Minisymposia: MS02

Monday, July 17 at 04:00pm

Minisymposia: MS02

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 MS01-ECOP-1.

  • Xingfu Zou University of Western Ontario (Mathematics)
    "On a predator-prey model with fear effect, predator-taxis and degeneracy in spatially heterogeneous environmen"
  • I will present a diffusive predator-prey model that includes fear effect, predator-taxis, spatial heterogeneity and degeneracy on some space dependent model parameters. I will report some recent results on local and global bifurcations of steady state solutions of the model system. This is a joint work with Dr. Jingjing Wang.
  • Yu Jin University of Nebraska-Lincoln (Mathematics)
    "The influence of a protection zone on population dynamics"
  • Protecting native species or endangered species has been an important issue in ecology. Differential equations have been applied to incorporate protection zones in the habitat of species to investigate the influence of protection zones on long-term population dynamics. We derive a reaction-diffusion model for a population in a one-dimensional bounded habitat, where the population is subjected to a strong Allee effect in its natural domain but obeys a logistic growth in a protection zone. We establish threshold conditions for population persistence and extinction via the principal eigenvalue of an associated eigenvalue problem, and then propose strategies for designing the optimal location of the protection zone under different boundary conditions in order for the population to persist in a long run.
  • Arwa Abdulla Baabdulla University of Alberta (Department of Mathematical and Statistical Sciences)
    "Mathematical Modelling of Reovirus in Cancer Cell Cultures"
  • Reovirus is a nonpathogenic virus that inhabits the enteric tract of mammals. It is a double-stranded RNA virus that showed the ability to naturally infect and lyse tumors under in vitro and in vivo conditions. Unmodified reovirus (T3wt) is currently being evaluated as an anti-cancer therapy in more than 30 clinical trials in different types of cancer such as metastatic breast cancer, prostate cancer, and colorectal cancer. Dr. Maya Shmulevitz from Li-Ka Shing Institute of Virology, University of Alberta and her PhD student Francisca Cristi focus in their laboratory to improve reovirus as a cancer therapy. In collaboration with them, we are trying to answer the following questions via mathematical modelling: How far does the virus spread depending on the binding rate? How does the viral invasion speed depend on the binding rate? How does reducing the binding rate affect the plaque size?
  • Domènec Ruiz-Balet Imperial College London (Mathematics)
    "The tragedy of the commons via traveling waves in mean-field games"
  • The main topic of the talk is to observe mathematically the tragedy of the commons in spatial models. Garret Hardin, in 1968, exposed in his seminal paper, several situations in which the uncoordinated action of selfish individuals can lead to the depletion of a common resource, the so-called tragedy of the commons. We will consider a population model that consists of the most basic reaction-diffusion equations and we will formulate a harvesting game. Making use of a mean-field game (MFG) formulation, we will observe how the MFG “reversed” travelling wave solutions in the sense that, in the absence of players the population would invade the whole domain but in the aforementioned Nash equilibria the population gets extinguished. We will also briefly discuss other population models in which this situation arises.

Multiscale Mechanistic Modeling in Immunology (in celebration of Denise Kirschner’s 60th birthday)

Organized by: Marissa Renardy, Caitlin Hult

  • Marissa Renardy Applied BioMath (Modeling)
    "Capturing CAR-T cell therapy dynamics through semi-mechanistic modeling"
  • Chimeric antigen receptor T (CAR T) cell therapy has shown remarkable success in treating various leukemias and lymphomas. CARs are engineered to redirect T cells to specific tumor associated antigens. Pharmacokinetic (PK) behavior of CAR T cell therapy is distinct from other therapies due to its 'living' nature; it is characterized by an exponential expansion, fast initial decline (contraction), and slow long-term decline (persistence). Previous models have not mechanistically described all three of these phases. In this work, we develop a semi-mechanistic model of CAR T PK/PD. We use this model to replicate published PK and efficacy data and to explore sources of variability.
  • Pariksheet Nanda University of Michigan Medical School (Microbiology and Immunology)
    "Calibrating multivariate models using CaliPro and approximate Bayesian computing"
  • Mathematical and computational models are increasingly complex and are typically comprised of one-or-more methods such as ordinary differential equations, partial differential equations, agent-based and rule-based models, etc. Lacking analytical methods, fitting such multivariate biological models to experimental datasets requires iterative parameter sampling-based approaches to establish appropriate ranges of model parameters that capture the corresponding experimental datasets. However, these models typically comprise large numbers of parameters and therefore large degrees of freedom. Thus, fitting these multivariate models to experimental datasets presents significant challenges. We build on our previously published mechanistic, multiscale model of lung granuloma formation from infection by Mycobacteria tuberculosis by calibrating to novel imaging data and metadata from non-human primates to more precisely simulate biological behavior. We apply our model agnostic Calibration Protocol (CaliPro) and explore approximate Bayesian computing (ABC) to highlight strengths and weaknesses among these calibration methods.
  • Maral Budak University of Michigan Medical School (Department of Microbiology & Immunology)
    "Optimizing regimen treatment during the host-pathogen interaction of tuberculosis using a multi-scale computational model"
  • Tuberculosis (TB) continues to be one of the deadliest infectious diseases in the world, causing ~1.5 million deaths every year. The World Health Organization initiated an End TB Strategy that aims to reduce TB-related deaths in 2035 by 95%. Recent research goals have focused on discovering more effective and more patient-friendly antibiotic drug regimens to increase patient compliance and decrease emergence of resistant TB. To that end, many antibiotics have been identified through in vivo studies and clinical trials that may improve the current standard regimen by shortening treatment time. However, testing every possible combination regimen either in vivo or clinically is not feasible due to experimental and clinical limitations. To identify better regimens more systematically, we simulated pharmacokinetics/pharmacodynamics of various regimens to evaluate efficacies, and then compared our predictions to both clinical trials and nonhuman primate studies. We used GranSim, our well-established hybrid multi-scale agent-based model that simulates granuloma formation and antibiotic treatment, for this task. In addition, we established a multiple-objective surrogate-assisted optimization pipeline using GranSim to discover optimized regimens based on treatment objectives of interest, i.e., minimizing total drug dosage and lowering time needed to sterilize granulomas. Our approach can efficiently test many regimens and successfully identify optimal regimens to inform pre-clinical studies or clinical trials and ultimately accelerate the TB regimen discovery process.
  • Christian Michael University of Michigan - Michigan Medicine (Microbiology & Immunology)
    "Towards digital partners of Mycobacterium tuberculosis infection within a virtual city framework"
  • Mycobacterium tuberculosis (Mtb) is an infectious, airborne microbe that causes tuberculosis (TB), a pandemic infecting roughly a third of the global population. The primary sites of infection are lung granulomas: structures comprising Mtb, immune cells and dead tissue. The high level of granuloma heterogeneity and the slow, complex progression of the disease impacts the relative efficacy of treatments. Considering the challenges of collecting data in TB, it is of critical importance to supplement both experimental and clinical data on TB with computational models that capture the variety of outcomes observed in granulomas both within and between patients . Our group has created HostSim, a host-scale agent-based model of granulomas. Our hybrid framework links lung, lymph node and blood models at multiple spatial scales and is calibrated to experimental data and synthetic data from our fine-grained cell-based granuloma-scale model (GranSim). We next used HostSim to build a Virtual City: a collection of virtual patients, each treated with various medical interventions to quantify impact. We are using Virtual City to build towards Digital Partners - a method for approximating the impact of interventions on specific patients via their most quantitatively similar virtual patients to obtain efficient predictions for effective personalized treatment.
  • Elsje Pienaar Purdue University (Biomedical Engineering)
    "Biofilm impacts in Non-tuberculous mycobacterial infections in the airway"
  • Incidence and prevalence of MAC infections are increasing globally, and reinfection is common. Thus, MAC infections present a significant public health challenge. We quantify the impact of MAC biofilms and repeated exposure on infection progression using a computational model of MAC infection in lung airways. MAC biofilms aid epithelial cell invasion, cause premature macrophage apoptosis, and limit antibiotic efficacy. In this computational work we develop an agent-based model that incorporates the interactions between bacteria, biofilm, and immune cells. In this computational model, we perform virtual knockouts to quantify the effects of the biofilm sources (deposited with bacteria vs. formed in the airway), and their impacts on macrophages (inducing apoptosis and slowing phagocytosis). We also quantify the effects of repeated bacterial exposures to assess their impact on infection progression. Our simulations show that chemoattractants released by biofilm-induced apoptosis bias macrophage chemotaxis towards pockets of infected and apoptosed macrophages. This bias results in fewer macrophages finding extracellular bacteria, allowing the extracellular planktonic bacteria to replicate freely. These spatial macrophage trends are further exacerbated with repeated deposition of bacteria. Our model indicates that interventions to abrogate macrophages’ apoptotic responses to bacterial biofilms and/or reduce frequency of patient exposure to bacteria will lower bacterial load, and likely overall risk of infection.

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

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

  • Esteban Abelardo Hernandez-Vargas University of Idaho (Department of Mathematics and Statistical Science)
    "The shape of antibody dynamics of severe and non-severe patients with COVID-19: A mathematical modeling approach"
  • The COVID-19 pandemic is a significant public health threat with unanswered questions regarding the immune system's role in the disease's severity level. In this paper, based on antibody kinetic data of patients with different disease severity, topological data analysis by the mapper algorithm highlights apparent differences in the shape of antibody dynamics between three groups of patients, which were non-severe, severe, and one intermediate case of severity. Subsequently, different mathematical models were developed to quantify the dynamics between the different severity groups. The best model was the one with the lowest median value of the Akaike Information Criterion for all groups of patients. Although high IgG level has been reported in severe patients, our findings suggest that IgG antibodies in severe patients may be less effective (affinity) than in non-severe patients due to early B cell production and early activation of the seroconversion process from IgM to IgG antibody. A bifurcation associated with a stable virus-positive steady state suggests that a sufficiently rapid viral replication can overcome the T cell response to cause the infection. Our work contributes to the in-host modeling of COVID-19 (and future related diseases), which can lead to effective treatments and an understanding of the disease from a systems perspective.
  • Veronika I. Zarnitsyna Emory University School of Medicine (Microbiology and Immunology)
    "Competing Heterogeneities in Vaccine Effectiveness Estimation"
  • According to epidemiological data, protection from the flu and COVID-19 vaccines could wane within a year. Accurately measuring this fast waning of vaccine effectiveness (VE) is crucial for protecting public health, guiding vaccine development, and informing individual health decisions. Population heterogeneities in underlying susceptibility to infection and vaccine response pose an additional challenge in VE estimation, as they can cause measured VE to change over time, even without pathogen evolution or actual waning of immune responses. VE studies often rely on time-to-infection data and the Cox proportional hazards model. An extension of the Cox proportional hazards model, which utilized scaled Schoenfeld residuals, is commonly used to capture VE waning. We found that this approach is unreliable in capturing both the degree of fast waning and its functional form, especially when vaccination is spread over months, and identified the mathematical factors contributing to this unreliability (Nikas et al., Clinical Infectious Diseases, 2022). We showed that a relatively simple method based on including time-vaccine interaction in the model, with further proposed optimization, performs significantly better. Using this method, we explored the effect of the competing heterogeneities on the estimation of VE waning by analyzing the synthetic data from a multi-scale agent-based model parameterized with epidemiological and immunological data.
  • Hana Maria Dobrovolny Texas Christian University (Department of Physics & Astronomy)
    "Virus-mediated cell fusion of SARS-CoV-2 variants of concern"
  • Many viruses, including SARS-CoV-2, have the ability to cause neighboring cells to fuse into multi-nucleated cells called syncytia. Much is still unknown about how syncytia affect the course of viral infection. Using data from a recent study of virus-mediated cell fusion for different SARS-CoV-2 variants of concern, we use mathematical modeling to estimate the syncytia formation rate and the fusing time of SARS-CoV-2 variants. We find that the alpha variant has a syncytia formation rate higher than other variants. We are also able to estimate the time it takes for fusion to occur, finding that the beta variant takes the longest, followed by the alpha variant, with the delta and original Wuhan strains fusing fastest. This study exemplifies the role that mathematical models can play in helping to quantify the biological characteristics of different viruses.
  • Suzan Farhang-Sardroodi University of Manitoba (Department of Mathematics)
    "Mathematical modelling of the humoral and B cell response to SARS-CoV-2"
  • Mechanistic modelling approaches have become integral to systems biology to describe known physiology and fill in the gaps in our understanding of which complex interactions drive host-pathogen responses. They, therefore, provide valuable insights for public health planning and infectious disease control. In this mini-symposium, I will present our work on developing a mathematical model to study humoral (antibody-mediated) immunity. B cells and their antibodies are critical to protecting against COVID-19 over time. However, it is increasingly evident that waning antibodies after natural infection or vaccination translate to reduced defence against repeated SARS-CoV-2 infections. To understand the dynamics of antibody production from B cells, we constructed a computational biology model describing B cells and IgG-neutralizing antibodies coupled with host-pathogen interactions. This model provides better insight into the kinetic processes and mechanisms driving the humoral response against SARS-CoV-2. Our model delineates the initiation of B cell responses through their differentiation to germinal center cells, long-lived plasma cells, and memory cells. It sheds light on how antibodies are produced in primary and secondary reactions.
  • Ruian Ke Los Alamos National Laboratory
    "The relationship between SARS-CoV-2 viral load and infectiousness and quantifying the infectiousness heterogeneity"
  • The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person’s infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop viral dynamic models of SARS-CoV-2 infection and fit them to data to estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking viral load (VL) to infectiousness and show a person’s infectiousness increases sublinearly with VL and that the logarithm of the VL in the upper respiratory tract is a better surrogate of infectiousness than the VL itself. By fitting mechanistic models to a wide variety of datasets, we directly quantified heterogeneity in individual infectiousness. Significant person-to-person variation in infectious virus shedding suggests that individual-level heterogeneity in viral dynamics contributes to ‘superspreading’.
  • Jane Heffernan York University (Mathematics & Statistics)
    "Modelling COVID-19 infection and vaccination"
  • Immunity is gained after infection and vaccination, but can also wane over time. We have developed mathematical models of COVID-19 infection and vaccination to track the accumulation and decay of effective COVID-19 immunity in individuals. The results from our in-host models are then embedded into epidemiological models of COVID-19 immunity distributions. In this talk I will review our in-host models and discuss our modelling results associated with mild, moderate, and severe COVID-19 infection, and vaccination using Astrazeneca, Moderna, or Pfizer vaccines. An example of immunity distribution modelling for Ontario Canada will also be discussed.

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 MS01-MEPI-1.

  • Carrie Manore Los Alamos National Laboratory (Theoretical Biology and Biophysics)
    "Coupling Earth Systems, Vector Population, and Disease Transmission Models to Predict Mosquito-borne Disease Under Climate Change"
  • Understanding the non-linear impacts of climate change on climate-driven pathogens such as mosquito-borne disease is an ongoing challenge. Recent research has shown that temperature will change vector species and virus distributions and dynamics. To further understand how temperature, along with changes in water availability, and human populations, will change the dynamics and ranges of West Nile virus and dengue, we developed a suite of coupled models to simulate disease spread across the Americas. This includes a global climate and earth systems model, mosquito population dynamics model, and disease transmission model with host species (e.g. humans and birds) driven by the climate model output and historical data. I will present the mosquito and disease transmission models along with our new tiling method for spatial partitioning along with validation results and challenges.
  • Nusrat Tabassum Texas Tech University (Applied Mathematics)
    "Stage-Structured Mosquito Larval Competition: Implications for Aedes Albopictus and Aedes Aegypti Population Dynamics"
  • Aedes aegypti and Aedes albopictus, two invasive mosquito species that are responsible for spreading a number of viral diseases, are a major danger to global public health. Their ability to reproduce in diverse container habitats, where competition influences population dynamics, is correlated with their capacity to successfully colonize new regions. This competition may influence the distribution and abundance of the species, thereby influencing the transmission of mosquito-borne diseases. The goal of this study is to examine the effects of environmental factors such as temperature and population density on the competitive dynamics between these two species in their larval phases. A stage-structured larval competition model has been developed to analyze both inter and intra-specific competition. Our model permits temperature-dependent competition and carrying capacity variations. We have used sensitivity analysis to evaluate the model’s efficacy and empirical observations to characterize how temperature influences the survival rate, growth rate, and development time of mosquito larvae. We have also conduct a stability analysis of the model to determine if mosquito species can persist under different environmental conditions. This helps to understand how competition between mosquito larvae is influenced by environmental factors, which in turn influences temperature-dependent viral transmission, and also allows us to predict and respond to outbreaks of mosquito-borne diseases.
  • Luis Fernando Chaves Indiana University - Bloomington (Environmental and Occupational Health)
    "Nonlinear impacts of climatic variability on vector population dynamics"
  • Mosquitoes and other vectors have complex life cycles, often including ontogenetic niche shifts. Under such circumstances changing environments could influence insect vector density-dependent regulation and propensity to sudden changes in abundance. Here, I will review results from modelling several mosquito species where field observed density-dependent regulation is strong. For most species, and settings, low environmental kurtosis was a good predictor of sharp changes in the abundance of mosquitoes. The identification of density-independent (i.e., exogenous) variables forcing sharp changes in disease vector populations using the exogenous factors statistical properties, especially higher order moments of their distribution, could be useful to assess the impacts of changing climate patterns on the transmission of vector-borne diseases.
  • Suzanne Robertson Virginia Commonwealth University (Department of Mathematics and Applied Mathematics)
    "The impact of changes in avian phenology in a stage-structured model for West Nile virus transmission"
  • West Nile virus (WNV) has remained an annual public health concern in the United States since its introduction in 1999, yet the ecological triggers leading to seasonal outbreaks are not well understood. Nestlings, birds within the first couple of weeks of hatching, are extremely vulnerable to mosquitoes and may receive a disproportionately high number of mosquito bites compared to other bird life stages. While total avian population size typically increases throughout the season, nestling abundance declines at the end of the brooding season. This temporal variation in host stage abundance can play an important role in structuring WNV transmission. The nesting curve of a species may differ regionally due to climate, and within a region, year to year differences in temperature may also result in year to year variation in the nesting curve of a given species. We use a stage-structured differential equation model for WNV incorporating vector preference for specific host life stages to investigate the impact of changes in the phenology of avian nesting and vector growth due to climate change on enzootic WNV transmission.

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 MS01-MFBM-1.

  • James Brunner Los Alamos National Laboratory (Biosciences)
    "Inferring microbial interactions with their environment from genomic and metagenomic data"
  • Microbial communities organize through a complex set of interactions between microbes and their environment, and the resulting metabolic impact on the host ecosystem can be profound. Microbial activity has been shown to impact human health, leading to a myriad of treatments meant to manipulate the resident microbiota of the human gut. Additionally, microbes of plant rhizospheres have a strong influence on plant growth and resilience. Finally, microbial communities impact decomposition in terrestrial ecosystems, influencing the way that carbon is stored in soil and removed from the atmosphere. In order to understand, predict, and influence these processes, genome-scale modeling techniques have been developed to translate genomic data into inferred microbial dynamics. However, these techniques have a strong dependence on unknown parameters and initial community compositions, and are often difficult to analyze qualitatively. With the goal of understanding microbial community metabolic dynamics, we infer the series of interaction networks underlying the resource-mediated community model defined by individual genome-scale models. I will present our tool, MetConSIN, for inferring these networks as well as our current efforts to analyze and simplify the model. Finally, I will discuss our future goals for the prediction of microbial community metabolic impact on their host ecosystem.
  • Tung Nguyen Texas A&M University (Department of Mathematics)
    "Absolute concentration robustness in multi-site phosphorylation networks with a bifunctional enzyme"
  • Shinar and Feinberg in 2010 introduced the concept of absolute concentration robustness (ACR) to mean the concentration of a certain species (called ACR species) is invariant across all positive steady states. Biological networks with ACR have been observed experimentally in certain signaling systems in E. coli, and recently have also been proposed as synthetic controllers by Kim and Enciso in 2020. Shinar and Feinberg gave a sufficient condition for the existence of an ACR species; that is the network must have a deficiency of one and there are two non-terminal complexes differing in the ACR species. While the condition is easily checked, many biologically important networks do not have a deficiency of exactly one. In this work, we present a large class of biological networks with arbitrary deficiency and capable of exhibiting ACR. Notably, this class contains multi-site phosphorylation cycles with a ``bifunctional' enzyme. We provide the necessary and sufficient conditions for ACR in such a class of networks, and highlight the essential role of bifunctionality for the existence of ACR.
  • Jiaxin Jin The Ohio State University (Mathematics)
    "Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective"
  • Given a dynamical system with a polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific {em dynamical} properties, such as existence or uniqueness of equilibria, persistence, permanence, or global stability. Here we focus on this problem in the context of weakly reversible deficiency one networks. In particular, we describe an algorithm for deciding if a polynomial dynamical system admits a weakly reversible deficiency one realization, and identifying one if it does exist. In addition, we show that weakly reversible deficiency one realizations can be partitioned into mutually exclusive Type I and Type II realizations, where Type I realizations guarantee existence and uniqueness of positive steady states, while Type II realizations are related to stoichiometric generators, and therefore to multistability.
  • Aidan S. Howells University of Wisconsin–Madison (Mathematics)
    "Stochastic reaction networks within interacting compartments"
  • Stochastic reaction networks, which are typically modeled as continuous-time Markov chains on $mathbb Z^d_{ge0}$, have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization, introduced by Duso and Zechner in 2020, involves a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. We will discuss results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, and explore a number of examples demonstrating some possible non-intuitive behaviors. Based on join work with David F. Anderson

Mathematical Ophthalmology

Organized by: Paul A. Roberts, Jessica Crawshaw
Note: this minisymposia has multiple sessions. The other session is MS01-NEUR-1.

  • Jessica Crawshaw University of Oxford (Mathematical Institute)
    "The role of hierarchical Bayesian inference in understanding macular degeneration treatment strategies"
  • Wet age-related macular degeneration (AMD) is a disease which slowly destroys ones’ central vision, with a huge impact on quality of life. It is the leading cause of central blindness worldwide. Wet AMD is characterised by neovascularisation, triggered by an unhealthy abundance of vascular endothelial growth factor (VEGF). These newly formed capillaries allow fluids to seep into the retina, damaging the local photoreceptors (critical light-sensing cells). Currently, there is no definitive cure for wet AMD. As such, intraocular injections of anti-angiogenic drugs to reduce the abundance of retinal VEGF is the clinical gold standard for disease management, slowing the progression of vision loss. However, injections into the eye are unpleasant, and the fluid dynamics within the eye leads to relatively rapid drug elimination, resulting in the need for regular intraocular injections. In this talk, we will present and analyse a pharmacokinetic/pharmacodynamic (PK/PD) model of a standard-of-care antibody, ranibizumab, targeting VEGF. This model has been developed to improve our understanding of the ocular pharmacology of ranibizumab and to provide a robust understanding of ranibizumab retention in the eye. Results from this PK/PD model are compared to published animal (cynomolgus monkey) and human data. We present a hierarchical Bayesian inference strategy to determine relevant parameter distributions. Using this strategy, we provide insight into the clinically observed inter-patient variability in VEGF suppression and drug retention. Finally, this model establishes the initial basis for a computational framework we are developing to mathematically compare the ocular PK/PD of ranibizumab with novel therapeutic strategies and other clinical anti-VEGF drugs in the treatment of AMD.
  • Moussa A. Zouache University of Utah (John A. Moran Eye Center, Department of Ophthalmology & Visual Sciences)
    "Predicting Physiology from Structure in the Human Choriocapillaris"
  • The choroidal vasculature and its microvascular bed, the choriocapillaris, support the metabolic requirements of the outer half of the retina, which includes the photoreceptors, cells that have one of the highest metabolic rates of any cell of the human body. The choriocapillaris has evolved a vascular geometry that differs markedly from branched vasculatures. It consists of a layer of densely organized capillaries contained between two continuous and approximately parallel sheets. Blood enters and leaves the choriocapillaris through a set of arterioles and venules connected to capillaries perpendicularly to its plane. Because of this unusual geometry, theoretical and experimental approaches traditionally applied to characterize blood flow and mass exchange in branched microvasculatures are not adapted to the choriocapillaris. As a result, it has been difficult to assess the role that this vascular bed plays in the onset and progression of inflammatory and degenerative diseases of the back of the eye. We developed a framework to predict aspects of the physiology of the choriocapillaris from experimentally accessible vascular parameters. This framework relies on three-dimensional mathematical models of the choriocapillaris informed by the angioarchitecture of the choroid as observed through immunohistochemistry of human tissue. Blood was modelled as a Newtonian fluid, and analytical and numerical solutions for the blood flow were obtained by solving the Navier-Stokes equation. The salient features of mass exchange with the retina were determined by solving the advection-diffusion equation for a scalar while imposing either a Dirichlet or a Neumann boundary condition on the surface of the choriocapillaris. Topological analysis of the flow field revealed that the blood flow in the choriocapillaris is decomposed into contiguous subsets separated by separation surfaces across which there is no flow. This segmentation is at the origin of the previously unexplained lobular appearance of the choriocapillaris observed during fluorescent dye angiography. The segmentation of the blood flow is associated with spatially heterogeneous dominant transport mechanisms. The boundaries between subsets of the flow field form regions, where the transport of material is dominantly diffusive. These regions represent areas of reduced exchange with the outer retina and are ubiquitous across the choriocapillaris. The width of diffusion-limited regions is determined by the relative distribution of arteriolar and venular insertions into the choriocapillaris, arterial flow rate and molecular diffusivity. Salient characteristics of the blood flow and passive transport in the choriocapillaris differ markedly from branched vasculatures. The geometry of the choriocapillaris is associated with segmented blood flow and spatially heterogeneous exchange with the outer retina. This heterogeneity may explain the spatial selectivity in pathologies associated with retinal diseases.
  • Richard Braun University of Delaware (Department of Mathematical Sciences)
    "Semi-automated Tear Breakup Detection and Modeling on the Ocular Surface"
  • The tear film is a thin fluid multilayer left on the eye surface after a blink. A good tear film is essential for health and proper function of the eye. Millions of people have a condition called dry eye disease (DED) that is thought to be closely linked to the tear film. DED inhibits vision and may lead to inflammation and ocular surface damage. However, there is little quantitative data about tear film failure, often called tear break up (TBU). Currently, it is not possible to directly measure important variables such as tear osmolarity (saltiness) within areas of TBU. We present a mostly automatic method that we have developed to extract data from video of the tear film dyed with fluorescein (for visualization). We have extracted data for 15 healthy subjects resulting in 467 instances of TBU. Using parameter identification from fits to appropriate math models, we estimate which mechanisms are most important in each instance and determine critical variables such as osmolarity within regions of TBU. Not only is new data obtained, but far more data, enabling statistical methods to be applied. So far, the methods provide baseline data for TBU in healthy subjects; future work will produce data from DED subjects.

Techniques and Methods in Modelling Cancer Treatment

Organized by: Kathleen Wilke, Gibin Powathil
Note: this minisymposia has multiple sessions. The other session is MS01-ONCO-1.

  • Annabelle Ballesta Inserm & Institut Curie (unit 900)
    "Quantitative Systems Pharmacology to Personalize Temozolomide-based Drug Combinations against Brain Tumors."
  • Objectives: Large inter-patient heterogeneity in anticancer drug response highlights the critical need for personalized cancer management which has favored the generation of multi-type individual patient data. However, quantitative systems pharmacology (QSP) approaches handling the complexity of multiple preclinical and clinical data types for designing patient-specific treatments are critically lacking [1-2]. This study aims to design such methodology, to individualize the combination of cytotoxic drugs with targeted molecules, towards a high benefit for patients. Multiple regulatory pathways may be altered initially or activated upon drug exposure in cancer cells, which advocates for the design of combination therapies simultaneously inhibiting multiple targets [3-4]. Such theoretical considerations are backed up by success stories of associating cytotoxic drugs with targeted therapies. The approach was developed here for Glioblastoma multiforme (GBM), the most frequent and aggressive primary brain tumors in adults, which is associated to a median overall survival <18 months despite intensive treatments combining maximal safe neurosurgery, radiotherapy and temozolomide (TMZ)-based chemotherapy. The objective was to develop a QSP pipeline to potentiate TMZ treatment by priming cancer cells with targeted molecules affecting key intracellular functions. Methods: A mathematical model of TMZ cellular pharmacokinetics-pharmacodynamics (PK-PD) based on ordinary differential equations (ODEs) was designed, building on existing works [5]. The model describes key regulatory networks that count among the most deregulated pathways in GBM according to TCGA [6]. Briefly, TMZ is a methylating agent that is spontaneously activated upon a two-step pH-dependent process. Four types of DNA adduct are formed upon TMZ exposure, which are handled either by base excision repair (BER) or by O6-methylguanine-DNA methyltransferase (MGMT). If these initial processes of DNA repair are unsuccessful, DNA single- or double-strand breaks are created, which triggers Homologous Recombination (HR), ATR/Chk1 and p53 activation, cell cycle arrest and possibly apoptosis. TMZ PK-PD model was connected to an ODE-based cell population model that represented cell viability during drug exposure. Model calibration consisted in a modified least square approach ensuring data best-fit under biologically-sound constraints. The minimization task was performed by the Covariance Matrix Evolutionary Strategy (CMAES) algorithm. The same algorithm was used for therapeutic optimization procedures. Results: Parameters of TMZ PK-PD model were estimated in sequential steps involving the use of longitudinal and dose-dependent datasets, informing on the concentrations of TMZ PK, DNA adducts, MGMT, double-stranded breaks, ATR, Chk1 and p53 phosphorylation, and cell death (295 datapoints in total). Most of the datasets were performed in two LN229 glioblastoma human cell lines: the parental TMZ sensitive (MGMT-) and the MGMT-overexpressing TMZ resistant (MGMT+) cells [7-11]. The model was able to faithfully reproduce these multi-type datasets coming from several independent studies. Next, the calibrated model was used as a powerful tool to investigate new therapeutic targets. As a start, we investigated drug combinations involving TMZ and only one targeted inhibitor, which was computationally represented by decreasing the value of the corresponding model parameter. The only strategy leading to a drastic increase of TMZ efficacy in both parental and resistant cell lines consisted in the complete (>90%) inhibition of the BER pathway, prior to TMZ exposure. Such high level of inhibition being challenging to achieve in the clinics, we further explored the combination of TMZ and two inhibitors. This numerical study revealed three possible parameters to be jointly targeted: MGMT protein level, BER activity, and HR activity. The optimal strategy, defined as the one requiring the smaller percentages of inhibition for both targets, was the combined administration of BER and HR inhibitors, prior to TMZ exposure. This therapeutic strategy was investigated experimentally in both LN229 cell lines and led to a drastic increase in TMZ efficacy. The model prediction of cell viability under exposure of TMZ after either BER inhibitor or HR inhibitor only, were also validated. Conclusions: A model of TMZ PK-PD model was carefully calibrated to data and allowed to identify a non-intuitive TMZ-based drug combination leading to a drastic increase of cell death in initially resistant cells. This QSP model is being personalized using multi-omics datasets available in GBM patient-derived cell lines towards the design of patient-specific therapeutic strategies.
  • Kévin Spinicci Swansea University
    "Mathematical modelling of HIF on regulating cancer cells metabolism and migration"
  • The number of studies on tumour metabolism has increased in the recent years as it appears to differ from normal cells. Effort has been put in order to assess dysregulated mechanisms to design new strategies aiming to target cancer cells specifically. It has been observed that the median oxygen level in tumour is less than 2%. This altered environmental condition leads to an adaptation of the cell energetic metabolism and induces angiogenesis. Furthermore, the literature shows that hypoxic cells are more resistant to radiotherapy and potentially more aggressive. Here, we will present a mathematical model of the Hypoxia Inducible Factor (HIF), the main actor in the cellular response to hypoxia, to study how it drives the cell metabolism [1] and the cell ability to migrate. To that end, we have implemented an agent-based model to simulate tumour growth in an in vitro setting using the PhysiCell software. The model includes ODEs to describe the genetic regulations of metabolic key genes with respect to the effect of HIF on those genes. Cells consumption and secretion are affected by the genetic regulation. The results of the model show the consequences on the Warburg Effect and on cancer cell migration.
  • Linh Nguyen Phuong Aix-Marseille University (COMPutational pharmacology and clinical Oncology Team)
    "Mechanistic modeling of the longitudinal tumor and biological markers combined with quantitative cell-free DNA"
  • Early prediction of resistance to immunotherapy is a major challenge in oncology. The ongoing SChISM (Size Cell-fre DNA (cfDNA) Immunotherapies Signature Monitoring) clinical study proposes an innovative approach based on patented cfDNA quantification methods, providing concentration and size profile fluctuations of plasmatic circulating DNA for early therapeutic management of immune checkpoint inhibitors treated patients. The main interest is that such measures can be performed in a less invasive, less expansive way, and especially much earlier than the first imaging evaluation, thanks to liquid biopsies. Five cancer types are investigated: melanoma, head and neck, renal, bladder and lung cancers, with a total of 260 patients at the end of the study, described by their clinical and classical biological data, and cfDNA features, such as concentration, first and second peak of the cfDNA size distribution, and specific size ranges of cfDNA fragments. We developed a mechanistic model of cfDNA joint kinetics with other longitudinal markers and tumor size imaging to help describe and understand the time dynamics of the quantitative profiles of cfDNA over time. The model consists of a dynamical system of differential equations that estimates specifically the component corresponding to cfDNA production by tumor lesions. Subsequently, the model is embedded within a nonlinear mixed-effects statistical framework in order to quantify inter-patient variability, and calibrated on the data. Future perspective will use machine learning models to predict early progression, progression-free survival or overall survival, combining these dynamic parameters and other variables available at baseline.
  • Heiko Enderling Moffitt Cancer Center (Department of Integrated Mathematical Oncology)
    "Mathematical modeling of cancer radiotherapy"
  • Radiation therapy is a mainstay of cancer treatment, with more than 50% of all cancer patients receiving radiation at some point of their clinical care. Mathematical modeling has a long history in radiation oncology, and recent modeling approaches saw translation into prospective clinical trials. Here, we will present the different mathematical modeling approaches to simulate radiation response, and their implication on personalizing radiation dose and dose fractionation, towards a novel concept of adaptive radiation therapy. We will focus on head and neck cancer, one of the few cancer types rising in incidence, that is routinely treated with definitive radiation. Using the data of 39 head and neck cancer patients, we develop, calibrate, and validate the model before making predictions on novel therapies.

Evolutionary game theory in cancer

Organized by: Anuraag Bukkuri, Katarina Stankova
Note: this minisymposia has multiple sessions. The other session is MS01-ONCO-2.

  • Kanyarat Jitmana The University of Utah (Department of Mathematics)
    "Mathematical modeling of the evolution of resistance and aggressiveness of ovarian cancer from HGSOC patient CA-125 time series."
  • We use time series of CA-125 levels from high-grade serous ovarian cancer patients from the Australian Ovarian Cancer Study to develop mathematical models of the evolution of resistance and response to therapy. We hypothesize that two key traits determine long-term patient outcomes: resistance as measured by the rate of decline of CA-125 during therapy, and aggressiveness as measured by the rate of CA-125 increase between lines. Statistical analysis shows the level of resistance increases as the number of lines increases. Low initial CA-125, residual disease less than or equal to 1 cm, and a high rate of decline during the first line of therapy predict a longer median of survival of patients after finishing the second line of therapy. We use mathematical models to investigate the mechanisms underlying the differences among HGSOC patients. Our simplest model has two cell types, sensitive and resistant, with resistant cells that could be present before therapy or be generated through mutation from sensitive cells. By fitting the models to HGSOC data using all data points, the first two lines, the first three lines, and the first four lines, these models can successfully capture the dynamic of the CA-125 level of HGSOC patients. Contradictory, the model cannot predict the great detail of the dynamic of CA-125 in the later lines, both the short and long run. By fitting these mathematical models to the clinical data for each patient, we estimate the parameters, which are the growth and death rate of sensitive cells and resistant cells. Despite the inability of the models to predict future CA-125, the patients with the low growth rate of sensitive cells, the low growth rate of the resistant cell, and the high death rate of the resistant cell show better survival chances after finishing the second line of therapy
  • Ranjini Bhattacharya Moffitt Cancer Center (Integrated Mathematical Oncology)
    "Angiogenesis: A Tragedy of Commons"
  • Cancer progression is the result of evolution within the tumor microenvironment. Natural selection selects for cells capable of efficient nutrient uptake. Cancer cells achieve this by overexpressing angiogenic factors (VEGF) that induce the formation of blood vessels that carry nutrients to the tumor. Traditionally, angiogenesis has been viewed as a cooperative phenomenon resulting in the evolution of free-loaders. Using a game theoretic framework, we model VEGF production as an evolutionary strategy and show that the over-production of VEGF is the result of a tragedy of commons. A cell’s investment in VEGF depends on the degree to which it aids its nutrient uptake. If higher production of VEGF leads to higher nutrient uptake, then cells are incentivized to produce VEGF. If nutrients are equally divided within a given neighborhood, an individual cell’s incentive to produce VEGF decreases. Our simulations predict that cancer cells produce 100 times more VEGF than what is typically seen in normal cells, and what would be their collective team optimum. This means that VEGF production by a cancer cell aims to co-opt nutrients from neighboring cells resulting in an evolutionary arms race. Increasing the number of cancer cells in a fixed neighborhood results in lower per-cell VEGF production while exacerbating the tragedy of the commons collectively. We simulate anti-angiogenic therapy and find that while therapy reduces the amount of VEGF in the neighborhood, cells adopt a low VEGF production strategy that can still sustain tumor proliferation. This results in evolutionary rescue. Our model challenges the existing paradigm of angiogenesis as a cooperative activity and provides novel insights into therapy in a clinical setting.
  • Monica Salvioli - Part 2 Delft University of Technology (Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands)
    "Using the Stackelberg evolutionary game approach in cancer treatment"
  • We present a game-theoretic cancer model based on Darwinian dynamics with two cancer cell types and treatment-induced resistance as an evolving trait. We first investigate whether a constant treatment dose can keep cancer at a viable tumor burden. The game is then expanded into a Stackelberg evolutionary game with the physician as its leader, who chooses drug dosage to maximize the patient's quality of life. The quality of life is modeled by an objective function that takes into account the following three aspects of tumor burden: 1) the population of cancer cells at the ecological equilibrium point, 2) the toxicity of the drug, and 3) treatment-induced resistance. In this study, the game's Stackelberg and Nash outcomes are compared to the maximum tolerable dose. We demonstrate that for large ranges of parameters, the Nash and Stackelberg treatment strategies can stabilize the tumor burden at viable levels even when the maximum tolerable dose cannot. As expected, the Stackelberg solution allows us to aim for a higher quality of life than the Nash solution. In general, we demonstrate that determining a patient's treatment dose by employing the Stackelberg evolutionary game approach results in an improvement in the patient's quality of life.
  • Shalu Dwivedi Matthias Schleiden Institute, Friedrich Schiller University, Jena (Department of Bioinformatics)
    "Go or grow: Game-theoretical description of metastasis in tumour development"
  • A medically important feature of several types of cancer is their ability to “decide” between staying at a primary site in the body or to leave it and form metastases. The present theoretical study is aimed at a better understanding of the proximate reasons for this so-called “go-or-grow” dichotomy. To that end, we use game theory, which has turned out to be useful in analyzing the competition between tumours and healthy tissue or among different tumour cells [1]. We start from a game-theoretical model presented by Basanta [2]. We determine the type of game, depending on parameter values, both for the basic model and for five modified variants that we suggest here. For example, in the basic model, the deadlock game, Prisoner’s Dilemma, and hawk-dove game can occur. The modified versions lead to several additional game types such as battle of the sexes, route-choice, and stag-hunt game. For some of the game types, all cells are predicted to stay on their original site (“grow phenotype”), while for other types, only a certain fraction stay and the other cells migrate away (“go phenotype”). If nutrient supply at the distant site is high, all cells are predicted to go. We discuss our predictions in terms of the pros and cons of caloric restriction, limitation of the supply of vitamins or methionine. Our results may help devise treatments that avoid metastases. References: 1. S. Hummert, K. Bohl, D. Basanta, A. Deutsch, S. Werner, G. Theißen, A. Schroeter, S. Schuster (2014). Evolutionary game theory: cells as players. Molecular Biosystems 10 (12), 3044 – 3065. 2. Basanta, D., Hatzikirou, H., & Deutsch, A. (2008). Studying the emergence of invasiveness in tumours using game theory. The European Physical Journal B, 63(3), 393–397.

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 MS01-OTHE-1.

  • Ashlee N. Ford Versypt University at Buffalo, The State University of New York (Department of Chemical and Biological Engineering)
    "Multiscale Modeling of Tissue Remodeling and Damage"
  • Dr. Ford Versypt leads the Systems Biomedicine and Pharmaceutics research lab, which develops and uses multiscale systems engineering approaches including mathematical modeling and computational simulation to enhance understanding of the mechanisms governing tissue remodeling and damage as a result of diseases and infections and to simulate the treatment of those conditions to improve human health. The lab specializes in (a) modeling mass transport of biochemicals through heterogeneous porous materials—primarily extracellular matrices—that change morphology dynamically due to the influence of chemical reactions and (b) modeling dynamic, multi-species biological systems involving chemical, physical, and biological interactions of diverse, heterogeneous cell populations with these materials and the chemical species in tissue microenvironments. In this presentation, Dr. Ford Versypt will reflect on the trajectory of her research program through the last decade starting from modeling protein transport through degradable biomaterials for drug delivery and pharmaceutical manufacturing to focusing on pathophysiology of tissue damage and disease progression and pharmacokinetics/pharmacodynamics of treatments. This work is currently supported by an NSF CAREER award and NIH R35 MIRA grant.
  • Angela Peace Texas Tech University (Department of Mathematics and Statistics)
    "Adaptive foraging behaviors in food web models"
  • Nutritional constraints are common as food resources are rarely optimally suited for grazing species. Elemental mismatches between trophic levels can influence population growth and foraging behaviors. Consumers utilize optimal foraging techniques, such as compensatory and complementary feeding strategies. Mathematical models developed under the framework of Ecological Stoichiometry can help shed light on population dynamics subject to stoichiometric constraints. I will give a brief overview of stoichiometric producer-grazer models and present some commonly used functional forms for incorporating stoichiometric constraints into trophic interactions. Model extensions explore adaptive grazer foraging behaviors in stoichiometrically explicit food webs.
  • Open Discussion
    "Open Discussion: Best Practices for Workshops for Young Researchers"
  • Topics for this discussion will be about how best to organize a workshop for young researchers in mathematical biology. For example, what activities would be included in a schedule, how would students be recruited, and how would one best assess the success of such a workshop.

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 MS01-OTHE-2.

  • Daisuke Takagi University of Hawaii at Manoa (Mathematics)
    "Larval fish counteract ram and suction to capture evasive prey"
  • Fish larvae are considered to be suction feeders that rely on suction flow to capture prey. However, recent observations of clownfish larvae revealed that they behave like ram feeders that accelerate towards copepod prey. Capturing copepods is challenging because they are highly evasive and sensitive to fluid deformation. To identify the strategies needed for successful capture, we developed a simple model based on potential flow theory. Our results show that fish larvae with weak ram and suction strengths can still capture copepods through hydrodynamic stealth. This suggests that suction by fish larvae is used primarily for stealth rather than capture.
  • Lisa J. Fauci Tulane University (Mathematics)
    "A closed-loop neuromechanical model of locomotion of lampreys with spinal injuries"
  • In some vertebrates such as lampreys, swimming function can be regained after spinal injuries, but the exact mechanism of this recovery is not well understood. One hypothesis is that amplified proprioceptive (body-sensing) feedback can allow an injured lamprey to regain functional swimming even if the descending signal is lost. Here we present a multiscale model of an undulatory swimmer whose neural signaling is driven by a phase oscillator model that is fully coupled to a viscous, incompressible fluid. We examine the effects of amplified feedback on swimming behavior, and show that in some cases, feedback amplification below a spinal lesion is sufficient to partially or entirely restore effective swimming behavior.

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.