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.

# Minisymposia: MS04

#### Tuesday, July 18 at 04:00pm

# Minisymposia: MS04

##### MS04-CARD-1:

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"**Alys Clark***University of Auckland, New Zealand (Auckland Bioengineering Institute)*

"The fetal circulation and its adaption to pathological placental development"**Joyce Lin***Cal Poly State University (Mathematics)*

"Conduction reserve theory in cardiac tissue with reduced gap junction coupling"**Nicolae Moise***Ohio State University (Biomedical Engineering)*

"Emergent Pacemaking and Tissue Heterogeneity in a Calcium Feedback Regulatory Model of the Sinoatrial Node"

##### MS04-CDEV-1:

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"**John Nardini***The College of New Jersey (Mathematics & Statistics)*

"Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images"**Anna Nelson***Duke University (Department of Mathematics)*

"Mathematical modeling of microtubule assembly and polarity in 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"

##### MS04-CDEV-2:

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"**Greg Conradi Smith***William & Mary (Applied Science / Neuroscience / CAMS Biomath)*

"Allosteric coupling and cycle kinetics of G protein-coupled receptor dimers"**Victor Matveev***New Jersey Institute of Technology (Department of Mathematical Sciences)*

"Accuracy of deterministic vs. stochastic modeling of Ca2+-triggered vesicle fusion latency"**Linh Huynh***University of Utah (Mathematics)*

"Stochastic Cancer Cell Dynamics under Environmental Stress"

##### MS04-ECOP-1:

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"**Brandon Legried***Georgia Institute of Technology (Mathematics)*

"Inferring phylogenetic birth-death models from extant lineages through time"**Colby Long***The College of Wooster (Mathematical and Computational Sciences)*

"Phylogenomic Models from Tree Symmetries"**Julia Chifman***American University (Mathematics and Statistics)*

"Cancer evolution: mathematical models and inference methods."

##### MS04-ECOP-2:

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"**Judith Miller***Georgetown University (Mathematics and Statistics)*

"Modeling neutrality with climate data: the spread of the cabbage white butterfly Pieris rapae in North America"**Artem Novozhilov***North Dakota State University (Department of Mathematics)*

"On a hypercycle equation with infinitely many members"**Max O. Souza***Universidade Federal Fluminense (Instituto de Matemática e Estatística)*

"Continuous approximations of fixation probabilities for large populations on star graphs"

##### MS04-EDUC-1:

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"**Suzanne Lenhart***University of Tennessee, Knoxville (Mathematics)*

"Teaching Discrete Time Modeling in Mathematics for the Life Sciences course"**Elissa Schwartz***Washington State University (Math/Biol Sci)*

"Creating a watershed for mathematical biology education: Recent outreach in Nepal"**Kathleen Hoffman***UMBC (Department of Mathematics and Statistics)*

"Integrating Quantitative Skills into Biology Courses"

##### MS04-IMMU-1:

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"**Ellie Mainou***The Pennsylvania State University (Department of Biology)*

"Investigating alternative models of acute HIV infection"**Jonathan Cody***Purdue University (Weldon School of Biomedical Engineering)*

"Potential for HIV viral control with IL-15 immunotherapy: Stability analysis of a mathematical model"**Baylor Fain***Texas Christian University (Physics and Astronomy)*

"Deconstructing agent-based model parameters"

##### MS04-MEPI-1:

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."**Derdei M. Bichara***California State University, Fullerton (Mathematics)*

"Effects of Heterogeneity in a Class of Bio-systems"**Paul Hurtado***University of Nevada-Reno (Mathematics & Statistics)*

"Finding Reproduction Numbers for ODE Models of Arbitrary Finite Dimension Using The Generalized Linear Chain Trick"**Zhuolin Qu***University of Texas at San Antonio (Department of Mathematics)*

"Multistage Spatial Model for Informing Release of Wolbachia-Infected Mosquitoes as Disease Control"

##### MS04-MFBM-1:

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"**Ruth Baker***University of Oxford (Mathematical Institute)*

"Efficient approaches for simulating and calibrating stochastic models of biological processes"**Jae Kyoung Kim***KAIST (Mathematical Sciences)*

"Inference of non-Markovian systems from cell signaling to infectious diseases"**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"

##### MS04-ONCO-1:

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."**Samuel Oliver***Swansea University (Department of Mathematics)*

"Cancer as a matter of fat: The role of adipose tissue in tumour progression"**Simone Bruno***Massachusetts Institute of Technology (Mechanical Engineering)*

"Stochastic analysis of chromatin modification circuits that control epigenetic cell memory"**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"