Minisymposia: MS04

Tuesday, July 18 at 04:00pm

Minisymposia: MS04

Integrating Mathematics Across the Cardiovascular System: A Mini-Symposium on Multilevel Modelling of Cardiovascular Biology

Organized by: Jessica Crawshaw, Vijay Rajagopal, Michael Watson, Mitchel Colebank, Seth Weinberg
Note: this minisymposia has multiple sessions. The other session is MS03-CARD-1.

  • Keith Chambers University of Oxford (Wolfson Centre for Mathematical Biology, Mathematical Institute)
    "Resolution vs chronic inflammation: A lipid/phenotype dual-structured model for early atherosclerosis"
  • Atherosclerosis is a chronic inflammatory condition of the artery wall. Despite being the underlying cause of approximately half the deaths in westernized society, the disease remains incompletely understood due to its biological complexity. A key component of the disease is the role played by monocyte-derived macrophages, which are the primary type of immune cell recruited to the lesion in response to artery wall lipid accumulation. Macrophages accumulate lipid by clearing their local environment of low-density lipoprotein particles and cellular debris, and can offload lipid to HDL particles to ferry out of the lesion. Further, macrophages can either promote further inflammation or disease resolution by contributing to signaling pathways according to their phenotype. Macrophage phenotype is strongly influenced by microenvironmental stimuli and is commonly represented as a spectrum from pro-inflammatory M1-like cells to anti-inflammatory M2-like cells in the biological literature. The balance of M1-like and M2-like cells determines the trajectory of atherosclerosis. In this talk, I present a differential equation model of early atherosclerosis with a macrophage population that is structured by both lipid load and phenotype. We consider firstly a discrete formulation in which lipid and phenotype are represented as indices taken from a bounded set of integers. We show that this model admits a closed subsystem by summing the equations of the full model. Numerical solutions indicate that if endothelial damage is ongoing, the model artery wall may exhibit chronic inflammation or oscillatory solutions that are induced by the partial resolution of inflammation. If endothelial damage is an initial transient, the model predicts a transition from a predominantly M1-like macrophage population at early times to a resolving M2-like population at later times; this behaviour reflects an acute inflammatory response.
  • Alys Clark University of Auckland, New Zealand (Auckland Bioengineering Institute)
    "The fetal circulation and its adaption to pathological placental development"
  • The placenta provides a critical exchange function between the mother and developing fetus. To effectively exchange nutrients and gases it develops a complex branching vasculature across pregnancy. Dysfunction in its exchange capacity impacts fetal growth trajectory, leading to a condition known as fetal growth restriction (FGR). FGR results in increased long term cardiovascular risk for the baby, compared to appropriately grown fetuses. FGR placentae exhibit impaired vascular function, increasing the resistance in this major vascular bed within the fetal circulation. In turn, this dysfunction is thought to impact cardiac development, with FGR hearts exhibiting structural changes such as hypertrophy. However, the biomechanical interactions between the heart and the placenta in pregnancy are not well-established. Computational modelling of the placenta and heart, as well as their interaction within the fetal circulation provides opportunities to better understand the contribution of pathological placental development to cardiac dysfunction in FGR pregnancies. Here we present an image and model based approach to understanding these interactions. First, we present detailed anatomical assessment of placental vascular structure, alongside model predictions of the impact of placental vascular network architecture on its haemodynamic function. We then assess the impact of placental vascular architecture embedded in a zero-dimensional fetal circulation model, that predicts the relationship between placental branching structure and clinically measurable ultrasound metrics. Finally, we show how we can extend this model and imaged based framework to animal models of placental dysfunction, where we have demonstrated a significant decrease in right ventricular cavity volume, alongside a reduction in placental vascular density.
  • Joyce Lin Cal Poly State University (Mathematics)
    "Conduction reserve theory in cardiac tissue with reduced gap junction coupling"
  • While many cardiac pathologies have been correlated with reduced gap junctional coupling, the relationship between phenotype and functional expression of the connexin gap junctional family of proteins is unclear. These proteins are an important modulator of cardiac conduction velocity, yet a 50% reduction of gap junctional protein has been shown to have little impact on myocardial conduction. We explore the theory of conduction reserve, which can operate through two mechanisms: The first mechanism, ephaptic coupling, maintains conduction with low gap junctional coupling by increasing the electrical fields generated in the sodium channel-rich clefts between neighboring myocytes. The other mechanism allows low gap junctional coupling to increase intracellular charge accumulation within myocytes, resulting in a faster transmembrane potential rate of change during depolarization that maintains macroscopic conduction. To provide insight into the role these two mechanisms play during gap junctional remodeling, we focus on the relationship between ephaptic coupling and charge accumulation using simulations as well as perfused mouse heart experiments. Mathematical modeling of conduction in a cardiac tissue as well as corresponding experimental heart studies will be presented. With insight from simulations, the relative contributions of ephaptic coupling and charge accumulation on action potential parameters and conduction velocities will be shown. Both simulation and experimental results support a common conclusion that low gap junctional coupling decreases and narrowing perinexal width increases the rate of the action potential upstroke when sodium channels are densely expressed at the ends of myocytes, indicating that conduction reserve may be more dependent on ephaptic coupling than charge accumulation under pathological conditions.
  • Nicolae Moise Ohio State University (Biomedical Engineering)
    "Emergent Pacemaking and Tissue Heterogeneity in a Calcium Feedback Regulatory Model of the Sinoatrial Node"
  • The sinoatrial node (SAN) is the primary pacemaker of the heart. SAN activity emerges at an early point in life, and maintains a steady rhythm for the lifetime of the organism. The ion channel composition and currents of the cells can be influenced by a variety of factors. Therefore, the emergent activity and long-term stability imply some form of dynamical feedback control of the SAN cell activity. Here, we adapt a recent neuronal model to the SAN rabbit cell. The model describes a minimal regulatory mechanism of neuronal ion channel conductance based on a feedback loop defined by an intracellular [Ca2+] level as its target. Briefly, the cell upregulates or downregulates its channel mRNA and membrane expression levels based on the difference between the intercellular Ca2+ level in the cell and a set intercellular Ca2+ target. Based on this feedback model, spontaneous electrical activity emerges in the SAN cell from a quiescent state with low initial conductances. As conductances increase, the intracellular [Ca2+] level reaches the target, and ion channel conductance reach a steady state consistent with sustained spontaneous activity. In a 2D tissue, variability in [Ca2+] target leads to heterogeneous ion channel expression and Ca2+ transients throughout the tissue. Further, dominant focal clusters appear, which interact with one another leading to a heterogeneous tissue cycle length, implying that variability in heart rate is an emergent property of the feedback model. Finally, the 2D tissue is robust to the silencing of leading cells or ion channel knock-outs. Thus, the calcium feedback regulatory model explains a number of experimental data using a minimal description of intracellular calcium and ion channel regulatory networks.

Data-driven, modeling, and topological techniques in cell and developmental biology

Organized by: Alexandria Volkening, Andreas Buttenschoen, Veronica Ciocanel
Note: this minisymposia has multiple sessions. The other session is MS03-CDEV-1.

  • Joel Dokmegang Northwestern University (Molecular Biosciences)
    "Spectral Decomposition of Morphogenesis"
  • Describing morphogenesis generally consists in aggregating the multiple high resolution spatiotemporal processes involved into repeatable low resolution morphological stories consistent across sample individuals of the same species or group. In order to achieve this goal, biologists have often had to submit movies issued from live imaging of developing embryos either to the eye test or to basic statistical analysis. Although successful, these methods however present noticeable drawbacks, as they can be time consuming, hence unfit for scale, and often lack standardisation. In this work, we leverage the power of continuum mechanics and spectral decomposition to propose a standardised framework for automatic detection and timing of morphological processes. First, we quantify shape changes in gastrulating ascidian embryos by evaluating strain-rate tensor fields at their surface. We then apply to this data a generalised Fourier transform, resulting in canonical spatio-temporal atlases that tell the story of morphogenesis in the studied embryos.
  • John Nardini The College of New Jersey (Mathematics & Statistics)
    "Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images"
  • Microvascular disease complications can alter vascular network morphology and disrupt tissue functioning. Such diseases are typically assessed by visual inspection of retinal images, but this can be challenging when diseases exhibit silent symptoms or patients cannot attend in-person meetings. We propose that statistical and topological summaries of segmented retinal vascular images provide promising avenues to automate and aid microvascular disease status and examine the performance of machine learning algorithms in detecting microvascular disease from these summaries. We apply our methods to three datasets and find that, among the 13 descriptor vectors we consider, either a statistical Box-counting descriptor vector or a topological Flooding descriptor vector achieves the highest accuracy levels. When we apply our methods to a fourth dataset consisting of data from multiple data sources, the Box-counting vector maintains its strong performance while the topological Flooding vector which is sensitive to differences in the annotation styles between the different datasets. Our work represents a first step to establishing which computational methods are most suitable for identifying microvascular disease as well as some of their current limitations. In the longer term, these methods could be incorporated into automated disease assessment tools.
  • Anna Nelson Duke University (Department of Mathematics)
    "Mathematical modeling of microtubule assembly and polarity in dendrites"
  • The microtubule cytoskeleton is responsible for sustained, long-range transport of cellular cargo inside neurons. However, microtubules must also be dynamic and rearrange their orientation, or polarity, in response to injuries. While mechanisms that control the minus-end out microtubule orientation in Drosophila dendrites have been identified experimentally, it is unknown how these mechanisms maintain both dynamic rearrangement and sustained, long-term function of the cell. To better understand these mechanisms, we introduce a spatially-explicit mathematical model of dendritic microtubule growth dynamics using parameters informed by experimental data. We explore several hypotheses of microtubule growth using both a stochastic model and a continuum model, and use fluorescence microscopy experiments to validate mechanisms such as limited tubulin availability and catastrophe events that depend on microtubule length. By incorporating biological experiments, our modeling framework can uncover the impact of various mechanisms on the collective dynamics and polarity of microtubules in Drosophila dendrites.
  • Shayne M. Plourde the Ohio State University (Molecular, Cellular, and Developmental Biology Program)
    "Asymmetric Centrosome Maturation in the Early C. elegans Embryo: Insights from Multi-scale Microscopy and Modeling"
  • Centrosomes are nucleus-associated organelles made up of a pair of tubular centrioles surrounded by a cloud of pericentriolar material. Centrosomes serve as the nucleation site for microtubule arrays that interact with motor proteins at the periphery of the cell which act together to position the nucleus prior to division. Proper positioning is especially important in asymmetric cell division, where daughter cells inherit unequal amounts of specific factors. How the two centriole pairs, and their centrosomes, are positioned is critically important to stem cell development and perturbations in this process can be observed in cancer metastasis. In the C. elegans first cell cycle, proper positioning of the centrosomes is required for the asymmetric division used to determine the germline lineage of cells. Previous work has shown an asymmetry in the microtubule arrays nucleated by the two centrosomes that set up these divisions. However, the functional origin of this asymmetry is unknown. Using in vivo data of the recruitment and recovery of GFP tagged AIR-1, a protein that localizes to centrosomes in the early C. elegans embryo, we parameterized a mathematical model of centrosome maturation. Analysis of a large set of parameters that fit our model to the in vivo data reveal that there are potential differences in the dynamics between the two centrosomes. Further, we tracked the inheritance of the oldest centrioles into the 4 cell stage and observed a potential age related inheritance pattern. The multi-scale microscopy and mathematical modeling together support our hypothesis that there is a previously uncharacterized asymmetry inside of the C. elegans centrosome that could be connected to cell fate decisions.

Stochastic effects in cell biology across scales

Organized by: James MacLaurin, Victor Matveev

  • Martin Falcke Max Delbrück Center for Molecular Medicine (Mathematical Cell Physiology)
    "Modeling IP3-induced Ca2+ signaling based on its interspike interval statistics"
  • Inositol 1,4,5-trisphosphate (IP3) induced Ca2+ signaling is used by almost all eukaryotic cells. Recent research demonstrated its randomness on all structural levels and large cell variability of the average interspike interval (ISI). Nonetheless, we compile eight general properties of Ca2+ spiking common to all cell types and pathways investigated hitherto. Stimulation response relation and moment relation of ISI exhibit specific robustness properties. We suggest an analytic theory of Ca2+ spiking calculating the moments of the ISI distribution. It captures all general properties, their robustness properties, cell variability and pathway specific behavior. We explain cell variability by variability of channel cluster coupling by Ca2+-induced Ca2+ release and the number of clusters. We predict the relation between puff probability and agonist concentration, and [IP3] and agonist concentration. Pathway and cell type specific behaviour is explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the general properties.
  • Greg Conradi Smith William & Mary (Applied Science / Neuroscience / CAMS Biomath)
    "Allosteric coupling and cycle kinetics of G protein-coupled receptor dimers"
  • Quantitative pharmacologists construct Markov chain models to give insight into the relationship between ligand concentration and the fraction of cell surface receptors in each of several molecular conformations. Pharmacologists use these stochastic models to understand the action of natural ligands and drugs on receptor-mediated cell responses. When receptors function as two or more similar protein subunits working in concert (i.e., homodimers or oligomers), receptor models must (i) account for symmetry, (ii) satisfy thermodynamic constraints, and (iii) properly account for subunit interactions (allostery) mediated by conformational coupling. The modeling framework that satisfies these three requirements will be explicated in the context of models of G protein-coupled receptors (GPCRs), such as metabotropic glutamate receptors, that function as multi-molecule signaling complexes. For equilibrium models of receptor dimers, this approach facilitates the inference of a parsimonious subset of allosteric interactions leading to conformational coupling and dependence of receptor subunits. I will also discuss progress on extending this framework to the analysis of non-equilibrium steady-state cycle kinetics of GPCRs (e.g., nucleotide exchange).
  • Victor Matveev New Jersey Institute of Technology (Department of Mathematical Sciences)
    "Accuracy of deterministic vs. stochastic modeling of Ca2+-triggered vesicle fusion latency"
  • High degree of variability is a characteristic feature of synaptic neurotransmitter release, which is important to consider in our understanding and modeling of this fundamental physiological process. Although stochastic Ca2+ channel gating is one of the primary source of this variability, it can be implemented in a computationally inexpensive way in combination with deterministic simulation of the downstream Ca2+ diffusion and binding. Another fundamental reason for the high variability of synaptic response is that only a small number of Ca2+ ions enter the synaptic terminal through a single channel during an action potential. This fact entails large fluctuations due to Ca2+ diffusion and its binding to Ca2+ buffers and vesicle release sensors, leading to a widely-held view that solving continuous deterministic reaction-diffusion equations does not provide high accuracy when modeling Ca2+-dependent cell processes. However, several comparative studies show a surprising close agreement between deterministic and trial-averaged stochastic simulations of Ca2+ dynamics, as long as Ca2+ channel gating is not Ca2+-dependent. This result deserves careful investigation. In this talk I will present further analysis and comparison of stochastic and mass-action modeling of vesicle release, showing that the discrepancy between deterministic and stochastic approaches remains small even when only as few as 40-50 ions enter per single channel-vesicle complex. The reason for the close agreement between stochastic and mass-action simulations is that the discrepancy between the two approaches is determined by the size of the correlation between the local Ca2+ concentration and the state of the vesicle release sensor, rather than fluctuation amplitude. Whereas diffusion and buffering increases fluctuation size, the same processes appear to de-correlate fluctuations in Ca2+ concentration from fluctuations in Ca2+ sensor binding state. Finally, contrary to naïve intuition, the mass action / mean-field reaction-diffusion description allows an accurate estimate of the entire probability distribution of vesicle release latency (first-passage time), rather than providing information about trial-averaged quantities only. These results may help in the choice of appropriate and efficient tools for the modeling of this and other fundamental biochemical cell processes.
  • Linh Huynh University of Utah (Mathematics)
    "Stochastic Cancer Cell Dynamics under Environmental Stress"
  • One reason cancer remains very difficult to eradicate is its remarkable adaptability to the environment. In this talk, I will discuss how stochasticity and collective behavior help cancer cells survive and adapt under environmental stress in two different contexts: (1) when ecological interactions between cells in a heterogeneous population facilitate cancer’s stochastic escape from drug treatments and (2) when inflammation in the tumor microenvironment facilitates stochastic tumor growth.

Current trends in phylogenetics

Organized by: Kristina Wicke, Laura Kubatko
Note: this minisymposia has multiple sessions. The other session is MS03-ECOP-1.

  • Nathan Kolbow University of Wisconsin-Madison (Department of Statistics)
    "Sorting gene trees by their path within a species network"
  • Reticulate evolution has been identified in the phylogenies of many species, and several methods have leveraged gene tree topologies to infer these species networks. Such methods are powerful for inferring reticulate phylogenies at the species level but do not provide any insights for individual genes. Here, we present a statistical method for accurately comparing subsets of gene trees based on the unknown displayed species tree they belong to within a species network. The result is an algorithm that accurately groups gene trees based on the path they follow in the species network. The displayed species tree corresponding to each group can then be inferred, deducing where individual genes did or did not follow horizontal gene transfer events in their evolutionary history.
  • Brandon Legried Georgia Institute of Technology (Mathematics)
    "Inferring phylogenetic birth-death models from extant lineages through time"
  • Birth-death processes have been used to study population growth, with broad-ranging biological applications such as identifying speciation and extinction rates, calibrating divergence times, and studying the dynamics of pathogens in infection trees. Recent theoretical work on phylogenetic birth-death models offer differing viewpoints on whether they can be estimated from lineages through time. Recently, Louca and Pennell (2020) demonstrated that time-varying birth and death rates are not identifiable from lineage-through-time data. This was a grave result, in view of thousands of published biological and computational studies that use this data. In this talk, I explain how identifiability can be restored, while re-focusing the discussion to what actually makes inference computationally challenging. This is based on joint work with Jonathan Terhorst (University of Michigan, Ann Arbor).
  • Colby Long The College of Wooster (Mathematical and Computational Sciences)
    "Phylogenomic Models from Tree Symmetries"
  • Models of genomic sequence evolution often include a coalescent process since different sites may evolve on different gene trees due to incomplete lineage sorting. Chifman and Kubatko initiated the study of such models, leading to the development of the SVDquartets method of species tree inference. A key observation was that symmetries in an ultrametric species tree led to symmetries in the joint distribution of bases at the taxa. In this talk, we will explore the implications of such symmetries more fully, defining new models incorporating only these symmetries, regardless of the mechanisms that might have produced them. We will also discuss phylogenetic invariants for these models and how the invariants can be used to establish identifiability of the species tree topologies.
  • Julia Chifman American University (Mathematics and Statistics)
    "Cancer evolution: mathematical models and inference methods."
  • The advent of single-cell sequencing provides the ability to model clonal evolution of tumors within individual patients. Inference of such within-patient tumor phylogenies has the potential to advance our understanding of the variation in the process of tumor progression. The process of tumor evolution has been reviewed extensively by many authors, with strong support for the view of a tumor as an ecosystem of evolving subpopulations that compete for space and resources in their microenvironment. Phylogenetic methods have been applied in numerous ways to model tumor evolution, for both bulk tumor samples and for single-cell data. For single-cell data, the data type considered in this presentation, these methods range from the use of inferred pairwise mutation orders to reconstruct the phylogeny to specification of a mutation model and possibly also an error model, from which either a likelihood or a Bayesian inferential framework can be adopted. This presentation investigates current models and methods and compares them to our method using both simulated and empirical data. We also compare the performance of methods using data simulated over a random phylogeny versus data simulated over a phylogeny constrained by the evolving tumor.

Modeling and Analysis of Evolutionary Dynamics Across Scales and Areas of Application

Organized by: Daniel Cooney, Olivia Chu
Note: this minisymposia has multiple sessions. The other session is MS03-ECOP-2.

  • Abdel H. Halloway University of Illinois at Urbana-Champaign (Plant Biology)
    "Maintenance of mutualistic variation within and between species"
  • Mutualistic interactions present shared and unique properties at different scales, such as ecological and evolutionary collapse and nestedness. One notable aspect is the presence of variation in mutualistic interactions at various ecological scales. Here, I present theoretical analysis on the maintenance of mutualism variation within and between species. Within species, I analyze how competition between plants in a mutualistic plant-microbe relationship of resource trade may promote or hinder variation in the strength of mutualistic interaction. Between species, I examine how coevolutionary niche dynamics affects variation in mutualistic association and the resulting community structure. Within a species, competition may hinder or hurt variation depending upon its mechanism. Competition may lead to more coexistence between mutualists and non-mutualists, specifically at the expense of mutualism fixation, when plants compete over some microbially obtained nutrient. However, if competition reduces the carbon used for trade, then plant abundance, and therefore competition, weakens mutualism. Between species, mutualism acts as a hinderance to within-guild diversification. Species seek to affiliate with a single mutualist leading to collapse of interspecific variation, sometimes to a single mutualistic species pair. Despite this, drift can prevent the collapse and maintain community structure. Species showed heterogeneity in niche breadth with a few generalized species and several specialized species. This heterogeneity in degree distribution also resulted in properties like nestedness. Going forward, combining within and between species processes will allow us to explore the full potential variation in mutualistic interactions.
  • Judith Miller Georgetown University (Mathematics and Statistics)
    "Modeling neutrality with climate data: the spread of the cabbage white butterfly Pieris rapae in North America"
  • A large body of theory has identified numerous factors that can play major roles in determining the speed and ultimate extent of range expansions. Among these are dispersal patterns, traits affecting fecundity, interspecific competition and adaptation or maladaptation to local environments. Yet few empirical studies establish the reasons for the range dynamics of particular species. We develop a detailed deterministic model of the initial spread of the cabbage white butterfly Pieris rapae in North America. We parametrize the model using climate and geographic data as well as physiological and life history parameter values from numerous studies of the species. The model does not allow for adaptive evolution. We find that the model’s output is a reasonable approximation of the recorded spread of P. rapae from east to west and from points of introduction southward. By contrast, no plausible parametrization appears to replicate the observed northward spread of P. rapae into Canada. These suggestive results point the way to a full understanding of our study species and a methodology that can be applied to other species and populations.
  • Artem Novozhilov North Dakota State University (Department of Mathematics)
    "On a hypercycle equation with infinitely many members"
  • We formulate a hypercycle equation with infinitely many types of macromolecules. This equations is studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. We present sufficient conditions for the existence, uniqueness, and non-negativity of solutions. Analytical evidence is provided for the existence of non-constant steady states. Finally, numerical simulations strongly indicate the existence of a stable nonlinear wave in the form of the wave train.
  • Max O. Souza Universidade Federal Fluminense (Instituto de Matemática e Estatística)
    "Continuous approximations of fixation probabilities for large populations on star graphs"
  • We consider a generalized version of the birth-death (BD) and death-birth (DB) processes introduced in the literature, in which two constant fitnesses, one for birth and the other for death, describe the selection mechanism of the population. Rather than constant fitnesses, in this work we consider more general frequency-dependent fitness functions (allowing any smooth functions) under the weak-selection regime. For a large population structured as a star graph, we provide approximations for the fixation probability which are solutions of certain ODEs (or systems of ODEs). For the DB case, we prove that our approximation has an error of order 1/N, where N is the size of the population. This class includes many examples of update rules used in the literature --- including the so-called BD-* and DB-* (where * can be either B or D) processes.

Mathematical-biology education in a post-COVID world

Organized by: Stacey Smith?
Note: this minisymposia has multiple sessions. The other session is MS03-EDUC-1.

  • Reginald McGee College of the Holy Cross (Mathematics and Computer Science)
    "Teaching reflections after five years on the tenure track"
  • Here's a little story all about how over the last five years my teaching got flipped-turned upside down. This talk is a sequel to my 2019 talk on reflections from my first year teaching full-time at a private liberal arts college. We will discuss some ongoing explorations into shifting course values towards intangibles like creativity and numeracy; innovations and desperations catalyzed by a once-a-century pandemic; attempts at injecting computation, biology, and other applications into a traditional math curriculum; and strategies for those who might be considering or are entering teaching at a liberal arts environment.
  • Suzanne Lenhart University of Tennessee, Knoxville (Mathematics)
    "Teaching Discrete Time Modeling in Mathematics for the Life Sciences course"
  • In our Mathematics for the Life Sciences course, we use the Rule of Five for different learning styles to meet needs of diverse students: Symbolically, Graphically, Numerically, Verbally, Data-driven. The concepts and skills in our course help students to appreciate the components of the modeling process, including assessing hypotheses based on data, formulating a mathematical description of a system based on assumptions, and by analyzing the resulting model. We begin our course with discrete mathematics involving analyzing data and discrete time modeling, instead of starting with calculus. We have incorporated MATLAB to introduce basic computer coding and the concepts of algorithms that are applied throughout computational methods in science. Some adaptations have been made to adjust to students in post-covid times. We have also developed an assessment tool to begin to evaluate the impact of biological examples on mathematics comprehension in courses for life sciences majors.
  • Elissa Schwartz Washington State University (Math/Biol Sci)
    "Creating a watershed for mathematical biology education: Recent outreach in Nepal"
  • The infrastructure for advanced mathematics and science degrees in Nepal is in its infancy and connections with research groups outside the country are minimal. To address disparities in educational opportunities, recent efforts have been made to develop programs on science, mathematics, and specifically, mathematical biology in Kathmandu. These include short courses, summer schools, workshops, and the formation of working groups that focus on research in mathematical epidemiology, infectious disease dynamics, and immunological modeling. Currently, these outreach efforts are establishing international collaborations as well as creating paths for professional development in mathematical biology in Nepal. Future goals aim to extend these efforts to set up mentorships and support higher education of women and other historically underserved populations.
  • Kathleen Hoffman UMBC (Department of Mathematics and Statistics)
    "Integrating Quantitative Skills into Biology Courses"
  • As a response to calls for changes in Biology education to include more quantitative reasoning skills, teams of instructors from University of Maryland, Baltimore County (UMBC), Howard Community College (HCC), Montgomery College (MC), and Community College of Baltimore County (CCBC) through the National Science Foundation Improving Undergraduate STEM Education (NSF IUSE) project designed novel group work modules for four core Biology courses that incorporate the application of mathematical skills in biological contexts. The modules focus on helping students improve quantitative competencies like demonstrating quantitative numeracy, interpreting data/graphs, demonstrating proficiency in statistical analyses, using mathematical models in biological systems, applying logic to problem solving, and using quantitative language to describe biological phenomena. Each module includes pre- and post-assessment questions to assess student learning gains in the quantitative competencies. Validity, reliability, and learning gains relative to the summative assessment will be presented across modules implemented in cell biology courses over several semesters and institutions, including over 600 students.

Viral dynamics and its applications

Organized by: Tin Phan, Ruian Ke, Ruy M. Ribiero, Alan S. Perelson
Note: this minisymposia has multiple sessions. The other session is MS03-IMMU-1.

  • Tin Thien Phan Los Alamos National Laboratory
    "Feasibility of using dynamic models with virus-immune interactions to predict early viral rebound dynamics following HIV-1 antiretroviral therapy interruption"
  • Most individuals living with HIV-1 experience rapid viral rebound once antiretroviral therapy stops; however, a small fraction retain viral remission for an extended duration. Understanding the factors that determine whether viral rebound is likely once treatment stops can enable the development of optimal treatment regime to potentially achieve a functional cure for HIV-1. We built upon the theoretical framework proposed by Conway and Perelson to construct dynamic models of virus-immune interaction to study factors that influence viral rebound dynamics. We evaluate these models using viral load data (up to one year) from 24 participants with diverse outcomes (9 post-treatment controllers and 15 non-controllers) post antiretroviral therapy interruption. The best performing model accurately captures the heterogeneity of viral rebound dynamics in a statistically robust manner. The model suggests that viral rebound dynamics is significantly influenced by the effector cell expansion rate, where post-treatment controllers and non-controllers can be distinguished based on how fast the effector cell population expands. Our results highlight the potential of using dynamic models incorporating virus-immune interactions to predict early viral rebound dynamics post antiretroviral therapy interruption.
  • Ellie Mainou The Pennsylvania State University (Department of Biology)
    "Investigating alternative models of acute HIV infection"
  • Understanding the dynamics to acute HIV infection may provide insights into the mechanisms of early viral control with potential implications for vaccine design. The standard viral dynamics model explains HIV viral dynamics during acute infection reasonably well. However, the model makes simplifying assumptions, neglecting some aspects of HIV. For example, in the standard model, target cells are infected by a single HIV virion. Yet, cellular multiplicity of infection (MOI) may have considerable effects in pathogenesis and viral evolution. Further when using the standard model, we take constant infected cell death rates, simplifying the dynamic immune responses. Here, we use four models—1) the standard viral dynamics model, 2) an alternate model incorporating cellular MOI, 3) a model assuming density-dependent death rate of infected cells and 4) a model combining (2) and (3)—to investigate acute infection dynamics in 43 people tested very early after HIV exposure. We find that all models explain the data, but different models describe differing features of the dynamics more accurately. For example, while the standard viral dynamics model may be the most parsimonious model, viral peaks are better explained by a model allowing for cellular MOI. These results suggest that heterogeneity in within-host viral dynamics cannot be captured by a single model. Thus depending on the aspect of interest, a corresponding model should be employed.
  • Jonathan Cody Purdue University (Weldon School of Biomedical Engineering)
    "Potential for HIV viral control with IL-15 immunotherapy: Stability analysis of a mathematical model"
  • Cytokines, the chemical messengers of the immune system, can be therapeutically applied to treat tumors and chronic viral infections. However, these cytokines can have multifaceted effects, both activating the immune response and triggering a suppressive regulation of that response. We studied the treatment ramifications of these effects using an ordinary differential equation model of interleukin-15 (IL-15) therapy of human immunodeficiency virus (HIV). Using parameter sets previously fitted to non-human primate data, we conducted numerical stability analysis based on a constant IL-15 effect control parameter. There was a moderate IL-15 effect which minimized viral load, but this was still above what would clinically be considered as safely controlling HIV. We next assessed how parameter changes altered the stability of the system, as an analog for combination therapy. It was found that IL-15 therapy in tandem with blockade of suppressive regulation yielded viral control in all parameter sets. These results highlight the need for a multi-drug approach for immune therapy of complex diseases.
  • Baylor Fain Texas Christian University (Physics and Astronomy)
    "Deconstructing agent-based model parameters"
  • The parameters of agent-based models can be hard to estimate, whether the model parameters are probabilistic or deterministic. The work here focuses on in-host virology and presents a systematic way of mathematically categorizing individual-level interactions as they contribute to the probability of infection. This method is applicable even as the agent-based model becomes more complex, and results in a partitioning of the parameter space that can be generalized to other systems.

Mathematical Epidemiology: Infectious disease modeling across time, space, and scale

Organized by: Lauren Childs, Michael Robert

  • Rosemary Aogo National Institutes of Health (Viral Epidemiology and Immunity Unit, Laboratory of Infectious Diseases, National Institute of Allergy and Infectious Diseases)
    "A new model framework offers insights into the role of immune boosting and waning in shaping dengue epidemic dynamics."
  • Infection with any of the four dengue virus serotypes (DENV1-4) induces serotype-specific and cross-reactive antibodies that may increase disease severity during secondary infection with a different serotype. However, following secondary infection, individuals are at significantly reduced risk of subsequent severe disease with even unexposed serotypes. Previous dengue modeling studies with two or four serotypes have shown that periodicity in dengue incidence can be explained by enhancement between serotypes, transient cross-protective immunity, as well as vector distribution, population size, geography, and seasonality. However, all models have assumed complete protection against previous infecting serotypes and most models have assume complete protection against all serotypes after two sequential infections. Conversely, a recent longitudinal cohort study showed that antibodies wane for many years after secondary DENV infection, at times to the level observed following first DENV infection, suggesting immunity after two infections may not be life-long. In this study, we use a dataset of antibody titers to DENV and ZIKV measured annually in Nicaraguan family and pediatric cohorts from 2017-2021 and developed an immunity-structured SIR-type model that tracks immunity by titer rather than number of prior infections. We show that boosting and waning occur following major dengue and Zika outbreaks in highly immune Nicaraguan adult populations. Using our framework, we show that boosts in highly immune individuals contribute to herd immunity, delaying their contribution to the susceptible population and lowering the rate of dengue cases in future epidemics. However, as their immunity wanes due to lower transmission intensity, the susceptible fraction builds up until a major epidemic that includes re-infection of those with high titers once again depletes the susceptible pool. Comparatively, lifelong immunity in highly immune individuals as previously assumed in most studies results in a complete disease eradication after disease introduction and subsequent epidemic bouts are only sustained with a constant influx of infected individuals into the population by migration. Our model validation shows the interaction of immune boosting and waning in highly exposed adults better explains observed dengue epidemic dynamics than models assuming transient immunity or lifelong immunity in highly immune adult populations. Moreover, we show that ZIKV exposure modulates dengue immunity and create further delays between dengue epidemics. These findings suggest boosting and waning in highly immune individuals contributes to shaping epidemic dynamics and moreover, our study may inform vaccine strategies to maintain immunity over the life-course.
  • Derdei M. Bichara California State University, Fullerton (Mathematics)
    "Effects of Heterogeneity in a Class of Bio-systems"
  • The role of heterogeneity in populations has long been recognized as a driving force in the spread of infectious diseases. Indeed, populations differ in their propensity to transmit or acquire infectious agents in terms of activities, socio-economic or genetic groups. Oftentimes, mathematical models in population dynamics that incorporate such heterogeneities use groups or classes as units and networks to describe the interactions between these units of the model. For many models that describe such phenomena, the complete global behavior of these systems have been open questions. In this talk, I provide a complete characterization of the some these problems.
  • Paul Hurtado University of Nevada-Reno (Mathematics & Statistics)
    "Finding Reproduction Numbers for ODE Models of Arbitrary Finite Dimension Using The Generalized Linear Chain Trick"
  • Reproduction numbers, like the basic reproduction number R0, play an important role in the analysis and application of dynamic models of contagion spread (and parallels exist elsewhere, e.g., in multispecies ecological models). One difficulty in deriving these quantities is that they must be computed on a model-by-model basis, since it is typically impractical to obtain general reproduction number expressions applicable to a family of related models, especially if these models are of different dimensions (i.e., differing numbers of state variables). For example, this is typically the case for SIR-type infectious disease models derived using the classical linear chain trick (LCT). In this talk, I will provide an overview of how to find general reproduction number expressions for such model families using the next generation operator approach in conjunction with the generalized linear chain trick (GLCT). This shows how the GLCT enables modelers to draw insights from these results by leveraging theory and intuition from continuous time Markov chains (CTMCs) and their absorption time distributions (i.e., phase-type probability distributions). I will show an example application of this technique to find reproduction numbers for a family of generalized SEIRS models with an arbitrary number of state variables. These results highlight the utility of the GLCT for the derivation and analysis of mean field ODE models, especially when used in conjunction with theory from CTMCs and their associated phase-type distributions.
  • Zhuolin Qu University of Texas at San Antonio (Department of Mathematics)
    "Multistage Spatial Model for Informing Release of Wolbachia-Infected Mosquitoes as Disease Control"
  • Wolbachia is a natural bacterium that can infect Aedes mosquitoes and block the transmission of mosquito-borne diseases, including dengue fever, Zika, and chikungunya. Field trials have been conducted worldwide to suppress local epidemics. We present a new partial differential equation model for the spread of Wolbachia infection in mosquitoes. The model accounts for both the complex Wolbachia vertical transmission cycle and detailed life stages in the mosquitoes, and it also incorporates the spatial heterogeneity created by mosquito dispersion in the two-dimensional release domain. Field trials and previous modeling studies have shown that the fraction of infection among mosquitoes must exceed a threshold level for the infection to persist. We use the spatial model to identify a threshold condition for having a self-sustainable Wolbachia infection in the field. When above this threshold, the model gives rise to a spatial wave of Wolbachia infection. We quantify how the threshold condition and invasion velocity depend on the diffusion process and other model parameters, and we study different intervention scenarios to inform the efficient releases.

Stochastic methods for biochemical reaction networks

Organized by: Wasiur KhudaBukhsh, Hye-Won Kang
Note: this minisymposia has multiple sessions. The other session is MS03-MFBM-1.

  • Wasiur R. KhudaBukhsh University of Nottingham (School of Mathematical Sciences)
    "Multiscale approximations for a simple transfection process"
  • The talk will focus on chemical reaction networks (CRNs) that describe creation, annihilation, combination or binding, and changes in the physical state of a collection of chemical species. Many prominent examples of intracellular dynamics, genetic switches, and dynamics of population interactions can be modelled by CRNs, where the interacting particles exhibit vastly different intrinsic scales in terms of abundance, or the reactions operate at different time scales varying over many orders of magnitude. The traditional deterministic approach to multiscale approximations used in such situations employs singular perturbation theory, often invoking Tikhonov’s theorem and Fenichel theory. In this talk, I will take a stochastic viewpoint and consider a probabilistic way to derive multiscale approximations. The talk will be fairly nontechnical, and no prior knowledge biology is required.
  • Ruth Baker University of Oxford (Mathematical Institute)
    "Efficient approaches for simulating and calibrating stochastic models of biological processes"
  • With the advent of a host of new experimental technologies, the last ten years has seen an explosion in the amount and types of data now being generated. As such, increasingly larger and more complicated processes are now being explored, including large signalling or gene regulatory networks, and the development, dynamics and disease of entire cells and tissues. Detailed mathematical models of these processes have the potential to provide vital insights where data alone cannot, but to achieve this goal requires meeting significant mathematical challenges in efficiently simulating models and calibrating them to experimental data. In this talk, I will outline some methods we have developed that leverage both low- and high-fidelity models and variance-reducing Monte Carlo approaches to make progress.
  • Jae Kyoung Kim KAIST (Mathematical Sciences)
    "Inference of non-Markovian systems from cell signaling to infectious diseases"
  • The complex processes involved in cell signaling and infectious diseases often include multiple hidden intermediate steps. However, it is possible to simplify these systems by replacing them with a single time delay distribution, such as a gamma distribution. This simplification reduces the number of variables, making it easier to infer parameters based on limited observations. Although this approach offers advantages, it presents a challenge. Since the model is non-Markovian, traditional inference techniques based on the Markov property (where dynamics depend only on the current state, not the past) cannot be directly applied. In my presentation, I will introduce a Bayesian inference framework specifically designed for non-Markovian systems. This framework enables us to identify the properties of the cell signaling network that reduce cell-to-cell heterogeneity in response to antibiotics. Additionally, I will discuss how our framework can be used to infer both the reproduction number and the distribution of infectious periods solely from confirmed case time series. This resolves the biased estimation issues associated with the conventional SEIR ODE model. 
  • Boseung Choi & Eunjin Eom Korea University (Division of Big Data Science; Department of Economics Statistics)
    "A Bayesian model for the relationship SARS-CoV-2 wastewater and community-wide seroprevalence with mutation and vaccination effect"
  • Since early in the COVID-19 pandemic, SARS-CoV-2 wastewater concentration has been measured as a surrogate for community prevalence. However, our knowledge remains limited regarding wastewater concentration and the effects of the COVID-19 vaccination on the overall disease burden as measured by hospitalization rates. We used weekly SARS-CoV-2 wastewater concentration, antibody test results, and spatially linked vaccination and hospitalization data, from April to August 2021. Our susceptible (S), vaccinated (V), variant-specific infected (I1 and I2), recovered (R), and seropositive (T) model (SVI2RT) tracked prevalence longitudinally. This was related to wastewater concentration for spatial analysis of strain mutation, vaccination effect, and overall hospitalization burden. To construct the SVI2RT compartment model, we utilized the dynamical survival analysis (DSA) framework for using survival analysis methods to build approximate models of individual-level ecological dynamics based on mean-field approximations and the Markov Chain Monte Carlo (MCMC) method based on the Bayesian approaches. We used the Bayesian linear regression model to identify the effect of the estimated prevalence according to the Alpha and Delta mutations on the community wastewater concentration and the hospitalization burden. We found strong linear association between wastewater concentration and estimated community prevalence. During the study period, the estimated effect of SARS-CoV-2 Delta variant emergence was seen as large as the increase in infection counts, corresponding to the increase in wastewater concentration. Hospitalization burden and wastewater concentration had the strongest correlation at 1 week lag time. Therefore, the wastewater samples can be used to estimate the effects of vaccination and hospitalization burden.

Dynamics of cellular heterogeneity: consequences of diverse regulatory mechanisms

Organized by: Mohit Kumar Jolly, Paras Jain
Note: this minisymposia has multiple sessions. The other session is MS03-ONCO-1.

  • Antara Biswas Rutgers Cancer Institute of New Jersey (Department of Pathology & Laboratory Medicine)
    "Transcriptional heterogeneity and cell state plasticity in urothelial bladder carcinoma."
  • Intra-tumor heterogeneity contributes towards treatment failure and poor survival in urothelial bladder carcinoma (UBC) patients, but underlying drivers are poorly understood. Analysis of single cell transcriptomic data from UBC patients suggests that intra-tumor transcriptomic heterogeneity is, partly due to, admixtures of tumor cells in epithelial and mesenchymal-like transcriptional states, which covary with other cancer hallmarks. Transition between these cell states likely occurs within and between tumor subclones, adding a layer of phenotypic plasticity and dynamic heterogeneity beyond genetic variations. We model spontaneous and reversible transition between partially heritable epithelial- and mesenchymal-like transcriptional states in UBC cell lines and characterize their population dynamics during in vitro evolution. Nutrient limitation, as in large tumors, and radiation treatment perturb the cell-state dynamics, initially selecting for a transiently resistant phenotype and then reconstituting heterogeneity and growth potential, facilitating adaptive evolution. Our data suggests that transcriptional state dynamics contributes towards phenotypic plasticity and non-genetic intra-tumor heterogeneity, modulating the trajectory of disease progression and adaptive treatment response in UBC.
  • Samuel Oliver Swansea University (Department of Mathematics)
    "Cancer as a matter of fat: The role of adipose tissue in tumour progression"
  • Ovarian cancer has the highest mortality rate of all gynaecological cancers, possessing a 5-year survival rate of less than 50% [1]. Numerous factors are responsible for the poor prognosis, including asymptomatic cases and accelerated chemoresistance. Malignant neoplasms achieve metastasis by interacting with stromal cells in the tumour microenvironment, enhancing proliferation and enabling key phenotypic changes. To quantify these links, we developed an agent-based 3D mathematical model using a PhysiCell framework [2] to simulate tumour growth and its dependence on the microenvironment. In-silico experiments were used to understand the adipose-tumour interactions for SKOV-3 and OVCAR-3 cell lines, with higher levels of fat in the tumour microenvironment being found to cause more aggressive cases of the disease with higher cell viability, EMT, and chemoresistance to paclitaxel treatment. These results, along with a rising abundance of obesity in the global population, underline the need for intensive research into adipose-tumour cell interactions to develop better treatments that hamper cancer progression by tackling the cells of the tumour microenvironment including adipocytes. Mathematical models such as the one used here are key in giving patient specific results by quantifying the impacts of changes in the microenvironment and treatment protocol. [1] G. C. Jayson, E. C. Kohn, H. C. Kitchener, and J. A. Ledermann, “Ovarian cancer,” The Lancet, vol. 384, no. 9951, pp. 1376–1388, 2014. [2] A. Ghaffarizadeh, R. Heiland, S.H. Friedman, S.M. Mumenthaler, and P. Macklin. PhysiCell: an Open Source Physics-Based Cell Simulator for 3-D Multicellular Systems, PLoS Comput. Biol. 14(2): e1005991, 2018.
  • Simone Bruno Massachusetts Institute of Technology (Mechanical Engineering)
    "Stochastic analysis of chromatin modification circuits that control epigenetic cell memory"
  • Epigenetic cell memory is a property of multi-cellular organisms that allows different cells to maintain different phenotypes, encoded by distinct gene expression patterns, despite a common genome. Covalent modifications to chromatin are thought to have a role in dictating the long-term stability of these mutually exclusive gene expression states. However, the underlying mechanisms are not well understood. Here, we analyze a chemical reaction model of the chromatin modification circuit within each gene of the mammalian chromosome and demonstrate how the time scale separation between key constituent processes is implicated in long-term maintenance of gene expression states. To achieve this goal, we use the mathematical framework of singularly perturbed continuous-time Markov chains, where the small parameter quantifies the degree of time-scale separation. Unique to our system, is the fact that the limiting behavior as the small parameter decreases is non-ergodic. We, therefore, developed new tools for the analysis of the behavior of stationary distributions as a function of the small parameter. Furthermore, in order to determine the behavior of these distributions and of mean first passage times as biological parameters are varied, we developed comparison theorems. These theorems, beyond being applicable to our system, provide a general stochastic ordering result that can be applied to chemical reaction networks in general.
  • Paras Jain Indian Institute of Science (Centre for BioSystems Science and Engineering)
    "Epigenetic memory acquired during long-term EMT induction governs the recovery to the epithelial state"
  • Epithelial–mesenchymal transition (EMT) and its reverse mesenchymal–epithelial transition (MET) are critical during embryonic development, wound healing and cancer metastasis. While phenotypic changes during short-term EMT induction are reversible, long-term EMT induction has been often associated with irreversibility. Here, we show that phenotypic changes seen in MCF10A cells upon long-term EMT induction by TGFβ need not be irreversible but have relatively longer time scales of reversibility than those seen in short-term induction. Next, using a phenomenological mathematical model to account for the chromatin-mediated epigenetic silencing of the miR-200 family by ZEB family, we highlight how the epigenetic memory gained during long-term EMT induction can slow the recovery to the epithelial state post-TGFβ withdrawal. Our results suggest that epigenetic modifiers can govern the extent and time scale of EMT reversibility and advise caution against labelling phenotypic changes seen in long-term EMT induction as ‘irreversible’.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak
  • Jeffrey West
SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak

  • Jeffrey West

SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.