Topographic mapping of the glioblastoma proteome reveals a triple-axis model of intra-tumoral heterogeneity

Glioblastoma is an aggressive form of brain cancer with well-established patterns of intra-tumoral heterogeneity implicated in treatment resistance and progression. While regional and single cell transcriptomic variations of glioblastoma have been recently resolved, downstream phenotype-level proteomic programs have yet to be assigned across glioblastoma’s hallmark histomorphologic niches. Here, we leverage mass spectrometry to spatially align abundance levels of 4,794 proteins to distinct histologic patterns across 20 patients and propose diverse molecular programs operational within these regional tumor compartments. Using machine learning, we overlay concordant transcriptional information, and define two distinct proteogenomic programs, MYC- and KRAS-axis hereon, that cooperate with hypoxia to produce a tri-dimensional model of intra-tumoral heterogeneity. Moreover, we highlight differential drug sensitivities and relative chemoresistance in glioblastoma cell lines with enhanced KRAS programs. Importantly, these pharmacological differences are less pronounced in transcriptional glioblastoma subgroups suggesting that this model may provide insights for targeting heterogeneity and overcoming therapy resistance.

Large Scaled Topographic Mapping and Issues in Depicting VGI and Open Data

Open data and geospatial data collected by volunteers are nowadays easy to obtain and available with worldwide coverage through projects like OpenStreetMap. However, the use of these datasets leads to new challenges in depiction especially in the field of large scale topographic cartography. In addition to quality research, new processing and depiction methods for integrating these data are emerging. In the course of this work, specific problems of maps based on OpenStreetMap and Open Data elevation models are pointed out and possible solutions are introduced. In addition, a method for the preprocessing of contour lines is presented and the process flow is described in more detail. The goal of this work is to give insight into a toolbox of specially adapted and (semi-)automated methods. In this way, the quality standard of the depiction of topographic maps based on Open Data is to be increased, but also limitations are being shown.

Extended Graph of the Fuzzy Topographic Topological Mapping Model

Fuzzy topological topographic mapping (FTTM) is a mathematical model which consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, FTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of FTTM, namely the homeomorphisms between its components, allows the generation of new FTTM. The generated FTTMs can be represented as pseudo graphs. A graph of pseudo degree zero is a special type of graph where each of the FTTM components differs from the one adjacent to it. Previous researchers have investigated and conjectured the number of generated FTTM pseudo degree zero with respect to n number of components and k number of versions. In this paper, the conjecture is proven analytically for the first time using a newly developed grid-based method. Some definitions and properties of the novel grid-based method are introduced and developed along the way. The developed definitions and properties of the method are then assembled to prove the conjecture. The grid-based technique is simple yet offers some visualization features of the conjecture.