Monday, June 14 at 11:30am (PDT)
Monday, June 14 at 07:30pm (BST)
Tuesday, June 15 03:30am (KST)


Mathematical modeling of emergent phenomena in cell colonies

Organized by: Shawn D. Ryan (Cleveland State University, United States), Mykhailo Potomkin (UC Riverside, United States), Jia Gou (UC Riverside, United States)
Note: this minisymposia has multiple sessions. The second session is MS01-CBBS.

  • Shawn D. Ryan (Dept. of Mathematics and Statistics, Cleveland State University, United States)
    "Role of hydrodynamic interactions in collective swimming of bacteria"
  • Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. Hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this talk, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a hybrid computational model that incorporates hydrodynamic interactions and adding components from a classical velocity jump model. It is shown that hydrodynamic interactions enhance the merging of the small aggregates into larger ones and lead to qualitatively different aggregate behavior than possible with pure chemotaxis models. Namely, differences in the shape, number, and dynamics of these emergent clusters.
  • Paul Kulesa (Stowers Institute for Medical Research, United States)
    "Coupling Invasion and Collective Migration of the Embryonic Neural Crest"
  • Several well-known models of collective cell migration, such as the Zebrafish lateral line or Drosophila border cells, feature tightly connected cells or cell-neighbor contacts through broad lamellipodial protrusions that together have led to cell adhesion and contact-inhibition of locomotion models. In contrast, neural crest cells travel in loosely connected, discrete streams and interact with each other through thin filopodial extensions. This has led to natural questions as to how neural crest cells invade through extracellular matrix and mesoderm, and communicate with each other over long distances to move collectively. Here, we set out to understand the molecular signals that drive collective neural crest cell migration using a combination of experimental perturbations, gene profiling, time-lapse imaging and computational modeling. We test the central hypothesis that lead neural crest cells express a distinct set of genes that are critical to invasion and the source of signals that communicate information to promote collective migration. By using a novel label free, unsorted single cell RNA sequencing method we derive the transcriptional states of migrating neural crest cells and the cellular landscape of the chick head, neck, and cardiac region. We identify a set of novel cell invasion genes common to the first four branchial arch streams and use time-lapse imaging and molecular perturbations to test their functional relevance. Cell behavioral and stream changes are compared to agent-based model simulations that incorporate the neural crest migratory domain and experimentally-derived measurements of tissue growth and chemotaxis. We conclude that local cell invasion signals and long-range communication between follower cells play a critical role in collective neural crest cell migration and may provide key insights to stem-cell based strategies that aim to repair birth defects to the face and neck and treatment of aggressive cancers.
  • Brian Camley (Johns Hopkins University, United States)
    "Collective cell migration on patterns with topological defects"
  • Sheets of eukaryotic cells migrate cooperatively in order to heal wounds or invade new locations - and these cell monolayers can be guided by ridges and patterns on their substrate. How do cells in a monolayer respond when given conflicting signals from their neighbors and the surface they are crawling on? We are motivated by recent experiments showing that fibroblasts crawling on target-shaped patterns can align to the pattern, but show increased cell density and decreased cell anisotropy near the center of the pattern [Endresen et al. Soft Matter 2021]. These induced topological defects within the liquid crystalline order of these cells are known to be important in both morphogenesis and cell death. We model our cells as self-propelled deformable ellipses that interact via a modified Gay-Berne potential. Consistent with experiment, cells are denser and more isotropic toward the center of the defect. This density change is driven by the combination of collective cell flow, the cell anisotropy, and the ability of the cells to deform their shapes. We also discuss how these factors alter the extent of coherent rotational motion in these systems.
  • Wouter-Jan Rappel (UC San Diego, United States)
    "Modeling the collective motion of amoebae"
  • Collective rotational motion is observed in a variety of experimental settings, including dense extracellular matrices and patterned substrates. Here we focus on the rotational vortex-like state observed when the social amoeboid Dictyostelium cells aggregate following starvation. We employ traction force microscopy to determine the force patterns during this aggregation process. We then develop a mathematical model that can provide insights into the mechanisms of this collective motion.

Multiscale modeling in tissue growth and morphogenesis to understand biological data

Organized by: Weitao Chen (University of California, Riverside, United States), Qixuan Wang (University of California, Riverside, United States)

  • Dagmar Iber (ETH Zurich, Switzerland)
    "From Networks to Function – Computational Models of Morphogenesis"
  • One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks and how do they evolve? Morphogenesis provides an excellent model system to study how simple molecular networks robustly control complex pattern forming processes and how mechanical constraints shape organs. In my talk, I will focus on self-organizing principles in organogenesis, with a particular focus on lung and kidney development, as well as on epithelial organisation.
  • Zhan Chen (Georgia Southern University, United States)
    "Anterior-Posterior patterning and scaling of Drosophila wing disc: Mathematical modeling"
  • Wing imaginal disc of Drosophila is one of the commonly used model systems for the studies of patterning, growth, and scaling. The development of the wing disc involves many interacting components as well as a variety of compound processes whose underlying mechanisms are still under investigation. For instance, it remains unclear about how to form compound experimentally-measured patterns of Decapentaplegic (Dpp) type-I receptor Thickveins (Tkv), as well as phosphorylated Mothers Against Dpp (pMad) which is the indicator of Dpp signaling activities. In this work, we proposed mathematical models that integrate established experimental data to investigate the formation of pMad and Tkv gradients. Our model is validated by the accurate reproduction of complex asymmetric profiles of Tkv and pMad in both anterior and posterior compartments of the wing disc. Moreover, it provides a comprehensive view of the formation of Tkv gradients in wing discs. We found that engrailed (En), Hedgehog (Hh) signaling and Dpp signaling cooperate to establish the asymmetric gradients of Tkv and pMad in the wing disc. Finally, our model suggests a Brinker-mediated mechanism of Dpp-dependent repression of Tkv.
  • John Dallon (Brigham Young University, United States)
    "Modeling collagen tissue: How structure affects mechanical properties"
  • The fibrous protein collagen is the main protein in mammalian connective tissue. Although the properties of a collagen filament are well understood, how they come together to form tissues with vastly different properties is not. In this talk, with the aid of a mathematical model, we will explore properties of a fibrous tissue and determine their impact on the elasticity of the tissue.

Stochastic models of cancer: An update of theory and data

Organized by: Marek Kimmel (Rice University, United States), Simon Tavare (Columbia University, United States)
Note: this minisymposia has multiple sessions. The second session is MS01-DDMB.

  • Katharina Jahn (Computational Biology Group, ETH Zurich, Zurich, Switzerland, Switzerland)
    "Dissecting Clonal Diversity Through High-Throughput Single-Cell Genomics"
  • Clonal heterogeneity allows tumours to adapt and survive under the selective pressure of treatment, leading to clinical resistance and relapse. An accurate dissection of the clonal architecture and the underlying mutational history is therefore of clinical importance and may help to design more effective treatment plans. Present studies on clonal diversity are primarily based on sequencing data obtained from bulk tumour tissue which systematically underestimate a tumour's mutational heterogeneity. However, through recent technological advances, high-throughput single-cell genomics has become a feasible alternative that allows to study clonal diversity at an unprecedented resolution. In this talk, I will present a Bayesian inference scheme for tumour mutation histories based on single-cell sequencing data and the insights we obtained from analysing longitudinal bone marrow samples of 123 AML patients. Using a microfluidics-based single-cell DNA sequencing platform, we genotyped over 700,000 cells for a panel of genes recurrently mutated in AML. We observed patterns of mutual exclusivity, mutational co-occurrence, as well as instances of convergent evolution. Moreover, the longitudinal nature of the data revealed patterns of clonal dynamics in response to targeted AML therapy which correlated with clinical resistance and relapse.
  • Ximo Pechuan Jorge (Institute of Cancer Research, London, UK, UK)
    "A Simple Computational Model to Infer Selective Coefficients in Barcode Evolution Experiments"
  • The advent of single cell sequencing technologies has propelled the usage of lineage barcoding to characterize the dynamics of heterogeneous cell populations. Following the population dynamics of tumor cells is of paramount importance to determine the details of their evolutionary process which, in turn, can influence therapeutic outcome. To characterize the evolutionary dynamics of barcoded organoids during the course of two years of serial passage extit{in vitro} after a genetic perturbation, we constructed a simple stochastic model accounting for drift and competition between lineages. We used sequential Monte Carlo to fit the model to the experimental data obtaining initial growth rate estimates for each lineage. Some of the samples exhibited evidence of mutation acquisition and thus required a model accounting for mutation accumulation. Our model explains the patterns observe in the data and shows the value of constructing simple interpretable models in the initial stages of data analysis.
  • Luis Zapata Ortiz (Institute of Cancer Research, London, UK, UK)
    "Evolutionary dynamics of cancer immunoediting predicts response to immunotherapy."
  • Cancer Immunoediting is an evolutionary force that shapes the genome of healthy and malignant cells in the human body. However, quantifying immunogenicity in the cancer genome and how the tumour-immune coevolutionary dynamics impact patient outcomes remain unexplored. Here, we developed a stochastic branching process coupled with an agent-based model to simulate the accumulation of mutations during immunoediting. We show how a metric of selection, the ratio of nonsynonymous to synonymous mutations in the immunopeptidome (immune dN/dS) quantifies tumor immunogenicity and differentiates between outcomes of immunoediting. We provide a theoretical explanation for the lack of signals of immune selection reported previously and analysed 8,543 primary tumors from TCGA and 376 metastatic tumors from immunotherapy trials. We validated immune dN/dS as a measure of CD8-T cell mediated selection in tumours that have not undergone immune escape. Moreover, In a cohort of 368 metastatic patients treated with checkpoint inhibitors, we observed that lesions of non-responders had strong immune selection (dN/dS < 1, negative), whereas responders did not show immune selection (dN/dS ~ 1, neutral), and instead harboured a higher proportion of genetic escape mechanisms. Our findings highlight the challenges of using dN/dS to estimate selection, suggest that the extent of immunogenicity can be read from the tumor genome, and that the evolutionary consequences of immunoediting determine immunotherapy efficacy.
  • Jan Poleszczuk (Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland, Poland)
    "Microsimulation-based optimization of colorectal cancer screening strategies"
  • Colorectal cancer (CRC) is a substantial public hearth burden and is in the top three cancers with respect to incidence and mortality in US and many other industrialized countries. CRC screening tests based on the endoscopic visualization of the colon have proven effective in reducing mortality, both by allowing CRC at earlier stages and by CRC prevention since adenomatous precursors of CRC can be removed during endoscopy. However, the starting age and time intervals of screening colonoscopies for optimal protection against CRC are unknown. We used microsimulation to systematically optimize screening colonoscopy schedules. We advanced our established open-source microsimulation model CMOST to simulate the effects of colonoscopy screening on the natural history and medical costs of CRC. In CMOST, carcinoma develops via early and advanced adenoma precursors. CMOST accounts for the gender- and age-dependent risks for adenoma development, the presence of multiple adenomas, as well as their locations within the colon. CMOST microsimulation tracks the history of a general population from birth until death for a maximum age of 100 years. Adenoma initiation, progression to advanced adenoma and cancer, cancer progression, screening and surveillance are all modeled in time increments of 3 months and are stochastically driven. We used CMOST to optimize colonoscopy schedules with one, two, three and four screening colonoscopies between 20 and 90 years of age. For each scenario, we calculated life years gained, incidence and mortality reduction, and cost-effectiveness. A single screening colonoscopy is most effective in reducing life years lost from CRC when performed at 55 years of age. Two, three and four screening colonoscopy schedules are optimal at earlier ages. For maximum reduction of incidence and mortality, screening colonoscopies need to be scheduled later in life compared to optimal age for life years lost. The optima are influenced by adenoma detection rates, individual CRC risk, and adherence to screening, with lower values for these parameters favoring a later starting age of screening. Incremental cost-effectiveness remained below 100’000 discounted US dollars per discounted life year gained except for an optimal four-colonoscopy schedule, which was not cost-effective. In a personalized approach, optimal screening would start earlier for high-risk patients and later for low-risk individuals. Our results support screening recommendations involving an early starting age of 45 years. Our optimized screening strategies are cost-effective and save more life years than currently

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 MS03-ECOP.

  • Chelsea Cook (Marquette University, Biological Sciences, Milwaukee Wisconsin, United States)
    "Individual Learning Phenotypes Drive Collective Foraging Behavior in Honey Bees"
  • Variation in cognition can influence how individuals respond to and communicate about their environment, which may scale to shape how a collective solves a cognitive task. However, few empirical examples of variation in collective cognition emerges from variation in individual cognition exist. Here, I show that interactions among individuals that differ in the performance of a cognitive task drives collective foraging behavior in honey bee colonies by utilizing a naturally variable and heritable learning behavior called latent inhibition (LI). I artificially selected two distinct phenotypes: high LI bees that are better at ignoring previously unrewarding familiar stimuli, and low LI bees that can learn previously unrewarding and novel stimuli equally well. I then provided colonies composed of these distinct phenotypes with a choice between a familiar feeder or a novel feeder. Colonies of high LI individuals preferred to visit familiar food locations, while low LI colonies visited novel and familiar food locations equally. However, in colonies of mixed learning phenotypes, the low LI bees showed a preference to visiting familiar feeders, which contrasts with their behavior when in a uniform low LI group. I show that the shift in feeder preference of low LI bees is driven by foragers of the high LI phenotype dancing more intensely and attracting more followers. I also present potential mechanisms that may be mediating the individual variation. These results reveal that cognitive abilities of individuals and their interactions drive emergent collective outcomes in social insects.
  • Hermann Eberl ( University of Guelph, Canada)
    "Between hive transmission of nosemosis by drifitng"
  • The vast majority of mathematical models of honeybee diseases is for single colonies that have no interaction with other colonies. This misses an important aspect of the ecoepidemiology in an apiary. For an earlier model of nosemosis with direct and indirect transmission routes we formulate a metapopulation model that accounts for the transmission of the disease between colonies by drifting. Since even the underlying single hive model is too complex for a thorough rigorous analysis, we explore the model in extensive numerical simulations. Our results suggest that for the model at hand the spread of the disease in the apiary is primarily controlled by seasonal effects, whereas the actual drifting rate has little quantitative effect.
  • Natalie J. Lemanski (Rutgers University New Brunswick (current), University of California Los Angeles (where work was performed), United States)
    "Individual learning affects the accuracy of collective decisions for honey bee colonies foraging on different quality resources"
  • To survive, animals need to find resources and make decisions about which resource patches to invest time in exploiting. Balancing these tasks can be a complex decision-making challenge, particularly when patches are rapidly changing, heterogeneously distributed, and variable in quality. Social insects, such as honeybees, navigate this challenge in the absence of centralized control by allocating different individuals to exploration or exploitation based on differences in individual behavior. To investigate how differences in individual learning affect a colony’s collective ability to locate and choose among different quality food resources, we develop an agent-based model and test its predictions empirically using two genetic lines of honey bees (Apis mellifera), selected for differences in their learning behavior. We show that colonies containing individuals that are better at learning to ignore unrewarding stimuli are worse at collectively choosing the highest quality resource. This work highlights how differences in individual behavior may have unexpected consequences for the emergence of collective behavior.
  • Gloria DeGrandi-Hoffman (USDA-ARS, United States)
    "Simulating how combinations of stress factors can affect honey bee colony growth and survival"
  • Biotic and abiotic factors can exert stress on honey bee colonies and limit their growth ultimately causing colony death. A colony population dynamics model was used to predict effects on colony growth of pesticide stress exerted during different times of year. Poor queen quality and infestation by parasitic Varroa mites were added into the simulations to determine the impact of multiple stress factors on colony growth and survival. The model predicts that colony survival after pesticide exposure depends on the time of year when exposure occurred. Poor queen quality makes colonies more vulnerable to loss from pesticide exposure as do high infestations of Varroa mites. Predictions highlight the difficulties is assigning causation of colony loss to a single factor.

Highlights of the Special Issue of BMB on Mathematical Biology Education

Organized by: John R Jungck (University of Delaware, USA), Raina Robeva (Randolph Macon College, USA), Louis Gross (University of Tennessee, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-EDUC.

  • Shernita Lee (Virginia Tech, USA)
    "Mathematical Biology: Expand, Expose, and Educate!"
  • Mathematical biology has made significant contributions and advancements in the biological sciences. Recruitment efforts focus on encouraging students, especially those who are underrepresented and underserved, to pursue the field of mathematical biology, regardless of their undergraduate institution type, and raise awareness about the countless professional and academic possibilities provided by this specialized training. This article examines the need to expand, expose, and educate others about mathematical biology. To support field expansion, we give several recommendations of ways to integrate mathematics applied curricula to attract broader student interest.  With this exposure-- whether it is led by an individual, a department, a university, or researchers in mathematical biology-- each can help to promote a base knowledge and appreciation of the field. In order to encourage the next generation of researchers to consider mathematical biology, we highlight current interdisciplinary programs share popular mathematical tools, and present some thoughts  on ways to support a thriving and inclusive mathematical biology community for years to come.
  • Luis A. Melara Jr. (Shippensburg University, USA)
    "The Case for Undergraduate Research Journals"
  • We address the important role of undergraduate research journals in the undergraduate research experience. Peer review by professional researchers is identified as the most essential ingredient in establishing the relevance of these journals as venues for research dissemination. We will introduce you to examples of three such journals—Spora, SIAM Undergraduate Research Online, and the American Journal of Undergraduate Research—with demonstrated success in supporting the undergraduate research experience.
  • Meredith Greer (Bates College, USA)
    "Paying Our Dues: The Role of Professional Societies in the Evolution of Mathematical Biology Education"
  • Mathematical biology education provides key foundational underpinnings for the scholarly work of mathematical biology. Professional societies support this work via funding, public speaking opportunities, web presence, publishing, workshops, prizes, opportunities to discuss curriculum design, and support of mentorship and other means of sustained communication among communities of scholars.  Such programs have been critical to the broad expansion of the range and visibility of research and educational activities in mathematical biology. We review these efforts, past and present, across multiple societies -- The Society for Mathematical Biology (SMB), the Symposium on Biomathematics and Ecology Education and Research (BEER), the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM). We then proceed to suggest ways that professional societies can serve as advocates and community builders for mathematical biologists at all levels, noting that education continues throughout a career and also emphasizing the value of educating new generations of students.
  • Kristin Jenkins (University of Texas at Austin, USA)
    "Building community-based approaches to systemic reform in mathematical biology education"
  • Starting in the early 2000’s, several reports were released recognizing the convergence of mathematics, biology and computer science, and calling for a rethinking of how undergraduates are prepared for careers in research and the science and technology workforce. This call for change requires careful consideration of the mathematical biology education system to identify key components and leverage points for change. This paper demonstrates the wide range of resources and approaches available to the mathematical biology education community to create systemic change by highlighting the efforts of four community-based education reform organizations. A closer look at these organizations provides an opportunity to examine how to leverage components of the education system including faculty, academic institutions, students, access to resources, and the power of community.

Non-equilibrium Thermodynamics in Biology: from Chemical Reaction Networks to Natural Selection

Organized by: John Baez (University of California, Riverside, USA), William Cannon (Pacific Northwest National Laboratory, USA), Larry Li (University of California, Riverside, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-EVOP.

  • Matteo Polettini (University of Luxembourg, Luxembourg)
    "Deficiency of chemical reaction networks and thermodynamics"
  • Deficiency is a topological property of a Chemical Reaction Network linked to important dynamical features, in particular of deterministic fixed points and of stochastic stationary states. Here we link it to thermodynamics: in particular we discuss the validity of a strong vs. weak zeroth law, the existence of time-reversed mass-action kinetics, and the possibility to formulate marginal fluctuation relations. Finally we illustrate some subtleties of the Python module we created for MCMC stochastic simulation of CRNs, soon to be made public.
  • Ken Dill (Stony Brook University, USA)
    "The principle of maximum caliber of nonequilibria"
  • Maximum Caliber is a principle for inferring pathways and rate distributions of kinetic processes. The structure and foundations of MaxCal are much like those of Maximum Entropy for static distributions. We have explored how MaxCal may serve as a general variational principle for nonequilibrium statistical physics - giving well-known results, such as the Green-Kubo relations, Onsager's reciprocal relations and Prigogine's Minimum Entropy Production principle near equilibrium, but is also applicable far from equilibrium. I will also discuss some applications, such as finding reaction coordinates in molecular simulations non-linear dynamics in gene circuits, power-law-tail distributions in 'social-physics' networks, and others.
  • Joseph Vallino (Marine Biological Laboratory, Woods Hole, USA)
    "Using the maximum entropy production principle to understand and predict microbial biogeochemistry"
  • Natural microbial communities contain billions of individuals per liter and can exceed a trillion cells per liter in sediments, as well as harbor thousands of species in the same volume. The high species diversity contributes to extensive metabolic functional capabilities to extract chemical energy from the environment, such as methanogenesis, sulfate reduction, anaerobic photosynthesis, chemoautotrophy, and many others, most of which are only expressed by bacteria and archaea. Reductionist modeling of natural communities is problematic, as we lack knowledge on growth kinetics for most organisms and have even less understanding on the mechanisms governing predation, viral lysis, and predator avoidance in these systems. As a result, existing models that describe microbial communities contain dozens to hundreds of parameters, and state variables are extensively aggregated. Overall, the models are little more than non-linear parameter fitting exercises that have limited, to no, extrapolation potential, as there are few principles governing organization and function of complex self-assembling systems. Over the last decade, we have been developing a systems approach that models microbial communities as a distributed metabolic network that focuses on metabolic function rather than describing individuals or species. We use an optimization approach to determine which metabolic functions in the network should be up regulated versus those that should be down regulated based on the non-equilibrium thermodynamics principle of maximum entropy production (MEP). Derived from statistical mechanics, MEP proposes that steady state systems will likely organize to maximize free energy dissipation rate. We have extended this conjecture to apply to non-steady state systems and have proposed that living systems maximize entropy production integrated over time and space, while non-living systems maximize instantaneous entropy production. Our presentation will provide a brief overview of the theory and approach, as well as present several examples of applying MEP to describe the biogeochemistry of microbial systems in laboratory experiments and natural ecosystems.
  • Gheorghe Craciun (University of Wisconsin-Madison, USA)
    "Persistence, permanence, and global stability in reaction network models: some results inspired by thermodynamic principles"
  • The standard mathematical model for the dynamics of concentrations in biochemical networks is called mass-action kinetics. We describe mass-action kinetics and discuss the connection between special classes of mass-action systems (such as detailed balanced and complex balanced systems) and the Boltzmann equation. We also discuss the connection between the 'global attractor conjecture' for complex balanced mass-action systems and Boltzmann's H-theorem. We also describe some implications for biochemical mechanisms that implement noise filtering and cellular homeostasis.

Mathematical tools for understanding viral infections within-host and between-host

Organized by: Hana Dobrovolny (Texas Christian University, United States), Gilberto Gonzalez-Parra (New Mexico Tech, United States)
Note: this minisymposia has multiple sessions. The second session is MS01-IMMU.

  • Benito Chen-Charpentier (University of Texas at Arlington, United States)
    "Deterministic and stochastic modeling of plant virus propagation with delay"
  • Plant diseases caused by a virus are mostly transmitted by a vector that bites an infected plant and bites a susceptible one. There is a delay between the time a plant gets bitten by an infected vector and the time it is infected. In this paper we consider two simple models of plant virus propagation and study different ways in which delays can be incorporated including the addition of an exposed class for the plants. Simulations are done and comparisons with the results for the models without delays are presented.
  • Kenichi Okamoto (University of St. Thomas, United States)
    "Opposing within-host and between-host selection pressures for virulence: Implications for disease surveillance"
  • For many infectious diseases, including SARS-Coronavirus-2 (SARS-CoV-2), disease surveillance followed by isolating, contact-tracing and quarantining infectious individuals is critical for controlling outbreaks. These interventions often begin by identifying symptomatic individuals. However, by actively removing pathogen strains likely to be symptomatic, such interventions may inadvertently select for strains less likely to result in symptomatic infections. Additionally, the pathogen’s fitness landscape is structured around a heterogeneous host pool. In particular, uneven surveillance efforts and distinct transmission risks across host classes can drastically alter selection pressures. Here we explore this interplay between evolution caused by disease control efforts, on the one hand, and host heterogeneity in the efficacy of public health interventions on the other, on whether less symptomatic, but widespread, pathogens evolving. Using an evolutionary epidemiology model parameterized for coronaviruses, we show that symptoms-driven disease control ultimately shifts the pathogen’s fitness landscape to select for asymptomatic strains. We find such outcomes result when isolation and quarantine efforts are intense, but insufficient for suppression. Moreover, when host removal depends on the prevalence of symptomatic infections, intense isolation efforts can select for the emergence and extensive spread of more asymptomatic strains. The severity of selection pressure on pathogens caused by these interventions likely lies somewhere between the extremes of no intervention and thoroughly successful eradication. Identifying the levels of public health responses that facilitate selection for asymptomatic pathogen strains is therefore critical for calibrating disease suppression and surveillance efforts and for sustainably managing emerging infectious diseases.
  • Baylor Fain (Texas Christian University, United States)
    "Validation of a GPU-based ABM for rapid simulation of viral infections"
  • We developed a new ABM/PDEM hybrid model for simulating virus spreading in a monolayer of a million cells. In this work, aspects of the simulations, such as the time step, are checked to verify the model is producing accurate data. Physical characteristics of the viral spread, such as the growth rate, decay rate, peak amount of virus, and time of peak virus, are compared with real data ranges for Influenza virus. Values for the parameters: viral production rate, rate of infection, amount of time in the eclipse phase, and the amount of time in the infectious phase, are found for H1N1pdm09-WT from fitting the model to experimental data by minimizing the SSR (Sum of Square Residuals).
  • Hayriye Gulbudak (University of Louisiana at Lafayette, United States)
    "A Delay Model for Persistent Viral Infections in Replicating Cells"
  • Persistently infecting viruses remain within infected cells for a prolonged period of time without killing the cells and can reproduce via budding virus particles or passing on to daughter cells after division. The ability for populations of infected cells to be long-lived and replicate viral progeny through cell division may be critical for virus survival in examples such as HIV latent reservoirs, tumor oncolytic virotherapy, and non-virulent phages in microbial hosts. We consider a model for persistent viral infection within a replicating cell population with time delay modelling the length of time in the eclipse stage prior to infected cell replicative form. We obtain reproduction numbers that provide criteria for the existence and stability of the equilibria of the system. Moreover, we characterize bifurcations in our model, including transcritical (backward and forward), saddle-node, homoclinic, and Hopf bifurcations, and provide evidence of a Bogdanov-Takens bifurcation. We investigate the possibility of long-term survival of the infection (represented by chronically infected cells and free virus) in the cell population by using the mathematical concept of robust uniform persistence. Using numerical continuation software with parameter values estimated from phage-microbe systems, we obtain two parameter bifurcation diagrams that divide parameter space into regions with different dynamical outcomes. We thus investigate how varying different parameters, including how the time spent in the eclipse phase, can influence whether the virus survives.

From Primate to Vectors to Humans: Understanding the underlying mechanisms of disease transmission and control

Organized by: Folashade Agusto (University of Kansas, United States), Majid Bani Yaghoub (University of Missouri Kansas City, United States)
Note: this minisymposia has multiple sessions. The second session is MS01-MEPI.

  • Wandi Ding (Middle Tennessee State University, United States)
    "Mathematical modeling and optimal control for malaria transmission"
  • We consider a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for sterile mosquitoes. We derive the basic reproduction number of infections. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived and the characterization of the optimal controls is established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. A combination of both strategies leads to a more rapid elimination of the wild mosquito population that can suppress Malaria transmission. Numerical simulations are provided to illustrate the results.
  • Eric Numfor (Augusta University, United States)
    "A malaria-HIV/AIDS co-infection model with treatment and insecticide-treated bednets"
  • Malaria and HIV, two of the world’s most deadly diseases, are endemic in several parts of the world, with overlapping distribution. The concurrent use of multiple strategies has been recommended as an effective strategy to reduce malaria and HIV prevalence. In this talk, we present a malaria-HIV/AIDS co-infection model with control in which malaria treatment, insecticide-treated bednets and HIV/AIDS treatment are incorporated. The local asymptotic stability of the disease-free equilibrium (DFE) of the malaria-only sub- model and co-infection model, and the global stability of the DFE of the HIV/AIDS-only sub-model are studied. The existence of a backward bifurcation and endemic boundary equilibria are established. Key parameters in determining the number of new cases of malaria-HIV/AIDS co-infection are identified. The impact of malaria treatment, insecticide-treated bednets and HIV/AIDS treatment are assessed by formulating and analyzing an optimal control problem. Our results present the importance of HIV/AIDS treatment in mitigating malaria and HIV prevalence.
  • Adeshina I. Adekunle (James Cook University, Australia)
    "Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh"
  • Tuberculosis (TB) is the seventh leading cause of morbidity and mortality in Bangladesh. Although the National TB control program (NTP) of Bangladesh is implementing its nationwide TB control strategies, more specific and effective single or combination interventions are needed to control drug-susceptible (DS) and multi-drug resistant (MDR) TB. In this study, we extended our two-strain mathematical model with amplification to account for the latent stage. The mathematical epidemiological properties of this extension follow from our previous analysis. Hence, we fit different variants of the model to the Bangladesh TB data to understand the transmission dynamics of DS and MDR TB. We further performed sensitivity analysis and evaluated the cost-effectiveness of varying combinations of four basic control strategies including distancing, latent case finding, case holding and active case finding, all within the optimal control framework. From our fitting, the model with different transmission rates between DS and MDR TB best captured the Bangladesh TB reported case counts. The estimated basic reproduction number for DS TB was 1.14 and for MDR TB was 0.54, with an amplification rate of 0.011 per year. The sensitivity analysis also indicated that the transmission rates for both DS and MDR TB had the largest influence on prevalence. To reduce the burden of TB (both DS and MDR), our finding suggested that a quadruple control strategy that combines distancing control, latent case finding, case holding and active case finding is the most cost-effective. Alternative strategies can be adopted to curb TB depending on availability of resources and policy makers’ decisions.
  • Hem Raj Joshi (Xavier University, United States)
    "Modeling transmission dynamics of rabies in Nepal"
  • We developed a mathematical model to describe the transmission dynamics of rabies in Nepal. In particular, this is an indirect interspecies transmission from jackals to humans through dogs, which is relevant to the context of Nepal. This indirect interspecies transmission dynamic is one of the novel features of our model. Our model utilizes annual dog-bite data collected from Nepal for a decade, allowing us to reasonably estimate parameters related to rabies transmission in Nepal. We calculated the basic reproduction number ($R_0$) as well as the intraspecies basic reproduction numbers for dogs ($R_0^D$) and jackals ($R_0^J$ ) in Nepal. We also applied the optimal control theory to identify an optimal control strategy for mitigating the rabies burden in Nepal. Our potential control strategies are human vaccination, dog vaccination, dog culling, dog sterilization, and jackal vaccination. We concluded that a combination of dog vaccination and dog culling is the most effective strategy to control rabies in Nepal. These results may be useful for designing effective prevention and control strategies for mitigating the rabies burden in Nepal and other parts of the world.

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 MS03-MFBM.

  • Gleb Pogudin (LIX, CNRS, Ecole Polytechnique, Institute Polytechnique de Paris, France)
    "Attractor stucture of Boolean networks of small canalizing depth"
  • Canalization property often occurs in Boolean networks used in systems biology literature. I will describe our computational experiments and mathematical results that indicate that the attractor structure of a random Boolean network with this property differs significantly from the attractor structure of a completely random Boolean network. In particular, there are usually less attractors and they are smaller. These properties turn out to be relevant to many biological applications. I will also discuss how further increase of canalization of a network impacts the attractor structure.
  • S. S. Ravi (Biocomplexity Institute & Initiative, University of Virginia, and Department of Computer Science, University at Albany, United States)
    "Efficient Algorithms for Boolean Nested Canalyzing Functions"
  • We study several computational problems for Boolean nested canalyzing functions (NCFs). We show that unlike general Boolean functions, there are simple algorithms for many computational problems for NCFs (e.g., equivalence & implication of NCFs, computing the probability of satisfying a given NCF, computing the sensitivity and expected sensitivity of a given NCF). The running times of these algorithms are O(n) or O(n log n), where n is the number of variables in the input function. We also present a linear time algorithm that converts any given NCF into an equivalent weighted threshold function, thus showing that weighted threshold functions generalize the class of NCFs.
  • Daniel Rosenkrantz (Biocomplexity Institute & Initiative, University of Virginia, and Department of Computer Science, University at Albany, United States)
    "Testing Phase Space Properties of Synchronous Dynamical Systems with Nested Canalyzing Local Functions: Complexity Results and Algorithms"
  • Discrete graphical dynamical systems serve as effective formal models in many contexts, including simulations of agent-based models, propagation of contagions in social networks and study of bio- logical phenomena. Motivated by the biological applications of nested canalyzing functions (NCFs), we study a variety of analysis problems for synchronous graphical dynamical systems (SyDSs) over the Boolean domain, where each local function is an NCF. Each analysis problem involves testing whether the phase space of a given SyDS satisfies a certain property. Problems considered include reachability, predecessor existence, fixed point existence and garden of Eden existence. We present intractability results for some properties as well as efficient algorithms for others. In several cases, our results clearly delineate intractable and efficiently solvable versions of problems.
  • Matthew Wheeler (Department of Medicine, University of Florida, United States)
    "Reducibility of Boolean Networks: Toward a Theory of Modularity"
  • Modularity is believed to be a fundamental characteristic of biological systems. As such, any model built to represent such a system should also exhibit some form of modularity. One common and powerful way of modeling biological systems is through Boolean networks. In this direction, we introduce the concept of Boolean network extensions. We will discuss what these extensions are and how these extensions relate to the concept of modularity.

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 MS03-MMPB.

  • Calina Copos (University of North Carolina, Chapel Hill, USA)
    "Chimenying movement from the perspective of a cell"
  • Cell migration is critical for many important physiological processes, such as embryogenesis, tissue repair, and cancer metastasis. In experiments, some cells have been shown to migrate using round membrane protrusions called blebs while confined between two surfaces, such as a gel and a glass coverslip. These cells do not need to adhere to the channel walls in order to migrate under confinement, yet it is unclear how traction forces are coordinated in space and time to generate motion. A dynamic 2D computational model of a blebbing cell in a narrow channel is presented. The model includes the mechanics of the cortical actin and cell membrane, intracellular fluid flow, and evolution equations for the cortical actin for bleb formation and retraction. Several channel models are considered, including two rigid walls and the combination of a rigid and elastic wall. Model outputs include cell velocity, intracellular pressure, and traction forces on the channel walls. The contribution of confinement pressure to total intracellular pressure is quantified, and model simulations show adhesion to the substrate is necessary for migration when the channel is modeled by two rigid walls.
  • Jorn Dunkel (Massachusetts Institute of Technology, USA)
    "Altruistic fluid transport during fly egg development"
  • Fluid flow plays an important role during egg cell development. From insects to mice, oocytes mature by acquiring cytoplasm from sister germ cells, yet the biological and physical mechanisms underlying this transport process remain poorly understood. To study the dynamics of “nurse cell dumping” in fruit flies, we combined direct imaging with flow-network modeling and found that the intercellular pattern and time scale of transport are in accordance with a fundamental hydraulic pressure law. Changes in actomyosin contractility are observed only in the second phase of nurse cell dumping as surface waves that drive transport to completion. These results show that tandem physical and biological mechanisms are required for complete and directional cytoplasmic transport into the egg cell. (Imran Alsous et al., PNAS 118: e2019749118, 2021)
  • Sarah Olson (Worcester Polytechnic Institute, USA)
    "Centrosome movement during mitosis"
  • Proper formation and maintenance of the mitotic spindle is required for faithful cell division. While much work has been done to understand the roles of the key molecular components of the mitotic spindle, identifying the consequences of force perturbations in the spindle remains a challenge. We develop a computational framework to account for centrosome movement within the cytoplasm and utilize live cell imaging to inform and validate the model. Specifically, we investigate the role of cortical dynein on spindle pole length fluctuations.
  • Arezoo Ardekani (Purdue University, USA)
    "Swimming near a surfactant laden interface"
  • The interaction of motile microorganisms and surrounding fluids is of importance in a variety of biological and environmental phenomena including the development of biofilms, colonization of microbes in human and animal bodies, formation of marine algal blooms and bacterial bioremediation. Many microorganisms, especially bacteria, actively search for nutrients via a process called chemotaxis. The physical constraints posed by hydrodynamics in the locomotion of microorganisms can combine with their chemotactic ability to significantly affect functions like colonization of nutrient sources. Motivated by bacterial bio-remediation of hydrocarbons released during oil spills, I will discuss the role of hydrodynamics toward dictating distribution of microbes around interfaces and drops in the presence and absence of surfactant. We find that the presence of the surfactant significantly alters the dynamics of the swimmers specially by affecting their reorientation.

How neuronal network circuit attributes influence neural activity, coding, and learning

Organized by: Cheng Ly (Virginia Commonwealth University, United States), Pamela Pyzza (Kenyon College, United States)

  • Paulina Volosov (Hillsdale College, United States)
    "How to Use Minimal Information to Reconstruct Neuronal Networks"
  • We investigate the relationship between functional and architectural connectivity in the cerebral cortex by means of network reconstruction via time-delayed spike-train correlation. We begin by reconstructing the entire network, and then we sample the matrix randomly and use the tool of matrix completion to fill-in the rest of the network. To be more experimentally valid, we next examine a small “slice” or submatrix of the network and determine how much information we can deduce about the whole network from this small piece. An examination of the spectral properties of connectivity matrices forms a major part of this analysis.
  • Michelle Craft (Virginia Commonwealth University, United States)
    "Analyzing the differences in olfactory bulb spiking with ortho- and retronasal stimulation"
  • Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb (a key odor processing center) with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reason for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction.
  • Andrea Barreiro (Southern Methodist University, United States)
    "Cell assembly detection in low firing-rate spike train data"
  • Cell assemblies, defined as groups of neurons forming temporal spike coordination, are thought to be fundamental units supporting major cognitive functions. Detecting cell assemblies is challenging since they can occur at a range of time scales and with a range of precisions, from synchronous spikes to co-variations in firing rate. A recently published cell assembly detection (CAD) algorithm (Russo and Durstewitz, 2017) addresses this ambiguity in time scale and precision; however, it is limited to spike trains with a relatively high number of total spikes, a condition which is frequently not met by the low temporal resolution data produced by calcium imaging. We first show how the CAD method can be modified to apply to sparse spike train data. This allows us to detect assemblies in calcium imaging data of neuronal activity in the CA1 region of the hippocampus, a brain region critical for encoding and generalizing contextual memories, during contextual fear conditioning training and tests. We found that assemblies in hippocampus play a role in encoding and retrieving contextual memories. In particular, there exists a group of assemblies whose exploratory activities predict the animal’s ability to distinguish different contexts. Moreover, the mechanisms for processing contextual information are different between two genetically distinct strains of mice that are included in the experiments.
  • Wilten Nicola (University of Calgary, Canada)
    "One-shot learning of spike-sequences in the hippocampus using theta-oscillations"
  • The hippocampus is capable of rapidly learning incoming information, even if that information is only observed once. Further, this information can be replayed in a compressed format during Sharp Wave Ripples (SPW-R). We leveraged state-of-the-art techniques in training recurrent spiking networks to demonstrate how primarily interneuron networks can: 1) generate internal theta sequences to bind externally elicited spikes in the presence of septal inhibition, 2) compress learned spike sequences in the form of a SPW-R when septal inhibition is removed, 3) generate and refine gamma-assemblies during SPW-R mediated compression, and 4) regulate the inter-ripple-interval timing between SPW-R’s in ripple clusters. From the fast time scale of neurons to the slow time scale of behaviors, interneuron networks and theta oscillations serve as the scaffolding for one-shot learningby replaying, refining, and regulating spike sequences.

Mathematical approaches to advance clinical studies in oncology

Organized by: Heyrim Cho (University of California Riverside, USA), Russell Rockne (City of Hope Comprehensive Cancer Center, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-ONCO.

  • Jacob Scott (Cleveland Clinic, USA)
    "Evolutionary Control on Game Landscapes"
  • Control of evolving populations has recently been postulated using control methods inspired by quantum computing and stochastic thermodynamics. These methods, which are essentially extensions of classical population genetics, require genotype-phenotype maps in the form of fitness seascapes, which are mapping from changes in drug dose to fitness in a combinatorially complete genotype space. These models rarely consider the interaction between individual types in heterogeneous populations (clonal interference) and are therefore of limited practical applicability. In this talk we will present a simplified deterministic (ODE) model of evolution on a landscape that includes these interactions (game landscape), show how the interactions can themselves drastically change the evolutionary dynamics, and sketch a path forward to evolutionary control.
  • Kristin Swanson (Mayo Clinic, USA)
    "Sex, Drugs and Radiomics of Brain Cancer"
  • Sebastien Benzekry (INRIA, France)
    "Quantitative modeling of metastasis: cancer at the organism scale"
  • In the majority of solid cancers, secondary tumors (metastases) are the main cause of death. Determining the burden of invisible metastases at diagnosis is a crucial challenge in the clinic, as it would allow personalization of therapeutic intervention, e.g. in the perioperative setting. I will present research efforts towards the establishment of such a predictive computational tools of metastatic development, with emphasis on the quantitative calibration of models to empirical data (experimental and clinical). The general framework is based on a physiologically-structured partial differential equation for the time dynamics of a population of metastases. Results will be presented in two clinical settings: brain metastasis from non-small cell lung cancer and early-stage breast cancer. In the first application, comparison of models relying on different biological hypotheses about dissemination and growth indicated periods of dormancy of the order of several months. In the second application, a combination of machine learning techniques and mixed-effects statistical modeling methods was used for individualized predictions of the model parameters from data available at diagnosis. In turn, this allowed patient-specific prediction of the time to metastatic relapse. Together, these results represent a step towards the integration of mathematical modeling as a predictive tool for personalized oncology.
  • Chengyue Wu (University of Texas at Austin, USA)
    "Towards patient-specific prediction of breast cancer response to neoadjuvant therapy"
  • Neoadjuvant therapy (NAT) has become the standard-of-care treatment for breast cancers. However, more than 50% of patients undergoing the standard NAT regimen show residual tumors which are associated with metastasis and recurrence. Patient-tailored treatment has been proposed to improve individual response. But with multiple factors to consider, including dose, schedule, and drug combinations, personalization of therapeutic regimens is a complex task which cannot be solved by population-based clinical trials. To address this problem, we develop a clinical-computational framework to systematically evaluate the response of breast cancer patients to different therapeutic regimens. Specifically, we employ quantitative MRI to measure tissue geometries and properties such as vessel permeability and drug diffusivity. Constrained by the patient-specific data, we establish a model consisting of an advection-diffusion equation for flow and drug transport, and a phase-filed equation for tumor growth and response. For each patient, we simulate a group of practical therapeutic regimens by varying administration schedules and doses, and drug combinations. The outcome of each regimen is assessed by the computed tumor cellularity and off-target ratio (accumulative drug outside tumor to that within tumor) at the end of treatment. Preliminary results indicate that the approach has the potential to personally optimize breast cancer NAT.