University of Utah
Utah-Arizona IGERT Biomathematics Summit

Interdisciplinary Workshop
May 13-15, 2005

• All talks will be in LCB Rm. 215
• The workshop has no registration fees. We ask you to register by contacting Laura Miller (miller@math.utah.edu) or Tom Robbins (robbins@math.utah.edu) to indicate attendance at the workshop.
• Light refreshments will be provided during the breaks.
  
• Friday dinner, 6:30PM at the Pie Pizzeria, 1320 E 200 S, Salt Lake City, UT. Dinner expenses will, unfortunately, not be covered.
• The cookout on Saturday night will be at Professor Keener's cabin from 7:30 - ? . A $10 fee will cover all you can eat. BYOB!
  

*A list of background references for all talks is available here!

• Julia Arciero, Department of Applied Mathematics, University of Arizona,

  Title: Regulation of blood flow in the microcirculation:  Role of red
  blood cells as oxygen sensors
  
  Abstract: The most critical role of the circulatory system is to adequately supply
  tissues with oxygen.  The amount of oxygen required by a tissue varies
  according to the tissue's local metabolic activity, growth, and response to
  external stimuli.  As oxygen consumption increases within tissue, blood
  oxygen levels drop, triggering blood vessels to dilate.  This vasodilation
  causes an increase in vessel diameter, thereby leading to increased flow
  through the vessel.  The mechanism of this response is not well
  understood.  Several studies suggest that red blood cells act not only as
  oxygen carriers but also as oxygen sensors.  After passing through
  capillaries, red blood cells that have been depleted of oxygen release
  adenosine triphosphate (ATP).  This ATP triggers an electrical signal that
  is conducted upstream along blood vessel walls, causing supplying
  arterioles to dilate.  We are developing a model to predict the
  concentration of ATP and oxygen downstream of capillaries by considering
  ATP release within vessels and oxygen consumption in tissue.  We begin by
  modeling ATP release along a single vessel.  We show that the amount of ATP
  release that our model predicts is consistent with that obtained in
  experimental studies.  In the future, we will develop a theoretical model
  that considers the contributions of conducted responses and responses to
  intravascular pressure, and wall shear stress to blood flow regulation in
  vascular networks.

• Elizabeth Doman, Department of Mathematics, University of Utah,

  Title: Consequences of Spatial Organization of Cellular Connections on
  Action Potential Propagation
  
  Abstract: Cells in the ventricular myocardium are excitable, enabling the
  propagation of action potentials, which causes the cells to contract. On
  the cellular level, propagation from one
  cell to another is not smooth, but rather jumpy with a time delay on the
  order of microseconds. Tissue architecture on the cellular level plays an
  important role in producing the reliable smooth wave fronts observed on
  the tissue level. The spatial organization of gap junctional connections
  is one characteristic of the tissue architecture. In particular,
  ventricular myocardial cells are each coupled to about ~11 neighboring
  cells via gap junction channels. Therefore, wave fronts of excitation have
  many opportunities to propagate through connections in all directions. So,
  how does the spatial organization of cellular connections via gap junction
  channels affect propagation on the macroscopic level? Does this
  spatial organization make propagation failure less likely? The model
  presented in this talk is a first approach to answering some of these
  questions.
  
  

• Jon Dyhr, Department of Neuroscience, University of Arizona,

  Title:  A Cybernetic Model for Visual Speed Estimation
  
  Abstract:  A multitude of behavioral studies have shown that honeybees
  rely on a visually based estimate of speed for a number of behaviors such
  as navigation, landing and odometry. While other visual motion
  computations (such as elementary motion detection) are well understood
  behaviorally, biologically and computationally, how and where speed is
  estimated in the brain is still poorly understood. We have developed a
  computational model of visual speed estimation based on the
  electrophysiological properties and anatomical organization of neurons in
  the early stages of visual processing with two goals in mind: First, to
  gain insight into the underlying neural circuit in order to suggest
  further biological experiments and, second, to develop a computationally
  efficient algorithm that can be applied to an artificial system.
  
  

• Katherine Fitzgerald, Department of Mathematics, University of Utah,

  Title: Unicoloniality and exotic ant invasions
  
  Abstract: Unicolonial ants have an unusual social structure in which
  intraspecific aggression is uncommon, and ants from separate nests
  may cooperate with one another.  A large proportion of invasive exotic
  ant species are unicolonial, leading one to wonder whether and how
  unicoloniality might make it easier for introduced ants to establish
  and spread.  I will discuss a simulation and a mathematical model
  addressing these questions.

• Brian Hallmark, Department of Applied Mathematics, University of Arizona,

  Title: Analysis of EMG Signals: An IGERT Lab Experience
  
  Abstract: As part of the IGERT program at the University of Arizona, fellowship
  recipients take part in projects in the IGERT lab. This semester
  students divided into three groups to look at different strategies to
  extract information from electromyographic signals. Specifically, we
  looked at the use of Fourier and wavelet techniques, independent
  component analysis (ICA) and spike-triggered averaging. In this talk I
  will present the results of this endeavor.
  
  

• Lise Johnson, Biomedical Engineering, University of Arizona,

  Title: Insect Inspired Visual Depth Estimation
  
  Abstract: Depth estimation is a critical function for successful
  navigation of real world environments.  A broad variety of species use the
  expansion of an image projected onto the retina to identify objects that
  are rapidly approaching. Neurons that respond to these so-called "looming"
  stimuli are often associated with the escape response, as is the case with
  the extensively studied LGMD neuron in the locust.  Recently two
  looming-sensitive neurons identified in the tobacco hawkmoth (Manduca
  sexta) have been implicated in navigation during hovering flight.  We have
  modeled the physiological characteristics of these neurons to recreate
  this characteristic hovering behavior in computer simulation.  In this
  model the neurons receive input from elementary motion detectors.  The
  simulated neuronal outputs are used to guide a virtual insect as it
  follows a target in a three-dimensional trajectory. This model
  demonstrates how a ubiquitously occurring two-dimensional motion detection
  system can be used to predict movement in the third dimension.
  
  

• Brynja Kohler, Department of Mathematics and Statistics, Utah State University,

  Title: Linking Biology and Mathematics in Undergraduate and Secondary Education
  
  Abstract: In recent years, there has been an explosion in nationwide efforts to
  strengthen interdisciplinary connections in undergraduate education to
  meet the challenges of current research in the biological sciences.
  For example, the National Research Council published "Bio 2010," which
  emphasizes the interdisciplinary nature of current research, and the
  increasingly complex mathematical and computational skills required to
  analyze biological questions. The Mathematical Association of America
  has also addressed these needs in several reports including their
  "Committee on the Undergraduate Program in Mathematics Curriculum Guide
  2004," and a report called "Math & Bio 2010." In this talk, I will
  summarize some of the recommendations in these reports, discuss some
  innovative programs at various types of institutions, and list
  resources that support these efforts. I will also talk about
  mathematics education in general, and what I have learned in my first
  year as a faculty member at Utah State University about training future
  teachers and keeping active in mathematical biology.
  
  

• Yong-Seon Lee, Department of Mathematics, University of Utah

  Title: Calcium alternans and intracellular calcium cycling in cardiac cells
  
  Abstract: Calcium (Ca2+) alternans in cardiac cells are beat-to-beat alternations
  in the amplitudes of the systolic Ca2+ transient. We will talk about the
  mechanisms by which intracellular Ca2+ cycling induces Ca2+ alternans.
  
  First, we set up a discrete time Ca2+ movement model with two compartments:
  cytoplasm and sarcoplasmic reticulum (SR). The model shows that reduced SR
  Ca2+ release can increase the SR content. When the SR content reaches a
  threshold, CICR becomes unstable and Ca2+ alternans are exposed. A primary
  mechanism for this instability is the steep, nonlinear SR Ca2+ release function.
  
  Second, we use a CICR model by Keizer and Smith (1998) to explore the
  relation between Ca2+ waves and Ca2+ alternans. We applied a local periodic
  Ca2+ stimulation with varying pacing interval (PI).  When the total Ca2+ is
  high (Ca2+ overload), the local Ca2+ stimulation with the large PI induces
  Ca2+ waves (1:1 rhythm). As PI is reduced, propagated Ca2+ waves alternate
   with waves that fail to propagate, giving a 2:2 rhythm. This results from
  slowed recovery from refractoriness of the SR Ca2+ channel at the
  reduced PI.
  

• Karin Leiderman, Department of Mathematics, University of Utah

  Title: Capillary Endothelial Glycocalyx: An Investigation of Structure and
  Material Properties
  
  Abstract: Endothelial cells line blood vessels in the body and are constantly
  exposed to blood flow, and thus, fluid shear stress. It is well known that
  when subjected to certain types of flow for short periods of time, these
  cells will rearrange themselves in the direction of the flow, a process
  thought to be driven by the reorganization of the cytoskeleton. It is
  unlikely that cytoskeletal rearrangement is simply superficial, so there
  is also believed to be biochemical signaling involved. On the luminal side
  of endothelial cells there is a "sugar coating" known as the glycocalyx, a
  network of glycoproteins and proteoglycans.  The glycocalyx may act as a
  mechanosensor to help transmit stress across the membrane to the
  cytoskeleton and on to the nucleus, the core of biochemical activity. The
  goal here was to survey literature and find out how the structure and
  material properties of the the glycocalyx affect what is sensed by the
  cytoskeleton.
  
  

• Megan McNulty, Department of Mathematics, University of Utah

  Title: A Mathematical Model of Airway Inflammation in Cystic Fibrosis
  
  Abstract: Patients with Cystic Fibrosis (CF) suffer chronic respiratory
  infections, the two most common being Staphylococcus aureus and
  Pseudomonas aeruginosa.  These pathogens cause intense neutrophil-
  mediated airway inflammation. While the inflammation helps to clear
  the pathogen, it can also damage the surrounding tissue
  and make the airways more susceptible to subsequent infections.  
  Our objective is to determine the role of alveolar macrophages
  and neutrophils in bacterial control. We propose a system of nonlinear
  ordinary differential equations to describe interactions between
  neutrophils, macrophages, and bacteria.  Our preliminary model
  describes the pathogen S. aureus, and can be extended to other
  pathogens.

• Will Nesse, Department of Mathematics, University of Utah

  Title: The Functional Significance of Reduced Conductance in the Sino-Atrial
  Node for Cardiac Rhythmicity
  
  Abstract: The Sino-Atrial node (SAN) cells has been shown to express lower
  conductance gap junction conexions than in the adjacent atrial myocytes.
  It has been hypothesized that reduced electrical conductance in the SAN
  serves to insulate the intrinsically more depolarized and oscillatory
  SAN cells from the larger and more hyperpolarized Atrial tissue. Using a
  continuum (PDE) model with a piecewise linear version of the
  Fitzhugh-Nagumo equations I show analytically that the reduction of SAN
  conductance induces greater depolarization in the steady state solution.
  If the conductance is reduced further I show that the steady state can
  undergo a Hopf bifurcation to an oscillatory solution. Furthermore, I
  analyze the dispersion relation of the Atrial media to show that reduced
  conductance in the SAN can increase the range of oscillation frequencies
  that support traveling wave solutions.
  
  

• Andrew Oster, Department of Mathematics, University of Utah

  Title: A developmental model of ocular dominance column formation
  on a growing cortex
  
  Abstract: We derive an activity-based developmental model of ocular
  dominance column formation in primary visual cortex that takes into account
  cortical growth. The resulting evolution equation for the densities of
  feedforward afferents from the two eyes exhibits a sequence of pattern
  forming instabilities as the size of the cortex increases. We use
  linear stability analysis to investigate the nature of the transitions
  between successive patterns in the sequence. We show that these
  transitions involve the splitting of existing ocular dominance
  columns, such that the mean width of an OD column is approximately
  preserved during the course of development. This is consistent with
  recent experimental observations of postnatal growth in cat.
  
  

• Suzanne Robertson, Department of Applied Mathematics, University of Arizona

  Title: Modeling Tribolium Populations: The Role of Inhibition
  
  Abstract: The complex population dynamics of Tribolium castaneum, a
  species of flour beetles, are well explained by the "Larva-Pupa-Adult" or
  LPA Model.  This model has been validated with laboratory data over the
  past 10 years.  I will discuss the modification and extension of this
  model to describe the dynamics of several related Tribolium species,
  including T. brevicornis, T. madens, and T. freemani.  These species
  exhibit major biological differences from T. castaneum, most notably
  differences in time scale of development and inhibition of larval pupation
  under crowded conditions.  I will also discuss implications for
  competition experiments between the different species.
  
  

• Nessy Tania, Department of Mathematics, University of Utah

  Title: Spatial Coupling and the Generation of Spontaneous Oscillation in a Model
  of Border Zone Arrhythmia
  
  Abstract: Acute coronary occlusion is caused by a sudden blockage of one of the
  coronary arteries which supply to the heart muscle and leads to tissue ischemia.
  The loss of oxygen supply to the affected tissue induces various changes from
  normal cellular physiology, such as build-up of lactic acid, depletion of ATP,
  increase in extracellular potassium, and failure of gap junctions. Border zones
  between normal and ischemic tissue have been implicated to be an important
  regions of arrhythmogenic activity. Using simple ionic models, it can be shown
  that spatial inhomogeneity can induce spontaneous oscillation corresponding to
  self-sustained reentrant activity. In this talk, we will explore how ectopic
  sources can be generated in this model of border-zone arrhythmia.
  
  

• John Zobitz, Department of Mathematics, University of Utah
  
Title: Using mathematical inverse theory to estimate respiratory and
photosynthetic fluxes in a heterogeneous conifer canopy

Abstract: Quantifying and understanding the mechanisms that drive terrestrial
uptake of carbon dioxide are important to understand the role that terrestrial
ecosystems will have in a changing climate.  Estimating respiratory and
photosynthetic fluxes from ecosystem-scale carbon dioxide flux measurements
is a first step to understand these mechanisms. Mathematically, estimating
respiration and photosynthesis is an inverse problem.  In this talk I will
present how we can use inverse theory to determine these fluxes and how a
measurement technique using stable isotopes of carbon could potentially
reduce the uncertainty in these partitioned photosynthesis and respiration fluxes.