2014 Undergraduate Capstone Conference

(August 11,2014 - August 15,2014 )

A student centered conference featuring talks and posters by students doing research in mathematical biology, keynotes by prominent mathematical biologists, a graduate studies recruitment fair, and other special features including a conference dinner and social event.

Graduate studies in the Mathematical Biosciences Panel: This panel will focus on opportunities for graduate studies in the Mathematical Biosciences. Presenters from Arizona State University (Fabio Milner) and Ohio State University (Elizabeth Stasny) will discuss the different types of graduate programs offered in the Mathematical Biosciences and how to position yourself to present your best case for admission and to be successful in your graduate training. Jennifer Slimowitz-Pearl from the National Science Foundation will describe the fellowship and research opportunities for graduate students available from NSF.   

Deadline for applications: July 12, 2014

Accepted Speakers

Emery Brown
Computational Neuroscience, Massachusetts Institute of Technology
Carolyn Cho
Quantitative Pharmacology & Pharmacometrics, Merck, Sharp & Dohme
Rebecca Doerge
Statistics, Purdue University
Bob Full
Department of Integrative Biology, University of California, Berkeley
Kirk Jordan
Computational Science, IBM T.J. Watson Research Center
Fabio Milner
School of Mathematics and Statistical Sciences, Arizona State University
Jeff Sloan
Health Sciences Research, Mayo Clinic
Elizabeth Stasny
Statistics, The Ohio State University
Monday, August 11, 2014
Time Session
07:45 AM

Shuttle to MBI

08:00 AM
08:30 AM

Breakfast

08:30 AM
09:00 AM

MBI and conference introductions

09:00 AM
09:30 AM
Jane Coons - Student Presentation: Combinatorics of k-Interval Cospeciation for Cophylogeny

Cophylogenetics is the study of the evolutionary relationships between taxonomical units that are believed to be evolving concomitantly. We examine the combinatorial properties of the cophylogenetic distance metric, k-interval cospeciation, which was introduced by Huggins, Owen and Yoshida in their 2012 paper, "First steps toward the geometry of cophylogeny." We determined that k-interval cospeciation is a unique discrete distance metric which can quantify a degree of global congruence between two phylogenetic trees while allowing for local incongruence. We counted the size of the neighborhood of trees which satisfy the largest possible k-interval cospeciation with a given tree. Due to the way this neighborhood of trees grows as a proportion of all possible trees, we believe that k-interval cospeciation may prove useful for analyzing data obtained through simulations.

09:30 AM
10:00 AM
Emma Rogge - Student Presentation: Statistical Method for Detection of Differential DNA Methylation

Abstract not submitted.

10:00 AM
10:30 AM
Paulina Spencer, Jamal Moss, Benjamin Hamm - Student Presentation: Analyzing Honey Bee Characteristics Using Digital Image Processing & In Vitro Queen Rearing

Abstract not submitted.

10:30 AM
11:00 AM

Break

11:00 AM
12:00 PM
Emery Brown - Keynote Presentation: The Dynamics of the Unconscious Brain Under General Anesthesia

General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. The mechanisms by which anesthetic drugs induce the state of general anesthesia are considered one of the biggest mysteries of modern medicine. We study three problems to decipher this mystery. First, we present findings from our human studies of general anesthesia using combined fMRI/EEG recordings, high-density EEG recordings and intracranial recordings which have allowed us to give a detailed characterization of the neurophysiology of loss and recovery of consciousness due to propofol. Second, we present a neuro-metabolic model of burst suppression, the profound state of brain inactivation seen in deep states of general anesthesia. We show that our characterization of burst suppression can be used to design a closed-loop anesthesia delivery system for control of a medically-induced coma. Finally, we demonstrate that the state of general anesthesia can be rapidly reversed by activating specific brain circuits. Our results show that it is now possible to have a detailed neurophysiological understanding of the brain under general anesthesia, and that this understanding, can be used to control anesthetic states. Hence, general anesthesia is not a mystery.

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:00 PM
Bohyun Kim - Student Presentation: The effect of locomotion on body temperature control mechanism

We created a mathematical model to describe core (body) temperature responses to exercise at different ambient temperatures based on an experiment data. In the experiment, rats were forced to run on a treadmill at different speeds. Their core temperature time-series were recorded during 15 min runs with speeds 0, 6, 12, and 18 m/min at 0 incline in cool (24C, T1) and hot (32C, T2) environment. At T1 there was a temperature drop during first 5 min, while at T2 temperature did not change during that period. After 5 min, temperature started rising linearly at both T1 and T2 until the treadmill was stopped. The slope of this linear increase remained constant for all four speeds at T1, whereas at T2 it progressively steepened with the speed increase. To explain these findings, we have designed a model which consisted of two body components exchanging heat: the core and muscles. The core dissipated heat proportionally to difference between the core and ambient temperatures. This model was formally described by a system of two differential equations. All parameters of the system were subject to fit the average temperature response curves obtained from the experiment. Hypothermia during the first 5 min at T1 was interpreted as a result of decreased thermogenesis in the core to compensate for the heat generated by locomotion on the treadmill. This drop was not observed at T2 because heat production in the core was too small, and no further decrease was possible. The linear increase of core body temperature after 5 min was a result of heat generation in muscles. We hypothesize that exercise activates thermoregulatory inhibition of thermogenesis and/or increases heat dissipation, which prevents excessive heat accumulation during exercise in cool environment. However, at high ambient temperature this thermoregulatory compensation is impossible because the core metabolism cannot be reduced any further, while heat dissipation is already at its maximum. Therefore, heat generation by exercise added to heat accumulation and presented itself as an increased rate of the temperature growth. We conclude that compensatory mechanisms in the thermoregulatory system may underlie some controversial results concerned with the role of locomotion in the body temperature dynamics.

02:00 PM
02:30 PM
02:30 PM
03:00 PM

Break

03:00 PM
03:30 PM
Neda Jamshidi-Azad - Student Presentation: Four Compartment Model Illustrating the Spread of Antibiotic Resistant Bacteria

Abstract not submitted.

03:30 PM
04:00 PM
Jamie Cyr, Tanya Karagiannis - Student Presentation: Modeling Actin Regulaton During the Formation of Invadopodia in Metastatic Mammary Carcinoma

Abstract not submitted.

04:00 PM
05:30 PM

Reception & Student Poster Session I

05:30 PM

Shuttle pick-up from MBI

Tuesday, August 12, 2014
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Yating Wang - Student Presentation: Networks of Spiking Neurons in the Brain Visual Cortex

Abstract not submitted.

09:30 AM
10:00 AM
Jennifer Houser - Student Presentation: Modeling Latency of Thalmocortical Fast-Spiking Interneurons in Schizophrenia

Neural thalamocortical circuits relay external sensations from to the thalamus to the cortex where sensory information is then processed. Feedforward inhibition involving a subtype of fast-spiking interneurons, which are marked by the calcium-binding protein parvalbumin, reduce the chance that a postsynaptic neuron will fire an action potential. Consequences on the circuit due to the absence of parvalbumin expression in fast-spiking neurons in schizophrenia patients are caused by fast-spiking latency. In this presentation, we present a conventional neuron model. We will show how to develop a mathematical model to incorporate a latency effect as well as show numerical simulations.

10:00 AM
10:30 AM
Benjamin Liska - Student Presentation: A Mathematical Approach to Uncovering Regulatory Mechanisms in Calcium Homeostasis

Calcium is a mineral essential to many systems of life. As such, the body regulates levels of calcium in the blood plasma very tightly through a process known as calcium homeostasis. The controlling mechanisms in this process include parathyroid hormone, calcitonin, vitamin D, and the mineral phosphate. Much research has been done on the biology of this system but it is not understood completely. Recently, work has been done to mathematically model this system, however, these models are very complex. In this talk, we will provide a simplified mathematical model of calcium homeostasis that still captures biologically relevant mechanisms. Using the modeling software COPASI (Hoops 2006), we will show numerical simulations and comparisons to experimental data. An analysis of the stability of our nonlinear model provides insights into our dynamical system. We will conclude by showing ways we can predict how various diseases can disturb calcium homeostasis and provide suggestions for further investigation that could lead to effective treatments.

10:30 AM
11:00 AM

Break

11:00 AM
12:00 PM
Bob Full - Keynote Presentation: Using Mathematical, Physical and Animal Models to Discover the Principles of Motion Science

Guided by direct experiments on many-legged animals, mathematical models and physical models (robots), we postulate a hierarchical family of control loops that necessarily include constraints of the body’s mechanics. At the lowest end of this neuromechanical hierarchy, we hypothesize the primacy of mechanical feedback – neural clocks exciting tuned muscles acting through chosen skeletal postures. Control algorithms appear embedded in the form and skeleton of the animal itself. The control potential of muscles must be realized through complex, viscoelastic bodies. Bodies can absorb and redirect energy for transitions. Tails can be used as inertial control devices. On top of this physical layer reside sensory feedback driven reflexes that increase an animal’s stability further and, at the highest level, environmental sensing that operates on a stride-to-stride timescale to direct the animal’s body. Most importantly, locomotion requires an effective interaction with the environment. Understanding control requires understanding the coupling to environment. Amazing feet permit creatures such as geckos to climb up walls at over meter per second without using claws, glue or suction - just molecular forces using hairy toes. Fundamental principles of animal locomotion have inspired the design of self-clearing dry adhesives and autonomous legged robots such as the Ariel, Mecho-gecko, Sprawl, RHex, RiSE, Stickybot and DASH that can aid in search and rescue, inspection, detection and exploration.

12:00 PM
01:30 PM

Pizza Lunch & Student Poster Session II

01:30 PM
02:00 PM

Break

02:00 PM
02:30 PM
Madeline Edwards, Akira Horiguchi - Student Presentation: Transcription Factors and Cascade Network

Transcription factors (TFs) often bind to specific DNA sequences to promote or block gene expression. The interactions between TFs and target DNA sequences may be regulated by DNA methylation. It has been well recognized that DNA methylation plays an important role in neural differentiation, which is determined by a cascade of TFs. However, the epigenetic regulated TF programs critical to brain development remain largely unexplored.

To fill in such a knowledge gap, we first analyzed mammalian brain methylomes to identify genomic loci differentially methylated during development. We compiled a set of experimentally validated TF binding sites from TRANSFAC 7.0, JASPAR 2014, and UniPROBE databases, and applied HOMER to identify TFs of which binding sites enriched in genomic regions hypomethylated in neurons and glial cells, respectively. Using MEME Suite and ClusterZ, we then determined pairs of TFs with binding sites frequently overlapped. With the Cytoscape program, we created a network of possible TF interactions, which can either be complex formation or regulatory. This predicted network provides novel insight to the epigenetic regulation controlling brain development.

02:30 PM
03:00 PM
China Mauck, William Duncan - Student Presentation: A Model for Transport in Stereocilia

Stereocilia are highly regulated structures vital for hearing and balance in mammals. However, it is not known how their lengths are maintained. Models have been made to study possible mechanisms for actin filament maintenance in cellular protrusions, but they rely on actin treadmilling, which recent work suggests does not occur in stereocilia. We modify an existing model of motor and cargo distributions in cellular protrusions to account for the absence of treadmilling. We consider cargo which is incorporated at the tip of stereocilia as would be typical of actin cross-linking proteins. The qualitative properties of the distributions do not change by removing retrograde flow from the model, but there is less cargo along the majority of the stereocilium with retrograde flow. With degradation of the motors and cargo, the proteins are concentrated at the tip of the stereocilium as is seen in experimental data.

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Brady Melton, Rebecca Law - Student Presentation: Evaluating the Strength of Evidence in DWI Cases Presented in North Carolina

Criminal penalties for driving while intoxicated (DWI) in North Carolina are based on hard thresholds; for example, having a blood alcohol content (BAC) at or above 0.08 is considered legally impaired. However, BAC measurements are typically taken using breathalyzers, which are subject to measurement error. Additionally, breathalyzer readings in North Carolina are truncated, i.e. a person blowing a 0.079 would have a breathalyzer reading of 0.07. The purpose of our research is to explore this error and to construct recommendations for both law enforcement and courtroom decisions. Using data collected from breathalyzer tickets in Orange County, we have estimated the measurement error using a truncated random effects model and have calculated a prediction interval to determine any individual’s true BAC given the individual’s breathalyzer results. We also ran a parallelized simulation study to determine the effects of the distribution parameters on our model, and plan on exploring factors such as temperature, humidity, and machine calibration. We have created two lookup tables to determine an individuals true BAC, one based on prediction intervals, and the other on the probability that an individual’s true BAC is above 0.08. Using these lookup tables, the courts can determine the strength of evidence in DWI cases.

04:00 PM

Shuttle pick-up from MBI

Wednesday, August 13, 2014
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Omar Khan - Student Presentation: Deciphering the Gating Properties of P2X4 Receptor Channels using Markov State Models

Purinergic P2X receptors are a family of seven (labeled P2X1-7R) ATP-gated non-selective cation channels, ubiquitously expressed in the body. Abnormalities in them could lead to tissue inflammation and chronic pain. All members of this family are trimeric channels with three agonist binding sites that are activated and opened when occupied by ATP. The kinetics of activation (rising phase of current), desensitization (decay of current in the presence of ATP) and deactivation (decay of current after removal of ATP) are receptor-specific. The P2X4 subunit is the most widely distributed in the brain. Homomeric P2X4Rs desensitize with moderate rates, and desensitization is coupled to extensive internalization and recycling of receptors to the membrane. P2X4R is allosterically modulated by ivermectin (IVM), which increases both the ATP potency and the peak amplitude of the current (i.e., induces receptor sensitization), reduces the desensitization rate, greatly prolongs deactivation of current after ATP removal, and alters the recycling process. Many aspects of P2X4R gating have not yet been clarified and there is no comprehensive mathematical model describing its kinetics. No rationale has been provided for how IVM rescues receptors from desensitization, why it slows receptor deactivation, or why it affects receptor recycling. Using electro-physiological (current-recording) data from Stojilkovic Lab (NIH), we will be developing Markov state models and conducting systematic model comparisons and parameter optimization methods by utilizing Markov Chain Monte Carlo techniques based on Bayesian Theory, to determine the most likely model and parameter set(s) that can capture the kinetics of these receptors. The goal is to produce a model that can successfully explain the underlying mechanism of desensitization, recycling, and IVM-dependent sensitization in P2X4Rs. The parameter set(s) will be retrieved from probability distributions generated from these iterative methods.

09:30 AM
10:00 AM
Gregory McCarthy - Student Presentation: Sensitivity Analysis of a Dynamical Systems Model of Gene Regulation in Drosophila Melanogaster

I am working with Jacqueline M. Dresch (Mathematics, Amherst College) and Robert A. Drewell (Biology, Amherst and Mount Holyoke Colleges) on parameter sensitivity analysis of a dynamic model of eukaryotic gene regulation in the Drosophila embryo. I am primarily concerned with understanding the relative importance of various components of the system, such as transcription and translation, as well as the biological and mathematical interpretations of. I performed sensitivity analysis on a model with initial inputs corresponding to both maternal genes and housekeeping genes in Drosophila melanogaster at various points across the anterior-posterior axis of the embryo as well as at various time points during early development. I compared my individual parameter sensitivities to values found experimentally in the study conducted by Li et. al. (PeerJ, 2014) and considered how these sensitivities change spatially and temporally during development. I found that the calculated parameter sensitivities on a simplified version of the reaction-diffusion model developed in Dresch et. al. (SIAM J. Appl. Math, 2013) are in agreement with those generated by the biological experiments of Li et al. As such, this appears to be a valid model to use for dynamic gene regulation. Additionally, the sensitivities for all genes considered exhibit competitive dynamic behavior across the development window. This suggests the importance of considering a dynamic model of gene regulation.

10:00 AM
10:30 AM
Mo Shen - Student Presentation: Shape Representation Via Rotational Descriptor

Abstract not submitted.

10:30 AM
11:00 AM

Break

11:00 AM
12:00 PM

Panel on Graduate Programs in the Mathematical Biosciences Panelists: Jennifer Slimowitz Pearl, NSF; Elizabeth Stasny, OSU Stats; Fabio Milner, ASU Math and Statistical Sciences

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:00 PM
Hannah Biegel - Student Presentation: Predicting Off-Treatment Duration in Prostate Cancer Patients: A Comparison Across Models (Part I)

Abstract not submitted.

02:00 PM
02:30 PM
Jake Weissman - Student Presentation: Predicting Off-Treatment Duration in Prostate Cancer Patients: A Comparison Across Models (Part II)

Abstract not submitted.

02:30 PM
03:00 PM

Break

03:00 PM
04:00 PM

Grad Program highlights (short presentations by programs taking part in Recruitment Fair)

04:00 PM
06:00 PM

Grad Studies Fair - top floor library (M. Reed - Duke, F. Milner - ASU, J. Arciero & Y. Molkov - IUPUI, R. Iyer - Texas Tech, A. Jilkine - Notre Dame, J. Keener - Univ. of Utah, L. Kubatko - OSU, J. Lowengrup - UCI, K. O' Hara - VBI)

06:10 PM

Shuttle pick-up from MBI

Thursday, August 14, 2014
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
10:00 AM
Rebecca Doerge - Keynote Presentation: Analysis of Next-Generation Sequencing Data and Related Statistical Issues

This is an exciting and influential time for the field of Statistics in science. Technological advances in genetic, genomic, and the other 'omic sciences are providing large amounts of complex data that are presenting a number of challenges for the biological community. Many of these challenges are deeply rooted statistical issues that involve experimental design. Although there are many different computational tools for processing these data, there are a limited number of statistical methods for analyzing them, and even fewer that acknowledge the unique nature of these data. After a discussion about experimental design for next-generation sequencing experiments, a simple approach based on a two-stage Poisson model for modeling RNA sequencing data will be presented for the purpose of testing biologically important changes in gene expression. If time allows, a new approach that addresses sequence tag abundance, and the need to adjust for it in next-generation sequencing data, will be presented. The advantages of these approaches are demonstrated through simulations and real data applications.

10:00 AM
10:30 AM

Break

11:00 AM
12:00 PM

Panel on Career Opportunities in Mathematical Biology Panelists: Carolyn Cho, Merck Pharmaceuticals; Jeff Sloan, Mayo Clinic; Kirk Jordan, IBM

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:00 PM
Spencer Whiteman - Student Presentation: A theoretical model of tissue oxygenation in the retina

Open-angle glaucoma (OAG) is characterized by progressive retinal ganglion cell death and vision loss. Although elevated intraocular pressure is the primary risk factor for OAG, several studies have shown that impaired perfusion and oxygen delivery to retinal ganglion cells may also contribute to OAG pathophysiology. In this study, a realistic vascular network model of the mouse retina is developed based on previously published confocal microscopy images and modeling data. A mathematical model based on Green’s functions is applied to this network to predict tissue oxygenation in a healthy retina. The model will be extended to predict the conditions that lead to observed tissue oxygenation changes in glaucoma patients. Preliminary model predictions suggest that theoretical models in combination with oximetry measures are needed to guide the differentiation and identification of the most relevant risk factors for OAG.

Mentor: Julia Arciero, Department of Mathematical Sciences, Purdue School of Science, IUPUI

02:00 PM
02:30 PM
Casey Shiring - Student Presentation: How to Deal with Missing Data: An Application to Prostate Cancer Model Parameterization

Real-life data is necessary for the application and validation of mathematical models. However, if data are missing from a dataset, the validity and usefulness of said dataset is diminished. One way to remedy this problem is by using multiple imputation - an advanced statistical method to predict the value of missing data points. As an application, we use a dataset containing clinical and other data for 109 patients through the course of a study on Intermittent Androgen Suppression therapy for prostate cancer. A model of prostate cancer treatment by Everett et al. is then fitted to the data. We examine the effects of multiple imputation on the parameter fitting and on prediction of off-treatment time span of the Everett et al. model by comparing the quality of fitting and the model’s performance in those predictions using the imputed data and using the unimputed data. Finally, we explore differences in model parameters between castration-sensitive and castration-resistant prostate cancer patients. We conclude that multiple imputation for time-series datasets improves the predictive ability of the Everett et al. model, although it does so somewhat inconsistently. Furthermore, in observing differences in parameterization between castration-sensitive and castration-resistant patients, we conclude that the androgen-independent castration-resistant cell death rate differs in a statistically significant manner between these patient types.

02:30 PM
03:00 PM

Break

03:00 PM
09:00 PM

Social event: Columbus Zoo and dinner

Friday, August 15, 2014
Time Session
08:15 AM

Shuttle to MBI

08:30 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Pranjal Singh, Dominick DiMercurio - Student Presentation: Simulated and Experimental Effects of RNA Interference on Cell Motility

Cell migration is a critical and recurrent phenomenon in animal biology; migration is a key feature in wound healing, immune function, and embryo development. In particular, egg chamber developmental stages in Drosophila melanogaster, a model organism for human genetics, provide a suitable opportunity to investigate migratory regulation. An important process in oogenesis is when the epithelial border cells on the anterior end of the egg chamber move toward the oocyte. A key molecular pathway in this process involves the uptake of the ligand Unpaired by follicle cells, which causes the signaling molecule Signal Transducer and Activator of Transcription (STAT) to activate transcription of downstream targets that promote migration. In genetic analyses of D. melanogaster ovaries that had reduced STAT expression via RNA interference (RNAi), we reproduced phenotypes of partially delayed or completely inhibited migratory behaviors compared to sibling controls. To investigate this phenomenon mathematically, we used a previously derived system of differential equations that modeled the signaling pathway, reduced the system with simplifying assumptions, and introduced a parameter to account for the effect of RNAi on mRNA that encoded STAT. Through computational methods, we simulated time courses of select proteins and created a bifurcation diagram of their steady states. Moving forward, research into this process could examine the biological bases for temporal variation in RNAi-based effects on protein expression as predicted in our mathematical models. This research will help biologists obtain a better understanding of mechanisms for cell migration, which may itself lead to insights on migratory pathways for the metastasis of cancer and the occurrence of other developmental defects.

This work was funded in part through an Undergraduate Biology Mathematics (UBM) Research Award from the National Science Foundation under Grant No. DBI 1031420, PIs Drs. Leips and Neerchal.

09:30 AM
10:00 AM
Danya Murali - Student Presentation: Investigating the Role of Chandelier Cells in Compensating for Inhibitory and Excitatory Reduction in Schizophrenia

Schizophrenia, a psychiatric disorder, is a condition of core cognitive defects partly due to reductions in gamma oscillations. Gamma oscillations (20-80Hz) are neural correlates of certain cognitive effects. They are created by the Pyramidal Interneuron Network Gamma containing inhibitory, excitatory and chandelier cells. Post-mortem schizophrenic brains have shown a reduction in synaptic connectivity of inhibitory and excitatory cells, and an increase in chandelier connectivity. We hypothesize that an increase in chandelier cell connectivity can compensate for the reduction in other synapses. Using the integrate-and-fire equations, we derive a firing rate model and later extend to a spiking model to test this hypothesis. We find that within a certain range of reversal potential and strength, chandelier cells have the ability to compensate for the reduction of both inhibition and excitation; and return the system to firing gamma oscillations.

10:00 AM
10:15 AM

Conference Photo

10:15 AM
10:45 AM

Break

10:45 AM
11:15 AM
Emily Meyer - Student Presentation: Mathematical Modeling of Chromosome Segregation in Bacteria

TBA

11:15 AM
11:45 AM
Lauren Lembcke - Student Presentation: Assessing the roles of arteriogenesis and angiogenesis following a major arterial occlusion

Peripheral arterial disease (PAD), in which arterial blockages prevent normal blood flow from perfusing the area distal of the blockage, can lead to claudication and limb ischemia. Collateral vessels provide an alternate pathway for the blood flow to reach that area. The collateral pathways compensate for the blockage by increasing diameter, number, and length of vessels. It remains unclear if the most significant compensation occurs by new small arteriole growth or an increase in the size of small arteries. A mathematical model of resistors is used to investigate the factors of collateral compensation which have the greatest influence on restoring blood flow.

11:45 AM

Shuttle pick-up from MBI (one to hotel, one to airport)

Name Email Affiliation
Agwamba, Kennedy kagwamba@hmc.edu Genome Sequencing and Analysis Program, Broad Institute
Arciero, Julia jarciero@math.iupui.edu Mathematics, Indiana University--Purdue University
Biegel, Hannah biegel15@up.edu Mathematics, University of Portland
Boribong, Brittany brittany.boribong@scranton.edu Department of Mathematics, University of Scranton
Brown, Lindsey lindsey.brown@duke.edu Mathematics, Duke University
Brown, Emery enb@neurostat.mit.edu Computational Neuroscience, Massachusetts Institute of Technology
Cho, Carolyn carolyn.cho@merck.com Quantitative Pharmacology & Pharmacometrics, Merck, Sharp & Dohme
Coons, Jane jic3@geneseo.edu Mathematics Department, Winthrop University
Cooper, Rebecca cooperbecca314@yahoo.com Mathematics, Colorado State University
Cyr, Jamie jcyr@smith.edu Mathematics, Smith College
DiMercurio, Dominick dimercurio@umbc.edu Biological Sciences, University of Maryland, Baltimore County
Doerge, Rebecca doerge@purdue.edu Statistics, Purdue University
Dowdy, Erin emdowdy@rams.colostate.edu Microbiology, Immunology, and Pathology, Colorado State University
Drendel, Dylan dhdrendel@gmail.com Mathematics, Colorado State University
Duncan, William wduncan@andrew.cmu.edu Mathematical Sciences, Carnegie Mellon University
Edwards, Madeline medwards13@elon.edu Mathematics, Elon University
Full, Robert rjfull@berkeley.edu Department of Integrative Biology, University of California, Berkeley
Furman, Marschall mlfurman@ncsu.edu Statistics, North Carolina State University
Gray, Dominic d.g.gray@spartans.nsu.edu Mathematics, Norfolk State University
Hamm, Benjamin Bihamm@ncsu.edu Biomathematics, North Carolina State University
Handagama, Winode winode.handagama@my.maryvillecollege.edu Chemistry, Maryville College
Herhold, Leigh laherhol@ncsu.edu Statistics Department, North Carolina State University
Horiguchi, Akira ahoriguchi9991@gmail.com Mathematics, University of Maryland
Houser, Jennifer houserjd@goldmail.etsu.edu Mathematics and Statistics, East Tennessee State University
Ireland, Nicholas nick.a.ireland@gmail.com Mathematics and Statistical Sciences, Arizona State University
Iyer, Ram ram.iyer@ttu.edu Mathematics and Statistics, Texas Tech University
Jamshidi-Azad, Neda nj59@duke.edu Mathematics, Duke University
Jilkine, Alexandra ajilkine@nd.edu ACMS, University of Notre Dame
Jordan, Kirk kjordan@us.ibm.com Computational Science, IBM T.J. Watson Research Center
Kapur, Nicholas npkapur@ncsu.edu Statistics, North Carolina State University
Karagiannis, Tanya tanyakarag4@gmail.com Math, Mount Holyoke College
Keener, James keener@math.utah.edu Mathematics and Bioengineering, University of Utah
Khan, Omar omar.khan@mail.mcgill.ca Physiology, McGill University
Kim, Bohyun bohyunk@uci.edu Mathematics, University of California, Irvine
Krishna, Nitin nitin.krishna@live.com NIMBioS, NIMBioS
Kurtek, Sebastian kurtek.1@stat.osu.edu Statistics, The Ohio State University
Lancaster, Amanda Lancaster.57@osu.edu Medicine, Ohio State University
Law, Rebecca rmlaw@ncsu.edu Statistics Department, North Carolina State University
Lee, Ray ray.lee@duke.edu Mathematics, Duke University
Lembcke, Lauren llembcke@iupui.edu Mathematics, Indiana University-Purdue University Indianapolis
Lin, Shili shili@stat.osu.edu Statistics, The Ohio State University
Liska, Benjamin liska@stolaf.edu Mathematics, St. Olaf College
Liu, Jeanette jmliu@hmc.edu Math, Harvey Mudd College
Lou, Shuyuan lou.59@osu.edu Mathematics, The Ohio State University
Mauck, China mauckchi@grinnell.edu Mathematics, Grinnell College
McCarthy, Gregory gm13@hampshire.edu 4CBC, Four College Bio-Math Consortium
McDaniel, Margaret mmcdan15@vols.utk.edu Biochemistry, Cellulaar, and Molecular Biology, University of Tennessee Knoxville
McDermott, Matthew mattmcdermott8@gmail.com Mathematics, Harvey Mudd College
Melton, Brady bsmelton@ncsu.edu Statistics, North Carolina State University
Meyer, Emily emily.m123@gmail.com Mathematics, Pomona College
Milner, Fabio milner@asu.edu School of Mathematics and Statistical Sciences, Arizona State University
Molkov, Yaroslav ymolkov@iupui.edu Department of Mathematical Sciences, Indiana University--Purdue University
Moss, Jamal jemoss@ncsu.edu Biomathemathics, North Carolina State University
Murali, Danya dmurali1@umbc.edu Mathematics and Statistics, University of Maryland Baltimore County
O Hara, Kathy kohara1@vbi.vt.edu Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University
Patritti Cram, Jennifer jennifer.8384@gmail.com Molecular Genetics, The Ohio State University
Pennington, Hannah hannah.pennington412@topper.wku.edu Mathematics, Western Kentucky University
Reed, Michael reed@math.duke.edu Mathematics, Duke University
Rogge, Emma emmarogge@gmail.com Applied Mathematics & Biology, Harvard University
Saylor, Maurisa sayloren@gmail.com Natural Science, Hampshire College
Schill, Megan mschill@ucmerced.edu Chemistry, University of California, Merced
Shayesteh, Rod rs237@duke.edu Mathematics, Duke University
Shen, Mo ms7805@nyu.edu Mathematics, New York University
Shiring, Casey shiring.case@uwlax.edu Mathematics, University of Wisconsin - La Crosse
Singh, Pranjal op20211@umbc.edu Mathematics and Statistics, University of Maryland Baltimore County
Sloan, Jeff jsloan@mayo.edu Health Sciences Research, Mayo Clinic
Spencer, Paulina paspence@ncsu.edu Entomology, North Carolina State University
Stasny, Elizabeth stasny.1@osu.edu Statistics, The Ohio State University
Wang, Yating ywang438@gatech.edu Department of Mathematics, Georgia Institute of Technology
Wasim, Tayyab mtw15@duke.edu Mathematics, Duke University
Weissman, Jake jw4336@bard.edu Division of Science, Mathematics and Computing: Mathematics and Biology Departments, Bard College
Weistuch, Corey corey.weistuch@stonybrook.edu Applied Mathematics and Statistics, Stony Brook University
Whiteman, Spencer slwhitem@iupui.edu Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis
You, Andrew andrew.kh.you@gmail.com Duke University Math Department, Duke University
Zhang, Michael mjz5@duke.edu Mathematics, University
Zheng, Wanlin wzheng4@ncsu.edu statistics, ncsu
Zhou, David dz54@duke.edu Mathematical Biology, Duke University
Genomic analysis of Candida albicans following serial passage identifies candidate virulence factors

Candida albicans is a commensal fungus found in most human oral, gastrointestinal, and genitourinary tracts and is known to seed life-threatening infections in immunocompromised humans. In many microbial pathogens, the serial propagation of a strain within the host has been shown to increase the strain’s virulence. However, most C. albicans isolates are well adapted to the mammalian environment, hindering microevolution events that could result in increased fitness or virulence. We hypothesized that extended passaging of clinical isolates of C. albicans would more readily allow the identification of novel fitness and virulence factors. There is limited knowledge around the microevolution of genes associated with pathogenicity in these cases, and our goal was to characterize the genetic differences between these pre-passaged and passaged strains of C. albicans. We used next-generation sequencing data generated on the Illumina HiSeq platform to study how isolates of three clinical isolates changed following passaging. Reads from the pre-passaged and passaged isolates were aligned to the C. albicans SC5314 reference using Burrows-Wheeler Aligner (BWA), and single nucleotide polymorphisms (SNPs), insertions, and deletions were detected using the GATK UnifiedGenotyper Variant Filtration. Given that we are particularly interested in identifying variants that reveal genetic differences between the pre-passaged and passaged isolates, we have begun to establish associations between shared genetic alterations and virulence. We have uncovered a number of initial candidate virulence factors, including transcriptional regulators of zinc cluster DNA-binding motif, putative GPI-anchored proteins, and ALS family proteins. These results may prove valuable for the future development of antifungal drugs.

Kennedy Agwamba1,3, Iuliana Ene2, Matthew Hirakawa2, Rhys Farrer3, Richard Bennett2, Christina Cuomo3

1Department of Mathematics and Department of Biology, Harvey Mudd College

2Department of Molecular Microbiology and Immunology, Brown University

3Genome Sequencing and Analysis Program, The Broad Institute of MIT and Harvard

Student Presentation: Predicting Off-Treatment Duration in Prostate Cancer Patients: A Comparison Across Models (Part I)

Abstract not submitted.

Keynote Presentation: The Dynamics of the Unconscious Brain Under General Anesthesia

General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. The mechanisms by which anesthetic drugs induce the state of general anesthesia are considered one of the biggest mysteries of modern medicine. We study three problems to decipher this mystery. First, we present findings from our human studies of general anesthesia using combined fMRI/EEG recordings, high-density EEG recordings and intracranial recordings which have allowed us to give a detailed characterization of the neurophysiology of loss and recovery of consciousness due to propofol. Second, we present a neuro-metabolic model of burst suppression, the profound state of brain inactivation seen in deep states of general anesthesia. We show that our characterization of burst suppression can be used to design a closed-loop anesthesia delivery system for control of a medically-induced coma. Finally, we demonstrate that the state of general anesthesia can be rapidly reversed by activating specific brain circuits. Our results show that it is now possible to have a detailed neurophysiological understanding of the brain under general anesthesia, and that this understanding, can be used to control anesthetic states. Hence, general anesthesia is not a mystery.

Student Presentation: Combinatorics of k-Interval Cospeciation for Cophylogeny

Cophylogenetics is the study of the evolutionary relationships between taxonomical units that are believed to be evolving concomitantly. We examine the combinatorial properties of the cophylogenetic distance metric, k-interval cospeciation, which was introduced by Huggins, Owen and Yoshida in their 2012 paper, "First steps toward the geometry of cophylogeny." We determined that k-interval cospeciation is a unique discrete distance metric which can quantify a degree of global congruence between two phylogenetic trees while allowing for local incongruence. We counted the size of the neighborhood of trees which satisfy the largest possible k-interval cospeciation with a given tree. Due to the way this neighborhood of trees grows as a proportion of all possible trees, we believe that k-interval cospeciation may prove useful for analyzing data obtained through simulations.

Student Presentation: Modeling Actin Regulaton During the Formation of Invadopodia in Metastatic Mammary Carcinoma

Abstract not submitted.

Student Presentation: Simulated and Experimental Effects of RNA Interference on Cell Motility

Cell migration is a critical and recurrent phenomenon in animal biology; migration is a key feature in wound healing, immune function, and embryo development. In particular, egg chamber developmental stages in Drosophila melanogaster, a model organism for human genetics, provide a suitable opportunity to investigate migratory regulation. An important process in oogenesis is when the epithelial border cells on the anterior end of the egg chamber move toward the oocyte. A key molecular pathway in this process involves the uptake of the ligand Unpaired by follicle cells, which causes the signaling molecule Signal Transducer and Activator of Transcription (STAT) to activate transcription of downstream targets that promote migration. In genetic analyses of D. melanogaster ovaries that had reduced STAT expression via RNA interference (RNAi), we reproduced phenotypes of partially delayed or completely inhibited migratory behaviors compared to sibling controls. To investigate this phenomenon mathematically, we used a previously derived system of differential equations that modeled the signaling pathway, reduced the system with simplifying assumptions, and introduced a parameter to account for the effect of RNAi on mRNA that encoded STAT. Through computational methods, we simulated time courses of select proteins and created a bifurcation diagram of their steady states. Moving forward, research into this process could examine the biological bases for temporal variation in RNAi-based effects on protein expression as predicted in our mathematical models. This research will help biologists obtain a better understanding of mechanisms for cell migration, which may itself lead to insights on migratory pathways for the metastasis of cancer and the occurrence of other developmental defects.

This work was funded in part through an Undergraduate Biology Mathematics (UBM) Research Award from the National Science Foundation under Grant No. DBI 1031420, PIs Drs. Leips and Neerchal.

Keynote Presentation: Analysis of Next-Generation Sequencing Data and Related Statistical Issues

This is an exciting and influential time for the field of Statistics in science. Technological advances in genetic, genomic, and the other 'omic sciences are providing large amounts of complex data that are presenting a number of challenges for the biological community. Many of these challenges are deeply rooted statistical issues that involve experimental design. Although there are many different computational tools for processing these data, there are a limited number of statistical methods for analyzing them, and even fewer that acknowledge the unique nature of these data. After a discussion about experimental design for next-generation sequencing experiments, a simple approach based on a two-stage Poisson model for modeling RNA sequencing data will be presented for the purpose of testing biologically important changes in gene expression. If time allows, a new approach that addresses sequence tag abundance, and the need to adjust for it in next-generation sequencing data, will be presented. The advantages of these approaches are demonstrated through simulations and real data applications.

Student Presentation: A Model for Transport in Stereocilia

Stereocilia are highly regulated structures vital for hearing and balance in mammals. However, it is not known how their lengths are maintained. Models have been made to study possible mechanisms for actin filament maintenance in cellular protrusions, but they rely on actin treadmilling, which recent work suggests does not occur in stereocilia. We modify an existing model of motor and cargo distributions in cellular protrusions to account for the absence of treadmilling. We consider cargo which is incorporated at the tip of stereocilia as would be typical of actin cross-linking proteins. The qualitative properties of the distributions do not change by removing retrograde flow from the model, but there is less cargo along the majority of the stereocilium with retrograde flow. With degradation of the motors and cargo, the proteins are concentrated at the tip of the stereocilium as is seen in experimental data.

Student Presentation: Transcription Factors and Cascade Network

Transcription factors (TFs) often bind to specific DNA sequences to promote or block gene expression. The interactions between TFs and target DNA sequences may be regulated by DNA methylation. It has been well recognized that DNA methylation plays an important role in neural differentiation, which is determined by a cascade of TFs. However, the epigenetic regulated TF programs critical to brain development remain largely unexplored.

To fill in such a knowledge gap, we first analyzed mammalian brain methylomes to identify genomic loci differentially methylated during development. We compiled a set of experimentally validated TF binding sites from TRANSFAC 7.0, JASPAR 2014, and UniPROBE databases, and applied HOMER to identify TFs of which binding sites enriched in genomic regions hypomethylated in neurons and glial cells, respectively. Using MEME Suite and ClusterZ, we then determined pairs of TFs with binding sites frequently overlapped. With the Cytoscape program, we created a network of possible TF interactions, which can either be complex formation or regulatory. This predicted network provides novel insight to the epigenetic regulation controlling brain development.

Keynote Presentation: Using Mathematical, Physical and Animal Models to Discover the Principles of Motion Science

Guided by direct experiments on many-legged animals, mathematical models and physical models (robots), we postulate a hierarchical family of control loops that necessarily include constraints of the body’s mechanics. At the lowest end of this neuromechanical hierarchy, we hypothesize the primacy of mechanical feedback – neural clocks exciting tuned muscles acting through chosen skeletal postures. Control algorithms appear embedded in the form and skeleton of the animal itself. The control potential of muscles must be realized through complex, viscoelastic bodies. Bodies can absorb and redirect energy for transitions. Tails can be used as inertial control devices. On top of this physical layer reside sensory feedback driven reflexes that increase an animal’s stability further and, at the highest level, environmental sensing that operates on a stride-to-stride timescale to direct the animal’s body. Most importantly, locomotion requires an effective interaction with the environment. Understanding control requires understanding the coupling to environment. Amazing feet permit creatures such as geckos to climb up walls at over meter per second without using claws, glue or suction - just molecular forces using hairy toes. Fundamental principles of animal locomotion have inspired the design of self-clearing dry adhesives and autonomous legged robots such as the Ariel, Mecho-gecko, Sprawl, RHex, RiSE, Stickybot and DASH that can aid in search and rescue, inspection, detection and exploration.

Student Presentation: Analyzing Honey Bee Characteristics Using Digital Image Processing & In Vitro Queen Rearing

Abstract not submitted.

Student Presentation: Transcription Factors and Cascade Network

Transcription factors (TFs) often bind to specific DNA sequences to promote or block gene expression. The interactions between TFs and target DNA sequences may be regulated by DNA methylation. It has been well recognized that DNA methylation plays an important role in neural differentiation, which is determined by a cascade of TFs. However, the epigenetic regulated TF programs critical to brain development remain largely unexplored.

To fill in such a knowledge gap, we first analyzed mammalian brain methylomes to identify genomic loci differentially methylated during development. We compiled a set of experimentally validated TF binding sites from TRANSFAC 7.0, JASPAR 2014, and UniPROBE databases, and applied HOMER to identify TFs of which binding sites enriched in genomic regions hypomethylated in neurons and glial cells, respectively. Using MEME Suite and ClusterZ, we then determined pairs of TFs with binding sites frequently overlapped. With the Cytoscape program, we created a network of possible TF interactions, which can either be complex formation or regulatory. This predicted network provides novel insight to the epigenetic regulation controlling brain development.

Student Presentation: Modeling Latency of Thalmocortical Fast-Spiking Interneurons in Schizophrenia

Neural thalamocortical circuits relay external sensations from to the thalamus to the cortex where sensory information is then processed. Feedforward inhibition involving a subtype of fast-spiking interneurons, which are marked by the calcium-binding protein parvalbumin, reduce the chance that a postsynaptic neuron will fire an action potential. Consequences on the circuit due to the absence of parvalbumin expression in fast-spiking neurons in schizophrenia patients are caused by fast-spiking latency. In this presentation, we present a conventional neuron model. We will show how to develop a mathematical model to incorporate a latency effect as well as show numerical simulations.

Opportunities in Math-Bio-Stat at Texas Tech University

Abstract not submitted.

Student Presentation: Four Compartment Model Illustrating the Spread of Antibiotic Resistant Bacteria

Abstract not submitted.

Student Presentation: Modeling Actin Regulaton During the Formation of Invadopodia in Metastatic Mammary Carcinoma

Abstract not submitted.

Student Presentation: Deciphering the Gating Properties of P2X4 Receptor Channels using Markov State Models

Purinergic P2X receptors are a family of seven (labeled P2X1-7R) ATP-gated non-selective cation channels, ubiquitously expressed in the body. Abnormalities in them could lead to tissue inflammation and chronic pain. All members of this family are trimeric channels with three agonist binding sites that are activated and opened when occupied by ATP. The kinetics of activation (rising phase of current), desensitization (decay of current in the presence of ATP) and deactivation (decay of current after removal of ATP) are receptor-specific. The P2X4 subunit is the most widely distributed in the brain. Homomeric P2X4Rs desensitize with moderate rates, and desensitization is coupled to extensive internalization and recycling of receptors to the membrane. P2X4R is allosterically modulated by ivermectin (IVM), which increases both the ATP potency and the peak amplitude of the current (i.e., induces receptor sensitization), reduces the desensitization rate, greatly prolongs deactivation of current after ATP removal, and alters the recycling process. Many aspects of P2X4R gating have not yet been clarified and there is no comprehensive mathematical model describing its kinetics. No rationale has been provided for how IVM rescues receptors from desensitization, why it slows receptor deactivation, or why it affects receptor recycling. Using electro-physiological (current-recording) data from Stojilkovic Lab (NIH), we will be developing Markov state models and conducting systematic model comparisons and parameter optimization methods by utilizing Markov Chain Monte Carlo techniques based on Bayesian Theory, to determine the most likely model and parameter set(s) that can capture the kinetics of these receptors. The goal is to produce a model that can successfully explain the underlying mechanism of desensitization, recycling, and IVM-dependent sensitization in P2X4Rs. The parameter set(s) will be retrieved from probability distributions generated from these iterative methods.

Student Presentation: The effect of locomotion on body temperature control mechanism

We created a mathematical model to describe core (body) temperature responses to exercise at different ambient temperatures based on an experiment data. In the experiment, rats were forced to run on a treadmill at different speeds. Their core temperature time-series were recorded during 15 min runs with speeds 0, 6, 12, and 18 m/min at 0 incline in cool (24°C, T1) and hot (32°C, T2) environment. At T1 there was a temperature drop during first 5 min, while at T2 temperature did not change during that period. After 5 min, temperature started rising linearly at both T1 and T2 until the treadmill was stopped. The slope of this linear increase remained constant for all four speeds at T1, whereas at T2 it progressively steepened with the speed increase. To explain these findings, we have designed a model which consisted of two body components exchanging heat: the core and muscles. The core dissipated heat proportionally to difference between the core and ambient temperatures. This model was formally described by a system of two differential equations. All parameters of the system were subject to fit the average temperature response curves obtained from the experiment. Hypothermia during the first 5 min at T1 was interpreted as a result of decreased thermogenesis in the core to compensate for the heat generated by locomotion on the treadmill. This drop was not observed at T2 because heat production in the core was too small, and no further decrease was possible. The linear increase of core body temperature after 5 min was a result of heat generation in muscles. We hypothesize that exercise activates thermoregulatory inhibition of thermogenesis and/or increases heat dissipation, which prevents excessive heat accumulation during exercise in cool environment. However, at high ambient temperature this thermoregulatory compensation is impossible because the core metabolism cannot be reduced any further, while heat dissipation is already at its maximum. Therefore, heat generation by exercise added to heat accumulation and presented itself as an increased rate of the temperature growth. We conclude that compensatory mechanisms in the thermoregulatory system may underlie some controversial results concerned with the role of locomotion in the body temperature dynamics.

Student Presentation: Evaluating the Strength of Evidence in DWI Cases Presented in North Carolina

Criminal penalties for driving while intoxicated (DWI) in North Carolina are based on hard thresholds; for example, having a blood alcohol content (BAC) at or above 0.08 is considered legally impaired. However, BAC measurements are typically taken using breathalyzers, which are subject to measurement error. Additionally, breathalyzer readings in North Carolina are truncated, i.e. a person blowing a 0.079 would have a breathalyzer reading of 0.07. The purpose of our research is to explore this error and to construct recommendations for both law enforcement and courtroom decisions. Using data collected from breathalyzer tickets in Orange County, we have estimated the measurement error using a truncated random effects model and have calculated a prediction interval to determine any individual’s true BAC given the individual’s breathalyzer results. We also ran a parallelized simulation study to determine the effects of the distribution parameters on our model, and plan on exploring factors such as temperature, humidity, and machine calibration. We have created two lookup tables to determine an individuals true BAC, one based on prediction intervals, and the other on the probability that an individual’s true BAC is above 0.08. Using these lookup tables, the courts can determine the strength of evidence in DWI cases.

Student Presentation: Assessing the roles of arteriogenesis and angiogenesis following a major arterial occlusion

Peripheral arterial disease (PAD), in which arterial blockages prevent normal blood flow from perfusing the area distal of the blockage, can lead to claudication and limb ischemia. Collateral vessels provide an alternate pathway for the blood flow to reach that area. The collateral pathways compensate for the blockage by increasing diameter, number, and length of vessels. It remains unclear if the most significant compensation occurs by new small arteriole growth or an increase in the size of small arteries. A mathematical model of resistors is used to investigate the factors of collateral compensation which have the greatest influence on restoring blood flow.

Student Presentation: A Mathematical Approach to Uncovering Regulatory Mechanisms in Calcium Homeostasis

Calcium is a mineral essential to many systems of life. As such, the body regulates levels of calcium in the blood plasma very tightly through a process known as calcium homeostasis. The controlling mechanisms in this process include parathyroid hormone, calcitonin, vitamin D, and the mineral phosphate. Much research has been done on the biology of this system but it is not understood completely. Recently, work has been done to mathematically model this system, however, these models are very complex. In this talk, we will provide a simplified mathematical model of calcium homeostasis that still captures biologically relevant mechanisms. Using the modeling software COPASI (Hoops 2006), we will show numerical simulations and comparisons to experimental data. An analysis of the stability of our nonlinear model provides insights into our dynamical system. We will conclude by showing ways we can predict how various diseases can disturb calcium homeostasis and provide suggestions for further investigation that could lead to effective treatments.

Student Presentation: A Model for Transport in Stereocilia

Stereocilia are highly regulated structures vital for hearing and balance in mammals. However, it is not known how their lengths are maintained. Models have been made to study possible mechanisms for actin filament maintenance in cellular protrusions, but they rely on actin treadmilling, which recent work suggests does not occur in stereocilia. We modify an existing model of motor and cargo distributions in cellular protrusions to account for the absence of treadmilling. We consider cargo which is incorporated at the tip of stereocilia as would be typical of actin cross-linking proteins. The qualitative properties of the distributions do not change by removing retrograde flow from the model, but there is less cargo along the majority of the stereocilium with retrograde flow. With degradation of the motors and cargo, the proteins are concentrated at the tip of the stereocilium as is seen in experimental data.

Student Presentation: Sensitivity Analysis of a Dynamical Systems Model of Gene Regulation in Drosophila Melanogaster

I am working with Jacqueline M. Dresch (Mathematics, Amherst College) and Robert A. Drewell (Biology, Amherst and Mount Holyoke Colleges) on parameter sensitivity analysis of a dynamic model of eukaryotic gene regulation in the Drosophila embryo. I am primarily concerned with understanding the relative importance of various components of the system, such as transcription and translation, as well as the biological and mathematical interpretations of. I performed sensitivity analysis on a model with initial inputs corresponding to both maternal genes and housekeeping genes in Drosophila melanogaster at various points across the anterior-posterior axis of the embryo as well as at various time points during early development. I compared my individual parameter sensitivities to values found experimentally in the study conducted by Li et. al. (PeerJ, 2014) and considered how these sensitivities change spatially and temporally during development. I found that the calculated parameter sensitivities on a simplified version of the reaction-diffusion model developed in Dresch et. al. (SIAM J. Appl. Math, 2013) are in agreement with those generated by the biological experiments of Li et al. As such, this appears to be a valid model to use for dynamic gene regulation. Additionally, the sensitivities for all genes considered exhibit competitive dynamic behavior across the development window. This suggests the importance of considering a dynamic model of gene regulation.

Student Presentation: Evaluating the Strength of Evidence in DWI Cases Presented in North Carolina

Criminal penalties for driving while intoxicated (DWI) in North Carolina are based on hard thresholds; for example, having a blood alcohol content (BAC) at or above 0.08 is considered legally impaired. However, BAC measurements are typically taken using breathalyzers, which are subject to measurement error. Additionally, breathalyzer readings in North Carolina are truncated, i.e. a person blowing a 0.079 would have a breathalyzer reading of 0.07. The purpose of our research is to explore this error and to construct recommendations for both law enforcement and courtroom decisions. Using data collected from breathalyzer tickets in Orange County, we have estimated the measurement error using a truncated random effects model and have calculated a prediction interval to determine any individual’s true BAC given the individual’s breathalyzer results. We also ran a parallelized simulation study to determine the effects of the distribution parameters on our model, and plan on exploring factors such as temperature, humidity, and machine calibration. We have created two lookup tables to determine an individuals true BAC, one based on prediction intervals, and the other on the probability that an individual’s true BAC is above 0.08. Using these lookup tables, the courts can determine the strength of evidence in DWI cases.

Student Presentation: Mathematical Modeling of Chromosome Segregation in Bacteria

TBA

Student Presentation: Analyzing Honey Bee Characteristics Using Digital Image Processing & In Vitro Queen Rearing

Abstract not submitted.

Student Presentation: Investigating the Role of Chandelier Cells in Compensating for Inhibitory and Excitatory Reduction in Schizophrenia

Schizophrenia, a psychiatric disorder, is a condition of core cognitive defects partly due to reductions in gamma oscillations. Gamma oscillations (20-80Hz) are neural correlates of certain cognitive effects. They are created by the Pyramidal Interneuron Network Gamma containing inhibitory, excitatory and chandelier cells. Post-mortem schizophrenic brains have shown a reduction in synaptic connectivity of inhibitory and excitatory cells, and an increase in chandelier connectivity. We hypothesize that an increase in chandelier cell connectivity can compensate for the reduction in other synapses. Using the integrate-and-fire equations, we derive a firing rate model and later extend to a spiking model to test this hypothesis. We find that within a certain range of reversal potential and strength, chandelier cells have the ability to compensate for the reduction of both inhibition and excitation; and return the system to firing gamma oscillations.

Student Presentation: Statistical Method for Detection of Differential DNA Methylation

Abstract not submitted.

Student Presentation: Shape Representation Via Rotational Descriptor

Abstract not submitted.

Student Presentation: How to Deal with Missing Data: An Application to Prostate Cancer Model Parameterization

Real-life data is necessary for the application and validation of mathematical models. However, if data are missing from a dataset, the validity and usefulness of said dataset is diminished. One way to remedy this problem is by using multiple imputation - an advanced statistical method to predict the value of missing data points. As an application, we use a dataset containing clinical and other data for 109 patients through the course of a study on Intermittent Androgen Suppression therapy for prostate cancer. A model of prostate cancer treatment by Everett et al. is then fitted to the data. We examine the effects of multiple imputation on the parameter fitting and on prediction of off-treatment time span of the Everett et al. model by comparing the quality of fitting and the model’s performance in those predictions using the imputed data and using the unimputed data. Finally, we explore differences in model parameters between castration-sensitive and castration-resistant prostate cancer patients. We conclude that multiple imputation for time-series datasets improves the predictive ability of the Everett et al. model, although it does so somewhat inconsistently. Furthermore, in observing differences in parameterization between castration-sensitive and castration-resistant patients, we conclude that the androgen-independent castration-resistant cell death rate differs in a statistically significant manner between these patient types.

Student Presentation: Simulated and Experimental Effects of RNA Interference on Cell Motility

Cell migration is a critical and recurrent phenomenon in animal biology; migration is a key feature in wound healing, immune function, and embryo development. In particular, egg chamber developmental stages in Drosophila melanogaster, a model organism for human genetics, provide a suitable opportunity to investigate migratory regulation. An important process in oogenesis is when the epithelial border cells on the anterior end of the egg chamber move toward the oocyte. A key molecular pathway in this process involves the uptake of the ligand Unpaired by follicle cells, which causes the signaling molecule Signal Transducer and Activator of Transcription (STAT) to activate transcription of downstream targets that promote migration. In genetic analyses of D. melanogaster ovaries that had reduced STAT expression via RNA interference (RNAi), we reproduced phenotypes of partially delayed or completely inhibited migratory behaviors compared to sibling controls. To investigate this phenomenon mathematically, we used a previously derived system of differential equations that modeled the signaling pathway, reduced the system with simplifying assumptions, and introduced a parameter to account for the effect of RNAi on mRNA that encoded STAT. Through computational methods, we simulated time courses of select proteins and created a bifurcation diagram of their steady states. Moving forward, research into this process could examine the biological bases for temporal variation in RNAi-based effects on protein expression as predicted in our mathematical models. This research will help biologists obtain a better understanding of mechanisms for cell migration, which may itself lead to insights on migratory pathways for the metastasis of cancer and the occurrence of other developmental defects.

This work was funded in part through an Undergraduate Biology Mathematics (UBM) Research Award from the National Science Foundation under Grant No. DBI 1031420, PIs Drs. Leips and Neerchal.

Student Presentation: Analyzing Honey Bee Characteristics Using Digital Image Processing & In Vitro Queen Rearing

Abstract not submitted.

Student Presentation: Networks of Spiking Neurons in the Brain Visual Cortex

Abstract not submitted.

Student Presentation: Predicting Off-Treatment Duration in Prostate Cancer Patients: A Comparison Across Models (Part II)

Abstract not submitted.

Student Presentation: A theoretical model of tissue oxygenation in the retina

Open-angle glaucoma (OAG) is characterized by progressive retinal ganglion cell death and vision loss. Although elevated intraocular pressure is the primary risk factor for OAG, several studies have shown that impaired perfusion and oxygen delivery to retinal ganglion cells may also contribute to OAG pathophysiology. In this study, a realistic vascular network model of the mouse retina is developed based on previously published confocal microscopy images and modeling data. A mathematical model based on Green’s functions is applied to this network to predict tissue oxygenation in a healthy retina. The model will be extended to predict the conditions that lead to observed tissue oxygenation changes in glaucoma patients. Preliminary model predictions suggest that theoretical models in combination with oximetry measures are needed to guide the differentiation and identification of the most relevant risk factors for OAG.

Mentor: Julia Arciero, Department of Mathematical Sciences, Purdue School of Science, IUPUI

Posters

A meta-analysis of coastal populations' genetic diversity of species throughout their range

Higher genetic diversity in the centers of many species’ ranges have been thought to account for the abundant-center hypothesis, which states that populations found in the center of their natural distribution are more abundant than those found at the edges. Despite the prevalence of the abundant-center hypothesis in population studies, the assumption of differential genetic diversity throughout ranges has rarely been tested in a rigorous way across many taxa. On the other hand, studies that have tested the genetic variation in plants and animals along their species’ ranges did not account for variation in sample sizes among studies. To better test the validity of the abundant center hypothesis, this study investigated how genetic diversity of populations distributing along world’s coastlines is affected by location within the species' range using a meta-analysis. As an explanatory factor of genetic diversity among populations, populations’ distance to the center of a range is hypothesized to be positively correlated with the genetic diversity. An effect size of correlation coefficient (Pearson’s r) for each genetic measurement of each species versus relative distance to center was calculated from the metaanalysis. Results showed positive correlations for most taxa and insignificant correlations for others. Independence tests using correlation matrix, pivot tables and two-way ANOVAs eliminated variables that might produce similar results, showing that the remaining ones would explain a wide range of variations. Factors such as range dimension, relative direction of sample sites and taxa showed significant associations with how genetic variables respond to populations’ distance to range centers, which is represented by r values. By determining if there is a difference in genetic diversity among populations throughout their ranges, conservation efforts can target individual populations, as opposed to protecting the entire species as one entity. This study can potentially give insights and directions for developing more effective and feasible coastal conservation practices.

A Biophysical Model of Mutually Inhibitory Neuronal Populations and Its Implications for Sleep-Wake Cycling in Young Mammals

Abstract not submitted.

Uniting Gene Expression Data with Infectious Disease Theory

A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation by Reynolds et al. describes a general model for the immune response to disease. The model variables are pathogen, pro-inflammatory mediators, anti-inflammatory agents, and damage. Genetic identification of unique immunological responses in mice infected with virulent and attenuated Francisella tularensis by Kingry et al. details an experiment involving the infection of mice with Schu4 and LVS strains of F. tularensis and provides murine lung and spleen gene expression data. The goal is to apply the experimental data to a subsystem of the model. Gene data curves were correlated with the integrated model curves to select genes which could serve as proxies for the variables. New parameter values were derived from the application of the gene data to a discretized subsystem. The subsystem was integrated using new parameters and proved to be qualitatively similar to the original integrated model, indicating that trends in gene expression may coincide with the behavior proposed by the general model.

TBD

Abstract not submitted.

Quantifying the performance of spatial and temporal early warning signals of disease elimination

The immune system is an intricate network of up-regulation and down-regulation, the strength and coordination of which defines whether the host lives or dies. Francisella tularensis is a Gram-negative coccobacillus that resides in the Northern Hemisphere. It is classified by the U.S. government as a Tier 1 bio-warfare agent and if pneumonic and untreated, may result in death within 4 to 6 days of infection. As of now, health Institutions must give a series of perhaps unnecessary antibiotics to attempt treatment of early infection of most diseases, waiting to see the outcome after a few days. With quantitative real time PCR, we have extracted the quantity of a series of selected cytokines from mouse tissue that will in turn relay to us the upregulation and downregulation of the host immune system. We are then combining these data with mathematical modeling, allowing for the preliminary establishment of a method of predicting the outcome of the infected host, be it death or health.

Identifying Homeostatic Cytokines as Disease Biomarkers via Clique Percolation Network Analysis

Abstract not submitted.

An Investigation of the Efficiency of Slime Mold as a Maze-Solving Algorithm

Physarum polycephalum, commonly known as slime mold, has recently been noted for its ability to find the shortest path between food sources. Unlike numerical approaches, the slime mold is a viable alternative because it will not break down across large-scale networks. We designed an experiment using a template of the streets of Manhattan and strategic food placement to further test the slime’s ability to efficiently find an optimal path. Our study used image tracking analysis to quantify and record the slime’s movement patterns for subsequent analyses. These analyses were compared to a variety of computational optimization algorithms as a means to assess the efficiency and success of the slime mold's actions. Our current results suggest that the slime mold has the ability to find a nearly perfect route over the course of 6 days. Thus far, it has performed in a relatively efficient manner, comparable to automated search algorithms. The ultimate goal is to develop a dynamic model to simulate the slime's search routine, as well as to determine situations in which slime mold optimization can be of use in real world planning.

Quantifying the performance of spatial and temporal early warning signals of disease elimination

Abstract not submitted.

TBD

Abstract not submitted.

TBD

Abstract not submitted.

An Investigation of the Efficiency of Slime Mold as a Maze-Solving Algorithm

Physarum polycephalum, commonly known as slime mold, has recently been noted for its ability to find the shortest path between food sources. Unlike numerical approaches, the slime mold is a viable alternative because it will not break down across large-scale networks. We designed an experiment using a template of the streets of Manhattan and strategic food placement to further test the slime’s ability to efficiently find an optimal path. Our study used image tracking analysis to quantify and record the slime’s movement patterns for subsequent analyses. These analyses were compared to a variety of computational optimization algorithms as a means to assess the efficiency and success of the slime mold's actions. Our current results suggest that the slime mold has the ability to find a nearly perfect route over the course of 6 days. Thus far, it has performed in a relatively efficient manner, comparable to automated search algorithms. The ultimate goal is to develop a dynamic model to simulate the slime's search routine, as well as to determine situations in which slime mold optimization can be of use in real world planning.

TBD

Abstract not submitted.

Stochastic Noise and Polarity Patch Wandering in Budding Yeast

Cell polarization is the process by which a cell assumes a spatial orientation and organizes its components accordingly. In budding yeast, polarization occurs during mating, in which haploid cells grow single, rounded mating projections called "shmoos" to fuse with that of a mating partner. The growth of this projection is oriented within each cell by the local clustering of specific polarity proteins on the membrane. This clustering occurs in the direction of pheromone released by potential mating partners, allowing yeast to bias growth toward a mate. Interestingly, this polarity cluster does not always develop and establish itself in a set location, but has instead been observed to wander along the cell membrane in a seeming "random walk". It has been suggested that this wandering behavior could explain the ability of yeast cells to re-orient initially misdirected growth of the mating patch. The mechanism behind patch wandering has been hypothesized to stem primarily from a process mediated by actin cables. However, cells treated with Latrunculin A to disrupt actin activity continue to demonstrate patch wandering, though the movement is significantly less pronounced. Could this residual movement emerge from the inherent randomness of biochemical interactions? To understand the extent to which biochemical noise could account for patch movement, yeast polarization was simulated after separately adding white noise and "Langevin-type" noise to an existing model. Though further investigation is required in order to characterize the impact of noise on polarity patch wandering, we have found that our formulations for noise were inadequate in reproducing the extent of patch movement observed in nature.

Inward Spreading of Surfactant on Thin Viscous Films

Abstract not submitted.

TBD

Abstract not submitted.

TBD

Abstract not submitted.

Student Presentation: TBA

TBA

TBD

Abstract not submitted.

A Mathematical Model for the Interactions of the Proteins MMP-1, TIMP-1 and ECM in a Wound

Abstract not submitted.

TBD

Abstract not submitted.

Modeling the Diffusion of Prion Aggregates in Budding Yeast

Abstract not submitted.

Determining the Role of Glycine in Glutathione Metabolism

Acetaminophen (APAP) overdose is the leading cause of acute liver failure in the United States, leading to approximately 56,000 emergency room visits every year. The liver metabolizes APAP and in so doing produces the toxic byproduct NAPQI. Glutathione, the body’s primary antioxidant, conjugates with NAPQI to allow for its safe removal. In patients suffering from APAP overdose the demand for glutathione exceeds the liver’s ability to produce it. In an effort to restore glutathione levels, current hospital protocol calls for the administration of N-acetyl cysteine (NAC): the precursors of glutathione are glutamate, glycine and cysteine, with cysteine usually assumed to be rate-limiting. However, experiments by Hong et al. have shown that glutamine supplementation partially preserves hepatic glutathione stores in rats during APAP overdose. A possible explanation for this lies with the glutamate/cystine antiporter, which could cause glutamate rather than cysteine to be rate-limiting. We found that inclusion of the glutamate/cystine antiporter in the model did indeed result in agreement with Hong's findings, but only after the reactions producing and consuming glycine in liver were included (prior to this only glycine transport and loss to glutathione synthesis were modeled). When these reactions are neglected, glycine in the model becomes depleted and additional glutamate (via glutamine) does not translate into higher glutathione levels.

Dynamics of Crypt Competition During Colorectal Carcinogenesis

The initiation of cancer (carcinogenesis) is primarily driven by genetic mutations at the cellular level that generate cancerous phenotypes. Mutations that result in the following phenotypes are particularly important in field cancerization because they facilitate the progression to invasive disease:

-Expander (E): increased proliferation rate

-Survivor (S): increased resistance to cell death (e.g. during inflammation)

In the context of epithelial tissues, field cancerization refers to the presence of pre-malignant cell populations that increase the risk of progression to cancer. Inflammatory bowel diseases (IBD) such as Crohn's disease and ulcerative colitis enhance field cancerization and hence the risk of progression to cancer in the colon. The lining of the surface of the colon, known as the surface epithelium, consists of small glands known as crypts that are lined with cells. At the bottom of each crypt, stem cells undergo mutations that ultimately populate the entire crypt with cells of a single phenotype, leading to the notion of a crypt phenotype. Crypts can divide and die, leading to crypt-level competition.

We present two distinct models for the dynamics influenced by Neuhauser as well as Durrett and Chan; these models are named the Neuhauser and Durrett models, respectively. The Neuhauser model contains only point inflammation, which inflames crypts individually. The Durrett model contains patch inflammation, which inflames an area of multiple crypts, in addition to point inflammation. We define a reproductive ratio ρ that allows prediction of which crypt dominates the colon, which is modeled as a 2D lattice of crypts. The initial condition of this lattice is an equal proportion of wild-type (WT), expander (E), and survivor (S) crypts. In the Neuhauser model, we find no scenarios of coexistence even if the reproductive ratio of E and S crypt types are equal; however, in the Durrett model, we find preliminary results that indicate coexistence.

Contributors: Tayyab Wasim1, Marc D. Ryser2

1 Pratt School of Engineering, Duke University, Durham, N.C.

2 Department of Mathematics, Duke University, Durham, N.C

Modeling Receptor Binding in HIV

Abstract not submitted.

Spatial Model for Quorum Sensing Bacteria

Quorum sensing (QS) is a signaling mechanism by which bacteria sense and respond to changes in their density. QS has proven to provide an advantageous strategy when regulating the production of costly yet beneficial exoproducts, in particular exoenzymes. These enzymes are "public goods" that are produced by the bacterial cells to combat noted stress on the entire colony. The quintessential example of such a stress is an antibiotic; however, the production of exoenzymes comes with great metabolic cost including cell death. In addition, not all bacterial cells produce these exoenzymes. My work involves devising a partial differential equation model (PDE) in order to understand the dynamics of exoenzymes in a heterogeneous, spatially-extended bacterial colony.

TBD

Abstract not submitted.

An Investigation of the Efficiency of Slime Mold as a Maze-Solving Algorithm

Physarum polycephalum, commonly known as slime mold, has recently been noted for its ability to find the shortest path between food sources. Unlike numerical approaches, the slime mold is a viable alternative because it will not break down across large-scale networks. We designed an experiment using a template of the streets of Manhattan and strategic food placement to further test the slime’s ability to efficiently find an optimal path. Our study used image tracking analysis to quantify and record the slime’s movement patterns for subsequent analyses. These analyses were compared to a variety of computational optimization algorithms as a means to assess the efficiency and success of the slime mold's actions. Our current results suggest that the slime mold has the ability to find a nearly perfect route over the course of 6 days. Thus far, it has performed in a relatively efficient manner, comparable to automated search algorithms. The ultimate goal is to develop a dynamic model to simulate the slime's search routine, as well as to determine situations in which slime mold optimization can be of use in real world planning.

TBD

Abstract not submitted.