Wednesday, September 30, 2015 - 11:05 , Location: Skiles 005 , Norbert Stoop , MIT , Organizer:
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.
Thursday, February 26, 2015 - 13:30 , Location: Skiles 006 , David Dynerman , University of Wisconsin-Madison , Organizer: Christine Heitsch
Cryo-electron microscopy (cryo-EM) is a microscopy technique used to discover the 3D structure of molecules from very noisy images. We discuss how algebra can describe two aspects of cryo-EM datasets. First, we'll describe common lines datasets. Common lines are lines of intersection between cryo-EM images in 3D. They are a crucial ingredient in some 2D to 3D reconstruction algorithms, and they can be characterized by polynomial equalities and inequalities. Second, we'll show how 3D symmetries of a molecule can be detected from only 2D cryo-EM images, without performing full 3D reconstruction.
Wednesday, February 18, 2015 - 11:00 , Location: Skiles 005 , Shelby Wilson , Morehouse College , firstname.lastname@example.org , Organizer:
An array of powerful mathematical tools can be used to identify the key underlying components and interactions that determine the mechanics of biological systems such as cancer and its interaction with various treatments. In this talk, we describe a mathematical model of tumor growth and the effectiveness of combined chemotherapy and anti-angiogenic therapy (drugs that prevent blood vessel growth). An array of mathematical tools is used in these studies including dynamical systems, linear stability analysis, numerical differential equations, SAEM (Stochastic Approximation of the Expectation Maximization) parameter estimation, and optimal control. We will develop the model using preclinical mouse data and discuss the optimal combination of these cancer treatments. The hope being that accurate modeling/understanding of experimental data will thus help in the development of evidence-based treatment protocols designed to optimize the effectiveness of combined cancer therapies.
Wednesday, October 22, 2014 - 11:05 , Location: Skiles 005 , Hayriye Gulbudak , School of Biology, GaTech , Organizer:
The emerging threat of a human pandemic caused by high-pathogenic H5N1avian inuenza virus magnifies the need for controlling the incidence ofH5N1 in domestic bird populations. The two most widely used controlmeasures in poultry are culling and vaccination. In this talk, I will discussmathematical models of avian inuenza in poultry which incorporate cullingand vaccination. First, we consider an ODE model to understand the dy-namics of avian inuenza under different culling approaches. Under certainconditions, complex dynamical behavior such as bistability is observed andanalyzed. Next, we model vaccination of poultry by formulating a coupledODE-PDE model which takes into account vaccine-induced asymptomaticinfection. In this study, the model can exhibit the \silent spread" of thedisease through asymptomatic infection. We analytically and numericallydemonstrate that vaccination can paradoxically increase the total numberof infected when the ecacy is not suciently high.1
Wednesday, September 3, 2014 - 11:05 , Location: Skiles 005 , James Moore , SoM GaTech , Organizer:
The immune system must simultaneously mount a response against foreign antigens while tolerating self. How this happens is still unclear as many mechanisms of immune tolerance are antigen non-specific. Antigen specific immune cells called T-cells must first bind to Immunogenic Dendritic Cells (iDCs) before activating and proliferating. These iDCs present both self and foreign antigens during infection, so it is unclear how the immune response can be limited to primarily foreign reactive T-cells. Regulatory T-cells (Tregs) are known to play a key role in self-tolerance. Although they are antigen specific, they also act in an antigen non-specific manner by competing for space and growth factors as well as modifying DC behaviorto help kill or deactivate other T-cells. In prior models, the lack of antigen specific control has made simultaneous foreign-immunity and self-tolerance extremely unlikely. We include a heterogeneous DC population, in which different DCs present antigens at different levels. In addition, we include Tolerogenic DC (tDCs) which can delete self-reactive T-cells under normal physiological conditions. We compare different mathematical models of immune tolerance with and without Tregs and heterogenous antigen presentation.For each model, we compute the final number of foreign-reactive and self-reactive T-cells, under a variety of different situations.We find that even if iDCs present more self antigen than foreign antigen, the immune response will be primarily foreign-reactive as long as there is sufficient presentation of self antigen on tDCs. Tregs are required primarily for rare or cryptic self-antigens that do not appear frequently on tDCs. We also find that Tregs can onlybe effective when we include heterogenous antigen presentation, as this allows Tregs and T-cells of the same antigen-specificity to colocalize to the same set of DCs. Tregs better aid immune tolerance when they can both compete forspace and growth factors and directly eliminate other T-cells. Our results show the importance of the structure of the DC population in immune tolerance as well as the relative contribution of different cellular mechanisms.
Patient-Specific Computational Fluid Dynamic Simulations for Predicting Inferior Vena Cava Filter PerformanceMonday, April 28, 2014 - 13:00 , Location: IBB 1128 , Suzanne M. Shontz , Department of Mathematics and Statistics, Mississippi State University. , Organizer:
Speaker is visiting the School of Biology, Georgia Tech
Pulmonary embolism (PE) is a potentially-fatal disease in which blood clots (i.e., emboli) break free from the deep veins in the body and migrate to the lungs. In order to prevent PE, anticoagulants are often prescribed; however, for some patients, anticoagulants cannot be used. For such patients, a mechanical filter, namely an inferior vena cava (IVC) filter, is inserted into the IVC to trap the blood clots and prevent them from reaching the lungs. There are numerous IVC filter designs, and it is not well understood which particular IVC filter geometry will result in the best treatment for a given patient. Patient-specific computational fluid dynamic (CFD) simulations may be used to predict the performance of IVC filters and hence can aid physicians in IVC filter selection and placement. In this talk, I will first describe our computational pipeline for prediction of IVC filter performance. Our pipeline involves several steps including image processing, geometric model construction, in vivo stress state estimation, surface and volume mesh generation based on virtual IVC filter placement, and CFD simulation of IVC hemodynamics. I will then present the results of our IVC hemodynamics simulations obtained for two patient IVCs. This talk represents joint work with several researchers at The Pennsylvania State University, Penn State Hershey Medical Center, the Penn State Applied Research Lab, and the University of Utah.
Wednesday, April 23, 2014 - 11:00 , Location: Skiles 005 , Zoi Rapti , University of Illinois at Urbana-Champaign , Organizer: Christine Heitsch
We will introduce a PDE model to investigate how epidemic metrics, such as the basic reproductive ratio R_0 and infection prevalence, depend on a pathogen's virulence. We define virulence as all harm inflicted on the host by the pathogen, so it includes direct virulence (increased host mortality and decreased fecundity) and indirect virulence (increased predation on infected hosts). To study these effects we use a Daphnia-parasite disease system. Daphnia are freshwater crustaceans that get infected while feeding, by consuming free-living parasite spores. These spores after they are ingested, they start reproducing within the host and the host eventually dies. Dead hosts decay releasing the spores they contain back in the water column. Visual predators, such as fish, can detect infected hosts easier because they become opaque, hence they prey preferentially on them. Our model includes two host classes (susceptible and infected), the free-living propagules, and the food resource (algae). Using experimental data, we obtain the qualitative curves for the dependence of disease-induced mortality and fecundity reduction on the age of infection. Among other things, we will show that in order the predator to keep the host population healthy, it needs to (i) detect the infected hosts very soon after they become infected and (ii) show very high preference on consuming them in comparison to the uninfected hosts. In order to address questions about the evolution of virulence, we will also discuss how we defined the invasion fitness for this compartmental model. We will finish with some pairwise invasibility plots, that show when a mutant strain can invade the resident strain in this disease system.
Wednesday, March 12, 2014 - 11:00 , Location: Skiles 005 , Chi-Jen Wang , Iowa State , Organizer: Christine Heitsch
Spatially discrete stochastic models have been implemented to analyze cooperative behavior in a variety of biological, ecological, sociological, physical, and chemical systems. In these models, species of different types, or individuals in different states, reside at the sites of a periodic spatial grid. These sites change or switch state according to specific rules (reflecting birth or death, migration, infection, etc.) In this talk, we consider a spatial epidemic model where a population of sick or healthy individual resides on an infinite square lattice. Sick individuals spontaneously recover at rate *p*, and healthy individual become infected at rate O(1) if they have two or more sick neighbors. As *p* increases, the model exhibits a discontinuous transition from an infected to an all healthy state. Relative stability of the two states is assessed by exploring the propagation of planar interfaces separating them (i.e., planar waves of infection or recovery). We find that the condition for equistability or coexistence of the two states (i.e., stationarity of the interface) depends on orientation of the interface. We also explore the evolution of droplet-like configurations (e.g., an infected region embedded in an all healthy state). We analyze this stochastic model by applying truncation approximations to the exact master equations describing the evolution of spatially non-uniform states. We thereby obtain a set of discrete (or lattice) reaction-diffusion type equations amenable to numerical analysis.
Wednesday, March 5, 2014 - 11:00 , Location: Skiles 005 , Professor Juan Gutierrez , UGA , email@example.com , Organizer:
The traditional epidemiological approach to characterize transmission of infectious disease consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and vectors into susceptible, exposed and infected (SEI), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). Compartmentalized models are based on a series of simplifying assumptions and have been successfully used to study a broad range of disease transmission dynamics. These paradigm is challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: An infection can include the simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus an individual might belong to multiple compartments simultaneously. This precludes the traditional calculation of the basic reproductive number. (ii) Antigenic diversity and variation: Antigenic diversity, defined as antigenic differences between pathogens in a population, and antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the host immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission.This talk explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics in environmental transmission. A basic propagation number is calculated that could guide public health policy.
Wednesday, February 19, 2014 - 11:00 , Location: Skiles 005 , Rigoberto Hernandez , GT Chem & Biochem , Organizer: Christine Heitsch
The behavior and function of proteins necessarily occurs during nonequilibrium conditions such as when a protein unfolds or binds. The need to treat both the dynamics and the high-dimensionality of proteins and their environments presents significant challenges to theoretical or computational methods. The present work attempts to reign in this complexity by way of capturing the dominant energetic pathway in a particular protein motion. In particular, the energetics of an unfolding event can be formally obtained using steered molecular dynamics (SMD) and Jarzynski’s inequality but the cost of the calculation increases dramatically with the length of the pathway. An adaptive algorithm has been introduced that allows for this pathway to be nonlinear and staged while reducing the computational cost. The potential of mean force (PMF) obtained for neuropeptide Y (NPY) in water along an unfolding path confirmed that the monomeric form of NPY adopts the pancreatic-polypeptide (PP) fold. [J. Chem. Theory Comput. 6, 3026-3038 (2010); 10.1021/ct100320g.] Adaptive SMD can also be used to reconstruct the PMF obtained earlier for stretching decaalanine in vacuum at lower computational cost. [J. Chem. Phys. 136, 215104 (2012); 10.1063/1.4725183.] The PMF for stretching decaalanine in water solvent (using the TIP3P water potential) at 300K has now been obtained using adaptive SMD. [J. Chem. Theory Comput. 8, 4837 (2012); 10.1021/ct300709u] Not surprisingly, the stabilization from the water solvent reduces the overall work required to unfold it. However, the PMF remains structured suggesting that some regions of the energy landscape act partially as doorways. This is also further verified through a study of the hydrogen-bond breaking and formation along the stretching paths of decaalanine in vacuum and solvent. (Rescheduled from Feb 12th.)