ef.: Teresa M. Przytycka:
An Important Connection Between Network Motifs and Parsimony Models. RECOMB 2006: 321-335
We demonstrate an important connection between network motifs in certain biological networks and validity of evolutionary trees constructed using parsimony methods.
We introduce a graph theoretical characterization that helps to select correct characters. Given a set of characters and a set of taxa, we construct a network called character overlap graph.
Here "
taxa" means a grouping or classifing of organisms. It does not implies the specific biological class of organisms.
Given a set of taxa and a set of characters, one could constcut the character overlap graph, that the vertices are characters and the edge exists iff. there exists a taxon contains both characters.
Each taxon is described by a binary vector of attributes. Those attributes so called characters. If a taxon has a attributes, then it assigns 1 to the attribute in the binary vector, otherwise assgins 0.
Therefore we could use those informations like taxon to build an evolution tree using parsimony approach, i.e., Maximum Parsimony Tree Problem. Most variations of it are in NP-C. In spite of it, the correctness problem, i.e., the correctness of the bulit evolution tree, is also open.
Intuitively, its correctness depends strongly on choosing appropriately charactors and taxa. The goal of this paper is to give a method to improve the correctness of evolution tree which is contructed by parsimony approach.
First, author defined "persistent," i.e., a charactor is persistent if it is gained exactly once and lost at most once, and persistent parsimony means all charactors are persistent.
The author found that the hole, chordless cycle of length at least four, is rare in charactor overlap graph whose charactors are chose as protein domains. In contrast, the hole is abundant in charactor overlap graph whose charactors are chose as introns. Furthermore the correctness of tree built by domain overlap graph is better than built by intron overlap graph. (refers the references [11], [27], [10], [29] of this paper.)
The author believe this phenomenon is meaningful. He prove that
If all charactors are persistent then corresponding charactor overlap graph is chordal.
Therefore we could measure whether the chosen charactors lead to incorrect evolutionary tree by the Edge-Deletion Problem of chordal graph. Unfortunately it is in NP-C.
The author adapt the idea of network motif. He just counts the number of squares, the chordless cycles with length 4, of the charactor overlap graph, and compare it to the number of squares of charactor overlap graph whose charactors gain or loss randomly.
Although the relation between non-persistent charactors and the number of squares is not so clear. Few non-persistent charactors might lead to large number of squares, and large number of squares might have small non-persistent charactors. We still could benefit from it by finding the charactors involved in a large number of squares. It is a significant noise of the data. (In domain overlap graph, those charactors, that involved in a large number of squares, are the promiscuous domains which are known to appear in many diverse multidomain proteins.)
