2011-2012 Colloquia

September 26, 2011 2:30 - 3:30PM
Abstract
Ecological systems may exhibit complex dynamics, yet the spatial and temporal scales over which these play out make them difficult to explore experimentally. An alternative approach is to develop models based on detailed biological information about the systems and then fit them to observational data using nonlinear time-series techniques. I will give two examples of this approach, both involving systems with alternative states. The first is the dynamics of midges in Lake Myvatn, Iceland, which show fluctuations with amplitudes >105 yet with irregular period. A nonlinear time-series analysis demonstrates that these dynamics could be caused by the system having two states, a stable point and a stable cycle, with the irregular period caused by the population stochastically jumping from the domain of one state to the other. The second example is the dynamics of salvinia, an aquatic weed, and the salvinia weevil that was introduced into the billabongs of Kakadu to control the weed. Here the alternative states are two environmentally (seasonally) forced cycles, one in which salvinia is kept in check by the weevil and one in which it escapes. Understanding complex ecological dynamics may improve our management of vigorously fluctuating natural systems.
October 03, 2011 2:30 - 3:30PM
Abstract
Expression of microRNAs, a new class of noncoding RNAs that hybridize to target messenger RNA and regulate their translation into proteins, has been recently demonstrated to be altered in acute myeloid leukemia (AML). Distinctive patterns of increased expression and/or silencing of multiple microRNAs (microRNA signatures) have been associated with specific cytogenetic and molecular subsets of AML. Changes in the expression of several microRNAs altered in AML have been shown to have functional relevance in leukemogenesis, with some microRNAs acting as oncogenes and others as tumor suppressors. Both microRNA signatures and a single microRNA have been shown to supply prognostic information complementing to that gained from cytogenetics, gene mutations, and altered gene expression. Moreover, it has been demonstrated experimentally that microRNAs contribute with signaling pathways to leukemogeneic networks and the antileukemic effects can be achieved by modulating microRNA expression by pharmacologic agents and/or increasing low endogenous levels of microRNAs with tumor suppressor function by synthetic microRNA oligonucleotides, or down-regulating high endogenous levels of leukemogenic microRNAs by antisense oligonucleotides (antagomirs). Therefore, it is reasonable to predict the development of novel microRNA-based diagnostic, prognostic and therapeutic approaches in AML.
October 17, 2011 2:30 - 3:30PM
Abstract
In this talk we use a realistic model to demonstrate how mathematics can be applied in real-life applications. An image-based human heart model with fluid-structure interactions (FSI) was introduced to evaluate human heart cardiac function before and after surgery and optimize human pulmonary valve replacement/insertion (PVR) surgical procedure and patch design. Cardiac Magnetic Resonance (CMR) imaging studies were performed to acquire ventricle geometry, flow velocity and flow rate for healthy volunteers and patients needing right ventricle (RV) remodeling and PVR before and after scheduled surgeries. CMR-based RV/LV/Patch FSI models were constructed to perform mechanical analysis and provide accurate assessment for RV mechanical conditions and cardiac function. These models include a) fluid-structure interactions, b) isotropic and anisotropic material properties, c) two-layer construction with myocardial fiber orientation, and d) active contraction. When validated, the computational modeling approach could be used to replace actual surgical experiments on real patients by "virtual" surgery using computational simulations to optimize surgical outcome.

Acknowledgement: This research was in collaboration with Pedro Del Nido, MD, William E. Ladd Professor of Surgery, Chairman of Cardiac Surgery, and Tal Geva, MD, Director of Cardiac MRI Department, Children's Hospital Boston, Harvard Medical School, USA. It was supported in part by NIH R01 HL089269 (del Nido, Tang, Geva), NIH-R01 HL63095 (PJdN), and NIH- 5P50 HL074734 (Clinical Trial, PI-Geva).
October 31, 2011 2:30 - 3:30PM
Abstract
The typical mammalian cortical neuron has about 5000 microns of dendrite. These dendrites are studded with synapses at a density of 1 per micron. The dendrites integrate this spatially distributed transient stimulus and coax, on occasion, the neuron to fire. Although the underlying mechanisms are known and well modeled, the sheer complexity has to date retarded attempts to incorporate such models in large network level simulations. In this talk we will couple structure preserving projection techniques for reducing the dynamics of the weakly excitable dendrites with discrete empirical interpolation near the spike initiation zone and arrive at a model with significantly fewer internal variables without sacrificing accuracy of the cell's input/output map. We will then demonstrate their ability to efficiently capture network level behavior.
November 07, 2011 2:30 - 3:30PM
Abstract
The development of mathematical models for chemical systems based on, for example, density functional theory, have provided key insight into the manner in which chemical transformations occur and the nature of intermediates that form in the course of the reaction. In enzymology, these approaches have proven very successful not only in establishing the chemical sequence of events involved in converting substrate to product but, importantly, how the enzyme accomplishes its critical task physiologically of making the reaction go so fast - typically 1012 to 1014 times faster than the uncatalyzed reaction. Here we dissect the reaction mechanism of the enzyme xanthine oxidase using the tools of density functional theory, and examine the basis for rate acceleration in the context of the enzyme's structure.
November 21, 2011 2:30 - 3:30PM
Abstract
Bacteria are the most abundant organisms on Earth and they significantly influence carbon cycling and sequestration, decomposition of biomass, and transformation of contaminants in the environment. This motivates our study of the basic principles of bacterial behavior and its control. We have conducted analytical, numerical and experimental studies of suspensions of swimming bacteria. In particular, our studies reveal that active swimming of bacteria drastically alters the material properties of the suspension: the experiments with bacterial suspensions confined in thin films indicate a 7-fold reduction of the effective viscosity and a 10-fold increase of the effective diffusivity of the oxygen and other constituents of the suspending fluid. The principal mechanism behind these unique macroscopic properties is self-organization of the bacteria at the microscopic level - a multiscale phenomenon. Understanding the mechanism of self-organization in general is a fundamental issue in the study of biological and inanimate system. Our work in this area includes

* Numerical modeling. Bacteria are modeled as self-propelled point force dipoles subject to two types of forces: hydrodynamic interactions with the surrounding fluid and excluded volume interactions with other bacteria modeled by a Lennard-Jones-type potential. This model, allowing for numerical simulations of a large number of particles, is implemented on the Graphical Processing Units (GPU), and is in agreement with experiments.

* Analytical study of dilute suspensions. We introduced a model for swimming bacteria and obtained explicit asymptotic formula for the effective viscosity in terms of known physical parameters. This formula is compared with that derived in our PDE model for a dilute suspension of prolate spheroids driven by a stochastic torque, which models random reorientation of bacteria ("tumbling"). It is shown that the steady-state probability distributions of single particle configurations are identical for the dilute and semi-dilute models in the limiting case of particles becoming spheres. Thus, a deterministic system incorporating pairwise hydrodynamic interactions and excluded volume constraints behaves as a system with a random stochastic torque. This phenomenon of stochasticity arising from a deterministic system is referred to as self-induced noise.

* Kinetic collisional model-work in progress. Most of the previous work on bacterial suspensions ignores collisions. These inelastic interactions lead to an alignment of the nearby-swimming bacteria, which has been indeed observed experimentally. To understand the onset of collective motion in the above model, we investigate the correlation of bacterial velocities and orientations as a function of the interparticle distance. We seek to capture a phase transition in the bacterial suspension - an appearance of correlations and local preferential alignment with an increase of concentration. A probabilistic model for the distribution function for bacterial positions and orientations will be derived in the presence of self-induced noise.

Collaborators: PSU students S. Ryan and B. Haines, and DOE scientists I. Aronson and D. Karpeev (both Argonne Nat. Lab)
January 09, 2012 2:30 - 3:30PM
Abstract

We review winner-loser models, the currently popular explanation for the occurrence of linear dominance hierarchies, via a three-part approach. 1) We isolate the two most significant components of the mathematical formulation of three of the most widely-cited models and rigorously evaluate the components' predictions against data collected on hierarchy formation in groups of hens. 2) We evaluate the experimental support in the literature for the basic assumptions contained in winner-loser models. 3) We apply new techniques to the hen data to uncover several behavioral dynamics of hierarchy formation not previously described. The mathematical formulations of these models do not show satisfactory agreement with the hen data, and key model assumptions have either little, or no conclusive, support from experimental findings in the literature. In agreement with the latest experimental results concerning social cognition, the new behavioral dynamics of hierarchy formation discovered in the hen data suggest that members of groups are intensely aware both of their own interactions as well as interactions occurring among other members of their group. We suggest that more adequate models of hierarchy formation should be based upon behavioral dynamics that reflect more sophisticated levels of social cognition.


January 23, 2012 2:30 - 3:30PM
Abstract

Numerical models and observational data are critical in modern science and engineering. Since both of these information sources involve uncertainty, the use of statistical, probabilistic methods play a fundamental role. I discuss a general Bayesian framework for combining uncertain information and indicate how various approaches (ensemble forecasting, UQ, etc.) fit in this framework. A paleoclimate analysis illustrates the use of simple physics and statistical modeling to produce inferences. A second example involves glacial dynamics and illustrates how updating models and data can lead to estimates of model error. A third example involves the extraction of information from multi-model ensembles in climate projection studies.


February 27, 2012 2:30 - 3:30PM
Abstract
Sequencing data are often obtained by biologists wishing to explore details of a system with which they are extremely familiar; however, analysis techniques exclude these experts and often rely on assumptions that may not be relevant to the experimental design. While biologists can manually explore their data using newer, high-capacity genome browsers, and can often suggest relevant hypotheses for statistical testing, fully informed and thorough data exploration is impossible to do by eye. We have created a biologically-based and statistically grounded tool for determining the correlation of genomewide data with other datasets or known biological features, intended to guide biological exploration of high-dimensional datasets and to act as a hypothesis generator (not intended to provide "answers"). The software enables several biologically motivated approaches to these data; in fact, each analytical approach was inspired by our own work. Our models and statistics are implemented in an R package that efficiently calculates the spatial correlation between two sets of genomic intervals (data and/or annotated features), for use as a metric of functional interaction. The software is accessible from the command line, through a Tk interface, and through a Galaxy plugin, and is intended to guide biologists and statisticians more quickly to the significant features of high-dimensional datasets.
March 05, 2012 2:30 - 3:30PM
Abstract
Sequencing studies, such as targeted, whole exome and whole genome sequencing studies, are increasingly being conducted to identify rare variants that are associated with complex traits. Design and analysis of such population based sequencing association studies face many challenges. The talk has three parts. I will first provide an overview of several methods for studying rare variant effects, including burden tests, SKAT and optimal unified tests. Analysis pipelines for whole exome sequencing association studies, such as filtering criteria and small sample adjustments of statistical methods, will be discussed. In the second part of the talk, I will discuss designs of sequencing association studies, such as sample size and power calculations, and pros and cons of extreme phenotype sampling and analysis strategies for extreme phenotype sequencing studies. In the last part of the talk, I will discuss the performance of imputation using GWAS data for studying rare variants effects. Simulation studies and real data will be used to illustrate the results.
April 02, 2012 2:30 - 3:30PM
Abstract

A number of phenomena in visual perception involve wave-like propagation dynamics. Examples include perceptual filling-in, migraine aura, and the expansion of illusory contours. Another important example is the wave-like propagation of perceptual dominance during binocular rivalry. Binocular rivalry is the phenomenon where perception switches back and forth between different images presented to the two eyes. The resulting fluctuations in perceptual dominance and suppression provide a basis for non-invasive studies of the human visual system and the identification of possible neural mechanisms underlying conscious visual awareness. In this talk we present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are taken to be inhibitory (cross-inhibition). Slow adaptationis incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a "symmetry breaking mechanism" that allows waves to propagate. We end by discussing recent work on the effects of noise.

April 09, 2012 2:30 - 3:30PM
Abstract

Odors are important cues for identification of many types of objects that animals need for survival. Natural odors are typically mixtures of up to a few dozen chemical components. Important information about odor 'objects' is often encoded in the ratio of components in the mixture. However, this odor mixture problem is complicated by two factors. First, many times the information channel is composed of a submixture of the overall mixture composition. Second, the ratios of components in the submixture can vary from one object to the next, which means that animals must learn to 'generalize' across a range of variation among objects that mean the same thing. Floral odors, for example, are important for honey bees to locate nectar and pollen sources that their colony needs for survival. Honey bees need to learn about the range of variation in odor composition so that they can optimally include flowers that have resources and exclude flowers with similar odors but which do not have nectar or pollen. I argue that nonassociative and associative plasticity in neural networks involved in early sensory coding is critical for extracting the relevant features of an odor mixture and setting up categories of odor objects. This plasticity can enhance decisions about pattern matching and multimodal associations in later processing in the brain.

April 23, 2012 2:30 - 3:30PM
Abstract

The genetic differences that separate humans from other great apes seem modest, yet we are a prominent phenotypic outlier in several regards. Although little is known about the genetic and molecular bases underlying uniquely human traits, changes in gene regulation are likely an important component. My group is currently investigating changes in the transcriptomes of multiple tissues that accompanied human origins. We use genome-wide functional assays to identify the molecular mechanisms that mediate evolutionary changes in transcription, including the role of chromatin configuration and the function of noncoding RNAs. These assays highlight genomic regions of particular interest, where we have carried out focused functional analyses that provide insights into the evolution of human diet and brain size.