Neutral mutation rate

The neutral mutation rate differs for each nucleotide in a gene and usually serves as a good indicator for the functional importance of encoded amino acid residue. For example, the C-peptide of proinsulin evolves at a rate (0.526PAM/10 years) much more rapid than that of the A- and B-chains of insulin (0.071 PAM(point accepted mutation)/10 years) because the C-peptide appears to promote the protein folding and is removed pro-teolytically after the insulin has folded to its correct conformation. The greater divergent rate of the C-peptide than that of the A and B-chains reflects the fewer constraints on its... 

Mutation is a stable, heritable change of a gene from one allele to another, which both creates and maintains genetic variability in populations. Most mutations adversely affect the survival and reproductive success of their bearers, but if the physical or biological environment changes, previously neutral or harmful alleles may become beneficial. Mutation rates typically are very low, but they are sufficient to create considerable genetic variation over many generations. 

Ideally, the most effective prevention of HIV infection would be a vaccine that blocks virus infection in individuals. Indeed, effective vaccines have been developed against most human viruses that cause serious diseases. While several different possible vaccines against HIV are under development, there are some theoretical reasons why it may be difficult to develop an effective one. First, HIV has the unique ability to evade the immune system in an infected individual. Briefly, this results from (1) the high mutation rate of the virus, particularly in the env gene (2) the ability of the virus to establish a latent state in some cells and (3) the ability of the virus to spread by cell-to-cell contact. The object of the vaccine is to raise a protective immune response to the infectious agent. Since HIV evades the immune system so efficiently, it may be difficult for a vaccine to prevent HIV infection in an individual, even if it can induce production of neutralizing antibodies or cell-mediated immunity. 

The mutation rate fx of the nucleotide (or amino acid) at a sequence site is related to the popular notion of a molecular clock (Zuckerkandl and Pauling, 1965), because it determines after which time the clock ticks and anew mutation arises because of a copying error during meiosis. Whether this clock ticks uniformly is a topic of prolonged debate (summarized in Li, 1997). The question is usually treated by comparing sequence difference at (supposedly) neutral sites with evolutionary distance between species. 

In an extant population the heterozygosity at a given site may be measured. Under the neutral hypothesis and assuming that the mutation rate is sufficiently low, one may calculate the product 4Ne/x, which is in the numerical range of the expected heterozygosity. A typical nucleotide heterozygosity is in the range of 5/10,000, which implies that if /x is 10-9 or (10 8) then Ne is 500,000 (or 50,000, respectively). 

Lotka s intrinsic rate of growth of the population. At an initial position and time, a neutral mutation occurs and afterwards no further identical mutations occur (infinite allele model). We are interested in the time and space dependence of the local fractions of the individuals, which are the offspring of the individual that carried the initial mutation. The goal of this analysis is the evaluation of the position and time where the mutation originated from measured data representing the current geographical distribution of the mutation. We limit our analysis to one-dimensional systems, for which a detailed theoretical analysis is possible. Eqs. (39) and (40) turn into a simpler form ... 

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.

Search on RNA secondary structure landscapes is distinctly different from search on the spin glass-like models. The difference is a result of the neutral networks that percolate the space. Note that, in practice, the sequences on neutral networks need not have exactly the same fitness, but fitnesses whose differences are below a threshold determined by the mutation rate and noise in the system. As with search on spin glass landscapes, this topic is quite extensive and is reviewed in several papers [39,67,69,113] as well as in Schuster s contribution to this collection, so I will only touch on a few key points. 

Van Nimwegen and Crutchfield (1999a) have constructed a theory for the optimization of evolutionary searches involving epochal dynamics. They showed that the destabilization of the epochs due to fluctuations in the finite population occurs near the optimal mutation rate and population size. Under these conditions, the epoch time is only constrained by the diffusion of the population to a neutral network boundary. Often the optimal parameters are very close to the region in which destabilization is an important effect. This emphasizes that, to utilize neutral evolution, it is important to tune the evolutionary parameters (such as mutation rate and population size) so that the time spent in an epoch is minimized without destabilizing the search. 

Simulations of RNA secondary structure landscapes provide insight into the necessary mutation rate to drive adaptation. Huynen etal. (1996) found that the ability of a population to adapt is determined by the error threshold of the fitness and not the sequence. Indeed, they found that any mutation rate greater than zero will cause the population to drift on the neutral network [The error threshold on landscapes with high neutrality approaches zero (Derrida and Peliti, 1991).] A second, higher mutation threshold causes the fitness information to be lost. To accelerate the diffusion of the population on the neutral network, it is necessary to be above the sequence error threshold and as close to the fitness error threshold as possible. Under these criteria, the population will diffuse rapidly without losing fitness information. On a flat landscape, the diffusion constant D0 for a population of M sequences of length N can be approximated by Eq. (37). 

Fig. 21. The diffusion constant on a neutral network D0 is plotted versus the mutation rate pm. The simulations ( ) are for RNA sequence length N = 76 and population size M = 1000 and are allowed to equilibirate before the statistics are taken. The solid line is the theoretical D0 and ( ) are flow-reactor simulations for a flat landscape. The dotted line is calculated for D0X, where A = 0.3 is the estimated fraction of neutral mutants. Reprinted from Huynen etal. (1996) with permission. Copyright (1996) National Academy of Sciences, USA.

The benefit of neutrality has yet to be captured with in vitro protein evolution. Neutral theory predicts the punctuated emergence of novel structure and function, however, with current methods, the required time scale is not feasible. Utilizing neutral evolution to accelerate the discovery of new functional and structural solutions requires a theory that predicts the behavior of mutational pathways between networks. Because the transition from neutral to adaptive evolution requires a multi-mutational switch, increasing the mutation rate decreases the time required for a punctuated change to occur. By limiting the search to... 

In addition to mutation rate, even the other molecular parameters turned out to be different from the expectations of selectionism. It was discovered, for example, that neutral mutations are not in the least a tiny minority with respect to adaptive mutations, and the actual ratio is probably the other way round. At the molecular level, in other words, the dominant mechanism of evolution is not natural selection but genetic drift, and this led Motoo Kimura to formulate the neutral theory of molecular evolution (1968, 1983). 

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. 

The development of an effective AIDS vaccine is difficult owing to the antigenic diversity of HIV strains. Because its mechanism for replication is quite error prone, a population of HI V presents an ever-changing array of coat proteins. Indeed, the mutation rate of HIV is more than 65 times higher than that of influenza virus. A few broadly neutralizing antibodies have been isolated from asymptomatic, HIV infected persons. Several of these antibodies show an unusual form, described in Section 33.3, that allows them to bind many types of HIV. 

The nearly neutral theory of Ohta (1971,1987, 1992) (t ig. l. C) "desaibed how the rate ofnwleatlar evolution could vary not only with changes in the mutation rate (as postulated by the neutral theory), hut also through the changing balance between selection and drift . As still phrased by Bromham and Penny (2003), the nearly neutral theory considered three categories of mutations mtnaikmsfar which selection is the predominant force > 3 ... 

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