2018 Capstone Conference

(August 6,2018 - August 9,2018 )

Organizers


Tony Nance
Mathematical Biosciences Institute, The Ohio State University

The MBI Capstone Conference is a student-centered conference featuring talks and posters by students doing research in the mathematical biosciences, keynote talks by prominent mathematical biologists, a graduate studies recruitment event, panels on mathematical biosciences fields of research and career opportunities, and a social event at the Columbus Zoo and Aquarium.

The Capstone Conference is open to all undergraduate students doing research in the mathematical biosciences, not only to students participating in the MBI REU. All accepted applicants will be given full-to-partial funding for hotel and travel!



Featured Keynote Talks:

Jonathan Rubin, Ph.D. – Professor and Chair, Department of Mathematics, University of Pittsburgh
Dr. Rubin majored in Mathematics as an undergraduate at The College of William and Mary and received his Ph.D. in Applied Mathematics from Brown University in 1996.  He was a Zassenhaus Assistant Professor and then a National Science Foundation Postdoctoral Fellow in the Department of Mathematics at The Ohio State University before joining the University of Pittsburgh Mathematics faculty in 2000.  In addition to his Mathematics position, he is a Graduate Faculty member, a Center for Neuroscience at University of Pittsburgh Graduate Training Faculty member, a member of the Center for the Basis of Neural Cognition, an affiliate of the McGowan Institute for Regenerative Medicine, and a Visiting Professor in Computational Biology.  Six students have completed their Ph.Ds at Pitt under Dr. Rubin's supervision.

The general topic of Dr. Rubin’s research is spatiotemporal pattern formation in coupled cell networks.  The overall goal of this research is to understand how the intrinsic dynamics of network elements interacts with the architecture and properties of coupling to drive network activity.  Most of his work is motivated by neuroscience applications, such as understanding transitions between activity patterns in respiratory pacemaker networks or figuring out the mechanism underlying the therapeutic efficacy of deep brain stimulation for Parkinson's disease.

Carolyn Cho, Ph.D. – Immunology Pharmacometrics Therapeutic Area Lead, Merck Research Laboratories (MRL)
Carolyn has worked in the pharmaceutical industry for 20 years, applying modeling and systems biology approaches to the discovery and development of therapeutic treatments for diabetes, osteoporosis, and immunology-related disease. She serves on the Board of Trustees of the Mathematical Biosciences Institute, and the boards of Propel Careers (past), and Mass. AWIS (past). She currently oversees modeling across the immunology pipeline at MRL, and has previously led the Systems Biology Targets group at Pfizer, was Global Head of Computational Systems Biology at Novartis Institutes for Biomedical Research (NIBR), and has held positions at Physiome Sciences (Princeton, NJ), SmithKline Beecham Pharmaceuticals (King of Prussia, PA), and Princeton University.  Carolyn received her Ph.D. in biological physics from the University of Toronto.

Nancy McMillan, Ph.D., PMP – Resource Group Manager, Advanced Analytics, Battelle
After earning a BS in Mathematics and Computer Science from Muskingum University and an MS and PhD in Statistics from The Ohio State University, Dr. McMillan completed a two-year postdoc with the National Institute of Statistical Sciences then started a 23-year career at Battelle.  Over that time period she has worked and published on environmental exposure and risk assessment, transportation safety benefits, quantitative risk assessment related to CBRN terrorism, and bioinformatics (analysis of genomic data).  Dr. McMillan’s environmental, transportation, risk assessment, and bioinformatics work have all focused on providing quantitative analysis that captures uncertainty to support science-based decision-making.  Dr. McMillan is currently working primarily in digital surveillance, including analysis of unstructured text data from scientific literature and social media.  Dr. McMillan has been a group manager for 12 years.  Her first 11 years of management experience involved leading a group of first 8-10 statisticians and then a larger team focused on knowledge management and cognitive computing that included computer scientists, statisticians, applied mathematicians, and knowledge management experts.  Currently Dr. McMillan is the manager of Battelle’s Advanced Analytics capability; her group supports data science activities across Battelle’s Health, Environment & Infrastructure, National Security Division, and Chemical, Biological, Radiological, Nuclear, and Explosive (CBRNE) Defense business units.

 

Graduate Programs Represented in the Recruitment Event:

Arizona State School of Mathematical and Statistical Sciences

Case Western Reserve University Department of Mathematics

Cornell University Center for Applied Math

Indiana University - Purdue University, Indianapolis Department of Mathematical Sciences

North Carolina State University Department of Biomathematics

Purdue University Department of Statistics

Ohio State University Department of Biostatistics

Ohio State University Interdisciplinary Biophysics Program

Ohio State University Department of Statistics

University of California, Irvine Department of Mathematics

University of Iowa Department of Biostatistics

University of Maryland, Baltimore County Department of Statistics

University of Michigan Department of Biostatistics

University of Michigan Department of Mathematics

University of Minnesota Department of Biostatistics

University of Pittsburgh Department of Mathematics 

Virginia Commonwealth University Department of Statistics

Virginia Tech Department of Statistics

 

 

Accepted Speakers

Carolyn Cho
Quantitative Pharmacology & Pharmacometrics, Merck, Sharp & Dohme
Nancy McMillan
Battelle, Battelle Memorial Institute
Jonathan Rubin
Mathematics Department, University of Pittsburgh
Monday, August 6, 2018
Time Session
08:30 AM

Shuttle to MBI

08:45 AM
09:15 AM

Daily Introductions and Workshop Preview with Breakfast

09:15 AM
09:45 AM

MBI and Conference Introductions

09:45 AM
10:15 AM
Lindsay Duvernoy - Developing Mathematical Models to Investigate Pathways Responsible for Protein Aggregation in Alzheimer's Disease

Every 65 seconds someone is diagnosed with Alzheimer€™s Disease (AD). AD is the 6th leading cause of death in the United States, and it has become a national healthcare crisis. AD is a neurodegenerative disorder, which atrophies the cerebral cortex and subcortical regions of the brain. The Amyloid Hypothesis of AD focuses on extracellular amyloid beta 42 ( ) protein plaques. Based on the model by Puri et al. (2010), different rates of input signaling received by neurons can be quantified by their unique synaptic weights. In this work, we have recreated the Puri model, a 7th order state variable system, which illustrates inputs of crosstalk between neuronal components including the neuron, astrocytes, and microglia. Our hypothesis states through quantifying increased rates of input signals of , we illustrate through mathematical modeling how negatively impacts neuronal survival and highlight the synergistic effect of from neurons and astrocytes on neuronal death ( ). This research demonstrates that produced by astrocytes plays a larger role in than previously reported. Our results will lead to a greater awareness of the biological origins of AD.

10:15 AM
10:45 AM
Javier Urcuyo - Quantifying tumor growth and therapeutic response from bioluminescence imaging in patient-derived xenografts

Glioblastoma is an aggressive primary brain cancer that is notoriously difficult to treat, in part due to its diffuse infiltration of brain tissue and the limitations of the blood-brain barrier (BBB), which often prevents drugs from reaching the entire tumor. Specifically, rapid tumor proliferation leads to accelerated angiogenesis resulting in a €˜leaky€™ BBB, which affects drug distribution. To address the differential impact of this BBB heterogeneity across patients, time series bioluminescence imaging (BLI) data was compiled from experiments treating murine orthotopic glioblastoma patient-derived xenografts (PDXs). The extent of BBB breakdown has been previously quantified for multiple PDX lines, allowing us to examine the heterogeneity in this feature among human patients. BLI data directly quantifies total tumor cell abundance, allowing us to observe how therapy affects tumor cell populations. After adjusting for lead time bias via a nonlinear mixed effects approach, we used the serial BLI data to obtain an overall growth rate for each PDX line across multiple subjects. These different growth kinetics were used to parametrize corresponding therapeutic models of the individual PDX lines. While further work is needed to verify our results across more PDX lines, they suggest that our existing characterization of tumor invasiveness may be able to aid in matching patients to the best therapy for their individual tumors.

10:45 AM
11:00 AM

Break

11:00 AM
11:30 AM
Sophia Kardadi - The Level Set Method for Topology Optimization

Topology optimization is a numerical method to find the optimal distribution of a given amount of material that maximizes the performance of the resulting structure, which is subjected to boundary conditions that include external forces and heat loads. An effective approach to solve a topology optimization problem is the use of the level set method. In this method, the boundary of an n-dimensional structure is defined as the zero level set map of a (n+1)-dimensional surface. Benefits of the level set method include an easily adaptive topology, the ability to set parameters that change complexity of the resulting object, and speed of the code. Drawbacks include intermittent re-initialization of the level set function and ill-posed, steady state solutions. This work studies various implementations of the level set method and compare them to traditional density-based methods, which are widely used in topology optimization.

11:30 AM
12:00 PM
Nicholas Thayer - Multinucleation in the stretched cells of Drosophila melanogaster

Polyploidy, in its many forms, is a mechanism that compensates for different needs of cells in tissues, including protein production and maintaining cell size/DNA content ratio. Using the stretched cells of Drosophila melanogaster as a model system, we studied polyploidy. We show that polyploidy (specifically, multinucleation) happens in these cells by cell fusion, not endomitosis. We show that the membranes of the stretched cells (soma) align with the nurse cells (germline), which raises questions about the possibility of membrane/protein exchange between these tissues. We also present evidence that stretched cell nuclei are "shared" between multiple cells simultaneously. Finally, we show that these traits evolved in an ancestor common to Drosophila species at least 40 million years ago. These findings together show that the Drosophila genus is a good model system to study polyploidy and soma to germline communication.

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:00 PM
Ariel Fitzmorris - Effects of Population Density on Germination Rates in Neurospora crassa Spores

Neurospora crassa is a filamentous fungus which can reproduce through asexual spores called conidia. These spores remain in a dormant state until they find a favorable environment, where they must germinate before they can begin exponential growth. Our goal for this project was to quantify the effect of population density on germination time, and to understand the physical mechanism behind this effect. We grew spores of two wild-type N. crassa strains, in both separate and mixed trials, at a broad range of initial spore densities. Then, we took images over a 12 hour period and analyzed them using MATLAB to accurately calculate growth rates and germination times. We have determined that N. crassa spores germinate sooner when there are more neighbors of the same strain present which indicates that they are using a form of quorum sensing. This is relevant to ecology and evolutionary biology because we have a living system which is simple enough to be mathematically analyzed and with a direct fitness relationship.

02:00 PM
02:30 PM
Julia Pelesko - A Combined Numerical, Mathematical, and Empirical Model to Predict the Evolution of Drug Resistance

Due to the evolution of resistance, drug therapies often fail to treat ailments such as bacterial infections, cancer, and viral diseases, despite initial successes. Improvements in next generation sequencing technologies already allow us to pinpoint resistance conferring mutations. Since evolution is a stochastic process, however, each evolutionary trajectory, or sequence of advantageous mutations, occurs with a certain, currently unknown, probability. By predicting the likelihoods of each trajectory, we can design treatment plans to genetically steer populations away from a resistant phenotype. To this end, we have constructed a morbidostat, an automated continuous culture device, to monitor the evolution of resistance. Using fitness data gathered from the morbidostat, we will parameterize our numerical Agent Based Model (ABM) model and Fokker-Plank mathematic model to predict under what conditions certain trajectories occur. In light of these results, we will update treatment plans for morbidostat experiments and monitor the resulting evolutionary dynamics to verify our predictions.

02:30 PM
02:45 PM

Break

02:45 PM
03:30 PM
Alanna Haslam, Yassine Dribki - Modeling Physarum polycephalum Decision-Making: Examining the Current Reinforcement and Reaction-Diffusion-Advection Models

Physarum polycephalum, commonly known as slime mold, is a large single-celled, multi-nucleated protist. As it searches for and exploits food sources, slime mold€™s amoeboid movement and network-like structure exhibit intelligent behavior such as maze-solving and network optimization. To explore the mechanisms behind this brainless intelligence we explore two models. The Reaction-Diffusion-Advection model attempts to describe the rhythmic contractions, chemical oscillations, and pattern formation observed in the plasmodium of slime mold. The Current Reinforcement model attempts to replicate the network formation and optimization of slime mold. Together these micro- and macro-level models can describe the known behavior of slime mold and suggest the possible mechanisms and methods that propel its surprising intelligence.

03:30 PM
05:30 PM

Poster Session and Reception

05:30 PM

Shuttle pick-up from MBI

Tuesday, August 7, 2018
Time Session
08:30 AM

Shuttle to MBI

08:45 AM
09:15 AM

Daily Introductions and Workshop Preview with Breakfast

09:15 AM
10:00 AM
Allison Torsey, Amy Carpenter - Analyzing the Dynamics of an Inflammatory Response to a Bacterial Infection in Rats

Sepsis is a serious health condition that is not well understood. It is defined as an overactive immune response that causes severe damage to healthy tissue, often resulting in death. Mathematical modeling has emerged as a useful tool to investigate key elements of the immune response and thus offers a useful method for studying sepsis. Here, a system of four ordinary differential equations is developed to simulate the dynamics of bacteria, the pro-inflammatory immune response, anti-inflammatory immune response, and tissue damage. The pro-inflammatory response is triggered by the presence of bacteria and leads to destruction of bacteria as well as damage to the tissue once the level of inflammation exceeds a certain threshold. The anti-inflammatory response works to temper the pro-inflammatory response, although it is not always capable of preventing sustained tissue damage. The model is used to assess the conditions under which health, aseptic (inflammation-driven) death, or septic (bacteria-driven) death is predicted in both the presence and absence of an induced E. Coli bacterial infection in rats. Model parameters are fit to experimental data from rat sepsis studies. The model is used to predict the survivability range for an infection while varying the initial amount, growth rate, or virulence of the bacteria in the system.

10:00 AM
10:30 AM
Susan Cheng - Estimating Gap Junction Properties of Electrically Coupled Neurons From Measurements Made in the Soma

The stomatogastric ganglion (STG) is a neuronal circuit found in lobsters and crabs that generates simple rhythmic behaviors such as walking and breathing. While the circuit as a whole can be observed, the smaller scale structure is mostly unknown and unstudied. In particular, the location of gap junctions electrically coupling one neuron to another is difficult to determine. This location affects errors made in studying coupled versus uncoupled neurons and can affect nearby chemical synapses. We aim to use computational modeling to better understand how different properties of electrically coupled neurons affect voltage measurements made in the soma (cell body). We then determine rudimentary fits to biological data that give a rough first estimate of the location of the gap junction.

10:30 AM
10:45 AM

Break

10:45 AM
12:00 PM
Nancy McMillan - Keynote: Healthcare Transformation Innovation Laboratory: Evaluation of Federally Qualified Health Centers Advanced Primary Care Practice Demonstration

There is broad support for transforming Payment and Service Delivery Models away from Fee For Service (FFS) and to Value-based Payments (VBP). Centers for Medicare and Medicaid Services Innovation (CMMI) Center has a primary role in testing various payment and service delivery models (PSDMs) that aim to achieve better care for patients, smarter spending and healthier communities. To date, the pilot tests run have been costly, risky, and inconclusive. In this work, we propose a simulation tool developed to improve decision-making before pilot implementation (decrease costs, reduce risk), support evaluation design by identifying key sources of uncertainty (yield more conclusive evaluations), and support program integrity studies (long term monitoring). Our simulation tool is in the early stages of development; we demonstrate it€™s value by comparing simulation results with a PSDM previously tested by CMMI, the Federally Qualified Health Centers (FQHC) Advanced Primary Care Practice (APCP) Demonstration.

12:00 PM
01:30 PM

Poster Session and Pizza Lunch with MBI Postdocs

01:30 PM
02:30 PM

Panel on Graduate School: Kellie Archer, Michael Pennell, Yuan Lou

02:30 PM
03:00 PM

Informal Discussion with Panelists

03:00 PM
03:15 PM

Break

03:15 PM
09:00 PM

Columbus Zoo Trip and Conference Dinner

Wednesday, August 8, 2018
Time Session
08:30 AM

Shuttle to MBI

08:45 AM
09:15 AM

Daily Introductions and Workshop Preview with Breakfast

09:15 AM
09:45 AM
Benjamin Brown - Towards a metric for the reproducibility of ChIP-exo data

ChIP-exo is a laboratory protocol used to identify the location of protein binding sites on DNA, with applications to the study of cancer and immune function. However, few methods exist for assessing the reproducibility of ChIP-exo data between different replicates in the same experiment. We used Euclidean distance to produce a reproducibility score for each potential binding event, determining a relationship between reproducibility and the presence of sequence motifs, as well as exploring ways to classify replicated events according to their reproducibility.

09:45 AM
10:30 AM
Maike Morrison, Emily Strong - Distinguishing Resource Selection from Heavy-Tailed Dispersal in Spatial Epidemic Models

The tail of the dispersal kernel of individual movement plays a critical role in the spatial spread of infectious disease, invasive species, and other spreading phenomena. However, most studies where the dispersal kernel has been estimated from observed natural systems have assumed homogeneous dispersal in space, even though non-uniform use of space (i.e., resource selection) has long been recognized as important in many systems. In our project, we explore the consequences of ignoring terrain heterogeneity when estimating parameters governing the tail of a dispersal kernel. We show that ignoring resource selection in general leads to estimates of dispersal kernels with heavier tails than the true kernels used for simulation. In addition, this often leads to predictions of the rate of spatial infectious disease spread that are much faster than the true spread through a population that is moving across patchy terrain.

10:30 AM
10:45 AM

Break

10:45 AM
12:00 PM
Carolyn Cho - Keynote: When Glucose Control Goes Wrong: Mathematics in Pharmaceutical Research

Homeostasis of blood glucose is the central tenet of metabolic disease and its treatment. This nonlinear dynamics problem is an obvious application of mathematical modeling. In particular, the practical questions of pharmaceutical research and development has offered several opportunities to bring modeling to an enterprise that is only recently accepting quantitative approaches on an equal footing with empirical approaches. Mathematical modeling of metabolic disease will be discussed in the context of pharmaceutical development from target discovery to translation of animal models informing clinical design to drug registration PK/PD.

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:00 PM
Maryam Amran - Effects of Wall Proximity on Red Blood Cell Interactions

Red blood cells play a vital role in transporting oxygen through microvessels. To help fulfil the body€™s oxygen needs, blood is composed of 40-45% red blood cells by volume. As blood flows in a vessel, cell-wall interactions push cells away from the vessel wall creating a region devoid of cells near that wall (cell-free layer) while cell-cell interactions push cells towards the wall and limit the size of that cell-free layer. How these cell-wall and cell-cell forces balance determine the size of the cell-free layer which can affect the speed and distribution of blood and its nutrients throughout the body. To understand these cell-cell and cell-wall interactions better, we simulate two-dimensional pairs of cells interacting in simple linear shear flow in a walled channel. Cells can experience dancing, swapping, and passing interactions depending on cells€™ relative positions and orientations as they enter an interaction region. Results indicate that although increased wall proximity decreases interaction strengths, cell orientation may have greater effects on these interactions. Moreover, decreased channel width decreases swapping interactions frequency. While additional analysis needs to be done, these results suggest that wall proximity and cell orientation can have appreciable effects on the cell-free layer and overall blood and nutrient distribution.

02:00 PM
02:30 PM
Keshav Patel - Maximizing Flux Along Microtubule via Cooperation Among Molecular Motors

Our work examines the effect of molecular motor binding reactions on intracellular transportation. Motor proteins (namely kinesin and dynein) carry cargo along microtubule at rates faster than diffusion would allow. However, molecular motors are known to have low processivity, thus spending a significant amount of time freely diffusing with their cargo. We therefore seek to model this system to connect aspects of this complex dynamic to its efficiency. This model is examined as a Partial Differential Equation, a probability density function, and a Monte Carlo simulation. Emphasis is placed on binding reactions needed to create active crosslinks between cargo and the microtubule. We have shown that when cargo have multiple motor binding sites, motors with low processivity optimize microtubule flux by increasing cargo binding while maintaining at least one active crosslink. Our work highlights the benefit of current molecular motor transport and presents an alternative process for engineering motors that could augment processes such as protein synthesis and modification, cell signaling, and cell repairing.

02:30 PM
02:45 PM

Break

02:45 PM
03:15 PM
Riley Juenemann - Particle tracking in live cell data

In contrast to in vitro particle tracking experiments, wherein there are great controls on particle and environmental homogeneity, live cell (in vivo) tracking features tremendous diversity in particle movement. In this work, we have developed a suite of €œfirst-pass€? statistical tools to categorize disparate types of particle trajectories. The data we used for this project was generated in the the lab of Prof. Christine Payne, using fluorescence microscopy in HeLa (model human) cells. Some particle paths were easily distinguishable as free diffusion, stuck diffusion, or directed transport, while other trajectories were difficult to categorize. Several of the more complex paths indicated the potential for tracking error. The tools we developed for the categorization process include the correlation between consecutive increments and effective diffusivity from a maximum likelihood estimation. The standard deviation for the major and minor axis and the creation of a parameterized path to represent a fictional moving anchor employed principal components analysis. This anchor estimation allowed the computation of effective velocity and the average distance the particle deviated from the anchor. Based on these data measures, K-means clustering was utilized to distinguish between free diffusion, stuck diffusion, directed transport, and tracker error. This automated categorization process proved to be successful on data simulated using stochastic differential equations and provided interesting results on the live cell data.

03:15 PM
03:30 PM

Graduate Studies Event Introduction

03:30 PM
05:30 PM

Graduate Studies Recruitment Event

05:30 PM

Shuttle pick-up from MBI

Thursday, August 9, 2018
Time Session
08:30 AM

Shuttle to MBI

08:45 AM
09:15 AM

Daily Introductions and Workshop Preview with Breakfast

09:15 AM
10:15 AM

Panel on Career Opportunities: Carolyn Cho, Nancy McMillan, Jonathan Rubin

10:15 AM
10:45 AM

Informal Discussion with Panelists

10:45 AM
11:00 AM

Break / Conference Photo

11:00 AM
12:15 PM
Jonathan Rubin - Keynote Talk

-

12:15 PM
12:30 PM

Wrap-up

12:30 PM

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

Name Email Affiliation
Adams, Jacqueline jacqueline.frances4@gmail.com Mathematics & Statisics, American University
Alexander, Alania alaniaalexander@gmail.com Department of Biological and Environmental Sciences, Alabama A&M University
Amran, Maryam mamran@uci.edu Mathematics, University of California, Irvine
Baker, Gillian baker.2502@buckeyemail.osu.edu Mathematics, The Ohio State University
Bendaoud, Amina ab847@njit.edu Mathematical Sciences, New Jersey Institute of Technology
Bond, Bailey bbond@butler.edu Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Brown, Benjamin brown_b1@denison.edu Mathematics and Computer Science, Denison University
Burkes, Jatwon jatwon.a.burkes@students.cookman.edu The College of Science, Engineering, and Mathematics (CSEM), Bethune-Cookman University
Carpenter, Amy acarpe01@leeu.edu Natural Sciences and Mathematics, Lee University
Cheng, Susan scheng1@andrew.cmu.edu Mathematics, University of Pittsburgh
Cho, Carolyn carolyn.cho@merck.com Quantitative Pharmacology & Pharmacometrics, Merck, Sharp & Dohme
Dribki, Yassine yd226@njit.edu Mathematics, New Jersey Institute Of Technology
Duvernoy, Lindsay lindsayduvernoy@gmail.com Department of Natural Sciences, Bethune-Cookman University
Fitzmorris, Ariel arielfitzmorris@ucla.edu Mathematics, University of California, Los Angeles
Frederickson, Bryce brycefred113@gmail.com Mathematics and Statistics, Utah State University
Harrison, Addie harram16@wfu.edu Mathematics, Wake Forest University
Haslam, Alanna ajhaslam@bowdoin.edu Mathematics, Bowdoin College
Juenemann, Riley rjuenemann@tulane.edu Mathematics, Tulane University
Kardadi, Sophia skardadi@nd.edu College of Science, University of Notre Dame
Lu, TingYing Math, Pennsylvania State University
Luong, Jack jackaham_luongcoln@mail.fresnostate.edu Mathematics, California State University, Fresno
Madrigal, Jamie jmadr002@ucr.edu Mathematics, University of California, Riverside
Maguire, Marina marinadelray1@gmail.com Mathematics, Edward Waters College
Mathers, Samuel smathers@princeton.edu Mathematics, Princeton University
McCann, William wjm9@njit.edu Department of Mathematical Sciences, New Jersey Institute of Technology
McConnell, Ryan mcconnell.296@osu.edu Mathematics, The Ohio State University
McKeough, Amber amcke005@ucr.edu Mathematics, University of California, Riverside
McMillan, Nancy McMillanN@battelle.org Battelle, Battelle Memorial Institute
Medina, Catalina catalinamedina@nevada.unr.edu Department of Mathematics and Statistics, University of Nevada
Mitchell, Moriah mm6948a@student.american.edu Mathematics and Biology, American University
Morrison, Maike maikem123@gmail.com Integrative Biology, University of Texas
Muktar, Saida saidam1@umbc.edu Mathematics, University of Maryland Baltimore County
Myers, Margaret maggie.myers95@gmail.com Department of Pediatrics, University of Tennessee Health Science Center
Nance, Tony tony@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Patel, Keshav keshavp0118@gmail.com Applied Mathematics, University of North Carolina, Chapel Hill
Pecha, Thomas tpecha422@gmail.com Biology, University of Dallas
Pelesko, Julia jlp192@case.edu Translational Hematology and Oncology, Cleveland Clinic Foundation
Reyes, Jessica jreyes34@students.kennesaw.edu Department of Mathematics, Kennesaw State University
Rubin, Jonathan rubin@math.pitt.edu Mathematics Department, University of Pittsburgh
Smith, TiGara tigara.smith@gmail.com Biology, Edward Waters College
Strong, Emily ers00083@sjfc.edu Mathematics, St. John Fisher College
Thayer, Nicholas thayern@reed.edu Computational and Integrative Biology, Rutgers University at Camden
Tindal, Rachael rtindal22@gmail.com Mathematics, Colorado State University
Torsey, Allison allison.torsey@gmail.com Mathematics, Buffalo State College
Urcuyo, Javier jurcuyo@asu.edu School of Mathematical and Statistical Sciences/School of Life Sciences, Arizona State University
Vasquez-Perez, Pedro pedro.vasquez1@upr.edu Mathematical Sciences, University of Puerto Rico at Mayaguez
Vesta, Jill jevesta@ku.edu Mathematics, University of Kansas
Wang, Jeremy jqw1@hotmail.com Computational and Integrative Biology, Rutgers University at Camden
Wilson , Rachel rwilson01@email.wm.edu Interdisciplinary Studies: Computational and Applied Mathematics and Statistics, College of William and Mary
Yan, Hao-Tong hyan1@swarthmore.edu Mathematics, Swarthmore College
Zhao, Erin erinzhao@iu.edu Mathematical Sciences, Indiana University-Purdue University Indianapolis
Zhu, Songning sjz5163@psu.edu engineering, Pennsylvania State University
Effects of Wall Proximity on Red Blood Cell Interactions

Red blood cells play a vital role in transporting oxygen through microvessels. To help fulfil the body’s oxygen needs, blood is composed of 40-45% red blood cells by volume. As blood flows in a vessel, cell-wall interactions push cells away from the vessel wall creating a region devoid of cells near that wall (cell-free layer) while cell-cell interactions push cells towards the wall and limit the size of that cell-free layer. How these cell-wall and cell-cell forces balance determine the size of the cell-free layer which can affect the speed and distribution of blood and its nutrients throughout the body. To understand these cell-cell and cell-wall interactions better, we simulate two-dimensional pairs of cells interacting in simple linear shear flow in a walled channel. Cells can experience dancing, swapping, and passing interactions depending on cells’ relative positions and orientations as they enter an interaction region. Results indicate that although increased wall proximity decreases interaction strengths, cell orientation may have greater effects on these interactions. Moreover, decreased channel width decreases swapping interactions frequency. While additional analysis needs to be done, these results suggest that wall proximity and cell orientation can have appreciable effects on the cell-free layer and overall blood and nutrient distribution.

Towards a metric for the reproducibility of ChIP-exo data

ChIP-exo is a laboratory protocol used to identify the location of protein binding sites on DNA, with applications to the study of cancer and immune function. However, few methods exist for assessing the reproducibility of ChIP-exo data between different replicates in the same experiment. We used Euclidean distance to produce a reproducibility score for each potential binding event, determining a relationship between reproducibility and the presence of sequence motifs, as well as exploring ways to classify replicated events according to their reproducibility.

Analyzing the Dynamics of an Inflammatory Response to a Bacterial Infection in Rats

Sepsis is a serious health condition that is not well understood. It is defined as an overactive immune response that causes severe damage to healthy tissue, often resulting in death. Mathematical modeling has emerged as a useful tool to investigate key elements of the immune response and thus offers a useful method for studying sepsis. Here, a system of four ordinary differential equations is developed to simulate the dynamics of bacteria, the pro-inflammatory immune response, anti-inflammatory immune response, and tissue damage. The pro-inflammatory response is triggered by the presence of bacteria and leads to destruction of bacteria as well as damage to the tissue once the level of inflammation exceeds a certain threshold. The anti-inflammatory response works to temper the pro-inflammatory response, although it is not always capable of preventing sustained tissue damage. The model is used to assess the conditions under which health, aseptic (inflammation-driven) death, or septic (bacteria-driven) death is predicted in both the presence and absence of an induced E. Coli bacterial infection in rats. Model parameters are fit to experimental data from rat sepsis studies. The model is used to predict the survivability range for an infection while varying the initial amount, growth rate, or virulence of the bacteria in the system.

Estimating Gap Junction Properties of Electrically Coupled Neurons From Measurements Made in the Soma

The stomatogastric ganglion (STG) is a neuronal circuit found in lobsters and crabs that generates simple rhythmic behaviors such as walking and breathing. While the circuit as a whole can be observed, the smaller scale structure is mostly unknown and unstudied. In particular, the location of gap junctions electrically coupling one neuron to another is difficult to determine. This location affects errors made in studying coupled versus uncoupled neurons and can affect nearby chemical synapses. We aim to use computational modeling to better understand how different properties of electrically coupled neurons affect voltage measurements made in the soma (cell body). We then determine rudimentary fits to biological data that give a rough first estimate of the location of the gap junction.

Keynote: When Glucose Control Goes Wrong: Mathematics in Pharmaceutical Research

Homeostasis of blood glucose is the central tenet of metabolic disease and its treatment. This nonlinear dynamics problem is an obvious application of mathematical modeling. In particular, the practical questions of pharmaceutical research and development has offered several opportunities to bring modeling to an enterprise that is only recently accepting quantitative approaches on an equal footing with empirical approaches. Mathematical modeling of metabolic disease will be discussed in the context of pharmaceutical development from target discovery to translation of animal models informing clinical design to drug registration PK/PD.

Developing Mathematical Models to Investigate Pathways Responsible for Protein Aggregation in Alzheimer's Disease

Every 65 seconds someone is diagnosed with Alzheimer’s Disease (AD). AD is the 6th leading cause of death in the United States, and it has become a national healthcare crisis. AD is a neurodegenerative disorder, which atrophies the cerebral cortex and subcortical regions of the brain. The Amyloid Hypothesis of AD focuses on extracellular amyloid beta 42 ( ) protein plaques. Based on the model by Puri et al. (2010), different rates of input signaling received by neurons can be quantified by their unique synaptic weights. In this work, we have recreated the Puri model, a 7th order state variable system, which illustrates inputs of crosstalk between neuronal components including the neuron, astrocytes, and microglia. Our hypothesis states through quantifying increased rates of input signals of , we illustrate through mathematical modeling how negatively impacts neuronal survival and highlight the synergistic effect of from neurons and astrocytes on neuronal death ( ). This research demonstrates that produced by astrocytes plays a larger role in than previously reported. Our results will lead to a greater awareness of the biological origins of AD.

Effects of Population Density on Germination Rates in Neurospora crassa Spores

Neurospora crassa is a filamentous fungus which can reproduce through asexual spores called conidia. These spores remain in a dormant state until they find a favorable environment, where they must germinate before they can begin exponential growth. Our goal for this project was to quantify the effect of population density on germination time, and to understand the physical mechanism behind this effect. We grew spores of two wild-type N. crassa strains, in both separate and mixed trials, at a broad range of initial spore densities. Then, we took images over a 12 hour period and analyzed them using MATLAB to accurately calculate growth rates and germination times. We have determined that N. crassa spores germinate sooner when there are more neighbors of the same strain present which indicates that they are using a form of quorum sensing. This is relevant to ecology and evolutionary biology because we have a living system which is simple enough to be mathematically analyzed and with a direct fitness relationship.

Modeling Physarum polycephalum Decision-Making: Examining the Current Reinforcement and Reaction-Diffusion-Advection Models

Physarum polycephalum, commonly known as slime mold, is a large single-celled, multi-nucleated protist. As it searches for and exploits food sources, slime mold’s amoeboid movement and network-like structure exhibit intelligent behavior such as maze-solving and network optimization. To explore the mechanisms behind this brainless intelligence we explore two models. The Reaction-Diffusion-Advection model attempts to describe the rhythmic contractions, chemical oscillations, and pattern formation observed in the plasmodium of slime mold. The Current Reinforcement model attempts to replicate the network formation and optimization of slime mold. Together these micro- and macro-level models can describe the known behavior of slime mold and suggest the possible mechanisms and methods that propel its surprising intelligence.

Particle tracking in live cell data

In contrast to in vitro particle tracking experiments, wherein there are great controls on particle and environmental homogeneity, live cell (in vivo) tracking features tremendous diversity in particle movement. In this work, we have developed a suite of “first-pass� statistical tools to categorize disparate types of particle trajectories. The data we used for this project was generated in the the lab of Prof. Christine Payne, using fluorescence microscopy in HeLa (model human) cells. Some particle paths were easily distinguishable as free diffusion, stuck diffusion, or directed transport, while other trajectories were difficult to categorize. Several of the more complex paths indicated the potential for tracking error. The tools we developed for the categorization process include the correlation between consecutive increments and effective diffusivity from a maximum likelihood estimation. The standard deviation for the major and minor axis and the creation of a parameterized path to represent a fictional moving anchor employed principal components analysis. This anchor estimation allowed the computation of effective velocity and the average distance the particle deviated from the anchor. Based on these data measures, K-means clustering was utilized to distinguish between free diffusion, stuck diffusion, directed transport, and tracker error. This automated categorization process proved to be successful on data simulated using stochastic differential equations and provided interesting results on the live cell data.

The Level Set Method for Topology Optimization

Topology optimization is a numerical method to find the optimal distribution of a given amount of material that maximizes the performance of the resulting structure, which is subjected to boundary conditions that include external forces and heat loads. An effective approach to solve a topology optimization problem is the use of the level set method. In this method, the boundary of an n-dimensional structure is defined as the zero level set map of a (n+1)-dimensional surface. Benefits of the level set method include an easily adaptive topology, the ability to set parameters that change complexity of the resulting object, and speed of the code. Drawbacks include intermittent re-initialization of the level set function and ill-posed, steady state solutions. This work studies various implementations of the level set method and compare them to traditional density-based methods, which are widely used in topology optimization.

Keynote: Healthcare Transformation Innovation Laboratory: Evaluation of Federally Qualified Health Centers Advanced Primary Care Practice Demonstration

There is broad support for transforming Payment and Service Delivery Models away from Fee For Service (FFS) and to Value-based Payments (VBP). Centers for Medicare and Medicaid Services Innovation (CMMI) Center has a primary role in testing various payment and service delivery models (PSDMs) that aim to achieve better care for patients, smarter spending and healthier communities. To date, the pilot tests run have been costly, risky, and inconclusive. In this work, we propose a simulation tool developed to improve decision-making before pilot implementation (decrease costs, reduce risk), support evaluation design by identifying key sources of uncertainty (yield more conclusive evaluations), and support program integrity studies (long term monitoring). Our simulation tool is in the early stages of development; we demonstrate it’s value by comparing simulation results with a PSDM previously tested by CMMI, the Federally Qualified Health Centers (FQHC) Advanced Primary Care Practice (APCP) Demonstration.

Distinguishing Resource Selection from Heavy-Tailed Dispersal in Spatial Epidemic Models

The tail of the dispersal kernel of individual movement plays a critical role in the spatial spread of infectious disease, invasive species, and other spreading phenomena. However, most studies where the dispersal kernel has been estimated from observed natural systems have assumed homogeneous dispersal in space, even though non-uniform use of space (i.e., resource selection) has long been recognized as important in many systems. In our project, we explore the consequences of ignoring terrain heterogeneity when estimating parameters governing the tail of a dispersal kernel. We show that ignoring resource selection in general leads to estimates of dispersal kernels with heavier tails than the true kernels used for simulation. In addition, this often leads to predictions of the rate of spatial infectious disease spread that are much faster than the true spread through a population that is moving across patchy terrain.

Maximizing Flux Along Microtubule via Cooperation Among Molecular Motors

Our work examines the effect of molecular motor binding reactions on intracellular transportation. Motor proteins (namely kinesin and dynein) carry cargo along microtubule at rates faster than diffusion would allow. However, molecular motors are known to have low processivity, thus spending a significant amount of time freely diffusing with their cargo. We therefore seek to model this system to connect aspects of this complex dynamic to its efficiency. This model is examined as a Partial Differential Equation, a probability density function, and a Monte Carlo simulation. Emphasis is placed on binding reactions needed to create active crosslinks between cargo and the microtubule. We have shown that when cargo have multiple motor binding sites, motors with low processivity optimize microtubule flux by increasing cargo binding while maintaining at least one active crosslink. Our work highlights the benefit of current molecular motor transport and presents an alternative process for engineering motors that could augment processes such as protein synthesis and modification, cell signaling, and cell repairing.

A Combined Numerical, Mathematical, and Empirical Model to Predict the Evolution of Drug Resistance

Due to the evolution of resistance, drug therapies often fail to treat ailments such as bacterial infections, cancer, and viral diseases, despite initial successes. Improvements in next generation sequencing technologies already allow us to pinpoint resistance conferring mutations. Since evolution is a stochastic process, however, each evolutionary trajectory, or sequence of advantageous mutations, occurs with a certain, currently unknown, probability. By predicting the likelihoods of each trajectory, we can design treatment plans to genetically steer populations away from a resistant phenotype. To this end, we have constructed a morbidostat, an automated continuous culture device, to monitor the evolution of resistance. Using fitness data gathered from the morbidostat, we will parameterize our numerical Agent Based Model (ABM) model and Fokker-Plank mathematic model to predict under what conditions certain trajectories occur. In light of these results, we will update treatment plans for morbidostat experiments and monitor the resulting evolutionary dynamics to verify our predictions.

Keynote Talk

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Distinguishing Resource Selection from Heavy-Tailed Dispersal in Spatial Epidemic Models

The tail of the dispersal kernel of individual movement plays a critical role in the spatial spread of infectious disease, invasive species, and other spreading phenomena. However, most studies where the dispersal kernel has been estimated from observed natural systems have assumed homogeneous dispersal in space, even though non-uniform use of space (i.e., resource selection) has long been recognized as important in many systems. In our project, we explore the consequences of ignoring terrain heterogeneity when estimating parameters governing the tail of a dispersal kernel. We show that ignoring resource selection in general leads to estimates of dispersal kernels with heavier tails than the true kernels used for simulation. In addition, this often leads to predictions of the rate of spatial infectious disease spread that are much faster than the true spread through a population that is moving across patchy terrain.

Multinucleation in the stretched cells of Drosophila melanogaster

Polyploidy, in its many forms, is a mechanism that compensates for different needs of cells in tissues, including protein production and maintaining cell size/DNA content ratio. Using the stretched cells of Drosophila melanogaster as a model system, we studied polyploidy. We show that polyploidy (specifically, multinucleation) happens in these cells by cell fusion, not endomitosis. We show that the membranes of the stretched cells (soma) align with the nurse cells (germline), which raises questions about the possibility of membrane/protein exchange between these tissues. We also present evidence that stretched cell nuclei are "shared" between multiple cells simultaneously. Finally, we show that these traits evolved in an ancestor common to Drosophila species at least 40 million years ago. These findings together show that the Drosophila genus is a good model system to study polyploidy and soma to germline communication.

Analyzing the Dynamics of an Inflammatory Response to a Bacterial Infection in Rats

Sepsis is a serious health condition that is not well understood. It is defined as an overactive immune response that causes severe damage to healthy tissue, often resulting in death. Mathematical modeling has emerged as a useful tool to investigate key elements of the immune response and thus offers a useful method for studying sepsis. Here, a system of four ordinary differential equations is developed to simulate the dynamics of bacteria, the pro-inflammatory immune response, anti-inflammatory immune response, and tissue damage. The pro-inflammatory response is triggered by the presence of bacteria and leads to destruction of bacteria as well as damage to the tissue once the level of inflammation exceeds a certain threshold. The anti-inflammatory response works to temper the pro-inflammatory response, although it is not always capable of preventing sustained tissue damage. The model is used to assess the conditions under which health, aseptic (inflammation-driven) death, or septic (bacteria-driven) death is predicted in both the presence and absence of an induced E. Coli bacterial infection in rats. Model parameters are fit to experimental data from rat sepsis studies. The model is used to predict the survivability range for an infection while varying the initial amount, growth rate, or virulence of the bacteria in the system.

Quantifying tumor growth and therapeutic response from bioluminescence imaging in patient-derived xenografts

Glioblastoma is an aggressive primary brain cancer that is notoriously difficult to treat, in part due to its diffuse infiltration of brain tissue and the limitations of the blood-brain barrier (BBB), which often prevents drugs from reaching the entire tumor. Specifically, rapid tumor proliferation leads to accelerated angiogenesis resulting in a ‘leaky’ BBB, which affects drug distribution. To address the differential impact of this BBB heterogeneity across patients, time series bioluminescence imaging (BLI) data was compiled from experiments treating murine orthotopic glioblastoma patient-derived xenografts (PDXs). The extent of BBB breakdown has been previously quantified for multiple PDX lines, allowing us to examine the heterogeneity in this feature among human patients. BLI data directly quantifies total tumor cell abundance, allowing us to observe how therapy affects tumor cell populations. After adjusting for lead time bias via a nonlinear mixed effects approach, we used the serial BLI data to obtain an overall growth rate for each PDX line across multiple subjects. These different growth kinetics were used to parametrize corresponding therapeutic models of the individual PDX lines. While further work is needed to verify our results across more PDX lines, they suggest that our existing characterization of tumor invasiveness may be able to aid in matching patients to the best therapy for their individual tumors.

Quantifying tumor growth and therapeutic response from bioluminescence imaging in patient-derived xenografts

Glioblastoma is an aggressive primary brain cancer that is notoriously difficult to treat, in part due to its diffuse infiltration of brain tissue and the limitations of the blood-brain barrier (BBB), which often prevents drugs from reaching the entire tumor. Specifically, rapid tumor proliferation leads to accelerated angiogenesis resulting in a ‘leaky’ BBB, which affects drug distribution. To address the differential impact of this BBB heterogeneity across patients, time series bioluminescence imaging (BLI) data was compiled from experiments treating murine orthotopic glioblastoma patient-derived xenografts (PDXs). The extent of BBB breakdown has been previously quantified for multiple PDX lines, allowing us to examine the heterogeneity in this feature among human patients. BLI data directly quantifies total tumor cell abundance, allowing us to observe how therapy affects tumor cell populations. After adjusting for lead time bias via a nonlinear mixed effects approach, we used the serial BLI data to obtain an overall growth rate for each PDX line across multiple subjects. These different growth kinetics were used to parametrize corresponding therapeutic models of the individual PDX lines. While further work is needed to verify our results across more PDX lines, they suggest that our existing characterization of tumor invasiveness may be able to aid in matching patients to the best therapy for their individual tumors.

Posters

Modeling Physarum polycephalum Decision-Making: Examining the Current Reinforcement and Reaction-Diffusion-Advection Models

Physarum polycephalum, commonly known as slime mold, is a large single-celled, multi-nucleated protist. As it searches for and exploits food sources, slime mold’s amoeboid movement and network-like structure exhibit intelligent behavior such as maze-solving and network optimization. To explore the mechanisms behind this brainless intelligence we explore two models. The Reaction-Diffusion-Advection model attempts to describe the rhythmic contractions, chemical oscillations, and pattern formation observed in the plasmodium of slime mold. The Current Reinforcement model attempts to replicate the network formation and optimization of slime mold. Together these micro- and macro-level models can describe the known behavior of slime mold and suggest the possible mechanisms and methods that propel its surprising intelligence.

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Particle tracking in live cell data
Riley Juenemann

In contrast to in vitro particle tracking experiments, wherein there are great controls on particle and environmental homogeneity, live cell (in vivo) tracking

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Keynote: When Glucose Control Goes Wrong: Mathematics in Pharmaceutical Research
Carolyn Cho

Homeostasis of blood glucose is the central tenet of metabolic disease and its treatment. This nonlinear dynamics problem is an obvious application of mathematical modeling. In particular, the practical questions of pharmaceutical research a

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Maximizing Flux Along Microtubule via Cooperation Among Molecular Motors
Keshav Patel

Our work examines the effect of molecular motor binding reactions on intracellular transportation. Motor proteins (namely kinesin and dynein) carry cargo along microtubule at rates faster than diffusion would allow. However, molecular motors

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Distinguishing Resource Selection from Heavy-Tailed Dispersal in Spatial Epidemic Models
Maike Morrison, Emily Strong

The tail of the dispersal kernel of individual movement plays a critical role in the spatial spread of infectious disease, invasive species, and other spreading phenomena. However, most studies where the dispersal kernel has been estimated f

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Towards a metric for the reproducibility of ChIP-exo data
Benjamin Brown

ChIP-exo is a laboratory protocol used to identify the location of protein binding sites on DNA, with applications to the study of cancer and immune function. However, few methods exist for assessing the reproducibility of ChIP-exo data betw

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Keynote: Healthcare Transformation Innovation Laboratory: Evaluation of Federally Qualified Health Centers Advanced Primary Care Practice Demonstration
Nancy McMillan

There is broad support for transforming Payment and Service Delivery Models away from Fee For Service (FFS) and to Value-based Payments (VBP). Centers for Medicare and Medicaid Services Innovation (CMMI) Center has a primary role in testing

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Estimating Gap Junction Properties of Electrically Coupled Neurons From Measurements Made in the Soma
Susan Cheng

The stomatogastric ganglion (STG) is a neuronal circuit found in lobsters and crabs that generates simple rhythmic behaviors such as walking and breathing. While the circuit as a whole can be observed, the smaller scale structure is mostly u

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Analyzing the Dynamics of an Inflammatory Response to a Bacterial Infection in Rats
Amy Carpenter, Allison Torsey

Sepsis is a serious health condition that is not well understood. It is defined as an overactive immune response that causes severe damage to healthy tissue, often resulting in death. Mathematical modeling has emerged as a useful tool to inv

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Modeling Physarum polycephalum Decision-Making: Examining the Current Reinforcement and Reaction-Diffusion-Advection Models
Yassine Dribki, Alanna Haslam

Physarum polycephalum, commonly known as slime mold, is a large single-celled, multi-nucleated protist. As it searches for and exploits food sources, slime mold€™s amoeboid movement and network-like structure exhibit intell

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A Combined Numerical, Mathematical, and Empirical Model to Predict the Evolution of Drug Resistance
Julia Pelesko

Due to the evolution of resistance, drug therapies often fail to treat ailments such as bacterial infections, cancer, and viral diseases, despite initial successes. Improvements in next generation sequencing technologies already allow us to

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The Level Set Method for Topology Optimization
Sophia Kardadi

Topology optimization is a numerical method to find the optimal distribution of a given amount of material that maximizes the performance of the resulting structure, which is subjected to boundary conditions that include external forces and

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Quantifying tumor growth and therapeutic response from bioluminescence imaging in patient-derived xenografts
Javier Urcuyo

Glioblastoma is an aggressive primary brain cancer that is notoriously difficult to treat, in part due to its diffuse infiltration of brain tissue and the limitations of the blood-brain barrier (BBB), which often prevents drugs from reaching

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Developing Mathematical Models to Investigate Pathways Responsible for Protein Aggregation in Alzheimer's Disease
Lindsay Duvernoy

Every 65 seconds someone is diagnosed with Alzheimer€™s Disease (AD). AD is the 6th leading cause of death in the United States, and it has become a national healthcare crisis. AD is a neurodegenerative disorder, which atro