97-11-081
Abstract:
Shaping Space: The Possible and the Attainable in RNA
Genotype-Phenotype Mapping
Walter Fontana and Peter Schuster
Understanding which phenotypes are accessible from which genotypes is
fundamental for understanding the evolutionary process. This notion of
accessibility can be used to define a relation of nearness among
phenotypes, independently of their similarity. Because of neutrality,
phenotypes denote equivalence classes of genotypes. The definition of
neighborhood relations among phenotypes relies, therefore, on the
statistics of neighborhood relations among equivalence classes of
genotypes in genotype space. The folding of RNA sequences (genotypes)
into secondary structures (phenotypes) is an ideal case to implement
these concepts. We study the extent to which the folding of RNA
sequences induces a ``statistical topology'' on the set of minimum
free energy secondary structures. The resulting nearness relation
suggests a notion of ``continuous'' structure transformation. We can,
then, rationalize major transitions in evolutionary trajectories at
the level of RNA structures by identifying those transformations which
are irreducibly discontinuous. This is shown by means of computer
simulations. The statistical topology organizing the set of RNA shapes
explains why neutral drift in sequence space plays a key role in
evolutionary optimization.
keywords:
Evolutionary trajectories, neutral evolution,
neutral networks, optimization, RNA secondary structures, statistical
topology
Submitted to J. Theor. Biol.
Return to 1997 working papers list.