Re: folding problem

[Judith Rosen <***>]

Hi Howard!

My father said some interesting things about Game Theory in "Anticipatory
Systems". Among them, in the notes section on page 262:

"Indeed, any kind of game thus constitutes a formal system. However, games
manifest additional structure, because the point of playing a game is to
win. This means that there are certain distinguished propositions ('wins')
in the system which a player attempts to establish, and others ('losses')
which he wishes to avoid establishing. The theory of games is thus dominated
by the idea of a strategy, the establishment of chains of propositions which
culminate in 'wins'. Ordinarily, such strategies are generated through
considerations of utility. The mathematical theory of games was originally
developed in a classic book: "The Theory of Games and Economic Behavior" by
J. von Neumann and O. Morgenstern, Princeton University Press (1944). It is
interesting to observe that, just as the rules of the game comprise a formal
system, the concept of utility which generates strategies relate game theory
to control and optimal control theory; this point is taken up further in
Note 4 below. Further, since the generation of 'good' strategies ordinarily
requires skill (i.e. intelligence) on the part of the players, it is not
surprising to find a good part of the literature in Artificial Intelligence
to be concerned with game-playing. Thus, game theory is an exceedingly
lively area. It also impinges directly on our present subject of
anticipatory behavior, since a strategy may obviously be regarded as a model
of the environment with which a player interacts."

Judith
PS: Pessimistic?

----- Original Message -----
From: "Howard Pattee" <***>
To: <***>
Sent: Thursday, March 18, 2004 7:55 PM
Subject: [ROSEN] folding problem


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