A comparative study of robustness measures for cancer signaling networks

Mingxing Zhou; Jing Liu; Shuai Wang; Shan He

doi:10.3934/bdia.2017011

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2017, Volume 2, Issue 1: 87-96. Doi: 10.3934/bdia.2017011

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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

* Corresponding author: Jing Liu
* Corresponding author: Jing Liu

Published: December 2016

The corresponding author is supported by NSF grant 61522311,61773300,61528205 and 2017JZ017.

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Abstract

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.

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Mathematics Subject Classification: Primary: 37F20, 68U05; Secondary: 65Y20.

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Table 1. Cancer survival probabilities and network statistics for CSN-EG and CSN-CO

Cancer site	5-y survival probability	CSN-EG		CSN-GO
Cancer site	5-y survival probability	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

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Table 2. Pearsons correlation coefficient between CSN robustness and 5-year survival rate are showed

CSN $\setminus\gamma$	$R$	$R_l$	$p_c^r$	$p_c^t$	$a(G)$	$\bar\lambda$
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

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Table 3. Pearsons correlation coefficient between the network parameters of CSN-GO and 5-year survival rate is showed

Network parameters	H	Q	λ
γ	-0.62	-0.21	-0.60

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Table 4. Degree, closeness centrality and betweenness centrality of important nodes measured by natural connectivity for each cancer site part 1

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

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Table 5. Degree, closeness centrality and betweenness centrality of important nodes measured by natural connectivity for each cancer site part 2

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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