2015-2016 Colloquia

September 21, 2015 3:00 - 3:50PM
Host: Greg Rempala
Abstract

We develop a model-based empirical Bayes approach to variable selection problems where the number of predictors is very large, possibly much larger than the number of responses (the so-called “large p, small n” problem). Motivated by QTL (quantitative trait loci) studies, we consider the multiple linear regression setting, where the response is assumed to be a continuous variable, and it is a linear function of the predictors. The explanatory variables in the linear model can have a positive effect on the response, a negative effect, or no effect. Thus, we model the effects of the linear predictors as a three-component mixture, where each component follows a normal distribution with mean μ, −μ, or 0. A key assumption in our approach is that only a small fraction of the candidate predictors have a non-zero effect on the response variable. By treating the putative variables as random effects we get shrinkage estimation, which results in increased power. This approach is computationally efficient because the number of parameters that have to be estimated is small, and remains constant regardless of the number of explanatory variables in the linear regression model. The model parameters are estimated using the EM algorithm which leads to significantly faster convergence, compared with simulation-based methods. Furthermore, we employ computational tricks which allow us to increase the speed of our algorithm, to handle a very large number of putative variables, and to avoid multicollinearity in the regression model.

October 05, 2015 3:00 - 3:00PM
Host: TBD
Abstract

Microbes are recently recognized as driving the energy and nutrient transformations that fuel Earth’s ecosystems in soils, oceans and humans. Where studied, viruses appear to modulate these microbial impacts in ways ranging from mortality and nutrient recycling to complete metabolic reprogramming during infection. As environmental virology strives to get a handle on the global virosphere (the diversity of viruses in nature) clear challenges are emerging where collaboration with mathematicians will be powerfully enabling. I will present a few ripe research avenues where we (environmental virologists) could use some help from mathematicians to better understand the nanoscale (viruses) and microscale (microbes) entities that drive Earth’s ecosystems.

October 19, 2015 3:00 - 3:50PM
Host: Ching-Shan Chou
Abstract

Phylogenetic construction algorithms based on k-mers of DNA or protein sequences are nonparametric distance methods for reconstructing phylogenetic trees from sequence data that do not depend on first constructing alignments. The methods are often used to construct the guide tree used in multiple sequence alignment. We show that when applied to data generated from a statistical model of sequence evolution, the standard k-mer methods are inconsistent, that is, even with arbitrary amounts of data, they will reconstruct the wrong tree. We also show how to derive model-based corrections that make the methods statistically consistent, and report on simulation studies comparing methods. This is joint work with Elizabeth Allman and John Rhodes.

November 02, 2015 3:00 - 3:50PM
Host: Adriana Dawes
Abstract

In the United States, the lifetime probability of developing cancer in one's lifetime is ~40%, and the lifetime probability of dying from cancer is ~20%. The second leading cause of death behind heart disease, cancer is a particularly challenging disease. Unlike heart disease, cancer includes multiple disorders dependent upon the specific tissue type and tumor cell. Cancer is largely driven by genes that push cancer progression, and is enabled by loss of tumor suppressors that normally confer feedback regulation and robustness to cells. For solid tumors, the metastatic process involving colonization of different tissues by cells from the primary tumor is actually the cause of death.

One of the major challenges to treatment of cancer is the evolutionary nature of the process that leads to tumor cell heterogeneity. This process enables cancer cells to adapt to stressful environments and eventual drug resistance. The mechanisms leading to such heterogeneity have largely been attributed to "genetic" processes that mutate DNA and "epigenetic" processes that modify transcription, e.g., the translation of DNA to RNA. However, we have recently published studies that demonstrate a role for very different stochastic, nongenetic processes (that can be either heritable or nonheritable) in establishing phenotypic heterogeneity.

In addition, since single drug treatments have been largely unsuccessful, we have been exploring conceptual frameworks for predicting optimal drug combinations to treat cancer. Cancer drugs ideally kill cancer cells while limiting harm to healthy cells. However, the inherent variance among cells in both cancer and healthy cell populations increases the difficulty of selective drug action. The lack of success with current cancer treatments suggests that we need alternative methodologies that would benefit from interdisciplinary approaches. The goal of my talk is to highlight these aspects of cancer that can potentially be addressed by mathematical analysis.

Frank, S.A., and Rosner, M.R., Nonheritable Cellular Variability Accelerates the Evolutionary Processes of Cancer. PLoS Biology, 10(4):e1001296. Epub. (2012) PMCID: PMC3317895

Lee, J., Yun, J., Yeung, K., Bevilacqua, Balzsi, G., and Rosner, M.R., BACH1 and RKIP participate in a Bistable Network that affects Progression to Metastasis in Breast Cancer, PNAS, 111(3):E364-73 (2014). PMCID: PMC4096871

Lee U1, Skinner JJ2, Reinitz J3, Rosner MR4, Kim EJ.PLoS One. Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations. 2015 Jul 23;10(7):e0132397. doi: 10.1371/journal.pone.0132397. eCollection 2015.

Lawlor PN1, Kalisky T2, Rosner R3, Rosner MR4, Kording KP. Conceptualizing cancer drugs as classifiers. PLoS One. 2014 Sep 23;9(9):e106444. doi: 10.1371/journal.pone.0106444. eCollection 2014.

November 09, 2015 3:00 - 3:50PM
Host: Andrej Rotter
Abstract

Bacterial biofilms are communities of single-celled organisms attached to solid surfaces that embed themselves in an extracellular polymeric slime matrix. Previous studies by our group and others have shown that mechanically biofilms behave as complex viscoelastic liquids. It has been hypothesized that this property is an adapted trait that allows bacteria to remain attached to surfaces when subjected to steady or transient overlying shear forces. Biofilms are ubiquitous in nature and the manmade world, causing serious problems including chronic implant infections, oral diseases, microbial contamination of industrial systems, and increased pressure drop and drag burdens in pipelines and ship hulls. In addition, the fossil record suggests that biofilm formation is an ancient adaptation of early life that allowed bacterial proliferation and survival on surfaces. Recent studies of ripple-like structures found in sedimentary fossils have raised the hypothesis that such structures may be the result of Kelvin-Helmholtz (KH) instabilities. We have recently discovered such instabilities can form in living biofilms with the use of a high-speed camera recording high-velocity water drop impacts to determine mechanical mechanisms of biofilm disruption. We found that the impact patterns rapidly dissipate (within milliseconds) and thus would fail to be detected by conventional microscopic methods. We have mathematically modeled the experimental data using a classical linear stability analysis, which supports the hypotheses that these instabilities are indeed of the KH type. These experiments provide strong support that living biofilms behave as liquids, and further go on to suggest they can develop internal turbulence.

January 25, 2016 3:00 - 4:00PM
Abstract

Networks of differential equations can be defined by directed graphs. The graphs (or network architecture) indicate who is talking to whom and when they are saying the same thing. We ask: Which properties of solutions of coupled equations follow from network architecture. Answers include "patterns of synchrony" for equilibria and "patterns of phase-shift synchrony" for time-periodic solutions. We show how these properties can be used to explain surprising results in binocular rivalry experiments and we discuss how homeostasis can be thought of as a network phenomenon.

February 15, 2016 3:00 - 3:50PM
Host: Catherine Calder
Abstract

Genome-wide association studies (GWAS) attempt to determine which genomic markers are predictors of genetic traits, most commonly human diseases. In practice, despite the extreme imbalance of having millions of markers recorded for only a few thousand individuals, it is of great interest to glean as much information as possible from this type of data. To this end, we propose a novel statistical model that exploits a hierarchical structure between markers and genes to leverage information between levels and alleviate the "large-p small-n" regimen while still attaining a reasonably complex and realistic model. Fitting the model is challenging due to the high number of variables to select, so we discuss efficient computational approaches that we explored to estimate the parameters. Finally, we illustrate the proposed model and estimation procedures on simulated data and on a real-world data set from the Wellcome Trust Consortium. If time permits, we also discuss a latent genotype procedure that aims to correct genotypical correlations. This is joint work with Ian Johnston.

March 07, 2016 3:00 - 3:50PM
Host: Catherine Calder
Abstract

We present a mathematical model of measles virus transmission that is tailored to a dataset on a large outbreak from rural Burundi in the 1980s, in which a major outbreak occurred despite reasonably high vaccination levels. So-called post-honeymoon outbreaks occur after the introduction of vaccination, and punctuate a vaccine-induced quiet period. These are demographic-epidemiologic phenomena, since they involve accumulation of cohorts of susceptible individuals when vaccination rates are below about 95%. We estimate an age-explicit "SEIR" PDE model with realistic demography, and discuss the insights for vaccination policy gleaned from the math model. Some of the insights are also applicable to the 2015 "Disneyland" measles outbreak.

April 04, 2016 3:00 - 3:50PM
Host: Karin Musier-Forsyth and Mark Foster
Abstract

The 5-leader of the HIV-1 genome directs the selection and packaging of two copies of the unspliced viral RNA into assembling virions. Using a suite of ^2 H-edited NMR methods, including a novel fragmentation-based ^2 H-edited approach, we have determined the structure of a 156-nucleotide 5-leader RNA element that binds the cognate nucleocapsid (NC) protein with high affinity and is independently capable of directing RNA packaging into virus-like particles (Core Encapsidation Signal, Ψ^CES ). The RNA adopts an unexpected secondary structure that differs considerably from models (more than 20) proposed on the basis of chemical and enzymatic probing. Residues important for splicing and translation are sequestered by base pairing within the core of the RNA, and clusters of unpaired “junction guanosines” are maintained in partially exposed conformations, apparently to promote high affinity NC binding. Long-range Adenosine Interaction Detection (lr-AID) NMR experiments indicate that the structure observed for the isolated Ψ^CES RNA also exists in the context of the full-length, 712 nucleotide dimeric 5-leader. The structure reveals how splicing is attenuated, and dimerization and Gag binding are promoted, by the RNA conformer that directs genome packaging. Progress toward the 3D structure determination of the intact, 712 nucleotide dimeric 5-leader will be presented.

April 11, 2016 3:00 - 3:50PM
Host: TBD
Abstract

The behavior of gene circuits is context-dependent, that is, the input/output functionality of a circuit depends on its context. Context includes other systems to which the circuit directly connects, which apply a load (retroactivity), and systems that are simply present in the cellular environment. The latter ones, in particular, also affect the functionality of the circuit due to sharing a common pool of limited resources. Because of these context-effects, a set of new “hidden” interactions appear in gene networks, which dramatically change the expected network’s behavior. These hidden interactions confound both the design of de novo systems in synthetic biology and the analysis of existing natural systems. In this talk, I will present a systematic modeling framework that captures hidden interactions in a network’s description and provides simple graphical rules to draw them. I will then present recent experimental results performed in our lab that validate these predictions. Finally, I will illustrate that a distributed control scheme, in which the local negative feedback at each node is realized through mRNA interference, can mitigate the effects of those hidden interactions due to scarcity of resources needed for gene expression.

April 18, 2016 3:00 - 3:50PM
Host: Joe Tien
Abstract

Understanding the properties of stationary populations is treated in this talk from the perspective of mathematical history of population dynamics as well as modern experiments conducted on insects longevity. The subject of population dynamics is hundreds of years old and is been studied by famous mathematicians such as Fibinocci, d’Alambert Daniel Bernoulli, Euler, etc, Concepts such as stability and stationarity of population are essential pillars of population dynamics. In the last century the works by Alfred Lotka laid the foundation for the population stability theory, which was developed further by William Feller through renewal equations. Ansley Coale and Norman Ryder (during 1960s and 1970s) brought several properties of stationary populations from the Life Table perspective. table perspective. During the last decade (early 2000s) new identities of stationary populations have emerged regarding life-lived and left, first with work by James Carey and his UC Davis colleagues Hans Mller and Jane-Ling Wang, followed by contributions by James Vaupel (who coined the identity Carey’s Equality) and Josh Goldstein. Rao & Carey (2013) have proved a fundamental theorem in stationary population using insights from Carey’s equality by blending with algebraic and combinatory principles. These newer results bring similar patterns that are comparable to renewal type of theory due to Lotka, Feller and others. This talk concludes with implications of Carey’s equality in other areas of population dynamics, including in non-stationary populations and direction of research in stationary populations.

April 25, 2016 3:00 - 3:50PM
Host: Catherine Calder
Abstract

Numerous gene signatures of patient prognosis for late-stage, high-grade ovarian cancer have been published, but diverse data and methods have made these difficult to compare objectively. However, the corresponding large volume of publicly available expression data creates an opportunity to validate previous findings and to develop more robust signatures. We thus built a database of uniformly processed and curated public ovarian cancer microarray data and clinical annotations, and re-implemented and validated 14 prognostic signatures published between 2007 and 2012. In this lecture I will describe the methodology and tools we developed for evaluating published signatures in this context. I will also use this application as the springboard for a more general discussion on how to evaluate statistical learning methods based on a collection of related studies.

May 02, 2016 3:00 - 3:50PM
Host: Grzegorz Rempala
Abstract

The control of physical, chemical, and biological phenomena are pervasive in the sciences. The dynamics involved span vast length and time scales with the associated controls ranging from shaped laser pulses out to the application of special chemical reagents and processing conditions. Despite all of these differences, there is clear common behavior found upon seeking optimal control in these various domains. Evidence of this common behavior will be presented from the control of quantum, chemical, and biological processes. The most evident finding is that control efforts can easily beat the so-called "curse of dimensionality" upon satisfaction of assumptions that are expected to widely hold. Quantum phenomena provide a setting to quantitatively test the control principles. The potential consequences of the observations will be discussed.