Seminars and Colloquia by Series

Comparative genomics meets topology: a novel view on genome median and halving problems

Series
Mathematical Biology Seminar
Time
Wednesday, March 15, 2017 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Max Alekseyev – George Washington University –
Genome median and genome halving are combinatorial optimization problems that aim at reconstruction of ancestral genomes by minimizing the number of possible evolutionary events between the reconstructed genomes and the genomes of extant species. While these problems have been widely studied in past decades, their known algorithmic solutions are either not efficient or produce biologically inadequate results. These shortcomings have been recently addressed by restricting the problems solution space. We show that the restricted variants of genome median and halving problems are, in fact, closely related and have a neat topological interpretation in terms of embedded graphs and polygon gluings. Hence we establish a somewhat unexpected link between comparative genomics and topology, and further demonstrate its advantages for solving genome median and halving problems in some particular cases. As a by-product, we also determine the cardinality of the genome halving solution space.

Constrained exact optimization in Phylogenetics

Series
Mathematical Biology Seminar
Time
Tuesday, October 18, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tandy Warnow – The University of Illinois at Urbana-Champaign
The estimation of phylogenetic trees from molecular sequences (e.g., DNA, RNA, or amino acid sequences) is a major step in many biological research studies, and is typically approached using heuristics for NP-hard optimization problems. In this talk, I will describe a new approach for computing large trees: constrained exact optimization. In a constrained exact optimization, we implicitly constrain the search space by providing a set X of allowed bipartitions on the species set, and then use dynamic programming to find a globally optimal solution within that constrained space. For many optimization problems, the dynamic programming algorithms can complete in polynomial time in the input size. Simulation studies show that constrained exact optimization also provides highly accurate estimates of the true species tree, and analyses of both biological and simulated datasets shows that constrained exact optimization provides improved solutions to the optimization criteria efficiently. We end with some discussion of future research in this topic. (Refreshments will be served before the talk at 10:30.)

Limits to estimating the severity of emerging epidemics due to inherent noise

Series
Mathematical Biology Seminar
Time
Wednesday, July 6, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bradford Taylor – School of Biology, Georgia Tech

Please Note: When a disease outbreak occurs, mathematical models are used to estimate the potential severity of the epidemic. The average number of secondary infections resulting from the initial infection or reproduction number, R_0, quantifies this severity. R_0 is estimated from the models by leveraging observed case data and understanding of disease epidemiology. However, the leveraged data is not perfect. How confident should we be about measurements of R_0 given noisy data? I begin my talk by introducing techniques used to model epidemics. I show how to adapt standard models to specific diseases by using the 2014-2015 Ebola outbreak in West Africa as an example throughout the talk. Nest, I introduce the inverse problem: given real data tracking the infected population how does one estimate the severity of the outbreak. Through a novel method I show how to account for both inherent noise arising from discrete interactions between individuals (demographic stochasticity) and from uncertainty in epidemiological parameters. By applying this, I argue that the first estimates of R_0 during the Ebola outbreak were overconfident because demographic stochasticity was ignored. This talk will be accessible to undergraduates.

Algebraic models of gene regulatory networks

Series
Mathematical Biology Seminar
Time
Wednesday, June 29, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Elena Dimitrova – Clemson University
Progress in systems biology relies on the use of mathematical and statistical models for system level studies of biological processes. This talk will focus on discrete models of gene regulatory networks and the challenges they present, in particular data selection and model stability. Careful data selection is important for model identification since the process is sensitive to the amount and type of data used as input. We will discuss a criterion for deciding when a set of data points identifies an algebraic model with special minimality properties. Stability is another important requirement for models of gene regulatory networks. Canalizing functions, a particular class of Boolean functions, show stable dynamic behavior and are thus suitable for expressing gene regulatory relationships. However, in practice, relaxing the canalizing requirement on some variables is appropriate. We will present the class of partially nested canalizing functions and some of their properties and applications.

What states in which to (not) commit a crime

Series
Mathematical Biology Seminar
Time
Wednesday, June 22, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Emily Rogers – Georgia Tech
Although DNA forensic evidence is widely considered objective and infallible, a great deal of subjectivity and bias can still exist in its interpretation, especially concerning mixtures of DNA. The exact degree of variability across labs, however, is unknown, as DNA forensic examiners are primarily trained in-house, with protocols and quality control up to the discretion of each forensic laboratory. This talk uncovers the current state of forensic DNA mixture interpretation by analyzing the results of a groundbreaking DNA mixture interpretation study initiated by the Department of Defense's Defense Forensic Science Center (DFSC) in the summer of 2014. This talk will be accessible to undergraduates.

Diffusion-Based Metrics for Biological Network Analysis

Series
Mathematical Biology Seminar
Time
Thursday, June 16, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lenore Cowen – Tufts University
In protein-protein interaction (PPI) networks, or more general protein-protein association networks, functional similarity is often inferred based on the some notion of proximity among proteins in a local neighborhood. In prior work, we have introduced diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture more fine-grained notions of similarity from the neighborhood structure that we showed could improve the accuracy of network-based function-prediction algorithms. Boehnlein, Chin, Sinha and Liu have recently shown that a variant of the DSD metric has deep connections to Green's function, the normalized Laplacian, and the heat kernel of the graph. Because DSD is based on random walks, changing the probabilities of the underlying random walk gives a natural way to incorporate experimental error and noise (allowing us to place confidence weights on edges), incorporate biological knowledge in terms of known biological pathways, or weight subnetwork importance based on tissue-specific expression levels, or known disease processes. Our framework provides a mathematically natural way to integrate heterogeneous network data sources for classical function prediction and disease gene prioritization problems. This is joint work with Mengfei Cao, Hao Zhang, Jisoo Park, Noah Daniels, Mark Crovella and Ben Hescott.

Virus-Immune Dynamics in Age-Structured HIV Model

Series
Mathematical Biology Seminar
Time
Wednesday, April 13, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Cameron Browne – U. of Louisiana
Mathematical modeling of viruses, such as HIV, has been an extensive area of research over the past two decades. For HIV, some important factors that affect within-host dynamics include: the CTL (Cytotoxic T Lymphocyte) immune response, intra-host diversity, and heterogeneities of the infected cell lifecycle. Motivated by these factors, I consider several extensions of a standard virus model. First, I analyze a cell infection-age structured PDE model with multiple virus strains. The main result is that the single-strain equilibrium corresponding to the virus strain with maximal reproduction number is a global attractor, i.e. competitive exclusion occurs. Next, I investigate the effect of CTL immune response acting at different times in the infected-cell lifecycle based on recent studies demonstrating superior viral clearance efficacy of certain CTL clones that recognize infected cells early in their lifecycle. Interestingly, explicit inclusion of early recognition CTLs can induce oscillatory dynamics and promote coexistence of multiple distinct CTL populations. Finally, I discuss several directions of ongoing modeling work attempting to capture complex HIV-immune system interactions suggested by experimental data.

Accounting for Heterogenous Interactions in the Spread Infections, Failures, and Behaviors_

Series
Mathematical Biology Seminar
Time
Wednesday, March 16, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
June Zhang – CDC.
Accounting for Heterogenous Interactions in the Spread Infections, Failures, and Behaviors_ The scaled SIS (susceptible-infected-susceptible) network process that we introduced extends traditional birth-death process by accounting for heterogeneous interactions between individuals. An edge in the network represents contacts between two individuals, potentially leading to contagion of a susceptible by an infective. The inclusion of the network structure introduces combinatorial complexity, making such processes difficult to analyze. The scaled SIS process has a closed-form equilibrium distribution of the Gibbs form. The network structure and the infection and healing rates determine susceptibility to infection or failures. We study this at steady-state for three scales: 1) characterizing susceptibility of individuals, 2) characterizing susceptibility of communities, 3) characterizing susceptibility of the entire population. We show that the heterogeneity of the network structure results in some individuals being more likely to be infected than others, but not necessarily the individuals with the most number of interactions (i.e., degree). We also show that "densely connected" subgraphs are more vulnerable to infections and determine when network structures include these more vulnerable communities.

Population biology of Schistosoma, its control and elimination: insights from mathematics and computations

Series
Mathematical Biology Seminar
Time
Wednesday, February 17, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor David Gurarie – CWRU –
Schistosoma is a parasitic worm that circulates between human and snail hosts. Multiple biological and ecological factors contribute to its spread and persistence in host populations. The infection is widespread in many tropical countries, and WHO has made control of schistosomiasis a priority among neglected tropical diseases.Mathematical modeling is widely used for prediction and control analysis of infectious agents. But host-parasite systems with complex life-cycles like Schistosoma, pose many challenges. The talk will outline the basic biology of Schistosoma, and the principles employed in mathematical modeling of macro parasites. We shall review conventional approaches to Schistosomiasis starting with the classical work of MacDonald, and discuss their validity and implications. Then we shall outline more detailed “stratified worm burden approach”, and show how combining mathematical and computer tools one can explore real-world systems and make reliable predictions for long term control outcomes and the problem of elimination.

Morphogenesis of curved bilayer membranes

Series
Mathematical Biology Seminar
Time
Wednesday, September 30, 2015 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Norbert Stoop – MIT
Morphogenesis of curved bilayer membranes Buckling of curved membranes plays a prominent role in the morphogenesis of multilayered soft tissue, with examples ranging from tissue differentiation, the wrinkling of skin, or villi formation in the gut, to the development of brain convolutions. In addition to their biological relevance, buckling and wrinkling processes are attracting considerable interest as promising techniques for nanoscale surface patterning, microlens array fabrication, and adaptive aerodynamic drag control. Yet, owing to the nonlinearity of the underlying mechanical forces, current theoretical models cannot reliably predict the experimentally observed symmetry-breaking transitions in such systems. Here, we derive a generalized Swift-Hohenberg theory capable of describing the wrinkling morphology and pattern selection in curved elastic bilayer materials. Testing the theory against experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictions separating distinct phases of labyrinthine and hexagonal wrinkling patterns. We highlight the applicability of the theory to arbitrarily shaped surfaces and discuss theoretical implications for the dynamics and evolution of wrinkling patterns.

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