SANA: simulated annealing far outperforms many other search algorithms for biological network alignment

Abstract

Every alignment algorithm consists of two orthogonal components: an objective function M measuring the quality an alignment, and a search algorithm that explores the space of alignments looking for ones scoring well according to M . We introduce a new search algorithm called SANA (Simulated Annealing Network Aligner) and apply it to protein-protein interaction networks using S 3 as the the topological measure. Compared against 12 recent algorithms, SANA produces 5-10 times as many correct node mappings as the others when the correct answer is known. We expose an anti-correlation in many existing aligners between their ability to produce good topological vs. functional similarity scores, whereas SANA usually outscores other methods in both measures. If given the perfect objective function encoding the identity mapping, SANA quickly converges to the perfect solution while many other algorithms falter. We observe that when aligning networks with a known mapping and optimizing only S 3 , SANA creates alignments that are not perfect and yet whose S 3 scores match that of the perfect alignment. We call this phenomenon saturation of the topological score. Saturation implies that a measure's correlation with alignment correctness falters before the perfect alignment is reached. This, combined with SANA's ability to produce the perfect alignment if given the perfect objective function, suggests that better objective functions may lead to dramatically better alignments. We conclude that future work should focus on finding better objective functions, and offer SANA as the search algorithm of choice.

An Introductory Guide to Aligning Networks Using SANA, the Simulated Annealing Network Aligner

“…Another measure called ICS Induced Conserved Substructure (Patro and Kingsford, 2012) measures AE divided by the number of painted edges that exist only between holes that have pegs in them. ICS has the significant disadvantage that it can be maximized by finding a network alignment that minimizes the number of edges between filled holes (Saraph and Milenković, 2014;Vijayan et al, 2015;Mamano and Hayes, 2017), which can hardly be said to be a good alignment. Consider again Figure 1.…”

“…Since network alignment is an NP-complete problem 3 , all such algorithms must use heuristics to navigate this enormous search space. Search methods abound; several good review papers exist (Clark and Kalita, 2014;Faisal et al, 2015b;Milano et al, 2017;Guzzi and Milenković, 2017); for an extensive comparison specifically showing that SANA outperforms about a dozen of the best existing algorithms, see Mamano and Hayes (2017). SANA is virtually unique in that it was designed from the start to be able to optimize any objective function, including the objective functions introduced by other researchers; a preliminary report shows that SANA outperforms over a dozen other algorithms at optimizing their own objective functions (Kanne and Hayes, 2017).…”

BioFabric Visualization of Network Alignments

“…Full Table of All Alignment Scores for Mixtures of Importance and Symmetric Substructure Score Table 9 lists the scores for the ten-hour SANA [16] runs between Yeast2K-Reduced and SC, in which we used combinations of Importance (I) [17] and Symmetric Substructure Score (S 3 ) [15] in the objective function. Note that all these scores, with the exception of Resnik, are available using the Alignment Measures tool in VISNAB.…”

“…Purple, pBp, pRp (P:P/pBp/pRp) 15 Purple Purple, pBb, pRp (P:P/pBb/pRp) 16 Purple Purple, pBp, pBb, pRp (P:P/pBp/pBb/pRp) 17 Purple pRr (P:pRr) 18 Purple Purple, pRr (P:P/pRr) 19 Purple pBp, pRr (P:pBp/pRr) 20 Purple pBb, pRr (P:pBb/pRr) 21 Purple pBp, pBb, pRr (P:pBp/pBb/pRr) 22 Purple pRp, pRr (P:pRp/pRr) 23 Purple Purple, pBp, pRr (P:P/pBp/pRr) 24 Purple Purple, pBb, pRr (P:P/pBb/pRr) 25 Purple Purple, pBp, pBb, pRr (P:P/pBp/pBb/pRr) 26 Purple Purple, pRp, pRr (P:P/pRp/pRr) 27 Purple pBp, pRp, pRr (P:pBp/pRp/pRr) 28 Purple pBb, pRp, pRr (P:pBb/pRp/pRr) 29 Purple…”

Graphettes: Constant-time determination of graphlet and orbit identity including (possibly disconnected) graphlets up to size 8

“…While more sophisticated methods such as spectral analysis [4,5] and topological indices [6] have been useful, the study of small subnetworks such as motifs [7] and graphlets [8,9] have become popular. They have been used extensively to globally classify highly disparate types of networks [10] as well as to aid in local measures used to align networks [11][12][13][14].…”