Tuesday, June 15 at 05:45pm (PDT)
Wednesday, June 16 at 01:45am (BST)
Wednesday, June 16 09:45am (KST)


Modeling and data analysis of dynamics from molecules, cells to populations

Organized by: Lei Zhang (Peking University, China)
Note: this minisymposia has multiple sessions. The second session is MS10-CBBS.

  • Hao Ge (Peking University, China)
    "The Nonequilibrium Mechanism of Noise-Enhanced Drug Synergy in HIV Latency Reactivation"
  • The “shock and kill” strategy has become a promising way to cure HIV by eliminating latent HIV reservoirs, the main barrier to a clinical cure. Recently, single-cell screening experiments have shown the Noise-enhanced drug synergy on reactivating latent HIV. However, the underlying biomolecular mechanism is still a mystery. We propose here a generic model for HIV regulation and Tat transcription/translation. Using this model, we find out that the drug synergy is mainly determined by the magnitude and direction of energy input into the genetic regulatory kinetics of HIV promotor. We further show that the Noise-enhanced drug synergy requires the timescale of HIV promoter entering into a transcriptionally non-permissive state without drugs presented to be slower than the timescale of Tat transactivation. Our model reveals a generic nonequilibrium mechanism underpinning the Noise-enhanced drug synergy, which is useful for improving the drug effect and identifying other drug synergies on lentivirus latency reactivation.
  • Yusuke Imoto (Kyoto University, Japan)
    "Topological Trajectory Inference for Single-cell RNA Sequencing Data"
  • This study develops a framework that extracts single-cell differentiation structures from single-cell RNA sequencing data (scRNA-seq data) by using a topological data analysis method, Mapper [G. Singh et al., SPBG 91 (2007)]. Because the scRNA-seq data is quite high-dimensional and contains technical noise, the scRNA-seq data analysis encounters the inconsistency of computational values between true and observed data due to the accumulation of noise; this problem is known as the curse of dimensionality. Since requiring a clustering in the high-dimensional space, Mapper is also affected by the curse of dimensionality. To overcome the problem, this study proposes the procedure using a statistical noise reduction method for scRNA-seq data, as the preprocessing of the Mapper. In this talk, we will verify the effect of the noise reduction method in Mapper and show some applications to biological data. Moreover, we will introduce a visualization method to help with biological inference by using biological metadata.
  • Suoqin Jin (University of California Irvine, U.S.)
    "Understanding the role of cell-cell communication in cell fate decisions from single-cell data"
  • Cell-cell communication via soluble and membrane-bound factors is critical for informing diverse cell fate decisions, including decisions to activate programmed cell death, undergo migration or differentiate along the lineage. Single-cell RNA-sequencing (scRNA-seq) technologies have led to discovery of cellular heterogeneity and differentiation trajectories at unprecedented resolution level. scRNA-seq data inherently contains gene expression information on signaling crosstalk between cells. This offers an unprecedented opportunity for comprehensively understanding how cell-cell communication drives diverse cellular decisions in tissues. In this talk, I will take about our recent efforts in how by applying systems biology and machine learning approaches, we can quantitatively build and analyze cell-cell communication networks in an easily interpretable way. Applying our framework to scRNA-seq datasets of embryonic mouse skin, we identify previously unrecognized signaling mechanisms regulating melanocyte migration during early hair follicle formation. Our framework can be potentially incorporated into cell lineage-based mechanistic models to further deepen our understanding of the signaling dynamics in cell fate decisions.
  • Dae Wook Kim (Korea Advanced Institute of Science and Technology, Korea)
    "Moment-based inference of cell-to-cell variability in signal transduction time"
  • As experimentally measuring biochemical reaction rates in single cells is costly and time-consuming, they are often estimated by fitting a mathematical model to time-lapse live-cell imaging data, which are relatively easy to measure. However, this is often limited because only the final output of a series of reactions (e.g. matured protein) can be observed. In this case, a series of hidden intermediate reactions can be replaced with a distributed time delay. However, the estimation of the delay distribution has remained challenging as models with the delay are non-Markovian. Here, we develop a moment-based Bayesian inference method for accurate and efficient estimation of the delay distribution in single-cell signal transduction by using queuing theory and mixed effects modeling. By applying our method to single-cell fluorescence trajectories that are the final output of cellular response to antibiotic stress, we find considerable magnitude of cell-to-cell heterogeneity in signal amplification rate and transduction delay of the stress. Surprisingly, we also find that the magnitude of cell-to-cell heterogeneity in signal amplification rate is positively correlated with the number of rate-limiting molecular steps underlying the stress response. To allow systematic estimation of the signal transduction time, we provide a user-friendly computational package, namely CMBI.

Machine Learning and Data Science Approaches in Mathematical Biology: Recent Advances and Emerging Topics

Organized by: Paul Atzberger (University of California Santa Barbara, USA), Smita Krishnaswamy (Yale University, USA), Kevin Lin (University of Arizona, USA)
Note: this minisymposia has multiple sessions. The second session is MS08-DDMB.

  • Zhuo-Cheng Xiao (Courant Institute, NYU)
    "A data-informed mean-field approach to mapping cortical landscapes"
  • Cortical circuits are characterized by a high degree of structural and dynamical complexity, and this biological reality is reflected in the large number of parameters in even highly idealized cortical models. A fundamental task of computational neuroscience is to understand how these parameters govern neuronal network dynamics. While some neuronal parameters can be measured in vivo, many remain poorly constrained due to limitations of available experimental techniques. Computational models can address this problem by relating difficult-to-measure parameters to observable quantities, but to do so one must overcome two challenges: (1) the computational expense of mapping a high dimensional parameter space, and (2) extracting biological insights from such a map. In this study, we address these challenges in the following ways: First, we propose a data-informed, parsimonious mean-field algorithm that efficiently predicts spontaneous cortical activity, thereby speeding up the mapping of parameter landscapes. Second, we show that lateral inhibition provides a basis for conceptualizing cortical parameter space, enabling us to begin to make sense of its geometric structure. We illustrate our approach on a biologically realistic model of the Macaque primary visual cortex.
  • Andrea Arnold (Worcester Polytechnic Institute, USA)
    "Data Assimilation for Time-Varying Parameter Estimation in Biological Systems"
  • Estimating and quantifying uncertainty in system parameters remains a big challenge in many biological applications. In particular, such problems may involve parameters that are known to vary with time but have unknown dynamics and/or cannot be measured. This talk will address the use of data assimilation in novel approaches to time-varying parameter estimation, with emphasis on how uncertainty in the parameter estimates affects the corresponding model predictions. Results will be demonstrated on several biological examples, including systems from computational neuroscience.
  • John Fricks (Arizona State University, USA)
    "A Bayesian Analysis of 2-D Motor-Cargo Complex Dynamics"
  • Molecular motors, such as kinesin and dynein, move along microtubules in cells while the tails of the motors are connected to cargos. The cargos can be tracked in fluorescence or dark field experiments yielding a stack of images. Processing allows for the localization of the cargos yielding a two-dimensional time series; typically, further processing projects the data on to one-dimension along the direction of the microtubule. However, curvature or misidentification of the microtubule may be relevant, but is generally not considered. In this talk, we will propose an analysis of the original two-dimensional time series, which can also extract additional information on the dynamics of these motor-cargo complexes.
  • Mengyang Gu (University of California, Santa Barbara, USA)
    "Uncertainty quantification and estimation in differential dynamic microscopy for biomaterials characterization"
  • Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present a comprehensive statistical framework that aims at quantifying error, reducing the computational order and enhancing the robustness of DDM analysis. We quantify the error, and propagate an independent noise term to derive a closed-form expression of the expected value and variance of the observed image structure function. Significantly, we propose an unbiased estimator of the mean of the noise in the observed image structure function, which can be determined experimentally and significantly improves the accuracy of applications of DDM. Furthermore, through use of Gaussian Process Regression (GPR), we find that predictive samples of the image structure function require only around 1% of the Fourier Transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with Uncertainty Quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization.

Spatial approaches to ecological population monitoring and management

Organized by: Tae-Soo Chon (Pusan National University/Ecology and Future Research Association, Republic of Korea), Fugo Takasu (Nara Women’s University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS10-ECOP.

  • Tae-Soo Chon (Ecology and Future Research Institute/Pusan National Univ., Republic of Korea)
    "Patterning local cooccurrence patterns of Nutria individuals using Geo-self-organizing map applied to telemetry data"
  • Nutria populations expanded rapidly in Korea since 1990s, causing biodiversity loss, local habitat disturbances and agricultural damages in ecosystems. The geo-self-organizing map (Geo-SOM) was applied to radio-tracked individual data to cluster geographical areas in association with plant types, land cover states and biological parameters. The minimum nearest neighbor distances for the different sexes were overall in accord with the minimum distances for the same sex. Local cooccurrences of female and male individuals were negatively associated with male-male cooccurrences compared with female-female cooccurrences, suggesting male dominance in group formations. Movement and cooccurrence information extracted by Geo-SOM aids understanding of population dispersal to help formulating management strategies for nutria populations.
  • Thakur Dhakal (Kangwon National Univ., Republic of Korea)
    "Unraveling Behavior States of Wild Boar Movements in Habitat Transitions Using Hidden Markov Model"
  • Wild boar (Sus scrofa) population dispersal is a critical issue in Korea nowdays, being closely linked with epizootics of African swine fever. Understanding movement of wild boar is a key issue in predicting spatial advancement patterns of the population. Movements of animals, however, are highly complex and difficult to analyze. We addressed behavior states of wild boar individuals by applying the hidden Markov model (HMM) to field data. Movements of wild boar individuals were continuously tracked at the Bukhan Mountain, Seoul, Korea, with the interval of approximately 2 hours up to 313 days from June, 2018 to May, 2019. Observable events were expressed as visiting by wild boar individuals to habitats with different resources (forest, leaf types and water). Transition probability matrices (TPMs) and emission probability matrices (EPMs) were estimated according to different initial conditions. Self-organizing map (SOM) was utilized to cluster output parameters produced from initial conditions to find the global optimum of parameters. Characteristic TPMs were observed according to different number of states. The event with most favorable habitat with “broad-leaf and water” shows the maximum probability of visit in EPM, followed by the habitats with “coniferous-leaf and water”. As the number of states increased, other habitats including “coniferous-leaf without water” and “no-forest without water” had higher probabilities of visit in EPMs. HMM in linking with SOM is useful for addressing behavior states of movements of wild boar individuals and would provide basic information on monitoring wild boar population dispersal.
  • Sung-Won Hong (Kyungpook National Univ., Republic of Korea)
    "Ensemble species distribution models proved habitat characteristics coincidence of dead and living long-tailed gorals (Naemorhedus caudatus) according to extreme snowfall"
  • Ensemble species distribution models (SDMs) have been used to define the vulnerable areas for critically endangered species and establish the conservation planning. The long-tailed goral (Naemorhedus caudatus) is a critically endangered herbivore in South Korea. Despite government efforts to recover the population through reintroduction programs, the animal remains vulnerable to heavy snowfall. From March to June 2010, 24 animals were found dead due to heavy snowfall in the Wangpi Stream basin. In this study, we hypothesized that gorals that died due to snowfall are low-status individuals that lived in the sub-optimal or non-suitable areas. Using the occurrence data from extensive field surveys from 2008 to 2010 in the Wangpi Stream and the carcass location data as well, we (1) defined the goral habitat characteristics and (2) compared the habitat characteristics between dead and living gorals using ensemble species distribution modeling (BIOCLIM, Domain, generalized linear models, generalized additive models, random forests, boosted regression trees, classification and regression trees and Maxent). The ensemble models had high levels of goodness-of-fit and suggested that the sites where dead gorals were found were closely related to typical goral habitats. These results implied that the optimal goral habitats could become uninhabitable following heavy snowfall. Most of the dead animals were pregnant females or were young, implying that they could not escape their primary habitats due to lower mobility. Thus, when there is a climate catastrophe, the optimal goral habitats should be considered for rescue and artificial feeding.
  • Taeyong Shim (Korea University, Republic of Korea)
    "Evaluating Distribution Shifts of Invasive Largemouth Bass under Climate Change"
  • The spread of largemouth bass (Micropterus salmoides) is a rising concern in South Korea. This study aims to evaluate the distribution shifts of largemouth bass in South Korea using classification algorithms. The candidate classification algorithms include RF (Random Forest), C5.0 and cforest (Conditional Inference Random Forest) which are built in the caret package in R. Largemouth bass occurrence records and environmental variables (temperature, precipitation, flow, water quality, and topography) from 2011 to 2015 were used in model training. In training, grid and random searching methods were compared for identifying the hyperparameters within an algorithm (RF, C5.0, and cforest). As a result, grid searching applied RF showed the highest accuracy. RF showed that largemouth bass will shift to the upstream regions in the Han river. This study is expected to be helpful for predicting distribution shifts and establishing management policy of largemouth bass.

The Study of Diffusive Dispersal in Population Dynamics

Organized by: Chiu-Yen Kao (Claremont McKenna College, United States), Bo Zhang (Oklahoma State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-EVOP. The third session is MS10-EVOP.

  • Rachidi Salako (University of Nevada at LasVegas, United States)
    "Study of a diffusive multiple-strains epidemic model"
  • Infectious diseases are one of the leading causes of many deaths around the world. As a result, health officials and the World Health Organization have devoted several resources to educate populations on safety measures which prevent the spread of infectious diseases. Hence restricting population’s movement has been widely used in an effort to limit the outbreak of an infectious disease. In this talk, we will study a multiple-strains PDE infectious disease epidemic model and discuss how population movement can affect the dynamics of the disease.
  • Kurt Anderson (Department of Evolution, Ecology, and Organismal Biology, University of California, Riverside, United States)
    "Body size dependent dispersal influences stability in heterogeneous metacommunities"
  • Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species' body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.
  • Harunori Monobe (Okayama University, Japan)
    "Singular limit of a mathematical model related to controlling invasive alien species"
  • In this talk, we suppose simple PDE models related to controlling invasive alien species. Also we consider the singular limit of the PDE and show that solutions of the PDE problem converge to that of free boundary problems called Fisher-Stefan problem.
  • King-Yeung Lam (Department of Mathematics, The Ohio State University, United States)
    "Defining the Ideal Free Distribution in Spatio-temporally Heterogeneous Environments."
  • A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using strategies that do not produce an ideal free distribution. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics.

Within-host modelling of SARS-CoV-2

Organized by: Thomas Hillen (University of Alberta, Canada), Carlos Contreras (University of Alberta, Canada)
Note: this minisymposia has multiple sessions. The second session is MS10-IMMU.

  • Morgan Craig (Sainte-Justine University Hospital Research Centre/Université de Montréal, Canada)
    " The impact of viral variants on immunopathology in COVID-19"
  • As SARS-CoV-2 continues its spread, the emergence of new variants has attracted increased attention, particularly as vaccination efforts ramped up. Throughout the pandemic, there has been a considerable effort to understand the genomic evolution of the virus. A quantitative picture of the evolution of SARS-CoV-2 in response to within-host pressures and their influence on the immunological response to infection is a crucial component to understanding and predicting COVID-19 outcomes. We have previously developed a mechanistic mathematical model of the immunological response to SARS-CoV-2 infection. Leveraging this framework, here we studied how viral variants influence immunopathology in COVID-19. Merging within-host SARS-CoV-2 evolutionary data and our cohort of realistic virtual patients, we predicted the combined effects of spike proteins and interferon-evading mutations on COVID-19 severity. Our results suggest that an individual’s immune response and their potential propensity for severe COVID-19 are the key factors distinguishing COVID-19 disease courses and outcomes.
  • Ashlee N. Ford Versypt (University at Buffalo, The State University of New York, USA)
    "Multiscale Simulation of Lung Fibrosis Induced by SARS-CoV-2 Infection and Acute Respiratory Distress Syndrome"
  • The 2019 novel coronavirus, SARS-CoV-2, is a pathogen of critical significance to international public health. Knowledge about immune system-virus-tissue interactions and how these can result in low-level infections in some cases and acute respiratory distress syndrome (ARDS) and other tissue damage in others is limited. We are developing an open-source, multi-scale tissue simulator that can be used to investigate mechanisms of intracellular viral replication, infection of epithelial cells, host immune response, and tissue damage. Our model can simulate fibroblast-mediated collagen deposition to account for the fibrosis at the damaged site in response to immune-response-induced tissue injury. The severity of infection and collagen deposition depends on the anti-inflammatory cytokine secretion rate, multiplicity of infection, and contact time for a CD8+ T cell to kill an infected cell. Additionally, the change in the ACE2 receptor concentration from the multiscale model has been used in a separate model of renin-angiotensin system to predict the change in ANGII, which is a biomarker for hypertension, pro-inflammation, and pro-fibrosis.
  • Paul Macklin (Indiana University, USA)
    "Community-driven multiscale model of SARS-CoV-2 dynamics and immune response"
  • The 2019 novel coronavirus, SARS-CoV-2, is a pathogen of critical significance to international public health. Knowledge of the interplay between molecular-scale virus-receptor interactions, single-cell viral replication, in-tracellular-scale viral transport, and emergent tissue-scale viral propagation is limited. Moreover, little is known about immune system-virus-tissue interactions and how these can result in low-level (asymptomatic) infections in some cases and acute respiratory distress syndrome (ARDS) in others, particularly with respect to presentation in different age groups or pre-existing inflammatory risk factors. Given the nonlinear interactions within and among each of these processes, multiscale simulation models can shed light on the emergent dynamics that lead to divergent outcomes, identify actionable “choke points” for pharmacologic interventions, screen potential therapies, and identify potential biomarkers that differentiate patient outcomes. Given the complexity of the problem and the acute need for an actionable model to guide therapy discovery and optimization, we introduce and iteratively refine a prototype of a multiscale model of SARS-CoV-2 dynamics in lung tissue. The first prototype model was built and shared internationally as open source code and an online interactive model in under 12 hours, and community domain expertise is driving regular refinements. In a sustained community effort, this consortium is integrating data and expertise across virology, immunology, mathematical biology, quantitative systems physiology, cloud and high performance computing, and other domains to accelerate our response to this critical threat to international health. More broadly, this effort is creating a reusable, modular framework for studying viral replication and immune response in tissues, which can also potentially be adapted to related problems in immunology and immunotherapy.
  • Adrianne Jenner (Queensland University of Technology, Australia)
    "Virtual patient cohort reveals immune mechanism driving COVID-19 disease outcomes"
  • Manifestations of SARS-CoV-2 infection are heterogeneous, and a large proportion of people experience asymptomatic or mild infections that do not require hospitalization. In severe cases, patients develop coronavirus disease (COVID-19), which is frequently accompanied by a myriad of inflammatory indicators and hospitalization. To understand the diversity of immune responses to SARS-CoV-2 and distinguish features that predispose individuals to severe COVID-19, we developed a mathematical model (system of delay differential equations) and from that interpolated a virtual patient cohort. Our results indicate that virtual patients with low production rates of IFN subsequently experienced highly inflammatory disease phenotypes, compared to those with early and robust IFN responses. In these in silico patients, the concentration of interleukin-6 (IL-6) was also a major predictor of CD8+ T cell depletion (a known marker of disease severity in hospitalised patients). Our analyses predicted that individuals with severe COVID-19 also have accelerated monocyte-to-macrophage differentiation that was mediated by increased IL-6 and reduced type I IFN signalling. Together, these findings identify biomarkers driving the development of severe COVID-19 and support early interventions aimed at reducing inflammation.

Advances in Infectious Disease Modeling

Organized by: Lihong Zhao (University of California Merced, United States), Ling Xue (Harbin Engineering University, China), Suzanne Sindi (University of California Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-MEPI.

  • Steve Krone (Department of Mathematics and Statistical Sciences, University of Idaho, United States)
    "The Timing and Nature of Behavioral Responses Affect the Course of an Epidemic"
  • During an epidemic, the interplay of disease and opinion dynamics can lead to outcomes that are different from those predicted based on disease dynamics alone. Opinions and the behaviours they elicit are complex, so modelling them requires a measure of abstraction and simplification. Here, we develop a differential equation model that couples SIR-type disease dynamics with opinion dynamics. We assume a spectrum of opinions that change based on current levels of infection as well as interactions that to some extent amplify the opinions of like-minded individuals. Susceptibility to infection is based on the level of prophylaxis (disease avoidance) that an opinion engenders. In this setting, we observe how the severity of an epidemic is influenced by the distribution of opinions at disease introduction, the relative rates of opinion and disease dynamics, and the amount of opinion amplification. Some insight is gained by considering how the effective reproduction number is influenced by the combination of opinion and disease dynamics.
  • Skylar Grey (University of Wisconsin Madison)
    "Contact Tracing during an Ebola Outbreak"
  • Be it Ebola, MERS, or SARS-CoV-2, contact tracing plays a key role in controlling an outbreak. To examine the role of contact tracers, we developed a system of ordinary differential equations to model the 2014-2016 Ebola outbreak in Sierra Leone. In the model we incorporated novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Utilizing data and simulations, we explore the role contact tracing played in eventually ending the outbreak and examine the potential impact of improved contact tracing on the death toll.
  • Lihong Zhao (Department of Applied Mathematics, University of California Merced, United States)
    "Association of Microbiome Dynamics with Chlamydia Infection"
  • Chlamydia trachomatics (C. trachomatics) is a major cause of bacterial sexually transmitted disease in the United States and is associated with adverse outcomes in the upper genital tract of women. It is unclear why some women are more likely to develop asymptomatic infection, have severe infection, or stay uninfected after exposure to C. trachomatics. Prior studies have shown a relationship between vaginal microbial composition and susceptibility to sexually transmitted infections including Chlamydia. However, little is known about the microbiome dynamics, especially in the upper genital tract, and its association with Chlamydia infection. We use mice as a model organism, seek to elucidate the association of genital tract microbiome dynamics with Chlamydia infection, and determining whether the time of infection affects the genital tract microbiome over time via analyzing the data collected before and over the course of infection.
  • Xiaotian Wu (College of Arts and Sciences, Shanghai Maritime University, China)
    "Modelling Triatomine Bug Population and Trypanosoma Rangeli Transmission: Co-feeding, Pathogenic Effect and Linkage with Chagas Disease"
  • A parasite of Trypanosoma rangeli is not pathogenic to human but pathogenic to the same vector species of Chagas disease. This parasite can induce the behavior changes of the infected vectors and subsequently impact the transmission dynamics of Chagas disease. In this talk, a mathematical model incorporating both systemic and co-feeding transmission routes and accounting for the pathogenic effect using infection-induced fecundity and fertility change of the triatomine bugs is presented. In terms of basic reproduction numbers R_v and R_0, the dynamical behaviors of the ecological and epidemiological systems are characterized. Moreover, when both R_v and R_0 are greater than unity, a unique parasite positive equilibrium E* appears which can be unstable and periodic oscillations can be observed where the pathogenic effect plays a significant role.

Emergent behavior across scales: locomotion, mixing, and collective motion in active swimmers

Organized by: Robert Guy (University of California Davis, United States), Arvind Gopinath (University of California Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS15-MFBM.

  • Henry Fu (University of Utah, United States)
    "Symmetry breaking propulsion of magnetically rotated spheres in nonlinearly viscoelastic fluids"
  • Symmetries have long been used to understand when propulsion is possible in microscale systems. Currently, artificially propelled magnetic micro- and nanoparticles are being utilized in a variety of techniques including hyperthermia, drug delivery, and magnetic resonance imaging. Rotation of rigid magnetic particles by an external magnetic field is a promising category of such artificial propulsion. Propulsion would seem to be prohibited by geometries with fore-aft symmetry along their rotation axis, such as a rotating sphere. We have shown that in nonlinearly viscoelastic fluids, a symmetry breaking propulsion is possible for rotating microspheres. We show that this propulsion occurs in both mucin and polyacrylamide solutions, and propose that it results from rod-climbing-like effects which squeeze the sphere and reinforce its translation. A perturbative analysis of the forces on a rotating sphere in a nonlinear polymeric fluid corroborates this mechanism.
  • Kathryn Link (University of California Davis, United States)
    "Emergent Properties of Flagellar Waveforms in Viscoelastic Fluids"
  • Eukaryotic cells move in rheologically complex environments via deformations of their flagella, which are slender threadlike structures that are powered by internal molecular motors. It is an ongoing scientific pursuit to determine how flagellar beat emerges from the coordination of the mechanics of the flagella, the interactions with the external fluid environment, and the mechano-chemical feedback of the molecular motors. Existing theories have shed light on the origins of this behavior in a viscous fluid, however, due to the inherent nonlinearity and mathematical complexity involved in modeling viscoelastic fluids, both analytical and numerical predictions require nonstandard approaches. In this work we propose an extension to the current models to make a prediction about how viscoelasticity changes the beat frequency of the emergent waveform.
  • Rudi Schuech (Tulane University, United States)
    "Viscoelastic Network Remodeling by Microswimmers"
  • Microorganisms often navigate a complex environment composed of a viscous fluid with suspended microstructures such as elastic polymers and filamentous networks. These microstructures can have similar length scales to the microorganisms, leading to complex swimming dynamics. Some microorganisms are known to remodel the viscoelastic networks they move through. In order to gain insight into the coupling between swimming dynamics and network remodeling, we use a regularized Stokeslet boundary element method to compute the motion of a microswimmer consisting of a spherical body and rotating helical flagellum. The viscoelastic network is represented by a cloud of points with virtual Maxwell element links. We consider two models of network remodeling in which (1) links break based on their distance to the microswimmer body, modeling enzymatic dissolution by bacteria or microrobots, or (2) links break based on a threshold tension force. We compare the swimming performance of the microbes in each remodeling paradigm as they penetrate and move through the network.
  • Sookkyung Lim (University of Cincinnati, United States)
    "Simulations of microswimmers propelled by multiple flagella"
  • Peritrichously flagellated bacteria swim in a fluid environment by rotating motors embedded in the cell membrane and consequently rotating multiple helical flagella. We present a novel mathematical model of a microswimmer that can freely run propelled by a flagellar bundle and tumble upon motor reversals. Our cell model is composed of a rod-shaped rigid cell body and multiple flagella randomly distributed over the cell body. These flagella can go through polymorphic transformations. We demonstrate that flagellar bundling is influenced by flagellar distribution and hence the number of flagella. Moreover, reorientation of cells is affected by the number of flagella, how many flagella change their polymorphisms within a cell, the tumble timing, different combinations of polymorphic sequences, and random motor reversals. Our mathematical method can be applied to numerous types of microorganisms and may help to understand their characteristic swimming mechanisms.

Multiscale simulations of biological fluid dynamics

Organized by: Matea Santiago (University of California, Merced, United States), Shilpa Khatri (University of California, Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-MMPB.

  • Lindsay Waldrop (Assistant professor, Chapman University, United States)
    "The effects of circulatory resistivity on performance of transport by systems with tubular, peristaltic hearts"
  • During individual development and evolutionary history, the chambered hearts of vertebrate animals begin as contracting, tubular hearts that pump peristaltically. This system has been extensively studied in computational models, but typically with a simple, racetrack circulatory system. The circulatory systems of animals are often resistive, including the closed systems of vertebrates consisting of capillary beds at its smallest diameters and the semi-closed systems of tunicates which have a connected bed of very small vessels in the pharyngeal basket. We used an immersed boundary model of peristaltic pumping attached to different circulatory systems that are more resistive: a branch that divides the top of the tube into two smaller tubes, a tube that widens and contain round, fixed obstacles, and a branched system with obstacles. We varied the Womersley number, compression ratio, and compress frequency of the pumping heart for each circulatory system and analyzed the system using uncertainty quantification with generalized polynomial chaos scheme and by calculating Sobol indices to quantify global sensitivity. We found that more resistive circulatory systems resulted in a 50% drop in average flow speed and a 33% drop in average volume flow rate within the circulatory systems of greater resistivity compared to the racetrack system. The pressure differential generated by the heart increased by 4.5 times in the system with the greatest resistivity. However, the cost of transport and work of pumping did not significantly increase, and the pattern of parameter sensitivity did not change with different circulatory systems. Results suggest that heart performance (cost of transport and flow) can be maximized by operating at lower pumping frequencies and higher Womersley numbers and that the relationship between performance and parameters do not change with the addition of resistive circulatory systems.
  • Laura Miller (Departments of Mathematics and Biomedical Engineering, University of Arizona, United States)
    "Slow and fast airflow past Saguaro and other cacti"
  • The cacti of the Sonoran desert in the southwest United States must deal with temperatures on the order of 120 degrees Farenheit and monsoons with wind speeds upwards of 100 miles per hour. It has been speculated that the ridges and spines of these cacti help dissipate heat in light wings, in addition to providing protection. It is also possible that the ridges and spines reduce drag acting on the cacti during strong winds. In this presentation, we use computational fluid dynamics to quantify the airflow around Saguaro and prickly pear cacti in both light and strong winds. The effects of the ridges and spines are systematically studied by smoothing the trunk and leaves. The resulting flow structures will be discussed in the context of drag reduction and heat dissipation.
  • Shilpa Kharti (Department of Applied Mathematics, University of California, Merced, United States)
    "Pulsing Soft Corals"
  • Soft corals of the family Xeniidae have a pulsing motion, a behavior not observed in many other sessile organisms. We are studying how this behavior may give these corals a competitive advantage, especially by allowing their symbiotic algae to photosynthesize to a greater extent. We will present computational simulations of the pulsations of the coral. Direct numerical simulations of the pulsing corals and the resulting fluid flow by solving the Navier-Stokes equations coupled with the immersed boundary method will be discussed. We will present results of how the fluid flow created by the corals is modified as we vary parameters of the fluid and the pulsing motion.
  • Matea Santiago (Department of Applied Mathematics, University of California, Merced, United States)
    "Soft Corals: Pulsing, Mixing, and Photosynthesis"
  • Some species of octocorals in the family Xeniidae actively pulse their tentacles. It is hypothesized that the pulsing mixes the fluid which enhances the photosynthesis of their symbiotic algae. We will present mathematical models and numerical methods for the tentacle motion and fluid flow coupled with the photosynthesis. The numerical simulations are analyzed to understand the benefit of pulsing for mixing and photosynthesis in different parameter regimes. The fluid flow is used to build Poincaré maps, a common tool in dynamical systems, used to understand fluid transport in periodic flows. This tool is coupled with the photosynthesis simulations to understand the enhancement of photosynthesis due to the flow.

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 MS03-NEUR.

  • Tom DeCoursey (Department of Physiology & Biophysics Rush University Medical Center, USA)
    "Proton Selective Conduction Through hHV1, the Human Voltage-gated Proton Channel"
  • Voltage-gated proton channels are unique ion channels, because the molecule is a free-standing voltage-sensing domain with an intrinsic proton conduction pathway. An exquisite proton selectivity mechanism excludes all other ions. How proton channels achieve this selectivity will be discussed. An essential element is an aspartic acid residue located within a narrow region at the center of the membrane. The aspartate is likely hydrogen-bonded to one of the three arginine residues. An approaching hydronium ion breaks the hydrogen bonds to allow proton conduction. When the channel is closed, a hydrophobic region prevents proton leakage through the pore.
  • Mingji Zhang (Mathematics, New Mexico Tech., USA)
    "Competition between Cations via Classical Poisson–Nernst–Planck Models with Small Permanent Charges"
  • We study a one-dimensional Poisson–Nernst–Planck system for ionic flow through a membrane channel. Nonzero but small permanent charge, the major structural quantity of an ion channel, is included in the model. Two cations with the same valences and one anion are included in the model, which provides more rich and complicated correlations or interactions between ions. The cross-section area of the channel is included in the system, providing important information on the geometry of the three-dimensional channel, which is critical for our analysis. Geometric singular perturbation analysis is employed to establish the existence and local uniqueness of solutions to the system for small permanent charges. Treating the permanent charge as a small parameter, through regular perturbation analysis, we are able to derive approximations of the individual fluxes explicitly, and this allows us to study the competition between two cations, which is related to the selectivity phenomena of ion channels. Numerical simulations are performed to provide a more intuitive illustration of our analytical results, and they are consistent.
  • Hamid Mofidi (Mathematics, U. Iowa, USA)
    "Effects of ion size on current and fluxes via hard-sphere PNP models"
  • This reports on studies of a one-dimensional version of a Poisson-Nernst-Planck-type system with a local hard-sphere potential model for ionic flow through a membrane channel with fixed boundary ion concentrations (charges) and electric potentials. The research is directed to set up a simple structure defined by permanent charges with two mobile ion species. A local hard-sphere potential that depends pointwise on ion concentrations is incorporated in the model to evaluate ion-size influences on the ionic flow. The model problem is treated as a boundary value problem of a singularly perturbed differential system, and the analysis is based on the geometric singular perturbation theory. We examine ion size effects on the flow rate of matter through a cross-section by treating the ion sizes as small parameters.
  • Weishi Liu (Mathematics, U. Kansas, USA)
    "Permanent charge effects on ionic flow"
  • Permanent charge is the most important structure of an ion channel.   In this talk, we will report our studies toward an understanding of permanent charges on ionic flow via a quasi-one-dimensional Poisson-Nernst-Planck (PNP) model.    The permanent charges are limited to a special case of piecewise constant with one non-zero portion. For ionic mixtures with one cation species and one anion species, a fairly rich behavior of permanent charge effects is revealed from rigorous analyses based on a geometric framework for PNP and from numerical simulations guided by the analytical results.   For ionic mixtures with two cation species and one anion species, richer behavior is expected and our preliminary analytical results identify a number of these, including some not-so-intuitive ones.

Recent development in mathematical oncology in Asia and Australia

Organized by: Yangjin Kim (Konkuk University, Korea, Republic of), Eunjung Kim (Korea Institute of Science and Technology, Korea)
Note: this minisymposia has multiple sessions. The second session is MS15-ONCO.

  • Shinji Nakaoka (Faculty of Advanced Life Science, Hokkaido University, Japan)
    "A computational pseudo-tracking method for cancer progression by microbiome data"
  • In this presentation, we would like to present recent research progress on applying a pseudotime reconstruction method to microbiome data. Pseudotime reconstruction methods have been originally developed in the field of single-cell RNA-seq analysis. Pseudotime reconstruction is also known as trajectory inference, which utilizes many samples to infer a developmental path such as cell differentiation, from a non-time series dataset. Although the validity of applying pseudotime reconstruction methods to microbiome data is not confirmed, the potential of its usefulness has been demonstrated on some datasets. In our ongoing work, we have been trying to apply a pseudotime reconstruction method to microbiome data obtained from patients who are diagnosed with some cancer. In this presentation, we will report a summary of computational results for the comparison of different pseudotime reconstruction methods to infer a possible trajectory of cancer progression.
  • Aurelio A. de Los Reyes V (University of the Philippines Diliman, Philippines)
    "Polytherapeutic strategies in cancer treatment"
  • This study aims to identify strategic infusion protocols of bortezomib, OV and natural killer (NK) cells to minimize cancer cells by utilizing optimal control theory. Three different therapeutic protocols will be presented: (i) periodic bortezomib and single administrations of both OV and NK cells therapy; (ii) alternating sequential combination therapy; and (iii) NK cell depletion and infusion therapy. The first treatment strategy shows that early OV administration followed by well-timed adjuvant NK cell infusion maximizes antitumour efficacy and the second scheme supports timely OV infusion. The last treatment protocol indicates that transient NK cell depletion followed by appropriate NK cell adjuvant therapy yields the maximal benefits. This study could provide potential combination therapies in cancer treatment.
  • Eunjung Kim (Korea Institute of Science and Technology, Korea)
    "Understanding the potential benefits of adaptive therapy for metastatic melanoma"
  • Understanding the potential benefits of adaptive therapy for metastatic melanoma Adaptive therapy is an evolution-based treatment approach that aims to maintain tumor volume by employing minimum effective drug doses or timed drug holidays. For successful adaptive therapy outcomes, it is critical to find the optimal timing of treatment switch points. Mathematical models are ideal tools to facilitate adaptive therapy dosing and switch time points. We developed two different mathematical models to examine interactions between drug-sensitive and resistant cells in a tumor. The first model assumes genetically fixed drug-sensitive and resistant populations that compete for limited resources. Resistant cell growth is inhibited by sensitive cells. The second model considers phenotypic switching between drug-sensitive and resistant cells. We calibrated each model to fit melanoma patient biomarker changes over time and predicted patient-specific adaptive therapy schedules. Overall, the models predict that adaptive therapy would have delayed time to progression by 6-25 months compared to continuous therapy with dose rates of 6%-74% relative to continuous therapy. We identified predictive factors driving the clinical time gained by adaptive therapy. The first model predicts 6-20 months gained from continuous therapy when the initial population of sensitive cells is large enough, and when the sensitive cells have a large competitive effect on resistant cells. The second model predicts 20-25 months gained from continuous therapy when the switching rate from resistant to sensitive cells is high and the growth rate of sensitive cells is low. This study highlights that there is a range of potential patient specific benefits of adaptive therapy, depending on the underlying mechanism of resistance, and identifies tumor specific parameters that modulate this benefit.
  • Masud MA (Korea Institute of Science and Technology, Korea)
    "The impact of spatial heterogeneity on treatment response"
  • A long-standing practice in cancer treatment is hit hard with maximum tolerated dose to eradicate the tumor. Such continuous therapy, however, selects for resistance cells leading to treatment failure. A different type of treatment strategy, adaptive therapy, has recently shown a degree of success in both preclinical xenograft experiments and clinical trials. Adaptive therapy aims to maintain tumor volume by exploiting the competition between drug-sensitive and resistance cells with minimum effective drug doses or timed drug holidays. To further understand the role of spatial competition between cancer cells, we develop a 2D on-lattice agent-based model. Specifically, we address the role of resistant cell distribution on the treatment outcomes. Our simulations show that the superiority of adaptive strategy over continuous therapy depends on the local competition shaped by the spatial distribution of resistant cells. Cancer cell migration and increased carrying capacity drive a faster tumor progression time under both types of treatment by reducing local competition. The intratumor competition can be modulated by fibroblasts, which produce microenvironmental factors that promote cancer cell growth. Our simulations show that the spatial architecture of fibroblasts modulates treatment outcomes. As proof of concept, we simulate adaptive therapy outcomes on multiple metastatic sites composed of different spatial distributions of fibroblasts and drug resistance cell populations. We predict that spatial distribution of resistance cells and fibroblasts metastatic lesions modulate the benefit of adaptive therapy.