Artificial Life VI

Computational Complexity in the Life Sciences

Christos H. Papadimitriou
Computer Science Dept., Univ. California - Berkeley

Martha Sideri
Computer Science Dept., Univ. California - Berkeley


The field of computational complexity has been investigating over the past three decades the reasons why some computational problems are so hard to compute. But it has more fascinating lessons to teach us than this, because many problems in science have latent algorithmic aspects. Among those, the {em protein folding problem} is one of the most intriguing. Proteins are polymer chains consisting of monomers of twenty different kinds, which tend to {em fold}, presumably by dint of attraction or repulsion forces between monomers, to form a very specific and stable geometric pattern, known as the protein's {em native state}. It is this geometric pattern that determines the macroscopic properties, behavior, and function of a protein. This surprising stability of the native state has led to the widespread belief that it must be the lowest-energy configuration of the chain. Thus Nature appears to be solving very rapidly an extremely complex combinatorial problem (a widely-studied discretized version of the protein folding problem has in fact recently proved NP-complete (cf. {em Proceedings of the 1998 RECOMB Conference/}). This conundrum is known as {em Levinthal's paradox}. However, a simple explanation proceeds along these lines: Proteins must cooperate in order to function in an organism, and such cooperation often involves ``locking'' of their shapes. Hence, there is evolutionary pressure towards protein forms that have a unique stable native state, and this pressure could have resulted in proteins with very {em flat energy landscapes.} Flat landscapes feature an overwhelmingly popular local optimum, which may not necessarily coincide with the global optimum. Computational experiments verify that such flat landscapes evolve very rapidly in a broad variety of optimization problems and circumstances. Protein folding is only one of the mysterious steps in the map from genotype to phenotype. There have been exciting results in recent years linking certain human diseases to specific genes. Some geneticists envision a coming ``last stage of the Mendelian revolution,'' in which all such macroscopic traits will be traced to their genetic causes. However, the vast majority of traits and diseases appear to be {em polygenic}, in that they involve the complex interactions, as in a many-input Boolean circuit, of many genes. There seem to be unsurmountable obstacles of computational complexity lying in the path of this ambitious and important research project.

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