Although technological developments may soon make it feasible to use amino acid and nucleotide sequences in measuring genic diversity in individuals and populations, thus far the most practical and productive model has involved the indirect assessment of variation in protein structure by the use of electrophoresis -- the allozyme technique introduced to population genetics by J.L. Hubby, R.C. Lewontin, and H. Harris in 1966. Early demonstrations of large amounts of polymorphism and heterozygosity at structural gene loci in fruit flies, house mice, and humans led to several major developments in population genetics, including a revision of concepts of genetic load and a revival of interest in genetic drift and the possibility of nonselective modification of gene pools (concepts, data, and literature summarized in references 1, 2, 3, 4, 5). As more species were studied, it became apparent that estimates of genic heterozygosity for Drosophila and other invertebrates are, on the average, twice as large as those for mammals and other vertebrates ( 6). Ecological correlates of this difference were suggested by Selander and Kaufman ( 7) and Gillespie ( 8), whereas Nei ( 4) and Soulé ( 9) attributed it to an average difference in species number. Another possibility (which has been examined in the work reported here) is that electrophoretically derived measures of heterozygosity provide a misleading picture, mammals and some other vertebrates only appearing to be less variable than invertebrates because in homeotherms there are greater selective constraints on amino acid substitutions affecting the net electrostatic charge of proteins.
The house mouse, Mus musculus, is a "typical" vertebrate in respect to the amount of electrophoretically demonstrable genic variation carried by natural populations. Estimates of mean individual heterozygosity over 41 loci for different populations vary from 6% to 11%, with an average of 8.0% ( 10, 11).
Increasingly in recent years it has been realized that, because electromorphs may be a special class of variants ( 12, 13), our estimates of genic variation may be heavily biased and, hence, unreliable. Even more importantly, recent considerations of various integer-step or "ladder" models postulating that alleles at structural gene loci are clustered in a generally small number of net-charge classes ( 14) have made it clear that there can be large amounts of allelic diversity underlying individual electromorphs, and that the extent of this diversity may depend on factors other than the proportion of amino acid substitutions that affects the net charge of proteins ( 15). Even the magnitude of the "hidden" fraction of allelic variation remains unknown ( 16), yet knowledge of the actual numbers and frequencies of alleles in populations is crucial to further advances in the field of molecular population genetics ( 17). Attempts to test the neutral theory and its recent derivatives, the mutation-equilibrium theory ( 18, 19) of molecular evolution, have failed largely because the available data pertain to electromorphs rather than actual alleles. For example, it has been argued that the neutral theory cannot account for geographic uniformity of molecular polymorphisms, combined with relatively small numbers of "alleles" (= electromorphs) in species of Drosophila and some other organisms. If migration sufficient to account for the uniformity is invoked ( 20, 21), effective population size is inflated and large numbers of alleles are expected ( 22). But what if electromorphs represent highly heterogeneous charge classes of alleles convergently evolving in different populations? Again, Milkman's ( 23) report of a small effective "allele" (= electromorph) number at each of five loci in Escherichia coli would seem to be incompatible with a theory of neutrality, but the results are not contrary to predictions of the mutation-equilibrium model, which, even for large populations, postulates the generation of a relatively small number of allelically heterogeneous electromorphs.
To detect structural variants of proteins of similar electrophoretic mobility, additional means of analysis, assessing physicochemical properties other than net charge, must be employed. By varying gel concentration and pH and applying a heat-stability test, Singh et al. ( 17) revealed a total of 37 allelic classes of xanthine dehydrogenase in 146 genomes of Drosophila pseudoobscura, where only six had previously been recognized in the species. (This may be an exceptionally polymorphic locus, as these authors note.) The major effect of varying gel concentration was to enhance the resolution of bands, so that small differences in mobility were increased.
The success of Singh et al. ( 17), Coyne ( 24), and others in revealing "hidden" variability in several enzymes in Drosophila by modifying electrophoretic conditions immediately raises the question: Are there equivalent amounts of this type of "hidden" variation as yet undetected in the house mouse? We think not. House mouse proteins already have been electrophoresed in many laboratories on both acrylamide and starch gels under a wide variety of conditions, including gel concentration and pH. For example, we have employed nine buffer types in screening enzymes and other proteins in our laboratory.
Although the recent work on Drosophila has demonstrated the existence of "hidden" variability at several loci, we as yet have no knowledge for any organism of the full extent of allelic heterogeneity of electromorphs. What is needed is a method of determining the actual number of alleles per locus over a randomly selected set of loci. In our recent work on electrophoretic mobility and thermostability of proteins in the house mouse ( 25), we have employed an experimental approach that potentially can yield reliable estimates of the total allelic diversity at structural gene loci. The results of this work are summarized here.
Strains of Mice. Our analysis was based on adults of 39 laboratory strains: A/He, Au/Ss, AKR, BALB/c, BDP, BUB/Bn, CBA, C3H/He, C57BL/10, C57BL/Ha, C57BR/cd, C58-waved, CE, DBA/2, DBA/LiHa, DE, DN, HRS, ICR/Ha, I/St, JB, LP, MA/My, NZB/BlN, P, PL, RF, RIII/2, SEC/Re, SJL, SM/J, ST/b, SWR, YBR, Yebt, 129, CALIF, MOR, ALBU. All but three of the strains were fully inbred and, hence, monogenic; MOR and ALBU were only partially inbred; CALIF is a heterogeneous group of hybrids between a wild stock of M. musculus from California and M. m. castaneus from Asia. Additionally, eight individuals each of M. m. castaneus and M. m. molossinus were used in analyzing esterases, PGI, and non-enzymatic proteins.
Tissue Extracts. Samples of plasma, hemolysate, and aqueous extracts of kidney and liver were prepared according to methods described by Selander et al. ( 26).
Treatment with Thiol Reagents. Twenty inbred strains were screened for variation in the effects of p-chloromercuribenzene sulfonate, cystamine, maleate, oxidized glutathione, and N-ethylmaleimide on the electrophoretic mobilities of 33 enzymes and other proteins. Reagent solutions of 10-2M concentration in a phosphate buffer, pH 6.0, were mixed in equal volume with plasma, hemolysate, or tissue extract and incubated at 37°C for 30 min before electrophoresis.
Heat Denaturation. Prior to electrophoresis, aliquots (30-65 microliters) of plasma, hemolysate, kidney extract, and liver extract, in 5 ml corked glass culture-tubes were heated for 20 min in a waterbath at temperatures ranging in 3°C steps from 44°C to 65°C.
Electrophoresis and Protein Staining. The procedures (including starch-gel types and stain recipes) were similar to those of Selander et al. ( 26). Details concerning the six gel-buffer systems used and other aspects of technique are given by Bonhomme and Selander ( 25).
The 18 proteins (14 enzymes and 4 non-enzymatic proteins), together with the corresponding tissue extracts used in this survey (Tables 1 and 2), were glutamic oxaloaacetic transaminase-2 ( GOT-2), liver extract; phosphoglucose isomerase ( PGI), hemolysate; malate dehydrogenase-1 ( MDH-1), kidney; lactate dehydrogenase-A and -B ( LDH-1 and LDH-2), kidney; 6-phosphoguconate dehydrogenase ( G-6PDH), hemolysate; phosphoglucomutase-1 and -2 ( PGM-1 and PGM-2), hemolysate and liver; esterase-A ( EST-A), hemolysate; esterase-1 ( EST-1), plasma; esterase-2 ( EST-2), plasma; esterase-3 ( EST3), hemolysate; esterase-D ( EST-D), plasma; albumin ( ALB), plasma; protein-A ( PROTEIN-A), plasma; protein-2 ( PROTEIN-2), hemolysate; and hemoglobin ( HBB), hemolysate.
Work on nine other proteins examined in preliminary studies was discontinued because the results could not be precisely replicated: two peptidases (in hemolysate); malate dehydrogenase-2 ( MDH-2), kidney; α-glycerophosphate dehydrogenase ( αGPDH), liver; sorbitol dehydrogenase ( SDH), liver; alcohol dehydrogenase ( ADH), liver; malic enzyme ( ME), kidney; isocitrate dehydrogenase-1 ( IDH-1), kidney; and glutamic oxaloacetic transaminase-1 ( GOT-1), liver.
Procedure. Two surveys were made, each involving extracts from one mouse of each strain. Some 9,000 aliquots were electrophoresed on 450 gels in the course of the study.
A method for detecting certain amino acid substitutions leading to the acquisition or loss of cysteine residues was developed by Hopkinson and Harris ( 27) for use in screening human populations for "silent" ("hidden") variants of peptidase and other enzymes in hemolysates. Allozymes differing in number of free reactive sulfhydryl (-SH) groups can be distinguished electrophoretically following treatment with thiol reagents. With each reagent, the reaction product exhibits a characteristic electrophoretic mobility that is either the same as the untreated enzyme or faster or slower, depending on whether the added moiety is neutral, acidic, or basic.
The electrophoretic mobility of 16 of the 33 proteins tested in the house mouse (including PGI, ALB, LDH-1, ME, IDH-1, GOT-1, and MPI) was modified in the "direction" and to the extent predicted by knowledge of the charge characteristics of the various reagents, and that of 17 of the proteins was unaffected. But for none of the proteins was there evidence of interstrain heterogeneity. Some enzymes (e.g., LDH, ME, and IDH) were inhibited by PCMB and/or by one or more other reagents, but, again, there was no interstrain heterogeneity in the reaction.
No interstrain heterogeneity was detected in the thermostability of the electromorphs of any of the four non-enzymatic proteins studied ( Table 1), and the electromorphs themselves did not differ in thermostability.
The 14 enzymes analyzed are represented in the 39 strains of mice by a total of 27 electromorphs. As shown in Table 1, for nine of the enzymes heat treatment revealed no heterogeneity within or between electromorphs. Thus, for example, the thermostability profiles of strains homozygous for either fast- or low-migrating electromorphs (allozymes) of GOT-2 were indistinguishable, and, similarly, the two electromorphs could not be distinguished.
But in the case of five esterases ( Table 2), the heat-denaturation technique revealed differences between electromorphs, and at four of these loci (EST-A, EST-1, EST-2 and EST-D), interstrain heterogeneity within electromorphs was detected. For example, at the electrophoretically monomorphic EST-A locus, most strains have an allele encoding a heat-resistant form of the enzyme (100R), which retains full activity at 50°C, but only a trace at 56°C. But the strains AKR and SJL have a heat-sensitive form of the protein that denatures between 44° and 50°C. Progeny tests demonstrated a simple co-dominant Mendelian segregation of the 100R and 100S alleles at the EST-A locus; and we have determined that both alleles (100R and 100S) are segregating in M. m. castaneus. The total number of new alleles detected in our survey was four, one each at four of the esterase loci.
Major changes in configuration of albumin and the other non-enzymatic proteins probably must occur on heating before we are able to detect decreases in concentration of the proteins at their normal positions on gels. But even minor changes in the tertiary (or quaternary) structure of an enzyme might lessen or eliminate its activity. Hence, the power of the heat-denaturation technique to detect heterogeneity among polypeptides undoubtedly is much greater for enzymes than for other proteins. In the following analysis and discussion, we will consider only the data derived from our studies of the 14 enzymes.
The total number of allelic classes detected in our survey of 14 enzyme loci was 31, which may not be considered as 27 electromorphs = 4 thermomorphs not detected by electrophoresis, or as 20 thermomorphs + 11 electromorphs not detected by heat-denaturation ( Table 3).
We will call allopeptides the distinctive polypeptides encoded by a structural gene locus; and the number of these is equivalent to the number of alleles segregating at a locus. Allomorphs are defined as sets of one or more allopeptides having the same properties in regard to the techniques of detection employed. Since an invariable locus is nevertheless represented by one polypeptide, a relevant measure of total variability is the number of allopeptides minus one; and the comparable measure of the variation revealed by a technique or several techniques is the number of allomorphs detected minus one.
For purposes of computation, let X = the (unknown) actual (total) number of allopeptides (or alleles) at L loci assayed, which in the present case is 14; A = the number of allomorphs demonstrated by joint application of electrophoresis and heat-denaturation and heat-denaturation = 31; Ev = the number of electromorph variants, which is E - L = 27 - 14 = 13; Tv = the number of thermomorph variants, which is T - L = 20 - 14 = 6; Jv = the number of allomorph variants detected by joint application of the two techniques, which is A - L = 31 - 14 = 17; and U = the (unknown) actual number of undetected allopeptide variants.
If the two techniques employed are orthogonal, such that the probability of an allopeptide variant being recognized electrophoretically is independent of the probability of its being detected by heat-denaturation, it can be shown that
U = (Jv - Ev) (Jv - Tv)/(Jv - (Jv - Ev) - (Jv - Tv))
U = (17- 13) (17-6)/(17 - (17-13) - (17 - 6)) = 44/2 = 22
Then, the estimated actual number of allopeptide variants, V = Jv + U = 17 + 22 = 39. And the estimated actual number of allopeptides or alleles at the 14 loci, X = V + L = 39 + 14 = 53 (or X = A + U = 31 + 22 = 53). Hence, the estimated mean number of alleles per locus is X/L = 53/14 = 3.8, which compares with 1.9 electromorphs per locus; 1.4 thermomorphs per locus; and 2.2 allomorphs per locus.
The power of electrophoresis to detect variants is Ev/V = 13/39 = 0.33, and that of heat-denaturation is Tv/V = 6/39 = 0.15. Jointly applied, the power of the two techniques is Jv/V = 17/39 = 0.44. Of the estimated 53 alleles at the 14 enzyme loci assayed, approximately 50% (E/X = 27/53) were detected by electrophoresis, 38% by heat-denaturation, and 58% by joint application of the techniques. The undetected proportion was 42%.
A significant finding from our research on the house mouse is that the heat-denaturation technique we have used apparently is rather efficient at differentiating proteins with amino acid differences at the level that characterizes electromorphs. (Whether or not this level is at or near the single substitution is another problem.) In half the pairwise comparisons of electromorphs, a thermostability difference was detected. The generally low level of demonstrable heterogeneity among the 27 electromorphs at 14 enzyme loci over 39 strains of the house mouse is important, since it immediately suggests that there cannot be large amounts of hidden variation at most of the loci examined. Our findings, when compared with those for XDH, ODH, and EST-5 in Drosophila ( 17, 24, 28) suggest that the differences in effective number of alleles and heterozygosity between Mus and Drosophila are greater than those indicated by electrophoretically derived estimates.
The value of our approach and results depends on the validity of several underlying assumptions. First, we have assumed that the 39 laboratory strains and a small number of individuals of the subspecies M. m. castaneus and M. m. molossinus represent the species Mus musculus as a whole insofar as the common alleles at the 14 enzyme loci studied are concerned. One could argue that this is a safe assumption because most of the high- and moderate-frequency, widespread electromorphs occurring in wild populations also are represented in the group of domestic strains used in our study ( 29, 30, 31, 32). But we cannot determine precisely how many genomes from wild populations are represented in the 39 strains, although the number probably is between 10 and 20. Laboratory strains were derived from wild populations in Europe and the United States and are a mixture of the subspecies M. m. domesticus, M. m. brevirostris, and M. m. musculus, but their origins cannot now be sorted out. To increase the representation of the species, we included individuals of M. m. castaneus and M. m. molossinus and the CALIF strain.
Second, we have assumed that charge-changing amino acid substitutions are a representative subset of substitutions with regard to their effect on thermostability. At present, we have no evidence bearing on this problem. If in fact thermostability differences are likely to be associated with charge-changing substitutions, we have erred in underestimating the mean number of alleles per locus. But even if the techniques are not strictly independent, our experimental approach can yield valuable insight into the problem of the amount of "hidden" variability in populations by providing information on the relative amounts of heterogeneity within and between electromorphs. Moreover, studies of a variety of organisms will provide a test of the predictions of Nei and Chakraborty ( 15) regarding the amounts of allelic diversity underlying electromorphs that would be expected according to the neutral and the mutation-equilibrium theories of molecular polymorphism.
On the theory that electromorphs are allelically heterogeneous charge classes that can convergently evolve in populations, several models of step-wise integer production of electromorphs recently have been investigated ( 14, 33, 34, 35). In these models, mean selection coefficients may be equal over electromorphs or may increase with increasing distance of an electromorph from that of the "type allele." But in any event, it is proposed that polymorphism can be maintained in populations by a balance between mutation to slightly deleterious alleles (whose products are manifested as electromorphs at integer states on gels) and selection against the mutants. Provisions of the models are that the product of the effective population size and the mutation rate is large and that the selection coefficient is larger than the mutation rate. Under these conditions, there will be in large populations a build-up of silent heterogeneity underlying electromorphic variation.
Nei and Chakraborty ( 15, 36, 37) have pointed out that the prevalent notion that electrophoresis detects some fixed proportion (e.g., 1/4) of variant polypeptides is erroneous. Rather, the proportion of alleles detectable by electrophoresis depends on population size. Using the infinite allele model of Kimura and Crow ( 38) to obtain the expected number of alleles at the codon level (neglecting selection), Ewens' ( 39) formula for the expected number of alleles in a sample of s genes at equilibrium, and Kimura and Ohta's ( 41) formula for the expected number of electromorphs per locus, they have calculated the proportion of alleles undetectable by electrophoresis for various values of L = Nev (where Ne is the effective population size and v the mutation rate at the codon level) and sample sizes (s). If L is smaller than 0.01, the ratio of numbers of silent alleles to electromorphs is very small (e.g., 1.2 alleles per 1.1 electromorphs in samples of 200), but if L is large (e.g., 4.0), the expected number of silent alleles per electromorph in samples of 200 is 8 (42 alleles at the codon level and 5 electromorphs). In general, they argue that L may actually be less than 1, since, as they note, the average heterozygosity for electromorphs is 0.3 or less in all bisexual organisms thus far studied.
The model is simplistic, but it has the advantage of making specific predictions that can be tested, even if we cannot determine the absolute values of Ne for different organisms. The proportion of hidden genetic variability relative to total variability or to that detectable electrophoretically should be large in species with large numbers; whereas in species with small numbers, most of the variability should be detectable electrophoretically. Where there is little or no hidden variability, adjacent electromorphs will differ at little more than one amino acid, on the average.
Chakraborty and Nei ( 36) have estimated the probability distributions of the number of codon differences between two identical electromorphs and between two electromorphs with a one-step difference in charge (M = 4Nev, and c is assumed to be 1/4). If M = 4Nev is 0.1, 87% of electromorphs will differ at one codon only; and there will be essentially no heterogeneity within electromorphs (there will be almost no hidden variation). As M increases (e.g., as Ne increases) to 10, the ratio of codon difference within electromorphs to those between electromorphs approaches 1, and the average number (and the variance) of codon differences increases to about 5. At M = 10, only 16% of one-step electromorphs differ in a single codon, and only 22% of identical electromorphs have identical codon structure.
According to Nei and Chakraborty's ( 36) model, in a sample of 40 genes, a ratio of 3.7 alleles at the codon level to 1.7 electromorphs per locus is expected when L = 0.2. If, for example, the mutation rate is 10-8, Ne would be 5 x 106. Since the mean numbers of alleles and electromorphs per locus estimated for the house mouse (3.8 alleles/1.9 electromorphs) are similar to those in the example, the question arises: Can the effective number for this species be as small as 5 x 106? In other words, is it a reasonable possibility that the house mouse, notwithstanding its present worldwide distribution, is, from an evolutionary standpoint, a relatively small species? We think so for the following reasons: 1) The present worldwide distribution and very large population size of Mus musculus were achieved in historical times; and prior to the Neolithic period (˜4,000 B.P.), the subspecies which now occupy Europe, the Western Hemisphere, Australia, and other areas of the world were confined tot he Middle East (see a review in reference 40). Since the effective size of a population is approximately the harmonic mean of numbers of breeding individuals over generations, the relatively recent expansion in size will have had very little effect on the effective species number. 2) Because subdivision of Mus musculus is extensive at several levels from the local breeding unit to the subspecies, Ne probably is not to be equated with the full species number (see discussion in reference 9). Soulé ( 9) suggests that Ne for Mus musculus is ˜107 and for some other mammals from 104 to 106. Compared with some widely distributed species of Drosophila and other small invertebrates, the effective species number of the house mouse, and of vertebrates in general, undoubtedly is several orders of magnitude smaller.
In sum, to a first approximation, our results seem compatible with predictions of the Nei-Chakraborty theory. For the house mouse, we estimate that, on the average, there are only 3.8 alleles per structural gene locus, and that half the existing allelic variation is detectable electrophoretically. Further testing of the theory, involving comparable studies of organisms having very large species numbers, such as Drosophila pseudoobscura and Escherichia coli, presently are in progress in our laboratory.
In a survey of variation in both electrophoretic mobility and thermostability of 14 enzymes in 39 laboratory strains of the house mouse (Mus musculus), 27 electromorphs and 20 thermomorphs were identified. Heat-denaturation detected 4 variants within electromorphs, and electrophoresis detected 11 variants within thermomorphs. The total number of distinctive polypeptides (allomorphs) distinguished by joint application of the techniques was 31. From these data, and on the assumption that heat-denaturation and electrophoresis are independent, orthogonal methods of detecting variation, it is estimated that the actual total number of alleles at the 14 enzyme loci is 53, or an average of 3.8 per locus (2.0 per electromorph). Electrophoresis apparently detects one-third of variant polypeptides, thus revealing about 50% of the alleles at structural gene loci in the house mouse. To a first approximation, the results of this analysis are consistent with predictions of the Nei-Chakraborty theory regarding the degree of allelic heterogeneity of electromorphs as a function of the species number.
No heterogeneity within or between electromorphs of four non-enzymatic proteins was detected by the heat-denaturation technique. And for 33 enzymes and other proteins, treatment with various thiol reagents failed to reveal heterogeneity among 16 strains of mice tested.
1Research supported by NIH Grant 2RO1 GM-22126.
2Present address: Laboratoire d'Electrophorése du C.E.R.E.M., Université des Sciences et Techniques du Languedoc, Montpelier, France.
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