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Register a new userThe Topology of Mutated Driver Pathways
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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.
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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 induced or uninduced. Many dynamical models have been proposed to capture this phenomenon. While most are based on complex mathematical formulations, it has been suggested that for other gene systems network topology is sufficient to produce the desired dynamical behavior. We present a Boolean network as a discrete model for the lac operon. We include the two main glucose control mechanisms of catabolite repression and inducer exclusion in the model and show that it exhibits bistability. Further we present a reduced model which shows that lac mRNA and lactose form the core of the lac operon, and that this reduced model also exhibits the same dynamics. This work corroborates the claim that the key to dynamical properties is the topology of the network and signs of interactions.
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 are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field.
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 have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. The Path Similarity Analysis (PSA) approach alleviates these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space. PSA employs the Hausdorff or Frechet path metrics---adopted from computational geometry---enabling us to quantify path (dis)similarity, while the new concept of a Hausdorff-pair map permits the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of many paths, including collections of transition ensembles. We use the closed-to-open transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for the assessment enhanced sampling algorithms---to examine multiple microsecond equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free form alongside transition ensembles from the MD-based dynamic importance sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for instance, that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis methods relying on pre-defined collective variables, such as native contacts or geometric quantities, can be used synergistically with PSA, as well as the application of PSA to more complex systems such as membrane transporter proteins.
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 on the cell-surface assisted by a membrane bound protein, and in addition, supply, clearance, production and sequestration of peptides and proteins. The model is used to produce equilibrium and kinetic-aggregation phase diagrams for aggregation onset and of reduced stable Abeta monomer concentrations due to aggregation. The methodology we implemented permits modeling of a phenomenon involving orders of magnitude differences in time scales and concentrations which can be retained in the simulation. We demonstrate how to identify ranges of parameter values that give monomer concentration depletion upon aggregation similar to that observed in Alzheimers disease. We show how very different behavior can be obtained as reaction parameters and protein concentrations vary, and discuss the difficulty reconciling results of experiments from two vastly different concentration regimes. The latter is an important general issue in relating in-vitro and mice based experiments to humans.
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 linear signal transduction events which we encode as Information Flow Gene Sets (IFGSs). We infer pathways from gene sets corresponding to these events subjected to a random permutation of genes within each set. In Stage I, we use a source separation algorithm to derive unordered and overlapping IFGSs from molecular profiling data, allowing cross talk among IFGSs. In Stage II, we develop a Gibbs sampling like algorithm, Gene Set Gibbs Sampler, to reconstruct signaling pathways from the latent IFGSs derived in Stage I. The novelty of this framework lies in the seamless integration of the two stages and the hypothesis of IFGSs as the basic building blocks for signal pathways. In the proof-of-concept studies, our approach is shown to outperform the existing Bayesian network approaches using both continuous and discrete data generated from benchmark networks in the DREAM initiative. We perform a comprehensive sensitivity analysis to assess the robustness of the approach. Finally, we implement the GSGS framework to reconstruct signaling pathways in breast cancer cells.
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