High-dimensional sequence space

Mandelbrot [23] has shown that the most random type of height distribution to be expected on earth is of a fractal type. The same should be true for a value distribution in the v-dimensional sequence space. Such a fractal distribution is highly connective, that is, anything but uncorrelated. Moreover, we know that functional efficiency is clustered around certain sequences. The functional efficiency of an enzyme depends on the correct spatial arrangement of certain amino acid residues that comprise the active center this is achieved by three-dimensional folding of the polypeptide chain [24]. Hence there exists a correlation ... 

The high dimensionality of sequence space aids the connectivity of fitness domains of (nearly) neutral mutants. 

In addition to conventional sequence motifs (Prosite, BLOCKS, PRINTS, etc.), the compilation of structural motifs indicative of specific functions from known structures has been proposed [268]. This should improve even the results obtained with multiple (one-dimensional sequence) patterns exploited in the BLOCKS and PRINTS databases. Recently, the use of models to define approximate structural motifs (sometimes called fuzzy functional forms, FFFs [269]) has been put forward to construct a library of such motifs enhancing the range of applicability of motif searches at the price of reduced sensitivity and specificity. Such approaches are supported by the fact that, often, active sites of proteins necessary for specific functions are much more conserved than the overall protein structure (e.g. bacterial and eukaryotic serine proteases), such that an inexact model could have a partly accurately conserved part responsible for function. As the structural genomics projects produce a more and more comprehensive picture of the structure space with representatives for all major protein folds and with the improved homology search methods linking the related sequences and structures to such representatives, comprehensive libraries of highly discriminative structural motifs are envisionable. 

Intrinsic dimensionality estimation is concerned with obtaining an estimate of the dimensionality of the manifold that is embedded in high-dimensional space. More often than not, although the dataset s ambient dimensionality may be high, its intrinsic dimensionality will be much lower. An example of this is shown in Fig.4.1 where a sequence of 32 x 32 pixel images (X e are taken. The estimated intrinsic... 

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