Replication constant, selective value

Accordingly, the frequency of correct copies of genotype Ik is given by = (1 -p)n and the fitness or the selective value of the phenotype associated with genotype Ik, vvk, can now be expressed in terms of the replication rate constants, /k, the replication accuracy, Q., and the degradation rate constant dk ... 

The variables xt denote the frequencies of the genotypes Ij (i = 1,. . . , V and Z-li Xj = 1) in the population. The superiority of the master sequence thus is always larger than one (am >1) except in the case of selective neutrality, = f2 =. . . = /N =/, where we have om = 1 (see forthcoming sections). A larger value of the superiority implies that lower accuracy of replication can be tolerated. Alternatively, longer sequences can be replicated at constant replication accuracy without losing stationarity of the quasispecies. Although the model that has been used in the derivation of the molecular quasispecies is rather simple, the results are also representative for replication and mutation in real populations. 

Figure 10. Quasi-species as function of single-digit accuracy of replication (q) for chain v = 5. We plot relative stationary concentration of master sequence ( (,),fum of relative stationary concentrations of alt one-error mutants ((i), of all two-error mutants ( j), etc. Note that we have only one five-error mutant 7,5, = /s, in this particular example. We observe selection of master sequence at g = 1. Then relative concentration of master sequence decreases with decreasing q. At value q = 0.5 all sequences are present in equal concentrations. Hence, sums of concentrations of two- and three-error mutants are largest—they have statistical weight of 10—those of the one-and four-error mutants are half as large—they have statistical weight of 5—and finally master sequence 7q and its complementary sequence, the five-error mutant /ji, are present in relative concentration ofonly. At q = 0 we have selection o( master pair", which consists of/o and /31 in our example. Thus we have direct replication with errors in range 1 > g > 0.5 and complementary replication with errors in range 0 < q < 0.5. Rate constants chosen as Aq = 10[U ] and A = 1 [t ] for all mutants Ic 0. Here we denote arbitrary reciprocal time unit by [t" ]. All degradation rate constants were put equal 7>o = D, = Dj = = D31 = 0.

For this constant-value model, the only consideration is how many times to replicate, since the conditions are constant. The selection of n can be logically determined from the confidence interval equation. The width of this interval is proportional to (the t variable for chosen confidence level and number of runs) and s / -Jn, the standard error of the average. More runs reduce the confidence interval in two ways. Increasing n decreases the standard error, since it is inversely proportional to the square root of n. Also, the value of t( 2,v decreases with increasing n as the number of degrees of freedom, v = n - 1, increases. After selecting n to obtain a desired confidence interval, it is a trial-and-error calculation, since 1 /2 depends upon n and is obtained from Table... 

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