BACKGROUND: As phenotypic features derived from heritable characters, the topologies of metabolic pathways contain both phylogenetic and phenetic components. In the post-genomic era, it is possible to measure the "phylophenetic" contents of different pathways topologies from a global perspective. RESULTS: We reconstructed phylophenetic trees for all available metabolic pathways based on topological similarities, and compared them to the corresponding 16S rRNA-based trees. Similarity values for each pair of trees ranged from 0.044 to 0.297. Using the quartet method, single pathways trees were merged into a comprehensive tree containing information from a large part of the entire metabolic networks. This tree showed considerably higher similarity (0.386) to the corresponding 16S rRNA-based tree than any tree based on a single pathway, but was, on the other hand, sufficiently distinct to preserve unique phylogenetic information not reflected by the 16S rRNA tree. CONCLUSION: We observed that the topology of different metabolic pathways provided different phylogenetic and phenetic information, depicting the compromise between phylogenetic information and varying evolutionary pressures forming metabolic pathway topologies in different organisms. The phylogenetic information content of the comprehensive tree is substantially higher than that of any tree based on a single pathway, which also gave clues to constraints working on the topology of the global metabolic networks, information that is only partly reflected by the topologies of individual metabolic pathways.

Both Takagi-Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. We investigate whether one type of fuzzy approximators is more economical than the other. The TS fuzzy systems are the typical two-input single-output TS fuzzy systems. We first establish necessary conditions on minimal system configuration of the TS fuzzy systems as function approximators. We show that the number of the input fuzzy sets and fuzzy rules needed by the TS fuzzy systems depend on the number and locations of the extrema of the function to be approximated. The resulting conditions reveal the strength of the TS fuzzy approximators. The drawback, though, is that a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. We then compare these necessary conditions with the ones that we established for the general Mamdani fuzzy systems in our previous papers. Results of the comparison unveil that the minimal system configurations of the TS and Mamdani fuzzy systems are comparable. Finally, we prove that the minimal configuration of the TS fuzzy systems can be reduced and becomes smaller than that of the Mamdani fuzzy systems if nontrapezoidal or nontriangular input fuzzy sets are used. We believe that all the results in present paper hold for the TS fuzzy systems with more than two input variables but the proof seems to be mathematically difficult. Our new findings are valuable in designing more compact fuzzy systems, especially fuzzy controllers and models which are two most popular and successful applications of the fuzzy approximators.