To facilitate comparisons between proteins, we calculated the mean pairwise amino acid diversity for each period, defined as the mean number of amino acid differences per site (in other words, the Hamming distance divided by the sequence length).
We used the sum of the branch lengths of each species in a pair to their nearest common ancestor as their sequence divergence, and normalized it to range from 0 to 1 by dividing by the maximum sequence distance.
If multiple best scoring hits fulfilled these criteria, the most representative sequence was selected by the following procedure: The average sequence distance (over the length of the whole sequences) between each hit and the other best scoring hits was calculated based on a distance matrix generated in ARB [33].
However, those expectations are not supported by the average sequence distances between those species calculated by Burgess and Yang (2008: table 1).
Our prediction methods are drawn from sequence space localization determined by the means of sequence distance measures, phylogenetic distance and clustering.
Orthologous relationships between HMG family genes were identified from phylogenetic-tree amino acid sequences determined by a sequence distance method and the Neighbor Joining (NJ) algorithm (41) using Vector NTI software (Invitrogen, Carlsbad, CA, USA).
The protein sequence similarity was converted from the global sequence distance obtained by ClustalO [14].
Possible outliers were determined by calculating every sequence distance from the centroid of cluster whose coordinates are xc = Σi xi/N, yc = Σi xi/N; where i = 1,..., N and N is the number of sequences, sequences with distances higher than 0.1 were removed.
Multiple sequence alignments using the GI proteins from the six monocot plants and Arabidopsis showed that the GI protein was characterized by the lowest overall mean sequence distance (0.18, Table 2, Figure 1c).
To examine this possibility, we restricted our analysis to residue pairs separated by a minimal primary sequence distance and recalculated the median physical distance of predicted coevolving pairs (Figure 4D).
