Mutations stochastic

Najera I, Richman DD, Olivares I, Rojas JM, Peinado MA, Perucho M, Najera R, Lopez GaHndez C (1994) Natural occurrence of drug resistance mutations in the reverse transcriptase of human immunodeficiency virus type 1 isolates. AIDS Res Hum Retroviruses 10 1479-1488 Nijhuis M, Boucher CAB, Schipper R Leitner T, Schuurman R, Albert J (1998) Stochastic processes strongly influence HIV-1 evolution during suboptimal protease inhibitor therapy. Proc Natl Acad Sci USA 95 14441-14446... 

Stochastic radiation effects are typically associated with those that occur over many months or years (i.e., are typically chronic instead of acute). Chronic doses are typically on the order of background doses (0.3 rem [0.003 Sv] or less) and are not necessarily associated with larger doses that could result from a terrorist attack with radiological weapons. However, stochastic health effects are defined here as effects that occur many years after chronic or acute exposure to radiological contaminants. Stochastic effects are categorized as cancers and hereditary effects. Because no case of hereditary effects (e.g., mutation of future generations) has been documented, this discussion focuses on cancer risk. 

Short-term tests. Tests for point mutations, numerical and structural chromosome aberrations, DNA damage/repair, and in vitro transformation provide supportive evidence of stochastic responses and may give information on potential mechanisms of action. A range of tests for each of the above responses helps to characterize the response spectrum of a substance. 

Evolution has been shown to be an efficient tool for the improvement of enzymes and pathways. Stochastic approaches to introduce point mutations in genes include error prone polymerase chain reaction (ePCR),11 the use of low-fidelity (mutator) strains,12 and chemical mutagens.13... 

The quasispecies model defines an optimal mutation rate for evolving populations (Eigen et al., 1988). At the critical mutation rate pmml (referred to as the error threshold), the distribution becomes too broad for selection to withstand the dispersion and it wanders stochastically on the fitness landscape. The optimal mutation rate for evolvability should be as close to pm Crit as possible without exceeding it. Indeed, it was found that viral mutation rates are very close to pm m,. By assuming that the mutation probability is the same at each residue, the error threshold in terms of mutation rate pm ai, was derived as... 

Greater variability of expression of the defect in females is due to random inactivation (lyoniza-tion) of one X chromosome during early embryonic development. Although all tissues from affected females contain cells that express the mutant gene, the relative distribution of normal and mutated cells among tissues is stochastic. Therefore, the clinical phenotype reflects primarily the combined effects of three independent factors ... 

We noted earlier that conventional iterative methods often contain adjustable parameters, the values of which had to be chosen with care, since they would influence the efficiency and success of the calculation. We have not escaped from these parameters by using an EA, and a set of variables is emerging whose values will affect the course of the calculation. There is the population size - how should that be chosen At what rate should individuals be mutated Should child solutions be selected deterministically or stochastically - or using some hybrid method ... 

Two implementations of genomes, a binary and a decimal (figure 2), were compared to study the dependence on a DNA-like and chemist-like crossover and mutation. Further variables were population size, mutation rate and the crossover strategy. In order to eliminate the stochastic differences between different GA runs, each parameter set was used in 100 parallel runs and the averages and standard deviations for the various results were calculated and displayed on the following figures. All results were compared with a "random" screening method that was simulated by a repeated random selection of new products from the library. 

Figure 7. The influence of the generation size non the average fitness of the nbest parents at a given generation, n was set to 5, 10, 20 or 80 using a binary genome and crossover by cutting between starting material genes (option c) and a fixed stochastic mutation rate of 1 %. Random selection of 80 new products as opposed to the GA driven selection is shown by the...

Figure 8. The activity of best reaction product found by the GA during the course of evolution depending on the stochastic mutation rate, crossover and generation size. The results are displayed as averages from 100 parallel runs for each GA parameter set and compared to random selection (20- and 80-random).

Several attempts to describe replication-mutation networks by stochastic techniques were made in the past. We cannot discuss them in detail here, but we shall brieffy review some general ideas that are relevant for the quasispecies model. The approach that is related closest to our model has been mentioned already [51] the evolutionary process is viewed as a sequence of stepwise increases in the populations mean fitness. Fairly long, quasi-stationary phases are interrupted by short periods of active selection during which the mean fitness increases. The approach towards optimal adaptation to the environment is resolved in a manner that is hierarchical in time. Evolution taking place on the slow time scale represents optimization in the whole of the sequence space. It is broken up into short periods of time within which the quasi-species model applies only locally. During a single evolutionary step only a small part of sequence space is explored by the population. There, the actual distributions of sequences resemble local quasispecies confined to well-defined regions. Error thresholds can be defined locally as well. 

Figure 30. Error threshold as function of population size. Stochastic replication-mutation dynamics in ensemble of polynucleotide sequences with chain length v = 20 simulated by Gillespie s algorithm [95]. Critical single-digit accuracy of replication (q in) at which ordered quasi-species is converted into changing population of sequences with finite lifetimes is plotted as function of 1/N, reciprocal population size (lower curve). For further details see ref. 96. Upper curve is theoretical prediction of Eqn. (V.l) based on ref. 51.

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