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Much progress has been made, and continues to be made, towards identifying candidate mutated driver pathways in cancer. However, no systematic approach to understanding how candidate pathways relate to each other for a given cancer (such as Acute myeloid leukemia), and how one type of cancer may be similar or different from another with regard to their respective pathways (Acute myeloid leukemia vs. Glioblastoma multiforme for instance), has emerged thus far. Our work attempts to contribute to the understanding of {em space of pathways} through a novel topological framework. We illustrate our approach, using mutation data (obtained from TCGA) of two types of tumors: Acute myeloid leukemia (AML) and Glioblastoma multiforme (GBM). We find that the space of pathways for AML is homotopy equivalent to a sphere, while that of GBM is equivalent to a genus-2 surface. We hope to trigger new types of questions (i.e., allow for novel kinds of hypotheses) towards a more comprehensive grasp of cancer.
The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is either induce
We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem a
Diverse classes of proteins function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. As such paths are curves in a high-dimensional space, they
Motivated by the biologically important and complex phenomena of Abeta peptide aggregation in Alzheimers disease, we introduce a model and simulation methodology for studying protein aggregation that includes extra-cellular aggregation, aggregation o
We propose a novel two-stage Gene Set Gibbs Sampling (GSGS) framework, to reverse engineer signaling pathways from gene sets inferred from molecular profiling data. We hypothesize that signaling pathways are structurally an ensemble of overlapping li