Insertion-Deletion Networks

Word networks - collections of words of a common length that can be joined by single-letter substitutions, such as the sequence BANKER-BANTER-BATTER-BETTER-SETTER-SETTEE-SETTLE linking BANKER and SETTLE - were studied in some detail in the May and August 1973 issues of Word Ways. Non-repeating sequences from word networks, commonly called word ladders and doublets, have a long history; Lewis Carroll, among others, challenged readers to join two specified words by a ladder. However, word networks have one serious flaw: they do not allow one to incorporate words of different lengths. This can be rectified by the concept of an insertion-deletion network, in which a word of n letters is linked to a word of n-1 letters if the first can be converted to the second by the deletion of a single letter. (In the reverse direction, the linage is called the insertion of a letter in a word to form another word.) Extremely complex insertion-deletion networks containing many loops and branches can be constructed; by examining them, one can easily ascertain whether or not one word can be reached from another by successive insertions and deletions. Further, one can calculate the minimum number of such steps required

Graph-Controlled Insertion-Deletion Systems

In this article, we consider the operations of insertion and deletion working in a graph-controlled manner. We show that like in the case of context-free productions, the computational power is strictly increased when using a control graph: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Insertion/deletion-related polymorphisms in the human T cell receptor beta gene complex.

Insertion/deletion related polymorphisms (IDRP) involving stretches of 15-30 kb within the human TCR-beta gene complex were revealed by pulse-field gel electrophoresis. Two independent IDRP systems were detected by analysis of Sfi I- and Sal I-digested human DNA samples using probes for TCR C and V region gene segments. The allelic nature of these systems was verified in family studies, and mapping data allowed localization of one area of insertion/deletion among the V gene segments and the other near the C region genes. All but one of 50 individuals tested could be typed for the two allelic systems, and gene frequencies for the two allelic forms were 0.37/0.61 and 0.46/0.54, indicating that these polymorphisms are widespread

Bovine polledness

The persistent horns are an important trait of speciation for the family Bovidae with complex morphogenesis taking place briefly after birth. The polledness is highly favourable in modern cattle breeding systems but serious animal welfare issues urge for a solution in the production of hornless cattle other than dehorning. Although the dominant inhibition of horn morphogenesis was discovered more than 70 years ago, and the causative mutation was mapped almost 20 years ago, its molecular nature remained unknown. Here, we report allelic heterogeneity of the POLLED locus. First, we mapped the POLLED locus to a ∼381-kb interval in a multi-breed case-control design. Targeted re-sequencing of an enlarged candidate interval (547 kb) in 16 sires with known POLLED genotype did not detect a common allele associated with polled status. In eight sires of Alpine and Scottish origin (four polled versus four horned), we identified a single candidate mutation, a complex 202 bp insertion-deletion event that showed perfect association to the polled phenotype in various European cattle breeds, except Holstein-Friesian. The analysis of the same candidate interval in eight Holsteins identified five candidate variants which segregate as a 260 kb haplotype also perfectly associated with the POLLED gene without recombination or interference with the 202 bp insertion-deletion. We further identified bulls which are progeny tested as homozygous polled but bearing both, 202 bp insertion-deletion and Friesian haplotype. The distribution of genotypes of the two putative POLLED alleles in large semi-random sample (1,261 animals) supports the hypothesis of two independent mutations

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Twisted trees and inconsistency of tree estimation when gaps are treated as missing data -- the impact of model mis-specification in distance corrections

Statistically consistent estimation of phylogenetic trees or gene trees is possible if pairwise sequence dissimilarities can be converted to a set of distances that are proportional to the true evolutionary distances. Susko et al. (2004) reported some strikingly broad results about the forms of inconsistency in tree estimation that can arise if corrected distances are not proportional to the true distances. They showed that if the corrected distance is a concave function of the true distance, then inconsistency due to long branch attraction will occur. If these functions are convex, then two "long branch repulsion" trees will be preferred over the true tree -- though these two incorrect trees are expected to be tied as the preferred true. Here we extend their results, and demonstrate the existence of a tree shape (which we refer to as a "twisted Farris-zone" tree) for which a single incorrect tree topology will be guaranteed to be preferred if the corrected distance function is convex. We also report that the standard practice of treating gaps in sequence alignments as missing data is sufficient to produce non-linear corrected distance functions if the substitution process is not independent of the insertion/deletion process. Taken together, these results imply inconsistent tree inference under mild conditions. For example, if some positions in a sequence are constrained to be free of substitutions and insertion/deletion events while the remaining sites evolve with independent substitutions and insertion/deletion events, then the distances obtained by treating gaps as missing data can support an incorrect tree topology even given an unlimited amount of data.Comment: 29 pages, 3 figure