Minisymposia: MS05

Wednesday, July 19 at 10:30am

Minisymposia: MS05

Connecting mathematical models of pattern formation & organization at cell and/or tissue level with experimental results

Organized by: Diana White

  • Kelsey Gasior University of Notre Dame (Department of Applied and Computational Mathematics and Statistics)
    "Understanding the influence of cell-cell contact and TGF-β signaling on the epithelial mesenchymal transition in MCF7 breast carcinoma cells"
  • The epithelial mesenchymal transition (EMT) is a process by which epithelial cells lose their characteristic adhesion and gain the migratory properties associated with mesenchymal cells. Triggered by exogenous factors from the surrounding microenvironment, EMT produces phenotypic and behavioral changes that are maintained even after the cell migrates away from a tumor to form a metastasis. Within the complex system of intracellular signaling pathways associated with EMT, we identify a feedback loop between E-cadherin, a transmembrane protein involved in cellular adhesion, and Slug, a transcription factor associated with the mesenchymal phenotype. Here we present a simple mathematical model using ordinary differential equations (ODEs) that examines the relationship between E-cadherin and Slug during EMT in response to exogenous pro-epithelial (cell-cell contact) and pro-mesenchymal (TGF-β signaling) factors. A cell’s ability to maintain the mesenchymal phenotype after leaving the tumor microenvironment suggests that there is a bistable switch underlying EMT. We hypothesize that a bistable switch due to a loss of cell-cell contact is reversible, while a switch due to TGF-β activation is irreversible. This model shows how changes in the tumor microenvironment and intracellular changes via signaling pathways are closely linked and the loss of cell-cell contact and activation of the TGF-β must work together to allow some cells to undergo EMT. The results of this model for E-cadherin and Slug levels are then compared to the experimental data recently generated using MCF7 breast carcinoma cells. Experiments examined changes in cell-cell contact and exogenous TGF-β and data were gathered using qPCR, flow cytometry, and immunocytochemistry (ICC). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments but struggles to predict the expression of either factor in high confluence environments. Ultimately, this work establishes a framework for modeling the influence of multiple factors on EMT, while also highlighting the issues that arise when comparing experimental results to theoretical predictions.
  • Ginger Hunter Clarkson University (Biology)
    "Investigating the rules of cell contact-mediated tissue patterning using the Drosophila peripheral nervous system"
  • The correct spatial organization of cell types within a tissue is critical for tissue development and homeostasis. The spot pattern of sensory bristles on the dorsal thorax of the fruit fly Drosophila Melanogaster is an example of a self-organizing tissue, and failure to form and organize sensory bristles leads to impaired function of the peripheral nervous system. Experimental and theoretical results support a role for cell protrusion based, contact mediated, signaling mechanisms in the spacing of sensory bristle precursors during patterning stages. Here, we present recent results from an RNAi-mediated genetic screen designed to identify these signaling mechanisms. An expected major phenotype of the RNAi screen is the disruption of the tissue-wide sensory bristle pattern. In order to facilitate our analysis, we have developed a quantitative, computational approach towards the classification of control and mutant spot patterns. Our approach involves the detection of sensory bristle precursors in a patterning tissue, followed by extraction of features that facilitate the reproducible measurement and detection of different bristle organizations. The results of these studies so far have identified a number of genes whose knockdowns result in defects in pattern formation. Furthermore our classification system has successfully been used to identify mutant spot patterns. We anticipate that results from our screen will identify new mechanisms of cell-cell communication during peripheral nervous system patterning, as well as new tools for the quantitative analysis of spot patterns in vivo.
  • Veronica Ciocanel Duke University (Mathematics)
    "Modeling and data analysis for actin-myosin dynamics and organization"
  • Actin filaments are polymers that interact with myosin motor proteins and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the reproductive system of the roundworm C. elegans, we use an agent-based modeling framework to simulate interactions between actin filaments and myosin motor proteins inside cells. We develop techniques based on topological data analysis to understand time-series data extracted from these filament network interactions, as well as from fluorescence experiments. These measures allow us to compare the filament organization resulting from myosin motors with different properties. In particular, we have studied how different myosin motor proteins may interact to regulate various actin organizations, and provided insights into parameters that may regulate structures observed in vitro and in vivo.
  • Diana White Clarkson University (Department of Mathematics)
    "Understanding the regulation of growth and shedding of disks in the rod cells of zebrafish"
  • Retinal photoreceptor cells, rods and cones, in the eye convert light energy into electrical signals that stimulate sight. In humans, peripherally located rods are important for night vision, while centrally located cones are responsible for daytime/color vision. Rods consist of a rod outer segment (ROS), inner segment, cell body and synaptic terminal. The ROS, consisting of stacked, discrete membraneous discs, undergoes a process of continuous renewal in which newly constructed discs are added at the base (growth) and the oldest discs are shed from the tip. In normal/healthy eyes, the ROS maintains a homeostatic length by balancing growth and shedding. How this balance is controlled is unknown. New experiments have shown that ROS, when made to grow faster with the growth factor rheb, do not accelerate shedding to offset increased growth. Here, we develop and analyze a model of ROS length control, to help provide insight into (1) normal cell dynamics, and (2) the overshoot of homeostatic length when rheb is added. A 3-D ODE model is used to describe the transitions of disks from compartments corresponding to disk addition at the base, disk translocation along the ROS when mature, and those disks that are shed and undergo phagocytosis.

The role of the microenvironment in controlling cell phenotypic decisions across scales

Organized by: Laura F. Strube, Adam L. MacLean

  • Tian Hong The University of Tennessee, Knoxville (Biochemistry & Cellular and Molecular Biology)
    "Diverse dynamical systems for understanding nongenetic heterogeneity of cells"
  • The phenotypic heterogeneity within cell populations, both signal-induced and self-generated, plays crucial roles in development, cancer progression, and drug resistance. However, our fundamental understanding of these phenomena at the dynamical systems level remains limited. Epithelial-mesenchymal transition (EMT) is one example of a cellular process that triggers heterogeneity-driving phenotypic changes. While multiple intermediate/hybrid EMT states have been observed in development and diseases, it is still unclear whether these intermediate states represent transient states for cells en route to M-like cells or stable phenotypes representing ordered attractors between E and M states. Our recent single-cell experiments with human mammary epithelial cells and analysis of published data have shown that both transient states and ordered attractors can explain intermediate EMT states. Additionally, our mathematical models of widespread RNA-decay regulatory networks have demonstrated that slow oscillations with diverging periods can drive self-generated heterogeneity in cell populations, achieving phenotypic diversity and multimodal gene expression patterns more robustly than commonly conceptualized multistability systems. This theoretical framework provides insight into the observations of heterogeneity in progenitor cells and cancer cells. In summary, our work has revealed diverse dynamical systems underlying nongenetic heterogeneity of cells, which were previously underappreciated.
  • MeiLu McDermott University of Southern California (Department of Biology)
    "Characterizing Intermediate States of Epithelial-Mesenchymal Transition in Cancer through Single-Cell RNA Sequencing and Mathematical Modeling"
  • The epithelial-mesenchymal transition (EMT) is a primary biological mechanism of cancer metastasis, involving cells transforming from an adhesive epithelial phenotype to a migratory mesenchymal phenotype. Recent research has identified intermediate EMT states, characterized by hybrid phenotypes experimentally shown to be metastatic. This comparative study investigates these hybrid EMT cells across multiple cancers using single-cell RNA sequencing data. We identified genes upregulated in multiple intermediate EMT states across cancers, particularly those related to β-catenin regulation. Additionally, we developed a mathematical model using ordinary differential equations (ODEs) to describe EMT rates and fitted the model to scRNAseq data. Incorporating data from multiple cancer types, our ODE model provides a discovery tool for identifying genes associated with stabilizing the existence of metastatic, hybrid EMT cells.
  • Ken J. Oestreich The Ohio State University School of Medicine (Microbial Infection and Immunity)
    "Regulation of T helper cell programming by the transcription factor Aiolos"
  • CD4+ cytotoxic T lymphocytes, or CD4-CTLs, comprise an effector subset capable of performing cytotoxic functions normally associated with CD8+ T and Natural Killer cells. CD4-CTLs play critical roles in many immunological contexts, including protective anti-viral responses to influenza infection. Despite their well-documented importance to healthy immune responses, the regulatory mechanisms that underlie their formation remain unclear. We have identified the Ikaros transcription factor Aiolos as a novel repressor of cytoxic programming in CD4 T cells. We demonstrate that Aiolos deficiency results in increased CD4-CTL responses in the lungs of influenza-infected mice, as assessed by elevated expression of Granzyme B and Perforin, as well as the CTL marker NKG2A/C/E. We further find that Aiolos-deficient CD4-CTLs exhibit increased expression of transcription factors associated with cytotoxic programming, including Eomes and Blimp-1. Mechanistically, we demonstrate that Aiolos-deficient cells have a heightened sensitivity to IL-2/STAT5 signaling due to enhanced expression of the IL-2 cytokine receptor and that this translates into increased STAT5 association at regulatory regions of hallmark CD4-CTL genes. Intriguingly, the STAT5 motif partially overlaps with that of the core Aiolos DNA binding motif, suggesting that Aiolos may function to broadly antagonize STAT5 activity throughout the genome. Collectively, this work establishes Aiolos as a novel repressor of CD4-CTL differentiation and highlights its potential as a therapeutic target for enhancing anti-viral immune responses.
  • Rachel A. Gottschalk University of Pittsburgh (Department of Immunology)
    "Modeling cytokine-induced signaling features and sensitivity to network variation"
  • Cells choose environment-specific functions by integrating stimuli through biochemical signaling pathways. Predicting functional outcomes of signaling is complicated by the complexity of network interactions and the diversity of signals which converge on a relatively small number of intracellular components. For example, over 50 cytokines and growth factors are distinguished by the JAK/STAT signaling pathways, comprised of 4 JAKs (Janus kinases) and 7 STATs (signal transducers and activators of transcription), to produce stimulus-specific cellular functions. In many cases, opposing phenotypes (pro- vs. anti-inflammatory) depend on the same STAT proteins to induce distinct patterns of gene expression. Predicting the relationship between signaling conditions and STAT phosphorylation profiles and then linking them to downstream gene expression remains an unaddressed challenge. We have developed a mechanistic-to-machine learning computational workflow that links STAT phosphorylation trajectories to global gene expression patterns via an ODE-simulated, rule-based model and machine learning. Our model is parameterized with STAT phosphorylation data from IL-6 and IL-10 stimulated macrophages. Machine learning is used to link these profiles to transcriptomic data under the same stimulation conditions. Parameter analysis of our mechanistic model identified JAK2 as having STAT-specific impacts on dynamic signaling features. Using the full computational workflow, we predicted and validated the impact of selective JAK2 inhibition on downstream gene expression and identified clusters of dynamically regulated genes that were sensitive and insensitive to JAK2 alterations. Thus, this work is an important step towards the use of multi-level prediction models to link stimuli to gene expression and to identify the effect of network perturbations. We are currently exploring sensitivity analysis approaches to derive biological insight from quantitative parameter relationships, with an interest in predicting parameters and parameter ratios that are highly sensitive to variation. Our objective is to enhance our understating of how altered expression of signaling network components impacts cellular responsiveness to cytokines and JAK inhibition in physiologically and clinically relevant contexts, such as cancer and human genetic variation.

Population-level impacts of ecological interactions across scales

Organized by: Amanda Laubmeier

  • Rebecca Everett Haverford College (Department of Mathematics and Statistics)
    "Nutrient driven dynamics of ecosystem diseases"
  • Autotrophs such as algae play an essential role in the cycling of carbon and nutrients, yet disease-ecosystem relationships are often overlooked in these dynamics. The availability of elemental nutrients like nitrogen and phosphorus impacts infectious disease in autotrophs, and disease can induce reciprocal effects on ecosystem nutrient dynamics. We use a mathematical model to illustrate the impact of disease-ecosystem feedback loops on both disease and ecosystem nutrient dynamics.
  • Mohammad Mihrab Uddin Chowdhury Texas Tech University (Department of Mathematics and Statistics)
    "Understanding Bsal Transmission Dynamics to Safeguard North American Salamander Populations"
  • Batrachochytrium Salamandrivorans (Bsal), a deadly fungal pathogen, is a significant threat to the survival of salamander populations in North America. It has led to the extinction of some salamander species in Europe and endangered others. Bsal's ability to spread through multiple routes with approximately zero recovery and high mortality underscores the crucial need for effective control measures. We developed a system of ordinary differential equations that incorporates direct and environmental transmission pathways across two spatial scales: aquatic and terrestrial environments. Alongside different routes of transmissibility, our study takes into account the environmental zoospore load, skin spore levels, population density, and temperature fluctuations. By simulating different scenarios and analyzing the results, the study aims to offer insights into effective control measures for reducing transmission and preventing epidemic outbreaks.
  • Joshua C. Macdonald Tel Aviv University (Faculty of Life Sciences)
    "Forward hysteresis and Hopf bifurcation in a NPZD model with application to harmful algal blooms"
  • Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) models, describing the interactions between phytoplankton, zooplankton systems and their ecosystem, are used to predict their ecological and evolutionary population dynamics. These organisms form the base two trophic levels of aquatic ecosystems. Hence understanding their population dynamics and how disturbances can affect these systems is crucial. Here, starting from a base NPZ modeling framework, we incorporate the harmful affects of phytoplankton overpopulation on zooplankton - representing a crucial next step in harmful algal bloom (HAB) modeling - and split the nutrient compartment to formulate a NPZD model. We then mathematically analyze the NPZ system upon which this new model is based, including local and global stability of equilibria, Hopf bifurcation condition and forward hysteresis, where the bi-stability occurs with multiple attractors. Finally, we extend the threshold analysis to the NPZD model, which displays forward hysteresis with bi-stability, and examine ecological implications after incorporating seasonality and ecological disturbances. Ultimately, we quantify ecosystem health in terms of the relative values of the robust persistence thresholds for phytoplankton and zooplankton and find (i) ecosystems sufficiently favoring phytoplankton, as quantified by the relative values of the plankton persistence numbers, are vulnerable to both HABs and (local) zooplankton extinction (ii) even healthy ecosystems are extremely sensitive to nutrient depletion over relatively short time scales.
  • Omar Saucedo Virginia Tech (Mathematics)
    "The impact of host movement on mosquito-borne disease dynamics"
  • Mosquitos are known for being a source of infectious diseases and are cause of great concern within the public health community. Throughout the world, there are a variety of mosquito species that are associated with different mosquito-borne pathogens. Diseases such as malaria have surfaced in areas where they previously have not been detected, and the incidence of these diseases have been steadily increasing. A better understanding of mosquito-borne pathogens is needed as this poses a severe threat to many communities. In this talk, we will explore how epidemiological and ecological features influence mosquito-borne disease dynamics via a multi-patch compartmental model.

Mathematical models of community: a journey through the scales

Organized by: Alexander Browning, Sara Hamis

  • Pierre Haas Max Planck Institute for the Physics of Complex Systems (Biological Physics)
    "Impossible ecologies: interaction networks and stability of coexistence in ecological communities"
  • Does an ecological community allow stable coexistence? In particular, what is the interplay between stability of coexistence and the network of competitive, mutualistic, and predator-prey interactions between the species of the community? These are fundamental questions of theoretical ecology, and, since meaningful analytical progress is generally impossible for communities of more than two species, they must be addressed statistically, as pioneered by May four decades ago. In this talk, I will thus show how we addressed this interplay between stability of coexistence and the network of interaction types by sampling Lotka–Volterra model parameters randomly and computing the probability of steady-state coexistence being stable and feasible in Lotka–Volterra dynamics. Surprisingly, our analysis, covering all non-trivial networks of interaction types of N less than or equal to 5 species, revealed 'impossible ecologies', very rare non-trivial networks of interaction types that do not allow stable and feasible steady-state coexistence. I will classify these impossible ecologies, and then prove, somewhat conversely, that any non-trivial ecology that has a possible subecology is itself possible. This theorem highlights the 'irreducible ecologies' that allow stable and feasible steady-state coexistence, but do not contain a possible subecology. I will conclude by showing the classification of all irreducible ecologies of N less than or equal to 5 species which indicates that the proportion of non-trivial ecologies that are irreducible decreases exponentially with the number N of species. Our results thus suggest that interaction networks and stability of coexistence are linked crucially by the very small subset of ecologies that are irreducible.
  • Aminat Yetunde Saula University of Bath (Department of Mathematical Sciences)
    "Immune cell-bacteria interactions in tuberculosis"
  • Tuberculosis (TB) is the second deadliest infectious disease in the world after COVID-19, with over 10 million people infected yearly. Although the causative agent - Mycobacterium tuberculosis (Mtb) has long been known, TB bacteria are still able to evade protective immune responses. Herein, as a response to TB infection, immune cells self-organise to form TB granulomas and isolate bacteria within their structures. While TB granulomas are capable of slowing or halting the growth of Mtb, it also provides a survival niche from which bacteria may disseminate. Hence, an increased understanding of the disease in the lung where the bacteria primarily attack is needed. In this work, we integrate the mechanisms involved in immune cell-bacteria interaction in tuberculosis following an established hybrid individual-based model for the development of a continuum model counterpart. The continuum model consists of a system of partial differential equations (PDEs) describing the dynamics of TB granulomas. The numerical and analytical results of the model allow the determination of different conditions under which the infection clears early, stays latent, or progresses to active disease. Our findings are compared to the results obtained using the hybrid individual-based model, where differential equations are used to track the diffusion of molecules and the individual-based model component facilitates the tracking of cellular interaction, thus, allowing the study of localised spatial effects.
  • Moriah Echlin Tampere University (Medicine and Health Technology)
    "Characterizing the Impact of Communication on Cellular and Collective Behavior Using a Three-Dimensional Multiscale Cellular Model"
  • Communication between cells enables the coordination that drives structural and functional complexity in biological systems. In both single and multicellular organisms, systems of communication have evolved for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell–cell communication. While research has elucidated the form and function of cell–cell communication in many biological systems, our knowledge is still limited by confounding effects from other biological phenomena as well as the bias of evolution. In this work, our goal is to push forward the context-free understanding of what impact cell–cell communication can have on cellular behavior at the cell and population levels. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. To explore communication, we focus on two key communication parameters: the effective distance at which cells can interact and the threshold at which the signal receptor is activated. We find that cell–cell communication can be divided into six different categories along the parameter axes, three asocial and three social. We characterize behavior at both the cellular and population level and show clear shifts in behavior between the different categories of communication. With this work, we also highlight the surprising diversity and flexibility in the responses of different cellular backgrounds to the same communication conditions. Thus, we describe some of the effects that cell-cell communication can introduce to cellular populations which can be fine-tuned for function via engineering, artificial modification, or natural selection.
  • Daniel Strömbom Lafayette College (Department of Biology)
    "Facilitating the emergence of collective biological controls to combat the spotted lanternfly and similar invasive pests"
  • The spotted lanternfly (Lycorma delicatula) is an emerging global invasive insect pest. Due to a lack of natural enemies in regions where it is invasive human intervention is required. Standard control measures have been extensively applied but the spread and growth of the population continues, and a recent study indicates that currently used approaches may be futile and suggests that non-standard approaches are necessary. Recently the idea of bird based biological controls has re-emerged and shown to be effective in a number of studies involving native birds and native pests. However, whether birds can be effective in dealing with invasive pests is unclear. In particular, if the invaders are occasionally toxic, it may take many generations before birds or other vertebrates will start contributing to controlling it naturally, if ever. Unless, perhaps, if the birds are effective social learners and the toxicity of the invaders is rare. For example, the Great Tit (Parus major) is an exceptional social learner and have been reported to eat lanternfly that have not fed on their toxicity inducing preferred host plant (Ailanthus altissima), but avoid eating them if they have. Here we introduce a simple mathematical model for social learning in a great tit-like bird to investigate the conditions for the emergence of a collective biological control of a pest that is occasionally toxic, like the lanternfly. We find that the relationship between the social observation rate and the proportion of toxic lanternfly effectively dictate when a collective biological control will emerge, and when it will not. We also implemented the mathematical social learning model into a spatially explicit model of collective motion in bird-like animals to investigate the conditions under which lanternfly eating would emerge in the simulated flocks as a function of lanternfly toxicity. We found that the spatially explicit model reproduces key predictions of the mathematical model over a range of parameters. Our work suggests that social birds may be useful in management of the spotted lanternfly, and that to facilitate the emergence of lanternfly eating communities of social birds, removal of the toxicity inducing preferred host of the lanternfly (Ailanthus altissima) should be a priority.

Immunobiology and Infection Subgroup Minisymposium 2023

Organized by: Morgan Craig, Daniel Reeves

  • E. Fabian Cardozo-Ojeda Fred Hutchinson Cancer Center (Vaccine and Infectious Disease Division)
    "HIV-1 reservoir dynamics during hematopoietic stem cell transplantation"
  • The five known cases of antiretroviral therapy (ART)-free HIV long-term remission have resulted in allogeneic hematopoietic stem cell transplantation (allo-HSCT). In these cases, allo-HSCT may have reduced HIV DNA and HIV RNA levels via conditioning or graft-vs-reservoir (GvR) effects. The international consortium IciStem investigates the potential for HIV cure via allo-HSCT. In this talk, I will present our assessment of the impact of conditioning and GvR effect in the control of HIV in IciSTEM participants using ordinarily differential equation models with a nonlinear mixed-effects approach. We explore two mechanistic assumptions on the impact of allo-HSCT on reservoir reduction: infected cells are depleted (1) by conditioning only or (2) by conditioning and by GvR directly proportional to the donor T-cell chimerism levels. We fit models to longitudinal CD4+ T cell concentrations, multiple viral levels, and anti-HIV antibody levels in blood using interpolated T-cell chimerism levels from 22 IciStem participants. Using model selection theory, we found that a model with conditioning and depletion of cells proportional to the observed T-cell chimerism best explains the timing and magnitude of HIV reduction dynamics. Our model predicts that T cell proliferation allows HIV reservoir levels to recover in response to cell loss during conditioning; therefore, the GvR effect is a primary driver of reservoir reduction dynamics after allo-HSCT.
  • Jessica M. Conway Penn State (Mathematics)
    "Modeling on-demand PrEP regimen to prevent HIV transmission"
  • In 2010, analysis of the iPrEx study results demonstrated that daily dosing with antiretroviral therapy (ART) in advance of exposure to HIV, termed pre-exposure prophylaxis (PrEP), can significantly reduce the risk of HIV transmission and population spread. However, daily adherence to a drug regimen can be difficult to maintain and may come with side-effects. In contrast, the IPERGAY study published in 2015 suggested that short-term use around the time of exposure may be just as effective at reducing HIV risk as daily use. Here we investigate short-term use, termed 'on-demand' or 'event-based' PrEP. We aim to make model-based predictions of effective on-demand drug regimen. Focusing on transmission through sexual exposure, we incorporate a deterministic model of tissue-level pharmacokinetics and pharmacodynamics (PK/PD) of Truvada into a branching-process model of early HIV infection. Thus, we predict the risk of HIV transmission and risk reduction associated with dose size and timing relative to exposure. To evaluate effectiveness of dosing strategies, we simulate strategies by sampling a virtual population and performing extensive sensitivity analyses. Hence, we aim to identify practical dosing strategies that most effectively reduce risk of HIV transmission through sexual exposure.
  • Chapin S. Korosec York University, 4700 Keele St, Toronto, M3J 1P3, ON, Canada. (Modelling Infection and Immunity Lab, Mathematics and Statistics)
    "Within-host evolution of SARS-CoV-2: how often are de novo mutations transmitted?"
  • As of March 10th, 2023, the total number of reported SARS-CoV-2 infections reached over 676 million worldwide. Despite a relatively low mutation rate, the large number of infections has allowed for substantial genetic change in SARS-CoV-2, leading to a multitude of “variants of concern”. Utilizing recently determined mutations rates (per site replication), as well as within-host parameter estimates for hospitalized SARS-CoV-2 infections, we applied a stochastic transmission bottleneck model to describe the survival probability of rare de novo SARS-CoV-2 mutations. In the first part of this talk I will briefly discuss the significance and relevance of our within-host parameters published in ref.[1]. I will then discuss our un-published work on SARS-CoV-2 within-host evolution where we compute the survival probability of neutral muta-tions (no phenotypic effect), and various mutations affecting viral life history. We examine transmission bottlenecks of varying sizes, estimating which mutations are most likely to occur de novo and be transmitted during a single infection. This work offers a null model for SARS-CoV-2 substitution rates and predicts which aspects of viral life history are most likely to suc-cessfully evolve, despite low mutation rates and repeated transmission bottlenecks. [1]. C.S. Korosec et al., JTB, vol. 564, 2023.
  • Adnan Khan Lahore University of Management Sciences (Mathematics)
    "Modeling Antibiotic Resistance and Effective Dosing Regimens"
  • In this talk we will present models for in-vivo transfer of antimicrobial resistance and determine efficient antibiotic regimens in the presence of drug resistant bacteria. We consider resistance acquisition via horizontal gene transfer (HGT) which has been identified as primary mechanism for in-vivo drug resistance. It is known that three different mechanisms are responsible for HGT, these include conjugation, transformation, and transduction. We propose deterministic ODE based models for the three processes incorporating the unique pathways involved in each one. We will look at different antibiotic dosing protocols and show that periodic dosing at a constant level may not be successful in eradicating the bacteria. We set up an optimal control problem for successful antibiotic administration and then use a numerical optimization algorithm to determine the ’best’ antibiotic dosing strategy. We study the effects of varying different model parameters on the qualitative behavior of the optimal dosing. We compare our results to those in the literature.

Zoonotic Infectious Diseases Models

Organized by: Rocio Caja Rivera, Iona McCabe, Dana Pittman, Linda J. Allen

  • Holly Gaff Old Dominion University (Department of Biological Sciences)
    "Understanding Ticks and Tick-borne Diseases through Agent-based Modeling"
  • Tick-borne diseases are on the rise worldwide, and there is a lot of interest to reduce the burden of these diseases. Ticks and tick-borne pathogens are not well studied partly owing to their challenging biology. The dynamics of tick-borne pathogens includes multi-year systems of weather, habitat, and environmental factors plus the availability of hosts required for each life stage. Mathematical models provide an ideal tool to explore this type of complex system by implementing the dynamics that are known and exploring the potential additional components that are less understood. A series of agent-based models will be presented that investigate tick-borne disease dynamics, control, and geographic spread. Each model was based on field and lab data, and the output from each help to identify future experiments.
  • Kat Husar & Dana C. Pittman Duke University; Texas A&M University (School of Public Health Epidemiology and Biostatistics)
    "Lyme Disease Models of Tick-Mouse Dynamics with Seasonal Variation in Births, Deaths, and Tick Feeding"
  • Lyme disease is the most prevalent vector-borne disease in the United States impacting the Northeast and Midwest at the highest rates. Recently, it has become established in southeastern and south-central regions of Canada. Lyme disease is passed by the black-legged tick, Ixodes scapularis, infected with the Borrelia burgdorferi bacterium. One of the hosts most commonly fed on by I. scapularis is Peromyscus leucopus, colloquially known as the white-footed mouse. Understanding this parasite-host interaction is critical as P. leucopus is one of the most competent reservoirs for Lyme disease. The cycle of infection is driven by larvae feeding on infected mice that molt into infected nymphs and then transmit the disease to another susceptible host such as a mouse or human. Lyme disease in humans is generally caused by the bite of an infected nymph. The main aim of this investigation is to study how demographic and seasonal variation and diapause in tick births, deaths, and feedings impact the infection dynamics of the tick–mouse cycle. To account for delays in molting and reproduction in the tick life cycle, we begin by formulating a system of ordinary differential equations (ODEs) describing the transmission cycle between ticks and mice before exploring the use of delay differential equations (DDEs) with fixed delays. Several different tick feeding rates are discussed. We then formulate a new system of ODEs with a more realistic Erlang-distributed delay. We also account for seasonal changes through periodic parameters that depend on the season (spring, summer, fall, or winter). The ODE model is generalized to a new stochastic model with demographic and seasonal variability, a continuous-time Markov chain (CTMC). We calculate and discuss the relevance of the basic reproduction number, R0, for the ODE and DDE models in a constant environment and numerically compute it for the ODE model in a seasonal environment. We also determine the numerical sensitivity of R0, to the prevalence of infected nymphs and mice and to the density of infected nymphs to changes in the parameters in the seasonal ODE model . Lastly, we use the CTMC model to investigate the probability of Lyme disease emergence in a small infection-free population of ticks and mice when a few infected mice or nymphs are introduced. The probability of disease emergence is highly dependent on the season the infection is introduced and which species (ticks or mice) are introduced. The numerical results show that introduction of infected mice during the summer has the highest probability of sustained infection and disease emergence.
  • Katherine Royce Harvard University (Law School)
    "Mathematically predicting intermediate host species for emerging zoonoses"
  • Intermediate host species provide a crucial link in the emergence of zoonotic infectious diseases, serving as a population where an emerging pathogen can mutate to become human-transmissible. Identifying such species is thus a key component of predicting and mitigating future epidemics. Despite this importance, intermediate host species have not been investigated in much detail, and have generally only been identified by testing for the presence of pathogens in multiple candidate species. This talk will present a mathematical model able to identify likely intermediate host species for emerging zoonoses based on ecological data for the candidates and epidemiological data for the pathogen. The model accurately identifies potential intermediate hosts of the three emerging coronaviruses of the twenty-first century, predicting palm civets as intermediate hosts for SARS-CoV-1 and dromedary camels as intermediate hosts for MERS. Further, it suggests mink, raccoon dogs, and ferrets as probable intermediate host species for SARS-CoV-2. With the capacity to evaluate intermediate host likelihood among different species, researchers can focus testing for possible infection sources and interventions more effectively.
  • Iona McCabe; Kaia Smith University of California, Santa Barbara; Scripps College (Department of Mathematics; Department of Mathematics)
    "Stochastic Models of Zoonotic Avian Influenza with Multiple Hosts, Environmental Transmission, and Migration in the Natural Reservoir"
  • Avian influenza virus (AIV) is an infectious disease that circulates among wild bird populations and regularly spills over into domestic animals, such as poultry and swine. This spread raises the risk of a mutation resulting in a human-to-human-transmissible strain, which would pose a serious threat to public health. Mathematical modeling can be a powerful tool to mitigate the risks associated with these strains. Prior models have included factors such as multiple host populations, spillover into humans, environmental transmission, seasonality, and migration. We develop an ordinary differential equation (ODE) model that combines all of these factors, and we translate this into a stochastic continuous-time Markov chain (CTMC) model. We examine and compare the numerical trajectories of the disease using the ODE and CTMC models. Linear approximation of the ODE model near the disease-free solution leads to the basic reproduction number R0, a threshold for both the ODE and CTMC models. Linearization of the CTMC near the disease-free solution leads to a branching process approximation and the corresponding backward Kolmogorov differential equation, which can be used to estimate the probability of disease extinction when R0. Seasonal variation in migration, transmission, birth rate and viral decay results in a seasonally-dependent probability of disease extinction (no disease outbreak). A parameter sensitivity analysis of the ODE model with respect to R0 indicates that our model is sensitive to the wild bird recovery rate and environmental transmission-related parameters, which may inform future research. Additionally, in the CTMC model, we examine the sensitivity of the frequency of a spillover event into the human population from domestic poultry. We find that wild birds can drive infection numbers in other populations even when transmission parameters for those populations are low, and that environmental transmission can be a significant driver of infections.

Data-driven methods for biological modeling

Organized by: John Nardini, Erica Rutter, Kevin Flores

  • Natalia Kravtsova The Ohio State University (Department of Mathematics)
    "Scalable Gromov-Wasserstein based comparison of biological time series"
  • A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that compares time series data relies on a pairwise distance between trajectories, and the choice of distance measure determines the accuracy and speed of the time series comparison. This work introduces an optimal transport type distance for comparing time series trajectories that are allowed to lie in spaces of different dimensions and/or with differing numbers of points possibly unequally spaced along each trajectory. The construction is based on a modified Gromov-Wasserstein distance optimization program, reducing the problem to a Wasserstein distance on the real line. The resulting program has a closed-form solution and can be computed quickly due to the scalability of the one-dimensional Wasserstein distance. We discuss theoretical properties of this distance measure, and empirically demonstrate the performance of the proposed distance on several datasets with a range of characteristics commonly found in biologically relevant data. We also use our proposed distance to demonstrate that averaging oscillatory time series trajectories using the recently proposed Fused Gromov-Wasserstein barycenter retains more characteristics in the averaged trajectory when compared to traditional averaging, which demonstrates the applicability of Fused Gromov-Wasserstein barycenters for biological time series. Fast and user friendly software for computing the proposed distance and related applications is provided. The proposed distance allows fast and meaningful comparison of biological time series and can be efficiently used in a wide range of applications.
  • Yordan P. Raykov University of Nottingham (Statistics and Probability)
    "Digital disease progression biomarkers for Parkinson's disease: algorithms for passive monitoring"
  • In order to facilitate truly passive monitoring of long-term diseases such as Parkinson’s disease (PD), there is a need for models which can reliably quantify symptom-related characteristics of the disease in the highly variable context of daily life, rather than reflect the spurious correlation between sensor-based measurements and desired clinical outcomes. Toward that end, we develop scalable Bayesian nonparametric latent variable models with the capacity to capture a sparser representation of IMU data in free-living and detect statistical fluctuations reflective of different PD symptomatics. We propose the use of Bayesian radial basis function layers as an augmentation mechanism in off-the-shelf symptom detection methods and demonstrate their applicability as a mediator learning framework in the detection of PD resting tremors. We outline formally some of the fundamental challenges in doing causal inference in digital monitoring clinical trials for PD and propose theoretically justified strategies for dealing with different types of observed and unobserved confounding in free-living digital biomarkers. Furthermore, we propose novel latent variable models for quantifying time-of-day symptom fluctuations in free-living and a framework for temporal causal estimation of variable time horizon causes and outcomes.

Digital twins for clinical oncology and cancer research

Organized by: Guillermo Lorenzo, Chengyue Wu, David A Hormuth II, Ernesto A. B. F. Lima, Lois C. Okereke, Thomas E. Yankeelov

  • Stéphane Bordas University of Luxembourg (Department of Engineering Sciences)
    "Digital twinning physiological processes: brain metabolism and cancer growth"
  • The Legato Team from the Department of Engineering at the University of Luxembourg is pleased to present three cutting-edge applications of bio-engineering that utilize advanced digital twin methods. These applications are focused on in vitro and in vivostudies at various scales, includ- ing cellular aggregate, cellular, and organ levels. The first digital twin application involves the reproduction of an experiment involving multi-cellular tumor spheroids encapsulated within alginate capsules [1]. This study aims to investigate the impact of mechanical forces on tumor growth by analyzing the deformation of the capsules, which provides insights into internal tumor pressure. The poromechanical model used in this study is rigorously calibrated and validated against various capsule geometries, and the results not only faithfully reproduce the experimental findings but also provide a refined interpretation of the ex- perimental results.The second example of digital twin application focuses on reproducing the metabolism of human astrocytes while considering their real 3D geometry [2]. By examining the influence of geometry on internal reaction-diffusion processes, this study provides a deep understanding of astrocyte functionalities in both normal physiological processes and neurodegenerative diseases. This ap- plication sheds light on the complex interactions within astrocytes and their role in neurodegener- ative conditions.The third example of digital twin application is performed in real-time computation under operation room conditions. Using patient 3D scan Lidar and clinical reference maps, the model generates patient-specific pre-operative drawings for breast conservative surgery [3]. This personalized approach has shown promising clinical applications and has the potential to improve surgical outcomes. The Legato Team is excited about the recent advancements in these digital twin applications, which have led to promising clinical applications [4, 5, 6, 7]. These studies demonstrate the po- tential of bio-engineering and digital twin methods to revolutionize medical research and clinical practice. References: 1]Ste ́phaneUrcun,Pierre-YvesRohan,WafaSkalli,PierreNassoy,Ste ́phaneP.A.Bordas,and Giuseppe Sciume`. Digital twinning of cellular capsule technology: Emerging outcomes from the perspective of porous media mechanics. PLOS ONE, 16(7):1–30, 07 2021. [2]SofiaFarina,SusanneClaus,JackSHale,AlexanderSkupin,andSte ́phanePABordas.Acut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing. Advanced Modeling and Simulation in Engineering Sciences, 8:1–32, 2021.[3] Arnaud Mazier, Sophie Ribes, Benjamin Gilles, and Ste ́phane PA Bordas. A rigged model of the breast for preoperative surgical planning. Journal of Biomechanics, 128:110645, 2021. [4] Ste ́phane Urcun, Pierre-Yves Rohan, Giuseppe Sciume`, and Ste ́phane P.A. Bordas. Cor- tex tissue relaxation and slow to medium load rates dependency can be captured by a two- phase flow poroelastic model. Journal of the Mechanical Behavior of Biomedical Materials, 126:104952, 2022. [5] Stephane Urcun, Davide Baroli, Pierre-Yves Rohan, Wafa Skalli, Vincent Lubrano, Ste ́phane PA Bordas, and Giuseppe Sciume. Non-operable glioblastoma: proposition of patient-specific forecasting by image-informed poromechanical model. Brain Multiphysics, page 100067, 2023. [6] Sofia Farina, Vale ́rie Voorsluijs, Sonja Fixemer, David Bouvier, Susanne Claus, Ste ́phane PA Bordas, and Alexander Skupin. Mechanistic multiscale modelling of energy metabolism in hu- man astrocytes indicates morphological effects in alzheimer’s disease. bioRxiv, pages 2022– 07, 2022.[7] Thomas Lavigne, Arnaud Mazier, Antoine Perney, Ste ́phane Pierre Alain Bordas, Franc ̧ois Hild, and Jakub Lengiewicz. Digital volume correlation for large deformations of soft tissues: Pipeline and proof of concept for the application to breast ex vivo deformations. Journal of the mechanical behavior of biomedical materials, 136:105490, 2022.
  • Jesús J. Bosque University of Castilla-La Mancha (Spain) (Mathematical Oncology Laboratory (MOLAB))
    "Less is more in glioma treatment: In silico and in vivo evidence towards a clinical trial"
  • Low-grade gliomas (LGG) are primary brain tumours that arise from glial cells. Patients typically have a prolonged survival (median 7 years), but LGG usually transform into a malignant state, eventually resulting in the patient's death. The alkylating agent temozolomide (TMZ) is the most important weapon used against LGG, but very often the patients end up developing drug resistance. Therefore, the treatment of LGG presents an important medical challenge. To investigate the optimum schedule for the administration of TMZ to LGG patients, we developed mathematical models based on ordinary differential equations and agent-based models. To model the acquisition of drug resistance, we considered an intermediate reversible phenotype of persister cells which evade therapy and turn to fully resistant under repeated TMZ exposure. We parametrised our models using data from mice experiments and magnetic resonance images from patients, and used them to generate cohorts of digital patients in which we tested different protocols of TMZ administration. The results from the in silico clinical trials showed that protocols using individual doses with intermediate rest weeks are more effective than the standard protocol to delay the appearance of resistance and increase the survival of the patients. Moreover, these results were further validated through animal experiments, confirming the efficacy of administration schedules with increased time between doses. Thus, our research lays the foundation for a prospective clinical trial that could improve the standard of care of LGG patients.
  • Renee Brady-Nicholls H. Lee Moffitt Cancer Center & Research Institute (Integrated Mathematical Oncology)
    "An In Silico Study of Hormone Therapy in Metastatic Prostate Cancer"
  • African American (AA) men have the highest incidence and mortality rates of prostate cancer (PCa) compared to any other racial group. The increased incidence as well as mortality are likely due to socioeconomic factors, environmental exposure, access to care, and biologic variations. Deciphering the specific drivers of increased incidence and mortality is difficult due to a scarcity in available data from AA patients. In silico modeling can be used to generate pseudo patient data that can be used to compare response dynamics between groups. Here, we use propensity score matching to conduct a in silico study of hormone treatment in AA and European American (EA) PCa patients. Using longitudinal prostate-specific antigen (PSA) data from 57 metastatic PCa patients (N = 47 EA, N = 10 AA), we used propensity score matching to identify 15 EA patients that most closely matched the 10 AA patients. A simple mathematical model describing stem cell, differentiated cell, and PSA dynamics was calibrated to the data. Model parameters were compared between the matched patients and identified a significantly higher stem cell self-renewal rate in AA patients. Using this, an in silico study was performed by sampling from the race-specific parameter sets to create 100 in silico patients (N = 50 EA, N = 50 AA). Response dynamics during both continuous and adaptive therapy were compared between AA and EA groups and found that patients with higher stem cell self-renewal rates received the most benefit from adaptive treatment. This is an important step in identifying race-specific, patient-specific treatment options that can be used to maximally delay time to progression.
  • Chase Christenson University of Texas at Austin (Biomedical Enginering)
    "Fast digital twin construction for modeling the response of breast cancer to therapy using proper orthogonal decomposition."
  • Introduction: Digital twins provide an avenue to personalize and optimize therapy for cancer by simulating response in the digital space, prior to physical delivery of treatment. Mathematical models that accurately predict spatial response to various therapies have been developed but are limited in their practical application due to their heavy computational loads. Reduced order modeling (ROM) techniques, such as proper orthogonal decomposition, can be used to alleviate this burden and make the construction of digital twins more tractable for clinical application. Methods: Our lab has developed a reaction-diffusion model that describes the spatio-temporal response of breast tumors due to cell invasion, proliferation, and response to neoadjuvant therapy (1). The model is initialized and calibrated with sequential magnetic resonance imaging (MRI) data from 50 patients. The MRI data consists of diffusion-weighted MRI and dynamic contrast enhanced MRI to inform tumor cellularity and drug concentration, respectively. We use a data driven ROM formulation, where patient-specific cellularity estimates are used to determine a reduction basis appropriate for the mathematical model and individual patient. Model parameters (e.g., spatial proliferation rates, global diffusivity, and treatment efficacy) are then estimated by fitting the reduced model to the patient-specific scans. The resulting digital twin is evaluated by its ability to predict future response, and its similarity to the output from a full order model (FOM). Results: The correlation between FOM and ROM for global (i.e., whole tumor ROI) changes in total tumor volume and total tumor cellularity both achieve concordance correlation coefficients >0.99 for the calibrated and predicted time points. At the local level (i.e., individual voxels), the ROM achieves a median percent difference from FOM of 1.59% at calibrated time points, and 6.60% for predictions across the 50 patients. Critically, the ROM output requires only 1.33 minutes, nearly 100× faster than the FOM time of 128.43 minutes. Conclusions: We have developed a computational framework that can accurately calibrate a digital twin to individual patient data in a fraction of the time previously required. This reduced model can then be used to make accurate predictions of spatial response to therapy. References: (1) Wu, Chengyue, et al. 'MRI-based digital models forecast patient-specific treatment responses to neoadjuvant chemotherapy in triple-negative breast cancer.' Cancer Research 82.18 (2022): 3394-3404. Acknowledgements: The authors thank the NIH for funding through NCI U01CA142565, U01CA174706, and U24CA226110. They thank the Cancer Prevention and Research Institute of Texas for support through CPRIT RR160005. T.E. Yankeelov is a CPRIT Scholar in Cancer Research

Preparing for the Next Pandemic: Modeling and Simulation in Drug Development

Organized by: Celeste Vallejo

  • Sriram Chandrasekaran University of Michigan (Biomedical Engineering)
    "Drug discovery and repurposing using hybrid machine learning and biochemical modeling"
  • By 2050, we may lose 10 million people a year to drug-resistant infections. Unfortunately, the pace of drug discovery has not kept up with the rapid emergence of these pathogens. Drug combinations have great potential to reduce the spread of drug-resistant bacteria. However, current drug-discovery approaches are unable to screen an astronomical number of drug combinations and do not account for pathogen heterogeneity or the complex in vivo environment. We have developed hybrid AI tools - INDIGO, MAGENTA, and CARAMeL, which predict the efficacy of drug regimens based on the properties of the drugs, the pathogen, and the immune and infection environment. Our hybrid AI methods combine engineering models with machine learning, which provides both predictive power and mechanistic insights. Using these methods, we have identified highly synergistic drugs to treat drug resistant infections including Tuberculosis, the world's deadliest bacterial infection. Our approach also accurately predicts the outcome of past clinical trials of drug regimens. Our ultimate goal is to create a personalized approach to treat infections using AI.
  • Amber Smith University of Tennessee Health Science Center (Department of Pediatrics)
    "PKPD modeling of Plasmodium falciparum ATP4 inhibitor SJ733 with the pharmacokinetic enhancer cobicistat"
  • SJ733 is a newly developed inhibitor of Plasmodium falciparum ATP4 with a favorable safety profile and rapid antiparasitic effect but insufficient duration to deliver a single-dose cure of malaria. To better understand the dynamics and predict cure regimens, we developed a PKPD model. The PK could be captured using a two-compartment model with enterohepatic recirculation. Pairing this with a mechanistic PD model suggested that efficacy was increased post-recirculation and that increasing exposure would be required for cure. This prompted us to measure PK profiles for multidose regimens with or without a pharmacoboost approach using cobicistat. Either approach could significantly increase exposure but with varying kinetics. Refitting the PK model and pairing it with the PD model predicted that an unboosted, multidose regimen would increase parasite clearance by ~3x compared to 5x in the cobicistat-boosted group. The simulations also showed that a reduction in parasite burden of 1e9 would require a minimum of 300 mg SJ733+cobicistat for 2 d or 600 mg SJ733 for 3 d or 200 mg for 4 d. These results provided candidate dosing approaches to move forward into Phase 2 trials against acute, uncomplicated malaria.
  • Celeste Vallejo Simulations Plus, Inc. (DILIsym Services)
    "Potential application of a mechanistic model of chronic lung disease to the treatment of post-COVID lung fibrosis and other respiratory pandemics"
  • Idiopathic pulmonary fibrosis (IPF) is a chronic condition in which the lungs become filled with scar tissue, reducing the amount of healthy lung tissue, thus making it difficult to breathe. There is no known cure for IPF, however some treatments have been shown to slow disease progression. IPFsym is a quantitative systems pharmacology (QSP) model for IPF developed to support drug development efforts. It mechanistically represents human pathophysiology including inflammation (e.g., neutrophils, macrophages, cytokines) and fibrosis (e.g., fibroblasts, extracellular matrix) based on human data. The integrated pathophysiology is linked to clinical outcomes like forced vital capacity (FVC). IPFsym includes simulated patients with disease progression comparable to real patients, and responses to approved treatments, pirfenidone and nintedanib, that align with clinical data. IPFsym has been applied to support clinical trial design for drugs in development. Because IPFsym includes many elements common to the fibrotic sequelae of infectious respiratory disease, there is tremendous opportunity to pivot towards pulmonary fibrotic diseases caused by respiratory pandemics (such as COVID-19). The process of model modifications and re-optimization involved in pivoting to a new indication (i.e., post-COVID-19 lung fibrosis) is illustrated through the successful conversion of IPFsym to a model of interstitial lung disease associated with systemic sclerosis (SSc-ILD).

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.