Plenary Talks

Avner Friedman, The Ohio State University

Title: Mathematical biomedicine, challenges and opportunities 

Abstract: Mathematical biomedicine is an area of research where questions that arise in medicine are addressed with mathematical models and simulations. Based on experimental and preclinical data, and clinical data wherever available, one can set up a network of interactions among the variables (cells, proteins, genes, drugs) that are needed to address a specific question and proceed to represent this network by a dynamical system with carefully estimated parameters. One then proceeds to simulate the system in order to address the biomedical question. The ongoing amazing growth of medical sciences offers challenges and opportunities for mathematical biology.  In this talk I will give some examples, such as cancer immune therapy, cancer metastasis, cancer side- effects, wound healing, autoimmune diseases, diabetes, and Alzheimer disease. 

Marty Golubitsky, The Ohio State University

Title: Network Dynamics

Abstract: This talk illustrates, using binocular rivalry and homeostasis, how network architecture affects the kind of solutions one can expect from networks of differential equations.  The results also illustrate some of the research done by MBI post-docs, early career awardees, and long term visitors.

Invited Talks

Fernando Antoneli, Universidade Federal de Sao Paulo, Brazil

Title: Homeostasis Input-Output Networks: Combinatorial Structure and Classification 

Abstract: Homeostasis occurs in a biological or biochemical system when some output variable remains approximately constant as some input parameters vary over some range.  Golubitsky and Stewart [Homeostasis, Singularities and Networks. J. Math. Biol. 74 (2017) 387-407] introduced the notion of 'infinitesimal homeostasis' allowing the use of implicit differentiation and singularity theory to study homeostasis in systems of differential equations.  Homeostasis occurs naturally in biochemical signaling modeled by networks.  Networks represented by directed graphs encode systems of differential equations.  Nodes correspond to state variables and arrows indicate which nodes are coupled to which.  What distinguishes a network dynamical system from a large system of differential equations is the capability to keep track of the output from each node individually.  Hence, in the context of network dynamical systems, infinitesimal homeostasis is related to occurrence of singularities at individual nodes.  In this talk we explain the combinatorial structure and classification of homeostasis in 'input-output networks', that is, networks where we keep track of the output from a fixed node, as well as the node(s) that depend on the external input parameters.

Joint work with Martin Golubitsky (Ohio), Ian Stewart (Warwick), Janet Best (Ohio), Michael Reed (Duke), Fred Nijhout (Duke), Yangyang Wang (Iowa), Zhengyuan Huang (Michigan), Jiaxin Jin (Ohio), William Duncan (Immunetrics) and João Luiz de Oliveira Madeira (Bath).

Janet Best, Ohio State University 

Title: Inflammation and the origins of depression 

Abstract: There are multiple routes to depression, generally involving inflammation. I’ll discuss ideas about why and collaborative work addressing the relationship between inflammation and depression as well as implications for treatment.

Anastasia Bizyaeva, University of Washington

Title: Nonlinear dynamics of collective belief formation 

Abstract: Many complex collective behaviors in nature, society, and technology are driven by social formation of beliefs on multiple alternatives. For example, groups may evaluate context-dependent options to allocate tasks and resources among their members, to vote in elections that involve multiple candidates or proposals, and to navigate their physical environments. Dynamic models of social belief formation provide a tool for systematic investigation of such belief-driven processes and for principled design of distributed algorithms for decision-making in technological teams. In the presented work we introduce a new mechanistic model for how agents evaluate alternatives and form beliefs through a nonlinear dynamic social evidence accumulation process. This general model accounts for typical constraints on information processing and for the expected mathematical symmetries that arise in multi-alternative decisions across contexts. Using this model, we show that groups can form strong beliefs despite individuals having limited access to information about option quality, despite sparse communication between group members, and despite the lack of a clear "best" option among the alternatives. We identify sufficient conditions for several broad classes of belief-forming behaviors that can arise from local deadlock-breaking bifurcations in the model, including commitment to a steady-state set of beliefs and sustained oscillations in beliefs within the group.

Allie Cruikshank, Duke University 

Title: Dynamical Questions in Volume Transmission

Abstract: In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities on the neuron. Many well-known neurotransmitters including serotonin (5HT), dopamine (DA), histamine (HA), Gamma-Aminobutyric Acid (GABA) and acetylcholine (ACh) participate in volume transmission. Typically, the cell bodies are in one volume and the axons project to a distant volume in the brain releasing the neurotransmitter there. These neurons are projecting changes in biochemistry over long distances in the brain. We introduce volume transmission and describe mathematically two natural homeostatic mechanisms. In some brain regions several neurotransmitters in the extracellular space affect each others' release. Serotonin increases histamine release and histamine inhibits serotonin release and we investigate the dynamics in the extracellular space induced by this co-modulation. We also investigate with mathematical models the co-modulation of HA, DA, GABA, and ACh in the striatum and compare to experimental data. Understanding this kind of co-modulation in different brain regions poses new dynamical questions for mathematicians as well as the question of how these biochemical networks influence the electrophysiological networks in the brain.

Judy Day, Applied MathBio

Title: From model development to business development: one mathematician’s journey 

Abstract: Nonlinear career paths can be an unfamiliar concept, especially when the more familiar linear academic trajectory is at the forefront of one’s options or interests while in grad school. I will share my experience pivoting from a successful academic career guiding mathematical modeling collaborations to a new industry career where I sell mathematical modeling services and software to pharmaceutical companies. My goal for this talk is to provide a bit of perspective on this topic based on my personal experience and to open the floor for questions and for others to share additional perspective.

Ana Dias, University of Porto 

Title: Coupled cell hypernetworks and collective dynamics 

Abstract: In the coupled cell network formalism developed by Golubitsky, Stewart and collaborators, the network interactions are captured by a directed graph which elucidates how the network structure shapes the collective dynamics. Interactions in this setup allows for generic, nonlinear interactions between all the input nodes. In the coupled cell weighted networks, the links have associated numerical values and these are realized as coupled cell systems with additive input structure allowing for interactions between pairs of nodes. Coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph have deserved attention due to recent research that has highlighted the dynamical importance of higher-order interactions (which are nonlinear in the state of more than two nodes).  In this talk, we plan to discuss the existence of robust (cluster) synchronization patterns in these different setups. Part of the talk is based on joint work with Aguiar (Porto, Portugal) and Bick (Amsterdam, The Netherlands). 

Casey Diekman, New Jersey Institute of Technology 

Title: Deep Hybrid Modeling of Neuronal Dynamics using Generative Adversarial Networks

Abstract:  Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. To address these shortcomings, we build Deep Hybrid Models (DeepHMs) that combine deep learning with mechanistic modeling to identify the distributions of mechanistic modeling parameters coherent to the data. We developed a DeepHM using conditional Generative Adversarial Networks (cGANs) to provide the inverse mapping from data to mechanistic model parameters. We then used it to identify which ionic conductances are responsible for the altered excitability properties of CA1 pyramidal neurons in mouse models of Alzheimer’s disease.

Allessio Franci, University of Liege 

Title: Bifurcations in biological and artificial intelligent behaviors

Abstract: Biological agents sense and interact dynamically with their environment in order to thrive and survive. They do so with high degrees of adaptability and energy efficiency. Taking inspiration from nature can be key in our quest of designing more sustainable, adaptable, and energy efficient intelligent machines, overcoming the rigidity and inefficiency of digital designs based on Von Neuman architectures. Starting from single neurons and single cells and arriving to animal groups and whole societies, I will review the fundamental role of bifurcation theory for understanding biological intelligence and discuss new ways in which bifurcation theory can help us design more sustainable intelligent machines.

Punit Gandhi, Virginia Commonwealth University 

Title: Conceptual modeling of dryland vegetation patterns across timescales 

Abstract: Strikingly regular, large-scale patterns of vegetation growth were first documented by aerial photography in the Horn of Africa circa 1950 and are now known to exist in drylands across the globe.  The patterns often appear on very gently sloped terrain as bands of dense vegetation alternating with bare soil, and models suggest that they may be a strategy for maximizing usage of the limited water available.  A particular challenge for modeling these patterns is appropriately resolving fast processes such as surface water flow during rainstorms while still being able to capture slow dynamics such as the uphill migration of the vegetation bands, which has been observed to occur on the scale of a band width per century.  We propose a pulsed-precipitation model that treats rainstorms as an instantaneous kick to the soil water. as it interacts with vegetation on the timescale of plant growth.  The model allows for predictions about the influence of storm characteristics on the large-scale pattern dynamics.  Analysis and simulations suggest that the distance water travels on the surface before infiltrating into the soil during a typical storm plays a key role in determining the spacing between the bands.  

Hayriye Gulbudak, University of Louisiana at Lafayette

Title: Multi-Scale Models of Infectious Disease Dynamics and Validating with Data

Abstract: The bidirectional feedback induced through population and individual-level infectious disease and host immune dynamics requires development of innovative multi-scale models. In this talk, I will introduce structured nonlinear partial differential equation models linking immunology and epidemiology, along with stability analysis and computational tools for simulating ODE-PDE hybrid systems to understand their nonlinear dynamics and application to biological data.  Applying the modeling framework to dengue virus,  we first demonstrate how intermediate levels of antibodies enhance infection severity within a host, and scale up to population wide antibody level distributions evolving through multiple infections by distinct strains and waning immunity. Then we fit primary and secondary dengue infection data to provide evidence of antibody dependent enhancement. These results have critical implications for optimal vaccination policy, and the modeling framework is currently being applied to examine the emergence of COVID-19 variants. 

Abba Gumel, University of Maryland 

Title: Mathematics of malaria transmission dynamics: the renewed quest for eradication 

Abstract: Malaria, a deadly disease caused by protozoan Plasmodium parasites, is spread between humans via the bite of infected adult female Anopheles mosquitoes. Over 2.5 billion people live in geographies whose local epidemiology permits transmission of P. falciparum, responsible for most of the life-threatening form of malaria. The widescale and heavy use of insecticide-based interventions, notably long-lasting insecticidal nets and indoor residual spraying), during the period 2000-2015, resulted in a dramatic reduction in malaria incidence and burden in endemic areas, prompting a renewed quest for malaria eradication. Numerous factors, such as Anopheles resistance to all currently-available insecticides and anthropogenic climate change, potentially pose important challenges to the eradication efforts. In this talk, I will discuss a genetic-epidemiology framework for assessing the impact of insecticide resistance on malaria. Specifically, questions on whether eradication can be achieved using existing insecticide-based control resources will be addressed. If time permits, I may briefly discuss the utility of some of the gene drive-based biological interventions being proposed as a plausible alternative pathway for achieving the laudable malaria eradication goal.

Samuel Handelman, Eli Lilly & Co 

Title: The Hard Problems for Mathematical Pharmacology in Chronic Pain 

Abstract: Chronic pain is estimated to affect 10% of the world’s population, over 700 million people.  Available treatments fall short in both safety and efficacy.  Opioids, broadly-speaking the most potent analgesic medicine class, are neither safe nor completely effective.  Opioid overdose deaths contributed to approximately 4 million years of life lost (YLL) in 2021 (comparable to the ~5 million YLL of the US Covid epidemic in 2021).  Furthermore, opioids are of limited benefit in the management of chronic pain, due to some combination of tolerance and poorly understood epidemiological phenomena.  Therefore, novel non-opioid strategies are urgently needed for the management of chronic pain, and mathematical biology can provide crucial insights.  The objective of these models will generally be to identify conditions associated with reduced excitability of different classes of neurons, but oscillatory neuron-only models are unfortunately of limited use.  In this talk, I will discuss or formally pose problems with the needed additional biological elements, including calcium signaling, interactions (chemical or electrical) with accessory cells, and crosstalk with the immune system or molecular damage pathways.  Finally, I will describe the necessary elements of these systems biology models which could support therapeutic development, including especially practical identifiability, experimental falsifiability, and epidemiologic relevance to large human pain populations.

Wenrui Hao, Penn State University 

Title: Computational Models for Cardiovascular Disease

Abstract: This talk will cover several computational models that are used to predict the long-term risk of cardiovascular disease, specifically atherosclerosis and aortic aneurysm growth. These models incorporate the complex multi-layered structure of the arterial wall as well as the pathophysiology of aneurysms. The heterogeneous multiscale method is utilized to account for different time scales, while the finite element method is employed to model the hyperelastic deformation of the arterial wall. A realistic three-dimensional cardiovascular fluid-structure interaction problem is simulated using CT scan data from patients to validate the accuracy of these models in predicting long-term cardiovascular risk.

Mary Ann Horn, Case Western Reserve University 

Title: Modeling multiphage-bacteria kinetics to predict phage therapy potency and longevity

Abstract: Pseudomonas aeruginosa is a frequent cause of life-threatening opportunistic infections in the critically ill and immunocompromised. Its treatment is challenging due to the increasing prevalence of resistance to most conventional antibiotics. Although numerous alternative therapies are currently under investigation, bacteriophage (phage) cocktail therapy appears poised for long-term success. Here, the potency and longevity of individual Pseudomonas phages in cocktail to determine viral co-factors that promote optimal treatment efficacy are investigated.  In vitro and in silico models are combined to predict sixty-eight treatment permutations with three phages that adsorb symmetrically and asymmetrically when administered singly, double simultaneously, or double sequentially. We showed that simultaneously administering two asymmetrically binding phages with high cell lysis efficiencies improved cocktail potency. Use of a higher-potency cocktail, along with a reduction in the net probability of independent gene mutations was associated with prolonged bacterial suppression. Nevertheless, in vitro we almost always observed evolution of multiphage resistance.  Simulations also predict that when combining phages with polar potencies, susceptible host cells are monopolized by the more efficiently replicating phage.  This further perpetuates the growth demise of the weaker phage in cocktail.  Our mathematical model was used to explore and predict changes in phage and bacterial populations that were difficult to measure experimentally. This framework has many inferential and exploratory uses for clinical investigation such as identifying the most sensitive parameters for phage selection and exploring different treatment regimens.  Collectively, our findings attempt to dissect the mechanisms of phage cocktails combating P. aeruginosa infections and highlight the viral co-factors necessary for treatment efficacy.

(With Zhiyuan Yu, Tiffany Luong, Selenne Banuelos, Andrew Sue, Aadrita Nandi, Hwayeon Ryu, Dwayne Roach, Rebecca Segal, and Qimin Huang.)

Bei Hu, University of Notre Dame 

Title: A free boundary problem for fungal infection in a general domain 

Abstract: Fungal infection is modeled as free boundary problem, with the free boundary separating the infected and uninfected region. In an earlier work by A. Friedman and K.Y. Lam, radially symmetric case is studied; wellposedness as well as asymptotic behaviors are studied. In reality, there are non-radially symmetric infections. However, the situation for the free boundary problem is much more challenging in the non-radially symmetric case, since the coupling of the system occurs at the free boundary, which is a priorily unknown. We extend the work to the non-radially case by exploring a weak solution. We shall illustrate that our weak solution is biologically reasonable. This is a joint work with Caihong Chang and Zhengce Zhang.

Paul Hurtado, University of Nevada Reno 

Title: A generalized linear chain trick (GLCT) for improving ODE model derivation & analysis

Abstract: ODE models are found throughout the life sciences, and are often viewed as deterministic approximations of the average behavior of stochastic systems (i.e., "mean field" models). Such applications include SIR-type infectious disease models, models of cancer cell proliferation, biochemical reactions, and many others. I will give an overview of our generalization of the well-known "linear chain trick" for the derivation and interpretation of such models. Our generalized linear chain trick reveals some very intuitive connections between Markov Chain models and the structure of corresponding ODE models, and this enables us as modelers to bring tools from stochastic processes into the analysis and interpretation of these ODE models. The accessibility and utility of these new techniques will be discussed and illustrated using some examples.

Jiaxin Jin, Ohio State University 

Title: Homeostasis in Gene Regulatory Networks.

Abstract: Gene regulatory networks (GRNs) control all aspects of development, from cell fate specification to differentiation. In this talk, we classify the patterns of infinitesimal homeostasis that can occur generically in an input-output gene regulatory network (GRN) and its associated protein-mRNA network (PRN). We will introduce the GRN and PRN, and a review of how to compute infinitesimal homeostasis in biochemical networks. The main results are to use the network structure of a GRN to determine its homeostasis structure by working with the associated PRN, which requires using the special bipartite structure of the associated PRN. This is a joint work with Fernando Antoneli, Janet Best, Marty Golubitsky, and Ian Stewart.

Kresimir Josic, University of Houston

Title: Correlated information and decisions in populations of agents

Abstract: Choice formation in humans and other animals is often described by normative models that treat deliberation as the accumulation of noisy evidence terminated by a commitment to one of the possible alternatives. Even when extended to groups, such models often assume that individuals make independent observations.  However,  we often gather evidence from overlapping sources, and our observations are  rarely independent. Here we ask what is the impact of correlations in accumulated evidence on the accuracy of decisions in a group of normative observers who do not exchange information.  We show that, even when agents are identical, the accuracy of decisions depends  on their order: On average, early decisions are less accurate than later ones when evidence is correlated.

Early decisions are more likely to  be based on faulty evidence when agents use the same decision criterion, which does not occur when all agents' observations are independent.  Although rational, early and late deciders are equally confident in their decisions even when the accuracy of these decisions differs considerably. Pooling early decisions does not necessarily resolve this problem, since early agents' decisions can be correlated. Although we describe an idealized, tractable setting, we argue that similar effects could impact group decisions generally.

Hye-Won Kang, University of Maryland, Baltimore County

Title: Stochastic modeling of enzyme-catalyzed reactions in biology 

Abstract: Inherent fluctuations may play an important role in biological or biophysical systems when the system involves some species with low copy numbers. In this talk, I will present my recent work on stochastic modeling of multienzyme complex formation in glucose metabolism. Enzymes in glucose metabolism have been spatially organized into multienzyme complexes with different sizes. We hypothesize that the size of enzyme complexes is related to their functional roles and model how glucose flux can be regulated under different scenarios using differential equations. After that, we will also see a microscopic stochastic model using the Langevin dynamics describing the movement and interactions of enzyme complexes. We will see how the modeling parameters affect the formation of enzyme complexes.

Jae Kyoung Kim, KAIST (South Korea)

Title: Modeling and inference for biological systems with hidden components 

Abstract: Despite dramatic advances in experimental techniques, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. In this talk, I will describe strategies to develop mathematical models with hidden parts: replacement of hidden components with either time delay and quasi-steady-state. Then, I will illustrate how the simplification with the time delay can be used to understand the processes of protein synthesis, which involves multiple steps such as transcription, translation, folding and maturation, but typically whose intermediates proteins cannot be measured. Furthermore, I will illustrate how the simplification with the quasi-steady-state can be used to develop an accurate method to estimate drug clearance, which occurs in multiple steps of metabolism, which greatly improved the canonical approach used in more than 65,000 published papers for last 30 years.  Finally, I will describe an inference method, GOBI (General Model-based Inference), that identifies hidden regulatory biochemical connections from timeseries data. This method adopts the advantage of model-free inference methods (broad applicability) and model-based inference methods (accuracy). 

Jinsu Kim, Pohang University of Science and Technology
Title: Stochastic model for in vivo DNA dynamics to reveal evidence of cooperativity
Abstract: TBD

Yangjin Kim, Konkuk University (South Korea)

Title: Role of senescent tumor cells in building a cytokine shield in the tumor microenvironment: mathematical modeling 

Abstract: Cellular senescence can induce dual effects (promotion or inhibition) on cancer progression. While immune cells naturally respond and migrate toward various chemotactic sources from the tumor mass, various factors including senescent tumor cells (STCs) in the tumor microenvironment may affect this chemotactic movement. In this work, we investigate the mutual interactions between the tumor cells and the immune cells that either inhibit or facilitate tumor growth by developing a mathematical model that consists of taxis-reaction-diffusion equations and receptor kinetics for the key players in the interaction network. We apply a mathematical model, based on a system of PDEs,  to a transwell Boyden chamber invasion assay used in the experiments to illustrate that STCs can play a pivotal role in negating immune attack through tight regulation of intra- and extra-cellular signaling molecules. In particular, we show that senescent tumor cells in cell cycle arrest can block intratumoral infiltration of CD8+ T cells by secreting a high level of CXCL12, which leads to significant reduction its receptors, CXCR4, on T cells, and thus impaired chemotaxis. The predictions of nonlinear responses to CXCL12 were in good agreement with experimental data. By using a hybrid approach, we also tested several hypotheses on immune-tumor interactions under various biochemical conditions in the tumor microenvironment and developed new concepts for anti-tumor strategies targeting senescence induced immune impairment.

Adrian Lam, The Ohio State University

Title: Analysis of a mathematical model of rheumatoid arthritis 

Abstract: We analyze a system of PDEs with a free boundary introduced by Moise and Friedman to model rheumatoid arthritis, as well as the effect of the drugs. Apart from existence of solution, we also prove qualitative properties of the free boundary and derive criterion for the cartilage region to persist or vanish in the large time limit. This is joint work with Avner Friedman.

Kang-Ling Liao, University of Manitoba, Canada

Title: The dual functions of CD200-CD200R in cancer treatment 

Abstract: CD200-CD200R complex is one of the immune check-point in cancer that tumor cells can use this complex to inhibit the functions of M1 and M2 macrophages and dendritic cells (DCs). However, blockade CD200-CD200R could induce opposite treatment outcomes in different types of cancers, due to the types of cells expressing CD200R. Thus, in this talk, I will introduce several PDE and ODE models to numerically and analytically investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200-CD200R complex in tumor growth.  

Yuan Lou, Shanghai Jiao Tong University, China

Title: On several PDE models from infectious disease 

Abstract: I will first present a SIS model to discuss how population mobility and environmental variability affect the disease dynamics. A SEIRS model will be introduced to study the effect of exposed populations on the disease persistence. The coexistence of multiple strains will be addressed via a multi-strain PDE model. An important analytical tool in our studies is the theory for the principal eigenvalue of 2nd order elliptic and parabolic operators, which is closely associated with the basic reproduction number.

Mike Reed, Duke University 

Title: Sex differences in metabolism 

Abstract: Many of the enzymes of one-carbon metabolism are affected by estrogen and testosterone and these effects are large. This means that during the years of menstruation women have very different livers than men and, in some cases, the evolutionary reasons are clear. Our mathematical models explain the differences and the health consequences. In addition, since changes in estrogen during the menstrual cycle are known we can describe the changes in metabolism during the cycle. In current work, we are studying how estrogen affects the production of glutathione, the main anti-oxidant in the body, and also alters brain metabolism.

Bjorn Sandstede, Brown University 

Title: Modeling and data analysis in developmental biology: From mRNA localization in Xenopus to zebrafish pigment-cell patterns

Abstract:  In this talk, I will discuss three projects that try to link genotype and phenotype using modeling and data science. The first project centers on biological and mathematical models for the spatial localization of mRNA on the vegetal cortex of Xenopus oocytes. The second project focuses on models that can help us understand the formation of pigment patterns on the skin of wild-type and mutant zebrafish (Danio rerio). The last project aims at aligning single-cell multi-omics data, such as gene expression, chromatin accessibility, and DNA methylation, using reliable, fast, and scalable approaches based on optimal transport.

Nourridine Siewe, Rochester Institute of Technology 

Title: TGF-β inhibition can overcome cancer primary resistance to PD-1 blockade: a mathematical model

Abstract: Background and methods. Immune checkpoint inhibitors have demonstrated, over the recent years, impressive clinical response in cancer patients, but some patients do not respond at all to checkpoint blockade, exhibiting primary resistance. Primary resistance to PD-1 blockade is reported to occur under conditions of immunosuppressive tumor environment, a condition caused by myeloid derived suppressor cells (MDSCs), and by T cells exclusion, due to increased level of T regulatory cells (Tregs). Since TGF-β activates Tregs, TGF-β inhibitor may overcome primary resistance to anti-PD- 1. Indeed, recent mice experiments show that combining anti-PD-1 with anti-TGF-β yields significant therapeutic improvements compared to anti-TGF-β alone.

Results: The present paper introduces two cancer-specific parameters and, corre- spondingly, develops a mathematical model which explains how primary resistance to PD-1 blockade occurs, in terms of the two cancer-specific parameters, and how, in combination with anti-TGF-β, anti-PD-1 provides significant benefits. The model is represented by a system of partial differential equations and the simulations are in agreement with the recent mice experiments. In some cancer patients, treatment with anti-PD-1 results in rapid progression of the disease, known as hyperprogression dis- ease (HPD). The mathematical model can also explain how this situation arises, and it predicts that HPD may be reversed by combining anti-TGF-β to anti-PD-1. Conclusion. The model is used to demonstrate how the two cancer-specific parameters may serve as biomarkers in predicting the efficacy of combination therapy with PD-1 and TGF-β inhibitors.

John Tyson, Virginia Tech 

Title: Time-keeping and decision-making in the cell cycle: a dynamical-systems perspective

Abstract: Cell growth, DNA replication, mitosis and division are the fundamental processes by which life is passed on from one generation of eukaryotic cells to the next. The eukaryotic cell cycle is intrinsically a periodic process but not so much a ‘clock’ as a ‘copy machine,’ making new, nearly identical copies (daughter cells) as warranted. Cells growing under ideal conditions divide with clock-like regularity, just like the departmental copy machine runs non-stop during exam periods. However, if the copy machine suffers a paper jam or the cell suffers a block to DNA synthesis, neither machine will progress to the next stage of the cycle until the damage is repaired. These ‘decisions’ (to exit and re-enter the copying cycle) are essential to maintain the mechanical integrity of the copier, in particular, the integrity of the cell’s genome from generation to generation. A crucial challenge for molecular cell biologists in the 1990’s was to unravel the genetic and biochemical mechanisms of cell cycle control in eukaryotes. Central to this effort were biochemical studies of the clock-like regulation of ‘mitosis promoting factor’ during synchronous mitotic cycles of fertilized frog eggs and genetic studies of the switch-like regulation of ‘cyclin-dependent kinases’ in yeast cells. In this talk I will delve into the complexities of cell cycle regulation by mathematical modeling of the molecular regulatory networks of cell cycle ‘clocks’ and ‘switches.’

References:
J.J. Tyson & B. Novak, Time-keeping and decision-making in the cell cycle, Interface Focus 12:20210075 (2022).
B. Novak & J.J. Tyson, Mitotic kinase oscillation governs the latching of cell cycle switches, Current Biology 32:1-6 (2022).

Matthew Wascher, University of Dayton
Title: Monitoring disease transmission and prevalence in a population under repeated testing
Abstract:  In this talk, I will describe a statistical methodology developed as part of the COVID-19 transmission monitoring efforts of The Ohio State University (OSU) and which is designed for monitoring disease transmission and prevalence in a population where individuals undergo repeated longitudinal testing and upon testing positive are subsequently isolated. We show that under such a scheme, naive estimation techniques may produce biased estimates of disease prevalence. Our method avoids this bias by incorporating a transmission model and using ideas from survival analysis. The other important novelty of our method is that it allows for changes in transmission dynamics and human behavior through changes in the model parameters without rendering the model computationally prohibitive. We demonstrate the performance of our model on both synthetic data and real SARS-CoV-2 testing data collected at the OSU Columbus campus. This is joint work with Patrick Schnell, Wasiur Khudabukhsh, Greg Rempala, Joe Tien, and Mikkel Quam.

Contributed Talks

Linh Huynh,  University of Utah
Title: Harnessing noise to parse out birth and death rates from population size time series data
Abstract: Models of population dynamics are usually formulated and analyzed with net growth rates. However, separately identifying birth and death rates is significant in various biological applications such as disambiguating (1) exploitation vs. interference competition in ecology, (2) bacteriostatic vs. bactericidal antibiotics in clinical treatments, and (3) enhanced-fecundity vs. reduced-mortality mechanisms in drug resistance. In each of these three contexts, the mechanisms are different, but could be manifest in the same mean-field population size.

In this talk, I will discuss a nonparametric method that utilizes stochastic fluctuations to extract birth and death rates from population size time series data. I will demonstrate the method on logistic growth to study density dependence, but the method can be applied to general birth-death processes and does not require a priori assumptions on the rates. I will also discuss how to implement the theory on sample data and our estimation error analysis. This talk is joint work with Peter Thomas (Case Western Reserve University) and Jacob Scott (Cleveland Clinic).

Wasiur KhudaBukhsh, University of Nottingham
Title: Multiscale Approximations in Chemical Reaction Networks
Abstract: The talk will focus on a particular area of applied mathematics studying 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 popula- tion 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 introduce, with the help of a number of examples, a probabilistic technique to derive multiscale approximations. I will then describe how such approximations could be used for the purpose of optimization and statistical learning. The talk will be fairly nontechnical, and no prior knowledge biology is required.

Lloyd Lee, University of Auckland
Title: Emergence of broad cytosolic Ca2+ oscillations in the absence of CRAC channels: A model for CRAC-mediated negative feedback on PLC and Ca2+ oscillations through PKC
Abstract: The role of Ca2+ released-activated Ca2+ (CRAC) channels mediated by ORAI isoforms in calcium signalling has been extensively investigated. It has been shown that the presence or absence of different isoforms has a significant effect on Store Operated Calcium Entry (SOCE). Yoast et al. [Nature Communications, 11(1), 2444 (2020)] showed that, in addition to the reported narrow-spike oscillations (whereby cytosolic calcium decreases quickly after a sharp increase), ORAI1 knockout HEK293 cells were able to oscillate with broad-spike oscillations (whereby cytosolic calcium decreases in a prolonged manner after a sharp increase) when stimulated with a muscarinic agonist. This suggests that Ca2+ influx through ORAI-mediated CRAC channels negatively regulates the duration of Ca2+ oscillations. We hypothesize that, through the activation of protein kinase C (PKC), ORAI1 negatively regulates phospholipase C (PLC) activity to decrease inositol 1,4,5-trisphosphate (IP3) production and limit the duration of agonist-evoked Ca2+ oscillations. Based on this hypothesis, we construct a new mathematical model, which shows that the formation of broad-spike oscillations is highly dependent on the absence of ORAI1. Predictions of this model are consistent with the experimental results.

Meaghan Parks, Case Western Reserve University School of Medicine
Title: Stochastic Model of Alzheimer’s Disease Progression Using Two-State Markov Chains
Abstract: In 2016, Hao and Friedman developed a deterministic model of Alzheimer’s disease progression using a system of partial differential equations. This model describes the general behavior of the disease, however it does not incorporate the molecular and cellular stochasticity intrinsic to the underlying disease processes. Here we extend the Hao and Friedman model by modeling each event in disease progression as a stochastic Markov process. This model identifies stochasticity in disease progression, as well as changes to the mean dynamics of key agents. We find that the pace of neuron death increases whereas the production of the two key measures of progression, Tau and Amyloid beta proteins, decelerates when stochasticity is incorporated into the model. These results suggest that the non-constant reactions and time-steps have a significant effect on the overall progression of disease.

Ngoc Anh Phan, University of Iowa
Title: Mixed mode oscillations in three-timescale coupled Morris-Lecar neurons
Abstract: One of the complex oscillatory dynamics frequently observed in multiple-timescale problems is mixed mode oscillations (MMOs) with large-amplitude oscillations interspersing small-amplitude oscillations (SAOs). It has been well known that SAOs in two-timescale problems emerge from either the canard explosion associated with folded nodes or a slow passage through a fast subsystem delayed-Andronov-Hopf. In the three-timescale context, these two separated mechanisms can coexist and interact at a canard-delayed-Hopf (CDH) singularity to produce MMOs. In this talk, we will discuss the role of the CDH singularity in the robustness of MMOs in a three-timescale coupled Morris-Lecar neuronal system. We find that if the CDH exists, MMOs are robust to timescale variations. In contrast, in the absence of CDH, complicated transitions occur between MMOs and non-MMOs.

Wenjing Zhang, Texas Tech University
Title: Studying Tuberculosis Progression via Sensitivity, Bifurcation, and Stochastic Analysis
Abstract: Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steady-state transitions can be the occurrence of transcritical and saddle-node bifurcations. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyses on transcritical bifurcation conditions and saddle-node bifurcation conditions. The sensitivity analysis results suggest that the macrophage’s apoptosis rate is the most significant factor affecting the transition in disease outcomes. This result agrees with the discovery that the programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interplay. Further, bifurcation analysis unfolds various disease outcomes induced by the variation of macrophage apoptosis rate, which depend on the number of bacteria engulfed and released by macrophages. We then develop an It^o SDE model, which considers demographic variations at the cellular level to study stochastic fluctuations at the cellular level.

Xinyue Zhao, Vanderbilt University
Title: Bifurcation Analysis of Critical Values for Wound Closure Outcomes in Wound Healing Experiments
Abstract: In this talk, I will present a nonlinear partial differential equation containing a nonlocal advection term and a diffusion term to study wound closure outcomes in wound healing experiments. There is an extensive literature of similar models for wound healing experiments. In our work, we study the character of wound closure in these experiments in terms of the sensing radius of cells and the force of cell-cell adhesion. We prove a bifurcation result which differentiates uniform closure of the wound from nonuniform closure of the wound, based on a critical value $\lambda_\star$ of the force of cell-cell adhesion parameter $\lambda$. For $\lambda < \lambda_\star$ the steady state solution $u\equiv1$ of the model is stable and the wound closes uniformly. For $\lambda > \lambda_\star$ the steady state solution $u\equiv1$ of the model is unstable and the wound closes nonuniformly. We provide numerical simulations of the model to illustrate our results. This is a joint work with Prof. Glenn Webb.

Poster Session 1

Seokjoo Chae, KAIST/IBS
Title: Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping 

Yi Fu, University of California, San Diego
Title: Comparison Theorems for Stochastic Chemical Reaction Networks

Chunyi Gai, University of British Colombia
Title: Localized outbreaks in SIR model with diffusion

Eui Min Jeong, Institute for Basic Science (IBS)
Title: Noise attenuation and ultrasensitivity in biological oscillators utilizing the multiple transcriptional repression mechanism

Hyeontae Jo, Institute for Basic Science
Title: Density Physics-Informed Neural Network: Inferring Sources of Cell-to-Cell Heterogeneity in Signaling Dynamics

Hyun Kim, Institute for Basic Science
Title: Enhancing dimensionality reduction in single-cell RNA sequencing: a novel tool for improved preprocessing and noise filtering

Jin Young Kim, Pohang university of science and technology
Title: Stochastic aggregation models in 2D and 3D spaces to describe Liquid-Liquid Phase Separation (LLPS)

Jinsu Kim, POSTECH
Title: Stochastic epigenome models reveal in vivo DNA cooperativity

Donggu Lee, Konkuk University
Title: Mathematical model of STAT signaling pathway in cancer development and optimal control approaches

Junho Lee, Konkuk University
Title: Atorvastatin-mediated rescue of cancer-related cognitive changes in combined anticancer therapies

Dongju Lim, Institute for Basic Science (IBS)
Title: Mood Prediction for Bipolar Disorder Patient with Sleep Pattern Information

Jingyi Liu, University of Notre Dame
Title: Stability of periodic solutions for the plaque formation problem

Yun Min Song, KAIST / IBS
Title: Universally valid reduction of multiscale stochastic biochemical systems with simple non-elementary propensities

Stanley Nicholson, Brown University
Title: Linear Systems Analysis of Molecular Dynamics

Farshad Shirani, Georgia Institute of Technology
Title: Spatio-Temporal Gamma Oscillations in a Mean Field Model of Electroencephalographic Activity in the Neocortex

Zhiyuan Yu, Case Western Reserve University
Title: Media-driven adaptive human behavior can affect pandemic outcomes

Adriana Zanca, The University of Melbourne
Title: Cellular mechanisms of re-epithelialisation

Poster Session 2

Amanda Alexander, University of Houston
Title: Population ratio control in auxotrophic bacterial consortia 

Richmond Crisostomo, University of Montpellier, France and Abdus Salam International Centre for Theoretical Physics Trieste, Italy
Title: From Neurons to Neural Networks: Leaky-Integrate-and Fire Computational Models for Spiking Dynamics

Francis Baffour-Awuah Junior, Florida State University
Title: A mathematical model of sepsis progression using longitudinal proteomic data

Hyukpyo Hong, Institute for Basic Science
Title: Systematic inference identifies a major source of heterogeneity in non-Markovian cell signaling dynamics

Hyeontae Jo, Institute for Basic Science
Title: Density Physics-Informed Neural Network: Inferring Sources of Cell-to-Cell Heterogeneity in Signaling Dynamics

Jaewook Joo, Cleveland Clinic/Case Western Reserve Univ.
Title: Rigorous results of limiting behaviors of total tumor size under cyclic intermittent therapy for the system of reversible phenotype-switchable tumor cells

Jinyoung Kim, Pohang University of Science and Technology
Title: Stochastic aggregation models to describe the qualitative differences in 2D and 3D spaces

Minjoon Kim, Postech
Title: Chemical reaction network modeling of the Boltzmann equation

Youngsuk Ko, Konkuk University
Title: A stochastic modeling study of EVD outbreak and anlaysis of delay-induced risks

Gordon R. McNicol, University of Glasgow
Title: A bio-chemo-mechanical continuum model for focal adhesion and ventral stress fibre formation

Louis M. Pecora, University of Maryland, College Park
Title: Statistics of Reservoir Computers

Merlin Pelz, University of British Columbia
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-D

Paco Castaneda Ruan, The University of Auckland
Title: Coexistence of two different calcium oscillatory mechanisms in immune system cells 

Hannah Scanlon, Duke University
Title: Microtubule Dynamics and Cargo Localization in Cellular Response to Axon Injury

Connor Shrader, University of Central Florida
Title: Predation and Harvesting in Spatial Population Models

Laura F. Strube, University of Pittsburgh
Title: Dynamical systems modeling of JAK/STAT signaling in macrophages: Parameter analysis to understand network sensitivity to signaling context

Lihong Zhao, University of California, Merced
Title: Modeling and Global Sensitivity Analysis of Strategies to Mitigate Covid-19 Transmission on a Structured College Campus