Exploring novel key regulators in breast cancer network

Abstract

The breast cancer network constructed from 70 experimentally verified genes is found to follow hierarchical scale free nature with heterogeneous modular organization and diverge leading hubs. The topological parameters (degree distributions, clustering co-efficient, connectivity and centralities) of this network obey fractal rules indicating absence of centrality lethality rule, and efficient communication among the components. From the network theoretical approach, we identified few key regulators out of large number of leading hubs, which are deeply rooted from top to down of the network, serve as backbone of the network, and possible target genes. However, p53, which is one of these key regulators, is found to be in low rank and keep itself at low profile but directly cross-talks with important genes BRCA2 and BRCA3. The popularity of these hubs gets changed in unpredictable way at various levels of organization thus showing disassortive nature. The local community paradigm approach in this network shows strong correlation of nodes in majority of modules/sub-modules (fast communication among nodes) and weak correlation of nodes only in few modules/sub-modules (slow communication among nodes) at various levels of network organization.

Fig 1. Work flow of breast cancer network construction from big data resources and method of finding key regulators from the constructed network with their analysis.

Fig 2

Showing the Degree distribution i.e P(k) vs. k graph, After Knock out experiment at 0, 10, 20, 30, 40, 50, 100 nodes removal and it is also fitted to the power law with exponent γ falling in range of Characteristic Heirarchial Networks i.e. (0 ≤ γ ≤ 2); Showing the Clustering Co-efficient i.e C(k) vs. k graph; After Knock out experiment at 0, 10, 20, 30, 40, 50, 100 nodes removal and it is also fitted to the power law with exponent α falling in range of Characteristic Heirarchial Networks i.e. (α ~ 1); Showing the Avg Neibourhood Connectivity i.e Cn(k) vs. k graph; After Knock out experiment at 0, 10, 20, 30, 40, 50, 100 nodes removal and it is also fitted to the power law with exponent β falling in range of Characteristic Heirarchial Networks i.e. (β ≤ 1), Showing the Betweeness Centrality, Closeness Centrality and Eigenvector Centrality i.e C_b, C_c and C_e vs. k graph respectively, After Knock out experiment at 0, 10, 20, 30, 40, 50, 100 nodes removal and it is also fitted to the power law with exponent ϵ, δ and μ in order.

Fig 3. System level organization of breast cancer network.

(a) Organization of modules/sub-modules at various levels (indicated by various concentric circles) and arrows show sub-modules constructed from previous modules. (b) Plots of modularity and LCP-correlation per node as a function of level of organization. (c) Popularity rankings of the first fifty leading hubs in the complete network: the plot also shows unpredictability of the these hubs at various levels of organization. Identification of key regulators of breast cancer network.

Fig 4. The structures of modules/sub-modules through which the first ten leading hubs passed through.

The probability distribution of the seven key regulators as a function og level of organization.

Fig 5. The modular path of p53 from complete network to motif with the structures of modules/sub-modules at various levels in which p53 is accommodated.

(a) The plots of LCP-correlation as a function of CN for each modules/submodules (plots corresponding to each module/sub-module of the network) of p53 path. (b) The plots of P_H and P_LCP as a function of level of organization.

Fig 6. Compactness of breast cancer network: LCP-correlation calculation as a function of CN for complete and first level modules when zero, five and fifty leading hubs are removed.

Fig 7

Compactness of breast cancer network: (a) LCP-correlation calculation as a function of CN for second and third level modules when zero, five and fifty leading hubs are removed. (b) Representation of modules/sub-modules based on the values of LCP-correlation values: modules with red color are for LCP − corr ≥ 0.8, and green color modules are for LCP − corr < 0.8.