Evolution quasi-species model

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. 

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 quasi-species model describes processes related to the Darwinian evolution of certain self-replicating entities within the framework of physical chemistry, the origin of life, and viral evolutionary dynamics. Catalytic... 

Recent work has examined the question of whether A OH is exclusively anode-sorbed or whether there is a continuum of species between the extremes of physisorbed and bulk hydroxyl radicals. Vatistas [13] has considered the dissociation of hydroxyl radicals from an adsorption layer ( true A OH) into a three-dimensional reactive layer close to the anode surface. A OH is thus a combination of surface and reactive layer species, both of which experience the anode electrostatically and, in principle, have a reactivity different from that of bulk OH(aq). Kapalka et al. [1] have estimated the profile of hydroxyl species adjacent to a BDD anode concurrent with the evolution of O2 in the absence or presence of an organic substrate. Their model describes the hydroxyl species as quasi-free. In the absence of substrate, the hydroxyl radicals form H2O2 within a stagnant layer of solution close to the anode. It is concluded that their concentration falls to <10 % of the value at the anode surface within 0.2 pm and almost to zero by 1 pm almost no hydroxyl radicals escape the anode surface completely and become bulk OH (aq). When a reactive organic substrate is also present, the hydroxyl radicals are trapped much closer to the anode because of the higher rate constant for reaction of OH with a substrate as compared with that for dimerization, and their concentration falls to almost zero within tens of nm. No data have yet appeared in which the reactivities of anode-sorbed and bulk hydroxyl radicals have been compared. 

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