Poster Session

Poster Abstracts

01. Mahya Aghaee

A synthesis of optimal controls for an Epidemiological model under vaccination and treatment

A SIR epidemiological model with time-varying population as a multi-input optimal control is considered. Vaccination and treatment strategies to limit the spread of the disease were studied. It is shown that the optimal vaccination schedule can be singular whereas the optimal treatment structure will be bang-bang.

 

02. Aleh Asipchuk

Age structure optimization in population dynamics

Our goal is to discuss stability of mathematical models which describe population dynamics with age structure and find optimal strategies for population growth.

 

03. Gabor Banyai

High frequency of RNA-templated repair of CRSIPR/Cas9 single and double-strand DNA breaks

Cells store their genetic information in their DNA molecules. This DNA can be exposed to damaging agents, such as chemicals or gamma radiation. In order to maintain genomic stability, DNA damage must be repaired. Cells have developed various methods to prevent fatal aberrations in the DNA molecules.

Our group has recently demonstrated that one mechanism to repair the damaged DNA is via homologous recombination using transcript RNA as a template. Our previous model used the yeast HO-endonuclease system, whereas our current system utilizes CRISPR/Cas9 to induce DNA double-strand breaks. In order to detect transcript RNA-mediated repair, we had to remove the genes coding for ribonuclease (RNase) H1 and H2, which cleave RNA when paired to complementary DNA, allowing enough time for the RNA molecule to provide a template for the damaged DNA. Our new system using CRISPR/Cas9 results in higher repair frequency than seen with the HO endonuclease, and we can detect DSB repair by RNA even while retaining both wild type RNase Hs. Furthermore, we tested the effectiveness of Cas9 nickases to study how single-strand breaks affect transcript RNA-templated DNA repair.

 

04. Aaron Barrett

An Adaptive Viscoelastic Fluid Solver

There have been many advances in the study of microorganism motility with a Newtonian fluid model. However, the fluids in which microorganisms typically swim give non-Newtonian responses to stresses and require more complicated fluid models, such as the Giesekus model, to give realistic results. These fluid models result in hyperbolic PDEs that are subject to areas of large stress concentrations and require high levels of spatial discretization to accurately resolve the fluid dynamics. This makes 3D simulations particularly untenable. Here, we present an adaptive viscoelastic fluid solver set in the framework of the IBAMR software package. We present the results of several examples demonstrating both the fluid solver with applications to bacterial locomotion.

 

05. Jasper Braun

An Annotation Algorithm for DNA Rearrangements

Complex genome rearrangements have been observed in certain organisms which contain two types of nuclei, such as the ciliated protist Oxytricha trifallax. During the conjugation, the precursor genome contained in the germline micronucleus is reorganized to form the product genome of the somatic macronucleus. This process requires the elimination of large portions of the precursor genome and the reordering and inversion of many of the remaining precursor segments. To properly study the biological mechanism behind such massive rearrangements, adequate processing of the DNA sequences of the two genomes is needed. We introduce an algorithm, which aligns precursor and product DNA sequences, annotates the segments of the precursor genome which rearrange to form the product genome and computes a range of properties which reflect the complexity of the rearrangement. The algorithm allows for customizability of the computation via user-defined parameters and is designed to work with actual real-world data.

 

06. Shivesh Chaudhary and Hang Lu

Improving interpretability of C. elegans whole-brain dynamics

Recently developed whole-brain imaging techniques allow researchers to capture neural activity of an entire brain in small model organisms, such as the nematode Caenorhabditis elegans. Global neural activity at single-cell resolution generated using these techniques hold great potential for uncovering how the brain integrates external cues to produce behavioral decisions. However, an unsolved problem in the field is determining biological identities of individual neurons in these videos. Without this information, our substantial knowledge of neuron properties and synaptic connectivity in C. elegans’ brain cannot be applied to infer roles of specific circuits. Conventionally, identities of neurons are determined by manual comparison against an atlas, but this method is slow, prone to human bias and error, and requires expert supervision. Here we present a method based on Conditional Random Fields (CRF) for automatically determining identities of all neurons in whole-brain videos. We take advantage of carefully introduced fluorescent landmarks in the worm’s brain as well as known geometrical and neighborhood relationships between 3D positions of neurons to generate a probabilistic label for each neuron in an unbiased manner. Our method is fast, insensitive to individual-to-individual variability in exact spatial location of neurons and can function in an unsupervised manner. Further, it is easily extensible to take advantage of training data if available. We expect that our algorithm will help realize full potential of whole-brain imaging techniques by enabling users to investigate the specific roles of neurons and circuits, and assess variability in neural activity between individual animals.

 

07. Thomas Eddy

Stick Knots and Generating Random Polygons in Confinement

Biological objects which form closed chains can be modeled as mathematical knots. In particular, it can be useful to think of these chains as being formed by straight line segments; in this case, we refer to these chains as stick knots. It is natural to ask how we might form a stick knot of a given type in the most efficient way possible, in the sense of having the least number of straight edges. Toward this end, we define the stick number of a knot to be the minimum number of edges needed to construct an equivalent stick knot. This number is unknown for most knots, although various theoretical and observed bounds are known. Previous research has attempted to improve the observed upper bounds for stick number by randomly generating polygons in three-dimensional space and identifying the knots they form. This poster presents a new variation on this method which generates equilateral polygons in tight confinement using an algorithm based on the toric symplectic structure of equilateral polygon space. We also describe original results obtained using this method.

 

08. Parker Edwards and Nikola Milicevic

Topological Data Analysis of Actin Networks

Networks of filaments assembled from the protein actin contribute significantly to cells' ability to move and change shape. These actin networks exhibit distinct local geometric structure. Some networks contain regions of straight and tightly packed fibers, for instance, as well as loops of varying sizes. We analyze actin networks starting from data that consist of high resolution live-cell microscopy images of cells' actin fibers. Our methodology detects localized features using image segmentation and tools from topological data analysis: relative persistent homology, a novel approach in the field, and persistence landscapes. We are presently experimenting with a number of subsequent machine learning methods using geometric summaries of each image as the feature vectors.

 

09. Alexander Elchesen

Virtual Persistence Diagrams

We study the algebraic and metric properties of the monoid of persistence diagrams with bounded total persistence. We show that the 1-Wasserstein distance is translation invariant on this space and use this to construct a metric on the Grothendieck group completion of the space. The Cauchy completion of the resulting metric group is Polish. We hope this structure will allow for further application of statistical methods to persistence diagrams.

 

10. Luis Fonseca

Modeling Host-Parasite Interactions in Malaria Blood-Stage Infections in Rhesus Macaques​

Malaria is globally the most deadly parasitic disease in humans, and the long-time coexistence with malaria has left indelible marks in the human genome that are the causes of a variety of genetic disorders. Anemia is the most common and severe complication of malaria, yet the root causes and mechanisms involved in malarial anemia are unclear and very difficult to study in humans. Non-human primate model systems enable the study and quantification of underlying, causative factors of malarial anemia, and particularly the onset of severe anemia.

A discrete recursive model was developed to simulate host-parasite interactions during the blood stage infection; it accounts for reticulocytes, red blood cells (RBCs), and infected RBCs. The parameters of this mechanistic model were optimized against the readouts of individual macaque data, which had been obtained in the course of Plasmodium coatneyi and P. cynomolgi infections of cohorts of malaria-naïve rhesus macaques (Macaca mulatta). The model allowed detailed estimations of the levels of erythropoietic output, reticulocyte lifespan, RBC removal, and the immune response against the parasite in each macaque.

The results showed that rhesus macaques have a response to a P. cynomolgi infection that is difficult to understand: As expected, the infection resulted in anemia, yet 60% of the RBCs were lost by bystander effect a mechanism other than parasite invasion. To compensate for the severe anemia, the host released younger reticulocytes and increased the erythropoietic output. These responses, however, appeared to be poorly coordinated, as the release of younger reticulocytes occurred too early, while anemia had not yet set in, thereby probably aiding the parasite more than the host. Increased production of RBCs was only detected after treatment that lowered the parasitemia. The model also showed that, similarly to humans, reticulocytes in rhesus macaques circulate for about 24h before becoming mature RBCs. Anemia, as a sequela of malaria, was due in 60% to bystander destruction of RBCs, and by an inability of the host to up-regulate erythropoiesis before suppression of parasitemia.

 

11. Alli L. Gombolay, Fredrik O. Vannberg, and Francesca Storici

Characterization of ribonucleotide incorporation in yeast genomic DNA using ribose-seq and Ribose-Map

Ribonucleotides incorporated into genomic DNA during DNA replication and repair can wreak havoc on genome stability. When left unrepaired, ribonucleotides can cause replication stress, spontaneous mutagenesis, and even deleterious breaks in the DNA strand. To understand the biological mechanisms that regulate the presence of ribonucleotides in DNA and ultimately the role that ribonucleotides play in the pathogenesis of human disease, we developed ribose-seq [1] and Ribose-Map [2]. Ribose-seq is an innovative next-generation sequencing method designed to capture and sequence the locations of ribonucleotides embedded in genomic DNA to single-nucleotide resolution. Next, we developed Ribose-Map, a novel bioinformatics toolkit that allows researchers to identify the exact sites of embedded ribonucleotides, study the nucleotide sequence context of these ribonucleotides, and explore their genome-wide distribution. To gain a better understanding of variation in ribonucleotide incorporation among different yeast species, we harnessed the power of ribose-seq and Ribose-Map to characterize patterns of ribonucleotide incorporation in the mitochondrial and nuclear DNA of S. cerevisiae, S. paradoxus, and S. pombe. By characterizing the sequence context, distribution, and hotspots of ribonucleotide incorporation, we were able to determine that the patterns of ribonucleotide incorporation in these three yeast species have biases that could help elucidate the rules that govern ribonucleotide incorporation in genomic DNA. In particular, we found biases in terms of the location and sequence context of ribonucleotide incorporation, as well as distinct motifs that are common to hotspots of ribonucleotide incorporation. We also found that the patterns of ribonucleotide incorporation in the two budding yeast species, S. cerevisiae and S. paradoxus, share more similarities to one another than to the more evolutionarily distantly related fission yeast, S. pombe.

 

12.  Xinqi Gong

Mathematical Intelligence Applications for Bio-Macromolecular Problems

The intersection among mathematics, information and biology has becoming more and more interesting and important. Many studies in this direction have led to developments of theories, methods and applications. But the too fast advancing of nowadays forefront information technology and biology knowledge, have triggered two obviously emerging phenomena, tremendous brand-new peaks accessible by new kinds of efforts, randomly meaningless results by in-correct intersections. Here I will show some of our recent results in developing and distinguishing efficiently intelligent approaches and applications for computational molecular biology and medical problems, such as protein structure-function-interaction prediction and pancreas cancer CT image analysis using algorithms like Fast Fourier transform, Monte Carlo, and deep learning, and some new designed physical and geometrical features.

 

13.  Xu Han

Intracellular Transport of Vesicles: Single Particle Tracking Challenges

Cellular heterogeneity is a characteristic of all cell populations. It is one feature by which biological systems enhance survival by expanding the response range to a constantly changing environment. Previous studies of cellular heterogeneity have investigated the function of phenotypic differences in cell populations. Our recent work focuses on intracellular vesicles and their transport as a marker of heterogeneity across generations. This includes the number of vesicles in each cell, the type of transport, and the speed of transport. The intracellular vesicles of human lung cancer epithelial cells (A549) were labeled with fluorescent dextran by pinocytosis. Images of the cells were analyzed to obtain distributions of the number of intracellular vesicles normalized over the area of each cell. Cells were imaged over a course of four generations to observe the relationship between parent and progeny vesicle densities. The difference between the distributions of vesicle density were determined by a Kolmogorov-Smirnov test. To examine intracellular heterogeneity, vesicle trajectories were analyzed to observe active transport, diffusion, and corralled diffusion. Genetically identical colonies were grown from single cells in a partitioned PDMS array and were subsequently isolated and grown in optical dishes for further vesicle number and transport observation. Using the same method to isolate progeny cells, individual colonies can be isolated for analysis by RNA sequencing. Vesicle-mediated cellular transport is essential for cellular function, including the processing of nutrients, investigation of its patterns across generations can offer insight into the relative genetic and environmental contributions.

 

14.  Md Rafiul Islam, Matthew J. Gray, Angela Peace

Mathematical Modeling and Uncertainty Quantification of Batrachochytrium salamandrivorans on the Eastern Newt

The recently discovered fungal pathogen, Batrachochytrium salamandrivorans (Bsal) is believed to be from Asia and was likely introduced into Europe through international trade that caused rapid die-offs of naive salamanders in Europe and Gray et al. (2015) predicts North America will soon experience similar devastation if no policy actions are taken and the pathogen emerges. In order to better understand Bsal pathogen dynamics, we develop Susceptible-Infected-Recovered-Susceptible (SIRS) models for this emerging fungal pathogen. Our models included two routes of pathogen transmission: direct transmission via contact between infected and susceptible individuals and environmental transmission via shed zoospores in the water. Unlike previous models, we categorized individuals into multiple stages of infection. We found the invasion probability for Bsal (i.e., the basic reproductive number, R0) into a population of the Eastern Newt adults. We performed numerical simulatons and parameter sensitivity analysis using latin hypercube sampling with partial rank coefficient correlation. We identified the dominant transmission pathway and suggested control strategies.

 

15.  Youngkyu Jeon

Identifying mechanisms of RNA-templated DNA repair in mammalian cells

Previously, we showed that transcripts of yeast cells are templates for DSB repair by a ‘cis system’ developed in our lab. Here, we examine whether RNA-templated DNA repair occurs in mammalian cells. We engineered the ‘cis system’ in a DNA plasmid, cis plasmid (pcis), using the DsRed red fluorescent marker gene. The DsRed was disrupted by an artificial intron, which can be correctly spliced in the antisense orientation. We induce one or two DSBs at the intron exon junctions by using the CRISPR-Cas9 system. DSB repair by the spliced antisense RNA can restore the sequence and function of the DsRed gene generating red fluorescent cells. We optimized such ‘cis system’ in mammalian cells by changing the position of the DSB/s and gRNA binding sites. We also made constructs in which the splicing is prevented by deletion of the 5’-splice site or deletion of the branch site of the intron. We then determined the frequency of red fluorescent cells in these constructs upon induction of Cas9 DSB/s in human embryonic kidney cells (HEK-293). We also transfected our cis system into HEK293T cells to see whether the replication process activated by the T antigen present in these cells could affect the RNAguided DSB repair process. The efficiency of repair was different in the different constructs, depending on the position of the DSB/s and on the cell line used. Preliminary results indicate that RNA could be an alternative template for DSB repair in mammalian cells.

 

16.  Samiksha Kaul

Using Polarity Establishment through par Genes as a Model to Study Genotype and Phenotype Relationship

The relationship between a genotype and its corresponding phenotype is often very complex. One reason for this complexity is that for any polygenic trait, the participating genes may interact with each other non-additively in determination of the phenotype. (Campbell et. al, 2018) An example of this is genetic background effects. Genetic background is defined as the alleles at all of the loci in the genome. (Chandler et. al, 2013) Variation in this background among individuals can affect how a focal allele influences phenotype, if the focal allele interacts non-additively with one or more alleles in the background. Resolving non-additive, or epistatic, interactions among genes is essential to understanding the relationship between genotype and phenotype for any trait of interest. The purpose of this project is to interrogate the role of epistasis by evaluating genetic background effects and gene-gene interactions within the context of a well-defined complex process, the establishment of polarity in the C. elegans early embryo. Does this vital process harbor functional variation in natural populations? How does genetic background affect the functioning of genes within this process? How does this affect evolution? By studying genetic interactions within a complex process, I aim to refine our understanding of the role and evolution of epistasis in the determination of quantitative traits.

 

17.  Jinsu Kim

Poisson control with ACR modules for chemical reaction networks

Reaction networks are graphical configurations that describe interactions between species in a biology or chemistry system. When the total copy numbers of species in a system is low, the system dynamics can be modeled with a stochastic process. The network deficiency is an integer that is solely determined by the network structure. If weakly reversible network has zero deficiency, a stationary distribution of the stochastic system dynamics exists and it is a product form of Poissons. However, broad classes of reaction networks do not satisfy the zero deficiency condition. In this work, we show how to control the copy number of a species of interest to be approximately Poisson centered at a desired mean in the long run even if the network has non zero deficiency. This Poisson control can be achieved by adding new reactions which is called absolute concentration robust (ACR) modules.

 

18.  Anna Kirkpatrick

RNA Pairing Properties under Uniform and Thermodynamically-Weighted Distributions

Understanding the structure of RNA is a problem of significant interest to biochemists.  An RNA molecule has both a linear structure, consisting of a sequence of nucleotides, and secondary and tertiary structures determined by how these nucleotides interact.  If the linear structure is known, algorithmically determining even the secondary structure, which can be viewed as a non-crossing matching, is a significant challenge, in part because the thermodynamic energy function used to make such predictions does not perform well on longer sequences.

This work attempts to understand the relationship between this energy function and properties of the structures it predicts.  Markov chain Monte Carlo computations are used to determine the distribution of certain properties under the thermodynamic energy function, and these are compared to properties of structures sampled uniformly.  Some relevant combinatorial results on non-crossing perfect matchings are also presented.

 

19.  Colin Klaus, Giovanni Caruso, Vsevolod Gurevich, Clint Makino, Heidi Hamm, Emmanuele DiBenedetto

Nonlinearity and Local Depletion Reduce Variability in the Single Photon Response of Vertebrate Rod Photoreceptors

Rod photoreceptors are known to signal in dim-light even at the threshold of a single photon event. This single photon response (SPR) is detected in spite of inherent randomness in the transduction cascade. Sources of variability include the spatial site of photon detection, the random walk undertaken by activated GPCR, and its randomly distributed sojourn times before phosphorylation and arrestin shut-off. Using a novel and homogenized 3D spatiotemporal PDE model of rod photoreceptor cells, mechanisms that suppress the cascade’s variability are numerically investigated. This model is a system for diffusing 2nd messengers cGMP and Ca^{2+} with nonlinear couple in their Neumann data. New numerical evidence demonstrates that nonlinear gating of ion channels by cGMP, as well as local depletion of cGMP at the site of photon capture, play significant roles in reducing cascade variability. The effects of 3D geometry on variability are also explored through comparison with 1D and Well-Stirred models.

 

20.  Samiksha Kaul

Using Polarity Establishment through par Genes as a Model to Study Genotype and Phenotype Relationship

The relationship between a genotype and its corresponding phenotype is often very complex. One reason for this complexity is that for any polygenic trait, the participating genes may interact with each other non-additively in determination of the phenotype. (Campbell et. al, 2018) An example of this is genetic background effects. Genetic background is defined as the alleles at all of the loci in the genome. (Chandler et. Al, 2013) Variation in this background among individuals can affect how a focal allele influences phenotype, if the focal allele interacts non-additively with one or more alleles in the background. Resolving non-additive, or epistatic, interactions among genes is essential to understanding the relationship between genotype and phenotype for any trait of interest. The purpose of this project is to interrogate the role of epistasis by evaluating genetic background effects and gene-gene interactions within the context of a well-defined complex process, the establishment of polarity in the C. elegans early embryo. Does this vital process harbor functional variation in natural populations? How does genetic background affect the functioning of genes within this process? How does this affect evolution? By studying genetic interactions within a complex process, I aim to refine our understanding of the role and evolution of epistasis in the determination of quantitative traits.

 

21.  Stephen Klusza, Christine Heitsch, Annalise Paaby

Utilizing mathematical prediction of RNA secondary structure to infer functional significance of natural genetic variation in C. elegans​

Far from the simplistic view of RNA as a ‘passive intermediate’ in gene expression between DNA and protein, we know that diverse classes of RNAs play active post-transcriptional roles. Like proteins, RNAs are dependent on correctly folding into proper structural forms for their functionality. For some classes of RNAs, such as tRNA, secondary structure is strictly maintained and its biological relevance is well understood. The role of secondary structure of messenger RNAs, however, is less well explored, likely due in part to serious difficulty in accurately predicting secondary structure from longer molecules using computational approaches. Research has shown that secondary structure at the start of mRNAs affects accessibility to the ribosome and overall translation rates. We hypothesize that mRNA structure may also play a dominant role in mediating the phenomena of splice variation, microRNA activity, and RNA interference.

A variety of methods have been developed to computationally predict of RNA secondary structure from sequence data. However, discrepancies arise between these approaches and also between computational and biochemical methods of inferring RNA structure. Furthermore, multiple lines of evidence now suggest that RNA structure is dynamic in-vivo, suggesting that the optimal RNA structures are only a small piece of the puzzle, and that a spectrum of alternative structures may also exist simultaneously in biological systems. We propose to query C. elegans genomes from hundreds of wild isolates to identify natural genetic variation that may induce variation in RNA structures, which in turn will shed light on the mechanisms that govern secondary structure itself.

 

22.  John LaGrone

Helical Buckling of Passive Fibers in Straining Flows

Subjecting the fibers to a straining flow results in the fibers stretching, compressing, and buckling. One of the difficulties of modeling a realistic straining flow is accounting for no slip boundary conditions on a fluid channel of varying cross-sectional area. We demonstrate a technique to simulate these flows using the method of regularized Stokeslets and we show examples of passive, elastic fibers buckling into helical shapes in the flow.

 

23.  Jingjing Lyu

A Comparison of the Trojan Y Chromosome Strategy to Harvesting Models for Eradication of Non-Native Species

The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of super-males that guarantee male offspring. We analyze and compare TYC to a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability, global boundedness of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting or hybrid strategy may work better than the TYC method at controlling an invasive species population.

 

24.  Chance Meers and Francesca Storici

RNA-templated DNA repair and modification

Organic life is continuously bombarded from various types of exogenous and endogenous DNA damaging agents throughout its life cycle. As such, cells have evolved specialized mechanisms to aid in the repair of DNA damage, typically with the aid of homologous DNA and specialized proteins. The Central Dogma of Molecular Biology generalizes the flow of information in a cell from DNA to RNA to proteins. However, we have found that RNA can directly facilitate the repair of a DNA double-stranded break in the form of a cDNA intermediate or by RNA directly in the absence of RNase H enzymes that degrade RNA/DNA hybrids. We show that overexpression of the endogenous retroelement of yeast (TY) stimulates the repair of DNA breaks by a cDNA intermediate. This process is strongly dependent on the recombination protein Rad52. However, we find that RNA can also guide DNA rearrangements in the absence of a DNA double-stranded break and this process is independent of Rad52. We found that the translesion DNA polymerase Zeta is required for RNA-mediated DNA modification in the absence of a break, an uncharacterized role of a translesion polymerase. This reveals an undiscovered role of RNA in the modification of DNA and outlines different mechanisms in which RNA affect genomic stability and ultimately play a role in genetic diseases like cancer.

 

25.  Devin Willmott, David Murrugarra, Qiang Ye.

Improving RNA secondary structure prediction via state inference with deep recurrent neural networks

The problem of determining which nucleotides of an RNA sequence are paired or unpaired in the secondary structure of an RNA, which we call RNA state inference, can be studied by different machine learning techniques. Successful state inference of RNA sequences can be used to generate auxiliary information for data-directed RNA secondary structure prediction. Typical tools for state inference, such as hidden Markov models, exhibit poor performance in RNA state inference, owing in part to their inability to recognize nonlocal dependencies. Bidirectional long short-term memory (LSTM) neural networks have emerged as a powerful tool that can model global nonlinear sequence dependencies and have achieved state-of-the-art performances on many different classification problems. This poster presents a practical approach to RNA secondary structure inference centered around a deep learning method for state inference. State predictions from a deep bidirectional LSTM are used to generate synthetic SHAPE data that can be incorporated into RNA secondary structure prediction via the Nearest Neighbor Thermodynamic Model (NNTM). This method, named predicted state directed NNTM, produces predicted secondary structures for a diverse test set of 16S ribosomal RNA that are, on average, 25 percentage points more accurate than undirected MFE structures. These improvements range from several percentage points for some sequences to nearly 50 percentage points for others. Accuracy is highly dependent on the success of our state inference method, and investigating the global features of our state predictions reveals that accuracy of both our state inference and structure inference methods are highly dependent on the similarity of the sequence to the dataset.

 

26.  Tung Nguyen

Tier structure of chemical reaction networks

Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. In this project, we introduce the notion of "tiers" - an analytic tool to study and characterize the behavior of reaction networks. First of all, we establish a connection between this analytic characterization and a well-known geometric characterization of reaction networks (strongly endotactic). Moreover, we apply this "tiers" argument to stochastic models of reaction networks: showing a class of reaction networks obeys a LDP, and another class is positive recurrent.

 

27.  Tamer Oraby and Andras Balogh

Multiplex Network Model of Parental Vaccine Acceptance and Disease Spread

People and households are connected to each other through different layers of social networks. In particular, two specific overlapping networks and their mutual influence are of interest. Those two networks are the biological (physical) networks, through which children make face-to-face contacts and pediatric disease transmission occur, and social networks through which information and opinions about the vaccine diffuse, shaping the decisions of parents. As the pediatric disease spreads on the biological network between households, it can also spread within them. Whereas information and opinion sharing transpire on the social network of parents to make them accept or reject to vaccinate their children. We established a stochastic model on two different types of networks: the Erd\H{o}s-R\'enyi (random) network model (ERN) and the Barab\'asi-Albert network model (BAN). The models also include birth process.  High performance computations were carried out in order to understand the mutual influence emerging on the multiplex network model. Among the findings is that the large the initial number of vaccine acceptors is, the more the information is shared on the social networks, and the smaller the disease epidemics are.

 

28.  Swati Patel

Eco-evolutionary feedbacks effects on genetic polymorphisms and linkage disequilibrium

Understanding the factors that allow for inter- and intra-specific diversity is a fundamental problem in evolution. By analyzing a novel multispecies, multilocus genetics model, we uncover how allele frequencies and linkage patterns within a species (intraspecific diversity) influence population densities in a community (interspecific diversity) and vice versa in previously unrecognized ways.

 

29.  Robert Ravier

Improved Biological Surface Registration via Forward Propagation

Accurate registration of biological surfaces has proven challenging when the group of surfaces in question exhibits significant variation in shape: examples of this can be found throughout evolutionary biology. We propose a robust method based on ideas from manifold learning for improving registration quality. We do so by using a simple metric condition to construct a Gibbs measure on a collection of registrations between two surfaces. We show via experimental evidence that our methodology improves correspondence quality between surfaces compared to other currently employed, less robust methods. As an application, we use our algorithms to create a novel method for computing homeomorphisms for collections of shapes after alignment.

 

30.  Michael A. Robert

Emergence of dengue and Zika virus in the United States: a model-based investigation

Dengue fever and Zika virus are two viral diseases vectored primarily by the mosquito species, Aedes aegypti.  Zika virus can also be transmitted sexually, although the frequency of sexual transmission is relatively unknown. While dengue has been endemic throughout tropical and subtropical regions of the world for over half a century, Zika recently emerged in countries worldwide following a pandemic that started in 2015. Transmission of both viruses depends upon interactions among humans, mosquitoes, and the viruses, and these interactions can be influenced by environmental variables such as temperature. I present a deterministic mathematical model developed to explore the relationships between temperature and mosquito survival and temperature and dengue virus incubation period and the impact of these relationships on the potential for emergence of the viruses in selected U.S. cities and San Juan, Puerto Rico.  I also discuss why understanding the magnitude of sexual transmission of Zika virus could be important by illustrating potential scenarios where sexual transmission of Zika virus alters epidemic dynamics. Finally, I discuss the sensitivity of the results to relatively unknown parameters.

 

31.  Perrin E. Schiebel

Exploring the connection between environment, sensing, and locomotion strategy in terrestrial snakes.

Limbless organisms like snakes use heterogeneity in the surrounding environment to propel themselves. Little is known about how these animals determine and subsequently coordinate appropriate shapes given the properties of the terrain. We studied the desert-dwelling shovel-nosed snake, Chionactis occipitalis, in the laboratory traversing a simple model for the desert habitat--a spatially uniform substrate and a single row of posts oriented perpendicular to the initial direction of travel. Snakes used lateral undulation, the typical undulatory gait in which horizontal, "s" shaped waves are passed from head to tail, to travel across the substrate, through the array, and continue travel. Combining many independently collected trajectories revealed the existence of preferred directions--the animals were scattered by the array in a manner reminiscent of the diffraction of subatomic particles. A geometric model reproduced the emergence of preferred trajectories, supporting our hypothesis that the pattern was the result of open-loop control supplemented by passive dynamics. Future work includes comparative study of different snake species and the nematode C. elegans.

 

32.  Vardges Tserunyan

Patronin and myosin localization dynamics during the formation of the ventral furrow in D. melanogaster embryos

Cells change shape by generating force that must be transmitted between cells during morphogenesis to affect tissue shape. For example, in D. melanogaster, the apical constriction of mesoderm cells leads to their invagination during gastrulation. Here, we discovered the dynamics of patronin localization during this process and its correlation with myosin. First, we found out that patronin co-localizes with medioapical myosin in constricting cells, while being enriched at intercellular junctions in non constricting cells. Second, we found out that stabilizing microtubules does not affect the pulsatile behavior of myosin and subsequent apical constriction. Finally, we found out that the detected concentrations of medioapical patronin and myosin closely correlate.

 

33.  Lei Wang

A molecular tool to increase protein content and broad disease resistance in crops        

Crop plants must integrate signals from the environment and prioritize responses to stresses that may occur individually or simultaneously throughout the growing season. Stress responses can adversely affect plant growth and quality traits such as protein. Enhancing the nutritional quality and disease resistance of crop species without sacrificing productivity is a key issue for developing varieties that are valuable to farmers and for simultaneously improving food security and sustainability. Higher protein is a desirable agronomic trait, and is particularly important in staple crops that provide food for large populations. Expression of the Arabidopsis thaliana species-specific AtQQS (Qua-Quine Starch) orphan gene or its interactor, NF-YC4 (Nuclear Factor Y, subunit C4), has been shown to increase levels of leaf/seed protein without affecting the growth and yield of agronomicspecies1-8. We demonstrate that overexpression of genes related to QQS network in Arabidopsis and soybean enhances resistance/reduces susceptibility to viruses, bacteria, fungus, soybean cyst nematodes, and aphids9. QQS is among the approximately 5-20% of gene models in eukaryotic genomes that encode proteins that lack sequence homology with any known motifs. QQS primary sequence is recognizable in Arabidopsis thaliana ecotypes, but not identifiable in any other sequenced species, not even in Arabidopsis lyrata.

 

34.  Hays Whitlatch

Genome Reversals and Graph Pressing Sequences

In the 1930's, two biologists, Dobzhansky and Sturtevant, introduced the idea that the degree of disorder between the genes in two genomes is an indicator of the evolutionary distance between two organisms. This has inspired extensive work in the fields of computational biology, bioinformatics and phylogenetics.  In particular, researchers have pursued the question of how a common ancestral genome may have been transformed by evolutionary events into distinct, yet homologous, genomes. In mathematics, we often represent genomes as signed permutations, and evolutionary events are encoded as operations on signed permutations. Hannenhalli and Pevzner famously showed that sorting such sequences can be done in polynomial time and that they are essentially equivalent to a certain sequences of operations - ``vertex pressing''- on bicolored graphs. In this poster we demonstrate how to construct these bicolored graphs and give some results that can be obtain by applying linear algebra to these graphs.

 

35.  Bin Xu

Modeling the Dynamics of Cdc42 Oscillation in Fission Yeast

Regulation of polarized cell growth is essential for many cellular processes, including spatial coordination of cell morphology changes during growth and division. We present a mathematical model of the core mechanism responsible for the regulation of polarized growth dynamics by the small GTPase Cdc42. The model is based on the competition of growth zones of Cdc42 localized at the cell tips for a common substrate that diffuses in the cytosol. We analyze the bifurcations in this model as the cell length increases. We find that a stable oscillation and a stable steady state can coexist, which is consistent with the experimental finding that only 50% of bipolar cells oscillate. We then use the Gillespie algorithm to explore the effect of intrinsic fluctuations. Numerical solutions suggest noisy limit cycles exist in the parameter regime in which the deterministic system converges to a stable limit cycle, and quasi-cycles exist in the parameter regime where the deterministic model has a damped oscillation.

 

36.  Penghao Xu, Alli Gombolay, Taehwan Yang, Sathya Balachander, Gary Newnam, Waleed​ Mohammed El Sayed, Fred Vannberg and Francesca Storici

Ribonucleotides incorporation characteristics around yeast autonomously replicating regions

As a nucleic acids, DNA is made by deoxyribonucleotides and constitutes the genetic material of cells. In contrast, ribonucleotides are basic units of RNA, which acts in coding, decoding and regulation of gene expression. Previous studies found that plenty of ribonucleotides are incorporated in DNA, driven by misincorporation by DNA polymerases in DNA replication process, causing DNA structural change and genome instability. Byexploiting the ribose-seq technique to map positions of ribonucleotides in genomic DNA, we can identify interesting hotspot sites of incorporation in any genomic DNA. In budding yeast, an autonomously replicating sequence (ARS) contains the origin of DNA replication, where replication process starts. Its flanks are generated from leading and lagging strands in DNA replication process by different types of DNA polymerase. With next generation sequencing data obtained from many ribose-seq libraries of nuclear DNA of yeast Saccharomyces cerevisiae cells, we studied ribonucleotides incorporated around ARSs, and analyzed whether there were different frequency and/or characteristics for ribonucleotide incorporation on the leading and lagging strands. Results show that ribonucleotides are more likely to be incorporated in the leading compared to the lagging strand, and with the extending of flank length, the ratio of leading versus lagging decreases. This shows that the ARS region’s effect of ribonucleotide incorporation is related to distance. Importantly, the composition of ribonucleotides, and their deoxyribonucleotide neighbors are also significantly distinct between leading and lagging strands, which means different DNA polymerases have their own preferences to incorporate ribonucleotides.

 

37.  Taehwan Yang, Alli Gombolay, Penghao Xu, Fredrik O. Vannberg, Baek Kim and Francesca Storici

Ribose-seq: An innovative technique to capture and map ribonucleotides incorporated in genomic DNA

Several studies have disclosed that genomic DNA is mostly contaminated by misincorporated ribonucleotides (rNMPs) which are the most abundant non-canonical nucleotides found in cellular DNA. It is known that rNMPs embedded in DNA modify DNA structure and stability. rNMPs are incorporated by DNA polymerases during replication, incomplete removal of Okazaki fragments during lagging strand synthesis, or hydroxyl radicals during oxidative stress. Type 2 ribonuclease H (RNase H2) initiates ribonucleotide excision repair (RER) in cells. Impaired RNase H2 causes massive accumulation of rNMPs in the genomic DNA. Many questions remain unanswered about rNMPs in DNA, such what is the distribution of rNMPs, what are functions of rNMPs, and hot spots of rNMPs in DNA. Lately, our lab invented a novel method, ribose-seq that can capture rNMPs incorporated into DNA by using alkaline cleavages of DNA and Arabidopsis thaliana tRNA ligase (AtRNL). Every ribose-seq library contains numerous rNMPs and is sequenced by a high-throughput sequencing system, which reveals the distribution of rNMPs in nuclear and mitochondrial DNA. The initial ribose-seq method was utilized to explore genomic DNA of budding yeast defective in RER. Now, we markedly improved the ribose-seq technique for mapping rNMPs in large genomes like that of humans, and also derived from RER proficient cells. As a result, the latest version of ribose-seq enhances rNMP capture efficiency by more than a factor of 1,000. We have built ribose-seq libraries from human genomic DNA derived from CD4+ T cells, macrophages, and HEK293T cells to reveal the rNMP incorporation patterns and hotspots. Furthermore, we designed a new scheme to quantify rNMPs found in every ribose-seq library. With these newly developed tools, we aim to study the phenomenon of rNMP incorporation in many cell types with a focus to reveal the spectrum of misincorporated rNMPs in human genomic DNA from cell lines and different sources of healthy and diseased primary cells to discover hotspots, specific signatures and biomarkers.

 

38.  Iris Yoon

Cellular cosheaves for distributed computation of persistent homology.

We present a distributed computation mechanism of persistent homology using cellular cosheaves. Our construction is an extension of the generalized Mayer-Vietoris principle to filtered spaces obtained via a sequence of spectral sequences. We discuss a general framework in which the distribution scheme can be adapted according to a user-specific property of interest. The resulting persistent homology reflects properties of the topological features, allowing the user to perform refined data analysis. Finally, we apply our construction to perform a multi-scale analysis to detect features of varying sizes that are overlooked by standard persistent homology. This is joint work with Robert Ghrist.

 

39.  Mondal Hasan Zahid and Christopher M. Kribs

Decoys and dilution: the impact of incompetent hosts on prevalence of Chagas disease

Biodiversity is commonly believed to reduce risk of vector-borne zoonoses. This study focuses on the effect of biodiversity, specifically on the effect of the decoy process (additional hosts distracting vectors from their focal host), on reducing infections of vector-borne diseases in humans. Here, we consider the specific case of Chagas disease and try to observe the impact of the proximity of chickens, which are incompetent hosts for the parasite but serve as a preferred food source for vectors. We consider three cases as the distance between the two host populations varies: short (when farmers bring chickens inside the home to protect them from predators), intermediate (close enough for vectors with one host to detect the presence of the other host type), and far (separate enclosed buildings such as a home and hen-house). Our analysis shows that the presence of chickens reduces parasite prevalence in humans only at an intermediate distance and under the condition that the vector birth rate associated with chickens falls below a threshold value, which is relative to the vector birth rate associated with humans and inversely proportional to the infection rate among humans.

40.  Keren Zhang

NeuroNex: Live Imaging of C. Elegans Connectome 

A connectome is the complete wiring diagram of a brain. The study of connectome, along with how such an enormously complex structure is assembled, maintained, and subject to change, will not only give us insight in brain function, but also allow us to study neural diseases. However, studying the connectome of human being is almost impossible in terms of scale. Therefore, we resort to simpler model organism C.elegans. C.elegans with only 302 neurons and 3526 connections (“edges”). The original wiring diagram of C.elegans  constructed using only 5 animals, thus lacking individual variability and accuracy in telling the strength of each synaptic pair. Moreover, previous methods are extremely labor -intensive and time-consuming. This NeuroNex project, combines genetic, microfluidics, image processing and mathematical modelling tool to automate the process of constructing the connectome. We aim to reconstruct a connectome atlas with pair-wise synapses for C.elegans with individual variance included. We want to bring up mathematical and statistical model to study other effects, such as genetic mutation, environment and development on connectome. We envision that our tools and pipeline will be distributed to the community. 

A NSF-Simons MathBioSys Research Center