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.

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.

Organized by: Alexandria Volkening, Andreas Buttenschoen, Veronica Ciocanel
Note: this minisymposia has multiple sessions. The other session is MS03-CDEV-1.

• Joel Dokmegang Northwestern University (Molecular Biosciences)
  "Spectral Decomposition of Morphogenesis"
Describing morphogenesis generally consists in aggregating the multiple high resolution spatiotemporal processes involved into repeatable low resolution morphological stories consistent across sample individuals of the same species or group. In order to achieve this goal, biologists have often had to submit movies issued from live imaging of developing embryos either to the eye test or to basic statistical analysis. Although successful, these methods however present noticeable drawbacks, as they can be time consuming, hence unfit for scale, and often lack standardisation. In this work, we leverage the power of continuum mechanics and spectral decomposition to propose a standardised framework for automatic detection and timing of morphological processes. First, we quantify shape changes in gastrulating ascidian embryos by evaluating strain-rate tensor fields at their surface. We then apply to this data a generalised Fourier transform, resulting in canonical spatio-temporal atlases that tell the story of morphogenesis in the studied embryos.
• John Nardini The College of New Jersey (Mathematics & Statistics)
  "Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images"
Microvascular disease complications can alter vascular network morphology and disrupt tissue functioning. Such diseases are typically assessed by visual inspection of retinal images, but this can be challenging when diseases exhibit silent symptoms or patients cannot attend in-person meetings. We propose that statistical and topological summaries of segmented retinal vascular images provide promising avenues to automate and aid microvascular disease status and examine the performance of machine learning algorithms in detecting microvascular disease from these summaries. We apply our methods to three datasets and find that, among the 13 descriptor vectors we consider, either a statistical Box-counting descriptor vector or a topological Flooding descriptor vector achieves the highest accuracy levels. When we apply our methods to a fourth dataset consisting of data from multiple data sources, the Box-counting vector maintains its strong performance while the topological Flooding vector which is sensitive to differences in the annotation styles between the different datasets. Our work represents a first step to establishing which computational methods are most suitable for identifying microvascular disease as well as some of their current limitations. In the longer term, these methods could be incorporated into automated disease assessment tools.
• Anna Nelson Duke University (Department of Mathematics)
  "Mathematical modeling of microtubule assembly and polarity in dendrites"
The microtubule cytoskeleton is responsible for sustained, long-range transport of cellular cargo inside neurons. However, microtubules must also be dynamic and rearrange their orientation, or polarity, in response to injuries. While mechanisms that control the minus-end out microtubule orientation in Drosophila dendrites have been identified experimentally, it is unknown how these mechanisms maintain both dynamic rearrangement and sustained, long-term function of the cell. To better understand these mechanisms, we introduce a spatially-explicit mathematical model of dendritic microtubule growth dynamics using parameters informed by experimental data. We explore several hypotheses of microtubule growth using both a stochastic model and a continuum model, and use fluorescence microscopy experiments to validate mechanisms such as limited tubulin availability and catastrophe events that depend on microtubule length. By incorporating biological experiments, our modeling framework can uncover the impact of various mechanisms on the collective dynamics and polarity of microtubules in Drosophila dendrites.
• Shayne M. Plourde the Ohio State University (Molecular, Cellular, and Developmental Biology Program)
  "Asymmetric Centrosome Maturation in the Early C. elegans Embryo: Insights from Multi-scale Microscopy and Modeling"
Centrosomes are nucleus-associated organelles made up of a pair of tubular centrioles surrounded by a cloud of pericentriolar material. Centrosomes serve as the nucleation site for microtubule arrays that interact with motor proteins at the periphery of the cell which act together to position the nucleus prior to division. Proper positioning is especially important in asymmetric cell division, where daughter cells inherit unequal amounts of specific factors. How the two centriole pairs, and their centrosomes, are positioned is critically important to stem cell development and perturbations in this process can be observed in cancer metastasis. In the C. elegans first cell cycle, proper positioning of the centrosomes is required for the asymmetric division used to determine the germline lineage of cells. Previous work has shown an asymmetry in the microtubule arrays nucleated by the two centrosomes that set up these divisions. However, the functional origin of this asymmetry is unknown. Using in vivo data of the recruitment and recovery of GFP tagged AIR-1, a protein that localizes to centrosomes in the early C. elegans embryo, we parameterized a mathematical model of centrosome maturation. Analysis of a large set of parameters that fit our model to the in vivo data reveal that there are potential differences in the dynamics between the two centrosomes. Further, we tracked the inheritance of the oldest centrioles into the 4 cell stage and observed a potential age related inheritance pattern. The multi-scale microscopy and mathematical modeling together support our hypothesis that there is a previously uncharacterized asymmetry inside of the C. elegans centrosome that could be connected to cell fate decisions.

Organized by: James MacLaurin, Victor Matveev

• Martin Falcke Max Delbrück Center for Molecular Medicine (Mathematical Cell Physiology)
  "Modeling IP3-induced Ca2+ signaling based on its interspike interval statistics"
Inositol 1,4,5-trisphosphate (IP3) induced Ca2+ signaling is used by almost all eukaryotic cells. Recent research demonstrated its randomness on all structural levels and large cell variability of the average interspike interval (ISI). Nonetheless, we compile eight general properties of Ca2+ spiking common to all cell types and pathways investigated hitherto. Stimulation response relation and moment relation of ISI exhibit specific robustness properties. We suggest an analytic theory of Ca2+ spiking calculating the moments of the ISI distribution. It captures all general properties, their robustness properties, cell variability and pathway specific behavior. We explain cell variability by variability of channel cluster coupling by Ca2+-induced Ca2+ release and the number of clusters. We predict the relation between puff probability and agonist concentration, and [IP3] and agonist concentration. Pathway and cell type specific behaviour is explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the general properties.
• Greg Conradi Smith William & Mary (Applied Science / Neuroscience / CAMS Biomath)
  "Allosteric coupling and cycle kinetics of G protein-coupled receptor dimers"
Quantitative pharmacologists construct Markov chain models to give insight into the relationship between ligand concentration and the fraction of cell surface receptors in each of several molecular conformations. Pharmacologists use these stochastic models to understand the action of natural ligands and drugs on receptor-mediated cell responses. When receptors function as two or more similar protein subunits working in concert (i.e., homodimers or oligomers), receptor models must (i) account for symmetry, (ii) satisfy thermodynamic constraints, and (iii) properly account for subunit interactions (allostery) mediated by conformational coupling. The modeling framework that satisfies these three requirements will be explicated in the context of models of G protein-coupled receptors (GPCRs), such as metabotropic glutamate receptors, that function as multi-molecule signaling complexes. For equilibrium models of receptor dimers, this approach facilitates the inference of a parsimonious subset of allosteric interactions leading to conformational coupling and dependence of receptor subunits. I will also discuss progress on extending this framework to the analysis of non-equilibrium steady-state cycle kinetics of GPCRs (e.g., nucleotide exchange).
• Victor Matveev New Jersey Institute of Technology (Department of Mathematical Sciences)
  "Accuracy of deterministic vs. stochastic modeling of Ca2+-triggered vesicle fusion latency"
High degree of variability is a characteristic feature of synaptic neurotransmitter release, which is important to consider in our understanding and modeling of this fundamental physiological process. Although stochastic Ca2+ channel gating is one of the primary source of this variability, it can be implemented in a computationally inexpensive way in combination with deterministic simulation of the downstream Ca2+ diffusion and binding. Another fundamental reason for the high variability of synaptic response is that only a small number of Ca2+ ions enter the synaptic terminal through a single channel during an action potential. This fact entails large fluctuations due to Ca2+ diffusion and its binding to Ca2+ buffers and vesicle release sensors, leading to a widely-held view that solving continuous deterministic reaction-diffusion equations does not provide high accuracy when modeling Ca2+-dependent cell processes. However, several comparative studies show a surprising close agreement between deterministic and trial-averaged stochastic simulations of Ca2+ dynamics, as long as Ca2+ channel gating is not Ca2+-dependent. This result deserves careful investigation. In this talk I will present further analysis and comparison of stochastic and mass-action modeling of vesicle release, showing that the discrepancy between deterministic and stochastic approaches remains small even when only as few as 40-50 ions enter per single channel-vesicle complex. The reason for the close agreement between stochastic and mass-action simulations is that the discrepancy between the two approaches is determined by the size of the correlation between the local Ca2+ concentration and the state of the vesicle release sensor, rather than fluctuation amplitude. Whereas diffusion and buffering increases fluctuation size, the same processes appear to de-correlate fluctuations in Ca2+ concentration from fluctuations in Ca2+ sensor binding state. Finally, contrary to naïve intuition, the mass action / mean-field reaction-diffusion description allows an accurate estimate of the entire probability distribution of vesicle release latency (first-passage time), rather than providing information about trial-averaged quantities only. These results may help in the choice of appropriate and efficient tools for the modeling of this and other fundamental biochemical cell processes.
• Linh Huynh University of Utah (Mathematics)
  "Stochastic Cancer Cell Dynamics under Environmental Stress"
One reason cancer remains very difficult to eradicate is its remarkable adaptability to the environment. In this talk, I will discuss how stochasticity and collective behavior help cancer cells survive and adapt under environmental stress in two different contexts: (1) when ecological interactions between cells in a heterogeneous population facilitate cancer’s stochastic escape from drug treatments and (2) when inflammation in the tumor microenvironment facilitates stochastic tumor growth.

Organized by: Diana White

• Kelsey Gasior University of Notre Dame (Department of Applied and Computational Mathematics and Statistics)
  "Understanding the influence of cell-cell contact and TGF-β signaling on the epithelial mesenchymal transition in MCF7 breast carcinoma cells"
The epithelial mesenchymal transition (EMT) is a process by which epithelial cells lose their characteristic adhesion and gain the migratory properties associated with mesenchymal cells. Triggered by exogenous factors from the surrounding microenvironment, EMT produces phenotypic and behavioral changes that are maintained even after the cell migrates away from a tumor to form a metastasis. Within the complex system of intracellular signaling pathways associated with EMT, we identify a feedback loop between E-cadherin, a transmembrane protein involved in cellular adhesion, and Slug, a transcription factor associated with the mesenchymal phenotype. Here we present a simple mathematical model using ordinary differential equations (ODEs) that examines the relationship between E-cadherin and Slug during EMT in response to exogenous pro-epithelial (cell-cell contact) and pro-mesenchymal (TGF-β signaling) factors. A cell’s ability to maintain the mesenchymal phenotype after leaving the tumor microenvironment suggests that there is a bistable switch underlying EMT. We hypothesize that a bistable switch due to a loss of cell-cell contact is reversible, while a switch due to TGF-β activation is irreversible. This model shows how changes in the tumor microenvironment and intracellular changes via signaling pathways are closely linked and the loss of cell-cell contact and activation of the TGF-β must work together to allow some cells to undergo EMT. The results of this model for E-cadherin and Slug levels are then compared to the experimental data recently generated using MCF7 breast carcinoma cells. Experiments examined changes in cell-cell contact and exogenous TGF-β and data were gathered using qPCR, flow cytometry, and immunocytochemistry (ICC). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments but struggles to predict the expression of either factor in high confluence environments. Ultimately, this work establishes a framework for modeling the influence of multiple factors on EMT, while also highlighting the issues that arise when comparing experimental results to theoretical predictions.
• Ginger Hunter Clarkson University (Biology)
  "Investigating the rules of cell contact-mediated tissue patterning using the Drosophila peripheral nervous system"
The correct spatial organization of cell types within a tissue is critical for tissue development and homeostasis. The spot pattern of sensory bristles on the dorsal thorax of the fruit fly Drosophila Melanogaster is an example of a self-organizing tissue, and failure to form and organize sensory bristles leads to impaired function of the peripheral nervous system. Experimental and theoretical results support a role for cell protrusion based, contact mediated, signaling mechanisms in the spacing of sensory bristle precursors during patterning stages. Here, we present recent results from an RNAi-mediated genetic screen designed to identify these signaling mechanisms. An expected major phenotype of the RNAi screen is the disruption of the tissue-wide sensory bristle pattern. In order to facilitate our analysis, we have developed a quantitative, computational approach towards the classification of control and mutant spot patterns. Our approach involves the detection of sensory bristle precursors in a patterning tissue, followed by extraction of features that facilitate the reproducible measurement and detection of different bristle organizations. The results of these studies so far have identified a number of genes whose knockdowns result in defects in pattern formation. Furthermore our classification system has successfully been used to identify mutant spot patterns. We anticipate that results from our screen will identify new mechanisms of cell-cell communication during peripheral nervous system patterning, as well as new tools for the quantitative analysis of spot patterns in vivo.
• Veronica Ciocanel Duke University (Mathematics)
  "Modeling and data analysis for actin-myosin dynamics and organization"
Actin filaments are polymers that interact with myosin motor proteins and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of interacting proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the reproductive system of the roundworm C. elegans, we use an agent-based modeling framework to simulate interactions between actin filaments and myosin motor proteins inside cells. We develop techniques based on topological data analysis to understand time-series data extracted from these filament network interactions, as well as from fluorescence experiments. These measures allow us to compare the filament organization resulting from myosin motors with different properties. In particular, we have studied how different myosin motor proteins may interact to regulate various actin organizations, and provided insights into parameters that may regulate structures observed in vitro and in vivo.
• Diana White Clarkson University (Department of Mathematics)
  "Understanding the regulation of growth and shedding of disks in the rod cells of zebrafish"
Retinal photoreceptor cells, rods and cones, in the eye convert light energy into electrical signals that stimulate sight. In humans, peripherally located rods are important for night vision, while centrally located cones are responsible for daytime/color vision. Rods consist of a rod outer segment (ROS), inner segment, cell body and synaptic terminal. The ROS, consisting of stacked, discrete membraneous discs, undergoes a process of continuous renewal in which newly constructed discs are added at the base (growth) and the oldest discs are shed from the tip. In normal/healthy eyes, the ROS maintains a homeostatic length by balancing growth and shedding. How this balance is controlled is unknown. New experiments have shown that ROS, when made to grow faster with the growth factor rheb, do not accelerate shedding to offset increased growth. Here, we develop and analyze a model of ROS length control, to help provide insight into (1) normal cell dynamics, and (2) the overshoot of homeostatic length when rheb is added. A 3-D ODE model is used to describe the transitions of disks from compartments corresponding to disk addition at the base, disk translocation along the ROS when mature, and those disks that are shed and undergo phagocytosis.

Organized by: Laura F. Strube, Adam L. MacLean

• Tian Hong The University of Tennessee, Knoxville (Biochemistry & Cellular and Molecular Biology)
  "Diverse dynamical systems for understanding nongenetic heterogeneity of cells"
The phenotypic heterogeneity within cell populations, both signal-induced and self-generated, plays crucial roles in development, cancer progression, and drug resistance. However, our fundamental understanding of these phenomena at the dynamical systems level remains limited. Epithelial-mesenchymal transition (EMT) is one example of a cellular process that triggers heterogeneity-driving phenotypic changes. While multiple intermediate/hybrid EMT states have been observed in development and diseases, it is still unclear whether these intermediate states represent transient states for cells en route to M-like cells or stable phenotypes representing ordered attractors between E and M states. Our recent single-cell experiments with human mammary epithelial cells and analysis of published data have shown that both transient states and ordered attractors can explain intermediate EMT states. Additionally, our mathematical models of widespread RNA-decay regulatory networks have demonstrated that slow oscillations with diverging periods can drive self-generated heterogeneity in cell populations, achieving phenotypic diversity and multimodal gene expression patterns more robustly than commonly conceptualized multistability systems. This theoretical framework provides insight into the observations of heterogeneity in progenitor cells and cancer cells. In summary, our work has revealed diverse dynamical systems underlying nongenetic heterogeneity of cells, which were previously underappreciated.
• MeiLu McDermott University of Southern California (Department of Biology)
  "Characterizing Intermediate States of Epithelial-Mesenchymal Transition in Cancer through Single-Cell RNA Sequencing and Mathematical Modeling"
The epithelial-mesenchymal transition (EMT) is a primary biological mechanism of cancer metastasis, involving cells transforming from an adhesive epithelial phenotype to a migratory mesenchymal phenotype. Recent research has identified intermediate EMT states, characterized by hybrid phenotypes experimentally shown to be metastatic. This comparative study investigates these hybrid EMT cells across multiple cancers using single-cell RNA sequencing data. We identified genes upregulated in multiple intermediate EMT states across cancers, particularly those related to β-catenin regulation. Additionally, we developed a mathematical model using ordinary differential equations (ODEs) to describe EMT rates and fitted the model to scRNAseq data. Incorporating data from multiple cancer types, our ODE model provides a discovery tool for identifying genes associated with stabilizing the existence of metastatic, hybrid EMT cells.
• Ken J. Oestreich The Ohio State University School of Medicine (Microbial Infection and Immunity)
  "Regulation of T helper cell programming by the transcription factor Aiolos"
CD4+ cytotoxic T lymphocytes, or CD4-CTLs, comprise an effector subset capable of performing cytotoxic functions normally associated with CD8+ T and Natural Killer cells. CD4-CTLs play critical roles in many immunological contexts, including protective anti-viral responses to influenza infection. Despite their well-documented importance to healthy immune responses, the regulatory mechanisms that underlie their formation remain unclear. We have identified the Ikaros transcription factor Aiolos as a novel repressor of cytoxic programming in CD4 T cells. We demonstrate that Aiolos deficiency results in increased CD4-CTL responses in the lungs of influenza-infected mice, as assessed by elevated expression of Granzyme B and Perforin, as well as the CTL marker NKG2A/C/E. We further find that Aiolos-deficient CD4-CTLs exhibit increased expression of transcription factors associated with cytotoxic programming, including Eomes and Blimp-1. Mechanistically, we demonstrate that Aiolos-deficient cells have a heightened sensitivity to IL-2/STAT5 signaling due to enhanced expression of the IL-2 cytokine receptor and that this translates into increased STAT5 association at regulatory regions of hallmark CD4-CTL genes. Intriguingly, the STAT5 motif partially overlaps with that of the core Aiolos DNA binding motif, suggesting that Aiolos may function to broadly antagonize STAT5 activity throughout the genome. Collectively, this work establishes Aiolos as a novel repressor of CD4-CTL differentiation and highlights its potential as a therapeutic target for enhancing anti-viral immune responses.
• Rachel A. Gottschalk University of Pittsburgh (Department of Immunology)
  "Modeling cytokine-induced signaling features and sensitivity to network variation"
Cells choose environment-specific functions by integrating stimuli through biochemical signaling pathways. Predicting functional outcomes of signaling is complicated by the complexity of network interactions and the diversity of signals which converge on a relatively small number of intracellular components. For example, over 50 cytokines and growth factors are distinguished by the JAK/STAT signaling pathways, comprised of 4 JAKs (Janus kinases) and 7 STATs (signal transducers and activators of transcription), to produce stimulus-specific cellular functions. In many cases, opposing phenotypes (pro- vs. anti-inflammatory) depend on the same STAT proteins to induce distinct patterns of gene expression. Predicting the relationship between signaling conditions and STAT phosphorylation profiles and then linking them to downstream gene expression remains an unaddressed challenge. We have developed a mechanistic-to-machine learning computational workflow that links STAT phosphorylation trajectories to global gene expression patterns via an ODE-simulated, rule-based model and machine learning. Our model is parameterized with STAT phosphorylation data from IL-6 and IL-10 stimulated macrophages. Machine learning is used to link these profiles to transcriptomic data under the same stimulation conditions. Parameter analysis of our mechanistic model identified JAK2 as having STAT-specific impacts on dynamic signaling features. Using the full computational workflow, we predicted and validated the impact of selective JAK2 inhibition on downstream gene expression and identified clusters of dynamically regulated genes that were sensitive and insensitive to JAK2 alterations. Thus, this work is an important step towards the use of multi-level prediction models to link stimuli to gene expression and to identify the effect of network perturbations. We are currently exploring sensitivity analysis approaches to derive biological insight from quantitative parameter relationships, with an interest in predicting parameters and parameter ratios that are highly sensitive to variation. Our objective is to enhance our understating of how altered expression of signaling network components impacts cellular responsiveness to cytokines and JAK inhibition in physiologically and clinically relevant contexts, such as cancer and human genetic variation.

Organized by: Wing-Cheong Lo, Weitao Chen, Wenrui Hao, Leili Shahriyari
Note: this minisymposia has multiple sessions. The other session is MS07-CDEV-1.

• Han-Wei Shen The Ohio State University (Computer Science and Engineering)
  "Neural Network Assisted Visual Analysis of yeast simulation data"
In the field of simulation sciences, a popular and effective strategy to address the challenges of high computational and storage costs is to create a simpler statistical/mathematical surrogate, mimicking the original expensive simulation mode. The surrogate is then utilized to perform detailed analysis tasks instead of the expensive simulation model. In this talk, I will describe collaborative research with Prof. Chou in which we designed an interactive visual analysis framework, backed by a neural network-based surrogate model, to assist in analyzing and visualizing a complex yeast cell polarization simulation model. The model simulates the concentration of important protein molecules along the membrane of a yeast cell (single-cell microorganism) during its mating process. The simulation model comprises 35 uncalibrated input parameters and generates a 400-dimensional output. we demonstrate the advantage of using neural networks as surrogate models for visual analysis by incorporating some of the recent advances in the field of uncertainty quantification, interpretability and explainability of neural network-based models. We utilize the trained network to perform interactive parameter sensitivity analysis of the original simulation at multiple levels-of-detail as well as recommend optimal parameter configurations using the activation maximization framework of neural networks. We also facilitate analysis of the trained network to extract useful insights about the simulation model, learned by the network, during the training process.
• Yutong Sha & Qing Nie University of California, Irvine (Department of Mathematics)
  "Reconstructing transition dynamics from static single-cell genomic data"
Recently, single-cell transcriptomics has provided a powerful approach to investigate cellular properties in unprecedented resolution. However, given a small number of temporal snapshots of single-cell transcriptomics, how to connect them to obtain their collective dynamical information remains an unexplored area. One major challenge to connecting temporal snapshots is that cells measured at one temporal point may divide at the next temporal point, leading to growth and differentiation in the system. It’s increasingly clear that without incorporating cellular growth dynamics, the inferred dynamics often becomes incomplete and less accurate. To fill these gaps, we present a novel method to reconstruct the growth and dynamic trajectory simultaneously as well as the underlying gene regulatory networks. A deep learning-based dynamic unbalanced optimal transport is developed to infer interpretable dynamics from high-dimensional datasets.
• Weitao Chen University of California, Riverside (Department of Mathematics)
  "A Mechanochemical Coupled Model to Understand Budding Behavior in Aging Yeast – An extension of Prof. Ching-Shan Chou’s work"
Cell polarization, in which a uniform distribution of substances becomes asymmetric due to internal or external stimuli, is a fundamental process underlying cell mobility and cell division. Budding yeast provides a good system to study how biochemical signals and mechanical properties coordinate with each other to achieve stable cell polarization and give rise to certain morphological change in a single cell. Recent experimental data suggests yeast budding develops into two trajectories with different bud shapes as mother cells become old. We first developed a 2D model to simulate biochemical signals on a shape-changing cell and investigated strategies for robust yeast mating. Then we extended and coupled this biochemical signaling model with a 3D subcellular element model to take into account cell mechanics, which was applied to investigate how the interaction between biochemical signals and mechanical properties affects the cell polarization and budding initiation. This 3D mechanochemical model was also applied to predict mechanisms underlying different bud shape formation due to cellular aging.
• Xinfeng Liu University of South Carolina (Mathematics)
  "Data-driven mathematical modeling, computation and experimental investigation of dynamical heterogeneity in breast cancer"
Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are a highly tumorigenic cell type found in developmentally diverse tumors that are believed to be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence. Thus understanding the tumor growth kinetics is critical for development of novel strategies for cancer treatment. For this talk, I shall introduce mathematical modeling to study Her2 signaling for the dynamical interaction between cancer stem cells (CSCs) and non-stem cancer cells, and our findings reveal that two negative feedback loops are critical in controlling the balance between the population of CSCs and that of non-stem cancer cells. Furthermore, the model with negative feedback suggests that over-expression of the oncogene HER2 leads to an increase of CSCs by regulating the division mode or proliferation rate of CSCs.

Organized by: Wanda Strychalski, Alexander Hoover
Note: this minisymposia has multiple sessions. The other session is MS07-CDEV-2.

• Wanda Strychalski Case Western Reserve University (Mathematics, Applied Mathematics, and Statistics)
  "Quantifying the role of fluid mechanics during confined cell migration"
Cell migration is critical for many vital processes, such as embryogenesis and tissue repair, as well as harmful processes, such as cancer cell metastasis. In experiments, cells have been shown to exhibit different migration strategies based on the properties of their external environment. Here, we leverage modeling and computational tools to reveal the step-by-step cycle of locomotion for cells in confined environments that use blebs as leading-edge protrusions. We present two models of a blebbing cell migrating in a confined microchannel to quantify the role of hydrodynamics on confined cell migration. One model consist of a cell modeled by an elastic membrane, poro-(visco)elastic cortex, membrane-cortex adhesion, and the fluid cytoplasm. The fluid-free model consists of a force balance that includes the cell membrane, cortex, membrane-cortex adhesion, and viscous drag with outside environment. The channel walls are modeled as rigid structures. The fluid model is formulated using the method of regularized Stokeslets. Results show that cells can effectively migrate only if the cortical turnover is included by modeling the cortex as a poro-viscoelastic structure. We also show that blebbing generates a favorable intracellular pressure gradient that aids migration in the fluid model.
• Jared Barber Indiana University-Purdue University Indianapolis (Mathematical Sciences)
  "A 2D model to assess stresses on flexible osteocytes and the influence of elastic properties"
Osteocyte are cells residing deep in bone that are widely believed to play a key role in regulating bone growth by sensing and responding to forces as we use our bodies daily. Despite several experimental and theoretical studies providing strong support for this paradigm, there are still several uncertainties surrounding the process by which the cells turn those forces into usable biochemical signals. For instance, studies suggest that to initiate any appreciable response from osteocytes, the average stresses we typically experience on a macroscale level must multiplied at least tenfold as they make their way towards the microscale level. In addition, there are several parts of the osteocyte that have been theorized to play a role in the mechanotransduction process. To help understand how forces may be magnified in and near the osteocyte region and which parts of the cell are more likely to be the location of subcellular mechanosensors, we have produced a two-dimensional model of a flexible osteocyte. The cell is represented by a network of interconnected viscoelastic elements (damped springs) immersed in interstitial flow that is, in turn, encased in rigid bone matrix material. We utilize a lattice-Boltzmann method combined with the immersed boundary method to produce simulations that allow us to explore the force distributions experienced by such cells. We share our results including pictures of where forces seem to centralize in such systems as well as how the elastic properties of different parts of the cell affect force localization in both steady state and oscillatory regimes.
• Thomas Fai Brandeis University (Mathematics)
  "Lubricated Immersed Boundary Method with Application to Fiber Bundles"
Fluid-mediated near contact of elastic structures is a recurring theme in biofluids. The thin fluid layers that arise in applications such as the flow of red blood through blood vessels are difficult to resolve by standard computational fluid dynamics methods based on uniform fluid grids. A key assumption of the lubricated immersed boundary method, which incorporates a subgrid model to resolve thin fluid layers between immersed boundaries, is that the average velocity of nearby boundaries can be accurately computed from under-resolved simulations to bridge between different spatial scales. Here, we present a one-dimensional numerical analysis to assess this assumption and quantify the performance of the average velocity as a multiscale quantity. We explain how this analysis leads to more accurate formulations of the method and present examples from two-dimensional simulations, including applications to filament bundles.
• Luoding Zhu Indiana University - Purdue Univiersity Indianapolis (Mathematics)
  "Computational modeling of stress/strain amplification of an osteocyte process interacting with a viscous flow in a 3D canaliculus"
Computational modeling of stress/strain amplification of an osteocyte process interacting with a viscous flow in a 3D canaliculus Jared Barber (1), Maxim Mukhin (2), Vanessa Maybruck (3), Luoding Zhu (4) 1. Indiana University – Purdue University Indianapolis, USA; 2. Vanderbilt University, USA; 3. University of Colorado Boulder, USA; 4. Indiana University – Purdue University Indianapolis, USA. Osteocytes are bone cells stationed in fluid-filled cavities (lacunae) within hard bone matrix. Each osteocyte is equipped with numerous finger-like structures (processes) radiating outwards through cylindrical openings (canaliculi). Osteocytes are responsible for mechanosensation in the body; however, the tissue level stress and strain needs to be amplified at least 10 times in order for osteocytes to respond on the cellular level. The mechanism for such magnification is not yet fully understood. Previous studies suggest that the processes are primary sites for mechanosensation thanks to the existence of tethering elements attaching the process membrane to the canalicular wall. However, other studies suggest that potential contributing factors may also include the canalicular wall geometry and pericellular matrix. In our work, computational modelling, based on the lattice Boltzmann immersed boundary framework, is designed and used to assess possible effects of canalicular wall roughness in stress/strain amplification and the underlying mechanism. Our results indicate that canalicular wall roughness contributes substantially to stress and strain amplification and the underlying reason is the increased resistance to flow induced by wall roughness. Acknowledgements This work was supported by grants DMS-1951531 and DMS-1852146 from NSF USA and SoS Near-Miss Grant from IUPUI.

Organized by: Wing-Cheong Lo, Weitao Chen, Wenrui Hao, Leili Shahriyari
Note: this minisymposia has multiple sessions. The other session is MS06-CDEV-1.

• Arthur D. Lander University of California Irvine, Irvine, CA (Center for Complex Biological Systems, and Department of Developmental and Cell Biology)
  "Control and Stability in Proliferative Dynamics"
The control of cell proliferation—the central process in creating, maintaining, and regenerating tissues of defined sizes and shapes—is a tricky business, because proliferation is fundamentally autocatalytic, and therefore prone to instability. Yet multicellular organisms achieve great feats of speed, precision, and stability in the production and maintenance of tissues. Moreover, they do so in the face of considerable stochasticity in the outcomes of cell divisions. Experimental studies have identified generic strategies—all based on some form of collective integral feedback—that can be shown, mathematically, to achieve many of these control objectives. However, the reliance of such strategies on cell-cell interaction creates fragilities, arising from limits on the distances over which intercellular signals spread; limits on the time scales over which perturbations can be managed; and situational ultrasensitivity to stochastic fluctuations. I will discuss the tradeoffs these fragilities impose, and how they influence what control organisms can achieve safely. I will raise the possibility that such fragilities create opportunities for rare, stochastic progression to states of uncontrolled growth, i.e., cancer, and suggest that such transitions provide a better model for cancer initiation than current models based on genetic determinism.
• Dongbin Xiu Ohio State University (Department of Mathematics)
  "Data driven modeling of partially observed biological systems"
We present a framework of flow map learning (FML) for predictive modeling of unknown dynamical systems from measurement data, with applications to biological systems. The method is designed to discover the flow map operator behind the data and utilize deep neural network (DNN) as the main numerical technique for the discovery. Once an accurate DNN model for the flow map is constructed, it serves as a predictive model for the unknown system and enables us to conduct long-term system prediction and analysis. The FML framework is highly versatile, as it allows one to construct accurate models when only a limited subset of the system parameters and state variables are observed.
• Tau-Mu Yi University of California, Santa Barbara (Molecular, Cellular, and Developmental Biology)
  "Systems Biology of Cell Polarity in Yeast"
Gradient sensing and response is a basic cellular behavior. Cells sense a chemical gradient and then respond by moving or projecting up the gradient. During this process of breaking symmetry, protein components localize to the front (or back) of the cell resulting in cell polarity. In this work, we characterized an information measure for cell polarity that applies to non-motile cells responding to a chemical gradient. The central idea is that polarization represents information about the direction of the gradient. Building upon previous work in the literature, we applied a theory of optimal gradient sensing and response in the presence of external noise based on the information capacity of a Gaussian channel. We compared the theory to experimental data on yeast mating projection growth in a pheromone gradient and demonstrated that slow ligand binding to receptor is the limiting factor in yeast gradient sensing. Finally, we showed that temporal averaging can help overcome the slow binding rate to achieve greater accuracy but resulting in a slow mating response.
• Avner Friedman Ohio State University (Department of Mathematics)
  "How breast cancer metastasize into the bone"
Bone marrow is a “fertile soil” for growth and proliferation of cancer cells. But in order to metastasize into the bone, breast cancer cells first need to degrade and weaken the hard layer at the bone surface. To facilitate this process they secret, sometime in advance, organelles (called exosomes) that contain DNA, mRNA , microRNA and proteins. It is now known that some of the microRNAs destroy the balance between bone formation and bone resorption, which results in bone lesions, and allow cancer cells to penetrate into the bone interior. In this talk I shall describe this process by a mathematical model, and introduce drugs that can increase bone density to the normal level and thus may protect the bone from invasion by cancer cells. This work is jointly with Nourridine Siewe.
• Chiu-Yen Kao Claremont McKenna College (Mathematical Sciences)
  "Our math and biology journey: A tribute to Ching-Shan Chou"
In this talk, I will bring you to a time machine ride to get to know Professor Ching-Shan Chou’s background, interests that we shared, and work that we had done together. In particular, highlight book projects, common interests, research works on propagation of cutaneous thermal injury, vibration of rods and plates, and fast sweeping methods for steady state problems for hyperbolic conservation laws.

Organized by: Wanda Strychalski, Alexander Hoover
Note: this minisymposia has multiple sessions. The other session is MS06-CDEV-2.

• Hongfei Chen Tulane University (Department of Mathematics)
  "Effects of Choanoflagellate Colony Shape on Hydrodynamic Performance"
Choanoflagellates are believed to be the closest animal relatives and are considered important in the study of animal tissue evolution. In their preferred environment, these microorganisms form a relaxed colony with flagella pointing-inward. However, when conditions become unfavorable, they contract and invert the colony, causing the flagella to point outward. Our proposed coarse model produces the same averaged far field flow as a single cell, and we use it to analyze the feeding and swimming behaviors of the two different colonies.
• Nigar Karimli Indiana University-Purdue University Indianapolis (Mathematics)
  "A three-dimensional mathematical model of a viscoelastic osteocyte immersed in flow"
Osteocytes make up 90-95% of all bone cells in an adult skeleton and are responsible for regulating bone remodeling through mechanotransduction (how the cells sense and convert mechanical signals into biochemical signals). In order to better understand the localization of forces on and around an osteocyte, which is essential for understanding mechanotransduction, we have developed a 3D mathematical model of an osteocyte and its interaction with surrounding flow. Our model includes the cell modeled as an interconnected network of viscoelastic elements. We have incorporated forces to model non-negligible bending rigidity, total and local area conservation of the membrane, and total volume conservation. We calculate these solid forces from the corresponding energy functions using the principle of virtual work. Additionally, we use the lattice-Boltzmann method (D3Q19) to model the flow in and around the osteocyte, and the immersed boundary method to handle fluid-structure interactions. After verifying proper model implementation, we have been able to produce simulations of an idealized ellipsoidal osteocyte immersed in flow and advecting along a channel. The model produces estimates for the typical motion and forces experienced by the osteocyte. In preparation for comparing our model with collaborators’ experiments involving stationary cells subjected to shear flow in a channel, we have also investigated and will share typical cellular dynamics that result when the cell is additionally anchored to an underlying surface.
• Sharon R. Lubkin North Carolina State University (Mathematics)
  "Geometry, pattern, and mechanics of notochords"
Chordocytes, in early zebrafish and other teleost notochords, have been shown to pack in a small number of stereotyped patterns. Mutations or treatments which disrupt the typical patterning are associated with developmental defects, including scoliosis. The dominant WT “staircase” pattern is the only regular pattern displaying transverse eccentricity. Morphometry and pattern analysis have established a length ratio governing which patterns will be observed. Physical models of cell packing in the notochord have established relationships between this geometric ratio, a mechanical tension ratio, the transverse aspect ratio, pattern, pressure, and taper. Since a major function of the early notochord is to act as both a column and a beam, we aim to understand the overall resistance to compression and bending in terms of these mesoscale cell/tissue properties. To frame the relationships between these properties, we have developed a model of the notochord as an elastic closed-cell foam, packed in either the “staircase” or “bamboo” pattern. A pressure study reveals a surprising lack of shape change as internal notochord pressure is varied, and determines the tension ratio between different surfaces in the notochord in terms of the relative stiffnesses and internal pressure. A bending study reveals that deformations of the model notochords are well described by classical beam theory, and determines the flexural rigidity of the model notochords in terms of relative stiffnesses and pressure. We find that the staircase pattern is more than twice as stiff as the bamboo pattern. Moreover, the staircase pattern is more than twice as stiff in lateral bending as in dorsoventral bending. This biomechanical difference may provide a specific developmental advantage to regulating the cell packing pattern in early-stage notochords.
• Kendall Gibson Tulane University (Mathematics)
  "Modeling the elastohydrodynamics of swimming choanoflagellates"
Choanoflagellates are aquatic single-cell microswimmers that prey on bacteria, and they are of interest in the study of the origins of multicellularity due to their ability to form large colonies. Structurally, they consist of a cell body, a flagellum, and a collar of microvilli. Our model treats the flagellum and the microvilli as elastic Kirchhoff rods whose shapes may be altered due to fluid-structure interactions. In addition to understanding the effect of compliance of these structures on the swimming of a single organism, we aim to study the hydrodynamic interaction of two choanoflagellates and how the collars might affect synchronization of the flagella.

• David Holloway British Columbia Institute of Technology
  "Size regulation of the lateral organ initiation zone and its role in determining cotyledon number in conifers"
Unlike most flowering plants, which have one or two cotyledons (embryonic leaves), many conifers form three or more cotyledons. These are arranged in a whorl, or ring, at a particular distance from the embryo tip. The number of cotyledons, nc, varies substantially within species, even in clonal cultures. nc variability reflects embryo size variability, with larger diameter embryos having higher nc. The radius of the whorl varies over three-fold for the naturally observed range of nc. In the model plant Arabidopsis, the initiation zone for leaf primordia occurs at a minimum between inhibitor zones of HD-ZIP III at the shoot tip and KANADI (KAN) encircling this farther from the tip. A similar mechanism is indicated in conifer embryos by the effects of overexpression of HD-ZIP III inhibitors on cotyledon formation. We developed a PDE model of HD-ZIP III / KAN spatial localization and used this to characterize the molecular regulation that could generate (a) the three-fold whorl radius variation (and associated nc variability) observed in conifer cotyledon development, and (b) the HD-ZIP III and KAN shifts induced experimentally in conifer embryos and in Arabidopsis. The model was used to find the sensitivity of mechanism components for positioning lateral organs (cotyledons or leaves) closer to or farther from the tip. Positional shifting is most readily driven by changes to the spatial extent of upstream regulator patterns and changes in HD-ZIP III / KAN mutual inhibition, and less efficiently driven by changes in upstream dosage or the activation kinetics of HD-ZIP III. Sharper expression boundaries can also be more resistant to shifting than shallower expression boundaries. The strong variability in whorl size reflected in conifer nc (commonly from 2 to 10) may indicate a freer variation in regulatory interactions, whereas flowering plants, with nc = 1 or 2, may require tighter control of such variation. The variability in conifer whorl size may have similarities to spatial scaling in fly embryos in which gene expression pattern variation compensates for embryo length variability. The model provides a framework for quantitative experiments on the positional control of lateral organ initiation. This could further understanding of the factors that control the leaf arrangements, or phyllotaxy, characteristic of species.
• Merlin Pelz University of British Columbia
  "The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-D"
Since Alan Turing’s pioneering publication on morphogenetic pattern formation obtained with reaction-diffusion (RD) systems, it has been the prevailing belief that two-component reaction diffusion systems have to include a fast diffusing inhibiting component (inhibitor) and a much slower diffusing activating component (activator) in order to break symmetry from a uniform steady-state. This time-scale separation is often unbiological for cell signal transduction pathways. We modify the traditional RD paradigm by considering nonlinear reaction kinetics only inside compartments with reactive boundary conditions to the extra-compartmental space which diffusively couples the compartments via two species. The construction of a nonlinear algebraic system for all existing steady-states enables us to derive a globally coupled matrix eigenvalue problem for the growth rates of eigenperturbations from the symmetric steady-state, on finite domains in 1-D and 2-D and a periodically extended version in 1-D. We show that the membrane reaction rate ratio of inhibitor rate to activator rate is a key bifurcation parameter leading to robust symmetry-breaking of the compartments. Illustrated with Gierer-Meinhardt, FitzHugh-Nagumo and Rauch-Millonas intra-compartmental reaction kinetics, our compartmental-reaction diffusion system does not require diffusion of inhibitor and activator on vastly different time scales. Bifurcation theoretic results for symmetric and asymmetric steady-state patterns obtained from our asymptotic theory are confirmed with full numerical PDE simulations. Our results reveal a possible simple mechanism of the ubiquitous biological cell specialization observed in nature.
• Renee Dale Donald Danforth Plant Science Center
  "Competition for resources during semi-sequential growth of developmental units drive allometric patterns in the grass Setaria"
Resource allocation drives the above-ground distribution of mass in grass plants across discrete developmental units called phytomers. Although the number of phytomers varies in genetically-identical grasses, plants with relatively more phytomers may not exhibit an increase in total biomass or height. To understand what may be driving this, we tracked the growth of 30 S. italica plants from genotypes B100 and A10.1. We experimentally observed that plants from the genotype B100 had between 20 and 22 phytomers, while plants from the genotype A10.1 had between 7 and 9 phytomers. B100 plants with more phytomers (e.g., 22) did not grow taller or have more total leaf length, despite having more leaves than plants with fewer phytomers (e.g., 20). A10.1 plants with more phytomers (e.g., 9) did grow taller and had more total leaf length than those with fewer phytomers (e.g., 7). We developed a dynamical model to determine if these patterns are emergent from the underlying growth structure. The model is parameterized using the number of phytomers and related developmental time parameters: leaf emergence, stem and leaf elongation time, and time of panicle emergence. The model uses the semi-sequential nature of phytomer growth as its structure. The model predicts that the number of phytomers, the length of time each phytomer grows, and the shift to reproductive growth determines the allometric patterns. Together, model and data suggest that allometric patterns are driven by competition for resources between phytomers and the shift to reproductive growth in Setaria. These results are further developed using 5 additional Setaria genotypes, and through exploration of predicting developmental time parameters from growth curves obtained in high-throughput.
• Samantha Ivings University of Sheffield
  "Connecting abstract maths to cell biology: A novel vertex model for predicting pluripotent stem cell lineage decisions, capturing cell symmetries through internal node dynamics"
Human pluripotent stem cells (hPSCs) are vastly promising for regenerative medicine, as they can self-renew indefinitely in vitro and become any cell type in the human body. Therefore, patients with damaged or lost tissue could be effectively treated by growing hPSCs into the required cell type for treatment. Unfortunately, how hPSCs make lineage decisions remains poorly understood. The process by which hPSCs acquire lineage is called differentiation, and a cell’s progress along this journey can be measured by its expression levels of genetic markers. At present, allowing cells to freely differentiate yields seemingly heterogeneous lineage patterning across unconstrained cultures. A ground-breaking study by Warmflash et al. (2014) showed that differentiating hPSCs spatially confined on discs yields reproducible lineage patterning across the cell culture, in the form of concentric rings. Later, Muncie et al. (2019) demonstrated reproducible patterning by differentiating hPSCs on a wider range of controlled geometries. How single hPSCs orchestrate these phenomena remains an interesting question. In this work, a novel cell-level modelling approach is proposed for explaining lineage patterning on controlled culture geometries. An undirected vertex model is introduced, where nodes represent single hPSCs. Cells are ‘neighbours’, and therefore share an edge, if their membranes are in contact. Nodes have internal dynamics in the form of an ordinary differential equation system, representing gene networks. These dynamics capture novel symmetry relations between nodes. Mimicking cell morphology in vitro, each node is represented by a Voronoi object which together tile the simulated geometry. Simulations of cell equilibria recapitulate experimental results, supporting that culture geometries may be designed to control lineage at low expense. The model is further developed by initialising a single cell with stochastic division until the culture is fully populated. Tracking the trajectory of each cell’s dynamics is hoped to provide insight into how different lineage paths are explored before each cell fully commits in the robust process of embryogenesis.

• Amanda M. Alexander University of Houston
  "Mathematical Models of Plasmid Partitioning and Loss in Dividing Cell Populations"
Plasmid DNA is common in bacterial populations and is used by synthetic biologists to alter the genetic makeup, and therefore function, of cells. At each cell division in a plasmid containing population, there is a probability of plasmid loss, giving rise to a differentiated population. The plasmid loss rate is difficult to measure, because it is small and quickly overshadowed by exponential growth of the subsequent plasmid free population. In addition, biologists observe complex intracellular plasmid dynamics, involving 1) formation of plasmid clusters that reduce plasmid diffusion, 2) plasmid localization to cell poles, and 3) plasmid replication with negative feedback. Mathematical models are useful in understanding how the plasmid loss rate is determined by these dynamics, but no previous works have incorporated this level of mechanistic detail. We will discuss simulation studies on the influence of the three mechanisms on the probability of plasmid loss, and under what conditions these effects can be captured by tractable mathematical models.
• Joseph Pollacco University of Oxford
  "Predicting the effects of antibiotics on the bacterial SOS response"
Many types of antibiotics are believed to cause DNA damage in bacteria. The bacterial SOS response is known to promote bacterial survival during antibiotic treatment by inducing the expression of proteins that repair DNA damage. However, the mechanisms by which antibiotics generate DNA damage and trigger the SOS response remain unclear. Here, we propose a delay differential equation model that predicts the temporal dynamics of the SOS response, under action of ciprofloxacin, a DNA-damaging antibiotic. We calibrate the model using ABC-SMC, with data from time-resolved single-molecule and single-cell microscopy experiments. The model allows us to grants insight into how antibiotic treatments induce complex cell behaviour, such as temporal variation and cell-to-cell heterogeneity in the SOS response.
• Kieran Boniface University of Surrey
  "Mechanotransduction in organoid development"
Organoids, mini engineered tissues, have become increasingly popular in recent years1. Indeed, we are experiencing an explosion of interest in organoids as three-dimensional test beds for biological experiments due to their complex structure and ability to mimic in-vivo tissues2. As a result, work must be done to accurately grow and develop organoids. However, the development of organoids, like all biological tissues, is sensitive to the mechanical signals that can influence behaviour from cell growth to determining cell type and shape3. These mechanical cues can even override biochemical signalling in directing type specification of stem cells4. This is made more complex in multicellular structures where mechanical signals operate over multiple length scales. Thus, mathematical models can provide an elegant framework to shed light on the underlying mechanics. One class of models are those founded in a consideration of continuum elasticity5 as applied to soft tissue mechanics, providing the opportunity to investigate the role of key mechanical factors6. The challenge is to produce models that can capture the active behaviour of cells and their ability to generate force as well as to describe the passive mechanical interactions of the system. We present here a model that captures key force generating mechanisms of organoids, namely cell contractility and cell growth. We describe the interaction between contractility and tissue growth and how their antagonistic behaviour can introduce key mechanical signals that may influence behaviour. As a final step, we consider the potential mechanisms by which mechanical feedback into cell control can be incorporated into our model and the impact this will have. References 1. Schutgens, F. & Clevers, H. Human Organoids: Tools for Understanding Biology and Treating Diseases. https://doi.org/10.1146/annurev-pathmechdis-012419-032611 15, 211–234 (2020). 2. Kim, J., Koo, B. K. & Knoblich, J. A. Human organoids: model systems for human biology and medicine. Nature Reviews Molecular Cell Biology vol. 21 571–584 Preprint at https://doi.org/10.1038/s41580-020-0259-3 (2020). 3. Orr, A. W., Helmke, B. P., Blackman, B. R. & Schwartz, M. A. Mechanisms of Mechanotransduction. Dev Cell 10, 11–20 (2006). 4. Engler, A. J., Sen, S., Sweeney, H. L. & Discher, D. E. Matrix Elasticity Directs Stem Cell Lineage Specification. Cell 126, 677–689 (2006). 5. Taber, L. Alan. Nonlinear theory of elasticity applications in biomechanics. Nonlinear theory of elasticity applications in biomechanics (World Scientific). 6. Littlejohns, E. & Dunlop, C. M. Mechanotransduction mechanisms in growing spherically structured tissues. New J Phys 20, 043041 (2018).

• Adriana Zanca The University of Melbourne
  "Comparison of locally and globally acting wound closure mechanisms"
Epidermal wound closure is a complex process involving the coordination of many mechanisms across multiple spatial scales. In this work we use cell-based modelling to investigate wound closure mechanisms acting on whole-wound and localised scales. We begin by exploring spatial effects on wound closure - specifically tissue compression due to cell division events and individual cellular compression. We then consider two key wound healing mechanisms: purse-string closure and cell crawling. The purse-string mechanism involves contraction of the acto-myosin cables in cells adjacent to the wound edge whereas the cell crawling mechanism describes active cellular migration due to lamellipodial protrusions. Previous cell-based models of wound healing have attempted to describe the purse-string mechanism at a cellular level scale. However, it has been established that purse-string behaviour occurs on a whole-wound scale. In particular, an actomyosin cable forms around the entire wound edge and contracts ‘globally’ during closure. In this work, we formulate a wound-scale model for purse-string closure and compare it to a locally acting model. Finally, we propose two models for cell crawling: one where cells respond to their local environment and another in which cells actively migrate in response to a global cue. We compare the two models and discuss the relative benefits of each. We conclude by summarising the overall differences between globally and locally acting mechanisms and propose more realistic extensions of each model.
• Gordon R. McNicol University of Glasgow
  "A one-dimensional continuum model for focal adhesion and ventral stress fibre formation"
To function and survive, cells need to be able to sense and respond to their local environment in a process called mechanotransduction. Crucially, mechanical and biochemical perturbations to a cell can initiate signaling cascades which can induce, among other responses, cell growth, apoptosis, proliferation and differentiation - focal adhesions and actomyosin stress fibres are at the heart of this process. The formation and maturation of these structures (connected by a positive feedback loop) is pivotal in non-motile cells, where stress fibres are generally of ventral type, interconnecting focal adhesions and producing isometric tension. We have formulated a one-dimensional bio-chemo-mechanical continuum model to describe the coupled formation and maturation of ventral stress fibres and focal adhesions. We use a set of reaction-diffusion-advection equations to describe three sets of biochemical events: the polymerisation of actin and bundling and activation of the resultant fibres; the formation and maturation of adhesions between the cell and substrate; and the upregulation of certain signaling proteins in response to focal adhesion and stress fibre formation. The evolution of these key proteins is then coupled to a Kelvin-Voigt viscoelastic description for the cell cytoplasm and for the ECM. We employ this model to understand how cells respond to external and intracellular cues in vitro. We are able to replicate various experimentally observed phenomena including demonstrating that stress fibres exhibit non-uniform striation, cells form weaker stress fibres and focal adhesions on compliant surfaces and myosin II inhibition leads to disruption of focal adhesions. The model hence provides a platform for systematic investigation into how the cell biochemistry and mechanics influence the growth and development of the cell and facilitates prediction of internal cell measurements that are difficult to ascertain experimentally, such as stress distribution.
• Kaiyun Guan University of North Carolina at Chapel Hill
  "How do yeast regulate polarity behavior to ensure successful mating?"
Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called the polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site often misaligns with the pheromone gradient. Therefore, to track pheromone gradients requires reorientation of the polarity site. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior as it moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are insufficient to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Inclusion of a pheromone-sensing pathway that acts over longer time scales than the pathways associated with the core polarity circuit generated a mobile polarity site with properties similar to those observed experimentally. This sensing pathway couples polarity establishment to the gradient sensing and, surprisingly, it also has a positive feedback architecture because polarity factors direct secretion of new pheromone receptors to the cell membrane. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.
• Sharon B. Minsuk Indiana University, Bloomington
  "Modeling the Mechanical Forces Driving Epithelial Morphogenesis and Cell Rearrangement during Zebrafish Epiboly"
Epithelial shape change is of major importance in early development across the animal kingdom. Using a new particle-based simulation framework, Tissue Forge (https://compucell3d.org/TissueForge), we set out to model the epithelial morphogenesis of zebrafish epiboly, in which the blastoderm epithelium, sitting atop a large yolk cell, gradually stretches downward over the yolk to completely engulf it. The forces driving this extension and shape change are believed to be generated within the yolk cell and act on the epithelial margin. We use single particles to represent cells, and global potentials and bonds to represent cellular interactions such as adhesion and tissue tension. Tissue extension occurs when exogenous force from the yolk cell is strong enough to overcome the internal tension of the epithelial layer. Dynamic, stochastic remodeling of intercellular bonds, with constraints on the neighborhood topology, allows for viscoelastic tissue deformation and cell rearrangement in response to exogenous forces, while maintaining tissue integrity. Stress and strain patterns within the epithelium show a spatial and temporal dependence on model parameters and may help to distinguish between hypothesized force generation mechanisms.