Abstract
Modules are common functional and structural properties of many social, technical and biological networks. Especially for biological systems it is important to understand how modularity is related to function and how modularity evolves. It is known that time-varying or spatially organized goals can lead to modularity in a simulated evolution of signaling networks. Here, we study a minimal model of material flow in networks. We discuss the relation between the shared use of nodes, i.e., the cooperativity of modules, and the orthogonality of a prescribed output pattern. We study the persistence of cooperativity through an evolution of robustness against local damages. We expect the results to be valid for a large class of flow-based biological and technical networks.
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M.E. Newman, Proc. Natl. Acad. Sci. USA 103, 8577 (2006)
R.P. Alexander, P.M. Kim, T. Emonet, M.B. Gerstein, Sci. Signal. 2, pe44 (2009)
L. Schulman, B. Gaveau, Bull. Sci. Math. 129, 631 (2005)
M. Rosvall, C.T. Bergstrom, Proc. Natl. Acad. Sci. USA 105, 1118 (2008)
A. Arenas, A. Diaz-Guilera, C. Perez-Vicente, Phys. Rev. Lett. 96, 114102 (2006)
C. Zhou, L. Zemanová, G. Zamora, C. Hilgetag, J. Kurths, Phys. Rev. Lett. 97, 238103 (2006)
M. Müller-Linow, C.C. Hilgetag, M.T. Hütt, PLoS Comput. Biol. 4, e1000190 (2008)
M.T. Hütt, A. Lesne, Front. Neuroinform. 3, 28 (2009)
L. Hartwell, J. Hopfield, S. Leibler, A. Murray, Nature 402, 47 (1999)
E.A. Variano, H. Lipson, Phys. Rev. Lett. 92, 188701 (2004)
N. Kashtan, U. Alon, Proc. Natl. Acad. Sci. USA 102, 13773 (2005)
N. Kashtan, E. Noor, U. Alon, Proc. Natl. Acad. Sci. USA 104, 13711 (2007)
N. Kashtan, M. Parter, E. Dekel, A.E. Mayo, U. Alon, Evolution 63, 1964 (2009)
C. Espinosa-Soto, A. Wagner, PLoS Comput. Biol. 6, e1000719 (2010)
G. Deco, V.K. Jirsa, A.R. Mcintosh, Nat. Rev. Neurosci. 12, 43 (2011)
P. Kaluza, A.S. Mikhailov, Europhys. Lett. 79, 48001 (2007)
P. Kaluza, M. Ipsen, M. Vingron, A. Mikhailov, Phys. Rev. E 75, 15101 (2007)
P. Kaluza, M. Vingron, A. Mikhailov, Chaos 18, 026113 (2008)
P. Kaluza, A.S. Mikhailov, Eur. Phys. J. B 85, 129 (2012)
K. Yan, G. Fang, N. Bhardwaj, R.P. Alexander, M. Gerstein, Proc. Natl. Acad. Sci. USA 107, 9186 (2010)
A. Kreimer, E. Borenstein, U. Gophna, E. Ruppin, Proc. Natl. Acad. Sci. 105, 6976 (2008)
M. Parter, N. Kashtan, U. Alon, BMC Evol. Biol. 7, 169 (2007)
E. Ravasz, A. Somera, D. Mongru, Z. Oltvai, A. Barabási, Science 297, 1551 (2002)
R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, S. Shen-Orr, I. Ayzenshtat, M. Sheffer, U. Alon, Science 303, 1538 (2004)
M.E. Beber, C. Fretter, S. Jain, N. Sonnenschein, M. Müller-Hannemann, M.T. Hütt, J. Roy. Soc. Interface 9, 3426 (2012)
C. Fretter, M. Müller-Hannemann, M.T. Hütt, Phys. Rev. E 85, 056119 (2012)
S. Fortunato, Phys. Rep. 486, 75 (2010)
E.A. Leicht, M.E.J. Newman, Phys. Rev. Lett. 100, 118703 (2008)
V.D. Blondel, J. Guillaume, R. Lambiotte, E. Lefebvre, J. Stat. Mech. 2008, P10008 (2008)
A. Lancichinetti, S. Fortunato, Phys. Rev. E 80, 056117 (2009)
O.S. Soyer, S. Bonhoeffer, Proc. Natl. Acad. Sci. USA 103, 16337 (2006)
R. Jothi, S. Balaji, A. Wuster, J. Grochow, J. Gsponer, T. Przytycka, L. Aravind, M. Babu, Mol. Syst. Biol. 5, 294 (2009)
J. Axelsen, S. Bernhardsson, K. Sneppen, BMC Syst. Biol. 2, 25 (2008)
E. Noor, E. Eden, R. Milo, U. Alon, Molecular Cell 39, 809 (2010)
N. Kashtan, E. Noor, U. Alon, Proc. Natl. Acad. Sci. USA 104, 13711 (2007)
I. Famili, J. Forster, J. Nielsen, B.Ø. Palsson, Proc. Natl. Acad. Sci. USA 100, 13134 (2003)
N.D. Price, J.L. Reed, B.Ø. Palsson, Nat. Rev. Microbiol. 2, 886 (2004)
J. Behre, T. Wilhelm, A. von Kamp, E. Ruppin, S. Schuster, J. Theor. Biol. 252, 433 (2008)
H. Nam, T.M. Conrad, N.E. Lewis, Curr. Opin. Biotechnol. 22, 595 (2011)
E. Borenstein, M. Kupiec, M.W. Feldman, E. Ruppin, Proc. Natl. Acad. Sci. USA 105, 14482 (2008)
Y.H. Eom, S. Lee, H. Jeong, J. Theor. Biol. 241, 823 (2006)
G. Basler, O. Ebenhöh, J. Selbig, Z. Nikoloski, Bioinformatics 27, 1397 (2011)
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Beber, M., Armbruster, D. & Hütt, MT. The prescribed output pattern regulates the modular structure of flow networks. Eur. Phys. J. B 86, 473 (2013). https://doi.org/10.1140/epjb/e2013-40672-3
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DOI: https://doi.org/10.1140/epjb/e2013-40672-3