How Predictable Are Biological Sequences?

A major challenge facing computational biology is the post-sequencing analysis of patterns and motifs in genomic DNA sequences. In this study, we apply asymptotically optimal Sampled Pattern Matching predictor, recently developed by us, to analyze biological sequences (i.e., proteins and DNA). The SPM predictor for a given sequence X1; : : : ; Xn predicts the next symbol Xn+1 (or next K symbols) based on selecting a context of Xn+1, that is, it predicts the value of the most frequent symbol appearing at the so called sampled positions. These positions follow the occurrences of a fraction of the longest suÆx of the original sequence that has another copy inside X1X2 : : : Xn. In our previous paper [11] we estimated the redundancy of the SPM universal predictor, that is, we established that the probability the SPM predictor makes worse decisions than the optimal predictor is O(n ) for some 0 < < 1 2 as n ! 1. When SPM is applied to molecular sequences it proves its suitability to protein prediction and DNA prediction. Finally, we should add that our ultimate goal is to bring solid methods of information theory to analysis of molecular sequences. This paper is our preliminary attempt.