The shape diversity of a particular conformer volume may be ascertained by clustering conformers of that volume with a certain shape diversity threshold (ST thresh ), which controls the "minimum" distance between any two clusters, and then by counting the number of reference shapes, each of which represents a cluster centroid and all conformers within ST thresh to the reference shape.
To determine which UCP cluster is functionally more divergent, we estimated the type-I functional distance between any two clusters, which is defined as dF = −ln(1 - θI).
The NMI value could be calculated using the Contingency Table (Vinh et al. 2010), which records co-occurrence between any two clusters in two different parcellation results.
The coefficients of Type-I and Type-II functional divergence (θ-I and θ-II, respectively) between any two clusters of interest were calculated.
From this a distance between any two clusters is computed, e.g., the minimum or maximum distance between any two members of the clusters, resulting in single-linkage and complete-linkage clustering [ 6].
Meta-edges are drawn between any two clusters that have at least one edge between at least one member in each of the two clusters (solid lines in Fig. 2).
We empirically set a threshold θ h for clustering, which means that for each class, the clustering procedure terminates when the distance between any two clusters is larger than θ h.
Meta-edges are drawn as blue lines between any two clusters that have at least one edge between at least one member in each of the two clusters, with the numbers next to each edge representing the total numbers of all edges existing between the members of the two clusters.
2. Calculate the distance between any two clusters (for example, the A and the B clusters): D A, B = 1 m ∑ k = 1 m PV k A − PV k B 2, where PV k A (PV k B ) is the k th PV of the subject in the A(B) cluster.
To estimate the level of functional divergence and to predict important amino acid residues among caleosin subfamilies, the coefficients of Type-I and Type-II functional divergence (θI and θII) between any two clusters were calculated using the methods suggested by Gu [ 45, 49] as implemented in DIVERGE2 [ 38].
