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Network medicine provides network theoretical tools, methods and properties to study underlying laws governing human interactome to identify disease states and disease complexity leading to drug discovery. Within this framework, we investigated the topological properties of ovarian cancer network (OCN) and the roles of hubs to understand OCN organization to address disease states and complexity. The OCN constructed from the experimentally verified genes exhibits fractal nature in the topological properties with deeply rooted functional communities indicating self-organizing behavior. The network properties at all levels of organization obey one parameter scaling law which lacks centrality lethality rule. We showed that $\langle k\rangle $ can be taken as a scaling parameter, where, power law exponent can be estimated from the ratio of network diameters. The betweenness centrality $C_B$ shows two distinct behaviors one shown by high degree hubs and the other by segregated low degree nodes. The $C_B$ power law exponent is found to connect the exponents of distributions of high and low degree nodes. OCN showed the absence of rich-club formation which leads to the missing of a number of attractors in the network causing formation of weakly tied diverse functional modules to keep optimal network efficiency. In OCN, provincial and connector hubs, which includes identified key regulators, take major responsibility to keep the OCN integrity and organization. Further, most of the key regulators are found to be over expressed and positively correlated with immune infiltrates. Finally, few potential drugs are identified related to the key regulators., (© The Author(s) 2022. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Background: Identification of key regulator/s in ovarian cancer (OC) network is important for potential drug target and prevention from this cancer. This study proposes a method to identify the key regulators of this network and their importance., Methods: The protein-protein interaction (PPI) network of ovarian cancer (OC) is constructed from curated 6 hundred genes from standard six important ovarian cancer databases (some of the genes are experimentally verified). We proposed a method to identify key regulators (KRs) from the complex ovarian cancer network based on the tracing of backbone hubs, which participate at all levels of organization, characterized by Newmann-Grivan community finding method. Knockout experiment, constant Potts model and survival analysis are done to characterize the importance of the key regulators in regulating the network., Results: The PPI network of ovarian cancer is found to obey hierarchical scale free features organized by topology of heterogeneous modules coordinated by diverse leading hubs. The network and modular structures are devised by fractal rules with the absence of centrality-lethality rule, to enhance the efficiency of signal processing in the network and constituting loosely connected modules. Within the framework of network theory, we device a method to identify few key regulators (KRs) from a huge number of leading hubs, that are deeply rooted in the network, serve as backbones of it and key regulators from grassroots level to complete network structure. Using this method we could able to identify five key regulators, namely, AKT1, KRAS, EPCAM, CD44 and MCAM, out of which AKT1 plays central role in two ways, first it serves as main regulator of ovarian cancer network and second serves as key cross-talk agent of other key regulators, but exhibits disassortive property. The regulating capability of AKT1 is found to be highest and that of MCAM is lowest., Conclusions: The popularities of these key hubs change in an unpredictable way at different levels of organization and absence of these hubs cause massive amount of wiring energy/rewiring energy that propagate over all the network. The network compactness is found to increase as one goes from top level to bottom level of the network organization.

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., Competing Interests: The authors have declared that no competing interests exist.

The mutifractal and long range correlation (C(r)) properties of strings, such as nucleotide sequence can be a useful parameter for identification of underlying patterns and variations. In this study C(r) and multifractal singularity function f(α) have been used to study variations in the genomes of a pathogenic bacteria Mycobacterium tuberculosis. Genomic sequences of M. tuberculosis isolates displayed significant variations in C(r) and f(α) reflecting inherent differences in sequences among isolates. M. tuberculosis isolates can be categorised into different subgroups based on sensitivity to drugs, these are DS (drug sensitive isolates), MDR (multi-drug resistant isolates) and XDR (extremely drug resistant isolates). C(r) follows significantly different scaling rules in different subgroups of isolates, but all the isolates follow one parameter scaling law. The richness in complexity of each subgroup can be quantified by the measures of multifractal parameters displaying a pattern in which XDR isolates have highest value and lowest for drug sensitive isolates. Therefore C(r) and multifractal functions can be useful parameters for analysis of genomic sequences.