This is an implementation of clustering algorithms for molecular configurations. User can choose between the below two methods:
-
c-RMSD as metric distance algorithm (implemented using LAPACKE library).
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Discrete Frechet as metric distance algorithm after shifting and rotating the molecular configurations to minimize the c-RMSD distance.
In bioinformatics, the root-mean-square deviation of atomic positions (or simply root-mean-square deviation, RMSD) is the measure of the average distance between the atoms (usually the backbone atoms) of superimposed proteins. In the study of globular protein conformations, one customarily measures the similarity in three-dimensional structure by the RMSD of the Cα atomic coordinates after optimal rigid body superposition.
A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the RMSD. Coutsias, et al. presented a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. They proved that the quaternion method is equivalent to the well-known Kabsch algorithm.
The Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. It is named after Maurice Fréchet.
Imagine a man traversing a finite curved path while walking his dog on a leash, with the dog traversing a separate one. Assume that the dog varies her speed to keep as much slack in her leash as possible: the Fréchet distance between the two curves is the length of the shortest leash sufficient for both to traverse their separate paths. Note that the definition is symmetric with respect to the two curves—the Frechet distance would be the same if the dog was walking her owner.
Silhouette refers to a method of interpretation and validation of consistency within clusters of data. The technique provides a succinct graphical representation of how well each object lies within its cluster. The silhouette value is a measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation). The silhouette ranges from −1 to +1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. If most objects have a high value, then the clustering configuration is appropriate. If many points have a low or negative value, then the clustering configuration may have too many or too few clusters.
The format of input text file, described by the following structure:
numConform: <integer>
N: <integer>
x11 y11 z11
x12 y12 z12
...
x1N y1N z1N
x21 y21 z21
...
x<numConform><N> y<numConform><N> z<numConform><N>
where numConform is the total molecular configurations, N the number of points in each molecular configuration.
The format of output text file, described by the following structure:
k: <integer>
s: <real in [-1,1]>
ID11 ID12 ID13 ID14
...
IDk1 IDk2 IDk3
where k the number of clusters, s the optimum silhouette value.
./makefile
./proteins –i [input file] -frechet (optional)