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If they are independent the residues in one of the networks mutate in sync with each other, but the residues from the other network mutate in a different rate. For example, If you compare two subfamilies the positions of one network all have a different residue in each of the two subfamilies (so they mutate between the two subfamilies), and the positions of the other network might be 100% conserved over the two subfamilies.

You can exploit explore this idea by making an alignment with two groups of proteins. Each group should contain functionally the same similar proteins but this function differs between the groups. For instance, a group can be made with enzymes all converting the same substrate, and a second group that convert another substrate. The correlated mutations then often reveal hotspots that determine the substrate specificity change. A very important note is that correlated mutations reflect functional changes and not environmental changes. This can easily be explained: You cannot use correlated mutations to find hotspots for thermostability. You could make an alignment of two groups: one composed of proteins from thermophilic organisms and another made from non-thermophilic organisms. Then the differences between these groups should show up as correlated mutations, right? This is not the case, because in fact these two groups cover all sequences of the complete superfamily alignment. You can investigate the differences between these groups just by comparing the amino acid contents between the groups. This concept will be discussed later. One more important note: The problem with functional grouping is that the functional annotations of proteins is often based only on sequence similarity and can therefore be wrong. You need to make sure that at least a high percentage of the sequences share the same function to make functional based hotspot finding work. There are examples though were the alignment was successfully grouped simply by using keyword searches in the protein descriptions and used to find novel enzymes. The group of Prof Uwe Bornscheuer has found R-selective amine transferases (Only S-selective enzymes where known) by deleting from the protein family groups of proteins that had other activities based on motifs that were associated with the different functions. This exercise was repeated with 3DM. The protein family was first grouped by giving keywords that were related to enzymes with unwanted reaction mechanism. The keywords lyase, for instance, was used to select of enzymes with likely the unwanted lyase activity. Then, this set of sequences was used to find a sequence motif specific for lyase activity. All sequences that had this lyase specific sequence motif were subsequently deleted from the alignment. This step ensures that all lyases that were not annotated as such still get deleted from the alignment. This procedure was repeated for all different unwanted enzyme activities. This exercise resulted in 42 sequences that most likely are all R-selective amine transferases.