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Statistical effects of making a consensus.

The overall strength of a binding site is found by summing the individual bit contributions. A distribution of these strengths is roughly Gaussian and shows that most natural binding sites have much less information than the consensus sequence [Schneider, 1997a]. The strict consensus (where only the most frequent base is used) is the strongest possible binding site and is on the far high end of the distribution. For example, only one in 270 acceptor sites matches the strict consensus. For this reason it is generally inappropriate to say that one has a consensus binding site at such-and-such a position on a sequence.

As mentioned earlier, using consensus sequences to find binding sites by counting mismatches can lead to errors. How does this compare to the information theory approach? If matches to the consensus are assigned to have 1 unit and mismatches 0 units, then the total count is an integer. In contrast, the information theory weights are , which includes the real numbers. Summing the information theory weights gives continuous results, while counting mismatches gives blocky results that will often be off the mark. The commonly used `percent identity' between two sequences, such as proteins, is flawed for the same reasons.

Sometimes counting matches or mismatches can give results opposite to the information measure weights so that a base in a site could have a mismatch to the consensus and yet that base could contribute positive information. For example, for a position that has 60% A, 30% T, 5% G, and 5% C the consensus base is A by two-fold, and yet a T in an individual binding site would contribute bits. Only by noting the total distribution can we learn that the T contributes positively to the information. A related effect that is hidden by a consensus is that the diversity of the less frequent bases affects the total sequence conservation. For example, a position with 70% A, 30% T, 0% G, and 0% C has 1.12 bits of conservation, but a position with 70% A and 10% for each of C, G and T has only 0.64 bits. The consensus for both cases, A, does not distinguish between these.

When there are very few sequences, statistical artifacts crop up. Even if there's no information in the set, it can look like there is. For example, if one has only 6 random sequences, one will frequently observe positions that have 50% or more of one base. If, as is commonly done, one uses 50% as the cutoff for writing the consensus base, then one can get the false impression that there is pretty good sequence conservation. In the example shown in Fig. 3, 25 of 41 positions would be identified as `conserved' even though the sequences were randomly generated! In general, of the 41 positions in 6 randomly generated sequences would be marked as the consensus.