Finite-state models in the alignment of macromolecules

Abstract

Minimum message length encoding is a technique of inductive inference with theoretical and practical advantages. It allows the posterior odds-ratio of two theories or hypotheses to be calculated. Here it is applied to problems of aligning or relating two strings, in particular two biological macromolecules. We compare the r-theory, that the strings are related, with the null-theory, that they are not related. If they are related, the probabilities of the various alignments can be calculated. This is done for one-, three-, and five-state models of relation or mutation. These correspond to linear and piecewise linear cost functions on runs of insertions and deletions. We describe how to estimate parameters of a model. The validity of a model is itself an hypothesis and can be objectively tested. This is done on real DNA strings and on artificial data. The tests on artificial data indicate limits on what can be inferred in various situations. The tests on real DNA support either the three- or five-state models over the one-state model. Finally, a fast, approximate minimum message length string comparison algorithm is described.

Sequence complexity for biological sequence analysis

“…The machine could be made to match or recognize a particular family of sequences but only if it were given one or more examples prepended to the data to be searched. To an extent, it models the process by which a sequence could be generated and it is natural to use the term machine for this reason, and also because it is common in compression, makes a distinction with the other kind of HMM and is consistent with earlier work (Allison et al, 1992).…”

“…The possibility of changes, insertions and deletions in a repeat allow instances to differ. In essence, states R, R2 and R3 embody a simple mutation machine, as can be used in the sequence alignment problem (Allison et al, 1992), here used to allow local alignments of the sequence with itself. For the analysis of DNA, approximate reverse complementary repeats are allowed by a further set of states R%, R2% and R3% and corresponding operations, not shown.…”

“…For example, linear costs for gaps (indels) within repeats can be modeled by states and operations for start-insert and continue-insert etc. as in the sequence alignment problem (Allison et al, 1992). One can even envisage a systematic search through simple machines to complex machines.…”

“…For short sequences one can perform a second backwards pass through the repeat graph and thus calculate the probability of the true path going through each node. This is analogous to the forward -backward dynamic programming algorithm which yields alignment density plots in sequence alignment (Allison et al, 1992). However, it requires either O(n 2 ) space or greater time-complexity and is impractical for long sequences.…”

A genome alignment algorithm based on compression

“…As in [25,26], our work is based on the premise that if two sequences are related, one sequence must tell something useful about the other: A predictive model can predict a sequence better if a related sequence is known. The information content of a sequence is measured by lossless compression.…”