Mapping the Single-Cell Differentiation Landscape of Osteosarcoma.

PURPOSE: The genetic intratumoral heterogeneity observed in human osteosarcomas poses challenges for drug development and the study of cell fate, plasticity, and differentiation, which are processes linked to tumor grade, cell metastasis, and survival. EXPERIMENTAL DESIGN: To pinpoint errors in osteosarcoma differentiation, we transcriptionally profiled 31,527 cells from a tissue-engineered model that directs mesenchymal stem cells toward adipogenic and osteoblastic fates. Incorporating preexisting chondrocyte data, we applied trajectory analysis and non-negative matrix factorization to generate the first human mesenchymal differentiation atlas. RESULTS: This "roadmap" served as a reference to delineate the cellular composition of morphologically complex osteosarcoma tumors and quantify each cell's lineage commitment. Projecting a bulk RNA-sequencing osteosarcoma dataset onto this roadmap unveiled a correlation between a stem-like transcriptomic phenotype and poorer survival outcomes. CONCLUSIONS: Our study quantifies osteosarcoma differentiation and lineage, a prerequisite to better understanding lineage-specific differentiation bottlenecks that might someday be targeted therapeutically.

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.

Unbalanced regularized optimal mass transport with applications to fluid flows in the brain.

As a generalization of the optimal mass transport (OMT) approach of Benamou and Brenier's, the regularized optimal mass transport (rOMT) formulates a transport problem from an initial mass configuration to another with the optimality defined by the total kinetic energy, but subject to an advection-diffusion constraint equation. Both rOMT and the Benamou and Brenier's formulation require the total initial and final masses to be equal; mass is preserved during the entire transport process. However, for many applications, e.g., in dynamic image tracking, this constraint is rarely if ever satisfied. Therefore, we propose to employ an unbalanced version of rOMT to remove this constraint together with a detailed numerical solution procedure and applications to analyzing fluid flows in the brain.

Dynamic network curvature analysis of gene expression reveals novel potential therapeutic targets in sarcoma.

Network properties account for the complex relationship between genes, making it easier to identify complex patterns in their interactions. In this work, we leveraged these network properties for dual purposes. First, we clustered pediatric sarcoma tumors using network information flow as a similarity metric, computed by the Wasserstein distance. We demonstrate that this approach yields the best concordance with histological subtypes, validated against three state-of-the-art methods. Second, to identify molecular targets that would be missed by more conventional methods of analysis, we applied a novel unsupervised method to cluster gene interactomes represented as networks in pediatric sarcoma. RNA-Seq data were mapped to protein-level interactomes to construct weighted networks that were then subjected to a non-Euclidean, multi-scale geometric approach centered on a discrete notion of curvature. This provides a measure of the functional association among genes in the context of their connectivity. In confirmation of the validity of this method, hierarchical clustering revealed the characteristic EWSR1-FLI1 fusion in Ewing sarcoma. Furthermore, assessing the effects of in silico edge perturbations and simulated gene knockouts as quantified by changes in curvature, we found non-trivial gene associations not previously identified.

Visualizing Fluid Flows via Regularized Optimal Mass Transport with Applications to Neuroscience.

The regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model serves as a powerful tool in computational fluid dynamics for visualizing fluid flows in the glymphatic system. In the present work, we describe how to modify the previous numerical method for efficient implementation, resulting in a significant reduction in computational runtime. Numerical results applied to synthetic and real-data are provided.