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Evolution by Gene Duplication and Compensatory Advantageous Mutations

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Evolution by Gene Duplication and Compensatory Advantageous Mutations Copyright 0 1988 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 inves- tigated by incorporating gene duplicationby unequal crossing over, selection, mutation and random genetic drift into Monte Carlo simulations. Compensatory advantageous mutations were introduced, andsimulations were carried out with andwithout relaxation, when genes 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 stepof 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 incorporatecompensatory advantageous mutations I evolve if mutations accumulatewhile selective con- into the model when the evolution of new genes is straints are relaxed by gene duplication (OHNO1970; studied. By gene redundancy, the first step of slight KIMURA 1983). This statement is rather vague and deterioration may be accelerated, and therefore gene not quantitative. I have attempted to construct popu- duplication may provide good opportunities for evo- lation genetic models for evolution by gene duplica- lution by compensatory advantageous mutations. In tion (OHTA 1987a,b; 1988a, b).In these models, this report simulation results are presented that show mutations are assumed to be definitely detrimental or the importance of interaction between gene duplica- beneficial, or completely neutral,and interaction tion and compensatory mutant substitutions, and the among unequal crossing over, random drift and nat- relationship of such acceleration to the relaxation of ural selection was investigated. Relaxation of selective selective constraint will be discussed. constraints of redundant genes was not satisfactorily examined in these studies. Althoughexact under- MODEL AND METHOD OF SIMULATIONS standing of relaxation is difficult, it is highly desirable The model is similar to aprevious one (OHTA to know how duplicated genes are tested by natural 1987a, 1988a), except for mutation that is compen- selection. satory. Each generation of Monte Carlo simulations A noteworthy fact concerning the abovediscussion consists of mutation, unequal crossing over, random is that multigene families which were established a sampling and selection. As before, let 7 be the rateof long time ago apparently do not enjoy relaxation of unequal crossing over per gene copy per generation. selective constraints, as can be seen for immunoglob- Adiploid model is adopted here, so thatunequal ulin genes and others(OHTA 1980; GOJOBORIand NEI crossing over is interchromosomal, and therightmost 1984). Relaxation may be observed by acceleration of gene of a gene array pairs with the next-rightmost amino acid substitutions in evolution (GOODMAN gene of another array atmeiosis (OHTA1988a). Note 1976; LI 1985), and seems to be limited to the short that this is nonhomologous pairing when there is a period at duplication. single locus on the chromosome. No lethal mutation Another related observation is the pattern of mo- is assumed, but with constant rate, u, per generation, lecular evolution where aminoacid or nucleotide sub- a deleterious mutation is assumed to occur at one of stitutions are often clustered, indicating slightly dele- the ten sites of a gene. Mutants are marked by minus terious mutant substitutions compensated by others integers, and the integer characterizing a gene de- (OHTA1973). Thisis understandable from our knowl- creases by one at each mutational occurrence of an edge of higher-order structure of proteins or nucleic experiment. Thus, integerof a gene meansan integer- acids (WATSONet al. 1987). Thus it is reasonable to valued indicator variable. Genetics 120: 841-847 (November, 1988) 842 T. Ohta Compensation between two mutants takes place deleterious mutations was assumed lethal. The posi- either within a gene or between genes of an array. It tive and negative selection are assumed to be multi- occurs as follows. plicative. Within-gene compensation:When a new mutant is In the other model, no relaxation is incorporated, marked by a multiple of -5, all integers of the gene so that Equation 2holds whether or not thereremains with this mutant are madepositive if this gene already a gene free of deleterious mutation. The two models has a mutant markedby a multiple of -5. may be compared to examine the effect of relaxation Between-gene compensation:When a new mutant by generedundancy. The simulated population is is marked by a multiple of -5, all integers of the gene made of 2N gametes, and unequal crossing over, with the mutant aremade positive if another gene of mutation, sampling and selection were carried out as the array already has a mutant marked by a multiple before (OHTA1988a, b). Mutation rate per gene copy of -5. Note that allelic state of only one gene with per generation is u, and positive and negative selection the new mutant changes. Furthermore, for simplicity, formulas (1) and (2) are combined to determine the this positive allelic state is assumed to remain even survival of a sampled individual. Each Monte Carlo when the two compensating genes are separated by experiment was continued for 1OON generations, and recombination. However such cases were very rare in 15 or 100 replications were donefor each set of the present simulations. At any rate, integers of the parameter values. As in my previous study, the prod- gene are made positive when this gene or another ucts, such as 2Nu (= 0.1) and 2Ny (= 0 - 0.2), are gene of the arrayhas already accumulated deleterious chosen to be realistic. mutations. In this report, as in my previous ones, the term “allele” is used to designate the mutational state RESULTS of genes at redundant loci. Genes may thus acquire positive allelic states. They are assumed to obey the Whole experiments fall into four groups: I, within- previous positive selection (OHTA1987a, 1988a), i.e., gene compensation and relaxation; 11, within-gene if the number of different beneficial alleles, marked compensation and no relaxation; 111, between-gene compensation and relaxation; IV, between-gene com- by a multiple of +lo, of a diploid individual is more pensation andno relaxation.For each group, two than the population average,such an individual enjoys a selective advantage accordingto thefitness function, levels of negative selection intensity were carried out, 2Ns- = 10 and 2. The former represents the cases w+,i = 1for k, L E where selection is strong enough to prevent random fixation of mutants if there is no unequal crossing w+,~= exp(-s+(E - k,)) for k, < E (1) over,and the latter represents the casesin which slightly deleteriousmutant substitution may occur where the subscript, i, denotes the ith individual, k, is even under the single-locus model. As a very rough the number of alleles in the ith individual, 1 is the estimate, the chance of spreading of mutants during population average, and s+ is a positive selection coef- lOON generations becomes, by using the formula of ficient. In the present model, the chance of being KIMURA(1 962), beneficial (multiple of 10) is one-half that of compen- u x 100 x 50 X 0.1 X - l)/(e4 - 1) = 0.38 sation (multiple of 5). Whena gene with positive integers accumulates negative integers again, it is as- when 2Ns- = 2, without unequal crossing over. In sumed that the gene loses its selective advantage of order to find out the effect of gene duplication, the positive integers, and negative selection dominates. rate of unequal crossing over is varied between 2Ny Two models of negative selection for deleterious = 0 - 0.2. mutations are introduced. In one model, deleterious To illustrate the general properties of the simula- mutations become neutral so long as there remains at tion results, some examples on the number of differ- least one gene free of such mutations in the array. ent beneficial alleles in a diploid individual at the 100 This is similar to my previous model (OHTA1987a, Nth generation are shown in Figure 1 for the case of 1988a), andin a sense is maximum relaxation by gene within-gene compensation. The abscissa represents redundancy. Once every gene of the array accumu- the unequal crossing-over rate in terms of 2N7, and lates one or more negative integers, selection works the ordinate represents the number of alleles as the in terms of the total number of mutants in the array. average of 100 replicates. Solid andbroken lines represent with and without relaxation respectively. w-,~= expi-s- mi/li) (2) The vertical bar is one standard error, and figures where mi is the total number of mutant sites in the ith beside lines are the values of ~Ns-.As can be seen array, li is the
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