Rearrangement and inference of chromosome structures

Abstract

The chromosome structure is defined as a set of chromosomes that consist of genes assigned to one of the DNA strands and represented in a circular or linear arrangement. A widely investigated problem is to define the shortest algorithmic path of chromosome rearrangements that transforms one chromosome structure into another. When equal rearrangement costs and constant gene content are considered, the solu tion to the problem is known. In this work, a principally novel approach was developed that presents an exact algorithm with linear time complexity for both equal and unequal costs, in which chromosome structures defined on the same set of genes were considered. In addition, to solve the problem of the inference of ances tral chromosome structures containing different sets of genes when the original structures are fixed in leaves, exact and heuristic algorithms were developed.

Algorithms for reconstruction of chromosomal structures

“…Detailed description of the model is given in the Section “Definition of the model of chromosome structure”. Significant constraints were imposed on the model in [ 1 ] and many other publications: constant gene content is provided in the sequence of transformations from one structure into another, paralogs are not allowed, operation weights are equal (thus, are not used), etc.…”

“…Although the algorithm proposed here conforms to the basic concept of the algorithm in [ 1 ], it is radically more complex; while the exactness proof was essentially trivial for the algorithm in [ 1 ], the exactness here is a kind of a theory. The current work introduces a sequence of lemmas constituting this proof, although certain details were given in [ 5 , 6 ].…”

“…Algorithms with such a property are called approximate algorithms. Part “Exact linear algorithm calculating the distance between chromosome structures” and [ 1 , 5 – 7 , 12 ] sets the coefficient k equal to 1, while in Part “Algorithm for the reconstruction of chromosome structures with cubic complexity and sufficient approximation ratio” it equals 2 or 11/6. These cases are fundamentally different from heuristic algorithms, whose results are in unknown relation to the minimum (“true”) solution.…”

“…Finally, Part “Reconstruction of chromosome structures for mitochondria of sporozoans and plastids of rhodophytic branch” illustrates the algorithms described in Parts “Exact linear algorithm calculating the distance between chromosome structures” and “Algorithm for the reconstruction of chromosome structures with cubic complexity and sufficient approximation ratio” and one more algorithm proposed in [ 1 ] by generating phylogenetic trees and reconstructing chromosome structures of mitochondria in sporozoans and plastids of rhodophytic branch. The test on artificial data is available at http://lab6.iitp.ru/en/chromoggl/ .…”

Highly Conserved Elements and Chromosome Structure Evolution in Mitochondrial Genomes in Ciliates

“…The distances between chromosome structures as well as the reconstruction of chromosome rearrangements were obtained by the methods described elsewhere [19,28,29]. The default operation costs were used, specifically: the linear variant and double-cut-and-paste, 1.2; sesqui-cut-and-paste, 1.1; a -edge insertion and b -edge deletion, 1; b -edge insertion or a -edge deletion, 0.9; deletion of special a -edges, 2.0; deletion of special b -edges, 2.5.…”