Sequence space, hierarchical

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. 

Yona, G., et al., A map of the protein space - an automatic hierarchical classification of all protein sequences. Ismb, 1998. 

Following the hierarchical nomenclature of protein structure, RNA tertiary structure represents a more global layout than secondary structure alone. The "kissing loops" motif is a prime example of an RNA tertiary structure contact not regularly seen in secondary structure [12]. In sequence and in secondary structure, the two loops of the motif may be distant. In the tertiary structure, the loops are seen to be close in space and form a hydrogen bond. Hence, the... 

Fig. 61 Cartoon presenting the mechanism of wax crystallization on polymer templates. According to the experimental findings such a mechanism yields multiscale structures evolving hierarchically with decrease in temperature a the single coil stage b the formation of polymer rods with modulated density (alternation of crystalline and amorphous sequences along the rod axis) c the shish-kebab-like morphology formed by correlated polymer-wax plates templated by the initial polymer rods d a detail of the polymer-wax common plates, basically the same structure as that shown in Fig. 55. At lower temperatures and high wax content the wax surplus fills the space between the platelets and transforms the shish-kebab into large-scale one-dimensional object...

We first grow the terrain by an infinitesimally small amount such that the connectivity of the free-space is retained. Then we triangulate the free-space into free triangles and obstacle triangles. Then using this triangulation G we construct a hierarchical structure (similar to that of [10]) as follows. We construct a sequence of triangulations Si, 52,, S/,( ), where Si=G, and S, is obtained from... 

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