Banishing Bias from Consensus Sequences

With the exploding size of genome databases it is becoming increasingly important to devise search procedures that extract relevant information from them One such procedure is particularly e ective in nding new distant members of a given family of related sequences start with a multiple alignment of the given members of the family and use an integral or fractional consensus sequence derived from the alignment to further probe the database However the multiple alignment constructed to begin with may be biased due to skew in the sample of sequences used to construct it We suggest strategies to overcome the problem of bias in building con sensus sequences When the intention is to build a fractional consensus sequence often termed a pro le we propose assigning weights to the sequences such that the resulting fractional sequence has roughly the same similarity score against each of the sequences in the family We call such fractional consensus sequences balanced pro les On the other hand when only regular sequences can be used in the search we propose that the consensus sequence have minimum maximum distance from any sequence in the family to avoid bias Such sequences are NP hard to compute exactly so we present an approximation algorithm with very good performance ratio based on randomized rounding of an integer pro gramming formulation of the problem We also mention applications of the rounding method to selection of probes for disease detection and to construction of consensus maps