Mathematical Biology Seminar

Resolving gene-to-cell state relationships in the developing mouse mammary gland

Benjamin Spike Huntsman Cancer Institute University of Utah
Wednesday, November 29, 2017, at 3:05pm LCB 219

The mammary gland is comprised of interacting cell types presumed to have distinct gene expression patterns relating to their cellular origins, function and spatio-temporal context. Yet, its cellular composition is understood principally from studies of mixed cell populations without detailed knowledge of the differences between the individual cells comprising it. This makes it difficult to understand how the tissue maintains its homoeostasis and balance of cell types and how this is perturbed in cancer development. We are addressing this problem by generating single cell transcriptomes from fetal, post-natal and adult mouse mammary epithelia. The resulting data provides new challenges and opportunities in understanding cell identity. These include dealing with sparse data, searching for higher order information embedded in the transcriptome as a network and understanding the relationship between heterogeneous transcriptional profiles and cell type.

Mathematical Biology Seminar

Understanding Transmission Dynamics in the Presence of Incomplete Data

Karim Khader Department of Internal Medicine University of Utah School of Medicine
Wednesday, November 15, 2017, at 3:05pm LCB 219

Statistical analysis of infectious outcomes is important for an optimal understanding of the kinds of interventions that can be used to limit the spread of infectious diseases. A principal challenge in the analysis of infectious diseases is the lack of fully observed data that are important for understanding the underlying dynamics of transmission. Multiple approaches have been developed that allow for missing data and misclassification. In this talk, we will review some of the previous work on modeling transmission with incomplete data. We will also discuss our recent developments of dynamic transmission models to estimate key parameters related to infectious diseases, particularly those related to antibiotic resistant bacteria.

Mathematical Biology Seminar

Uncertainty Quantification for Biomedical Decision Making: A Critical Informatics Contribution to Precision Medicine

Julio Facelli Department of Biomedical Informatics University of Utah
Wednesday, November 8, 2017, at 3:05pm LCB 219

There is concern about the lack of reproducibility of biomedical studies, but the research community has not taken advantage of formal Uncertainty Quantification (UQ) methods to better understand this issue. Here we show the importance of UQ in Translational Science and Precision Medicine. This presentation describes the use of UQ methods in biomedical research with applications to breast cancer classification, family history risk assessment and gene co-expression network determination. The results presented here show that UQ methods can be applied to biomedical sciences. UQ provides useful clinical and translational information, and arguable UQ should become a common tool in translational science and precision medicine because UQ methods can provide a better understanding of the underlying factors leading to the lack of reproducibility.

Mathematical Biology Seminar

Parameter identifiability and effective theories in physics, biology, and beyond

Mark Transtrum Department of Mathematics Brigham Young University
Wednesday, October 25, 2017, at 3:05pm LCB 219

The success of science is due in large part to the hierarchical nature of physical theories. These effective theories model natural phenomena as if the physics at macroscopic length scales were almost independent of the underlying, shorter-length-scale details. The efficacy of these simplified models can be understood in terms of parameter identifiability. Parameters associated with microscopic degrees of freedom are usually unidentifiable as quantified by the Fisher Information Matrix. I apply an information geometric approach in which a microscopic, mechanistic model is interpreted as a manifold of predictions in data space. Model manifolds are often characterized by a hierarchy of boundaries—faces, edges, corners, hyper-corners, etc. These boundaries correspond to reduced-order models, leading to a model reduction technique known as the Manifold Boundary Approximation Method. In this way, effective models can be systematically derived from microscopic first principles for a variety of complex systems in physics, biology, and other fields.

Mathematical Biology Seminar

Variational analysis of traveling waves in stochastic neural fields

James MacLaurin Department of Mathematics University of Utah
Wednesday, September 27, 2017, at 3:05pm LCB 219

In this work we develop a variational formalism for decomposing the effect of stochastic noise on traveling waves in neural fields. The noise is decomposed into two parts: a shift of the wavefront, and a small perturbation about the wavefront. We find that the decomposition is accurate on timescales that are exponential in the inverse of the strength of the noise. The decomposition is applied to various neural field waves in product spaces, and also waves that are induced by a stimulus.

Mathematical Biology Seminar

A mathematical model of leukocyte dynamics during maintenance therapy of childhood acute lymphoblastic leukemia

Thuy T. T. Le Department of Mathematics Otto-von-Guericke Universität Magdeburg
Wednesday, September 13, 2017, at 3:05pm LCB 219

Acute lymphoblastic leukemia (ALL) is the most common cancer in children, comprising approximately 25% of all childhood malignancies. ALL is characterized by the overproduction and accumulation of immature, abnormal white blood cells (lymphoblasts) and consecutive displacement of normal hematopoiesis. The backbone of maintenance therapy includes daily oral 6-Mercaptopurine and weekly oral Methotrexate.

This talk introduces a complete model of chemotherapy-induced leukopenia during maintenance therapy of ALL, taking the effects of two drugs in combination into consideration. Patient-specific parameters of the model are estimated. Furthermore, the ability of the proposed model to predict leukocytes over a given duration is justified by appropriate methods. All of the results here are conducted based on a real dataset collected from a local hospital.

Mathematical Biology Seminar

Data-driven modeling of trait dependent populations

Jason Griffiths Department of Mathematics University of Utah
Wednesday, September 6, 2017, at 3:05pm LCB 219

Individuals within a population differ in attributes such as size, sex, spatial location, behaviour and age. Structured population models allow us to understand the effects of within population trait variation on demographic and population level processes. Data-driven modelling approaches allow parameters and functional relationships of a model to be statistically estimated from actual individual observations. This help our models reflect reality.

Integral projections models (IPM’s) are a data-driven structured population modelling approach, in which individuals are described by continuous traits, rather than being classified into arbitrary categories. They can be used to obtain quantitative and predictive inferences about a wide range of population types. They can describe secies with a very broad range of life histories, ranging from plants with dormant seed banks, to animals with size dependent growth, survival and reproduction.

I will demonstrate how IPM’s can be constructed in order to make full use of precious experimental and field observation. I will show current work that is being undertaken to advance IPM’s and I will outline future directions for the application of these models in cancer research.