Initial Cluster Analysis

We study a simple abstract problem motivated by a variety of applications in protein sequence analysis. Consider a string of 0s and 1s of length L, and containing D 1s. If we believe that some or all of the 1s may be clustered near the start of the sequence, which subset is the most significantly so clustered, and how significant is this clustering? We approach this question using the minimum description length principle and illustrate its application by analyzing residues that distinguish translational initiation and elongation factor guanosine triphosphatases (GTPases) from other P-loop GTPases. Within a structure of yeast elongation factor 1[Formula: see text], these residues form a significant cluster centered on a region implicated in guanine nucleotide exchange. Various biomedical questions may be cast as the abstract problem considered here.