Natalie 2.0: Sparse Global Network Alignment as a Special Case of Quadratic Assignment^{ †}
Abstract
:1. Introduction
1.1. Previous Work
1.2. Contribution
2. Preliminaries
3. Methods
3.1. Solving Strategies
3.1.1. Subgradient Optimization
Algorithm 1: SubgradientOpt$(\lambda ,M,N)$ 

3.1.2. Dual Descent
Algorithm 2: DualDescent$(\lambda ,L)$ 

3.1.3. Overall Method
Algorithm 3: Natalie$(K,L,M,N)$ 

4. Experimental Evaluation
Species  Nodes  Annotated  Interactions 

cel (c)  5948  4694  23,496 
sce (s)  6018  5703  131,701 
dme (d)  7433  6006  26,829 
rno (r)  8002  6786  32,527 
mmu (m)  9109  8060  38,414 
hsa (h)  11,512  9328  67,858 
4.1. Topological Measures
4.2. GO Similarity
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
 Szklarczyk, D.; Franceschini, A.; Wyder, S.; Forslund, K.; Heller, D.; HuertaCepas, J.; Simonovic, M.; Roth, A.; Santos, A.; Tsafou, K.P.; et al. STRING v10: Proteinprotein interaction networks, integrated over the tree of life. Nucleic Acids Res. 2015, 43. [Google Scholar] [CrossRef] [PubMed]
 Sharan, R.; Ideker, T. Modeling cellular machinery through biological network comparison. Nat. Biotechnol. 2006, 24, 427–433. [Google Scholar] [CrossRef] [PubMed]
 Kanehisa, M.; Goto, S.; Hattori, M.; AokiKinoshita, K.F.; Itoh, M.; Kawashima, S.; Katayama, T.; Araki, M.; Hirakawa, M. From genomics to chemical genomics: New developments in KEGG. Nucleic Acids Res. 2006, 34. [Google Scholar] [CrossRef] [PubMed]
 Alon, U. Network motifs: Theory and experimental approaches. Nat. Rev. Genet. 2007, 8, 450–461. [Google Scholar] [CrossRef] [PubMed]
 Elmsallati, A.; Clark, C.; Kalita, J. Global alignment of proteinprotein interaction networks: A survey. IEEE/ACM Trans. Comput. Biol. Bioinf. 2015, 99. [Google Scholar] [CrossRef] [PubMed]
 Singh, R.; Xu, J.; Berger, B. Global alignment of multiple protein interaction networks with application to functional orthology detection. Proc. Natl. Acad. Sci. USA 2008, 105, 12763–12768. [Google Scholar] [CrossRef] [PubMed]
 Klau, G.W. A new graphbased method for pairwise global network alignment. BMC Bioinf. 2009, 10. [Google Scholar] [CrossRef] [PubMed]
 Kuchaiev, O.; Milenkovic, T.; Memisevic, V.; Hayes, W.; Przulj, N. Topological network alignment uncovers biological function and phylogeny. J. R. Soc. Interface 2010, 7, 1341–54. [Google Scholar] [CrossRef] [PubMed]
 Patro, R.; Kingsford, C. Global network alignment using multiscale spectral signatures. Bioinformatics 2012, 28, 3105–3114. [Google Scholar] [CrossRef] [PubMed]
 Neyshabur, B.; Khadem, A.; Hashemifar, S.; Arab, S.S. NETAL: A new graphbased method for global alignment of proteinprotein interaction networks. Bioinformatics 2013, 29, 1654–1662. [Google Scholar] [CrossRef] [PubMed]
 Aladağ, A.E.; Erten, C. SPINAL: Scalable protein interaction network alignment. Bioinformatics 2013, 29, 917–924. [Google Scholar] [CrossRef] [PubMed]
 Chindelevitch, L.; Ma, C.Y.; Liao, C.S.; Berger, B. Optimizing a global alignment of protein interaction networks. Bioinformatics 2013, 29, 2765–2773. [Google Scholar] [CrossRef] [PubMed]
 Hashemifar, S.; Xu, J. HubAlign: An accurate and efficient method for global alignment of proteinprotein interaction networks. Bioinformatics 2014, 30, i438–i444. [Google Scholar] [CrossRef] [PubMed]
 Vijayan, V.; Saraph, V.; Milenković, T. MAGNA++: Maximizing accuracy in global network alignment via both node and edge conservation. Bioinformatics 2015, 31. [Google Scholar] [CrossRef] [PubMed]
 Clark, C.; Kalita, J. A multiobjective memetic algorithm for PPI network alignment. Bioinformatics 2015, 31, 1988–1998. [Google Scholar] [CrossRef] [PubMed]
 MalodDognin, N.; Przulj, N. LGRAAL: Lagrangian graphletbased network aligner. Bioinformatics 2015, 31, 2182–2189. [Google Scholar] [CrossRef] [PubMed]
 Natalie 2.0. Available online: http://software.cwi.nl/natalie (accessed on 15 November 2015).
 ElKebir, M.; Brandt, B.W.; Heringa, J.; Klau, G.W. NatalieQ: A web server for proteinprotein interaction network querying. BMC Syst. Biol. 2014, 8. [Google Scholar] [CrossRef] [PubMed]
 NatalieQ. Available online: http://www.ibi.vu.nl/programs/natalieq/ (accessed on 15 November 2015).
 Karp, R.M. Reducibility Among Combinatorial Problems. In Complexity of Computer Computations; Miller, R.E., Thatcher, J.W., Eds.; Plenum Press: New York, NY, USA, 1972; pp. 85–103. [Google Scholar]
 Lawler, E.L. The quadratic assignment problem. Manage Sci. 1963, 9, 586–599. [Google Scholar] [CrossRef]
 Adams, W.P.; Johnson, T. Improved linear programmingbased lower bounds for the quadratic assignment problem. DIMACS Ser. Discr. Math. Theor. Comput. Sci. 1994, 16, 43–77. [Google Scholar]
 Kuhn, H.W. The Hungarian method for the assignment problem. Naval Res. Logist. Q. 1955, 2, 83–97. [Google Scholar] [CrossRef]
 Munkres, J. Algorithms for the assignment and transportation problems. SIAM J. Appl. Math. 1957, 5, 32–38. [Google Scholar] [CrossRef]
 Edmonds, J.; Karp, R.M. Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 1972, 19, 248–264. [Google Scholar] [CrossRef]
 Edmonds, J. Path, trees, and flowers. Can. J Math 1965, 17, 449–467. [Google Scholar] [CrossRef]
 Guignard, M. Lagrangean relaxation. Top 2003, 11, 151–200. [Google Scholar] [CrossRef]
 Held, M.; Karp, R.M. The travelingsalesman problem and minimum spanning trees: Part II. Math. Progr. 1971, 1, 6–25. [Google Scholar] [CrossRef]
 Caprara, A.; Fischetti, M.; Toth, P. A heuristic method for the set cover problem. Oper. Res. 1999, 47, 730–743. [Google Scholar] [CrossRef]
 Egerváry Research Group on Combinatorial Optimization. LEMON Graph Library. Available online: http://lemon.cs.elte.hu/ (accessed on 15 November 2015).
 Ashburner, M.; Ball, C.A.; Blake, J.A.; Botstein, D.; Butler1, H.; Cherry, J. M.; Davis, A.P.; Dolinski, K.; Dwight, S.S.; Eppig, J.T.; et al. Gene Ontology: Tool for the unification of biology. Nat. Genet. 2000, 25, 25–29. [Google Scholar] [CrossRef] [PubMed]
 Couto, F.M.; Silva, M.J.; Coutinho, P.M. Measuring Semantic Similarity between Gene Ontology Terms. Data Knowl. Eng. 2007, 61, 137–152. [Google Scholar] [CrossRef]
 Wohlers, I.; Andonov, R.; Klau, G.W. Algorithm Engineering for optimal alignment of protein structure distance matrices. Optim. Lett. 2011, 5, 421–433. [Google Scholar] [CrossRef] [Green Version]
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ElKebir, M.; Heringa, J.; Klau, G.W. Natalie 2.0: Sparse Global Network Alignment as a Special Case of Quadratic Assignment. Algorithms 2015, 8, 10351051. https://doi.org/10.3390/a8041035
ElKebir M, Heringa J, Klau GW. Natalie 2.0: Sparse Global Network Alignment as a Special Case of Quadratic Assignment. Algorithms. 2015; 8(4):10351051. https://doi.org/10.3390/a8041035
Chicago/Turabian StyleElKebir, Mohammed, Jaap Heringa, and Gunnar W. Klau. 2015. "Natalie 2.0: Sparse Global Network Alignment as a Special Case of Quadratic Assignment" Algorithms 8, no. 4: 10351051. https://doi.org/10.3390/a8041035