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The distance between two clusters is given by the height of the horizontal line connecting two clusters.

Average-linkage: The distance between two clusters is defined as the average of all distances between the observations in one cluster and the other cluster: average- linkage dist ance=frac{1}{N_X{N}_Y}{displaystyle sum_{xin X}}{displaystyle sum_{yin Y}} distleft x,yright); where X and Y are two different clusters; N X,N Y are the corresponding numbers of observations.

Single-linkage: The distance between two clusters is defined as the minimum of all distances between the observations in one cluster and the other cluster: single- linkage distance= minleft{ distleft x,yright):xin X,kern0.75em yin Yright}; where X and Y are two different clusters.

Complete-linkage: The distance between two clusters is defined as the maximum of all distances between the observations in one cluster and the other cluster: complete- linkage distance= maxleft{ distleft x,yright):xin X,kern0.75em yin Yright}; where X and Y are two different clusters.

We used the Ward's linkage: the distance between two clusters is the increase of variance observed after merging the two clusters.

In complete linkage clustering, the distance between two clusters is defined as the largest distance between two elements, one in each cluster.

(3) The gateways between two clusters are located on the boundary lines.  .

Transitions between two clusters were counted if dimer conformations traversed to another cluster in the subsequent time step (frame).

When the minimal distance between two clusters was larger than 1 Å, the clustering was stopped.

For cluster analysis, the distance between two clusters was measured by Ward's method (Ward, 1963).

The coefficients of Type-I and Type-II functional divergence (θI and θII) between two clusters were calculated.