title: Algorithms for reconstruction of chromosomal structures.
abstract: BACKGROUND
  One of the main aims of phylogenomics is the reconstruction of objects defined in the leaves along the whole phylogenetic tree to minimize the specified functional, which may also include the phylogenetic tree generation. Such objects can include nucleotide and amino acid sequences, chromosomal structures, etc. The structures can have any set of linear and circular chromosomes, variable gene composition and include any number of paralogs, as well as any weights of individual evolutionary operations to transform a chromosome structure. Many heuristic algorithms were proposed for this purpose, but there are just a few exact algorithms with low (linear, cubic or similar) polynomial computational complexity among them to our knowledge. The algorithms naturally start from the calculation of both the distance between two structures and the shortest sequence of operations transforming one structure into another. Such calculation per se is an NP-hard problem.
  
  
  RESULTS
  A general model of chromosomal structure rearrangements is considered. Exact algorithms with almost linear or cubic polynomial complexities have been developed to solve the problems for the case of any chromosomal structure but with certain limitations on operation weights. The computer programs are tested on biological data for the problem of mitochondrial or plastid chromosomal structure reconstruction. To our knowledge, no computer programs are available for this model.
  
  
  CONCLUSIONS
  Exactness of the proposed algorithms and such low polynomial complexities were proved. The reconstructed evolutionary trees of mitochondrial and plastid chromosomal structures as well as the ancestral states of the structures appear to be reasonable.
authors.affiliation: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Bolshoi Karetnyi lane, 19, 127051, Moscow, Russia. lyubetsk@iitp.ru.
authors.forename: Vassily
authors.initials: V
authors.lastname: Lyubetsky
authors.affiliation: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Bolshoi Karetnyi lane, 19, 127051, Moscow, Russia. gershr@mail.ru.
authors.forename: Roman
authors.initials: R
authors.lastname: Gershgorin
authors.affiliation: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Bolshoi Karetnyi lane, 19, 127051, Moscow, Russia. slvstv@iitp.ru.
authors.forename: Alexander
authors.initials: A
authors.lastname: Seliverstov
authors.affiliation: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Bolshoi Karetnyi lane, 19, 127051, Moscow, Russia. gorbunov@iitp.ru.
authors.forename: Konstantin
authors.initials: K
authors.lastname: Gorbunov
mesh_terms: D000465:Algorithms; D022004:Chromosome Structures / Q000737:chemistry*; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D008958:Models, Molecular; D010802:Phylogeny; D012984:Software