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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 between 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.

The brain’s high bioenergetic state is paralleled by high metabolic waste production. Authentic lymphatic vasculature is lacking in brain parenchyma. Cerebrospinal fluid (CSF) flow has long been thought to facilitate central nervous system detoxification in place of lymphatics, but the exact processes involved in toxic waste clearance from the brain remain incompletely understood. Over the past 8 yr, novel data in animals and humans have begun to shed new light on these processes in the form of the “glymphatic system,” a brain-wide perivascular transit passageway dedicated to CSF transport and interstitial fluid exchange that facilitates metabolic waste drainage from the brain. Here we will discuss glymphatic system anatomy and methods to visualize and quantify glymphatic system (GS) transport in the brain and also discuss physiological drivers of its function in normal brain and in neurodegeneration.

In this work, we utilized network features of cancer gene interactomes to cluster pediatric sarcoma tumors and identify candidate therapeutic targets in an unsupervised manner. RNA-Seq data were mapped to protein-level interactomes to construct weighted networks for mathematical analysis. We employed a geometric approach centered on a discrete notion of curvature, which provides a measure of the functional association between genes in the context of their connectivity. Specifically, we adopted a recently proposed dynamic extension of graph curvature to extract features of the non-Euclidean, multiscale structure of genomic networks. We propose a hierarchical clustering approach to reveal preferential gene clustering according to their geometric cooperation which captured the characteristic EWSR1-FLI1 fusion in Ewing sarcoma. We also performed in silico edge perturbations to assess systemic response to simulated interventions quantified by changes in curvature. These results demonstrate that geometric network-based features can be useful for identifying non-trivial gene associations in an agnostic manner.

Multiple myeloma (MM) prognosis incorporates a variety of metrics including treatment received, clinical factors, and genomic characteristics, with several specific genomic features predicting for shorter progression free survival (PFS). No study to date has integrated genomic data from a systems view, incorporating interactions between biomarkers in a network. We use a geometric network analysis that integrates complex interactions to characterize patterns of biological behavior not captured by individual genomic events. The methodology is mathematically well-defined and has no fitting parameters. We hypothesized that such a systems mathematical approach applied to gene interaction networks may delineate biologically relevant MM subtypes and potential new therapeutic targets. We overlaid RNA-Seq and copy number alteration data from the MMRF CoMMpass study (IA19) on a gene interactome derived from the Human Protein Reference Database using a novel graph metric of network robustness — Ollivier-Ricci curvature (ORC). Results were clustered, with the optimal number determined via silhouette score. Survival analysis for PFS was performed employing Kaplan-Meier and log-rank tests. A differential gene expression analysis between high and low risk groups was conducted. Differences in scalar ORC between the low-risk and high-risk groups were examined and contextualized using a pathway analysis. Pathway analysis was performed using the Broad Institute’s Gene Set Enrichment Analysis tool and the pathways used are from the hallmark gene set from the Human MSigDB collection. The dataset included 659 patients and the incorporated protein-protein interactions resulted in a network with 8,468 nodes and 33,695 edges. The ORC analysis discovered 6 clusters, with specific genomic features being associated with clusters predicting for long [hyperdiploidy, t(11:14)], and short [t(4;14), MAF/MAFB translocations] PFS. A differential gene expression analysis comparing the high risk and low risk groups identified 118 key genes. These genes were associated with various pathways both known and unknown to be associated with multiple myeloma, including mitotic spindle, DNA repair, inflammatory response, and the P53 pathways. Further scalar curvature analysis showed differences in the apoptosis, TGF beta signaling, and other signaling pathways. In summary, we applied the geometric network analysis tool ORC to multi-omics data in MM represented as biological networks to identify individuals at high risk of short PFS and relevant biological correlates. Decreased robustness of signaling near immune-related genes was associated with shorter survival, highlighting the plausible utility of using these methods to uncover new biological insights. Citation Format: Anish K. Simhal, Kylee H. Maclachlan, Rena Elkin, Jiening Zhu, Saad Z. Usmani, Jonathan J. Keats, Larry Norton, Joseph O. Deasy, Jung Hun Oh, Allen Tannenbaum. Protein network analysis uncovers a poor-survival subtype in multiple myeloma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 2061.

Oncogenic driver mutations in different pediatric sarcoma subtypes have been identified but may not be druggable. In general, identifying novel therapeutic targets and biomarkers for response remains a major challenge. We hypothesize that considering the structure of the interaction network in which the genes operate as a system is crucial for understanding a gene's role. We propose to use the protein interaction network geometry to characterize the shape of network architecture and identify key aspects of direct and indirect cooperation pertaining to the cancer network and prognosis using geometrical methods. We model gene networks as weighted graphs where edges indicate protein-level interactions and edge weights estimate the strength of the interaction. The Human Protein Reference Database was used to define the gene network topology. RNA-Seq data from pediatric sarcoma tissues extracted from patients treated at MSK (n=12 Ewing sarcoma; n=29 osteosarcoma; n=20 desmoplastic small round cell tumor) was employed to prescribe correlation-based weights to create pediatric sarcoma subtype-specific weighted graphs. The geometry of the weighted gene networks was computed via a discrete notion of Ricci curvature. Intuitively, the curvature provides a measure of feedback (triangles) in the network. Positive curvature reflects robust communication and ease of information transfer, while negative curvature reflects bridge-like architecture or bottlenecks of information flow. We utilized a dynamic (multi-scale) notion of curvature to quantify the functional associations between genes, computed as a function of scale between diffusion processes initially localized on each node (i.e., gene). The curvature becomes more positive on edges between communal genes and more negative on bridge-like edges between communities, until reaching the critical scale. Curvature therefore, as we demonstrate, partitions the cancer networks into functionally associated communities. Community detection by removing bridge-edges, determined as edges with negative curvature at the critical scale, revealed sarcoma subtype-specific preferential gene associations. In particular, we agnostically found the EWSR1-FLI1 association in a cluster that was unique to the Ewing sarcoma network. Interestingly, we found ETV6 in the same community as the characteristic Ewing sarcoma EWSR1-FLI1 feature, suggesting a novel implication of ETV6 in Ewing sarcoma. These results suggest that persisting communities found by leveraging the cancer network geometry may identify potential mechanisms of drug resistance and actionable therapeutic targets. Citation Format: Rena Elkin, Jung Hun Oh, Filemon Dela Cruz, Larry Norton, Joseph O. Deasy, Andrew L. Kung, Allen R. Tannenbaum. Geometry of gene expression network reveals potential novel indicator in Ewing sarcoma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 6541.

PurposeNetwork analysis methods can potentially quantify cancer disturbances in gene networks without introducing fitted parameters or variable selection. A new network curvature-based method is introduced to provide an integrated measure of variability within cancer gene networks. The method is applied to high grade serous ovarian cancers (HGSOCs) to predict response to immune checkpoint inhibitors (ICIs), and to rank key genes associated with prognosis.MethodsCopy number alterations (CNAs) from targeted and whole exome sequencing data were extracted for HGSOC patients (n= 45) treated with ICIs. CNAs at a gene level were represented on a protein-protein interaction network to define patient-specific networks with a fixed topology. A version of Ollivier-Ricci curvature was used to identify genes that play a potentially key role in response to immunotherapy and further to stratify patients at high risk of mortality. Overall survival (OS) was defined as the time from the start of ICI treatment to either death or last follow-up. Kaplan-Meier analysis with log-rank test was performed to assess OS between the high and low curvature classified groups.ResultsThe network curvature analysis stratified patients at high risk of mortality with p=0.00047 in Kaplan-Meier analysis. Genes with high curvature were in accordance with CNAs relevant to ovarian cancer.ConclusionNetwork curvature using CNAs has the potential to be a novel predictor for OS in HGSOC patients treated with immunotherapy.

Current state-of-the-art models for estimating the pharmacokinetic parameters do not account for intervoxel movement of the contrast agent (CA). We introduce an optimal mass transport (OMT) formulation that naturally handles intervoxel CA movement and distinguishes between advective and diffusive flows. Ten patients with head and neck squamous cell carcinoma (HNSCC) were enrolled in the study between June 2014 and October 2015 and under-went DCE MRI imaging prior to beginning treatment. The CA tissue concentration information was taken as the input in the data-driven OMT model. The OMT approach was tested on HNSCC DCE data that provides quantitative information for forward flux (ΦF) and backward flux (ΦB). OMT-derived ΦF was compared with the volume transfer constant for CA, Ktrans, derived from the Extended Tofts Model (ETM). The OMT-derived flows showed a consistent jump in the CA diffusive behavior across the images in accordance with the known CA dynamics. The mean forward flux was 0.0082 ± 0.0091 (min-1) whereas the mean advective component was 0.0052±0.0086 (min-1) in the HNSCC patients. The diffusive percentages in forward and backward flux ranged from 8.67–18.76% and 12.76–30.36%, respectively. The OMT model accounts for intervoxel CA movement and results show that the forward flux (ΦF) is comparable with the ETM-derived Ktrans. This is a novel data-driven study based on optimal mass transport principles applied to patient DCE imaging to analyze CA flow in HNSCC.

Unbalanced optimal mass transport (OMT) seeks to remove the conservation of mass constraint by adding a source term to the standard continuity equation in the Benamou-Brenier formulation of OMT. In this study, we show how the unbalanced case fits into the vector-valued OMT framework simply by adding an auxiliary source layer and taking the flow between the source layer and the original layer(s) as the source term. This allows for unbalanced models both in the scalar and vector-valued density settings. The results are demonstrated on a number of synthetic and real vector-valued data sets.

The glymphatic system (GS) hypothesis states that advective driven cerebrospinal fluid (CSF) influx from the perivascular spaces into the interstitial fluid space rapidly transport solutes and clear waste from brain. However, the presence of advection in neuropil is contested and solutes are claimed to be transported by diffusion only. To address this controversy, we implemented a regularized version of the optimal mass transport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption required. rOMT analysis with a Lagrangian perspective of GS transport revealed that solute speed was faster in CSF compared to grey and white matter. Further, rOMT analysis also demonstrated 2-fold differences in regional solute speed within the brain. Collectively, these results imply that advective transport dominates in CSF while diffusion and advection both contribute to GS transport in parenchyma. In a rat model of cerebral small vessel disease (cSVD), solute transport in the perivascular spaces (PVS) and PVS-to-tissue transfer was slower compared to normal rats. Thus, the analytical framework of rOMT provides novel insights in the local dynamics of GS transport that may have implications for neurodegenerative diseases. Future studies should apply the rOMT analysis approach to confirm GS transport reductions in humans with cSVD.

The presence of advection in neuropil is contested and solute transport is claimed to occur by diffusion only. To address this controversy, we implemented a regularized version of the optimal mass transport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption required. rOMT analysis with a Lagrangian perspective of glymphatic system (GS) transport revealed that solute speed was faster in cerebrospinal fluid (CSF) compared to grey and white matter. rOMT analysis also demonstrated 2-fold differences in regional particle speed within the brain parenchyma. Collectively, these results imply that advective transport dominates in CSF while diffusion and advection both contribute to transport in parenchyma. In rats with chronic hypertension, solute transport in perivascular spaces (PVS) and PVS-to-tissue transfer was slower compared to normotension. Thus, the analytical framework of rOMT provides novel insights in local variation and dynamics of GS transport that may have implications for neurodegenerative diseases.

The glymphatic system (GS) is a transit passage that facil-itates brain metabolic waste removal and its dysfunction has been asso-ciated with neurodegenerative diseases such as Alzheimer's disease. The GS has been studied by acquiring temporal contrast enhanced magnetic resonance imaging (MRI) sequences of a rodent brain, and tracking the cerebrospinal fluid injected contrast agent as it flows through the GS. We present here a novel visualization framework, GlymphVIS, which uses regularized optimal transport (OT) to study the flow behavior between time points at which the images are taken. Using this regularized OT app-roach, we can incorporate diffusion, handle noise, and accurately capture and visualize the time varying dynamics in GS transport. Moreover, we are able to reduce the registration mean-squared and infinity-norm error across time points by up to a factor of 5 as compared to the current state-of-the-art method. Our visualization pipeline yields flow patterns that align well with experts' current findings of the glymphatic system.