SUMMARY: We introduce SteadyCellPhenotype, a browser-based interface for the analysis of ternary biological networks. It includes tools for deterministically finding all steady states of a network, as well as the simulation and visualization of trajectories with publication quality graphics. Simulations allow us to approximate the size of the basin for attractors and deterministic simulations of trajectories nearby specified points allow us to explore the behavior of the system in that neighborhood. AVAILABILITY AND IMPLEMENTATION: https://github.com/knappa/steadycellphenotype MIT License.

Although the role of evolutionary process in cancer progression is widely accepted, increasing attention is being given to the evolutionary mechanisms that can lead to differences in clinical outcome. Recent studies suggest that the temporal order in which somatic mutations accumulate during cancer progression is important. Single-cell sequencing (SCS) provides a unique opportunity to examine the effect that the mutation order has on cancer progression and treatment effect. However, the error rates associated with single-cell sequencing are known to be high, which greatly complicates the task. We propose a novel method for inferring the order in which somatic mutations arise within an individual tumor using noisy data from single-cell sequencing. Our method incorporates models at two levels in that the evolutionary process of somatic mutation within the tumor is modeled along with the technical errors that arise from the single-cell sequencing data collection process. Through analyses of simulations across a wide range of realistic scenarios, we show that our method substantially outperforms existing approaches for identifying mutation order. Most importantly, our method provides a unique means to capture and quantify the uncertainty in the inferred mutation order along a given phylogeny. We illustrate our method by analyzing data from colorectal and prostate cancer patients, in which our method strengthens previously reported mutation orders. Our work is an important step towards producing meaningful prediction of mutation order with high accuracy and measuring the uncertainty of predicted mutation order in cancer patients, with the potential to lead to new insights about the evolutionary trajectories of cancer.

Dysregulation of iron metabolism in cancer is well documented and it has been suggested that there is interdependence between excess iron and increased cancer incidence and progression. In an effort to better understand the linkages between iron metabolism and breast cancer, a predictive mathematical model of an expanded iron homeostasis pathway was constructed that includes species involved in iron utilization, oxidative stress response and oncogenic pathways. The model leads to three predictions. The first is that overexpression of iron regulatory protein 2 (IRP2) recapitulates many aspects of the alterations in free iron and iron-related proteins in cancer cells without affecting the oxidative stress response or the oncogenic pathways included in the model. This prediction was validated by experimentation. The second prediction is that iron-related proteins are dramatically affected by mitochondrial ferritin overexpression. This prediction was validated by results in the pertinent literature not used for model construction. The third prediction is that oncogenic Ras pathways contribute to altered iron homeostasis in cancer cells. This prediction was validated by a combination of simulation experiments of Ras overexpression and catalase knockout in conjunction with the literature. The model successfully captures key aspects of iron metabolism in breast cancer cells and provides a framework upon which more detailed models can be built.

MOTIVATION: Increasing attention has been devoted to estimation of species-level phylogenetic relationships under the coalescent model. However, existing methods either use summary statistics (gene trees) to carry out estimation, ignoring an important source of variability in the estimates, or involve computationally intensive Bayesian Markov chain Monte Carlo algorithms that do not scale well to whole-genome datasets. RESULTS: We develop a method to infer relationships among quartets of taxa under the coalescent model using techniques from algebraic statistics. Uncertainty in the estimated relationships is quantified using the nonparametric bootstrap. The performance of our method is assessed with simulated data. We then describe how our method could be used for species tree inference in larger taxon samples, and demonstrate its utility using datasets for Sistrurus rattlesnakes and for soybeans. AVAILABILITY AND IMPLEMENTATION: The method to infer the phylogenetic relationship among quartets is implemented in the software SVDquartets, available at www.stat.osu.edu/∼lkubatko/software/SVDquartets.