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. 2016 Jun;42(3):339-50.
doi: 10.1007/s10867-016-9410-y. Epub 2016 Mar 24.

Thermodynamic Measures of Cancer: Gibbs Free Energy and Entropy of Protein-Protein Interactions

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Thermodynamic Measures of Cancer: Gibbs Free Energy and Entropy of Protein-Protein Interactions

Edward A Rietman et al. J Biol Phys. .
Free PMC article


Thermodynamics is an important driving factor for chemical processes and for life. Earlier work has shown that each cancer has its own molecular signaling network that supports its life cycle and that different cancers have different thermodynamic entropies characterizing their signaling networks. The respective thermodynamic entropies correlate with 5-year survival for each cancer. We now show that by overlaying mRNA transcription data from a specific tumor type onto a human protein-protein interaction network, we can derive the Gibbs free energy for the specific cancer. The Gibbs free energy correlates with 5-year survival (Pearson correlation of -0.7181, p value of 0.0294). Using an expression relating entropy and Gibbs free energy to enthalpy, we derive an empirical relation for cancer network enthalpy. Combining this with previously published results, we now show a complete set of extensive thermodynamic properties and cancer type with 5-year survival.

Keywords: 5-year survival; Cancer; Entropy; Gibbs free energy; Protein-protein interactions; Signaling networks.


Fig. 1
Fig. 1
An example of a small protein–protein interaction network created using Cytoscape®. The nodes (A–F) represent individual proteins, the lines, called edges, represent protein–protein interactions. No information about directionality of the interactions is implied. Protein D, for example, represents a protein connected to E, C, and F by its edges (or links). To compute the Gibbs free energy for node D in this network, we start with the normalized gene expression data as a surrogate for protein concentration of each node. Gibbs free energy for node D would be: normalized gene expression value divided by the sum of normalized expression of node D + the normalized gene expression values of the neighbors (E, F, C). This quotient becomes the argument for the natural logarithm. The coefficient of the natural logarithm is the normalized expression value for node D. All of this is summarized in (2)
Fig. 2
Fig. 2
Gibbs free energy and the probability of 5-year survival. Data from the TCGA gene list were overlaid on BioGRID® in order to merge protein–protein interaction network data with transcription data using Eq. (3). As evident, Gibbs free energy can be correlated with 5-year survival with an r coefficient of –0.72. We have excluded KIRC and KIRP because the biology of neuroectodermal and epithelial cancers differ from KIRC and KIRP. The inclusion of KIRC and KRIP in the calculation decreased correlation to –0.21

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