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Statistics on quadruplet frequencies as observed from the training set protein chains

There are a total of 8855 possible quadruplets that could be observed in each of the five classes of tetrahedra (class {1-1-1-1},{2-1-1},{2-2},{3-1} and {4} ). Thus there are a total of 8855 x 5 = 44275 tetrahedral compositions as defined by the four-body potentials. Of course some of the quadruplet compositions would never occur in nature due to the Chemistry and structure of the participating amino acids. A summary of quadruplet observations for each of the five classes of tetrahedra as recorded from the Delaunay tessellations of the 1167 training set protein chains is given below.

I. Class {1-1-1-1}

# quadruplets observed (at least once) = 8723

# quadruplets observed at least 3 times = 8260

average number of observation per quadruplet = 29.9

II. Class {2-1-1}

# quadruplets observed (at least once) = 8804

# quadruplets observed at least 3 times = 8582

average number of observation per quadruplet = 41.7

III. Class {2-2}

# quadruplets observed (at least once) = 8306

# quadruplets observed at least 3 times = 6960

average number of observation per quadruplet = 13.3

IV. Class {3-1}

# quadruplets observed (at least once) = 8579

# quadruplets observed at least 3 times = 7929

average number of observation per quadruplet = 25.8

V. Class {4}

# quadruplets observed (at least once) = 7107

# quadruplets observed at least 3 times = 4939

average number of observation per quadruplet = 6.4