folding problem

[Howard Pattee <***>]

Judith, Tim and all,
Bob Rosen was much too pessimistic about both the folding problem and
evolution (see Chapt. 11, LI). There is now a large literature on the
folding problem that helps explain why evolution works as well as it does.
Darwinian theory, i.e., heritable random mutations and natural selection,
has always been criticized as inadequate because of the apparently low
probabilities of finding so much complex adaptation from what was assumed
to be random search. A second major problem common to both macromolecular
folding and evolutionary adaptation is trapping on local minima or peaks of
the energy or adaptive landscape respectively. However, a combination of
physical, theoretical, and simulation studies have revealed much more
favorable search and selection processes. I have not kept up to date
because of the volume of literature, but here are some recent references.

Briefly, the physical approach to folding, while still intractable ab
initio, has made progress with statistical hierarchical and relaxation
methods. These studies rely on sophisticated computer simulations and they
reveal both the complexity and the physical robustness of the folding
process, as well as how trapping is avoided.  (e.g., Frauenfelder and
Wolynes, ?Biomolecules, Where the physics of complexity and simplicity
meet,? Physics Today, 47, 58-64, 1994).

The success of evolution depends on nature of the mapping from linear 1-D
sequence space (the gene?s base sequences) to 3-D shape space (folded
proteins) and then to n-D function space. The actual assignments of these
mappings can make or break success. The genetic code is the first step and
folding is the second step. A recent summary of how the code works to avoid
mistakes and to speed up adaptation is in the April 2004 Scientific
American, ?Evolution encoded? by Freeland and Hurst.

A second article on coevolution selection strategies using game theory
instead of fitness maximizing is in Feb. 6 Science, Nowak and
Sigmund, ?Evolutionary dynamics of biological games,? 303, 793-799, 2004..

Finally, simulations of sequence space to shape space mappings have
uncovered remarkable redundancies that allow efficient search. The main
result of these studies is what is called ?shape space covering? which
shows that only a small fraction of the immense sequence space has to be
searched to find a sequence that folds into a specific structure. In other
words, the search does not need to find the needle in the haystack, but
only one of many needles uniformly distributed over the haystack. Following
Eigen?s concept of quasi species, Schuster also has shown how populations
of neutral mutations can prevent trapping. (e.g., Schuster, ?Artificial
life and molecular evolutionary biology? in Advances in Artificial Life,
Moran, et al. eds. Springer, 1995, pp. 3-19, or any of Schuster?s recent
papers, ?Landscapes and molecular evolution? in Physica D, 1997).

Howard