Tumor dormancy is a highly prevalent stage in cancer progression. We have previously generated and characterized in vivo experimental models of human tumor dormancy in which micro-tumors remain occult until they spontaneously shift into rapid tumor growth. We showed that the dormant micro-tumors undergo a stable microRNA (miRNA) switch during their transition from dormancy to a fast-growing phenotype and reported the identification of a consensus signature of human tumor dormancy-associated miRNAs (DmiRs). miRNA-190 (miR-190) is among the most upregulated DmiRs in all dormant tumors analyzed. Upregulation of miR-190 led to prolonged tumor dormancy in otherwise fast-growing glioblastomas and osteosarcomas. Here we investigate the transcriptional changes induced by miR-190 expression in cancer cells and show similar patterns of miR-190 mediated transcriptional reprogramming in both glioblastoma and osteosarcoma cells. The data suggests that miR-190 mediated effects rely on an extensive network of molecular changes in tumor cells and that miR-190 affects several transcriptional factors, tumor suppressor genes and interferon response pathways. The molecular mechanisms governing tumor dormancy described in this work may provide promising targets for early prevention of cancer and may lead to novel treatments to convert the malignant tumor phenotype into an asymptomatic dormant state.

In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome.With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of aC₆network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.

Protein-protein interaction networks associated with diseases have gained prominence as an area of research. We investigate algebraic and topological indices for protein-protein interaction networks of 11 human cancers derived from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a strong correlation between relative automorphism group sizes and topological network complexities on the one hand and five year survival probabilities on the other hand. Moreover, we identify several protein families (e.g. PIK, ITG, AKT families) that are repeated motifs in many of the cancer pathways. Interestingly, these sources of symmetry are often central rather than peripheral. Our results can aide in identification of promising targets for anti-cancer drugs. Beyond that, we provide a unifying framework to study protein-protein interaction networks of families of related diseases (e.g. neurodegenerative diseases, viral diseases, substance abuse disorders).

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions.

The sequential changes occurring with cancer progression are now being harnessed with therapeutic intent. Yet, there is no understanding of the chemical thermodynamics of proteomic changes associated with cancer progression/cancer stage. This manuscript reveals a strong correlation of a chemical thermodynamic measure (known as Gibbs free energy) of protein-protein interaction networks for several cancer types and 5-year overall survival and stage in patients with cancer. Earlier studies have linked degree entropy of signaling networks to patient survival data, but not with stage. It appears that Gibbs free energy is a more general metric and accounts better for the underlying energetic landscape of protein expression in cells, thus correlating with stage as well as survival. This is an especially timely finding because of improved ability to obtain and analyze genomic/proteomic information from individual patients. Yet, at least at present, only candidate gene imaging (FISH or immunohistochemistry) can be used for entropy computations. With continually expanding use of genomic information in clinical medicine, there is an ever-increasing need to understand the thermodynamics of protein-protein interaction networks.