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Reciprocal best match graphs.

Manuela Geiß1,2, Peter F Stadler1,2,3,4,5,6,7,8, Marc Hellmuth9,10

  • 1Bioinformatics Group, Department of Computer Science, Leipzig University, Härtelstraße 16-18, 04107, Leipzig, Germany.

Journal of Mathematical Biology
|November 7, 2019
PubMed
Summary
This summary is machine-generated.

We mathematically characterized reciprocal best match graphs (RBMGs), crucial for orthology assessment. For 3 species, we identified three distinct RBMG classes and developed a polynomial-time recognition method for RBMGs that are also cographs.

Keywords:
Hierarchically colored cographPairwise best hitPhylogenetic treeReciprocal best match heuristicsVertex colored graph

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Area of Science:

  • Computational biology
  • Graph theory
  • Phylogenetics

Background:

  • Reciprocal best matches (RBMs) are fundamental in computational biology, particularly for orthology assessment tools.
  • Despite their importance, the mathematical structure of reciprocal best match graphs (RBMGs) remains largely unexplored.

Purpose of the Study:

  • To investigate and mathematically characterize the structure of reciprocal best match graphs (RBMGs).
  • To define RBMs abstractly as pairwise most closely related leaves in a gene tree, bridging theoretical concepts with practical heuristics.

Main Methods:

  • Defined RBMGs based on pairwise most closely related leaves in gene trees.
  • Investigated graph properties, including quotient graphs and connected components, in relation to RBMG structure.
  • Developed a characterization for RBMGs with 3 colors/species and an approach for arbitrary colors.

Main Results:

  • A graph G is an RBMG if and only if its quotient graph under a specific thinness relation is an RBMG.
  • All connected components of a graph must be RBMGs for the entire graph to be an RBMG.
  • Complete characterization of 3-color RBMGs into three distinct classes related to phylogenetic tree structures was achieved.
  • A polynomial-time recognition algorithm was developed for RBMGs that are also cographs (co-RBMGs).

Conclusions:

  • The study provides a foundational mathematical understanding of RBMGs.
  • Efficient recognition of co-RBMGs is possible, with their structure linked to hierarchically colored cographs.
  • While a general polynomial-time RBMG recognition remains an open question, significant progress has been made for specific cases.