Background: In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NPhard problems. Most previous algorithmic work on network alignments is heuristic in nature. We introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem. Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and -unlike those computed by pure heuristics -come with a quality guarantee. Computational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LISA library. In systems biology, complex biological systems are often modeled as networks. Examples include protein-protein interaction (PPI), metabolic, gene-regulatory, and signal transduction networks. The increasing quality and quantity of available data creates the need for automated analysis methods to better understand cellular processes, network organization, evolutionary changes, and disease mechanisms [1, 2] . Based on the assumption that evolutionary conservation implies functional significance, comparative approaches may help improve the accuracy of data, elucidate protein pathways and complexes, generate, investigate, and validate hypotheses about the underlying networks, and transfer functional annotations. In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes
Klau formulate the problem based on maximum weight trace and suggests a lagrangian relaxation approach REF .
A new graph-based method for pairwise global network alignment
BMC Bioinformatics
BMC Bioinformatics
Computer Science Medicine