Genetic sequences are two-dimensional

In attempting to align divergent homologs of a conserved developmental enhancer, a flaw in the homology concept embedded in gapped alignment (GA) was discovered. To correct this flaw, we developed a methodological approach called maximal homology alignment (MHA). The goal of MHA is to rescue internal microparalogy of biological sequences rather than to insert a pattern of gaps (null characters), which transform homologous sequences into strings of uniform size (1-dimensional lengths). The core operation in MHA is the \"cinch\", whereby inferred tandem microparalogy is represented in multiple rows across the same span of alignment columns. Thus, MHAs have a second (vertical) paralogy dimension, which re-categorizes most indel mutations as replication slippage and attenuates the indel problem. Furthermore, internally-cinched, inferred microparalogy in a self-MHA can later be relaxed to restore uniformity to 2-dimensional widths in a multiple sequence alignment. This de-cinching operation is used as a first resort before artificial null characters are used. We implement MHA in a program called maximal, which is composed of a series of modules for cinching and cyclelizing divergent tandem repeats. In conclusion, we find that the MHA approach is of higher utility than GA in non-protein-coding regulatory sequences, which are unconstrained by codon-based reading frames and are enriched in dense microparalogical content.