Evolution by Gene Duplication and Compensatory Advantageous Mutations

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1 Copyright by the Genetics Society of America Evolution by Gene Duplication and Compensatory Advantageous Mutations Tomoko Ohta National Institute of Genetics, Mishima, 41 I Japan Manuscript received April 27, 1988 Revised copy accepted July 14, 1988 ABSTRACT Relaxation of selective constraint is thought to playan important role for evolution by gene duplication, in connection with compensatory advantageous mutant substitutions. Models were investigated by incorporating gene duplication by unequal crossing over, selection, mutation and random genetic drift into Monte Carlo simulations. Compensatory advantageous mutations were introduced, and simulations were carried out with andwithoutrelaxation,whengenes are redundant on chromosomes. Relaxation was introduced by assuming that deleterious mutants have no effect on fitness, so long as one or more genes free of such mutations remain in the array. Compensatory mutations are characterized by the intermediate deleterious step of their substitutions, and therefore relaxation by gene redundancy is important. Through extensive Monte Carlo simulations, it was found that compensatory mutant substitutions require relaxation in addition to gene duplication, when mutant effects are large. However when mutant effects are small, such that the product of selection coefficient and population size is around unity, evolution by compensatory mutation is enhanced by gene duplication even without relaxation. T has been customary to suppose that new genes I evolve if mutations accumulate while selective constraints are relaxed by gene duplication (OHNO 1970; KIMURA 1983). This statement is rather vague and not quantitative. I have attempted to construct population genetic models for evolution by gene duplication (OHTA 1987a, b; 1988a, b). In these models, mutations are assumed to be definitely detrimental or beneficial, or completely neutral, and interaction among unequal crossing over, random drift and natural selection was investigated. Relaxation of selective constraints of redundant genes was not satisfactorily examined in these studies. Although exact understanding of relaxation is difficult, it is highly desirable to know how duplicated genes are tested by natural selection. A noteworthy fact concerning the above discussion is that multigene families which were established a long time ago apparently do not enjoy relaxation of selective constraints, as can be seen for immunoglobulin genes and others (OHTA 1980; GOJOBORI and NEI 1984). Relaxation may be observed by acceleration of amino acid substitutions in evolution (GOODMAN 1976; LI 1985), and seems to be limited to the short period at duplication. Another related observation is the pattern of molecular evolution where amino acid or nucleotide substitutions are often clustered, indicating slightly deleterious mutant substitutions compensated by others (OHTA 1973). This is understandable from our knowledge of higher-order structure of proteins or nucleic acids (WATSON et al. 1987). Thus it is reasonable to incorporate compensatory advantageous mutations into the model when the evolution of new genes is studied. By gene redundancy, the first step of slight deterioration may be accelerated, and therefore gene duplication may provide good opportunities for evolution by compensatory advantageous mutations. In this report simulation results are presented that show the importance of interaction between gene duplication and compensatory mutant substitutions, and the relationship of such acceleration to the relaxation of selective constraint will be discussed. MODEL AND METHOD OF SIMULATIONS The model is similar to a previous one (OHTA 1987a, 1988a), except for mutation that is compensatory. Each generation of Monte Carlo simulations consists of mutation, unequal crossing over, random sampling and selection. As before, let 7 be the rate of unequal crossing over per gene copy per generation. A diploid model is adopted here, so that unequal crossing over is interchromosomal, and the rightmost gene of a gene array pairs with the next-rightmost gene of another array at meiosis (OHTA 1988a). Note that this is nonhomologous pairing when there is a single locus on the chromosome. No lethal mutation is assumed, but with constant rate, u, per generation, a deleterious mutation is assumed to occur at one of the ten sites of a gene. Mutants are marked by minus integers, and the integer characterizing a gene decreases by one at each mutational occurrence of an experiment. Thus, integer of a gene means an integervalued indicator variable. Genetics 1: (November, 1988)

2 842 T. Ohta Compensation between two mutants takes place either within a gene or between genes of an array. It occurs as follows. Within-gene compensation: When a new mutant is marked by a multiple of -5, all integers of the gene with this mutant are made positive if this gene already has a mutant marked by a multiple of -5. Between-gene compensation: When a new mutant is marked by a multiple of -5, all integers of the gene with the mutant are made positive if another gene of the array already has a mutant marked by a multiple of -5. Note that allelic state of only one gene with the new mutant changes. Furthermore, for simplicity, this positive allelic state is assumed to remain even when the two compensating genes are separated by recombination. However such cases were very rare in the present simulations. At any rate, integers of the gene are made positive when this gene or another gene of the array has already accumulated deleterious mutations. In this report, as in my previous ones, the term allele is used to designate the mutational state of genes at redundant loci. Genes may thus acquire positive allelic states. They are assumed to obey the previous positive selection (OHTA 1987a, 1988a), i.e., if the number of different beneficial alleles, marked by a multiple of +lo, of a diploid individual is more than the population average, such an individual enjoys a selective advantage according to the fitness function, w+,i = 1 for k, L E w+,~ = exp(-s+(e - k,)) for k, < E (1) where the subscript, i, denotes the ith individual, k, is the number of alleles in the ith individual, 1 is the population average, and s+ is a positive selection coefficient. In the present model, the chance of being beneficial (multiple of ) is one-half that of compensation (multiple of 5). When a gene with positive integers accumulates negative integers again, it is assumed that the gene loses its selective advantage of positive integers, and negative selection dominates. Two models of negative selection for deleterious mutations are introduced. In one model, deleterious mutations become neutral so long as there remains at least one gene free of such mutations in the array. This is similar to my previous model (OHTA 1987a, 1988a), and in a sense is maximum relaxation by gene redundancy. Once every gene of the array accumulates one or more negative integers, selection works in terms of the total number of mutants in the array. w-,~ = expi-s- mi/li) (2) where mi is the total number of mutant sites in the ith array, li is the copy number of the array, and s- is the selection coefficient. Note that, in my previous model, an array for which every gene contains one or more deleterious mutations was assumed lethal. The positive and negative selection are assumed to be multiplicative. In the other model, no relaxation is incorporated, so that Equation 2 holds whether or not there remains a gene free of deleterious mutation. The two models may be compared to examine the effect of relaxation by gene redundancy. The simulated population is made of 2N gametes, and unequal crossing over, mutation, sampling and selection were carried out as before (OHTA 1988a, b). Mutation rate per gene copy per generation is u, and positive and negative selection formulas (1) and (2) are combined to determine the survival of a sampled individual. Each Monte Carlo experiment was continued for 1 OON generations, and 15 or 0 replications were done for each set of parameter values. As in my previous study, the products, such as 2Nu (= ) and 2Ny (= 0 - ), are chosen to be realistic. RESULTS Whole experiments fall into four groups: I, withingene compensation and relaxation; 11, within-gene compensation and no relaxation; 111, between-gene compensation and relaxation; IV, between-gene compensation and no relaxation. For each group, two levels of negative selection intensity were carried out, 2Ns- = and 2. The former represents the cases where selection is strong enough to prevent random fixation of mutants if there is no unequal crossing over, and the latter represents the cases in which slightly deleterious mutant substitution may occur even under the single-locus model. As a very rough estimate, the chance of spreading of mutants during loon generations becomes, by using the formula of KIMURA (1 962), u x 0 x 50 X X - l)/(e4-1) = 0.38 when 2Ns- = 2, without unequal crossing over. In order to find out the effect of gene duplication, the rate of unequal crossing over is varied between 2Ny = 0 -. To illustrate the general properties of the simulation results, some examples on the number of different beneficial alleles in a diploid individual at the 0 Nth generation are shown in Figure 1 for the case of within-gene compensation. The abscissa represents the unequal crossing-over rate in terms of 2N7, and the ordinate represents the number of alleles as the average of 0 replicates. Solid and broken lines represent with and without relaxation respectively. The vertical bar is one standard error, and figures beside lines are the values of ~Ns-. As can be seen from the figures, unequal crossing over is effective for increasing the number of beneficial alleles through gene duplication, but the effect is more pronounced

3 Evolution by Gene Duplication 843 C I ZN, FIGURE 1.-Effect of unequal crossing over on the number of different beneficial alleles per genome at the 1 OONth generation of the simulated population for the case of within-gene compensation (average of 0 replications). Solid and broken lines represent with and without relaxation of selective constraint. Figures beside lines are the values of ~Ns-. Vertical bar is one standard error. Other parameters are 2Ns+ =, and 2Nu = with 2N = 0. when the constraint is relaxed. It is also noted that a difference between strong and weak selection is observed for the cases with relaxation, but not for the cases without relaxation. These effects of unequal crossing over are also found by examining other quantities such as gene divergence and copy number per genome. Positive gene divergence is the fraction of sites with positive integers averaged over all redundant loci. Figure 2 presents results of positive divergence as the average of 0 replications. Again, the abscissa is the unequal crossing-over rate (2Ny), and the ordinate is the positive divergence. Standard error is not quite meaningful, because the copy number is different among runs, and not given here. The same tendencies can be observed on the effects of relaxation and selection intensity as in Figure 1. Gene divergence clearly increases when the unequal crossing-over rate becomes higher. When the constraint is not relaxed, little acceleration is observed for strong selection. When selection is weak, acceleration is seen even without relaxation. Tables 1 and 2 present results for the copy number, the number of different beneficial alleles, the number of genes with deleterious mutations, and positive and negative gene divergence for more cases but with a smaller number of repetitions. Except divergence, the results are given as the average k SD of 15 replications. As in previous models, the SD is as large as the mean, showing that the chance effect is very important (OHTA 1987a, 1988a, b). Effects of unequal crossing over and relaxation are found not only by the number of beneficial alleles and divergence, but also by other measures. As seen above, relaxation has a large effect on a ""- """ -" - """"_ - _"" Nv of unequal crossing over on the positive gene FIGURE 2.-Effect divergence at the loonth generation of the simulated population for the case of within-gene compensation (average of 0 replications). Solid and broken lines, figures beside lines, and other parameters are same as in Figure 1. evolution by gene duplication when compensatory advantageous mutations occur. There is another point that is relevant for discussion of the evolution of duplicated genes. Construction of phylogenetic trees is a very popular analysis of molecular evolutionists, but branch lengths are much influenced by relaxation. The following two phylogenetic trees in Figure 3 show the influence. The left tree contains a branch that is free of mutation, but the right has one no such branch. The former is typical for the cases with relaxation, and the latter for the cases without relaxation, Note that the negative selection is weaker for the right tree than for the left one, and mutants accumulated in the right tree even without relaxation. By considering that the molecular evolutionary rate is roughly constant as many data show, the right tree seems to be more realistic than the left one. Thus, the maximum relaxation modeled here may not be realistic. Under the present set of parameter values, compensation within a gene and that between duplicated genes are not very different for th evolution of gene families, but the latter is slightly more efficient than the former. This is because the chance of having compensatory mutations is increased by gene redundancy. From the viewpoint of various molecular interactions, within-gene compensation would be more realistic. At any rate, it is clear from the present simulations that gene redundancy is needed for evolution by compensatory mutations. When selection is strong, relaxation of a selective constraint becomes a prerequisite, but when it is mild, relaxation is not necessarily required. Acceleration of amino acid substitutions following gene duplication, observed by GOODMAN (1976) and LI (1985), may reflect relaxation. Also, mildly deleterious mutant substitutions may be accelerated by gene duplication even without relaxation, if

4 844 T. Ohta TABLE 1 Properties of gene families at the IOONth generation in the simulated populations for the case of within-gene compensation 2Ns+ 2Ns- With relaxation 0 Without relaxation 0 No. of different No. Divergence of genes Negative Positive Copy no. beneficial with deleterious mutations alleles 1.62 f f f f f f f f f t f f f f f t f k f f f f f & ? f f f f f & f f f f f f f f f f f f f f f f 1.12 f f f C f f f & f f f f & f f f f f f f f f f f 5 4 f k f f f f f C f f 3.22 f 0.87 f f f f f f f f zt f f f f f f & f f f f 7 6 f 0.35 f f f f f t f f Figures are the average f SD for 15 replications. Only the average is given for divergence because the SD is not very meaningful when copy number and so on are very different among the runs. For all simulations, 2Nv = with 2N = 0. the selection coefficient is averaged over redundant genes as modeled here. DISCUSSION For folding of proteins or nucleic acids, amino acid or base sequences play important roles. If an amino acid at the critical site of a protein is replaced by another amino acid with different properties, the folding may be disturbed, and the protein function may 8 9 be seriously impaired. This is one of the major causes of genetic defects (VOGEL and MOTULSKY 1979). In such cases, it is sometimes noted that the protein function is recovered by another replacement of an amino acid at an other site of the protein (WATSON et ae. 1987, pp ). For example, if glycine at position 2 of tryptophan synthetase A is replaced by glutamic acid, the protein loses enzymatic function, but when an additional replacement at position 174 occurs, function is restored (YANOFSKY, HORN and

5 Duplication Evolution by Gene 845 TABLE 2 Properties of gene families at the loonth generation in the simulated populations for the case of between-gene compensation 2Ns- With relaxation No. of different No. beneficial 2Ns+ 2Nr Negative Copy Positive no. mutations alleles Without relaxation 0 0. I 2.51 f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f 0.49 f 1.09 f f f f f f f f f f f f f f f f f f f f f f f f f f f f 7 I.oo 1.66 f f f 5.09 of Divergence genes with deleterious 0.47 f f f f f f f f f f f f f f f f f f f f f f f f f f f f f f 7 1 f 7 1 f f & 6 1 f f f 8 f f 2.97 ~ ~ Figures are the average f SD of 15 replications. Only the average is given for divergence because the SD is not very meaningful when copy number and so on are very different among the runs. For all simulations, 2Nu = with 2N = THORPE 1964). Restoration reflects interaction among amino acids, and in the above example, the recovered state is close to the original one, i.e. compensatory neutral mutations. Ribosomal RNA genes are other examples which show compensatory nucleotide substitutions (e.g. BRIMACOMBE 1984). KIMURA (1 985) formulated the process of compensatory neutral evolution by means of diffusion equations. He found that tight linkage between the interacting sites enhances the rate of compensatory substitutions, be- cause the two mutations are not separated. Compensatory evolution proceeds through an intermediate deleterious state, and is related to the slightly deleterious mutation theory of molecular evolution (OHTA 1973, 1976, 1987~). This theory states that the rate of molecular evolution is determined largely by the mutational pressure of very slightly deleterious mutations, and is based on our understanding of the higher order structure of proteins and nucleic acids. If proteins and nucleic acids have

6 846 T. Ohta I 1 L I FIGURE 3.-Phylogenetic trees of duplicated genes on a sampled chromo some from simulated populations at the loonth generation. The left tree is for the case with relaxation, and the 675 one for the case without relaxation. Pa- rameters are 2Ns+ = 2Ns- =, 2Nu = 848 and 2N-y = for the left one, and I 2Ns- = 2, 2Ns+ =, 2Nu = and 62 2N-y = for the right one, both within gene compensation. Figures beside the tree are mutant marks without minus sign. Beneficial ones are circled. evolved a long time ago, their structures are well organized, and any random mutations would disturb such an organization. When the effect is very small, random drift and mutational pressure dominate over selection. Here compensatory mutant substitutions prevent deterioration of genes. When the effect is not mild such that Ns- >> 1, the probability of fixation of mutants becomes very small. Even under the most favorable condition of complete linkage, mutation rate in terms of Nv must be fairly high in order to have compensatory mutant substitutions within a reasonably short period of time (KIMURA 1985). For example, the fixation time of compensatory mutations is about 5N generations, when 4Ns- = - and 4Nv = 1 under complete linkage. In our simulations, the corresponding parameter, 4Nv, for compensatory neutral or advantageous mutation is /5 =, i.e., 1/25 of KIMURA'S value. When this parameter is 1/25, the fixation time would become 25' times larger from KIMURA'S result for s >> v, and one would expect 625 X (5N) = 3125N generations for compensatory neutral mutants to be fixed in our simulations. This value is much longer than the length of time of our simulations. Furthermore, KIMURA'S result shows that the fixation time increases further by bringing 4Ns- larger than. Thus, there is increasing likelihood of establishing compensatory mutations from the case of single locus gene through that of duplication without relaxation to that of duplication with relaxation. The evolution is much dependent on whether or not gene duplication is involved. In view of commonly observed redundant genes in eukaryote genomes, this point has an important bearing for evolutionary theory. Here not only compensatory neutral but also compensatory advantageous mutant substitutions need attention. There may be cases where new gene function is acquired only through an intermediate deleterious state. It would be expected that the greater the difference between the new and the old gene functions, the larger is the intermediate deleterious effect. If there exist only single copy genes, evolution of such new function would never occur. However when the selective constraint is relaxed by gene redundancy, evolution of compensatory advantageous mutations may be much enhanced. There are several interesting examples that apparently have evolved through deleterious intermediate with redundant genes. The hemoglobin a-chain of the opossum is unusual in that the invariant histidine (His) at amino acid position 58 is replaced by glutamine (Gln). Also it is characterized by rapid evolution, suggesting compensatory substitutions to this unusual replacement (STENZEL 1974). In man, substitution of this His to another amino acid is known as methahemoglobin and causes chronic cyanosis (GERALD and EFRON 1961). Without relaxation of the constraint allowed in redundant copies, the His 4 Gln substitution in the opossum hemoglobin would have been impossible. Another example is seen in plant ferredoxins. Coupled substitutions are found between duplicated genes of horsetail ferredoxin, and the amino acid positions of the substitutions are close to each other in the higher order structure, suggesting compensatory function (TSUKIHARA et al. 1982). A final example is the unusual codon usage of Mycoplasma. In this organism, an ordinary stop codon, UGA, is read as triptophane (Trp)(YAMAO et al. 1985). By considering GC +- AT mutational pressure characteristic for this species, JUKEs (1985) proposed the following steps for this evolutionary change. First, the pressure to replace G by A could lead to replacements of UGA stop codons by UAA stop codons. Second, a duplication of the gene for trna"p(cca) occurred. Third, a mutation of one of them to trnatrp(uca) took place. Note that trna"p(cca) reads UGG, and trnatt(uca), UGA because of RNA code system. Furthermore trnatrp(uca) can decode the universal Trp codon UGG by wobble pairing. Now, if all the UGA stop codons had been replaced by UAA, the emergence of trnat'p(uca) would have been acceptable. The fourth step was the replacement of Trp UGG codons by UGA through mutational pressure. The above picture of evolutionary steps has been strengthened by the finding that the two trnatv genes are tandemly arranged in a strain of Mycoplasma (MUTO, YAMAO and OSAWA 1987). In the above steps, gene

7 Evolution by Gene Duplication 847 duplication with subsequent substitution would have been beneficial for tolerating strong GC + AT pressure, since trna"p gene usually exists as single copy. Thus gene duplication played a crucial role on the evolutionary change ordinarily unacceptable. In the usual process of evolution by gene duplication, the number of genes increases by acquiring new functions. The above examples seem to be slightly different from such a pattern. The number of genes has remained almost unchanged and gene duplication was used in a restricted period in which relaxation was needed. If a kind of positive selection as considered in the previous section works for a long period of time, the gene number increases, and the present model would be appropriate for such cases of evolution by gene duplication. Of course, we do not know how often compensatory advantageous mutations occur. My previous model, in which detrimental, neutral and beneficial mutations were taken into account without compensation, may be more realistic in some cases. The intermediate deleterious step would be unavoidable when new genes are created by "exon shuffling," as supposed to have occurred in many supergene families (GILBERT 1985; BALTSCHEFFSKY, JORN- VALL and RICLER 1986). Thus, evolution by exon shuffling is thought to occur by using dispensable genes, that are often redundant. A more elaborate modeling is needed for quantitative understanding of such processes. I thank B. S. Weir, J. B. Walsh and an anonymous referee for their many valuable suggestions and comments. This work is supported by a grant-in-aid from the Ministry of Education. Contribution no from the National Institute of Genetics, Mishima 41 1, Japan. LITERATURE CITED BALTSCHEFFSKY, H., H. JORNVALL and R. RICLER (editors), 1986 Molecular Evolution of Lfe. Cambridge University Press, Cambridge. BRIMACOMBE, R., 1984 Conservation of structure in ribosomal RNA. Trends Biochem. Sci GERALD, P. S., and M. L. EFRON, 1961 Chemical studies of several varieties of HB M. Proc. Natl. Acad. Sci. USA 47: GILBERT, W., 1985 Genes-in-Pieces revisited. Science 228: GOJOBORI, T., and M. NEI, 1984 Concerted evolution of the immunoglobulin VH gene family. Mol. Biol. Evol. 1: GOODMAN, M., 1976 Protein sequences ih phylogeny. pp In: Molecular Evolution, Edited by F. J. AYALA. Sinauer Associates, Sunderland. JUKU, T. H., 1985 A change in the genetic code in Mycoplasma capricolum. J. Mol. Evol. 22: KIMURA, M., 1962 On the probability of fixation of mutant genes in a population. Genetics 47: KIMURA, M., 1983 The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge. KIMURA, M., 1985 Diffusion models in population genetics with special reference to fixation time of molecular mutants under mutational pressure. pp In: Population Genetics and Molecular Evolution, Edited by T. OHTA and K. AOKI. Japan Science Society Press, Tokyo. LI, W.-H., 1985 Accelerated evolution following gene duplication and its implication for the neutralist-selectionist controversy. pp In: Population Genetics and Molecular Evolution, Edited by T. OHTA and K. AOKI. Japan Science Society Press, Tokyo MUTO, A., F. YAMAO and S. OSAWA, 1987 The genome of Mycoplasma capricolum. Prog. Nucleic Acid Res. Mol. Biol OHNO, S., 1970 Evolution by Gene Duplication. Springer-Verlag, New York. OHTA, T., 1973 Slightly deleterious mutant substitutions in evolution. Nature 246: OHTA, T., 1976 Role of very slightly deleterious mutations in molecular evolution and polymorphism. Theor. Popul. Biol. : OHTA, T., 1980 Evolution and VariatMn of Multigene Families (Lecture Notes in Biomathematics, Vol. 37). Springer-Verlag, New York. OHTA, T., 1987a Simulating evolution by gene duplication. Genetics 115: OHTA, T., 1987b A model of evolution for accumulating genetic information. J. Theor. Biol. 124: OHTA, T., 1987c Very slightly deleterious mutations and the molecular clock. J. Mol. Evol OHTA, T., 1988a Further simulation studies on evolution by gene duplication. Evolution 42: OHTA, T., 1988b Time for acquiring a new gene by duplication. Proc. Natl. Acad. Sci. USA STENZEL, P., 1974 Opossum Hb chain sequence and neutral mutation theory. Nature 252: TSUKIHARA, T., KOBAYASHI, M., NAKAMURA, M., KATSUBE, Y., FUKUYAMA, K., HASE, T., WADA, K. and H. MATSUBARA, 1982 Structure-function relationship of [2Fe-2S] ferredoxins and design of a model molecule. Biosystems VOGEL, F., and A. G. MOTULSKY, 1979 Human Genetics. Springer- Verlag, New York WATSON, J. D., N. H. HOPKINS, J. W. ROBERTS, J. A. STEITZ and A. M. WEINER, 1987 Molecular Biology of the Gene, Ed. 4. The Benjamin, Menlo Park, Calif. YAMAO, F., MUTO, A., Y. KAWAUCHI, M. IWAMI, S. IWAGAMI, Y. AZUMI and S. OSAWA, 1985 UGAis read as tryptophan in Mycoplasma capricolum. Proc. Natl. Acad. Sci. USA 84: YANOFSKY, C., V. HORN and D. THORPE, 1964 Protein structure relationships revealed at mutational analysis. Science Communicating editor: B. S. WEIR