The optimization principle in phylogenetic analysis tends to give incorrect topologies when the number of nucleotides or amino acids used is small

In the maximum parsimony (MP) and minimum evolution (ME) methods of phylogenetic inference, evolutionary trees are constructed by searching for the topology that shows the minimum number of mutational changes required (M) and the smallest sum of branch lengths (S), respectively, whereas in the maximum likelihood (ML) method the topology showing the highest maximum likelihood (A) of observing a given data set is chosen. However, the theoretical basis of the optimization principle remains unclear. We therefore examined the relationships of M, S, and A for the MP, ME, and ML trees with those for the true tree by using computer simulation. The results show that M and S are generally greater for the true tree than for the MP and ME trees when the number of nucleotides examined (n) is relatively small, whereas A is generally lower for the true tree than for the ML tree. This finding indicates that the optimization principle tends to give incorrect topologies when n is small. To deal with this disturbing property of the optimization principle, we suggest that more attention should be given to testing the statistical reliability of an estimated tree rather than to finding the optimal tree with excessive efforts. When a reliability test is conducted, simplified MP, ME, and ML algorithms such as the neighbor-joining method generally give conclusions about phylogenetic inference very similar to those obtained by the more extensive tree search algorithms.

Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications.

Small, single-module proteins that fold in a single cooperative step may be paradigms for understanding early events in protein-folding pathways generally. Recent experimental studies of the 64-residue chymotrypsin inhibitor 2 (CI2) support a nucleation mechanism for folding, as do some computer stimulations. CI2 has a nucleation site that develops only in the transition state for folding. The nucleus is composed of a set of adjacent residues (an alpha-helix), stabilized by long-range interactions that are formed as the rest of the protein collapses around it. A simple analysis of the optimization of the rate of protein folding predicts that rates are highest when the denatured state has little residual structure under physiological conditions and no intermediates accumulate. This implies that any potential nucleation site that is composed mainly of adjacent residues should be just weakly populated in the denatured state and become structured only in a high-energy intermediate or transition state when it is stabilized by interactions elsewhere in the protein. Hierarchical mechanisms of folding in which stable elements of structure accrete are unfavorable. The nucleation-condensation mechanism of CI2 fulfills the criteria for fast folding. On the other hand, stable intermediates do form in the folding of more complex proteins, and this may be an unavoidable consequence of increasing size and nucleation at more than one site.