Modelling Simple Operations for Gene Assembly

Abstract

Summary. The intramolecular model ) for gene assembly in ciliates considers three operations, ld, hi, and dlad that can assemble any micronuclear gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and may consist of many coding and non-coding blocks. We consider in this paper some restricted variants of the three operations, where only one coding block is rearranged at a time. We present in this paper the molecular model of these simple operations. We also introduce a mathematical model for the simple operations, on three levels of abstractions: MDS descriptors, signed permutations, and signed double occurrence strings. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful strategy.

Complexity Measures for Gene Assembly

“…The molecular model for simple ld, hi, and dlad was introduced in [11]. Due to lack of space, we only give here a short intuitive presentation, followed by its formalization as rewriting rules for signed permutations.…”

“…Due to lack of space, we only give here a short intuitive presentation, followed by its formalization as rewriting rules for signed permutations. For formalizations on the level of MDS descriptors and signed double occurrence strings we refer to [11].…”

Extending the Overlap Graph for Gene Assembly in Ciliates

“…The motivation for this restricted model is that it is less involved but still general enough to allow for the successful assembling of all known experimental obtained micronuclear genes [5]. The restricted model, called simple gene assembly, was originally defined on signed permutations, see [4,9]. The model can also be defined as string rewriting rules (in an equivalent way) as done for the general model above.…”

“…Both systems are 'almost equivalent', and we refer to these as the general model. In [4] a restriction of this general model has been proposed. While this model is less powerful than the general model, it is powerful enough to allow each known gene [5] in its micronuclear form to be transformed into its macronuclear form.…”

“…Moreover this model is less involved and therefore called the simple model. The simple model was first defined using signed permutations [4], and later proved equivalent to a string rewriting system [6]. The graph rewriting system of the general model is based an overlap graphs.…”