Posters-04

CDEV

CDEV-21 (Session: PS04)
Olivia N.J.M. Marasco University of Lethbridge
"Cycles of self-limiting ATF4 regulation: a potential dynamical motif."

The ATF4 transcription factor network plays a critical role in controlling the shift from pro-survival to pro-apoptosis regimes when mammalian cells experience starvation, viral infection, ER or oxidative stresses. Continued activation of pro-survival pathways with failure to initiate apoptosis under chronic stress is associated with dysfunction of the ATF4 network and is a feature of cells undergoing tumorigenesis. The shift between the pro-survival and pro-apoptosis regimes is observed to be switch-like over time but the mechanisms by which this shift occurs, or which components contribute to this emergent behaviour, are not fully understood. It may be possible to gain a better understanding of the factors that control this network by studying it in contextually isolated modules identifying unique dynamical motifs that may contribute to the ATF4 network's emergent dynamical behaviour. Self-limiting ATF4 regulation has been observed with respect to CARE (C/EBP-ATF Response Element)-containing targets under amino acid limitation and describes behaviour in which the expression of these targets is initially promoted and then later repressed by other targets in a timed program. A model of ATF4's regulation of Cat-1, an amino-acid transporter that is upregulated in response to amino-acid starvation, is evaluated as a potential example of a self-limiting motif.

CDEV

CDEV-22 (Session: PS04)
Akshay Paropkari University of California, Merced
"Using Machine Learning to Predict Novel Gene Regulatory Interactions During Candida albicans Biofilm Development"

Candida albicans is a common fungal pathogen of humans, capable of forming biofilms which are surface-adhered fungal cells within an extracellular matrix. C. albicans biofilms are attributed for over 50% hospital acquired infections. Previously, our lab identified six core transcription factors (TFs) required for the formation of mature biofilms in C. albicans. In this study, we utilize previously published data sets to identify the transcriptional network controlling C. albicans biofilm formation. We implemented a support vector machine classifier to identify novel TF binding sites by utilizing binding site 3D DNA shape and motif features. For each of the six TFs, novel TF-gene interactions were observed. Finally, active and inactive TF-gene interactions were identified by integrating novel TF-gene interactions with time-series gene expression data. This work, using interdisciplinary approaches, provides insights into potential molecular targets for therapeutic applications.

CDEV

CDEV-24 (Session: PS04)
Youngmin Park Brandeis University
"The Dynamics of Vesicles Driven Through Closed Constrictions by Molecular Motors"

We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We explore the effects of noise on the reduced lubrication model proposed in [Fai et al, Active elastohydrodynamics of vesicles in narrow, blind constrictions. Phys. Rev. Fluids, 2 (2017), 113601]. The Fokker-Planck approximation fails to capture mean first passage times of velocity switching (tug-of-war effect), and the agent-based model is computationally expensive. For relatively efficient computations, we turn to the master equation and find that it requires an additional calculation to account for non-equilibrium dynamics in the underlying myosin motor population. We discuss remaining questions and future directions in this ongoing work.

CDEV

CDEV-25 (Session: PS04)
Michael Norman North Carolina State University
"Contraction and Connectivity in Simulated Cytoskeletal Networks"

The structure and mechanics of cytoskeletal networks are fundamental to cell morphology, migration and division. In this work, we develop methods to quantify the connectivity of fiber-motor networks and identify geometrical conditions that ensure network contraction through a mechanism known as polarity sorting. We then derived, for such conditions, a theory that quantitatively predicts the rate of network contraction as a function of its connectivity and biochemical and physical parameters such as motor speed, binding rates, filament lengths and medium viscosity. Predictions are tested using the physics simulator CytoSim. Lastly we discuss how those outcomes are affected by the introduction of crosslinking proteins, which can increase connectivity but frustrate the contraction mechanisms.

CDEV

CDEV-26 (Session: PS04)
Elizabeth Diaz-Torres Center for Research and Advanced Studies
"Cell recruitment may work as a temporal controller of size in the Drosophila wing"

A fundamental question in developmental biology is how organs robustly attain a final size despite perturbations in cell growth and proliferation rates. Since organ growth is an exponential process driven mainly by cell proliferation, even small variations in cell proliferation rates, when integrated over a relatively long time, will lead to large differences in size, unless an intrinsic control mechanism compensates for these variations. Here, we use a mathematical model to propose the hypothesis that in the developing wing of Drosophila, cell recruitment, a process in which undifferentiated neighboring cells are incorporated or recruited into the wing primordium, determines the time in which growth is arrested in this system. As a consequence, perturbations in proliferation rates of wing-committed cells are compensated by an inversely proportional growth time to ensure a robust size of the wing. Furthermore, we show that growth control is lost when fluctuations in cell proliferation affects both wing-committed and recruitable cells. Our model suggests that cell recruitment may act as a temporal controller of growth to buffer fluctuations in cell proliferation rates and offers a plausible solution to a long-standing problem in the field.

CDEV

CDEV-27 (Session: PS04)
Ryan Godin Cleveland State University
"Stripe Heterogeneity Affects Global Coordination of Oscillations in Synthetic Microbial Consortia"

Researchers recently utilized a sixteen delay-differential equations model to investigate globally-linked oscillations in two-strain, synthetic microbial consortia. Naturally, their model's complexity makes it challenging to comprehend and analyze, both analytically and numerically. In this presentation, we will discuss the work we have done towards developing a much simpler, non-dimensionalized model consisting of two diffusion equations based on one of the strain's underlying network topology. We will show that our model captures the consortia's qualitative behavior and is more suitable for analysis.

CDEV

CDEV-28 (Session: PS04)
Ariana Chriss Department of Biology, Geology and Environmental Sciences and Department of Mathematics and Statistics, Cleveland State University
"Modeling Chromosome Dynamics During Prophase I of Meiosis"

This study describes a mathematical model for dynamics between chromosomes in the cell nucleus, with a primary aim to predict matching times for homologous chromosomes. The pairing of homologous chromosomes during prophase I of meiosis allows for the exchange of genetic material and proper chromosome segregation during cell splitting. Hence, in order to elucidate meiotic defects that can lead to miscarriages or birth defects, it is crucial to understand this significant process. While homolog pairing can be monitored in the laboratory, the same cell cannot be followed for the duration of pairing. Cell samples die upon analysis, and thus different cells are evaluated at each timepoint. By simulating chromosome dynamics based on experimental data, we can track chromosome movement within one cell for the duration of pairing. Our agent-based model of chromosome dynamics involves capturing chromosome self-propulsion, collision dynamics, and thermal noise within the nucleus. The results are compared to the experimental data, and we observe the same pairing pattern. Our model validates the experimental method and strengthens the results. This model may then provide insight into the effects of mutations on pairing.

CDEV

CDEV-29 (Session: PS04)
Lachlan Elam Brandeis University
"Diffusion on Dynamical Networks with Applications to Cell Biology"

The topic of research is the membranous networks of endoplasmic reticulum that transport proteins. The goal of the research is to develop accurate computational models to make inferences on the intended destination of a protein based on changes within the network. The morphology of these networks is a mysterious topic that only now may be uncovered with advances in technology and computing. One of the sub-goals is to accurately model the types of change that occur in these networks, through the discoveries made with testing on artificial networks. This is an important topic as it sheds light on the interactions that occur inside a cell and thus will help to understand how natural networks make decisions.

IMMU

IMMU-10 (Session: PS04)
Emmanuel Mhrous Texas Christian University
"Incorporating Symptom Scores into Viral Kinetic Models"

Previous studies indicate that there is a correlation between the amount of virus produced by a patient (the viral load) and the severity of the disease as indicated by their symptoms. We examine the correlation between symptom score and viral load for several viral respiratory infections. We then incorporate a prediction of symptom scores into mathematical models of viral growth and test the validity and applicability of these models to data from influenza A and other viral infections.

IMMU

IMMU-11 (Session: PS04)
Angelica Bloomquist San Diego State University
"Modeling the risk of HIV infection for drug abusers"

In many parts of the world, drugs of abuse, specifically opiates, are one of the leading causes of HIV transmission. Morphine, a metabolite of common opiates, affects the expression of receptors on the surface of target cells (CD4+ T-cell) of HIV leading to a higher risk of acquiring HIV for individuals under drugs of abuse. In this study, we incorporate the difference in T-cell expression into the model to compute the risk of infection for drug abusers. We quantify how morphine conditioning causes a heightened risk of infection, depending on the relative timings of virus exposure and morphine intake. With a better understanding of the viral dynamics and the increased risk of infection for these individuals, we further evaluate how preventive therapies, such as pre- and post-exposure prophylaxis, reduce the risk of infection for drug abusers. These results are helpful for health professionals to better create treatment protocols to overcome the several obstacles that those under drugs of abuse face.

IMMU

IMMU-12 (Session: PS04)
Laura Strube Virginia Tech, Department of Mathematics
"Logical models reveal the complex immune cell phenomena produced by the MISA gene regulatory motif"

The immune system is simultaneously life-saving and dangerous. Dysregulation leads to life-threatening conditions such as sepsis and severe cases of Covid-19. Successful responses protect the body from viruses, pathogens, and cellular damage. Regulation of immune responses is accomplished through the decentralized interactions of dynamically shifting cellular populations and chemical signals. Central to this process is the differentiation of progenitor cells into effector cells and the appropriate production of chemical signals called cytokines. Understanding how this regulation is accomplished requires a systems-level understanding of the cellular and molecular mechanisms that integrate stimuli into gene expression decisions. Boolean and Fuzzy-Logic modeling have been instrumental in establishing the MISA (mutually-inhibitory, self-activating) gene-regulatory motif as a fundamental component of immune cell differentiation responses. Here we describe the work of a number of mathematical biologists, reframing the regulatory networks they study, to emphasize the array of biological phenomena that can be produced when the MISA motif is embedded in complex gene regulatory networks. These phenomena include: hierarchical differentiation, dose-dependent decisions, differentiation memory, and the production of heterogeneous cell populations from uniform signaling environments. The perspective provided by this work allows for the formation of new hypotheses about the network structures underlying newly discovered biological phenomena.

IMMU

IMMU-13 (Session: PS04)
Michael Pablo UCSF | Gladstone Institutes
"Multiscale modeling of a self-renewing, self-deploying antiviral for SARS-CoV-2"

While vaccine deployment is reducing the risk of infection and transmission of SARS-CoV-2, effective antiviral therapies are still needed. Antivirals with a mechanism of action distinct from current vaccines are especially key in the event that vaccine-resistant variants evolve. One such class of antivirals consists of non-pathogenic viral mutants that compete with wild-type virus, and conditionally replicate in its presence. In principle, these biologically-derived antivirals prey upon SARS-CoV-2 to reduce viral load, self-renew as long as the infection is sustained, and could be transmitted from one individual to another. This class of antivirals are known as ‘Therapeutic Interfering Particles’ (TIPs) and have been theoretically and experimentally characterized for HIV-1. Here, we develop multiscale models for the efficacy of a TIP against SARS-CoV-2 in reducing patient viral load via targeted administration, and in reducing population-level COVID-19 mortality via self-deployment. Specifically, we modeled within-host replication, between-host transmission, and epidemiological spread. Our models are parameterized using in vitro data for a TIP against SARS-CoV-2, and by in vitro, in vivo, and epidemiological data for wild-type SARS-CoV-2 replication and transmission. We make predictions for the promising efficacy of TIPs for individual patients, propose key considerations for delivery of TIPs to individuals, and identify barriers to self-deployment.

IMMU

IMMU-4 (Session: PS04)
Kristen Windoloski North Carolina State University
"A dynamic inflammatory model for bolus vs. continuous administration of endotoxin"

Uncontrolled, persistent inflammation is a hallmark of individuals with medical conditions such as sepsis, a leading cause of death in U.S. hospitals. While a bolus administration of lipopolysaccharide (LPS) to healthy volunteers is a common short-term inflammation model, a continuous infusion of LPS over an extended time frame better represents the sustained inflammation present in conditions like sepsis. Numerous studies have used mathematical modeling to examine the inflammatory feedback in response to a bolus administration of endotoxin, and these models were validated against bolus murine and human data. Analysis of bolus versus continuous administration of endotoxin data reveals that a continuous administration of LPS results in delayed peaks of pro and anti-inflammatory cytokines and increases in peak magnitude of TNF-a and IL-10. To further the understanding behind these differences, we adapt a 2 ng/kg bolus-dose inflammatory response model formulated as a system of ordinary differential equations tracking selected cytokines and cells to study the inflammatory response to a continuous infusion of endotoxin over an extended period of time. Using sensitivity analysis and parameter estimation, we validate the model using experimental data from a study where 2 ng/kg of LPS is administered over a 4-hour period in nine healthy volunteers.

IMMU

IMMU-5 (Session: PS04)
Brian Orcutt-Jahns University of California, Los Angeles
"Multivalent Binding Model Explains Immune Cell Responses to Engineered γ-chain Cytokine Muteins"

The common γ-chain cytokines are promising immune therapies due to their central role in coordinating the abundance and activity of immune cell populations. One of these cytokines, interleukin (IL)-2, is an approved therapy for metastatic melanoma but is limited in effectiveness due to its induction of non-specific proliferation of off-target immune cell types. IL-2 muteins with altered receptor-ligand binding kinetics improve the cell type selectivity of the signaling response. Furthermore, muteins that are made dimeric through antibody Fc fusion have exhibited desirable pharmacokinetic benefits. Here, we analyze the response of four key immune cell types to a panel of muteins in both monomeric and dimeric Fc formats. We used a structured dimensionality reduction scheme to decompose the mean responses of each cell population to each ligand, and show that dimeric muteins are uniquely specific for regulatory T cells (Tregs) cells at intermediate ligand concentrations. To dissect the mechanism of enhanced Treg specificity in dimeric ligands, we used a simple multivalent binding model to determine whether the changes in signaling could be explained by binding avidity on its own, and found that our model was able to translate between cell surface binding and cellular response with high accuracy.

IMMU

IMMU-7 (Session: PS04)
Nora Heitzman-Breen Virginia Tech
"Mathematical models of Usutu virus infection"

Usutu virus is a mosquito-borne virus maintained in wild bird populations, which leads to mosquito infections, and occasional spillover in humans. It has been hypothesized that increased Usutu virus replication in birds and/or decreased bird immune competence leads to increased mosquitoes infection and increased transmission to humans. To provide insight into the intrinsic complexity of host-virus processes in birds, we developed mathematical models of Usutu virus infection and fitted them against four Usutu virus strains data from chicken infections. We have also investigated the effect of antibody on virus dynamics by fitting the models to chickens that were genetically engineered to have low and high antibody count. Parameter distributions for virus production, virus replication, host responses, and basic reproduction number were generated using non-linear mixed-effects models. We observed differences in virulence amongst the four virus strains, and found that birds with high antibody count have higher infected cell killing and higher virus clearance rates, indicative of non-neutralizing antibody function. These results can be used to better determine which virus strain is the most likely to spillover in the human population.

IMMU

IMMU-8 (Session: PS04)
Aadrita Nandi University of Michigan
"Developing a whole-host model to study combination drug therapy for tuberculosis"

Inhalation of Mycobacterium tuberculosis (Mtb) leads to tuberculosis (TB) disease, one of the biggest threats to global health. The first-line drug regimen consists of four antibiotics – rifampin, isoniazid, pyrazinamide and ethambutol – for six to nine months. Additional antibiotics are also available and may be suitable for drug-resistant TB or may offer the possibility of shorter treatment times. Assessment of the efficacy of all potential drug combinations is only feasible with the use of a computational model. Previously, we compared efficacy of several drug regimens using our agent-based model GranSim to follow treatment of a single granuloma, solid structures in Mtb-infected lungs containing immune cells and bacteria. To simulate multiple heterogeneous granulomas simultaneously along with immune cells generated within lymph nodes and passing through blood, we developed a whole-host model, HostSim, which is able to capture the progress of infection in the lungs and the recruitment of immune cells. We then integrated pharmacodynamic and pharmacokinetic modeling into HostSim to investigate effects of various drug regimens on multiple heterogeneous granulomas. The model is calibrated against in vitro and in vivo data. This model can aid in identifying optimal treatment regimens for further testing in animal models of TB.

IMMU

IMMU-9 (Session: PS04)
Miranda Lynch Hauptman-Woodward Medical Research Institute
"Computational geometry, Delaunay tessellations and alpha shapes for protein interactions: Exploring Coronavirus Mpro drug binding"

This work discusses application of techniques of computational geometry and topological persistence to the problem of comparing drug interactions with SARS-CoV-2 main protease (Mpro). We use alpha-shape methods and Delaunay triangulations, which generalize convex hulls of point sets in 3D and are an efficient way of representing molecular shapes and between-atom relationships in proteins. Weighted Delaunay triangulations are needed to accommodate different Van der Waals radii of atoms, and formation of alpha complexes from those tessellations permit characterization of the protein pockets that enable drug binding. This work applies the tools of computational geometry to a comparative analysis of drug binding to Mpro, which is a primary target for therapeutic development against Covid-19. Mpro functions to enzymatically cleave the SARS-CoV-2 polypeptide encoded by the RNA genome into its constituent functional parts, critical for viral replication. There are nearly 300 Mpro structures deposited to the PDB with various ligands bound, including inhibitors and small molecule fragments. We also have structures of the apo- form of Mpro, with no ligand bound. Our analyses of Mpro drug binding sites from these structures reveal variations in the binding pockets that can influence specificity and strength of ligand binding ability.

MEPI

MEPI-47 (Session: PS04)
Lucia Wagner St. Olaf College
"Modeling Public Health Impact of E-Cigarettes on Adolescents and Adults"

Since the introduction of electronic cigarettes into the United States market in 2007, vaping usage has surged in both adult and adolescent populations. E-cigarettes are advertised as a safer alter-native to traditional cigarettes and as a method of smoking cessation, but the US government and health professionals are concerned that e-cigarettes attract young non-smokers. Here we develop and analyze a dynamical model of competition between traditional and electronic cigarettes for adult and adolescent users. With this model, we address three urgent questions: (1) how did the introduction of e-cigarettes influence the prevalence of smoking, (2) what is the predicted number of traditional smokers diverted to vaping after its inception, and (3) from a public health perspective, do e-cigarettes present a net benefit or harm to society?

MEPI

MEPI-48 (Session: PS04)
Benjamin Adam Catching UCSF
"Examining face-mask usage as an effective strategy to control COVID-19 spread"

The COVID-19 global crisis is facilitated by high virus transmission rates and high percentages of asymptomatic and presymptomatic infected individuals. Containing the pandemic hinged on combinations of social distancing and face mask use. Here we examine the efficacy of these measures, using an agent-based modeling approach that evaluates face masks and social distancing in realistic confined spaces scenarios. We find face masks are more effective than social distancing. Importantly, combining face masks with even moderate social distancing provides optimal protection. The finding that widespread usage of face masks limits COVID-19 outbreaks can inform policies to reopening of social functions.

MEPI

MEPI-51 (Session: PS04)
Majid Bani Yaghoub University of Missouri-Kansas City
"Characterizing spread of infection in cattle farms using wavefronts of a reaction-diffusion coinfection model"

The present work studies the transmission dynamics of Escherichia coli O157:H7 in a dairy farm using a coinfection Reaction-Diffusion Susceptible-Infected-Susceptible model. Analysis of the model includes existence and stability of equilibria, and calculation of the basic reproduction number. Furthermore, it is numerically shown that the model exhibits stationary and traveling wavefronts. Existence of a stationary wavefront implies that the likelihood of infection transmission is a function of host's location. This is in contrast with recent studies that use Turing patterns to determine the likelihood of infection. In addition, formation of a one-hump traveling wavefront characterizes establishment of an endemic equilibrium in the entire spatial domain.

MEPI

MEPI-52 (Session: PS04)
Pedro Henrique Pinheiro Cintra Gleb Wataghin Institute of Physics, University of Campinas
"Evaluating the effect of non pharmaceutical interventions on COVID-19 infection dynamics through agent based models"

In order to provide both qualitative and quantitative results regarding the efficacy of non pharmaceutical interventions, we use an agent based model, considering typical epidemiological parameter distributions for COVID-19 in an age-stratified population in each case. We suppose individuals can assume the following states: susceptible, asymptomatic, infected, exposed, recovered and dead. They move and exchange contact inside a defined area. Introducing agglomeration sites and social distancing, we evaluate the effect of different non pharmaceutical interventions through simulation results of attack rate, death rate and epidemic curves created in each scenario. Lastly, we suppose the interventions are lifted at a given time and evaluate how the duration of interventions change the infection dynamics.

MEPI

MEPI-53 (Session: PS04)
Alex Busalacchi San Diego State University
"Modeling transmission dynamics of black band disease on coral reefs: temperature dependent microbiomes"

Black band disease (BBD) is one of the most prevalent diseases causing significant destruction of coral reefs. Coral reefs acquire this deadly disease from bacteria in the microbiome community, the composition of which is highly affected by the environmental temperature. While previous studies have provided useful insights into various aspects of BBD, the temperature-dependent microbiome composition has not been considered in existing models. We develop a transmission dynamics model, incorporating the effects of temperature on the microbiome composition, and subsequently on BBD of coral reef. Based on our model, we calculate the basic reproduction number, providing an environmental threshold for the disease to exist in the coral reef community. Our results suggest that temperature has a significant impact on coral reef health, with higher environmental temperatures resulting in more coral infected with BBD in general. Our model and related results are useful in investigating potential strategies to protect reef ecosystems from stressors, including BBD.

MEPI

MEPI-54 (Session: PS04)
Jingjing Xu University of Alberta
"A spatio-temporal model for the spread of chronic wasting disease"

Chronic wasting disease (CWD) is a prion-based transmissible spongiform encephalopathy in deer species (cervids) that results in 100% mortality. It poses a threat to cervid populations and the local ecological and economic communities that depend on them. Although empirical studies have shown that host social grouping, home range overlap, and male dispersal are essential in the disease spread, few mechanistic models explicitly consider those factors. We present a spatio-temporal, differential equation model in 2D space for CWD spread. This model includes direct and environmental transmission for an age-structured population where vital rates are influenced by CWD infection, and grouping, home range sizes, and habitat preferences change with the season. We show how the spreading speed of CWD and the basic reproduction number in 2D space respond to the seasonal changes in demographics, resource distribution, and epidemiological parameters. We will use this framework to assess demographic and spatial harvesting strategies in the future.

MEPI

MEPI-55 (Session: PS04)
João Pedro Valeriano Miranda Institute for Theoretical Physics, State University of São Paulo, São Paulo, Brazil
"Memory effect in time-window epidemic curve forecasting using Approximate Bayesian Computation"

Fitting compartmental models to epidemiological data aiming to produce reasonable forecasts can become a very complex task, especially when the data assume a behavior difficult to be attained by models with constant parameters. A common alternative is to build models with time-dependent parameters, which does not necessarily simplify the fitting process, but can make the model more descriptive. In this work we propose to adopt a simple SEIRD model with constant parameters, but dividing the epidemiological data into different time-windows, in which it is assumed that the data can be piecewise fitted, as an alternative way of adopting time-dependent parameters. Using Approximate Bayesian Computation , posterior distributions of parameters obtained in previous windows are used as prior distributions of corresponding parameters in subsequent windows. We show that taking advantage of this information does improve the predictive capacity of the model, when compared to the strategy in which noninformative priors are adopted for each window. Finally, we assess the combination of time-windows with different lengths, seeking for more accurate forecasts.

MEPI

MEPI-58 (Session: PS04)
Daniel Cardoso Pereira Jorge Instituto de Física Teórica - UNESP
"Estimating the effective reproduction number for heterogeneous models using incidence data"

The effective reproduction number, R(t), is a central point in the study of infectious diseases. It establishes in an explicit way the extent of an epidemic spread process in a population. The current estimation methods for the time evolution of R(t), using incidence data, rely on the generation interval distribution, g(tau), which is usually obtained from empirical data or already known distributions from the literature. However, there are systems, especially highly heterogeneous ones, in which there is a lack of data and an adequate methodology to obtain g(tau). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining an explicit expression of the R(t) and g(tau) provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of Covid-19 in municipalities of the state of Rio de janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others. Our results point out the importance of mathematical modelling to provide epidemiological meaning of the available data.

ONCO

ONCO-22 (Session: PS04)
Ellen Swanson Centre College
"Enhancing CAR-T Immunotherapy to Attack Both Tumor and Cancer Stem Cells"

The stem cells hypothesis suggests that there is a small group of malignant cells, the cancer stem cells, that initiate the development of tumors, encourage its growth, and may even be the cause of metastases. Traditional treatments, such as chemotherapy and radiation, primarily target the tumor cells leaving the stem cells to potentially cause a recurrence. Chimeric antigen receptor (CAR) T-cell therapy is a form of immunotherapy where the immune cells are genetically modified to fight the tumor cells.Traditionally, the CAR T-cell therapy has been used to treat blood cancers and only recently has shown promising results against solid tumors. We create an ODE model which allows for the infusion of trained CAR-T cells to specifically attack the cancer stem cells that are present in the solid tumor microenvironment. Additionally, we incorporate the influence of TGF-Beta which has a both a regulatory and promotion effect on the growth of the tumor. We verify the model by comparing it to available data and then examine different immunotherapy treatments that attack the tumor cells, stem cells, and both.

ONCO

ONCO-23 (Session: PS04)
Stefano Casarin Houston Methodist Research Institute
"Depicting Radium223 therapy efficacy for prostate cancer bone metastasis: a mathematical modeling approach"

Radium223 (Rad223) has lately improved survival in prostate cancer bone metastatic patients. However, clinical response is often followed by relapse and disease progression, and associated mechanisms of efficacy and resistance are poorly understood. Research efforts to overcome this gap require substantial time and resource investment. Computational models, integrated with experimental data, can overcome this limitation and drive research in a more effective fashion. Accordingly, we developed an agent-based model of prostate cancer bone metastasis progression and response to Rad223 as an agile platform to maximize its efficacy. The driving coefficients were calibrated on ad hoc experimental observations retrieved from intravital microscopy and the outcome further validated, in vivo. The in silico tumor growth matched in vivo trend with 98.3% confidence. Tumor size determined efficacy of Rad223, with larger lesions insensitive to therapy, while medium- and micro-sized tumors displayed up to 5.02 and 152.28-fold size decrease compared to control-treated tumors, respectively. Eradication events occurred in 65 ± 2% of cases in micro-tumors only. In addition, Rad223 lost any therapeutic effect, also on micro-tumors, for distances bigger than 400 μm from the bone interface. This model has the potential to be further developed to test additional bone targeting agents such as other radiopharmaceuticals or bisphosphonates.

ONCO

ONCO-24 (Session: PS04)
Emily Yang The University of Texas at Austin
"Characterizing Phenotypic Dynamics of Chemoresistance in Breast Cancer Cells"

Despite the continuing advancements in chemotherapy for breast cancer, the development of chemoresistance remains a significant cause of treatment failure. Intratumoral and inter-patient heterogeneity pose critical challenges to designing patient-specific optimized treatment plans. We posit that a mathematical understanding of chemoresistance dynamics could be key to developing clinically-feasible, successful treatment regimens. In this study, we develop a model that describes the effects of a standard neoadjuvant drug (doxorubicin) on a common breast cancer cell line (MCF7). We assume that the tumor is composed of two subpopulations: drug-resistant cells, which continue proliferating after treatment, and drug-sensitive cells, which gradually transition from proliferating to treatment-induced death. The model is calibrated with time-resolved microscopy data including variations in drug concentration, inter-treatment interval, and number of doses. Our results show that the model can recapitulate tumor growth dynamics in all of these scenarios (CCC>0.95). We observe that higher dosages resulted in significantly lower drug-resistant fraction and proliferation rates (p<0.05). Our results also show superior tumor control with a higher number of doses and shorter inter-treatment intervals (p<0.05). Thus, we believe that our model may contribute to our understanding of doxorubicin action and may guide the selection of therapeutic regimens that achieve optimal tumor control.

ONCO

ONCO-25 (Session: PS04)
Joshua Scurll University of British Columbia
"A new inter-cluster similarity measure for high-dimensional data can facilitate analysis of heterogeneous mass-cytometry data"

Mass cytometry (CyTOF) is a high-dimensional, high-throughput technology to analyze quantities of 30–40 proteins simultaneously in single cells and is widely used to investigate heterogeneity in tumour tissue samples. Also, by detecting phospho-proteins, (phospho-)CyTOF can be used to investigate intracellular signalling-pathway activity. Analysis of CyTOF data usually involves clustering and visualization of the high-dimensional data, which are typically performed using independent methods and are strongly influenced by user-controlled input parameters. To reduce user influence on CyTOF analysis results and harmonize the clustering and visualization processes, I developed ASTRICS, a new measure of similarity between clusters of high-dimensional data points based on local dimensionality reduction and triangulation of alpha shapes. I propose a multi-stage clustering strategy called CytoClue in which ASTRICS is used to automatically generate a weighted graph from an initial set of fine-grained clusters, which are obtained by an existing algorithm (e.g. FlowSOM) and are represented by graph nodes. The graph is visualized by force-directed layout and used for further clustering by a graph-based algorithm. This poster introduces ASTRICS and CytoClue and presents results of applying them to phospho-CyTOF experiments that were conducted to investigate heterogeneity between and within diffuse large B-cell lymphoma (DLBCL) cell lines.

ONCO

ONCO-26 (Session: PS04)
Alexander Brummer Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, Beckman Research Institute, City of Hope National Medical Center
"Destabilization of CAR T-cell treatment efficacy in the presence of dexamethasone"

CAR T-cell therapy has proven to be a highly effective targeted immunotherapy for glioblastoma multiforme. Yet, there is presently little known about the efficacy of CAR T-cell treatment when combined with the widely used anti-inflammatory and immunosuppressant glucocorticoid Dexamethasone. We present an analysis of glioblastoma organoid cell lines treated along gradients of CAR T-cell therapy and Dexamethasone. We demonstrate that Dexamethasone antagonizes CAR T-cell efficacy, and promotes tumor growth and recurrence. Advanced experimental technologies allow for highly resolved temporal dynamics of in vitro studies of combination therapies of CAR T-cell and Dexamethone, making this a valuable model system for studying the rich dynamics of nonlinear biological processes with translational applications. We model the system as a non-autonomous, two-species, type I, predatory-prey interaction of tumor cells and CAR T-cells, with explicit time-dependence in the clearance rate of Dexamethasone. Using time as a bifurcation parameter, we show that (1) the presence of Dexamethasone destabilizes coexistence equilibria between CAR T-cells and tumor cells and (2) as Dexamethasone is cleared from the system, a stable coexistence equilibrium returns in the form of a Hopf bifurcation.

ONCO

ONCO-27 (Session: PS04)
John Metzcar Indiana University
"Impacts of communication length-scale on cellular invasion of tumor stroma using a novel ECM model"

Understanding long-range cellular migration is key to an understanding of cancer metastasis as well as other biological processes such as embryogenesis and formation of tissue morphology. Due to constraints on cellular and tissue level imaging, gaining that understanding as it emerges from cell-cell and cell-environmental interactions is challenging. To aid in gaining that understanding with respect to the physical environment, we developed a novel mathematical extracellular matrix (ECM) model capturing three components of ECM: fiber orientation, alignment, and density. This model is notable in its stripping down the ECM to its most essential components. We implemented this model in PhysiCell, a cell-based modeling framework, thus allowing coupling between it and cell-agents. We then explored rules of interactions between cells, their physical environment (the ECM), and the diffusive chemical environment. We observed that locally sensed, long range (on the order of a few cell diameters) physical signals communicated via ECM remodeling alter the dynamics of cellular invasion, producing new results. Comparing these results to simulations lacking long-range permanently written signals, we see more cellular trafficking and movement. This advance brings us one step closer to understanding processes of collective cellular migration and closer to understanding the initial steps of cancer metastasis.

ONCO

ONCO-28 (Session: PS04)
Nathan Lee University of Washington, Department of Applied Mathematics
"Inferring parameters of cancer evolution from sequencing and clinical data"

As a cancer develops, its cells accrue new mutations, resulting in a heterogeneous, complex genomic profile. We make use of this heterogeneity to derive simple, analytic estimates of parameters driving carcinogenesis and reconstruct the timeline of selective events following initiation of an individual cancer. Using stochastic computer simulations of cancer growth, we show that we can accurately estimate mutation rate, time before and after a driver event occurred, and growth rates of both initiated cancer cells and subsequently appearing subclones. We demonstrate that in order to obtain accurate estimates of mutation rate and timing of events, observed mutation counts should be corrected to account for clonal mutations that occurred after the founding of the tumor, as well as sequencing coverage. We apply our methodology to reconstruct the individual evolutionary histories of chronic lymphocytic leukemia (CLL) patients. Fitting our model to longitudinal patient data reveals that the first driver mutation typically occurs very early in life in patients that go on to develop CLL, and that the appearance of the first driver mutation and the diagnosis of CLL are typically separated by 30-50 years.

ONCO

ONCO-29 (Session: PS04)
Jaewook Joo Cleveland Clinic Foundation
"Optimal path to fluctuation-driven extinction of tumors with phenotypic switching in temporally varying environment"

Phenotypic plasticity/switching, in contrast to irreversible genetic intratumor variation, allows cancer cells to engage adaptive responses to the changed tumor microenvironment in a reversible fashion and begins to emerge as the explanatory mechanisms for therapy resistance. We consider a simple stochastic model of reversible phenotypic switching between two phenotypic states, a growing yet sensitive state and a quiescent yet tolerant state, in response to a time-varying tumor microenvironmental cue. An environmental stress induces the switching to a quiescent state and the absence of stress reverses its state back to a growing state. We utilized the WKB theory of large deviations, i.e., the eikonal approximation to the master equation, to find the optimal path to fluctuation-induced tumor extinction. This path to tumor extinction is forbidden in a deterministic model, but a rare event with large fluctuations brings the system from its long-lived quasi-stationary state to extinction. We also presented the necessary conditions for the temporal modulation of the environmental stress that could reduce the mean time to extinction exponentially.

ONCO

ONCO-30 (Session: PS04)
Harsh Jain University of Minnesota Duluth
"Simulating Heterogeneity in Deterministic Models of Prostate Cancer Response to Immunotherapy with Standing Variations Modeling"

Advanced, hormonally refractive prostate cancer is typically treated with docetaxel, a chemotherapeutic compound that inhibits cell division. However, this treatment eventually fails due to onset of resistance. Multiple mechanisms driving docetaxel resistance have been identified and several drugs targeting these mechanisms are in various stages of clinical trial, including immunotherapy in the form of a vaccine. However, optimizing strategies to overcome such resistance remains a critical challenge because the problem is inherently multiscale due to characteristic variability at the subcellular, cellular and individual levels. In this talk, I present a simple dynamical systems model of prostate cancer response to immunotherapy. I then introduce our novel modeling approach, Standing Variations Modeling, which exploits uncertainty and variability in data to inform the probability distributions - rather than specific values - from which model parameters most likely arise. This differs from traditional modeling approaches that only use static or mean expression levels and cellular responses, thereby ignoring the significant variance that exists across cell populations as well as individuals being treated. Sampling from these posterior distributions allows us to generate a virtual cohort of individuals on which in silico clinical trials are conducted to predict optimal dosing combinations and subpopulations that would benefit most from such an intervention.

ONCO

ONCO-31 (Session: PS04)
Heber Rocha Indiana University
"A multiscale model for tumoral vascular growth: blood flow and cell dynamics"

Vascularization is a fundamental factor in the progression of tumor growth. The vascular phase is characterized by angiogenesis, responsible for the growth of new blood vessels in tumor direction from an original vascular network. Through an additional supply of nutrients, the tumor acquires unlimited resources for its uncontrolled progress. Besides, the risk of metastasis increases with the eventual invasion of blood vessels by cancer cells. In this work, we developed a multiscale model to represent the growth of vascular tumors, integrating angiogenesis and blood flow dynamics. Dynamics on the cell scale are represented discretely using agent-based modeling, while oxygen dispersions and pro-angiogenic factors are modeled using partial diffusion-reaction equations. Blood flow is obtained by solving Kirchhoff's circuit equations for flow in a connected network. The new blood vessels are formed through a set of rules based on stimuli of factors secreted by cancer cells submitted to the oxygen structure. The coupling between the models can capture phenomena that occur at the cellular and tissue scales, qualitatively representing the growth of vascular tumors. The computational model was developed using PhysiCell, an open-source C ++ framework that allows the construction of multicellular models at various scales in 2D and 3D.

OTHE

OTHE-10 (Session: PS04)
William Annan Clarkson University, NY
"Modeling the homeostatic length of the rod outer segment in zerbrafish"

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 oldest discs are shed from the tip. The ROS maintains a homeostatic length by balancing growth and shedding. How this balance is controlled is unknown. If ROS homeostatic length control is lost, for example by ROS shortening, the rods can degenerate leading to blindness. We develop a model of ROS homeostatic length control, supported by experiments using data from zebrafish where ROS renewal is controlled experimentally. An ODE describes the length of ROS over time according to constant growth and ROS length-dependent shortening. Here, equilibrium analysis helps us understand the balance between growth and shortening mechanisms in maintaining homeostatic length. Also, an advection-reaction PDE describes disk addition (through a boundary condition), translocation (via advection), and shedding (reaction) in populations of ROS.

OTHE

OTHE-11 (Session: PS04)
Mackenzie Dalton Clarkson University
"Modeling the Spread of COVID-19 in Response to Various Surveillance Testing Strategies"

Since early March 2020, government agencies have utilized a wide variety of non-pharmaceutical interventions to mitigate the spread of COVID-19. At many universities, fundamental issues relating both to the spread of the disease and the ability of administrators to respond to a sudden rise in cases remain. Surveillance testing strategies have been implemented in places that have reopened, to simultaneously monitor community spread and isolate discovered cases. On college campuses, the question remains as to what kind of testing is required to remain safely open. Here, we propose an extension of the SIR model to investigate the effectiveness of various techniques that have been used throughout the pandemic to slow the spread of COVID-19 on college campuses. In particular, we present a minimal mathematical model that includes time-varying testing strategies viewed as a control. We use numerical simulations to show how testing strategies may change in response to averaged disease transmission rates, where such rates are governed by university-specific guidelines (e.g. classroom sizes, ventilation, etc). We show that surveillance testing can be effective if isolation guidelines are followed. Further testing strategies are presented which are more robust to either non-compliance of distancing mandates, or so-called 'superspreader' events.

OTHE

OTHE-12 (Session: PS04)
Christian Michael Department of Mathematics, University of California, Riverside
"Multi-scale computational model for understanding the mechanisms controlling tissue shape and structure in the shoot apical meristem of Arabidopsis thaliana"

The shoot apical meristem (SAM) of Arabidopsis thaliana is a developmental organ that maintains a constant set of stem cells. It resides at the tip of the plant's growing stem and is responsible for all above-ground organ production. While SAM cells continually expand and divide throughout the plant’s life cycle, effluxing from the organ, the SAM maintains both a dome-like shape and a distinct layered structure of cells. Since plant cells are strongly adhered together and do not slip along one another, the principal factors influencing SAM shape and structure are placement of cell division planes and preferentially oriented anisotropic expansion of cells. Previous work has shown that there are multiple factors controlling these cell behaviors, including the plant hormones WUSCHEL and cytokinin. Since patterns of cell growth and division further influence cell shape and tensile forces, it becomes difficult to experimentally differentiate how cells respond to chemical and mechanical signaling, and what impact hypothesized growth mechanisms might have in maintaining SAM shape and structure. In an effort to understand this system, we constructed a mechanistic and data-calibrated multiscale subcellular element model in two dimensions, including both mechanical and chemical signaling. This model was used to generate several in silica cross-sections of the SAM whose cells followed various hypothesized cell behavior. Specifically, we tested whether WUSCHEL and cytokinin control both cells' anisotropic expansion and division plane placement, or whether patterns of cell division emerged from mechanical signaling. Our results revealed that the best match between model output and experimental data is when there is a layer-specific dependence of cell behavior on either chemical or mechanical signaling. Moreover, cells in the SAM's epidermal cell layers are known to experience substantial mechanical tension; the role of such an external source of tension in establishing the structure and shape of the SAM is currently not well understood. Preliminary simulations demonstrate that adequate peripherally-sourced tension is sufficient to recover the characteristic dome shape of the SAM.

OTHE

OTHE-13 (Session: PS04)
Zhao(Wendy) Wang McGill University
"Novel Operon Dynamics in the Presence of State-Dependent Delays"

In operon gene expression, transcription and translation processes occur with delays. Mathematical models of operon dynamics incorporating constant delays have been developed and show similar dynamics to the model without delay. Namely with constant delays, the repressible operon has a unique steady state which may undergo a Hopf bifurcation leading to a stable period orbit. In the inducible operon there is either a globally stable steady state or two locally stable steady states and an unstable intermediate steady state. Taking into account that in practice the delays are likely to be state-dependent, we extend the modeling to operon dynamics with state-dependent transcription and translation delays and explore the dynamics. Our results demonstrate that the incorporation of distributed state-dependent delays gives rise to expanded possibilities of operon dynamics. Namely, both repressible and inducible systems may display multiple steady states as well as novel bifurcations, which may result in interesting scenarios such as bistability and tristability among stable steady states and stable limit cycles.

OTHE

OTHE-9 (Session: PS04)
Micaeli Mendola Theodoro Graduate Program in Biometrics - Unesp
"Fractional modeling of the population dynamics of COVID-19 in Brazil"

At the end of December 2019, there was an outbreak of pneumonia accompanied by fever, dry cough, fatigue and possible gastrointestinal problems, which initially occurred in Wuhan, China, the virus responsible for the infection was sequenced and became known as SARS-CoV-2 and the disease caused by its infection, such as Coronavirus Disease, 2019 (COVID-19). The first case of COVID-19 in Brazil was on February 25, 2020. On March 23, we reached the mark of 12.047.526 cases and 295.425 deaths from COVID-19. In this work, we present a model of fractional differential equations, aiming to embed the effect of simplifications in the non-integer order of the derivative. We use FracPECE, which is an algorithm to find the numerical solution of a system of non-linear fractional differential equations (FDE) and the least squares method to estimate the model parameters.