Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature

Multi-scale geometric network analysis identifies melanoma immunotherapy response gene modules

Melanoma response to immune-modulating therapy remains incompletely characterized at the molecular level. In this study, we assess melanoma immunotherapy response using a multi-scale network approach to identify gene modules with coordinated gene expression in response to treatment. Using gene expression data of melanoma before and after treatment with nivolumab, we modeled gene expression changes in a correlation network and measured a key network geometric property, dynamic Ollivier-Ricci curvature, to distinguish critical edges within the network and reveal multi-scale treatment-response gene communities. Analysis identified six distinct gene modules corresponding to sets of genes interacting in response to immunotherapy. One module alone, overlapping with the nuclear factor kappa-B pathway (NFkB), was associated with improved patient survival and a positive clinical response to immunotherapy. This analysis demonstrates the usefulness of dynamic Ollivier-Ricci curvature as a general method for identifying information-sharing gene modules in cancer.

Multi-Scale Geometric Network Analysis Identifies Melanoma Immunotherapy Response Gene Modules

Melanoma response to immune-modulating therapy remains incompletely characterized at the molecular level. In this study, we assess melanoma immunotherapy response using a multi-scale network approach to identify gene modules with coordinated gene expression in response to treatment. Using gene expression data of melanoma before and after treatment with nivolumab, we modeled gene expression changes in a correlation network and measured a key network geometric property, dynamic Ollivier-Ricci curvature, to distinguish critical edges within the network and reveal multi-scale treatment-response gene communities. Analysis identified six distinct gene modules corresponding to sets of genes interacting in response to immunotherapy. One module alone, overlapping with the nuclear factor kappa-B pathway (NFKB), was associated with improved patient survival and a positive clinical response to immunotherapy. This analysis demonstrates the usefulness of dynamic Ollivier-Ricci curvature as a general method for identifying information-sharing gene modules in cancer.

Theory for nanoscale curvature induced enhanced inactivation kinetics of SARS-CoV-2

We develop a novel theory for the nanomorphology dependent outer sphere heterogeneous electron transfer (ET) rate constant () based on an energy level alignment approach. is modelled through the activation free energy, which is a product of the water monolayer covered metal work function (WF) and the fractional electronic charge exchanged at the transition state (attained through the alignment of the metal Fermi and HOMO/LUMO energy levels of the electroactive species). The theory shows that is an exponentially increasing and decreasing function of the mean curvature in concave and convex nanomorphologies, respectively, for electroactive species or proteins involving their HOMO energy. For the specific spike protein of SARS-CoV-2, we have estimated the half lifetime (t_1/2) and degree of inactivation as a function of the metal WF, nanostructure mean curvature, spike protein HOMO energy, and the environmental temperature (T). By varying the metal from Ag to Au, t_1/2 is reduced from 7 h to 4 min, respectively. The reduction in the copper nanoparticle size from 50 to 5 nm increases the degree of inactivation from 60 to 99.6% (with a reduction factor of 10 in t_1/2). Similarly, the increase in T from 10 °C to 65 °C causes a 100 times lowering of the t_1/2 and t_99.9% of SARS-CoV-2 on Cu metal. The theory predicts that involving the HOMO energy level of a protein follows the surface nanostructure shape dependent order as follows: spherical nanoparticle > cylindrical nanorod > cylindrical nanopore > spherical nanocavity, while the opposite trend is observed in the case of the LUMO energy level participation. Finally, the theory shows agreement with the reported experimental data of the degree of inactivation of SARS-CoV-2 on Ag and Cu nanoparticles.