Monday, June 14 at 5:45pm (PDT)
Tuesday, June 15 at 01:45am (BST)
Tuesday, June 15 09:45am (KST)


Mathematics of Biochemical Reaction Networks

Organized by: Matthew Johnston (Lawrence Technological University, United States), Angelyn Lao (De La Salle University, Phillipines)

  • Matthew Johnston (Lawrence Technological University, United States)
    "Analyzing Steady States of Mass Action Systems through Network Splitting"
  • The process of network translation corresponds a mass action system to a generalized mass action system with equivalent dynamics. Recent research has shown that, when the generalized chemical reaction network underlying the second network has desirable structure, such as weak reversibility and low deficiency, then we may use the network to establish properties of the steady state set and to explicitly construct a steady state parametrization. In this talk, we will extend this theory by introducing the method of 'splitting' networks. In a split network, we allow the original network to be partitioned into subnetworks, called 'slices', while imposing that the union of the subnetworks preserves the stoichiometry of the original network. We show that this process expands the scope of mass action systems whose steady states can be characterized by the method of network translation.
  • Editha Jose (University of the Philippines Los Banos, Philippines)
    "Absolutely complex balanced power law kinetic systems"
  • In this talk, we will focus on absolutely complex balanced (ACB) power law kinetic systems. We say that a kinetic system is absolutely complex balanced if every positive equilibrium is complex balanced. First, we will identify a weakly reversible kinetic system where absolute complex balancing implies zero deficiency, that is, we derived a partial converse to Feinberg's theorem stating that any weakly reversible kinetic system with zero deficiency is absolutely complex balanced. Then, we will describe several methods for constructing new classes of ACB systems and illustrate them with new classes of ACB power law kinetic systems with positive deficiency.
  • Polly Yu (University of Wisconsin-Madison, United States)
    "Conditions for stability of mass-action systems"
  • We present a sufficient condition based on the directed species-reaction graph for linear stability of equilibrium, independent of rate constants. The conditions are in terms of cycles, which could be understood as feedback loops, and a special case is when the graph has no cycles at all. The same conditions also imply stability for the chemical system where products are made with a time lag.
  • Bryan Hernandez (University of the Philippines Diliman, Philippines)
    "Independent Decompositions of Chemical Reaction Networks and Some Applications"
  • In this talk, we will present some questions and answers concerning independent decompositions of a chemical reaction network. In particular, we will discuss a condition that gives a necessary and sufficient condition for the existence of a nontrivial independent decomposition given a network, and consequently creating a method that gives this specific decomposition, if it exists. We will also deal with what we call the Feinberg Decomposition Theorem, which established equality of the set of positive equilibria of a kinetic system and the intersection of equilibria sets of its subsystems resulting from an independent decomposition of the underlying network. We will specify some implications of the theorem and consequently apply these to examples of reaction networks and kinetic systems existing in literature.

Diverse quantitative approaches integrating data and modelling in development and medicine

Organized by: Adriana Dawes (Ohio State University, USA), Sungrim Seirin-Lee (Hiroshima University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS04-CDEV.

  • Sungrim Seirin-Lee (Hiroshima University, Japan)
    "A one-line mathematical model that solved the mystery of urticaria"
  • Urticaria is a common skin disease characterized by the rapid appearance and disappearance of local skin edema and flares with itching. It affects about one in 5 people at some point in their lives and globally about 56/100000 population suffer from urticaria daily. It is characterized by various macroscopic skin eruptions unique to patients with respect to shape, size, and/or duration of eruptions. Nevertheless, the mechanism underlying multifarious eruptions in urticaria is largely unknown in medicine. The eruptions are believed to be evoked by histamine release from mast cells in the skin. However, the majority of visible characteristics of urticaria cannot be explained by a simple injection of histamine to the skin. In this study, we succeeded in developing a mathematical model that can explain various geometrical shapes of eruptions typically observed in patients. Our mathematical model suggests that simultaneous self-regulation of positive and negative feedback of histamine through mast cells plays a critical role in generating the wide-spread wheal patterns. The study findings increase the understanding of the pathogenesis of urticaria and may aid decision-making for appropriate treatments.
  • Yoichiro Mori (University of Pennsylvania, USA)
    "Mathematical Justification of Slender Body Theory"
  • Systems in which thin filaments interact with the surrounding fluid abound in science and engineering. The computational and analytical difficulties associated with treating thin filaments as 3D objects has led to the development of slender body theory, in which filaments are approximated as 1D curves in a 3D fluid. In the 70-80s, Keller, Rubinow, Johnson and others derived an expression for the Stokesian flow field around a thin filament given a one-dimensional force density along the center-line curve. Through the work of Shelley, Tornberg and others, this slender body approximation has become firmly established as an important computational tool for the study of filament dynamics in Stokes flow. An issue with slender body approximation has been that it is unclear what it is an approximation to. As is well-known, it is not possible to specify some value along a 1D curve to solve the 3D exterior Stokes problem. What is the PDE problem that slender body approximation is approximating? Here, we answer this question by formulating a physically natural PDE problem with non-conventional boundary conditions on the filament surface, which incorporates the idea that the filament must maintain its integrity (velocity along filament cross sections must be constant). We prove that this PDE problem is well-posed, and show furthermore that the slender body approximation does indeed provide an approximation to this PDE problem by proving error estimates. This is joint work with Laurel Ohm, Will Mitchell and Dan Spirn.
  • Benjamin Walker (University of Oxford, UK)
    "Hypothesis generation and hypothesis testing in spermatozoa"
  • Spermatozoa are perhaps the canonical microscopic swimmer, propelled along the path to fertilisation via the wavelike motion of a long slender flagellum. Owing not least to their key role in fertility, they have long been the subject of significant study, driving both experimental and theoretical developments. In this talk, I hope to survey a number of recent advances in the way in which we are able to study and investigate the microscale world of sperm, with applications beyond these cellular swimmers. These new methodologies promise to enable the next generation of quantitative analysis of flagellated swimmers, with the potential to both enhance clinical diagnostics in the future and investigate fundamental and widely conserved cellular biology. In particular, I will begin by recounting recent step changes in data acquisition, with fully automated schemes now replacing tiresome by-hand analysis. Further, I will then highlight how these developments can be coupled to population-level statistical analyses that incorporate the fine details of the flagellar beat, which have classically been absent from quantitative study. Finally, I will touch upon another exciting area of rapid development with broad applicability, that of flagellar simulation, which is enabling sophisticated data-driven modelling and hypothesis generation in spermatozoa, in addition to newly realising exploratory in silico study of these complex microscale organisms.
  • Kang-Ling Liao (University of Manitoba, Canada)
    "The role of CD200-CD200R in cancer immunotherapy"
  • CD200 is a cell membrane protein that interacts with CD200 receptor (CD200R) of myeloid lineage cells. CD200-positive tumor cells can interact with M1 and M2 macrophages through CD200–CD200R-compex and downregulate IL-10 and IL-12 productions secreted primarily by M2 and M1 macrophages, respectively. In this talk, I will introduce a PDEs model to determine the combined effect of CD200–CD200R interaction on tumor proliferation. We demonstrate that blocking CD200 on tumor cells may have opposite effects on tumor proliferation depending on the “affinity” of the macrophages to form the CD200–CD200R-complex with tumor cells. We also extend these results to an ODEs model to study how the populations of M1 and M2 macrophages affect the tumor growth.

Mathematics of Cryopreservation: from tissue preparation to freezing and ice formation

Organized by: Robyn Shuttleworth (University of Saskatchewan, Canada), James Benson (University of Saskatchewan, Canada)

  • Adam Higgins (Oregon State University, United States)
    "Rational design of less toxic cryoprotectant solutions for cryopreservation"
  • Cryoprotectants (CPAs) are essential components of vitrification mixtures because they promote formation of a non-crystalline glassy state. However, CPAs can be toxic, and it remains a challenge to identify minimally toxic CPA mixtures for vitrification. This difficulty stems from two main issues. First, there are many different CPA types that can be combined in an infinite number of ways to create vitrification mixtures. It is therefore impractical to empirically determine the best vitrification mixture from among this infinite set. Second, the mechanisms of CPA toxicity are not well understood, making it difficult to identify promising mixtures using conceptual reasoning. To address these issues, we have developed a mathematical model of CPA toxicity that accounts for specific and nonspecific toxicity mechanisms, as well as formation of complexes between CPA pairs. We fit this model to experimental data for cultured endothelial cells exposed to five common CPAs [i.e., glycerol (Gly), dimethyl sulfoxide (DMSO), ethylene glycol (EG), propylene glycol (PG) and formamide (FA)], as well as their binary mixtures. The resulting best-fit model parameters were examined using Sloppy Model analysis to provide clues about the toxicity mechanisms. The results suggest that FA and Gly have the highest specific toxicity, PG exerts the most nonspecific toxicity, and that complexes between Gly-FA, DMSO-FA and Gly-EG affect the toxicity of mixtures containing these CPAs. To examine the predictive ability of the model, we predicted the toxicity of ternary CPA solutions, which resulted in reasonable agreement with experimental data. We then combined the toxicity model with a previously published model of glass formation in CPA mixtures to predict promising compositions for vitrification. The combined model predicts that the least toxic CPA cocktail that will result in formation of a glass is a mixture of Gly, FA and DMSO at concentrations of 7.5, 2.1 and 1.4 molal, respectively.
  • Ross Warner (Oregon State University, United States)
    "A general strategy for modeling the distribution of cryoprotectants in tissues"
  • The ability to successfully cryopreserve any biological specimen would undoubtedly change the face of modern medicine and scientific research. Single cell cryopreservation is a difficult problem by itself, but cryopreservation of complex specimens—mainly tissues and organs—is arguably an order of magnitude more difficult and is an active area of research. Vitrification is a promising avenue for successful complex specimen cryopreservation, but toxicity remains a major hurdle to overcome, as vitrification requires a high concentration of cryoprotectants (CPAs) to completely suppress ice formation. In the past, our group has leveraged mathematical modeling to minimize CPA toxicity for single cells. To do so, we developed a toxicity cost function and used mathematical optimization to minimize its value, which resulted in the prediction of a novel vitrification protocol that was experimentally verified to be less toxic than conventional methods. To extend this promising approach to tissues, an appropriate mass transfer model is needed. Fick’s law is commonly used, but it is limited due to its dilute assumption, as well as not accounting for tissue-specific phenomena such as fixed electrical charges, tissue size changes, and the coupling between cell membrane and extracellular mass transfer. In this work, we propose a general modeling paradigm for mass transfer in tissues. To accomplish this, we augmented an acellular mixture theory model in the literature for articular cartilage by incorporating cellular effects. With this augmentation, we show that the model can not only predict changes in CPA concentration and tissue size for the low cell density, rigid tissue of articular cartilage but also for the high cell density, elastic tissue of pancreatic islets. As such, this modeling paradigm is a promising general tissue model that can be used to further our mathematical optimization approach to cryopreservation and to better understand observations during tissue cryopreservation.
  • Fatemeh Amiri (University of Saskatchewan, Canada)
    "Agent based tissue modeling of ice propagation"
  • We model intracellular ice formation (IIF) in large multicellular tissues using Monte Carlo and agent-based modeling techniques. The previous implementa- tions have not allowed for within-tissue cell phenotype (i.e. parameter) het- erogeneity, nor have they coupled the models with key substrate diffusion and reaction equations. Therefore, to account for these critical differences and to understand IIF in large tissues, we have developed and validated a Monte Carlo method. In this model the tissue is described by a regular lattice in which each lattice site represents a cell, and intercellular ice propagation is allowed only between nearest neighbors. In our approach, each cell in the tissue is considered as an agent using the open source software PhysiCell, a multicellular system simulator which is designed to model tissues involving many interacting cells in multi-substrate 3D-microenvironments. We have validated the Monte Carlo method against theoretical Markov chain model for linear two-cell, four-cell and 2 × 2-cell constructs. Unlike the Markov model that involves exponential computational complexity associated with the tissue size, the Monte Carlo model has been successfully applied for large tissues with high numbers of cells. We also investigate the effects of tissue size on IIF in large tissues constructs and model IIF in mouse embryos.
  • Janet A. W. Elliott (University of Alberta, Canada)
    "Thermodynamics of Cell and Tissue Cryopreservation"
  • Cryobiology is the study of the effects of low temperature on biological systems with a major application being cryopreservation—the use of extremely low temperatures for the effectively indefinite storage of cells and tissues for later use. Cryoprotectants are used that modify the amount and location of ice formation during cryopreservation procedures. The ice–cryoprotectant-solution phase diagram and the osmotic and cryoprotectant transport across cell membranes and across tissues during cryoprotectant addition/removal and cooling/warming play crucial roles in whether or not cells survive. Thermodynamics is a broadly applicable subject whereby equations describing relationships among properties are derived from a few core postulates using multivariable calculus. Over more than 20 years our group has been developing equilibrium thermodynamic and nonequilibrium thermodynamic (transport) equations to describe cryobiological processes and gain insight to optimize cryopreservation protocols for a variety of cells and tissues. This talk will briefly introduce various areas of our prior and current work in cryobiological thermodynamics.

The complex adaptive dynamics of honeybee societies

Organized by: Jun Chen (Arizona State University, USA), Yun Kang (Arizona State University, USA), Gabriela Zuloaga (Arizona State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS02-ECOP.

  • Adrian Fisher II (Arizona State University, School of Life Sciences, United States)
    "A widely-used mito-toxic fungicide negatively affects honey bee (Apis mellifera) health"
  • The honey bee (Apis mellifera) is an essential contributor to crop pollination in the United States. However, honey bees, and other pollinators, have been undergoing population declines for poorly understood reasons. Pollinators may frequently encounter fungicides in foraging environments as they are applied to crop plants during bloom. To assess the impact of the fungicide Pristine® (25.2% boscalid, 12.8% pyraclostrobin) we partially tested the hypothesis that Pristine® negatively affects protein digestion or absorbance. Field colonies were maintained for 13 months with pollen containing four concentrations of Pristine®, bracketing concentrations measured in pollen collected by bees while foraging on fungicide-sprayed almond trees We found that Pristine® negatively affects colony growth and winter survival. Additionally, we observed several individual outcomes including early foraging, elevated rates of pollen foraging and consumption, and reduced longevity. Pristine® consumption also lowered hemolymph protein levels, and this effect increased with bee age. Together, these findings support the hypothesis that fungicides such as Pristine® negatively impact honey bee health at least partly by impairing protein balance. This research was supported by USDA 2017-68004-26322.
  • Yixiang Wu (Middle Tennessee State University, United States)
    "An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination"
  • We develop a model of honey bee colony collapse based on the contamination of forager bees in environmental regions contaminated with pesticides. An important feature of the model is the daily homing capacity each day of foragers bees. The model consists of difference equations describing the daily homing of uncontaminated and contaminated forager bees, with an increased homing failure of contaminated bees. The model quantifies colony collapse in terms of the fraction of contaminated bees subject to this increased homing failure. If the fraction is sufficiently high, then the hive falls below a viability threshold population size that leads to rapid disintegration. If the fraction is sufficiently low, then the hive can rise above the viability threshold and attain a stable population level.
  • Mary R Myerscough (School of Mathematics and Statistics University of Sydney, Australia)
    "Modelling the role of temperature stress in honeybee colony collapse."
  • Honey bees raise their brood (bee larvae and pupae) inside the hive, ideally at a temperature of between 34 and 36 degrees Celsius. If the brood experiences lower temperatures then it will develop into sub-standard adult bees. These low quality adults will have an impact on the hive as they will less effective workers. Previous modelling work has strongly suggested that effective foraging and, in particular, the prevention of premature death of foragers is crucial for hive health and survival. In this talk we will examine the effect of temperature stress on hive populations, using a delay-differential equation model that includes the effect on adult bees of poor temperature regulation when they were pupae. We show that the equilibrium of these equations has two fold bifurcations. The right most fold bifurcation produces hive collapse in the model. We show that increasing temperature stress makes the hive more prone to collapse if it experiences increased rates of premature forager death.
  • M. Gabriela Navas-Zuloaga (School of Human Evolution and Social Change, Arizona State University, United States)
    "From Individual Phenotypes to Collective Behavior in Honeybee Foragers: A Mathematical Model"
  • Recent studies have shown that discrete heritable attention phenotypes in individual honey-bee foragers drive their foraging behavior, thus affecting colony fitness. In particular, individual and collective preference for familiar or novel resources is dependent on the relative presence of high and low attention individuals in the colony. Previous models of honey-bee foraging have not included this phenotype-dependent preference. In order to understand how colony-level preferential exploitation of novel and familiar resources emerges from the interactions between individuals with different preferences and levels of influence, I developed an ordinary differential equation model of self-organized foraging based on the different phenotypes. The model reproduces the observed increased foraging activity in colonies with higher proportions of high-attention foragers, as well as the preference for familiar sources in such colonies. It also provides mechanistic support for the empirical hypothesis that individual preference, amplified by efficient communication, is sufficient to produce collective preference at the observed levels in different colonies. The model contributes to understanding the role of individual cognitive variation in regulating the collective trade-off between exploring for new resources and exploiting known ones.

Modeling and Simulations of COVID-19 impact and mitigation strategies

Organized by: Preeti Dubey and Christopher Hoover (Francis I. Proctor Foundation, UCSF, USA)

  • Ranjit Upadhyay (Indian Institute of Technology (ISM) Dhanbad, India)
    "Modeling the recent outbreak of COVID-19 in India and its Control strategies using NPIs and vaccination"
  • Robust testing and tracing are key to fighting the menace of coronavirus disease 2019 (COVID19). This outbreak has progressed with tremendous impact on human life, society and economy. In this work, we propose few models (an age-structured SIQR model, SEQIR model and an SEICR model with comorbidity) to track the progression of the pandemic in India taking into account the different age structures of the country. We have made predictions about the disease dynamics, identified the most infected age groups and analysed the effectiveness of social distancing measures taken in the early stages of infection. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of qualitative dynamics, and optimal control problem for non-pharmaceutical interventions (NPIs) and vaccination events such that the cost of the combined measure is minimized. The investigation reveals that disease persists with the increase of exposed individuals having comorbidity in society. The extensive computational efforts show that mean fluctuations in the force of infection increase with corresponding entropy. Further, an increasing trend to the mean force of infection has been indicated through the composite effect. Higher Shannon entropy production, i.e., more disorder in mean force of infection has indicated more strengthen the force of infection according to dynamical perspective. This might cause a dangerous situation in the population. This is a piece of evidence that the outbreak has reached a significant portion of the population. However, optimal control strategies with combined measures provide an assurance of effectively protecting our population from COVID-19 by minimizing social and economic costs. From an epidemiological perspective, comorbidity individuals get gradually infection due to lack of precautions and surveillance and like, social distancing, proper sanitation wearing masks, etc. In this situations, susceptible individuals become infected and turned to exposed individuals. Indeed, exposed individuals can prevent COVID-19 infection due to strong immunity in this connection. Based on the observed data, 7-days moving average curves are plotted for pre-lockdown, lockdown and unlock 1 phases. Following the trend of the curves for the infection, a generalized exponential function is used to estimate the data and corresponding 95% confidence intervals are simulated to estimate the parameters. The effect of control measures, such as quarantine and isolation are discussed and systematically explore the impact of lockdown strategy in order to control the recent outbreak of COVID-19 transmission in India.
  • Christopher Hoover (Francis I. Proctor Foundation, UCSF, USA)
    "Targeted allocation of testing and vaccination reduces transmission of SARS-CoV2 and improves health equity: An agent-based modeling study"
  • Effectively allocating scarce resources to combat infectious disease outbreaks is essential to reducing their impact. The ongoing pandemic of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) has been characterized by extreme heterogeneity in individual spread and higher spread among underserved sub-populations such as the Latinx community in San Francisco and New York City, and similarly marginalized racial and ethnic minority groups across the U.S. This heterogeneity in transmission creates challenges for control efforts when those experiencing the highest rates of transmission also have limited access to resources to mitigate transmission. However, even imperfect interventions that are efficiently targeted to individuals or groups driving transmission can have a far greater impact than interventions that are evenly distributed in the population. Here we describe an agent-based model (ABM) developed to simulate the transmission of SARS-CoV2 in the City and County of San Francisco (SF). The ABM incorporates a synthetic population developed to capture drivers of racial and ethnic disparities in transmission observed in SF over the course of the pandemic. Challenges in ABM calibration are discussed in light of the large parameter space and limited reliable data sources on which to calibrate. We then describe how the ABM can be used to explore counterfactual scenarios in which resources such as testing, work from home support, and vaccination are targeted towards population strata with the highest rates of infection. Using the ABM, we demonstrate the benefit of these targeted strategies on both reducing the spread of SARS-CoV2 and improving metrics of health equity.
  • Morganne Igoe (University of Tennessee, Knoxville, USA)
    "ZCTA-level Predictors of COVID-19 Hospitalization Risk in the St. Louis Area"
  • COVID-19 has overwhelmed U.S. healthcare systems, with almost 30 million cases and over 500,000 deaths as of March 28, 2021. Older age, male gender, race, and underlying medical conditions have been identified as factors among hospitalized patients. There are also geographic disparities in COVID-19 hospitalization risk that are at least partly driven by geographic differences in sociodemographic, economic, and co-morbid factors. If these factors could be identified, they could help inform control efforts. The aim of this study is to identify ZCTA-level predictors of COVID-19 hospitalization risk in the St. Louis Area using sociodemographic, economic, and chronic disease factors. ZCTA-level sociodemographic, economic, and chronic disease factors were evaluated for correlation with each other and univariable associations with the age-adjusted number of COVID-19 hospitalizations. The ZCTA population was used as the offset. A multivariable negative binomial regression model was then fit using a backwards elimination process. Percent black population, percent of the population with some college education, number of diabetes discharges per 100 population, and population adjusted cases were all positively associated with COVID-19 hospitalization risk. A number of sociodemographic and chronic conditions are important determinants of disparities in COVID hospitalization risk. These findings will inform health care systems of where large numbers of patients may occur to reduce overburdening of hospitals and to guide vaccination efforts.
  • Preeti Dubey (Francis I. Proctor Foundation, UCSF, USA)
    "Optimal vaccine prioritization for COVID-19 between high-risk and core group in California"
  • The COVID-19 pandemic has caused record numbers of daily confirmed cases and deaths in USA during the winter of 2020-2021. With the approval of Moderna and Pfizer vaccines, a substantial mitigation of the epidemic is expected by mid-2021. During the initial rollout, it was unclear whether or not vaccine should be targeted at elderly individuals at highest risk of mortality and morbidity, or towards younger individuals responsible for a majority of transmission. In this study, we sought to investigate the optimal prioritization of COVID-19 vaccination in California. We constructed a compartmental model based on the natural history of COVID-19 transmission. The model involved two transmission risk groups (low and high), and two age prioritization groups. We considered the case of random mixing vs. positive assortative mixing, as well as the relative rate of high COVID-19 risk behavior in the high transmission risk group. The model considered incomplete reporting and reporting delays and was calibrated to California case data. All 24 possible orderings of age/risk prioritization were simulated suggesting that age prioritization was optimal when the relative riskiness of the high-risk group was low. The randomness in mixing has also played a role in making the decision of optimality of risk prioritization when the relative riskiness was high. Our results are aligned with the findings of other modeling groups that some risk targeting can be a valuable consideration in controlling the pandemic.

Collaboration and calibration: modelling with experimental and clinical data

Organized by: Adriana Zanca (The University of Melbourne, Australia), Jennifer Flegg (The University of Melbourne, Australia), Helen Byrne (University of Oxford, UK)
Note: this minisymposia has multiple sessions. The second session is MS04-IMMU.

  • Alison Betts (Applied BioMath, USA)
    "Modeling strategies for preclinical to clinical translation of T cell engager bispecific antibodies: using math to unravel counter intuitive dose responses"
  • T cell engager (TCE) bispecific antibodies are a promising therapeutic approach for the treatment of cancer. They have a complex mechanism of action, binding to CD3 on T cells and a tumor associated antigen on tumor cells to form a trimolecular complex (trimer), mimicking the normal immune synapse. Trimer formation stimulates the T cell and redirects cytotoxicity against the tumor cell. This results in some interesting mechanistic behaviors, including bell shaped concentration response relationships, which can result in non-intuitive dose response relationships. To understand these complex quantitative relationships, and to provide a tool for decision making from early discovery through to clinical trials, a translational quantitative systems pharmacology (QSP) model is proposed for TCE molecules.  The model predicts trimer formation between drug, T-cell and tumor cell, which can be linked to downstream pharmacodynamics, efficacy or toxicity. Two case studies are discussed; in the first the model is used to optimize design of a PSMA/CD3 TCE and in the second the model is used for preclinical to clinical translation of a Pcad/CD3 TCE to predict clinical efficacious dose.
  • Allison Lewis (Lafayette College, USA)
    "Bayesian information-theoretic calibration of tumor models for informing effective scanning protocols"
  • With new advancements in technology, we can now collect data describing tumor growth using numerous metrics. For any tumor growth model, we observe large variability among individual patients’ parameter values, particularly those relating to treatment response; thus, exploiting the use of these various metrics for model calibration can be helpful to infer such patient-specific parameters both accurately and early. Since clinicians are limited to a sparse collection schedule, the determination of optimal times and metrics for which to collect data in order to best inform model calibration is essential. Here, we employ a Bayesian information-theoretic calibration protocol for experimental design in order to identify the optimal times at which to collect data for informing treatment parameters. Data collection times are chosen sequentially to maximize the reduction in parameter uncertainty with each added measurement, ensuring that a budget of n measurements results in maximum information gain about the model parameter values.
  • Leili Shahriyari (University of Massachusetts Amherst, USA)
    "A data-driven mathematical model of colon cancer"
  • Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we introduce a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. We then compare the tumor sensitivity and progression in each of these groups of patients and observe differences in the patterns of tumor growth as well as response to FOLFIRI treatment.
  • Min Song (University of Southern California, USA)
    "Quantitative analysis of endothelial sprouting mediated by FGF- and VEGF-induced MAPK and PI3K/Akt pathways"
  • The essential role of blood vessels in delivering nutrients makes angiogenesis important in wound healing and tumor growth. Targeting angiogenesis is a prominent strategy in tissue engineering and cancer treatment. However, not all approaches to regulate angiogenesis lead to successful outcomes. There is a limited understanding of how pro-angiogenic factors such as VEGF and FGF combine together to stimulate angiogenesis. We aim to quantitatively characterize the crosstalk between VEGF- and FGF-mediated angiogenic signaling and endothelial sprouting, to gain mechanistic insights and identify novel therapeutic strategies. We constructed a hybrid agent-based model that characterizes endothelial sprouting driven by FGF and VEGF-mediated MAPK and PI3K/Akt signaling. The experimentally fitted and validated model predicts that FGF induces stronger angiogenic responses in the long-term compared to VEGF stimulation. Also, FGF plays a dominant role in the combination effects in endothelial sprouting. Moreover, the model suggests that ERK and Akt pathways and cellular responses contribute differently to the sprouting process. Furthermore, the model predicts that the strategies to modulate endothelial sprouting are context dependent. Thus, our model can identify potential effective pro- and anti-angiogenic targets under different conditions and study their efficacy. The model provides mechanistic insight into VEGF and FGF interactions in sprouting angiogenesis.

Control Interventions for New, Rare and Neglected Infectious Diseases

Organized by: Stacey Smith? (The University of Ottawa, Canada) & Aurelio A. de los Reyes V (University of the Philippines Diliman)

  • Hyojung Lee (National Institute of Mathematical Sciences,, South Korea)
    " Effects of social distancing on transmission dynamics of COVID19 in Republic of Korea"
  • The novel coronavirus outbreak has rapidly spread out from Wuhan, Hubei Province, China to other countries since December, 2019. The World Health Organization (WHO) declared the COVID-19 outbreak a global pandemic on March 11, 2020. The Korean government implemented the combined interventions including social distancing, and work-at-home policies. In this research, first, the epidemiological characteristics were analyzed in seven geographical areas in Korea. Second, we constructed a mathematical model to assess the control interventions including the social distancing. Third, the effective reproduction numbers by geographical area were estimated. Finally, we assessed the effect of the control strategies as time-dependent interventions using mathematical model approach on the COVID-19 spread to suggest the most effective intervention.
  • Stacey Smith? (The University of Ottawa, Canada)
    "Modelling the daily risk of Ebola in the presence and absence of a potential vaccine"
  • Ebola virus --- one of the deadliest viral diseases, with a mortality rate around 90% --- damages the immune system and organs, with symptoms including episodic fever, chills, malaise and myalgia. The Recombinant Vesicular Stomatitis Virus-based candidate vaccine (rVSV-ZEBOV) has demonstrated clinical efficacy against Ebola in ring-vaccination clinical trials. In order to evaluate the potential effect of this candidate vaccine, we developed risk equations for the daily risk of Ebola infection both currently and after vaccination. The risk equations account for the basic transmission probability of Ebola and the lowered risk due to various protection protocols: vaccination, hazmat suits, reduced contact with the infected living and dead bodies. Parameter space was sampled using Latin Hypercube Sampling, a statistical method for generating a near-random sample of parameter values. We found that at a high transmission rate of Ebola (i.e., if the transmission rate is greater than 90%), a large fraction of the population must be vaccinated ($>$80%) to achieve a 50% decrease in the daily risk of infection. If a vaccine is introduced, it must have at least 50% efficacy, and almost everyone in the affected areas must receive it to effectively control outbreaks of Ebola. These results indicate that a low-efficacy Ebola vaccine runs the risk of having vaccinated people be overconfident in a weak vaccine and hence the possibility that the vaccine could make the situation worse, unless the population can be sufficiently educated about the necessity for high vaccine uptake.
  • May Anne Mata (University of the Philippines Mindanao, Philippines)
    "Models of rabies incidence in Davao City, Philippines and their implications for policy makers"
  • Rabies is a fatal zoonotic disease and remains to be a priority health concern in the Philippines. The call to eradicate rabies in the Philippines by 2023 led Davao City public health officials to intensify the rabies control interventions. Despite the efforts done to mitigate the disease, rabies cases in dogs remain endemic. In this talk, I will present the status of canine rabies in Davao City as well as the modelling approaches we used to determine the associated factors affecting rabies incidence, explain the mechanisms behind the trend in monthly reported rabies cases, and to evaluate the impact of government-initiated interventions, climate variables, and dog information, which are known as potential disease drivers. Our results revealed that from model estimates, rabies in the city is not epidemic and in order to control the disease, the target vaccination coverage must be consistently met, and that dog population must be regulated. We recommend that the local government unit should consider our findings when conducting strategic planning sessions for achieving a rabies-free Davao City.
  • Victoria May Mendoza (University of the Philippines Diliman, Philippines)
    "A mathematical model and optimal control of Schistosomiasis in Agusan del Sur, Philippines"
  • Schistosomiasis is a neglected tropical disease and remains endemic in the Philippines, covering 28 provinces in 12 regions. Schistosomiasis in the Philippines is caused by Schistosoma japonicum, a zoonotic parasite which infects other mammalian hosts aside from humans. In this work, we develop a mathematical model to study the transmission dynamics of schistosomiasis in Agusan del Sur, Philippines and investigate strategies to control and possibly eliminate the disease. We consider humans and carabaos as definitive hosts, and snails as intermediate hosts. Using the available schistosomiasis data from the Philippine Department of Health, we estimate the transmission probability and contact rate between snails and humans, and infectivities from humans and carabaos to snails. Implementation of multiple control strategies highlight the significance of an integrated approach in mitigating the disease. Improved surveillance and monitoring of cases, and the importance of accurate and updated data are strongly emphasized.

Generalized Boolean network models and the concept of canalization

Organized by: Claus Kadelka (Iowa State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS02-MFBM.

  • Claus Kadelka (Iowa State University, United States)
    "Collective canalization"
  • In this talk, I introduce collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for regulatory networks, and the class of collectively canalizing functions captures a key feature of biological network dynamics, namely that a subset of one or more variables, under certain conditions, can dominate the value of a Boolean function, to the exclusion of all others. These functions have rich mathematical properties to be explored. We show how the number and type of such sets influence a function’s behavior and define a new measure for the canalizing strength of any Boolean function. We further connect the concept of collective canalization with the well-studied concept of the average sensitivity of a Boolean function. The relationship between Boolean functions and the dynamics of the networks they form is important in a wide range of applications beyond biology, such as computer science, and has been studied with statistical and simulation-based methods. However, the rich relationship between structure and dynamics remains largely unexplored, and we attempt a first step towards its mathematical foundation.
  • Elena Dimitrova (California Polytechnic State University, United States)
    "Revealing the canalizing structure of Boolean functions — algorithms and applications"
  • Nested canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Boolean functions, however, can be represented in many ways, including logical forms, truth tables, and polynomials, as well as different canonical representations such as minimal disjunctive normal form. These representations may obscure the canalizing structure of a Boolean function making its extraction a challenge. In this talk, we show that the problem of determining the specific layer structure of a Boolean function is NP-hard and present and compare algorithms for finding the canalizing layers. Further, we discuss applications of these algorithms for computing disjunctive normal forms and for reverse engineering of Boolean functions according to a prescribed layering format.
  • Matthew Macauley (Clemson University, United States)
    "Toggling independent sets as an asynchronous Boolean network"
  • The notion of 'generalized toggle groups' has been a recent popular topic in the field of dynamic algebraic combinatorics. In this talk, I will introduce what it means to toggle independent sets of a graph. Loosely speaking, toggling at a vertex adds it (if possible) when it is absent, removes it if it is present, and otherwise does nothing. I will frame this problem in terms of asynchronous Boolean networks, and summarize the mathematics that we have developed to analyze it. If your interest is piqued by covering spaces consisting of (co-)snakes on a plane that project down to a (co-)ouroborus on a torus, and how the (co-)snake and (co-)ouroborous groups act on the (co)-slithers, then you won't want to miss this talk. It will be widely accessible, and there will be no shortage of open problems, colorful pretty pictures, and puns.
  • Alan Veliz-Cuba (University of Dayton, Ohio, United States)
    "Identification of control targets in Boolean networks via computational algebra"
  • Many problems in biology have the goal of finding strategies to change an undesirable state of a biological system into another state through an intervention. The identification of such strategies is typically based on a mathematical model such as Boolean networks. In this talk we will see how to find node and edge interventions using computational algebra.

Complex Fluids and Flows in Mathematical Biology

Organized by: Calina Copos (University of North Carolina at Chapel Hill, USA), Tony Gao (Michigan State University, USA), On Shun Pak (Santa Clara University, USA), Yuan-nan Young (New Jersey Institute of Technology, USA)
Note: this minisymposia has multiple sessions. The second session is MS02-MMPB.

  • Tony Gao (Michigan State University, USA)
    "Q-tensor model for undulatory swimming in a liquid crystal"
  • Microorganisms may exhibit rich swimming behaviors in anisotropic fluids, such as liquid crystals, that have direction-dependent physical and rheological properties. Here we construct a two-dimensional computation model to study the undulatory swimming mechanisms of microswimmers in a solution of rigid, rodlike liquid-crystalline polymers. We describe the fluid phase using Doi's Q-tensor model, and treat the swimmer as a finite-length flexible fiber with imposed propagating traveling waves on the body curvature. The fluid-structure interactions are resolved via an Immersed Boundary method. Compared to the swimming dynamics in Newtonian fluids, we observe non-Newtonian behaviors that feature both enhanced and retarded swimming motions in lyotropic liquid-crystalline polymers. We reveal the propulsion mechanism by analyzing the near-body flow fields and polymeric force distributions, together with asymptotic analysis for an idealized model of Taylor's swimming sheet.
  • David Stein (Simons Foundation, USA)
    "The many behaviors of deformable active droplets"
  • Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motion. In some cases, these phenomena have been well characterized, and theory can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this talk, I will discuss the behavior of droplets of an active nematic fluid. Through a mix of linear stability analysis and nonlinear simulations, we identify parameter regimes where single modes dominate and droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zig-zaggers, washing machines, wanderers, and pulsators.
  • Herve Nganguia (Indiana University of Pennsylvania, USA)
    "Swimming in a fluid pocket enclosed by a porous medium"
  • This talk presents a minimal theoretical model to investigate how heterogeneity created by a swimmer affects its own locomotion. As a generic locomotion model, we consider the swimming of a spherical squirmer in a purely viscous fluid pocket (representing the liquified or degelled region) surrounded by a Brinkman porous medium (representing the mucus gel). We obtain analytical expressions for the swimming speed, flow field, and power dissipation of the swimmer. Depending on the details of surface velocities and fluid properties, our results reveal the existence of a minimum threshold size of mucus gel that a swimmer needs to liquify in order to gain any enhancement in swimming speed.
  • Anup Kanale (University of Southern California, USA)
    "Flow-mediated instabilities in ciliary carpets"
  • Motile cilia that densely cover epithelial tissues are known to coordinate their beating in metachronal waves to transport fluid. Although hydrodynamic coupling seems to drive this coordination, the exact mechanisms leading to the emergence of ciliary waves remain unclear. Here, we propose a minimal model in which each cilium is a rotating bead driven by a phase-dependent active force, and we accordingly construct a coarse-grained continuum model. Isotropic states are unstable relative equilibria. Perturbations to these equilibria lead, beyond the transient regime, to noisy wave-like patterns that propagate along the direction of the ciliary beating. These noisy patterns seem globally attracting for all initial conditions, and depend only on the nature of the forcing at the level of an individual cilium. We use the continuum model to analyze the linear stability of both the synchronized and isotropic states to perturbations of all wavelengths and show that both states are unstable with growth rates that are in good agreement with the discrete cilia simulations. Our findings demonstrate a set of minimal conditions necessary to create wave-like coordination in ciliary carpets.

Ionic Flow through Membrane Channels

Organized by: Peter Bates (Michigan State University), Weishi Liu (Mathematics, U. Kansas, USA), Mingji Zhang (Mathematics, New Mexico Tech., USA)
Note: this minisymposia has multiple sessions. The second session is MS09-NEUR.

  • Bob Eisenberg (Molecular Biophysics & Physiology, Rush University, USA)
    "Maxwell’s Core Equations Exact, Universal, and Scary"
  • When the Maxwell equations are written without a dielectric constant, they are universal and exact, for biological and technological applications, from inside atoms to between stars. Dielectric and polarization phenomena need then to be described by stress strain relations for charge, that show how charge redistributes when the electric field is changed, in each system of interest. Conservation of total current (including the ethereal displacement current ε_0  ∂E∕∂t) is then as exact as the Maxwell equations themselves and independent of any property of matter. It is a consequence of the Lorentz invariance of the elementary charge, a property of all locally inertial systems, described by the theory of relativity. Exact Conservation of Total Current allows a redefinition of Kirchhoff’s current law that is itself exact. In unbranched systems like circuit components or ion channels, conservation of total current becomes equality. Spatial dependence of total current disappears in that case. Hopping phenomena disappear. Spatial Brownian motion disappears. The infinite variation of a Brownian model of thermal noise becomes the zero spatial variation of total current. Maxwell’s Core Equations become a perfect (spatial) low pass filter. An Exact and Universal theory of Electrodynamics is a scary challenge to scientists like me, trained to be skeptical of all sweeping claims to perfection.
  • Jianing Chen (Mathematics, New Mexico Tech., USA)
    "Effects on zero-current ionic flows from ion sizes via PNP system with boundary layers"
  • We study the qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems for two oppositely charged particles with boundary layers. Local Bikerman’s hard-sphere model is included in the system to account for finite ion size effects. Of particular interest is to examine the effects on the zero-current ionic flows from finite ion sizes, diffusion coefficients, ion valences and boundary layers due to the violation of electroneutrality boundary conditions. The nonlinear interplays among those system parameters are characterized in detail, which provides better understandings of the internal dynamics of ionic flows through membrane channels.
  • Francisco Bezanilla (Biochemistry and Molecular Biology and Institute for Biophysical Dynamics, University of Chicago and CINV, University of Valparaiso, Chile., USA)
    "Voltage sensors and ion channel opening"
  • The generation of the nerve impulse (action potential) depends on voltage-dependent sodium channels that must open before voltage-dependent potassium channels. We will briefly explain the voltage sensors that give voltage dependence of the ion channels. The voltage sensors have intrinsic charges in the channel protein which move in the cell membrane electric field and generate gating currents. Experiments with voltage clamp and site-directed fluorescence describe molecular details of the voltage sensor operation indicating the paths followed by the charged arginine residues within the protein core. A detailed study of the residues in the core show that the nature of the side chains determine that Na channels are faster than K channels. The canonical coupling of the voltage sensor to the conduction pore is via the linker between transmembrane segments S3 and S4. We will describe that the proximity of the S4 segment of the voltage sensor and the S5 segment of the pore region makes another noncanonical coupling pathway. The molecular basis of this pathway will be described.
  • Pei Liu (Mathematics, U. Minnesota, USA)
    "Ion-dependent DNA Configuration in Bacteriophage Capsids"
  • Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure, and experimental results have confirmed that it depends on environmental ionic conditions. In this work, we propose a biophysical model to describe the dependence of DNA configurations inside bacteriophage capsids on ions types and concentrations. The total free energy of the system combines the liquid crystal free energy, the electrostatic energy and the Lennard--Jones energy. The equilibrium points of this energy solve a highly nonlinear, second order partial differential equation (PDE) that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach to simulate predictions of our model. The numerical results show good agreement with existing experiments and molecular dynamics simulations.

Systems Biology Models of Tumor Metabolism

Organized by: Shubham Tripathi (Rice University, USA), Abhinav Achreja (University of Michigan, USA)

  • Dongya Jia (Laboratory of Integrative Cancer Immunology, National Cancer Institute, National Institutes of Health, USA)
    "Elucidating cancer catabolism and anabolism by coupling gene regulation with metabolic pathways"
  • Cancer cells can adapt their metabolic phenotypes to meet various bioenergetic and biosynthetic needs, and to survive the therapeutic treatments. It remains largely unclear how cancer cells orchestrate different metabolic phenotypes (glycolysis, oxidative phosphorylation etc.) and various metabolic ingredients (glucose, fatty acids, glutamine, etc.). Since recent efforts in targeting individual cancer metabolic pathways have been largely ineffective, a better understanding of cancer metabolic network and its plasticity will progressively facilitate the development of more effective therapeutic strategies. The goal of this study is to elucidate the mechanisms underlying cancer metabolic plasticity within both catabolism and anabolism by integrated theoretical-experimental approaches. We constructed a metabolic modeling framework featuring regulation by the master gene regulators (AMPK, HIF-1, MYC etc.) and their cross-talk with metabolic pathways. The beauty of the framework is at least two-fold. First, it has considered all three most important metabolic ingredients (glucose, fatty acids, glutamine) for tumorigenesis and metastasis. Second, it has allowed us to investigate the interaction between catabolism (glucose/glutamine oxidation, etc.) and anabolism (reductive glucose/glutamine metabolism), therefore offering a higher-level view of cancer metabolism. Our work elucidates how cancer cells can mix and match different metabolic phenotypes. For example, we show that cancer cells can acquire a hybrid metabolic phenotype where both glycolysis and OXPHOS are actively used, and a metabolically “low-low” phenotype where cells exhibit low activity of glycolysis and OXPHOS. Importantly, the hybrid metabolic phenotype characterizes highly metastatic breast cancer cells and the low-low phenotype can characterize drug-tolerant melanoma cells. Consequently, an accurate characterization of cancer metabolism enabled us to present effective combination therapies targeting metabolism in breast cancer.
  • Prahlad Ram (The University of Texas MD Anderson Cancer Center, USA)
    "4D Ex-vivo CRISPR / CAS9 Whole-genome Screen to Identify Genes Regulating Early Lung Cancer Metastasis"
  • Metastatic lung cancer has a 5-year survival rate of 5%. Lung cancers tend to be asymptomatic until late stages, and almost 90% are not diagnosed until they are advanced. The genomic events early in the metastatic process has not been completely deciphered. Utilizing CRISPR/Cas9 whole genome knockout screen in the A549 lung adenocarcinoma cell line and coupling it with a novel ex vivo 4D lung metastasis model has now allowed us to examine early genomic events in metastasis. Using this approach we recovered genes previously implicated in lung cancer and metastasis validating this approach. Additionally we identified a transcription factor network driven by SPI1 which was enriched in our screen. Experimental validation of SPI1 uncovered a novel role of this network in the metastatic process.
  • Andrew Raddatz (The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, USA)
    "Kinetic Modeling of Redox Metabolism in Head and Neck Cancer"
  • Reactive oxygen species (ROS) levels are frequently elevated in head and neck tumors because of downstream tumor-promoting outcomes. Moderate levels of ROS promote tumorigenesis because they increase proliferation, initiate angiogenesis, and trigger survival signaling pathways. Additionally, treatment options such as radiation, chemotherapy, and even immunotherapy have been shown to involve tumor redox biology. A greater mechanistic understanding of how redox-based expression profiles in cancer affect susceptibility to certain treatments is needed to improve clinical decisions. Here, we developed an intracellular ODE model to represent how a cancer cell’s redox state would respond to treatment with a ROS-generating drug. The following antioxidant systems were included in the model based on previous H2O2 clearance modeling: catalase, peroxiredoxin, glutathione, and the protein thiol pool. Initial parameterization of the model included taking values reported in the literature and scanning the BRENDA database for remaining rate constants where available. To validate our model, we experimentally silenced antioxidant enzymes represented in the model by siRNA and observed the effect on production of H2O2. We found that knocking down PRDX1 (peroxiredoxin 1), CAT (catalase), and TXNRD1 (thioredoxin reductase 1) via siRNA led to a relative increase in extracellular H2O2 upon drug application. Then, using scRNA-seq data, we generated single cell models to predict how transcriptome variability across patients and within tumors can influence ROS accumulation and redox potentials within the cell under drug treatment.
  • Stacey Finley (University of Southern California, USA)
    "Modeling tumor-stromal metabolic crosstalk in colorectal cancer"
  • Colorectal cancer (CRC) is a major cause of morbidity and mortality in the United States. Tumor-stromal metabolic crosstalk in the tumor microenvironment promotes CRC development and progression, but exactly how stromal cells, in particular cancer-associated fibroblasts (CAFs), affect the metabolism of tumor cells remains unknown. Here we take a data-driven approach to investigate the metabolic interactions between CRC cells and CAFs, integrating constraint-based modeling and metabolomic profiling. Using metabolomics data, we perform unsteady-state parsimonious flux balance analysis to infer flux distributions for central carbon metabolism in CRC cells treated with or without CAF-conditioned media. We find that CAFs reprogram CRC metabolism through stimulation of glycolysis, the oxidative arm of the pentose phosphate pathway (PPP), and glutaminolysis as well as inhibition of the tricarboxylic acid cycle. To identify potential therapeutic targets, we simulate enzyme knockouts and find that inhibiting the hexokinase and glucose-6-phosphate dehydrogenase reactions exploits the CAF- induced dependence of CRC cells on glycolysis and oxidative PPP. Our work gives mechanistic insights into the metabolic interactions between CRC cells and CAFs and provides a framework for testing hypotheses towards CRC-targeted therapies.