Minisymposia: MS03

Tuesday, July 18 at 10:30am

Minisymposia: MS03

Integrating Mathematics Across the Cardiovascular System: A Mini-Symposium on Multilevel Modelling of Cardiovascular Biology

Organized by: Jessica Crawshaw, Vijay Rajagopal, Michael Watson, Mitchel Colebank, Seth Weinberg
Note: this minisymposia has multiple sessions. The other session is MS04-CARD-1.

  • Miguel Bernabeu The University of Edinburgh (The Bayes Centre)
    "Red blood cell dynamics in complex vascular networks: implications in development and disease"
  • In this talk, I will review recent progress on the application of cellular flow simulations (with the HemeLB flow solver) to characterise red blood cell (RBC) dynamics in complex vascular networks. First, I will demonstrate an intriguing association between reduced RBC flow and vascular remodelling during vascular development. Second, I will present two recently published studies relating vascular phenotypes encountered in the tumour microenvironment with anomalous RBC transport and potential tumour tissue hypoxia, a mechanism previously unreported. Finally, I will outline future research directions related to predicting vascular network function from its structure and how this can become a tool for biomedical investigation and eventually clinical translation.
  • Mette Olufsen North Carolina State University (Mathematics)
    "Multiscale approach for assessment of hemodynamics in Pulmonary Hypertension"
  • This study discusses the use of multiscale models for the assessment of pulmonary hypertension (PH). This heterogeneous disease with multiple subtypes is categorized as pre-capillary (leading to remodeling of the pulmonary arteries), or post-capillary, also referred to as venous PH. The latter is often associated with left heart failure. Common for both types is an increase in pulmonary arterial pressure. This study will use 1D and systems-level modeling to assess changes and propose treatments for PH patients. The focus is on patient-specific predictions using a computational framework merging imaging and dynamic data with computational models. The systems-level model allows us to study the effects of high pulmonary arterial pressure on the cardiovascular system as a whole, particularly how a right heart disease can affect the left heart via ventricular-ventricular interaction. Whereas the spatial pulmonary network model can help predict lung perfusion. Both properties are essential to assess patient health. We extract pulmonary networks represented by a directed graph extracted from computed tomography images. In the large vessels, we solve the 1D Navier Stokes equations. In contrast, in the systems level model and the network of small vessels and capillaries, we solve linearized equations coupled to large vessels via outflow boundary conditions. We demonstrate the importance of sensitivity analysis and parameter inference to render the model patient-specific and show how the calibrated models can be used to predict treatment effects for patients with thromboembolic pulmonary hypertension.
  • Fabian Spill University of Birmingham (Mathematics)
    "The Human Cardiac Age-OME: Multi-omics analysis and mechanistic modelling of the ageing heart"
  • The heart is a mechanical pump, whose function is essential to life. Reduced heart function in ageing is a key contributor to frailty, and heart diseases are among the major causes of death. An impediment to understanding age-related heart diseases is our lack of understanding of healthy cardiac ageing. This limits our ability to distinguish data from age-related diseases to data from healthily aged hearts, identifying the true causes of these diseases. A challenge to understanding healthy ageing is a lack of available data from healthy donors. Making use of the unique resources of the Sydney Heart Bank, we present an integrated mathematical modelling and bioinformatics analysis of human cardiac ageing. We performed transcriptomics, proteomics, metabolomics, and lipidomics analysis, and obtained a holistic picture of metabolic and mechanical alterations that characterize the ageing heart. In older hearts, we observed a downregulation of proteins involved in calcium signalling and of the contractile apparatus itself. In addition, we found a potential counteractive upregulation of central carbon generation of fuel, upregulation of glycolysis and increases in long-chain fatty acids. We then developed predictive mechanistic models that demonstrated how calcium signalling and oxidative phosphorylation, two key pathways regulating cardiomyocyte function, are altered in the ageing heart.

Data-driven, modeling, and topological techniques in cell and developmental biology

Organized by: Alexandria Volkening, Andreas Buttenschoen, Veronica Ciocanel
Note: this minisymposia has multiple sessions. The other session is MS04-CDEV-1.

  • Dhananjay Bhaskar Yale University (Department of Genetics)
    "Analyzing Spatiotemporal Signaling Patterns using Geometric Scattering and Persistent Homology"
  • Cells communicate with one another through a variety of signaling mechanisms. The exchange of information via these mechanisms allows cells to coordinate their behavior and respond to environmental stress and other stimuli. To facilitate quantitative understanding of complex spatiotemporal signaling activity, we developed Geometric Scattering Trajectory Homology (GSTH), a general framework that encapsulates time-lapse signals on a cell adjacency graph in a low-dimensional trajectory. GSTH captures the signal at multiple spatial scales and over time by applying manifold-geometry preserving dimensionality reduction to geometric scattering features obtained from a cascade of graph wavelet filters. We tested this framework using computational models of collective oscillations and calcium signaling in the Drosophila wing imaginal disc, as well as experimental data, including in vitro ERK signaling in human mammary epithelial cells and in vivo calcium signaling from the mouse epidermis and visual cortex. We found that the geometry and topology of the trajectory are related to the degree of synchrony (over space and time), intensity, speed, and quasi-periodicity of the signaling pattern. We recovered model parameters and experimental conditions by training neural networks on trajectory data, showing that our approach preserves information that characterizes various cell types, tissues, and drug treatments. We envisage the applicability of our framework in various biological contexts to generate new insights into cell communication.
  • Keisha Cook Clemson University (School of Mathematical and Statistical Sciences)
    "Predictive Modeling of the Cytoskeleton"
  • Biological systems are traditionally studied as isolated processes (e.g. regulatory pathways, motor protein dynamics, transport of organelles, etc.). Although more recent approaches have been developed to study whole cell dynamics, integrating knowledge across biological levels remains largely unexplored. In experimental processes, we assume that the state of the system is unknown until we sample it. Many scales are necessary to quantify the dynamics of different processes. These may include a magnitude of measurements, multiple detection intensities, or variation in the magnitude of observations. The interconnection between scales, where events happening at one scale are directly influencing events occurring at other scales, can be accomplished using mathematical tools for integration to connect and predict complex biological outcomes. In this work we focus on building statistical inference methods to study the complexity of the cytoskeleton from one scale to another by relying on two main components facilitating intracellular transport; that is microtubule network organization and cargo transport.
  • Calina Copos Northeastern University (Biology and Mathematics)
    "From microscopy to the distribution of mechanochemical efforts across a pair of cells"
  • In a model organism, we use a combination of mathematical and experimental tools to tease apart the distribution of forces in a pair of cells responsible for forming the heart (and the pharynx). The heart progenitors provide one of the simplest examples of collective cell migration whereby just two cells migrate with a defined leader-trailer “assignment” between two tissues. The cells are also capable of moving individually, albeit by a shorter distance, with imperfect directionality, and with altered morphology. Thus, maintaining contact and the leader-trailer roles is important for directed migration to the destination. However, it is unclear why a two-cell system is better at migration than an individual cell. Based on in-vivo fluorescence imaging of the embryo, we obtain morphological measurements of the cells. Borrowing on the formulation of active droplet theory, we extract intracellular pressure and forces at the intersection of interfaces (e.g. cell-cell, cell-surface, cell-environment). These extracted measurements are then tested in the active droplet pair framework, and we observe that the 2-cell system does migrate and migrate persistently due to the difference in contact angle at the leading of the leader cell and the trailing edge of the rear cell.
  • Daniel A. Cruz University of Florida (Department of Medicine)
    "Topological data analysis of pattern formation in stem cell colonies"
  • Confocal microscopy imaging provides both positional information and expression levels from in vitro cell cultures; however, few methods exist to quantify the spatial organization of such cultures. Current quantitative tools generally rely on human annotation, require the a priori selection of parameters, or potentially lack biological interpretability. To address these limitations, we develop a modular, general-purpose pipeline that uses topological data analysis to extract structural summaries from cellular patterns at multiple scales. We apply our pipeline to study the pattern formation of human induced pluripotent stem cell (hiPSC) cultures, which have become powerful, patient-specific test beds for investigating the early stages of embryonic development. Our analysis captures both subtle differences in the spatial organization of hiPSCs based on different biological markers and progressive changes in patterning across incremental modifications of certain experimental conditions. These results imply the existence of directed cellular movement and morphogen-mediated, neighbor-to-neighbor signaling in the context of hiPSC differentiation.

Polarity and patterns meet biophysical and biochemical dynamics

Organized by: Adriana Dawes, S. Seirin-Lee

  • Adriana Dawes The Ohio State University (Department of Mathematics/Department of Molecular Genetics)
    "The interplay between biochemistry and geometry in polarization of the early C. elegans embryo"
  • Centrosomes are nucleus-associated organelles that serve as the nucleation site for microtubule arrays. Microtubules nucleated from these arrays interact with motor proteins such as dynein at the periphery of the cell which act to transport the nucleus and position it prior to division. In polarized cells, where specific factors are segregated to opposite ends of the cell as seen in early embryos of the nematode worm C. elegans, proper centrosome positioning is particularly important, determining whether the division process is symmetric or asymmetric. Using a combination of stochastic and continuum models with experimental validation in early C. elegans embryos, we demonstrate that the geometry of the early embryo is critical for proper centrosome positioning in the polarized C. elegans embryo, and that biochemical suppression of dynein pulling forces in specific regions of the embryo ensures reliable timing of centrosome movement.
  • Sungrim Seirin-Lee Kyoto University (Kyoto University Institute for the Advanced Study of Human Biology (ASHBi))
    "Mind the gap: Space inside eggs steers first few steps of life"
  • In multicellular systems, cells communicate with adjacent cells to determine their positions and fates, an arrangement important for cellular development. Orientation of cell division, cell-cell interactions (i.e. attraction and repulsion) and geometric constraints are three major factors that define cell arrangement. In particular, geometric constraints are difficult to reveal in experiments, and the contribution of the local contour of the boundary has remained elusive. In this study, we developed a multicellular morphology model based on the phase-field method so that precise geometric constraints can be incorporated. Our application of the model to nematode embryos predicted that the amount of extra-embryonic space, the empty space within the eggshell that is not occupied by embryonic cells, affects cell arrangement in a manner dependent on the local contour and other factors. The prediction was validated experimentally by increasing the extra-embryonic space in the Caenorhabditis elegans embryo. Overall, our analyses characterized the roles of geometrical contributors, specifically the amount of extra- embryonic space and the local contour, on cell arrangements. These factors should be considered for multicellular systems [1]. [1] S. Seirin-Lee*, K. Yamamoto, A. Kimura*, The extra-embryonic space and the local contour are critical geometric constraints regulating cell arrangement (2022) Development. 149, dev200401.
  • Masatoshi Nishikawa Hosei University (Department of Frontier Bioscience)
    "PAR polarization in less contractile cell"
  • PAR polarity establishment in C. elegans zygote requires coupling between molecular interactions between PAR proteins and the flow of contractile actomyosin cortex. One of the daughter cell, P1 cell, also shows PAR polarity while its cortex exhibits low contractility, suggesting other mechanisms to establish the PAR polarity. We will show the dynamics of pattern formation and molecular interactions involved in polarity establishment, with the aim of developing mathematical description based on reaction diffusion model.
  • Eric Cytrynbaum The University of British Columbia (Mathematics)
    "Mechanisms and models of spatiotemporal patterns in reptile polyphyodont dentition"
  • For over a century, the development and replacement of reptile teeth has been of interest originally for its value in comparative anatomy and evolutionary biology due to the prevalence of teeth in the fossil record. More recently, it has been used as a model system for understanding spatiotemporal patterning in developmental biology and for delving into the mechanisms of tooth formation. In collaboration with the Richman Lab (Joy Richman, UBC Dentistry), we are using the Leopard Gecko as a model organism to address the question of the mechanisms underlying the regular and long-lasting spatiotemporal patterns of tooth replacement seen in many polyphyodonts. In this talk, I will describe the data and our implementation and analysis of several mechanisms/models that have been proposed (but not implemented in mathematical form) in the past to explain the observations. Finding shortcomings in these models, we propose a new model, the Phase Inhibition Model, which does better at explaining the data. I will conclude by discussing ideas for how this model might be integrated with existing reaction-diffusion models of early development of dentition in reptiles.

Current trends in phylogenetics

Organized by: Kristina Wicke, Laura Kubatko
Note: this minisymposia has multiple sessions. The other session is MS04-ECOP-1.

  • Hector Banos Dalhousie University (Department of Mathematics and statistics)
    "When Are Profile Mixture Models affected by Over-parameterization?"
  • Phylogenetic models of protein sequence evolution not accounting for site heterogeneity are prone to long-branch attraction (LBA) artifacts, especially when reconstructing relationships on a billion-year time scale. Profile mixture models have been developed to approximate protein sequence evolution on a billion-year timescale by considering a finite mixture of stationary amino acid frequency vectors. Recently there have been questions about such models being affected by over-parameterization. Notably, people have argued that over-parameterization can negatively affect tree topology estimation if many frequency vectors are considered. We demonstrate that this is not the case based on classical statistical results, extensive simulations, and empirical examples. Moreover, our results can be applied to other types of mixture models used in phylogenetics.
  • Peter Beerli Florida State University (Scientific Computing)
    "Population genetics processes impact Species Trees estimation"
  • We investigate the effects of DNA mutation models, population growth, and gene flow on the power to correctly infer a species tree from genomic data. These inferences are complicated by the commonly used representation of the sequence data as single nucleotide polymorphisms instead of the full DNA sequences. This data representation choice reduces the potential variability in the data and biases parameters such as the effective population size of a species downwards. Methods that may work for species with small population sizes, such as primates, will most likely fail with species that have large population sizes, such as mosquitoes.
  • Lena Collienne Fred Hutch Cancer Center (Computational Biology)
    "Spaces of Discrete Time Trees"
  • Many algorithms for phylogenetic tree inference navigate treespace to find trees that are optimal according to some criterion. Though some software packages aim to reconstruct a distribution of trees rather than a single best tree, there is a lack of tools to analyse such distributions or samples thereof. In order to develop statistical methods for analysing distibutions over treespace, different ways of defining proximity of trees in treespace have been proposed, each of which provides a different definition of a metric space containing all possible trees. These definitions of treespace depend on the type of trees considered, for example time trees where branch lengths represent times, which we will focus on in this talk. Gaining insights into the timing of evolutionary events is important in many applications including cancer and virus evolution, which is why some software, including the popular BEAST packages, infer phylogenetic trees with timing information. In this talk we will discuss why the choice of treespace (or distance measure) should depend on the application. In particular, we consider a definition of treespace for discrete versions of time trees, which have integer-valued branch lengths. Our definition of a metric space for trees is based on tree rearrangement operations that take times of internal nodes, i.e. evolutionary events in the tree, into account. Distances in these spaces can be computed efficiently, which leads us to discussing further properties of this distance measure and how it can be used in practice.
  • Tandy Warnow University of Illinois Urbana-Champaign (Computer Science)
    "New methods for very-large scale maximum likelihood tree estimation"
  • Maximum likelihood estimation of phylogenetic trees is one of the basic analytical steps of many biological research projects involving evolutionary questions. With increasing amounts of sequence data, the interest in estimating large phylogenies, with up to hundreds of thousands, or even millions of sequences, is increasing. Yet these estimations are challenging, since maximum likelihood is NP-hard and standard heuristics (employed in leading software, such as RAxML-ng and IQ-TREE) are not designed for these ultra-large datasets. Recent work in my lab has produced alternative strategies based on divide-and-conquer for ultra-large maximum likelihood tree estimation that show potential to enable better results on very large datasets. Among these approaches are the 'Disjoint Tree Merger' methods (originally introduced by Erin Molloy) that operate in three stages: the input sequences are divided into disjoint sets, a tree is estimated on each set, and then the trees are merged into a tree on the full set using auxiliary information computed from the input. These Disjoint Tree Merger methods have strong theoretical guarantees (e.g., statistical consistency is maintained) and surprisingly good empirical performance on large datasets. In this talk I will present our progress using this approach on large biological datasets, and discuss future directions.

Modeling and Analysis of Evolutionary Dynamics Across Scales and Areas of Application

Organized by: Daniel Cooney, Olivia Chu
Note: this minisymposia has multiple sessions. The other session is MS04-ECOP-2.

  • Anuraag Bukkuri Moffitt Cancer Center (Integrated Mathematical Oncology)
    "Evolution of Resistance in Structured Neuroblastoma Populations"
  • Neuroblastoma is a pediatric brain cancer of variable clinical presentation. The causes behind the initiation, progression, and ultimate resistance of this cancer is unknown, though it is recognized that two cellular phenotypes underpin its deadliness: adrenergic (ADRN) and mesenchymal (MES). How these phenotypes influence the eco-evolutionary dynamics of neuroblastoma cell populations (especially under therapy) remains a mystery. This is due to the confu- sion surrounding whether the ADRN and MES phenotypes represent different cell types (species) or cell states (stages in the life cycle of a single species). This distinction is critical in understanding and ultimately treating neuroblas- toma. In this talk, we will introduce theoretical methods to model the eco- evolutionary dynamics in state-structured neuroblastoma populations and use these models to tease apart cell type vs. cell state hypotheses. We will then expand and generalize this framework to continuous-structured models and discuss implications for cancer and bacterial resistance more generally.
  • Olivia J. Chu Dartmouth College (Mathematics)
    "An Evolutionary Game Theory Model of Altruism via Arrhenotoky"
  • Arrhenotoky is a unique biological mechanism in which unfertilized eggs give rise to haploid male offspring, while fertilized eggs give rise to diploid female offspring. In this work, we build a mathematical model for the arrhenotoky replicator dynamics of a beehive by adopting an evolutionary game theory framework. Using this model, we investigate the evolution of altruistic behavior in a beehive, looking particularly at hive success over a variety of parameters, controlling for altruism in workers and the queen. We find that the most reproductively successful hives have completely altruistic workers that donate all of their resources to the queen, as well as a somewhat altruistic queen that donates a small proportion of her resources to drone bees. Through these results, our model explains in part the evolutionary adoption of altruistic behavior by insects with arrhenotoky reproductive dynamics.
  • Nicole Creanza Vanderbilt University (Department of Biological Sciences)
    "Modeling and analysis of cultural evolution: insights from humans and birds"
  • Cultural traits—behaviors that are learned from others—can change more rapidly than genes and can be inherited not only from parents but also from teachers and peers. How does this complex process of cultural evolution differ from and interact with genetic evolution? In this talk, I will discuss the dynamics of culturally transmitted behaviors on dramatically different evolutionary timescales: the learned songs of a family of songbirds and the spoken languages of modern human populations. Both of these behaviors enable communication between individuals and facilitate complex social interactions that can affect genetic evolution. My lab's work on models and analyses of these two systems demonstrate that learned behaviors, while less conserved than genetic traits, can retain evolutionary information across great distances and over long timescales.
  • Wai-Tong (Louis) Fan Indiana University (Mathematics)
    "Stochastic waves on metric graphs and their genealogies"
  • Stochastic reaction-diffusion equations are important models in spatial population genetics and ecology. These equations arise as the scaling limit of discrete systems such as interacting particle models, and so they are robust against model perturbation. In this talk, I will discuss methods to compute the probability of extinction, the quasi-stationary distribution, the asymptotic speed and other long-time behaviors for stochastic reaction-diffusion equations of Fisher-KPP type. Importantly, we consider these equations on general metric graphs that flexibly parametrize the underlying space. This enables us to not only bypass the ill-posedness issue of these equations in higher dimensions, but also assess the impact of space and stochasticity on the coexistence and the genealogies of interacting populations.

Mathematical-biology education in a post-COVID world

Organized by: Stacey Smith?
Note: this minisymposia has multiple sessions. The other session is MS04-EDUC-1.

  • Glenn Ledder University of Nebraska-Lincoln (Mathematics)
    "Using NetLogo for Modeling of Virtual Worlds"
  • We learn modeling by creating models for physical settings. Whereas real world settings have confounding factors that make modeling difficult, virtual world settings are governed by a limited set of individual-based rules, an example being the zombie-vs-human games whose modeling has become a popular area for undergraduate research. In addition to virtual worlds based on human activities, we can also create in silico virtual worlds using agent-based models that can be conveniently implemented in NetLogo. Students watch a NetLogo simulation and use their observations to build a mechanistic model; an example of this is my BUGBOX-predator program, which implements C.S. Holling's forager experiment. Additional challenges occur when we want to study the effect of a parameter on a system. Standard NetLogo includes the BehaviorSpace facility, which automates the choice of experiments but not the data analysis. In this talk, we illustrate how to write NetLogo code that automates the data analysis as well as the choice of experiments.
  • Dmitry Kondrashov University of Chicago (Biological Sciences Collegiate Division)
    "Comparison of assessment and teaching modalities for a quantitative biology course"
  • Teaching quantitative skills for biology majors presents a set of challenges, in particular related to the perceived relevance of the material to their own educational goals, as well as the confidence of students in their own efficacy in learning these skills. The course Introduction to Quantitative Modeling for Biology is integrated into the biological sciences curriculum at University of Chicago and serves around two hundred students every year. Over the past three years, the pandemic disruption has prompted changes both in mode of delivery and course assessments, as the course moved to remote learning for two years and then back to in-person instruction in spring of 2022. In particular, I abolished all timed exams, allowed students opportunities to revise and resubmit assignments, and introduced open-ended projects involving data analysis or modeling in lieu of final exams. I will report the results of pre- and post-course surveys of student perceptions and satisfaction of the course, as well as measures of their performance and learning. My general conclusions from this experience are that replacing timed exams with revisable assignments and projects a) does not seem to have a negative impact on student learning; b) increases student satisfaction and self-efficacy; and that student engagement appeared to diminish after an extended period of remote instruction.
  • Stacey Smith? The University of Ottawa (Mathematics)
    "How getting cheaters to reflect on their actions turned my worst course into my best course"
  • I had a high cheating ratio in my Summer 2022 online course. At least 50% of the class used materials they should not have or consulted with other students. The chair and the dean were reluctant to prosecute, so I decided to switch tactics and use the carrot instead of the stick. I offered them the chance to admit what they're done wrong in exchange for potential extra marks. The results were outstanding: students who had failed and/or cheated stepped up in ways I had not expected. We can learn lessons from approaching this situation with kindness.

Viral dynamics and its applications

Organized by: Tin Phan, Ruian Ke, Ruy M. Ribiero, Alan S. Perelson
Note: this minisymposia has multiple sessions. The other session is MS04-IMMU-1.

  • Stanca Ciupe Virginia Tech (Mathematics)
    "Mathematical models of Usutu Viral Infection"
  • Usutu virus, an emerging zoonotic flavivirus that is maintained in the environment through an enzootic cycle involving mosquitoes and birds, is associated with decreased bird populations and occasional spillover to humans. To determine the relationship between Usutu virus kinetics and disease incidence we built a multiscale vector-borne disease mathematical model that connects individual bird infections with the probability of bird-to-mosquito transmission and disease incidence in the bird population. We parametrize the model using viral titer data from birds infected with different Usutu virus strains and bird-to-mosquito transmission probability data and use the results to make predictions on bird infection incidence. Lastly, we investigate the effect of data scarcity on predicted incidence and propose solutions for improving model accuracy.
  • Elissa Schwartz Washington State University (Math/Biol Sci)
    "Equine Infectious Anemia Virus (EIAV) dynamics and applications to vaccine development"
  • Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions of horses have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. We then investigate the effects of repeated immunizations through antibody infusions on both the wild- type and mutant strains of the virus. The model is then extended to include cytotoxic T lymphocyte responses. Numerical analysis shows that stability of the biologically-relevant endemic equilibrium, characterized by coexistence of antibody and CTL responses, requires that the parameters promoting CTL responses need to be boosted over parameters promoting antibody production. This result may seem counterintuitive (in that a weaker antibody response is better) but can be understood in terms of a balance between CTL and antibody responses that is needed to permit existence of CTLs. Thus, an intervention such as a vaccine that is intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. In sum, these results suggest a route forward to design vaccine strategies to control lentivirus infection.
  • Wenjing Zhang Texas Tech University (Department of Mathematics and Statistics)
    "Detecting and Resetting Tipping Points to Create More HIV Post-treatment Controllers with Bifurcation and Sensitivity Analysis"
  • The existence of HIV post-treatment controllers (PTCs) gives a hope for HIV functional cure. Understanding the critical mechanisms determining PTCs represents a key step toward this goal. In this talk, we have studied these mechanisms by analyzing an established mathematical model for HIV viral dynamics. In mathematical models, critical mechanisms are represented by parameters that affect the tipping points to induce qualitatively different dynamics and, in cases with multiple stability, the initial conditions of the system also play a role in determining the fate of the solution. As such, for the tipping points in parameter space, we developed and implemented a sensitivity analysis of the threshold conditions of the associated bifurcations to identify the critical mechanisms. Our results suggest that the infected cell death rate and the saturation parameter for cytotoxic T lymphocyte proliferation most significantly affect post-treatment control. For the case with multiple stability, in state space of initial conditions, we first investigated the saddle-type equilibrium point to identify its stable manifold, which delimits trapping regions associated to the high and low viral set points. The identified stable manifold serves as a guide for the loads of immune cells and HIV virus at the time of therapy termination to achieve post-treatment control.
  • Jasmine A. F. Kreig Los Alamos National Laboratory (T6: Theoreticacl Biology and Biophysics)
    "Using an agent-based model to explore affinity maturation of B cells: a SARS-CoV-2 case study"
  • Successive variants of concern of SARS-CoV-2 have demonstrated an increase in antigenic distance from the original strain. These variants of concern (VOC), with differing amounts of escape from pre-existing immunity, are causing concerns about continued protection gained from vaccination and prior infection. B cells, which are key players in the body’s humoral immune response, undergo a process called affinity maturation in which activated B cells produce antibodies with increased affinity for antigen with the goal of limiting antigen ability to infect more cells. As the antigen moves away from the initial strain, the ability of the body to cross-reactively neutralize the antigen decreases. We investigated this idea via an agent-based model (ABM) that simulates the humoral immune response to SARS-CoV-2. We represent B cells (naïve, plasma, memory), antibodies, and antigens (virus strain or vaccine) as agents. We focus on binding that occurs between receptors (B cells, antibodies) and epitopes (antigens), representing these proteins in Euclidean shape space. In addition to interactions among B cells and antigens, we simulate other cell processes such as division, mutation, and death. In this talk, we will present preliminary results from our ABM. We hope to use this model to inform vaccination strategies in the future, especially given the constantly changing nature of this virus.

Stochastic methods for biochemical reaction networks

Organized by: Wasiur KhudaBukhsh, Hye-Won Kang
Note: this minisymposia has multiple sessions. The other session is MS04-MFBM-1.

  • Grzegorz A. Rempala The Ohio State University (Biostatistics)
    "Agent-based, aggregated dynamics for chemical reaction networks"
  • In this talk I will present a modeling framework for approximating stochastic dynamics of a single tagged molecule in a large biochemical network (CRN). This framework is based on approximating the dynamics of the CRN representing a biological system with hybrid dynamics combining the stochastic laws of individually-tagged molecules with the mean-field laws of the remaining species comprising the CRN. The approximation is well-defined over the entire process evolution time and leads to efficient and fully parallelizable simulation techniques. Moreover, it also allow for principled and efficient statistical inference for model parameters, which is difficult or even impossible in traditional agent-based models (ABM). As part of the development of the ABA approach, one could also consider how to incorporate different individual features (e.g., when molecules of the same species have individual characteristics or spatial features). I will present some molecular examples illustrating potential applications, including the HIV virus dendritic cell invasion models and models of multi-stage transcriptional bursting.
  • Hye-Won Kang University of Maryland, Baltimore County (Department of Mathematics and Statistics)
    "Stochastic oscillations in the enzyme-catalyzed chemical reaction network in glycolysis"
  • We consider a simple chemical reaction network in glycolysis. In a large volume limit of this system, species concentrations can exhibit a steady or an oscillatory behavior depending on the choice of the parameter values. To investigate how the inherent fluctuations affect the oscillatory behavior of the species copy numbers, we compare stochastic and deterministic dynamics of the system with selected parameter values near a separatrix. Due to the inherent fluctuations, a parameter region of the stochastic model cannot be separated clearly by the system behavior. We test several chemical reaction networks modified from the original system in glycolysis and investigate how the effects of the inherent fluctuations can be regulated. This is joint work with Luan Nguyen at UMBC.
  • Yi Fu University of California, San Diego (Bioinformatics and Systems Biology PhD Program)
    "Comparison Theorems for Stochastic Chemical Reaction Networks"
  • Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. Our proof also yields a method for simultaneously simulating the sample paths of two comparable SCRNs. Our tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. We illustrate our results with applications to models of chromatin regulation and enzymatic kinetics.
  • Arnab Ganguly Louisiana State University (Mathematics)
    "Statistical inference of stochastic differential equations with applications to biochemical reactions"
  • Stochastic differential equations (SDES) are potent tools in modeling temporal evolution of a variety of systems. For the model to be accurate it is necessary to learn or estimate certain key parameters of the underlying SDE or sometimes the entire driving functions from the available data. Although computational methods for these types of learning problems have been studied in the literature, there is a critical lack of theoretical results on limiting behavior of the underlying estimators even for one-dimensional SDEs. The complexity of the SDE dynamics hinders usage of standard statistical tools in deriving the relevant properties. The goal of this talk is to partly fill this gap in theoretical understanding of these types of inference problems. In particular, we will discuss recent results on desirable asymptotic properties including consistency and central limit theorem of some of the estimators. We will specifically illustrate these results for SDEs that are used to model biochemical reaction systems.

Inference, analysis, and control of Boolean network models

Organized by: David Murrugarra

  • Elena Dimitrova California Polytechinc State University, San Luis Obispo (Mathematics)
    "A unified approach to reverse engineering and data selection for unique network identification"
  • Due to cost concerns, it is optimal to gain insight into the connectivity of biological and other networks using as few experiments as possible. Data selection for unique network connectivity identification has been an open problem since the introduction of algebraic methods for reverse engineering for almost two decades. In this talk we determine what data sets uniquely identify the unsigned wiring diagram corresponding to a system that is discrete in time and space. Furthermore, we answer the question of uniqueness for signed wiring diagrams for Boolean networks. Computationally, unsigned and signed wiring diagrams have been studied separately, and in this talk we also show that there exists a polynomial ideal capable of encoding both unsigned and signed information. This provides a unified approach to studying reverse engineering that also gives significant computational benefits.
  • Brandilyn Stigler Southern Methodist University (Mathematics)
    "Computational Algebraic Methods for Boolean Network Modeling"
  • Biological data science is a field replete with many substantial data sets from laboratory experiments and myriad diverse methods for modeling, simulation, and analysis. As a data set can have a large number of associated models, model selection is often required as a post-processing step. In parallel experimental design can be utilized as a preprocessing step to minimize the number of resulting models, many of which may be biologically irrelevant. In this talk we focus on the problem of inferring Boolean models of biological networks from data. We will outline theoretical results and computational algorithms related to model construction and model selection. This work draws from algebraic geometry and algebraic combinatorics, and has been used to model a variety of biological processes including tissue development and tumor progression.
  • Claus Kadelka Iowa State University (Department of Mathematics)
    "A modular design of gene regulatory networks emerges naturally in response to an evolutionary multi-objective optimization problem"
  • Building complicated structures from simpler building blocks is a widely observed principle in both natural and engineered systems. In molecular systems biology, it is also widely accepted, even though there has not emerged a clear definition of what constitutes a simple building block, or module. For a Boolean network, we recently proposed to define its modules as the strongly connected components of its wiring diagram. This structure-based definition of modularity implies a decomposition of the dynamics of a Boolean network. In this talk, I show through simulation studies that modularity allows Boolean networks to maximize both their phenotypical robustness and their dynamical complexity. The former is biologically desirable as gene regulatory networks need to robustly maintain a phenotype in the presence of perturbations. At the same time, meaningful biological networks must harbor multiple phenotypes (corresponding to attractors of the Boolean network), allowing the network to dynamically shift from one phenotype to another based on its current need. These findings provide evidence that modularity, defined using the graph-theoretical concept of strong connectedness, is evolutionarily advantageous.
  • Daniel R. Plaugher University of Kentucky (Department of Toxicology and Cancer Biology)
    "Phenotype control techniques for gene regulatory networks"
  • Modeling cell signal transduction pathways with Boolean networks (BNs) has become an established method for analyzing intracellular communications over the last few decades. What's more, BNs provide a course-grained approach, not only to understanding molecular communications, but also for targeting pathway components that alter the long-term outcomes of the system. This has come to be known as phenotype control theory. In this presentation we discuss the interplay of various approaches for controlling gene regulatory networks. We will also explore comparisons between the methods on a specific cancer model, and highlight some challenges facing each technique.

Dynamics of cellular heterogeneity: consequences of diverse regulatory mechanisms

Organized by: Mohit Kumar Jolly, Paras Jain
Note: this minisymposia has multiple sessions. The other session is MS04-ONCO-1.

  • Amy Brock University of Texas at Austin (Biomedical Engineering)
    "Heritability and plasticity of therapeutic resistance mechanisms within heterogeneous cancer cell populations"
  • Individual cancer cells within a tumor cell population display distinct responses to chemotherapeutic agents. We have developed a novel genetic tracking technology, ClonMapper to elucidate the pre-existent and de novo cell states that arise from chemotherapeutic intervention. By tracking longitudinal clonal dynamics and cell state changes, we elucidate the contributions of heterogeneity to survival and re-growth of cancer cells following specific selective pressures. Here we will examine the distinct survivorship trajectories that characterize breast cancer cells treated with chemotherapy. Subpopulations differ significantly in growth dynamics and the interactions among heterogeneous subpopulations impact the population composition of surviving cells. Models that include subpopulation interactions may improve the ability to predict the composition and sensitivity of cancer cells under varying therapeutic pressures.
  • Morgan Craig Sainte-Justine University Hospital Research Centre / Université de Montréal (Immune Disorders and Cancer / Mathematics and Statistics)
    "Impact of cellular and spatial heterogeneity on immunotherapies to treat glioblastoma"
  • Glioblastoma is a rare but deadly central nervous system and brain cancer. In most patients, current standard-of-care, which includes maximal safe surgical resection, radiotherapy, and chemotherapy, fails due to recurrences, translating to a median survival of just 15 months. There is therefore high interest in developing improved approaches to treat glioblastoma, including immunotherapies (e.g., immune checkpoint blockade, oncolytic viruses etc.). Unfortunately, clinical trials of immunotherapies to treat glioblastoma have thus far failed to show significant benefits to patients. In this talk, I will discuss the role of spatial and cellular heterogeneity on treatment success through the integration of agent-based modelling with clinical samples from patients. Our results suggest avenues of continued drug development to provide improved patient outcomes.
  • Yogesh Goyal Northwestern University (Cell and Developmental Biology)
    "Tracing origin and consequences of rare cell plasticity in cancer drug resistance"
  • Single cell variations within a genetically homogeneous population of cells can lead to significant differences in cell fate in response to external stimuli. This is particularly relevant in cancer cells, where a small population of cells can evade therapies to develop resistance. In this talk, I will present ongoing work on tracing the origins, nature, and manifestations of single cell variations in response to a variety of cytotoxic chemotherapies and targeted therapies in various cancer models. By combining clonal barcoding-based and imaging-based lineage tracing frameworks with computational analysis, I will discuss the commonalities and differences in cell fate outcomes across cancers and therapies. Our experimental and computational designs will provide a foundation for controlling single-cell variabilities in cancer and other biological contexts, such as stem cell reprogramming.
  • Geena Ildefonso University of Southern California (Alfred E. Mann Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA)
    "A data-driven Boolean model explains memory subsets and evolution in CD8+ T cell exhaustion"
  • T cells play a key role in a variety of immune responses, including infection and cancer. Upon stimulation, naïve CD8+ T cells proliferate and differentiate into a variety of memory and effector cell types; however, failure to clear antigens causes prolonged stimulation of CD8+ T cells, ultimately leading to T cell exhaustion (TCE). The functional and phenotypic changes that occur during CD8+ T cell differentiation are well characterized, but the underlying gene expression state changes are not completely understood. Here, we utilize a previously published data-driven Boolean model of gene regulatory interactions shown to mediate TCE. Our network analysis and modeling reveal the final gene expression states that correspond to TCE, along with the sequence of gene expression patterns that give rise to those final states. With a model that predicts the changes in gene expression that lead to TCE, we could evaluate strategies to inhibit the exhausted state. Overall, we demonstrate that a common pathway model of CD8+ T cell gene regulatory interactions can provide insights into the transcriptional changes underlying the evolution of cell states in TCE.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak
  • Jeffrey West
SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak

  • Jeffrey West

SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.