Master sequence

Provision for other control such as master sequence control, protective shiitdovvm devices (e,g, bearing overternperatiire, overtravel, pump high pressure, remote control, etc,),... 

The predictions of the theory of evolution can be tested on natural systems. Charles Weissmann and his co-workers10 " have obtained the following results for Q(3 viruses. The wild-type has a defined sequence, which, however, does not mean that the majority of viruses share exactly the same sequence. It means merely that the superposition of all sequences gives an unambiguous majority or master sequence, namely, that of the wild-type. 

Different tRNA molecules within a species appear as mutants of a master sequence. 

The original master sequence is largely capable of reconstruction. 

Fig. 7. Correlation analysis of the repetition of purine in tRNA. A tRNA sequence is divided into triplets, beginning at the S end and in phase with the anticodon. The frequency with which a purine (R) in the first position of the triplet occurs n positions later is counted and plotted against n. The period of three which emerges indicates clearly a triplet structure of the form RNY. The curves show values for the averaged sequences of E. coli and of all tRNAs investigated to date these are compared with that of the master sequence arising from the superposition of all tRNAs. The fact that the correlation is clearer in the master sequence suggests that this may represent a "memory of the earliest phase of evolution.

The conditions under which a population approaches a stationary, i.e. time independent, mutant distribution were derived from the kinetic differential equations. In this stationary distribution called quasispecies, the most frequent genotype of highest fitness, the master sequence, is surrounded by closely related mutants1 (Figure 10). 

Increasing the mutation rate implies creation of more diversity in populations and accordingly, the relative weights between master sequence and mutants decrease in the quasispecies (Figure 11). The mutation rate, however, cannot be enlarged... 

Figure 10. The molecular quasispecies and its support in sequence space. Due to unavoidable non-zero mutation rates, replicating populations form distributions of genotypes or polynucleotide sequences. As shown in the sketch these distributions are centered around a most frequent genotype called the master sequence. A population thus occupies a connected region in sequence space which, according to usual mathematical terminology, is called the support of the population.

The superiority of the master sequence is denoted by am and represents a measure for its advantage in selection. It can be expressed (in the case of equal degradation rate constants) as the ratio of the replication rate constant of the master genotype, /m, and the mean replication rate constant of the rest of the population,7 ... 

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. 

The phenotype of highest fitness is called the master phenotype in complete analogy to the fittest genotype, the master sequence. A derivation that is closely related to those for the conventional (genotypic) error threshold yields the conditions for the existence of stationary phenotype distributions which is tantamount to a phenotypic error threshold occurring at a minimum accuracy (Figure 12 Schuster, 1997b) ... 

Relatedness refers to the Hamming distance between master sequence and mutant and is expressed by the number of mutation events that are required to produce the mutant from the master. The frequency of individual mutants in the quasispecies is determined by their fitness and the Hamming distance from the master sequence. 

The result is true for most fitness landscapes and seems to hold for all realistic landscapes in molecular evolution. There are, however, very smooth distributions of fitness values sometimes used in population genetics for which the transition between stationary quasispecies and drifting populations is smooth. A simple landscape showing a sharp transition is the single-peak fitness landscape that assigns a higher fitness value to the master sequence and the same lower fitness value to all mutants. It has some similarity to mean field approximations often applied in physics. 

Master sequence, 186 Membrane potential, 223, 255 Mesoderm, 105 Microinjection, 269 Molecular evolution, 171 etseq. MOPCs, 4-8 Morphogens, 106, 108 Mutagenesis, 124, 126, 133, 134 Myelomas, 34... 

CTP), which are the building blocks for polynucleotide synthesis. The rate of RNA synthesis (lower part) is measured through incorporation of radioactive GTP into the newly produced RNA molecules. The rate of replication shows stepwise increase. An early decrease is observed, because first a quasi-species is formed by the master sequence through production of mutants of lower fitness. The figure is redrawn from the data in [12]. 

Fig. 2.5. A quasi-species-type mutant distribution around a master sequence. The quasi-species is an ordered distribution of polynucleotide sequences (RNA or DNA) in sequence space. A fittest genotype or master sequence /m, which is commonly present at highest frequency, is surrounded in sequence space by a cloud of closely related sequences. Relatedness of sequences is expressed (in terms of error classes) by the number of mutations which are required to produce them as mutants of the master sequence. In case of point mutations the distance between sequences is the Hamming distance. In precise terms, the quasi-species is defined as the stable stationary solution of Eq. (2) [16,19, 20], In reality, such a stationary solution exists only if the error rate of replication lies below a maximal value called the error threshold. In this region, i.e. below...

Equation (2) sustains a stationary state that can be characterized as a mutation equilibrium provided the replication process is sufficiently accurate, q>qmin. This minimal accuracy of replication is readily obtained from a straightforward estimate that is based on the condition of non-vanishing frequency of the master sequence... 

An interesting detail of the quasi-species concept was predicted more than twelve years ago [24] and has been observed recently with virus populations [25] and computer simulations [26] We assume two genotypes of high fitness, each one surrounded by a specific mutant doud (Fig. 2.5). Genotype Iml has higher fitness compared to Im2 but less efficient mutants in the sense of a mutant cloud with lower mean fitness. The quasi-species considered as a function of the mutation rate p may show a rearrangement reminiscent of a phase transition at some critical replication accuracy qa = 1 - pCT. At low mutation rates, p>pCI, the difference in fitness values determines selection and hence, the master sequence with higher fitness, fml, dominates. Above the critical mutation rate, p>pCI, however, mutational backflow to the master is decisive and then fm2 is selected. 

For exclusively real eigenvalues of fV the time dependence of the average excess production is determined by the choice of initial conditions. As shown in Appendix 5, optimization of (t) is restricted to initial conditions in the positive orthant [yt(0) >0 k = 0,1,.. ., n]. These initial conditions are not difficult to fulfil, and they will apply to many cases in reality. We should keep in mind, nevertheless, that there are other choices of initial conditions, such as the start with a pure master sequence, for which the simple principle does not hold. For one particular type of choice, yi (0) > 1 and y/j(0) < 0 for all /c 1, the average excess production decreases monotonically. 

It should be briefly pointed out that simply decreasing the replication rates of other sequences to increase the superiority of the master does not indefinitely postpone the error threshold. Once the replication rates for mutant sequences fall below the destruction rate for the master sequence, the domain of viable existence for the quasi-species is limited by A Q > D . In Section III.3 a more fundamental statistical argument restricts the effective superiority to a finite value of order 1. 

Here /(H represents an underlying probability distribution from which (in a possibly correlated manner) replication rates of different mutants are sampled. IV is average of this distribution and tVg the additionally specified maximum value (which truncates distribution in latter cases). This maximum value is assigned to master sequence m, so we may write iV = Wg. 

The quasi-species was introduced in Section II as a mutant distribution localized in a certain region of sequence space where it is centered around one or several degenerate master sequences. The transition from a nonlocalized to a localized distribution, or the transition among two localized distributions triggered by the appearance of an advantageous mutant, has been shown to be analogous to a phase transition in physical space. In Section III the threshold relations that govern such phase transitions in sequence space have... 

One approach to calculating the stationary mutant distributions for longer sequences is to form classes of sequences within the quasi-species. These classes are defined by means of the Hamming distance between the master sequence and the sequence under consideration. Class 0 contains the master sequence exclusively, class 1 the v different one-error mutants, class 2 all v(v —1)/2 two-error mutants, and so on. In general we have all (JJ) fe-error mutants in class k. In order to be able to reduce the 2 -dimensional eigenvalue problem to dimension v 1, we make the assumption that all formation rate constants are equal within a given class. We write Aq for the master sequence in class 0, Ai for all one-error mutants in class 1, 4 2 for all two-error mutants in class 2, and in general A for all k error mutants in class k. 

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.

At large values of the accuracy of replication (g 1) we observe a quasispecies characteristic for direct replication, /n 2/ predominantly. The master sequence Iq is most frequent, followed by some one-error mutants, two-error mutants, and so on. 

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