Selection mutation, selectively neutral

Figure 11. The error threshold of replication and mutation in genotype space. Asexually reproducing populations with sufficiently accurate replication and mutation, approach stationary mutant distributions which cover some region in sequence space. The condition of stationarity leads to a (genotypic) error threshold. In order to sustain a stable population the error rate has to be below an upper limit above which the population starts to drift randomly through sequence space. In case of selective neutrality, i.e. the case of equal replication rate constants, the superiority becomes unity, Om = 1, and then stationarity is bound to zero error rate, pmax = 0. Polynucleotide replication in nature is confined also by a lower physical limit which is the maximum accuracy which can be achieved with the given molecular machinery. As shown in the illustration, the fraction of mutants increases with increasing error rate. More mutants and hence more diversity in the population imply more variability in optimization. The choice of an optimal mutation rate depends on the environment. In constant environments populations with lower mutation rates do better, and hence they will approach the lower limit. In highly variable environments those populations which approach the error threshold as closely as possible have an advantage. This is observed for example with viruses, which have to cope with an immune system or other defence mechanisms of the host.

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 12. The error threshold of replication and mutation in phenotype space. The genotypic error threshold approaches zero in the case of selective neutrality. Despite changing genotypes a phenotype may be conserved in evolution whenever it has higher fitness than the other phenotypes in the population. The concept of error threshold can easily be extended to competition between phenotypes. The distribution of phenotypes is stationary provided the error rate does not exceed the maximum value pmax which is a function of the mean fraction of nearest neighbors, X, and the superiority of the master phenotype, a. The illustration shows the position of the phenotypic error threshold in the X, p plane. Selective neutrality allows more errors to be tolerated and pmax increases accordingly with increasing X. If X approaches the inverse superiority, X — a-1, the tolerated error may grow to pmax = 1, and this means the phenotype will never be lost, no matter how many errors are made in replication.

Fig. 4. The role of neutral networks in evolutionary optimization through adaptive walks and random drift. Adaptive walks allow to choose the next step arbitrarily from all directions where fitness is (locally) nondecreasing. Populations can bridge over narrow valleys with widths of a few point mutations. In the absence of selective neutrality (upper part) they are, however, unable to span larger Hamming distances and thus will approach only the next major fitness peak. Populations on rugged landscapes with extended neutral networks evolve along the network by a combination of adaptive walks and random drift at constant fitness (lower part). In this manner, populations bridge over large valleys and may eventually reach the global maximum ofthe fitness landscape.

Neutral mutations are neutral with respect to fitness. This does not mean they are neutral with respect to all enzyme behaviors. In fact, many neutral mutations will be deleterious to stability, catalytic ability, or any other property that does not contribute directly to fitness. Properties not protected by the purifying effects of natural selection can change as mutations accumulate, but the process is random and contains litde information that can be used to elucidate mechanisms (Benner and Ellington, 1990 Benner, 1989). 

This theory, in Kimura s own words, states that The great majority of evolutionary mutant substitutions are not caused by positive Darwinian selection but by random fixation of selectively neutral or nearly neutral mutants (it is important to underline that the adjective neutral does not mean without function it only means that a mutation is adaptively indifferent, i.e. it is neither better nor worse than the previous one in respect to the organism s adaptation to the environment). 

The third and most common method is to follow the increase in frequency of a selectively neutral mutation which can be easily screened, like T5R. A monoculture is started. This monoculture will linearly accumulate the neutral mutations at the mutation rate. Being asexual, these... 

The hypothesis forwarded by Kimura and others (Kimura, 1968 King and Jukes, 1969) proposed a way to solve all such empirical problems. In their view if it is assumed that the vast majority of amino acid substitutions are selectively neutral, then substitutions will occur at approximately a constant rate (assuming that mutation rates do not vary over time) and it will be easy to maintain lots of polymorphism within populations with apparently no cost of selection. 

In the case of selective neutrality—this means that all variants have the same selective values—evolution can be modeled successfully by diffusion models. This approach is based on the analysis of partial differential equations that describe free diffusion in a continuous model of the sequence space. The results obtained thereby and their consequences for molecular evolution were recently reviewed by Kimura [2]. Differences in selective values were found to be prohibitive, at least until now, for an exact solution of the diffusion approach. Needless to say, no exact results are available for value landscapes as complicated as those discussed in Section IV.3. Approximations are available for special cases only. In particular, the assumption of rare mutations has to be made almost in every case, and this contradicts the strategy basic to the quasi-species model. 

The example above assumed that selection acts on structure as a trait in and of itself. Hence, many mutated variants of the third fold were assumed to be selectively neutral, simply because they result in the same structure. Selection will also act on a protein s function, which may be more sensitive to specific changes in the underlying sequence. As noted above, we have employed structure as a surrogate for function, but in reality both features are important. Protein structural properties are more easily generalized than functional properties, and so the former feature tends to be more amenable to theoretical treatments. 

---