Signaling Complexity Measured by Shannon Entropy and Its Application in Personalized Medicine

Abstract

Traditional approaches to cancer therapy seek common molecular targets in tumors from different patients. However, molecular profiles differ between patients, and most tumors exhibit inherent heterogeneity. Hence, imprecise targeting commonly results in side effects, reduced efficacy, and drug resistance. By contrast, personalized medicine aims to establish a molecular diagnosis specific to each patient, which is currently feasible due to the progress achieved with high-throughput technologies. In this report, we explored data from human RNA-seq and protein–protein interaction (PPI) networks using bioinformatics to investigate the relationship between tumor entropy and aggressiveness. To compare PPI subnetworks of different sizes, we calculated the Shannon entropy associated with vertex connections of differentially expressed genes comparing tumor samples with their paired control tissues. We found that the inhibition of up-regulated connectivity hubs led to a higher reduction of subnetwork entropy compared to that obtained with the inhibition of targets selected at random. Furthermore, these hubs were described to be participating in tumor processes. We also found a significant negative correlation between subnetwork entropies of tumors and the respective 5-year survival rates of the corresponding cancer types. This correlation was also observed considering patients with lung squamous cell carcinoma (LUSC) and lung adenocarcinoma (LUAD) based on the clinical data from The Cancer Genome Atlas database (TCGA). Thus, network entropy increases in parallel with tumor aggressiveness but does not correlate with PPI subnetwork size. This correlation is consistent with previous reports and allowed us to assess the number of hubs to be inhibited for therapy to be effective, in the context of precision medicine, by reference to the 100% patient survival rate 5 years after diagnosis. Large standard deviations of subnetwork entropies and variations in target numbers per patient among tumor types characterize tumor heterogeneity.

Modeling Basins of Attraction for Breast Cancer Using Hopfield Networks

“…Higher entropy values are associated with aggressive tumor phenotypes. This correlation was found when comparing cancer and control cells, advanced and initial stages of tumor development, aggressive cancer types and good prognosis cancer types (Breitkreutz et al, 2012;Winterbach et al, 2013;Banerji et al, 2015;Conforte et al, 2019).…”

“…Specific target combinations were derived from the gene expression profile of each patient, with the potential to mitigate side effects and enhance the treatment outcome. Among the parameters tested to indicate gene priority, the node degree has been indicated as a key factor (Carels et al, 2015;Tilli et al, 2016;Conforte et al, 2019). Other topological measures of gene regulatory networks (GRNs) have also been widely used in the identification of new therapeutic targets (Peng and Schork, 2014;Azevedo and Moreira-Filho, 2015).…”

“…We obtained the clinical data of each patient from the TCGA data set in TCGA-GDC, accessed in June 2019 ( Supplementary Table 2), and appended data of molecular subtype, entropy, and overall survival. The molecular subtypes were defined according to the classification of The Cancer Genome Atlas Network (2012); the entropy values were obtained from Supplementary File 5 of Conforte et al (2019); the overall survival (OS) of each patient were determined based on the OS data available in Liu et al (2018). The OS data was analyzed with the Kaplan-Meier curve using GraphPad Prism software, where 1 is indicative of death, and 0 is indicative of censored data.…”

“…The difference among ED considering all samples and ED considering samples that converged to each attractor can be explained by the fact that five tumor samples converged to the control attractor, and because of that, were included in the ED measurement of the control basin of attraction. Interestingly, these samples were classified by (i) molecular subtypes with good prognosis (LumA or LumB); (ii) being in the initial stages of tumor development (stages i and iib); and (iii) most of them (A0BM, A0C3, A1EU, and A2FF) presenting the smallest entropies among patients ( Supplementary Table 2), which is associated with a low level of aggressiveness (Breitkreutz et al, 2012;Conforte et al, 2019). When comparing the clinical data with the EDs between the control attractor and the tumor samples that converged toward the tumor attractor, we found that the averages among the groups of tumor stages, molecular subtypes, and entropies were not significantly different when considering the non-parametric Kruskal-Wallis test.…”

“…Most one-size-fits-all medicine approach may cause harmful side effects due to low selectivity that might affect both tumor and healthy cells (Siegel et al, 2012). In contrast, personalized medicine considers the tumor of a patient as unique, and identifies genes differentially expressed in tumors in comparison to the surrounding tissue (stroma), which is used as a control (Carels et al, 2015;Conforte et al, 2019). For this reason, personalized medicine is expected to mitigate the side effects and improve treatment efficacy.…”