for the first group is 21% compared to 20% for the latter group if we exclude the highly deviant Hb-Austin, whose anomalous migration appears to be caused by migration as a dimer rather than a tetramer). Note also that Hb-S, which shows significant deviation from its step, has been reported to cause more severe clinical manifesta- tions than either Hb-C or Hb-E, which do not deviate significantly (LIVINGSTONE 1971 ) . Polymorphic “silent” variants have been reported in several primates (BOYER et al. 1972) and in the rabbit (GARRICK et al. 1974), which contain amino acid substitutions with no apparent shift in electrophoretic mobilities or apparent phenotypic effect on carriers. Our results are therefore potentially biased because some human variants were initially identified primarily because
198 P. A. FUERST AND R. E. FERRELL
of some effect on health. It is possible that, in a survey in which this bias does not occur (i.e., in standard population surveys), most variants encountered will show predominantly stepwise mobility. The results of COBBS and PRAKASH (1977), for instance, suggest just such a result.
A further difference between human variants and the evolutionary substitu- tions in nonhuman hemoglobins concerns the conservation of molecular charge. BOYER et al. (1972) have commented upon the preponderance of substitution by like-charged amino acids. Consider the primate hemoglobins. Amino acid sub- stitutions between the human alpha and beta chain sequences and the alpha and beta chains of other primates have occurred at 34 sites. However, at only three sites, and only in comparisons with the sequence from the slow loris, does a charge change occur. From the remaining eight primates, no charge change whatsoever can be deduced. These sequences incorporate a minimum of 24 sub- stitutions. Taking into account the ancestral sequence and considering the prob- ability of amino acid change as given in Table 3.2 of NEI (1975), the probability that no charge change has occurred is 9.7 x clearly an improbable event. PERUTZ (1978) has recently summarized the importance of electrostatic effects in many aspects of protein structure and function. The apparent conservation of overall charge in the primates reflects the maintenance of specific charged residues involved in subunit cooperativity and stability of the hemoglobin mol- ecule. Other differences between human variant types and evolutionary substi- tutions in hemoglobin have been reviewed by FITCH (1974). In the human variants studied here, there is an almost complete absence of “neutral” substitu- tions, contrasting with the preponderance of such substitutions with no change in charge in the nonhuman material. The question of whether single substitu- tions by like-charged amino acids are detectable at the same rate as the other single substitutions considered in this study remains unanswered.
Taken as a whole, this evidence suggests that our estimate of 30 to 40% deviation from the stepwise model may be at the upper limit of the disparity to be expected during a survey of proteins from a randomly sampled population. However, as stated above, if deviation is expressed purely in terms of detect- ability of alleles, the proportion of deviation will be somewhat larger. Exactly how large cannot, unfortunately, be answered by our study. Using a “standard” screening method on acrylamide gels, RAMSHAW, COYNE and LEWONTIN (1 979) revealed 23 electrophoretic classes from 53 human hemoglobin variants (43 % detectability), a value basically equivalent to our results. They, too, were unable to show the existence of discrete mobility classes over most of the range of migra- lion for human hemoglobin variants.
RAMSHAW, COYNE and LEWONTIN (1 979) have investigated some of the deter- minants of electrophoretic mobility differences for human hemoglobins. It ap- pears that partial charge (due to partial shielding of charged substitutions in the internal regions of the tetramer) can account for many mobility differences between theoretically like-charged variants. BASSET et al. (1978) studied the isoelectric point of 70 hemoglobin variants, 20 of which have been included here. If we assume that isoelectric point reflects partial charges on the molecule, we
STEPWISE MUTATION MODEL 199
can compare the relative ranking of isoelectric points and the mobilities as given in Tables 1 and 2. It should be kept in mind that mobility at p H 8.9 will not be a direct function of the ranking of isoelectric points because the percentage ionization of several amino acids change when pH is shifted from about pH 7.0 (the PI of hemoglobin) to pH 8.9. We have compared the relative rank of mobility for starch gel electrophoresis and for isoelectric point for the 20 variants common to our study and to that of BASSET et al. (1978). Comparison was per- formed using the Kendall rank-correlation coefficient. The calculated rank correlation, T = 0.87, was very highly significant. We interpret this to mean that most small differences we observe are attributable to partial charge changes.
The most appropriate approach to the problem of modeling electrophoretically detected genetic variability in natural populations appears to be that taken by LI (1976). His model, called the mixed model of mutation, includes both step- wise and nonstepwise mutation. LI found that when the proportion of nonstep changes is greater than about 20%, data may be more appropriately represented by WRIGHT’S (1949) infinite-allele model than by the stepwise mutation model of OHTA and KIMURA (1973). Our results and those of RAMSHAW, COYNE and LEWONTIN (1979) suggest that this may be the case. In the present study, 30 to 40% of variants migrated in a nonstepwise fashion. In concordance with this interpretation, a recent analysis of a large number of allele-frequency distribu- tions from natural populations found that the infinite allele model gave a con- sistently better fit to data than did the step-mutation model (CHAKRABORTY, FUERST and NEI 1980).
We acknowledge the assistance of ROSE SCHNEIDER, HOWARD HAMILTON, BRADFORD THERRELL, T. H. J. HUISMAN, RICHARD T. JONES, PETER E. NUTE and ROBERT M. SCHMIDT in obtaining samples of human hemoglobin variants, and R. E. TASHIAN: JAMES S. HARPER, THOMAS B. CLARKSON, BRENT SWENSON, KURT BENIRSCHKE and GARY W. GOLDENBOGEN, for providing blood specimens from the nonhuman primates. We thank R. H. WARD and M. NEI for critical comments on the manuscript. We thank TERRY BERTIN and BEULAH HARRIEL for expect techni- cal assistance, and JERYL SILVERMAN for preparation of the manuscript. This work was sup- ported by Public Health Service grants GM 19513, CA 19311, RO 07148 and GM 00230, a grant from the Texas Diabetes Research Foundation, and a direct grant from S. FOSHEE.
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