Minisymposia: MS01

Monday, July 17 at 10:30am

Minisymposia: MS01

Applications of Reaction-Diffusion Models in Biological Systems

Organized by: Yu Jin, Daniel Gomez, King Yeung (Adrian) Lam
Note: this minisymposia has multiple sessions. The other session is MS02-ECOP-1.

  • Nancy Rodriguez University of Colorado Boulder (Applied Mathematics)
    "Animal movement"
  • A successful wildlife management plan relies on two key factors: (1) the understanding of driving factors influencing the movement of social animals and (2) the understanding of what movement strategies are optimal depending on the environment. In this talk, I will first discuss results from work focused on determining how some social animals, such as Meerkats, move. We present a non-local reaction-advection-diffusion model along with an efficient numerical scheme that enables the incorporation of data. The second part of the talk will focus on how directed movement can help species overcome the strong Allee effect on both bounded and unbounded domains. I will also discuss the connection to optimal movement strategies in the context of the strong Allee effect.
  • Andreas Buttenschön University of Massachusetts Amherst (Department of Mathematics and Statistics)
    "Spatio-Temporal Heterogeneities in a Mechano-Chemical Model of Collective Cell Migration"
  • Small GTPases, such as Rac and Rho, are well known central regulators of cell morphology and motility, whose dynamics also play a role in coordinating collective cell migration. Experiments have shown GTPase dynamics to be affected by both chemical and mechanical cues, but also to be spatially and temporally heterogeneous. This heterogeneity is found both within a single cell, and between cells in a tissue. For example, sometimes the leader and follower cells display an inverted GTPase configuration. While progress on understanding GTPase dynamics in single cells has been made, a major remaining challenge is to understand the role of GTPase heterogeneity in collective cell migration. Motivated by recent one-dimensional experiments (e.g. micro-channels) we introduce a one-dimensional modelling framework allowing us to integrate cell bio-mechanics, changes in cell size, and detailed intra-cellular signalling circuits (reaction-diffusion equations). Using this framework, we build cell migration models of both loose (mesenchymal) and cohering (epithelial) tissues. We use numerical simulations, and analysis tools, such as local perturbation analysis, to provide insights into the regulatory mechanisms coordinating collective cell migration. We show how feedback from mechanical tension to GTPase activation lead to a variety of dynamics, resembling both normal and pathological behavior.
  • Daniel Gomez University of Pennsylvania (Mathematics)
    "Multi-Spike Solutions in the Fractional Gierer-Meinhardt System"
  • The singularly perturbed Gierer-Meinhardt (GM) system is a model reaction-diffusion system used to study the pattern forming effects of short-range activation and long-range inhibition in biological systems. The singularly perturbed limit in which the activator has an asymptotically small diffusivity leads to the formation of multi-spike solutions in which the activator is strongly localized at discrete points. Using formal asymptotic methods we can obtain detailed descriptions of both the structure and linear stability of these multi-spike solutions. In this talk we will discuss recent work on the formal asymptotic analysis of multi-spike solutions to the one-dimensional fractional GM system in which both the activator and inhibitor exhibit Lévy flights. We will highlight how the singular behaviour of the corresponding fractional Green's function plays a crucial role in the asymptotic analysis of spike solutions and how, depending on the fractional order, this leads to direct analogies with spike solutions to the classical GM system in one-, two-, and three-dimensional domains.
  • Yixiang Wu Middle Tennessee State University (Department of Mathematical Sciences)
    "Concentration phenomenon in a reaction-diffusion epidemic model with nonlinear incidence mechanism"
  • I will talk about our recent work on a reaction-diffusion epidemic model with nonlinear incidence mechanism. I will discuss about the global boundedness and existence of solutions of the model. I will show that the infected people may concentrate on certain hot spots when the movement rates of infected people are limited. The hot spots will be characterized by the coefficients of the model, and if the hot spots consist with a single point then the infected people concentrate as a Dirac Delta measure. Numerical simulations will be performed to illustrate the results.

Within-host SARS-CoV-2 viral and immune dynamics

Organized by: Esteban A. Hernandez-Vargas, Hana Dobrovolny

  • Nora Heitzman-Breen Virginia Tech (Mathematics)
    "Modeling within-host and aerosol dynamics of SARS-CoV-2: the relationship with infectiousness"
  • The relationship between the dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a host’s upper respiratory tract and in surrounding aerosols is key in understanding SARS-CoV-2 transmission and informing intervention strategies. We developed a within-host and aerosol mathematical model, accounting for both total RNA and infectious RNA, and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.
  • Melanie Moses University of New Mexico (Computer Science)
    "Spatial Immune Model of Coronavirus (SIMCoV) in the lung"
  • A key question in SARS-CoV-2 infection is why viral loads and patient outcomes vary dramatically across individuals. Because spatial-temporal dynamics of viral spread and immune response are challenging to study in vivo, we developed Spatial Immune Model of Coronavirus (SIMCoV), a scalable computational model that simulates hundreds of millions of lung cells, including respiratory epithelial cells and T cells. SIMCoV replicates viral growth dynamics observed in patients and shows how spatially dispersed infections can lead to increased viral loads. The model also shows how the timing and strength of the T cell response can affect viral persistence, oscillations, and control. By incorporating spatial interactions, SIMCoV provides a parsimonious explanation for the dramatically different viral load trajectories among patients by varying only the number of initial sites of infection and the magnitude and timing of the T cell immune response. When the branching airway structure of the lung is explicitly represented, we find that virus spreads faster than in a 2D layer of epithelial cells, but much more slowly than in an undifferentiated 3D grid or in a well-mixed differential equation model. We further validate the branching model of the lung by showing that SIMCoV simulations of the spread of inflammation have similar growth rates and shapes to CT scans of SARS-CoV-2 infected lungs. We additionally model spread in the nasal cavity and compare to viral dynamics in that compartment. These results illustrate how realistic, spatially explicit computational models can improve understanding of within-host dynamics of SARS-CoV-2 infection.
  • Lars Kaderali Univesity Medicine Greifswald (Institute of Bioinformatics)
    "Modelling the intracellular replication of SARS-CoV-2 and related RNA viruses"
  • Positive-stranded RNA viruses are the largest group of viruses, and include human pathogens such as Dengue virus, haptitis C virus and coronaviruses, including SARS-CoV-2. They share many similarities in their lifecycle, albeit the diseases they cause show a wide spectrum of manifestations, from mild acute infections over long-term chronic infection to vigorous, life-threatening acute disease. We have developed detailed mathematical models of several positive stranded RNA viruses, and use these models to understand their within-host replication strategies, pan-viral similarities as well as virus-specific differences. In the talk, I will present our models on hepatitis C virus, dengue virus and coxsackievirus B3, and will compare these models to our ongoing work on modeling SARS-CoV-2, including detailed kinetic data and first results we have obtained in modeling the SARS-CoV-2 replication dynamics.
  • Hwayeon Ryu Elon University (Mathematics)
    "Mathematical Modeling of Immune Response to SARS-CoV-2"
  • Despite a tremendous volume of research in understanding the transmission of SARS-CoV-2 virus during the pandemic, how the human immune system responds to SARS-CoV-2 has not been yet fully understood due to limited analysis of the experimental or clinical information to date. In this work, we develop and analyze an in-host model to understand the role of various molecular pathways in successful viral clearance and to identify the key mechanisms responsible for disease severity exhibited by some patients. Our model explicitly represents the virus, innate immune cells, selected cytokines, and their interactions, which is formulated in a system of coupled ordinary and delay differential equations. With calibrated parameters against experimental data and literature we conduct numerical and sensitive analysis to determine the implications of variation of parameters. Our model demonstrates key aspects of immune response to SARS-CoV-2, specifically its sensitive pathways, which might be responsible for differences in disease severity exhibited by COVID-19 patients. Our results of the mechanisms involved in COVID-19 pathology could identify several therapeutic targets that would provide hypotheses to be tested clinically, thus, serving as a foundation for the development of evidence-based therapeutic strategies.
  • Mélanie Prague Univ. Bordeaux, Inria, Inserm, Bordeaux Population Health, France (Statistics in Immunology and translational medicine)
    "Joint modeling of viral and humoral response in Non-human primates to define mechanistic correlates of protection for SARS-CoV-2"
  • Determining correlates of protection is critical to the development of next-generation SARS-CoV-2 vaccines. And even when a correlate of protection has been identified, it is important to understand what level of that correlate needs to be achieved to provide protection from an event (which may be infection, transmission, or symptom severity...). In Alexandre et al. (eLife, 2022), we proposed a model-based approach to identify mechanistic correlates of protection based on dynamic modeling of viral dynamics and data mining of immunological markers using non-human primates studies (NHP). We have shown that RBD/ACE2 binding inhibition is a potent mechanism of protection against infection. Based on the analysis of the reproductive number in the animals, we propose a quantitative method to define a threshold for this correlate of protection against infection. We also extend the model to jointly describe the viral dynamics and the dynamics of the humoral response in naive, convalescent, and vaccinated NHP infected with SARS-CoV-2. We apply the method to three different studies in NHP investigating SARS-CoV-2 vaccines based on CD40 targeting, two-component spike nanoparticles, and mRNA.

Climate and vector-borne disease: insights from mathematical modeling

Organized by: Michael Robert, Zhuolin Qu, Christina Cobbold
Note: this minisymposia has multiple sessions. The other session is MS02-MEPI-1.

  • Christina Cobbold University of Glasgow (School of Mathematics and Statistics)
    "Vector population dynamics and trait variation drive trends in global disease incidence"
  • Climate change is having profound effects on the incidence of vector borne disease. However, developing effective measures of disease risk on a global scale are challenged by the complex ways in which environmental variation acts in vector-host-pathogen systems. Current models over-simplify the interaction between vector traits and environmental variation and so risk mis-estimating disease risk. Here, we derive a mathematical model for Aedes albopictus, the vector of dengue, and demonstrate how the interaction of vector traits and population dynamics explain the location, magnitude and timing of historical dengue outbreaks. We find long lived individuals that developed under favourable conditions can persist within the population long after the environmental conditions that created them have passed and may consequently have a disproportionate effect on pathogen transmission dynamics that cannot be accounted for by approaches that omit trait dynamics.
  • Morgan Jackson Virginia Commonwealth University (Department of Mathematics and Applied Mathematics)
    "Evaluating a Temperature-dependent Mosquito Population Model"
  • Dengue Virus causes over 390 million infections and around 40,000 deaths each year. This virus is primarily transmitted by the mosquito Aedes aegypti. The life cycle of these mosquitos is significantly impacted by temperature, however, temperature in often neglected in mechanistic models. Predictive models of mosquito populations thus require the inclusion of temperature and are valuable for helping medical officials plan for the impact of outbreaks. Using mosquito and climate data collected in Córdoba, Argentina from 2010-2013, we developed a non-autonomous ordinary differential equations model that includes temperature dependent parameters associated with mosquito life history. We performed local sensitivity and identifiability analysis to determine which model parameters should be estimated. We explored the effects of incorporating temperature in different combinations of life history characteristics to find the most parsimonious model that includes temperature. Additionally, we estimated values for combinations of density-dependent parameters to improve the model fit. These parameters control nonlinear population regulation but are often difficult to estimate from data alone. We found that including even just three temperature-based parameters: eggs laid per adult female, development rate of juveniles to adults, and adult mortality rate, produced a model that matches the data well. Additionally, we fit a density-dependent parameter and combinations of density dependent parameters to improve the model fit. We discuss these results in the context of improving mosquito population and dengue epidemiological models.
  • Stacey Smith? The University of Ottawa (Department of Mathematics and Faculty of Medicine)
    "Comparing malaria surveillance with periodic spraying in the presence of insecticide-resistant mosquitoes: Should we spray regularly or based on human infections?"
  • There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes that is entirely immune to the insecticide. The impulse is triggered either due to periodic spraying or when a critical number of malaria cases are detected. For small mutation rates, the mosquito-only submodel exhibits either a single mutant-only equilibrium, a mutant-only equilibrium and a single coexistence equilibrium, or a mutant-only equilibrium and a pair of coexistence equilibria. Bistability is a likely outcome, while the effect of impulses is to introduce a saddle-node bifurcation, resulting in persistence of malaria in the form of impulsive periodic orbits. If certain parameters are small, triggering the insecticide based on number of malaria cases is asymptotically equivalent to spraying periodically.

Recent advances in the mathematics of biochemical reaction networks

Organized by: Tung Nguyen, Matthew Johnson, Jiaxin Jin
Note: this minisymposia has multiple sessions. The other session is MS02-MFBM-1.

  • Hyukpyo Hong Institute for Basic Science (Biomedical Mathematics Group)
    "Network translation allows for revealing long-term dynamics of stochastic reaction networks"
  • Long-term behaviors of biochemical systems are described by steady states in deterministic models and stationary distributions in stochastic models. Their analytic solutions can be obtained for limited cases, such as linear or finite-state systems. Interestingly, analytic solutions can be easily obtained when underlying networks have special topologies, called weak reversibility (WR) and zero deficiency (ZD). However, such desired topological conditions do not hold for the majority of cases. Thus, we propose a method of translating networks to have WR and ZD while preserving the original dynamics was proposed. Additionally, we prove necessary conditions for having WR and ZD after translation. Our method provides a valuable tool for analyzing and understanding the long-term behavior of biochemical systems, and we demonstrate its efficacy with several examples.
  • Angelyn Lao De La Salle University (Department of Mathematics and Statistics)
    "A Reaction Network Analysis of Insulin Signaling"
  • The insulin signaling system is an important metabolic system that initiates the uptake of glucose into the cell. This reduced ability of cells to use available insulin for energy metabolism is viewed as a common factor in diseases such as obesity, type 2 diabetes, metabolic syndrome, and cancer, and more recently to brain insulin resistance in connection with mild cognitive impairment and Alzheimer’s disease (AD). The complexity of the insulin signaling system, both in terms of the number of molecular components involved as well as the intricate combination of positive and negative feedback loops, clearly warrants the application of mathematical modeling and computational tools. This talk presents the construction of the insulin signaling reaction network and the analysis of its robustness and stability using Chemical Reaction Network Theory.
  • M. Ali Al-Radhawi Northeastern University (Department of Electrical and Computer Engineering)
    "Contraction and entrainment in reaction networks"
  • In previous work, we have developed an approach to understanding the long-term dynamics of classes of chemical reaction networks, based on “rate-dependent Lyapunov functions”, and developed an effective computational package. In this talk, we show that stronger notions of convergence can be established by proving contraction with respect to non-standard norms. This enables us to show that such networks entrain to periodic inputs. We illustrate our theory with examples from signalling pathways and genetic circuits.
  • Jinsu Kim POSTECH (Mathematics / Mathematical biology)
    "Recent studies about mixing times of stochastically modeled reaction networks"
  • Molecular counts of small-size biological systems can be modeled with continuous-time Markov chains on infinite positive integer grids with polynomial rates. In this talk, we will discuss recent studies about mixing times of continuous-time Markov chains modeling chemical reaction systems. The mixing time, which indicates the time for the distance between the distribution of the stochastic process and its stationary distribution, is typically investigated with the Lyapunov function method and canonical path method. Recently, we discovered examples that do not lend themselves easily to analysis via those two methods but are shown to have either fast mixing or slow mixing with our new technique.

Integration of data and modeling for multiscale biology

Organized by: Yuchi Qiu, Heyrim Cho

  • Jianhua Xing University of Pittsburgh (Computational and Systems Biology)
    "Reconstructing cellular dynamics from single cell data"
  • A grand challenge in single cell studies is to construct a quantitative, predictive, and genome-wide mathematical model describing cellular dynamics. Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. A frontier of research is how to extract dynamical information from the snapshot data. In this talk I will first discuss our recently developed dynamo framework (Qiu et al. Cell, 2022), focusing on the underlying mathematical framework. Then I will discuss our recent efforts of reconstructing full dynamical equations using discrete calculus on graphs (Zhang et al. to be submitted). I will conclude with an example of applying the formalism, together with transition path analyses originally developed in chemical physics, to study how epithelial-to-mesenchymal transition couples with cell cycle (Wang et al. Sci Adv 2020, eLife 2022, Hu et al., in preparation).
  • Aden Forrow University of Maine (Mathematics and Statistics)
    "Trajectory inference with lineage tracing"
  • Over the past decade, rapid advances in experimental techniques have produced a flood of data on biological systems at single cell resolution. A key goal for the field is to understand dynamic processes by inferring the trajectories of cell states over time. Time-dependent information typically cannot be recovered directly because standard high-throughput measurements destroy the measured cells. That experimental constraint leads to strict mathematical limits on what it is possible to learn from the data. To get around those limits, we need different measurements, such as recording the history of cell divisions with lineage tracing. In this talk, I will show how lineage tracing helps disentangle complex trajectories that could not be resolved from traditional single-cell data, including identifying disparate ancestry among nearly identical cells.
  • Yuchi Qiu Michigan State University (Department of Mathematics)
    "Interpretable AIs in data-driven biology: from topological data analysis to multiscale modeling"
  • Artificial intelligence (AI) has become increasingly prominent in analyzing biological data on both large-scale and single-cell levels, leading to a revolution in deciphering functions and dynamics of complex biological systems. Despite its success, traditional black-box AIs often struggle to provide comprehensive understanding and interpretation of the multiscale processes in complex, heterogeneous, and noisy data. To address these challenges, we combine topological data analysis (TDA) and multiscale modeling to enhance AI interpretability. Our TDA-driven models capture the intricate patterns in complex data. Additionally, data-driven multiscale modeling infers temporal dynamics within biological systems. By incorporating these innovative techniques, we aim to accelerate protein design and understand cell fate dynamics from single-cell omics data, ultimately improving the applicability and interpretability of AI models in the analysis of complex biological data.

Mathematical Ophthalmology

Organized by: Paul A. Roberts, Jessica Crawshaw
Note: this minisymposia has multiple sessions. The other session is MS02-NEUR-1.

  • Paul A. Roberts University of Birmingham (Centre for Systems Modelling and Quantitative Biomedicine)
    "Mathematical and Computational Ophthalmology: Coming of Age"
  • This talk will set the scene for those which follow in the Mathematical Ophthalmology minisymposium. I will begin by defining what we mean by the terms Mathematical Ophthalmology (a new term which I have coined) and Computational Ophthalmology (an existing term) and how these fields relate both to each other and to more established experimental and clinical disciplines. I shall give a brief history of these emerging fields, highlighting key case studies, and discuss their future prospects. I will also be announcing and inviting participation in a number of exciting opportunities and initiatives aimed at promoting these fields and supporting those working within them.
  • Brendan C. Fry Metropolitan State University of Denver (Department of Mathematics and Statistics)
    "Modeling metabolic blood flow regulation and oxygenation in the human retinal microcirculation"
  • The retinal microcirculation perfuses the retinal cells responsible for vision, and impairments in retinal blood flow and oxygenation are involved in the progression of eye diseases such as glaucoma. Here, an established theoretical hybrid model of a retinal microvascular network will be presented and extended to include effects of local blood flow regulation on oxygenation. A heterogeneous description of the arterioles based on confocal microscopy images is combined with a compartmental representation of the downstream capillaries and venules. To simulate oxygen transport in the arterioles, a Green’s function method is used; in the capillary and venular compartments, a Krogh cylinder model is applied. Acute regulation of blood flow is simulated in response to changes in pressure, shear stress, and metabolism. The model results predict that both an increase in intraocular pressure and an impairment in blood flow regulation can lead to decreased tissue oxygenation, indicating that both mechanisms represent factors that can lead to the impaired oxygenation observed in eye disease. Results from the model further imply that the metabolic response mechanism reduces the fraction of poorly-oxygenated tissue, but that the pressure- and shear-stress-dependent response mechanisms may actually hinder the vascular response to changes in oxygenation. Importantly, the heterogeneity of the microvascular network structure demonstrates that traditionally-reported average values of tissue oxygen levels hide significant localized defects in tissue oxygenation that may be involved in eye disease processes. Going forward, the model framework will help provide comparisons to sectorial-specific clinical data, in order to better assess the role of impaired blood flow regulation in glaucoma.
  • Julia Arciero Indiana University - Purdue University Indianapolis (Mathematical Sciences)
    "Predicting the impact of capillary density on retinal vessel and tissue oxygenation using a theoretical model"
  • Impairments in retinal blood flow and oxygenation have been shown to contribute to the progression of glaucoma. In this study, a theoretical model of the human retina is used to predict blood flow and tissue oxygenation in retinal vessels and tissue for varied levels of capillary density. The model includes a heterogeneous representation of retinal arterioles and a compartmental representation of capillaries and venules. A Green’s function method is used to model oxygen transport in the arterioles, and a Krogh cylinder model is used in the capillaries and venules. In our clinical observations, early glaucoma patients are shown to exhibit a 10-12% reduction in capillary density compared to healthy individuals. The model is simulated for capillary density values ranging from 250 to 750 capillaries/mm^2. Oxygen extraction fraction, defined as the ratio of oxygen consumption to oxygen delivery, is calculated for each model simulation. The model predicts a 6% and 53% decrease in mean PO_2 in retinal vessels immediately downstream of the capillaries when capillary density is decreased from its reference value of 500 capillaries/mm^2 by 10% and 50%, respectively. Ultimately, the mathematical model demonstrates the significant detrimental impact of such decreases in capillary density on the oxygenation of retinal tissues.
  • Remi Hernandez University of Liverpool (Department of Cardiovascular and Metabolic Medicine)
    "Virtual populations of the retina to characterize hypoxia in wet AMD"
  • Retinal angiograms with high resolution are taken routinely in eye clinics. Several studies have highlighted the association between angiographic parameters and several retinal diseases, including wet age-related macular degeneration (wAMD). These parameters indicate a decline in retinal perfusion which may lead to hypoxia. Because hypoxia may be a trigger of the pathological angiogenesis seen in eyes with wAMD, quantifying it in diseased eyes is important to understand and model the disease and find optimal treatment strategies. We have created synthetic vasculatures using an algorithm mimicking angiogenesis along with convection and reaction-diffusion models of oxygen perfusion. We propose to develop a framework to computationally study hypoxia in 3-dimensional virtual populations of the retina, in health and disease.

Techniques and Methods in Modelling Cancer Treatment

Organized by: Kathleen Wilke, Gibin Powathil
Note: this minisymposia has multiple sessions. The other session is MS02-ONCO-1.

  • Jana Gevertz The College of New Jersey (Department of Mathematics & Statistics)
    "Guiding model-driven combination dose selection using multi-objective synergy optimization"
  • The biomedical community has long sought to identify synergistic drugs for which the combined effect is greater than additive. However, lack of consensus on the definition of additivity has complicated this goal, particularly because a combination classified as synergistic by one definition can be classified as antagonistic by another. In this talk, I introduce the Multi-Objective Optimization of Combination Synergy – Dose Selection (MOOCS-DS) method as a rigorous approach to bring clarity and consistency to selecting an optimally synergistic dose for a pre-selected drug combination. MOOCS-DS bridges the gap between efficacy-based additivity definitions focused on improving effectiveness and potency-based definitions focused on reducing toxicity. It does this by identifying the Pareto optimal doses, defined as the set of possible combination doses for which one synergy metric cannot be improved without compromising the other. I demonstrate the potential of this approach to guide dose and schedule selection using a model fit to pre-clinical data of the combination of the PD-1 checkpoint inhibitor pembrolizumab and the antiangiogenic drug bevacizumab on two lung cancer cell lines.
  • Mohammad Zahid H. Lee Moffitt Cancer Center & Research Institute (Integrated Mathematical Oncology)
    "Fractionated Photoimmunotherapy to Stimulate an Anti-Tumor Immune Response"
  • Introduction: Photodynamic therapy (PDT) is an anti-cancer therapy where a photosensitizer (e.g. verteporfin) is delivered to cells and then near-infrared light is used to kill the cells that have taken up the photosensitizer. Current PDT is applied locally but does not discriminate between cancer and non-cancer cells. Photoimmunotherapy (PIT) utilizes photosensitizers conjugated to antibodies targeted against cancer cells with the idea that this will lead to more targeted cancer killing and sparing of other cell types in the area. We aim to use preliminary in vitro measurements to inform a modeling investigation of how PIT may impact tumor-immune dynamics and inform methods of best utilizing PIT to promote an anti-cancer immune response. Materials and Methods: Dose response curves of tumor cells (OVCAR5 ovarian cancer cell line) and T-cells (murine T-cells) to PDT (verteporfin + 665 nm light), PIT (cetuximab-verteporfin + 665 nm light), and chemotherapy (cisplatin) were measured in order to measure relative tumor and T-cell viability. These results were used in conjunction with a mathematical model of tumor and immune effector cell interaction consisting of a system of coupled ordinary differential equations that combine logistic tumor growth, immune-mediated tumor cell kill, and immune exhaustion. This model yields a phase plane that separates all combinations of initial conditions into two basins of attraction corresponding with uncontrolled tumor and immune-mediated cancer control. The in vitro viability analyses were used as inputs to the math model to search for potential dosing regimes and treatment schedules that could lead to immune-mediated cancer control. Results and Discussion: The PDT and chemotherapy treatments showed typical sigmoidal dose response curves with both tumor and T-cell kill increasing with increasing dose. However, in the case of PIT with the cancer-cell targeted immunoconjugate, low intensity light doses (< 10 J/cm2) yielded an increase in T-cell numbers (i.e. immunostimulatory response) relative to the no-treatment control. We leveraged this immunostimulatory regime to simulate fractionated PIT dosing schedules that increase the number of immune effector cells and decreasing the number of tumor cells. Simulation results of tumor-immune dynamics with PIT delivered in 6 fractions of 1 J/cm2 each, where each PIT fraction stimulates T-cell growth, gradually moved the immune state of the system into the cancer control region of the phase plane. We further calculated the minimum number for fractions needed for tumor control for all initial conditions over the entire immunostimulatory dose range from 1-10 J/cm2. These results present hypotheses that can be tested with in vitro co-culture measurements in a feedback loop of experiment and modeling. Conclusions: Here we demonstrated a first application of a simple model of tumor-immune interaction with inputs of in vitro measurements of cell survival in order to motivate fractionated PIT using an immunostimulatory dose regime.
  • Kira Pugh Swansea University (Mathematics)
    "In silico approaches to study the synergy of DDR inhibitor drugs"
  • DNA damage occurs thousands of times per cell per day with the DNA damage response (DDR) pathway aiding detection and repair. Some of the pathways involved in the DDR can be exploited for anti-cancer treatments, whereby inhibitor drugs can be used to cause certain pathways to stop working, facilitating cancer growth inhibition and/or death. The ataxia-telangiectasia and Rad3-related (ATR) inhibitor ceralasertib and the poly (ADP-ribose) polymerase (PARP) inhibitor olaparib have shown synergistic activity, in vitro, in the FaDu ATM-KO cell line. Experimental data shows that when these drugs are combined, lower doses and shorter treatment times can induce greater toxicity in cancer cells than using either drug as a monotherapy. We have developed a biologically-motivated mathematical model including cell cycle-specific interactions for both olaparib and ceralasertib, implemented using both a deterministic ordinary differential equation (ODE) model and a stochastic agent-based model (ABM). We study the differences between using an ODE model that considers a homogenous population of cancer cells and using an ABM where the cell population is heterogeneous as each cell has its own characteristics.
  • Kathleen Wilkie Toronto Metropolitan University (Mathematics)
    "Modelling Radiation Cancer Treatment with Ordinary and Fractional Differential Equations"
  • Fractional calculus has recently been applied to mathematical modelling of tumour growth, but it’s use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.

Evolutionary game theory in cancer

Organized by: Anuraag Bukkuri, Katerina Stankova
Note: this minisymposia has multiple sessions. The other session is MS02-ONCO-2.

  • Helena Coggan University College London (Mathematics)
    "Simulations of 3D organoids suggest inhibitory neighbour-neighbour cell signalling as a possible growth mechanism in early lung cancer"
  • Cancer is driven by the development of genetic mutations. Some mutations which appear in aggressive lung cancers, particularly in people who have never smoked, have also been found to exist quite harmlessly in perfectly healthy people. Although inflammatory cytokines have been highlighted as important promoters of tumour formation, it is unclear what additional stimuli are required in order to drive a `normal cell' harbouring an oncogenic mutation into an invasive tumour. Game-theoretic models suggest that cell fitness may depend on interactions with neighbouring cells. To examine this hypothesis, we looked at the behaviour of stem cells with an activating mutation in EGFR, L858R, when they were given all the nutrients and space required to grow uninhibited in three dimensions. We used computational simulations to model their growth, and predicted that these cells seemed to be suppressing the division of any other cells they touch. We hypothesise that in the very early stages of cancer development, this mutation gives cells a reproductive advantage by preventing the division of non-mutant cells in their environment and driving down competition for space and resources. This also suggests that the success of these pre-cancerous cells depends on their spatial environment and the surrounding cell ecology. We hope that this insight into early cancer development will drive more research into the consequences of cell-cell interaction dysfunction on early tumour initiation.
  • Monica Salvioli - Part 1 Delft University of Technology (Institute for Health Systems Science)
    "Validation of the polymorphic Gompertzian model of advanced cancer through in vitro and in vivo data"
  • Mathematical modeling plays an important role in forming our understanding of therapy resistance mechanisms in cancer. Gompertzian model, analyzed recently by Viossat and Noble in the context of adaptive cancer therapy, describes a heterogeneous cancer population consisting of therapy-sensitive and -resistant cells interacting with each other. Their mathematical analysis demonstrates advantages of adaptive therapy in such models. However, before the theoretical findings can be implemented to cancer therapy design, the model should be validated with real-world data. In our study, we show that the polymorphic Gompertzian model successfully captures trends in both in vitro and in vivo data on non-small cell lung cancer (NSCLC) dynamics under treatment. Biological interpretation of the model’s fit to in vitro data allowed us to confirm previously reported anti-treatment effects of cancer-associated fibroblasts. For the in vivo data, we showed the superiority of the polymorphic Gompertzian model over the monomorphic classical models in fitting the U-shape trend of tumor dynamics and comparable accuracy in other trend categories. In general, the polymorphic Gompertzian model corresponds well to real-world data, thus, its theoretical conclusions can be implemented to the development of clinical studies on adaptive cancer therapy.
  • Christin Nyhoegen Max Planck Institute for Evolutionary Biology (RG Stochastic Evolutionary Dynamics)
    "Mathematical models for the optimization of multi-drug treatment strategies"
  • The evolution of resistance in bacteria and other pathogens, as well as in cancer, poses a major challenge for patient treatment worldwide. One option to reduce the risk of resistance during treatment is to increase the genetic barrier to resistance, which can, for example, be achieved by increasing the number of drugs applied. Different drugs could be alternated (sequential therapy) or administered simultaneously (combination therapy). With multiple drugs in combination, applying the different drugs at the same concentration as in mono-therapy may not be necessary to clear the population of susceptible cells. In fact, reducing the doses might even be required to avoid toxicity. However, lowering the dose might reduce the benefits of combination therapy in controlling resistance. How should we thus choose the number of drugs and their doses to minimize the risk of resistance while efficiently treating a patient and avoiding side effects? In this talk, I will present a pharmacodynamic model for the combination of multiple antibiotics, which can be adapted to study other resistance problems. This model allows us to compare the probability of resistance under mono-therapy at high drug doses and combination therapies at lower doses, keeping the 'total dose' constant. For most of the parameter space, combination therapy with two drugs leads to a lower probability of resistance than mono-therapy. Still, it is not always superior to the treatment with just one drug. Especially the pharmacodynamic properties and the mode of action of the drugs influence the optimal treatment choice. Our mathematical analysis allows us to disentangle the effects of a strategy on the appearance of mutations from those on their establishment probability, allowing us to understand what leads to a strategy's success.
  • Alanna Sholokhova University of Washington (Applied Mathematics)
    "Quantifying neoantigen evolution and response to immunotherapy in colorectal cancer"
  • Each cancerous colorectal tumor contains tumor-specific antigens (neoantigens). Because these neoantigens are present only in the tumor and not in healthy tissue, they are excellent targets for cancer immunotherapies. Checkpoint-blockade immunotherapy enables the patient’s native immune system to recognize tumor cells that were previously invisible due to immune escape, but this therapy has extremely heterogeneous patient outcomes, ranging from total failure to complete remission. We seek to understand how the mutagenic landscape of the tumor is related to therapeutic outcomes. First, we model neoantigen evolution using a stochastic branching-process model. Next, we use a dynamical model of anti-PD1 checkpoint-blockade therapy to predict response to therapy in these in-silico tumors. We relate therapeutic outcomes to heterogeneity of tumor mutational landscape, quantified by both the number of mutations in the tumor as well as the clonality of the neoantigens present in the tumor. We find that mutational burden, the total number of neoantigenic mutations present in the tumor, is insufficient to determine therapeutic outcome. Neoantigenic clonality, the fraction of tumor cells that contain a particular neoantigen, is key in determining response to therapy.

The 10th anniversary of MBI’s 2013 Workshop for Young Researchers in Mathematical Biology

Organized by: Rebecca Everett, Angela Peace
Note: this minisymposia has multiple sessions. The other session is MS02-OTHE-1.

  • Hayriye Gulbudak University of Louisiana at Lafayette (Mathematics)
    "A delay model for persistent viral infections in replicating cells"
  • Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system and provide bifurcation diagrams illustrating transcritical (backward and forward), saddle-node, and Hopf bifurcations, and provide evidence of homoclinic bifurcations and a Bogdanov–Takens bifurcation. We investigate the possibility of long term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether or not the virus survives.
  • Amy Buchmann University of San Diego (Mathematics)
    "A decade of modeling microscale biofluids"
  • One area of research within mathematical biology is computational biofluids. This includes understanding the mechanics of biological fluid flow systems in the human body (the circulatory and respiratory systems), cells, and microorganism motility. I became interested in biofluids right around the time that I attended the Workshop for Young Researchers in Mathematical Biology in 2013, and have spent most of my career working in this area focusing on microscale biofluids. In this talk, I will discuss several of my collaborative projects that study microorganisms by modeling the interactions between elastic structures in a viscous fluid.
  • Reginald McGee College of the Holy Cross (Mathematics and Computer Science)
    "Towards A Modeling Framework For Pediatric Sickle Cell Pain"
  • Sickle cell pain presents in acute episodes in pediatric patients, as opposed to the chronic pain observed in adults. The episodic nature of pain events in pediatric patients necessitates a distinct approach from what has been used to mathematically model pain severity levels in adults. Statistical studies have examined interactions between sleep actigraphy measurements --- like sleep quality and sleep efficiency --- and pain levels in pediatric populations, and we propose a framework for modeling pediatric pain dynamics that incorporates the effects of sleep actigraphy and electronic survey data over varying time windows. We hypothesize that cumulative effects of these measurements will be more important than daily measurements in both replicating pain severity levels and determining markers of a pain episode. The ability to identify markers preceding the onset of a pain episode will be crucial in improving patient quality of life. We present work in progress towards developing this modeling framework.
  • Michael A. Robert Virginia Tech (Department of Mathematics)
    "Investigating impacts on malaria transmission of altered bioamine levels in Anopheles mosquitoes"
  • Malaria is caused by Plasmodium species that are transmitted to humans primarily by Anopheles mosquitoes. Currently, over half of the world’s population is at risk of malaria, and after decades of progress towards eradication led to declines in cases reported globally, cases have increased since 2020, with 247 million cases and 619,000 deaths reported in 2021. Malaria infection is known to influence levels of biogenic amines in human blood. Specifically, individuals with severe malaria may exhibit increased concentrations of histamine and/or decreased concentrations of serotonin. The altered amine levels may also impact the biology and behavior of Anopheles mosquitoes that ingest them in bloodmeals, but it remains to be seen what role these changes may have on mosquito population dynamics and malaria transmission. We developed a stage-structured discrete time mathematical model of mosquito population dynamics coupled with population-level malaria transmission dynamics to investigate how these altered amine levels may play a role in the malaria transmission cycle. We incorporated demographic, behavioral, and parasite reproduction data into the model and explored scenarios that consider different possible concentrations of histamine and serotonin in bloodmeals and different effects thereof by studying differences in mosquito population size and malaria incidence and prevalence. We explore different possible extensions of the model and discuss our findings in the context of malaria control as well as future experimental work.

Recent Studies on the Biomechanics and Fluid Dynamics of Living Systems: Locomotion and Fluid Transport

Organized by: Alexander Hoover, Matea Santiago
Note: this minisymposia has multiple sessions. The other session is MS02-OTHE-2.

  • Alexander P. Hoover Cleveland State University (Mathematics)
    "Interfacing in-Situ and in-Silico Experiments in Organismal Fluid Pumping"
  • Far from the surface, the ocean's midwater present a rich frontier of biodiversity that is not well understood. Part of this gap in our knowledge is the great expense involved in collecting data with remotely operated vehicles. In this presentation, we will discuss the pipeline of developing in-silico computational experiments in concert with in-situ experimental data. Using a combination of particle image velocimetry data, optical scans, and confocal microscopy, we will discuss the creation of fluid-structure interaction models for organismal pumping and fluid transport, with the goal of developing an intuition on the physical mechanisms that drive their success. Using a combination of simplified geometries and scanned body meshes, we will employ the immersed boundary/finite element (IB/FE) method to simulate chambered, valveless pumping mechanism generated by the pelagic tunicate known as a larvacean. Additionally, we will use the same modeling methodology to explore the metachronal motion and fluid transport of the parapodial paddles of the pelagic, midwater polychaete known as tomopterids. All motion described in these systems will not be prescribed and will emerge from the interaction of active muscular tension, passive elastic recoil, and the local fluid environment.
  • Silas Alben University of Michigan (Mathematics Department)
    "Efficient bending and lifting patterns in snake locomotion"
  • We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10-100% higher.
  • Matea Santiago University of Arizona (Mathematics)
    "The role of elasticity and tension in soft coral pulsing"
  • The pulsing behavior of Xeniid soft corals is characterized by active muscle contraction and passive expansion, similar to many other swimming marine invertebrates. However, soft corals are sessile animals and do not locomote. Previous experimental and computational studies have indicated that the pulsing behavior mixes the surrounding fluid and enhances the photosynthesis of their zooxanthellae. Symbiotic photosynthesis is hypothesized to be the coral’s main energy source. Past computational work directly prescribed motion to the coral tentacles. This work instead drives motion by modeling the muscle contraction as applied active tension and expansion through the passive elasticity of the coral body. The role of elasticity and muscle tension is explored in the coral’s kinematics and the resulting fluid flow using the immersed finite element-finite difference (IFED) method implementation in the software library IBAMR to simulate the elastic-structure fluid interaction of the tentacles and surrounding fluid. These results will provide insight into the underlying biomechanics of the pulsing behavior by observing the emergent behavior of the system. The results of this study contribute to cnidarian biomechanics knowledge and have implications in soft robotics design.

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.