Generic Properties of the Sequence-structure Relations of Biopolymers

Biological evolution is a highly sophisticated dynamical phenomenon, and its complexity is often confusing. For the purpose of analysis it may be partitioned into the four partial processes depicted in gure 1 25]: population dynamics, (population) support dynamics, genotype-phenotype mapping, and tness evaluation. These components are properly visualized as map-pings between abstract metric spaces: ? the concentration space of biochemical reaction kinetics, ? the sequence space of polynucleotide sequences, ? the shape space of biopolymer structures, and ? the parameter space of kinetic rate constants. Kinetics of chemical reactions or changes in populations are recorded in concentration space, the conventional space of chemical reaction kinetics. Variables count numbers of particles, molecules, virions, cells, or organisms, for example, and display their changes over time. Population dynamics is commonly described by diierential equations, by diierence equations in case of synchronized generations, or by a stochastic process in case of small particle numbers 12]. Concentration space deals only with the classes of genotypes actually present. Sequence space (Q n ; d) is a metric point space containing all n possible genotypes of given chain length n, where denotes the size of the polynu-cleotide or amino acid alphabet. Distances in sequence space are expressed by the minimum number of single nucleotide exchanges or point mutations