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A clustering based mate selection for evolutionary optimization
A comparative study of robustness measures for cancer signaling networks
1. | Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi'an 710071, China |
2. | School of Computer Science, University of Birmingham, Birmingham, U.K |
Network robustness stands for the capability of networks in resisting failures or attacks. Many robustness measures have been proposed to evaluate the robustness of various types of networks, such as small-world and scale-free networks. However, the robustness of biological networks is different for their special structures related to the unique functionality. Cancer signaling networks which show the information transformation of cancers in molecular level always appear with robust complex structures which mean information exchange in the networks do not depend on skimp pathways in which resulting the low rate of cure, high rate of recurrence and especially, the short time in survivability caused by constantly destruction of cancer. So a network metric that shows significant changes when one node is removed, and further to correlate that metric with survival probabilities for patients who underwent cancer chemotherapy is meaningful. Therefore, in this paper, the relationship between 14 typical cancer signaling networks robustness and those cancers patient survivability are studied. Several widely used robustness measures are included, and we find that the natural connectivity, in which the redundant circles are satisfied with the need of information exchange of cancer signaling networks, is negatively correlated to cancer patient survivability. Furthermore, the top three affected nodes measured by natural connectivity are obtained and the analysis on these nodes degree, closeness centrality and betweenness centrality are followed. The result shows that the node found are important so we believe that natural connectivity will be a great help to cancer treatment.
References:
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R. Albert, H. Jeong and A. -L. Barabási,
Error and attack tolerance of complex networks, Nature, 406 (2000), 378-382.
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M. Andrec, B. N. Kholodenko, R. M. Levy and E. Sontag,
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On variants of shortest-path betweenness centrality and their generic computation, Social Networks, 30 (2008), 136-145.
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D. S. Callaway, M. E. J. Newman, S. H. Strogatz and D. J. Watts,
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R. Cohen, K. Erez, D. Ben-Avraham and S. Havlin,
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R. Cohen, K. Erez, D. Ben-Avraham and S. Havlin,
Breakdown of the Internet under intentional attack, Physical Review L, 86 (2001), 3682-3685.
doi: 10.1103/PhysRevLett.86.3682. |
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C. Dong and K. Hemminki,
Multiple primary cancers of the colon, breast and skin (melanoma) as models for polygenic cancers, International Journal of Cancer, 92 (2001), 883-887.
doi: 10.1002/ijc.1261. |
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E. J. Edelman, J. Guinney, J.-T. Chi, P. G. Febbo and S. Mukherjee,
Modeling cancer progression via pathway dependencies, PLoS Comput Biol, 4 (2008), e28.
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E. Estrada, D. J. Higham and N. Hatano,
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J. D. Feala, J. Cortes, P. M. Duxbury, C. Piermarocchi, A. D. McCulloch and G. Paternostro,
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M. Fiedler,
Algebraic connectivity of graphs, Czechoslovak Mathematical Journal, 23 (1973), 298-305.
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[15] |
H. Frank and I. T. Frisch,
Analysis and design of survivable networks, IEEE Transactions on Communication Technology, 18 (1970), 501-519.
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P. Hage and F. Harary,
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G. Paul, S. Sreenivasan and H. E. Stanley,
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doi: 10.1103/PhysRevE.72.056130. |
[22] |
C. A. Penfold, V. Buchanan-Wollaston, K. J. Denby and D. L. Wild,
Nonparametric bayesian inference for perturbed and orthologous gene regulatory networks, Bioinformatics, 28 (2012), i233-i241.
doi: 10.1093/bioinformatics/bts222. |
[23] |
C. M. Schneider, A. A. Moreira, J. S. Andrade, S. Havlin and H. J. Herrmann,
Mitigation of malicious attacks on networks, Proc. Natl. Acad. Sci. U.S.A., 108 (2011), 3838-3841.
doi: 10.1073/pnas.1009440108. |
[24] |
B. Shargel, H. Sayama, I. R. Epstein and Y. Bar-Yam,
Optimization of robustness and connectivity in complex networks, Physical Review L, 90 (2003), 068701.
doi: 10.1103/PhysRevLett.90.068701. |
[25] |
C. Sonnenschein and A. M. Soto,
Theories of carcinogenesis: an emerging per-275 spective, in: Seminars in cancer biology, Seminars in Cancer Biology, 18 (2008), 372-377.
|
[26] |
K. Takemoto and K. Kihara,
Modular organization of cancer signaling networks is associated with patient survivability, Biosystems, 113 (2013), 149-154.
doi: 10.1016/j.biosystems.2013.06.003. |
[27] |
J. Wu, M. Barahona, Y.-J. Tan and H.-Z. Deng,
Spectral measure of structural robustness in complex networks, IEEE Transactions on Syst. Man Cybern. A Syst. and Humans, 41 (2015), 1244-1252.
doi: 10.1109/TSMCA.2011.2116117. |
[28] |
M. A. Yildirim, K.-I. Goh, M. E. Cusick, A.-L. Barabási and M. Vidal,
Drug-target network, Nature Biotechnology, 25 (2007), 1119-1126.
|
[29] |
A. Zeng and W. Liu,
Enhancing network robustness against malicious attacks, Physical Review E, 85 (2012), 066130.
doi: 10.1103/PhysRevE.85.066130. |
show all references
References:
[1] |
R. Albert, H. Jeong and A. -L. Barabási,
Error and attack tolerance of complex networks, Nature, 406 (2000), 378-382.
doi: 10.1038/35019019. |
[2] |
M. Andrec, B. N. Kholodenko, R. M. Levy and E. Sontag,
Inference of signalingand gene regulatory networks by steady-state perturbation experiments: Structure and accuracy, Journal of Theoretical Biology, 232 (2005), 427-441.
doi: 10.1016/j.jtbi.2004.08.022. |
[3] |
D. Bauer, F. Boesch, C. Suffel and R. Tindell, Connectivity extremal problems and the design of reliable probabilistic networks, The Theory and Application of Graphs, Wiley, New York, (1981), 45–54. |
[4] |
P. Bonacich,
Some unique properties of eigenvector centrality, Social Networks, 29 (2007), 555-564.
doi: 10.1016/j.socnet.2007.04.002. |
[5] |
U. Brandes,
On variants of shortest-path betweenness centrality and their generic computation, Social Networks, 30 (2008), 136-145.
|
[6] |
D. Breitkreutz, L. Hlatky, E. Rietman and J. A. Tuszynski,
Molecular signalingnetwork complexity is correlated with cancer patient survivability, Proceedings of the National Academy of Sciences, 109 (2012), 9209-9212.
|
[7] |
D. S. Callaway, M. E. J. Newman, S. H. Strogatz and D. J. Watts,
Network robustness and fragility: Percolation on random graphs, Physical Review L, 85 (2000), 5468-5471.
doi: 10.1103/PhysRevLett.85.5468. |
[8] |
R. Cohen, K. Erez, D. Ben-Avraham and S. Havlin,
Resilience of the Internet to random breakdowns, Physical Review L, 85 (2000), 4626-4628.
doi: 10.1103/PhysRevLett.85.4626. |
[9] |
R. Cohen, K. Erez, D. Ben-Avraham and S. Havlin,
Breakdown of the Internet under intentional attack, Physical Review L, 86 (2001), 3682-3685.
doi: 10.1103/PhysRevLett.86.3682. |
[10] |
C. Dong and K. Hemminki,
Multiple primary cancers of the colon, breast and skin (melanoma) as models for polygenic cancers, International Journal of Cancer, 92 (2001), 883-887.
doi: 10.1002/ijc.1261. |
[11] |
E. J. Edelman, J. Guinney, J.-T. Chi, P. G. Febbo and S. Mukherjee,
Modeling cancer progression via pathway dependencies, PLoS Comput Biol, 4 (2008), e28.
doi: 10.1371/journal.pcbi.0040028. |
[12] |
E. Estrada, D. J. Higham and N. Hatano,
Communicability betweenness in 315 complex networks, Physica A: Statistical Mechanics and its Applications, 388 (2009), 764-774.
|
[13] |
J. D. Feala, J. Cortes, P. M. Duxbury, C. Piermarocchi, A. D. McCulloch and G. Paternostro,
Systems approaches and algorithms for discovery of combinatorial therapies, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 2 (2010), 181-193.
doi: 10.1002/wsbm.51. |
[14] |
M. Fiedler,
Algebraic connectivity of graphs, Czechoslovak Mathematical Journal, 23 (1973), 298-305.
|
[15] |
H. Frank and I. T. Frisch,
Analysis and design of survivable networks, IEEE Transactions on Communication Technology, 18 (1970), 501-519.
|
[16] |
P. Hage and F. Harary,
Eccentricity and centrality in networks, Social Networks, 17 (1995), 57-63.
doi: 10.1016/0378-8733(94)00248-9. |
[17] |
F. Harary,
Conditional connectivity, Networks, 13 (1983), 347-357.
doi: 10.1002/net.3230130303. |
[18] |
V. H. Louzada, F. Daolio, H. J. Herrmann and M. Tomassini,
Generating robust and efficient networks under targeted attacks, Propagation Phenomena in Real World Networks, 85 (2015), 215-244.
doi: 10.1007/978-3-319-15916-4_9. |
[19] |
R. Merris,
Laplacian matrices of graphs: A survey, Linear Algebra and its Applications, 197 (1994), 143-176.
doi: 10.1016/0024-3795(94)90486-3. |
[20] |
J. C. Nacher and J.-M. Schwartz,
A global view of drug-therapy interactions, BMC pharmacology, 8 (2008), 5pp.
doi: 10.1186/1471-2210-8-5. |
[21] |
G. Paul, S. Sreenivasan and H. E. Stanley,
Resilience of complex networks to random breakdown, Physical Review E, 72 (2005), 056130, 6pp.
doi: 10.1103/PhysRevE.72.056130. |
[22] |
C. A. Penfold, V. Buchanan-Wollaston, K. J. Denby and D. L. Wild,
Nonparametric bayesian inference for perturbed and orthologous gene regulatory networks, Bioinformatics, 28 (2012), i233-i241.
doi: 10.1093/bioinformatics/bts222. |
[23] |
C. M. Schneider, A. A. Moreira, J. S. Andrade, S. Havlin and H. J. Herrmann,
Mitigation of malicious attacks on networks, Proc. Natl. Acad. Sci. U.S.A., 108 (2011), 3838-3841.
doi: 10.1073/pnas.1009440108. |
[24] |
B. Shargel, H. Sayama, I. R. Epstein and Y. Bar-Yam,
Optimization of robustness and connectivity in complex networks, Physical Review L, 90 (2003), 068701.
doi: 10.1103/PhysRevLett.90.068701. |
[25] |
C. Sonnenschein and A. M. Soto,
Theories of carcinogenesis: an emerging per-275 spective, in: Seminars in cancer biology, Seminars in Cancer Biology, 18 (2008), 372-377.
|
[26] |
K. Takemoto and K. Kihara,
Modular organization of cancer signaling networks is associated with patient survivability, Biosystems, 113 (2013), 149-154.
doi: 10.1016/j.biosystems.2013.06.003. |
[27] |
J. Wu, M. Barahona, Y.-J. Tan and H.-Z. Deng,
Spectral measure of structural robustness in complex networks, IEEE Transactions on Syst. Man Cybern. A Syst. and Humans, 41 (2015), 1244-1252.
doi: 10.1109/TSMCA.2011.2116117. |
[28] |
M. A. Yildirim, K.-I. Goh, M. E. Cusick, A.-L. Barabási and M. Vidal,
Drug-target network, Nature Biotechnology, 25 (2007), 1119-1126.
|
[29] |
A. Zeng and W. Liu,
Enhancing network robustness against malicious attacks, Physical Review E, 85 (2012), 066130.
doi: 10.1103/PhysRevE.85.066130. |
Cancer site | 5-y survival probability | CSN-EG | CSN-GO | ||
Nodes | Edges | Nodes | Edges | ||
Acute myeloid leukemia | 23.6% | 57 | 152 | 32 | 39 |
Basal cell carcinoma | 91.4% | 47 | 304 | 13 | 11 |
Bladder cancer | 78.1% | 29 | 46 | 21 | 19 |
Chronic myeloid leukemia | 55.2% | 73 | 185 | 44 | 47 |
Colorectal cancer | 63.6% | 49 | 104 | 34 | 33 |
Endometrial cancer | 68.6% | 46 | 88 | 24 | 23 |
Glioma | 33.4% | 69 | 209 | 55 | 61 |
Melanoma | 91.2% | 70 | 282 | 22 | 23 |
Nonsmall-cell lung cancer | 18.0% | 73 | 183 | 36 | 43 |
Pancreatic cancer | 5.5% | 67 | 134 | 43 | 43 |
Prostate cancer | 99.4% | 99 | 333 | 40 | 45 |
Renal cell carcinoma | 69.5% | 57 | 104 | 36 | 33 |
Small cell lung cancer | 6.2% | 86 | 238 | 31 | 37 |
Thyroid cancer | 97.2% | 28 | 49 | 18 | 14 |
Cancer site | 5-y survival probability | CSN-EG | CSN-GO | ||
Nodes | Edges | Nodes | Edges | ||
Acute myeloid leukemia | 23.6% | 57 | 152 | 32 | 39 |
Basal cell carcinoma | 91.4% | 47 | 304 | 13 | 11 |
Bladder cancer | 78.1% | 29 | 46 | 21 | 19 |
Chronic myeloid leukemia | 55.2% | 73 | 185 | 44 | 47 |
Colorectal cancer | 63.6% | 49 | 104 | 34 | 33 |
Endometrial cancer | 68.6% | 46 | 88 | 24 | 23 |
Glioma | 33.4% | 69 | 209 | 55 | 61 |
Melanoma | 91.2% | 70 | 282 | 22 | 23 |
Nonsmall-cell lung cancer | 18.0% | 73 | 183 | 36 | 43 |
Pancreatic cancer | 5.5% | 67 | 134 | 43 | 43 |
Prostate cancer | 99.4% | 99 | 333 | 40 | 45 |
Renal cell carcinoma | 69.5% | 57 | 104 | 36 | 33 |
Small cell lung cancer | 6.2% | 86 | 238 | 31 | 37 |
Thyroid cancer | 97.2% | 28 | 49 | 18 | 14 |
CSN |
||||||
CSN-EG | 0.31 | 0.28 | -0.11 | 0.34 | 0.049 | 0.24 |
CSN-GO | 0.18 | 0.17 | -0.56 | 0.36 | 0.21 | -0.60 |
CSN |
||||||
CSN-EG | 0.31 | 0.28 | -0.11 | 0.34 | 0.049 | 0.24 |
CSN-GO | 0.18 | 0.17 | -0.56 | 0.36 | 0.21 | -0.60 |
Network parameters | H | Q | λ |
γ | -0.62 | -0.21 | -0.60 |
Network parameters | H | Q | λ |
γ | -0.62 | -0.21 | -0.60 |
Cancer site | Degree | Closeness | Betweenness | |
Acute myeloid leukemia | Top 1 | 6.00 | 14.92 | 545.00 |
Top 2 | 7.00 | 12.55 | 269.83 | |
Top 3 | 5.00 | 14.45 | 500.17 | |
Average | 2.43 | 10.17 | 98.00 | |
Basal cell carcinoma | Top 1 | 5.00 | 6.45 | 60.00 |
Top 2 | 2.00 | 5.28 | 50.00 | |
Top 3 | 2.00 | 4.92 | 48.00 | |
Average | 1.82 | 4.46 | 22.73 | |
Bladder cancer | Top 1 | 3.00 | 5.17 | 38.00 |
Top 2 | 3.00 | 4.83 | 26.00 | |
Top 3 | 3.00 | 4.67 | 26.00 | |
Average | 1.78 | 3.99 | 13.33 | |
Chronic myeloid leukemia | Top 1 | 7.00 | 12.38 | 217.00 |
Top 2 | 5.00 | 12.09 | 303.00 | |
Top 3 | 5.00 | 11.67 | 318.00 | |
Average | 2.15 | 8.44 | 78.85 | |
Colorectal cancer | Top 1 | 5.00 | 8.59 | 188.00 |
Top 2 | 4.00 | 7.71 | 147.00 | |
Top 3 | 4.00 | 8.74 | 274.00 | |
Average | 2.09 | 6.73 | 91.39 | |
Endometrial cancer | Top 1 | 5.00 | 7.30 | 85.00 |
Top 2 | 3.00 | 6.88 | 121.00 | |
Top 3 | 3.00 | 6.88 | 142.00 | |
Average | 2.00 | 5.62 | 57.65 | |
Glioma | Top 1 | 5.00 | 9.70 | 78.00 |
Top 2 | 4.00 | 10.25 | 141.17 | |
Top 3 | 4.00 | 9.15 | 36.17 | |
Average | 2.42 | 7.61 | 36.74 |
Cancer site | Degree | Closeness | Betweenness | |
Acute myeloid leukemia | Top 1 | 6.00 | 14.92 | 545.00 |
Top 2 | 7.00 | 12.55 | 269.83 | |
Top 3 | 5.00 | 14.45 | 500.17 | |
Average | 2.43 | 10.17 | 98.00 | |
Basal cell carcinoma | Top 1 | 5.00 | 6.45 | 60.00 |
Top 2 | 2.00 | 5.28 | 50.00 | |
Top 3 | 2.00 | 4.92 | 48.00 | |
Average | 1.82 | 4.46 | 22.73 | |
Bladder cancer | Top 1 | 3.00 | 5.17 | 38.00 |
Top 2 | 3.00 | 4.83 | 26.00 | |
Top 3 | 3.00 | 4.67 | 26.00 | |
Average | 1.78 | 3.99 | 13.33 | |
Chronic myeloid leukemia | Top 1 | 7.00 | 12.38 | 217.00 |
Top 2 | 5.00 | 12.09 | 303.00 | |
Top 3 | 5.00 | 11.67 | 318.00 | |
Average | 2.15 | 8.44 | 78.85 | |
Colorectal cancer | Top 1 | 5.00 | 8.59 | 188.00 |
Top 2 | 4.00 | 7.71 | 147.00 | |
Top 3 | 4.00 | 8.74 | 274.00 | |
Average | 2.09 | 6.73 | 91.39 | |
Endometrial cancer | Top 1 | 5.00 | 7.30 | 85.00 |
Top 2 | 3.00 | 6.88 | 121.00 | |
Top 3 | 3.00 | 6.88 | 142.00 | |
Average | 2.00 | 5.62 | 57.65 | |
Glioma | Top 1 | 5.00 | 9.70 | 78.00 |
Top 2 | 4.00 | 10.25 | 141.17 | |
Top 3 | 4.00 | 9.15 | 36.17 | |
Average | 2.42 | 7.61 | 36.74 |
Cancer site | Degree | Closeness | Betweenness | |
Melanoma | Top 1 | 3.00 | 6.58 | 73.00 |
Top 2 | 3.00 | 6.50 | 58.00 | |
Top 3 | 3.00 | 6.06 | 43.00 | |
Average | 2.00 | 5.15 | 26.77 | |
Nonsmall-cell lung cancer | Top 1 | 5.00 | 12.45 | 346.73 |
Top 2 | 5.00 | 11.42 | 91.67 | |
Top 3 | 5.00 | 11.42 | 91.67 | |
Average | 2.45 | 9.25 | 110.19 | |
Pancreatic cancer | Top 1 | 5.00 | 6.95 | 45.00 |
Top 2 | 4.00 | 6.78 | 61.00 | |
Top 2 | 3.00 | 5.95 | 7.00 | |
Average | 2.33 | 5.24 | 22.17 | |
Prostate cancer | Top 1 | 12.00 | 18.07 | 850.67 |
Top 2 | 3.00 | 13.16 | 546.00 | |
Top 3 | 4.00 | 8.33 | 93.00 | |
Average | 2.29 | 9.92 | 156.29 | |
Renal cell carcinoma | Top 1 | 5.00 | 9.08 | 160.00 |
Top 2 | 3.00 | 7.20 | 28.00 | |
Top 3 | 3.00 | 7.20 | 28.00 | |
Average | 2.00 | 6.06 | 34.38 | |
Small cell lung cancer | Top 1 | 7.00 | 8.75 | 126.00 |
Top 2 | 3.00 | 5.78 | 67.00 | |
Top 3 | 2.00 | 6.65 | 98.00 | |
Average | 2.00 | 5.65 | 38.80 | |
Thyroid cancer | Top 1 | 3.00 | 4.17 | 18.00 |
Top 2 | 3.00 | 4.17 | 18.00 | |
Top 3 | 2.00 | 4.00 | 18.00 | |
Average | 1.71 | 3.38 | 7.71 |
Cancer site | Degree | Closeness | Betweenness | |
Melanoma | Top 1 | 3.00 | 6.58 | 73.00 |
Top 2 | 3.00 | 6.50 | 58.00 | |
Top 3 | 3.00 | 6.06 | 43.00 | |
Average | 2.00 | 5.15 | 26.77 | |
Nonsmall-cell lung cancer | Top 1 | 5.00 | 12.45 | 346.73 |
Top 2 | 5.00 | 11.42 | 91.67 | |
Top 3 | 5.00 | 11.42 | 91.67 | |
Average | 2.45 | 9.25 | 110.19 | |
Pancreatic cancer | Top 1 | 5.00 | 6.95 | 45.00 |
Top 2 | 4.00 | 6.78 | 61.00 | |
Top 2 | 3.00 | 5.95 | 7.00 | |
Average | 2.33 | 5.24 | 22.17 | |
Prostate cancer | Top 1 | 12.00 | 18.07 | 850.67 |
Top 2 | 3.00 | 13.16 | 546.00 | |
Top 3 | 4.00 | 8.33 | 93.00 | |
Average | 2.29 | 9.92 | 156.29 | |
Renal cell carcinoma | Top 1 | 5.00 | 9.08 | 160.00 |
Top 2 | 3.00 | 7.20 | 28.00 | |
Top 3 | 3.00 | 7.20 | 28.00 | |
Average | 2.00 | 6.06 | 34.38 | |
Small cell lung cancer | Top 1 | 7.00 | 8.75 | 126.00 |
Top 2 | 3.00 | 5.78 | 67.00 | |
Top 3 | 2.00 | 6.65 | 98.00 | |
Average | 2.00 | 5.65 | 38.80 | |
Thyroid cancer | Top 1 | 3.00 | 4.17 | 18.00 |
Top 2 | 3.00 | 4.17 | 18.00 | |
Top 3 | 2.00 | 4.00 | 18.00 | |
Average | 1.71 | 3.38 | 7.71 |
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