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Many protein motifs cannot be represented by a simple consensus pattern of letters.
One good  example is the helix-turn-helix motif from prokaryotes shown here.
These proteins bind to specific DNA sequences and regulate gene expression
One would not expect this set of regulatory sequences to show a discrete pattern because
Although each of these sequences forms the same helix-turn-helix structure
each sequence binds to a different DNA target sequence.
On the one hand, there is information in each of these sequences to encode this structural property, there are also residues involved in specific DNA binding. 
This is an excellent example of how nature uses structural redundancy to encode two functions in one sequence.
Such motifs have generally been approached by probabilistic methods such as weight matrices,  blocks, or profiles.