Complex Biological and Biomedical Systems Subgroup (CBBS)

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Sub-group minisymposia

Mathematical modeling of emergent phenomena in cell colonies

Organized by: Shawn D. Ryan (Cleveland State University, United States), Mykhailo Potomkin (UC Riverside, United States), Jia Gou (UC Riverside, United States)
Note: this minisymposia has multiple sessions. The second session is MS02-CBBS.

  • Gil Ariel (Bar Ilan University, Israel)
    "A Phase Diagram for Bacterial Swarming"
  • Bacterial swarming is a mode of motion in which dense collectives of rod-shaped flagellated cells migrate rapidly on surfaces. The transition into swarming involves several cellular processes, including changes in cell aspect ratio, suggesting that bacteria manipulate these properties in order to promote physical conditions that are favorable for swarming. New results with monolayer swarms of Bacillus subtilis with different aspect ratios were analyzed at different cell-densities. A comprehensive analysis of the individual and collective dynamics of bacteria in a swarm brings forth a phase diagram, showing sharp transitions between phases corresponding to qualitatively different swarm statistics. From a biological perspective, we find that under standard conditions bacteria inhabit a region of phase space in which the swarm dynamics is highly robust and insensitive to fluctuations. In this regime, bacteria do not form very large clusters and lack global orientational order, properties which may reduce the colony's ability to expand rapidly in the absence of external directional cues.
  • Fernando Peruani (CY Cergy Paris University, France)
    "A mathematical approach to bacterial infections: models for bacterial exploration, aggregation, and infection"
  • Combining mathematical models and bacterial experiments, we have learned how pathogenic bacteria explore surfaces, form early aggregates, and infect cells. I will provide a brief summary of main challenges behind these bacterial phenomena. References: Perez Ipina et al., Nature Physics 15, 610-615 (2019); Otte et al., Nature Communications 12, 1-9 (2021)
  • Silke Henkes (University of Bristol, United Kingdom)
    "Flow, fluctuate, freeze: Cell sheets as soft active matter"
  • Kevin Painter (Politecnico di Torino, Italy)
    "Sticking together by going against the flow"
  • Forming colonies, swarms, schools, flocks, herds, etc is a classical example of self organization, with the benefits of forming a high density group ranging from efficient migration to higher fecundity. Often, groups form through a mechanism of chemical signaling between population members, an evolutionary ancient communication used by both microscopic and macroscopic species. Populations in fluid environments, though, must contend with complex and turbulent flows, potentially detrimental (e.g. splitting up groups) or beneficial (e.g. coalescing individuals) to the formation and maintenance of a group. As a counter to flow, rheotaxis describes a behavior in which individuals orient their body axis with respect to the current and is observed in both unicellular and multicellular organisms. Here we investigate the extent to which rheotaxis and flow impact on chemically-mediated aggregation, revealing these can impact both negatively and positively according to the population state and flow conditions. A hypothesized density-dependent rheotaxis appears capable of optimizing group formation and maintenance, exploiting the positive benefits from each of flow and rheotaxis.

Mathematical modeling of emergent phenomena in cell colonies

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

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

Mathematics of Biochemical Reaction Networks

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

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

Data-driven approaches to understanding collective behavior

Organized by: Maria Bruna (University of Cambridge, United Kingdom), Ulrich Dobramysl (University of Cambridge, United Kingdom), Simon Garnier (New Jersey Institute of Technology, USA)

  • Meg Crofoot (Max Planck Institute of Animal Behavior & University of Konstanz, Germany)
    "Locomotor compromise underlies coordination in heterogeneous groups on the move"
  • When members of a group differ in locomotor capacity, coordinating collective movement poses a challenge: some individuals may have to move faster (or slower) than their preferred speed to remain together. Such compromises have energetic repercussions yet research in collective behavior has largely neglected locomotor consensus costs. Here we integrate high-resolution tracking of wild baboon locomotion and movement with simulations to demonstrate that size-based variation in locomotor capacity poses an obstacle to collective movement. While all baboons modulate their gait and move-pause dynamics during collective movement, the costs of maintaining cohesion are disproportionately borne by smaller group members. Although consensus costs are not distributed equally, all group-mates do make locomotor compromises, suggesting a shared decision-making process drives the pace of collective movement in this highly despotic species. These results highlight the importance of considering how social dynamics and locomotor capacity interact to shape the movement ecology of group-living species.
  • Colin Torney (School of Mathematics & Statistics, University of Glasgow, United Kingdom)
    "Inferring microscale properties of interacting systems from macroscale observations"
  • Emergent dynamics of complex systems are observed throughout nature and society. The coordinated motion of bird flocks, the spread of opinions, fashions and fads, or the dynamics of an epidemic, are all examples of complex macroscale phenomena that arise from fine-scale interactions at the individual level. In many scenarios, observations of the system can only be made at the macroscale, while we are interested in creating and fitting models of the microscale dynamics. This creates a challenge for inference as a formal mathematical link between the micro and macro scale is rarely available. In this talk, I will describe an inferential framework that bypasses the need for a formal link between scales and instead uses sparse Gaussian process regression to learn the drift and diffusion terms of an empirical Fokker-Planck equation which describes the time evolution of the probability density of a macroscale variable. This gives access to the likelihood of the microscale properties of the system and a second Gaussian process can then be used to emulate the log-likelihood surface, allowing the implementation of a fast, adaptive MCMC sampler which iteratively refines the emulator when needed. The performance of the method can be illustrated by applying it to simple models of collective motion.
  • Yuko Ulrich (Institute of Integrative Biology, ETH Zurich, Switzerland)
    "Behavioral organization in heterogeneous groups of a social insect"
  • The composition of social groups has profound effects on their function, from collective decision-making to foraging efficiency. But few social systems afford sufficient control over group composition to precisely quantify its effects on individual and collective behavior. Here we combine experimental and theoretical approaches to study the effect of group composition on individual behavior and division of labor (DOL) in a social insect. Experimentally, we use automated behavioral tracking to monitor 120 colonies of clonal raider ants, with controlled variation in three key correlates of social insect behavior: genotype, age, and morphology. We find that each of these sources of heterogeneity generates a distinct pattern of behavioral organization, including the amplification or dampening of inherent behavioral differences in mixed colonies. Theoretically, we use a well-studied model of DOL to explore potential mechanisms underlying the experimental findings. We find that the simplest implementation of this model, which assumes that heterogeneous individuals differ only in response thresholds, could only partially recapitulate the empirically observed patterns of behavior. However, the full spectrum of observed phenomena was recapitulated by extending the model to incorporate two factors that are biologically meaningful but theoretically rarely considered: variation among workers in task performance efficiency and among larvae in task demand. Our results thus show that different sources of heterogeneity within social groups can generate different, sometimes non-intuitive, behavioral effects, but that relatively simple models can capture these dynamics and thereby begin to elucidate the basic organizational principles of DOL in social insects.
  • Adrien Blanchet (Toulouse School of Economics, France)
    "Mathematical model of disinformation"
  • For a couple of decades, the social network revolution has dramatically changed the way in which people access or share information. Information appears now to be decentralised, spreads faster and faster and seems difficult to control, predict or even understand. However the understanding of the spreading of information is absolutely crucial as it shapes the modern society: the opinion of citizens, the consumption of consumers, the behaviour of agents, or the political decisions. The problem of disinformation is fundamental and has been identified by the World Economic Forum as one of the threats to the economy. In this talk we will present a model of such phenomenon based on a game theory framework and using optimal transport and we will present an ongoing project. Co-authors: G. Carlier, F. Santambroggio, P. Mossay

Exploring the processes of bacteria self-organization using mathematical modelling and experimental studies

Organized by: Diane Peurichard (Inria Paris, France), Marie Doumic (Inria Paris, France)

  • Nicolas Desprat (Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France)
    "Mutliscale morphogenesis of bacterial microcolonies"
  • Unicellular microorganisms are unicellular in the sense, that each individual is able to establish a new population. However, populations of microorganisms are not limited to a collection of individuals, but are highly organized so that the group can perform better than the sum of its individuals. In this presentation, we'll explore how the asymmetric distribution of adhesins on single rod-shaped bacteria shapes the organization of the group and how this affects higher level functions.
  • Sophie Hecht (Inria Paris, France)
    "On the modelling of the morphogenesis of rod-shaped bacteria micro-colony."
  • Bacteria are abundant organisms whose roles are included in many processes such as medicine, agriculture, ecology, industry... From a single organism, they quickly develop into organised micro-colonies and biofilm structures. The formation of these microcolonies, while broadly studied in the past decade, is still poorly understood. We consider an individual-based model where each bacterium is modelled by a spherocylinder and bacteria interact only through non-overlapping constraints. Introducing asymmetric friction and mass for the bacterium, which are taking into account the asymmetry of the pole of the bacteria, we retrieve mechanical behaviours of micro-colony growth, this without implementing attraction or adhesion. We compare our model to various sets of experiments, discuss our results, and propose several quantifiers to compare model to data in a systematic way.
  • Laura Kanzler (Laboratoire Jacques-Louis Lions, Sorbonne Université, France)
    "Kinetic Modelling of Myxobacteria"
  • Myxobacteria are rod-shaped, social bacteria that are able to move on flat surfaces by ’gliding’ and form a fascinating example of how simple cell-cell interaction rules can lead to emergent, collective behavior. Observed movement patterns of individual bacteria in such a colony include straight runs with approximately constant velocity, alignment interactions and velocity reversals. Experimental evidence shows that above mentioned behavior is a consequence of direct cell-contact interaction rather than diffusion of chemical signals, which indicates the suitability of kinetic modeling. In this talk a new kinetic model of Boltzmann-type for such colonies of myxobacteria will be introduced and investigated. For the spatially homogeneous case an existence and uniqueness result will be shown, as well as exponential decay to an equilibrium for the Maxwellian collision operator. The methods used for the analysis combine several tools from kinetic theory, entropy methods as well as optimal transport. The talk will be concluded with numerical simulations confirming the analytical results.
  • Marc Hoffmann (INRIA, Mamba team & University Paris-Dauphine, France)
    "Statistical estimation of the interaction kernel in McKean-Vlasov model in a mean-field limit"
  • We consider the problem of detecting or estimating the interaction in a large system of particles over a fixed time horizon. The particles are subject to a common external force and diffusion, and they interact via a smooth interaction kernel in a mean-field sense, and possibly via a common noise term. We identify some properties of the model that enables one to identify the presence of interactions, in a large population limit, from a statistical perspective.

Wave propagation and pattern formation phenomena in biological models

Organized by: Bogdan Kazmierczak (Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland), Je-Chiang Tsai (Department of Mathematics, National Tsing Hua University, Taiwan)

  • Hirofumi Izuhara (University of Miyazaki, Japan)
    "On the spreading front arising in mathematical models of population dynamics"
  • Understanding the invasion processes of biological species is a fundamental issue in ecology. Several mathematical models have been proposed to estimate the spreading speed of species. In recent decades, it was reported that some mathematical models of population dynamics have an explicit form of the evolution equations for the spreading front, which are represented by free boundary problems such as the Stefan-like problem. To understand the formation of the spreading front, we consider the singular limit of reaction-diffusion models and give some interpretations for spreading front from the viewpoint of modeling.
  • Dariusz Wrzosek (University of Warsaw, Poland)
    "Chemical signalling and pattern formation in predator-prey models"
  • Chemical signalling is an ubiquitous mechanism which impacts distribution of species in space and time . Its role seems to be crucial in the case of patterning in homogeneous landscapes. Many chemicals (e.g. pheromones, kairomones) released by plants and animals are used as means of inter and intraspecific communication. Olfaction is a primary means by which prey detect predators and trigger anti-predator responses. In this talk based on joint papers with Purnedu Mishra we consider the role of repulsive chemotaxis in predator-prey models and using qualitative analytical methods and simulations show complex behaviour of solutions depending on model structure and parameters.
  • Tomasz Lipniacki (Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland)
    "Traveling and standing fronts on curved surfaces"
  • We analyze heteroclinic traveling waves propagating on two dimensional manifolds to show that the geometric modification of the front velocity is proportional to the geodesic curvature of the front line. As a result, on surfaces of concave domains, stable standing fronts can be formed on lines of constant geodesic curvature. These lines minimize the geometric functional describing the system’s energy, consisting of terms proportional to the front line-length and to the inclosed surface area. Front stabilization at portions of surface with negative Gaussian curvature, provides a mechanism of pattern formation. In contrast to the mechanism associated with the Turing instability, the proposed mechanism requires only a single scalar bistable reaction–diffusion equation and connects the intrinsic surface geometry with the arising pattern. By considering a system of equations modeling boundary-volume interactions, we show that polarization of the boundary may induce a corresponding polarization in the volume.
  • Tilmann Glimm (Western Washington University, USA)
    "Modeling interplay of pattern formation and cell phenotype transitions during limb cartilage formation"
  • A regulatory network consisting of two  galactoside-binding proteins, galectins  Gal-1A and Gal-8 and their counterreceptors, mediates the spatial patterning  of the avian limb skeleton through the patterned morphogenesis of mesenchymal  condensations. Formation of the pattern can be modeled as a reaction-diffusion-adhesion process, wherein the galectins form a mutually self-enhancing expression network via the respective counterreceptors, while their diffusion, Gal-1A-mediated cell adhesion and its antagonism  by Gal-8 determines the spatial separation of mesenchymal protocondensations. A mathematical consists of a system of parabolic PDEs with nonlocal advection terms that model cell-cell adhesion. Apart from generating spatial patterns, the dynamical system of the underlying galectin reaction network is interesting in its own right and can be completely examined with analytical means. We identify two stable steady states: where the concentrations of both the galectins are respectively, negligible and very high.  We give an explicit Lyapunov function, which shows that there are no periodic solutions. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time without any intermediate states.  We verify these predictions in experiments  performed with high density micromass cultures of chick limb mesenchymal cells and observe that cells inside and outside the precartilage protocondensations exhibit distinct behaviors with respect to galectin expression, motility, and spreading. The interactional complexity of the Gal-1 and -8-based  patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell-types, which can be spatially patterned when incorporated into a diffusion-enabled system.

Waves and traveling phenomena in living systems

Organized by: Stephanie Dodson (University of California, Davis, United States), Scott McCalla (Montana State University, United States)

  • Stephanie Dodson (University of California, Davis, United States)
    "One-dimensional spiral waves and reflection-induced cardiac arrhythmia"
  • When propagated action potentials in cardiac tissue interact with local heterogeneities, counter propagating or reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of the unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect. Through a combination of direct numerical simulation and continuation methods, we investigate its existence and stability in a qualitative ionic model to determine how the systems propensity for reflections are influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits and we identify key parameters and physiological processes that promote and deter reflection behavior.
  • Matt Holzer (George Mason University, United States)
    "Locked fronts in a discrete time discrete space population model"
  • A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking where rational speed invasion fronts are observed to persist as parameters are varied. In this article, we construct locked fronts for a particular piecewise linear reproduction function. These fronts are shown to be linear combinations of exponentially decaying solutions to the linear system near the unstable state. Based upon these front solutions we then derive expressions for the boundary of locking regions in parameter space. We obtain leading order expansions for the locking regions in the limit as the migration parameter tends to zero. Strict spectral stability in exponentially weighted spaces is also established.
  • Tracy Stepien (University of Florida, United States)
    "Traveling Waves of a Go-or-Grow Model of Glioma Growth"
  • Glioblastoma multiforme is an aggressive brain tumor that is extremely fatal. Gliomas are characterized by both high amounts of cell proliferation as well as diffusivity, which make them impossible to remove with surgery alone. To gain insight on the mechanisms most responsible for tumor growth and the difficult task of forecasting future tumor behavior, we investigate a mathematical model in which tumor cell motility and cell proliferation are considered as separate processes. We explore the existence of traveling wave solutions and determine conditions for various wave front forms.
  • Scott McCalla (Montana State University, United States)
    "Nonlocal interfacial dynamics in biological systems"
  • Biological pattern formation has been extensively studied using reaction-diffusion and agent-based models. In this talk we will discuss nonlocal pattern forming mechanisms in the context of bacterial colony formation and surface striping on animals with an emphasis on arrested fronts. This will lead to a novel nonlocal framework to understand the interfacial motion in biological systems. We will then use this approach to model an interesting bacterial phenomenon, and to understand simple microscopic requirements for flat stripe solutions to persist in nature. We will then examine moving defect patterns in the nonlocal framework.

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

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

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

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

Organized by: Lei Zhang (Peking University, China)
Note: this minisymposia has multiple sessions. The second session is MS09-CBBS.

  • Lei Zhang (Peking University, China)
    "Computable Early C. elegans Embryo with a Data-driven Phase Field Model"
  • Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis consisting of both cell proliferation and cell migration. However, unlike the progress in discovering molecular activity that regulate morphogenesis, general and extensible in silico model based on cell-level interaction has not been well established yet, especially for comprehensive reconstruction and prediction on morphological features observed in live embryo (e.g., cell shape, cell-cell contact relationship). In this talk, using Caenorhabditis elegans as model animal, we present a data-driven phase field model to simulate the morphogenesis procedure within a confined compressed eggshell. We first collected three-dimensional time-lapse (4D) cellular morphological information from the in vivo imaging experiments. Based on the developmental properties obtained, we not only successfully reconstructed the evolution of cell location, cell morphology and cell-cell contact relationship observed in real embryo, but also provided mechanical perspectives on several significant developmental events such as Wnt signaling from P2 to EMS, establishment of the three orthogonal body axes and spatial robustness against external compression.
  • Masakazu Akiyama (Meiji University, Japan)
    "A three-dimensional vertex dynamics model for understanding the twisting phenomenon of the hindgut of Drosophila"
  • Epithelial tissue morphogenesis requires morphologic changes such as migration or deformation of individual epithelial cells constituting the tissue. To reveal 3D morphologic changes of the cells contributing to the tissue deformation, we constructed a 3D vertex dynamics model in which the hindgut epithelial cells were represented by hexagonal cylinders. Numerical simulations suggested that twisting of individual cells along apico-basal axes can induce the directional tube twist. To see whether the cell twisting predicted by the simulation occurs in vivo, we quantified the cell shape change using time-lapse imaging of the whole hindgut. As a result, the hindgut epithelial cells directionally twist before and during the twisting.
  • Chunhe Li (Fudan University, China)
    "A Dimension Reduction Approach for Energy Landscape"
  • Dimension reduction is a challenging problem in complex dynamical systems. We propose a dimension reduction approach of landscape (DRL) for complex dynamical systems, by mapping a high-dimensional system on a low-dimensional energy landscape. The DRL approach is applied to three biological networks, which validates that new reduced dimensions preserve the major information of stability and transition of original high-dimensional systems. The consistency of barrier heights calculated from the low-dimensional landscape and transition actions calculated from the high-dimensional system further shows that the landscape after dimension reduction can quantify the global stability of the system. The epithelial-mesenchymal transitions (EMT) and abnormal metabolism are two hallmarks of cancers. With the DRL approach, a quadrastable landscape for EMT-metabolism network is identified, including epithelial (E), abnormal metabolic (A), hybrid E/M (H), and mesenchymal (M) cell states. The quantified energy landscape and kinetic transition paths suggest that for the EMT process the cells at E state need to first change their metabolism, then enter the M state. This work proposes a general framework for the dimension reduction of a stochastic dynamical system, and advances the mechanistic understanding of the underlying relationship between EMT and cellular metabolism.
  • Chansoo Kim (Korea Institute of Science and Technology, Korea)
    "Kinetic Monte Carlo and the infectious disease dynamics with age and region"

Recent advances in random and deterministic modeling in biology/health sciences

Organized by: Maria C.A. Leite, (University of South Florida St.Petersburg), Juan Carlos Cortés López (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain), Rafael J. Villanueva Micó (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain)
Note: this minisymposia has multiple sessions. The second session is MS17-CBBS.

  • Óscar Angulo (Universidad de Valladolid, Spain)
    "Numerical integration of an age-structured model with unbounded age-domain"
  • The analysis of an unbounded life-span age-structured population model is motivated because, not only new models continue to appear in this framework, but also it is required by the study of the asymptotic behaviour of its dynamics. The numerical integration of the corresponding model is usually performed in bounded domains through the truncation of the age life-span. Here, we present a new numerical method that avoids the truncation of the unbounded age domain. We completely analyze it and we establish its second order of convergence. We finish with some experiments to exhibit numerically the theoretical results and the behaviour of the problem in the simulation of the evolution of the Nicholson's blowflies model.
  • Carla Pinto (School of Engineering, Polytechnic of Porto, Portugal)
    "Modified SIQR model for the COVID-19 outbreak"
  • In this talk we consider a generalization of the Susceptible-Infected-Quarantine-Recovered model, the mSIQR, for the COVID-19 pandemic. The main goal is to study the importance of the value of the contact rate, proportion of unkown infectious, and hospital care in the disease propagation. We test the model and fit the results for COVID-19 pandemic data from some countries, including France, US, and Portugal. We discuss the epidemiological relevance of the results and provide insights on future patterns, subjected to health policies.
  • Clara Burgos (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain)
    "A computational procedure describe breast tumor growth capturing the uncertainty in the volume data"
  • The aim of this talk is to describe a theoretical-computational approach to model the breast tumor growth taking into account the uncertainty of the retrieved data. To do it, we will seek suitable random inputs of a discretized version of a logistic model. The random model parameters will be described via its probability density function. The theoretical-computational approach seems to be flexible enough to be adapted to describe different biological dynamics problems.
  • Gilberto Gonzalez-Parra (Department of Mathematics, New Mexico Tech, USA)
    "Mathematical modeling of COVID-19 pandemic under social behavior uncertainty (Pre-recorded)"
  • Mathematical modeling of COVID-19 pandemic has been challenging due to the complexity of the phenomena including the variability of the social behavior. The uncertainty in some of the mechanisms involved in the transmission of the SARS-CoV-2 and its fatality rate make forecasting an extremely difficult problem as the outcomes have shown. In this talk, we present a mathematical model approach to study the effect of uncertainty in social behavior on the COVID-19 pandemic. Specifically, we rely on stochastic differential equations to give some insights regarding this topic. We illustrate with some scenarios the consequences of social behavior uncertainty on the COVID-19 pandemic. Finally, we will show an application of computational tools such as bootstrapping and Markov chain Monte Carlo that allow us to investigate some uncertainties related to the mathematical modeling of COVID-19 pandemic.

Lattice Models and Agent-Based Models in Biology: Linking Individual Properties to Population Properties

Organized by: Bhargav Karamched (Florida State University, United States of America)
Note: this minisymposia has multiple sessions. The second session is MS13-CBBS.

  • Bhargav Karamched (Florida State University, United States of America)
    "Spatial Model of Oncolytic Virotherapy: Targeting Drug-Resistant Mutants"
  • Oncolytic virotherapy has emerged as a viable treatment for cancers. Although successful cancer treatments with viruses have been observed, they are few and far between. Here, we explore whether combining virotherapy with other methods of cancer treatment may lead to more robust, reliable cancer treatment. For example, cancer cells sometimes undergo mutations that allow them to develop resistance to treatment drugs. To address such a mutation, we explore the possibility of targeting drug-resistant mutants with viruses so that standard drug treatments of cancerous tumors may be used to target cancerous cells. We develop a lattice model that describes cancer tumor growth dynamics and mutant cell dynamics. We find that when mutant cells have a disadvantageous mutation, virus infection amplifies the nature of the disadvantage, with a slight caveat. When infectivity is too high, the population-level death rate is increased so that for a tumor to reach a given size, more cell divisions are necessary. This leads to the presence of more mutants than when no virus is present. We explore this nuanced system with a mean field equation and discuss how viruses used in such a way can progress cancer treatments in the future.
  • Cicely Macnamara (University of St Andrews, Scotland)
    " Computational modelling and simulation of tumour growth and development within a 3D heterogeneous tissue"
  • The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Cancer cells can arise from any type of cell in the body; cancers can grow in or around any tissue or organ making the disease highly complex. My research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modelling. In this talk I shall present a 3D individual-based force-based model for tumour growth and development in which we simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent is fully realised, for example, cells are described as viscoelastic sphere with radius and centre given within the off-lattice model. Interactions are primarily governed by mechanical forces between elements. However, as well as he mechanical interactions we also consider chemical interactions, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells, as well as intercellular aspects such as cell phenotypes.
  • Hamid Teimouri (Rice University, United States of America)
    "The impact of the temporal order of mutations on cancer initiation dynamics"
  • Cancer is a set of genetic diseases that are driven by mutations. It was recently discovered that the temporal order of genetic mutations affects the cancer evolution and even the nature of the disease itself. The mechanistic origin of these observations, however, remain not well understood. We present a theoretical model for cancer initiation dynamics that allows us to quantify the impact of the temporal order of mutations. In our approach, the cancer initiation process is viewed as a set of stochastic transitions between discrete states defined by the different numbers of mutated cells. Using a first-passage analysis, probabilities and times before the cancer initiation are explicitly evaluated for two alternative sequences of two mutations. It is found that the probability of cancer initiation is determined only by the first mutation, while the dynamics depends on both mutations. In addition, it is shown that the acquisition of a mutation with higher fitness before mutation with lower fitness increases the probability of the tumor formation but delays the cancer initiation.
  • Namiko Mitarai (University of Copenhagen, Denmark)
    "Emergence of diversity in a model ecosystem of sessile species with mutually exclusive interactions"
  • The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a lattice model ecosystem of sessile (immobile) and mutually excluding organisms competing for space. The competition is controlled by an interaction network with fixed links chosen randomly. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that patches of isolated meta-population spontaneously formed by the collapse of cyclic relations are essential for the transition to the state of high diversity. The high-diversity state is robust against small disturbance or spontaneous death. When new species evolve by mutating the species interaction network from ancestry species, the high-diversity state appears as long as there is a cost associated with the ability to invade another species.

Lattice Models and Agent-Based Models in Biology: Linking Individual Properties to Population Properties

Organized by: Bhargav Karamched (Florida State University, United States of America)
Note: this minisymposia has multiple sessions. The second session is MS12-CBBS.

  • Tom Chou (University of California - Los Angeles, United States of America)
    "RNA polymerase and ribosome interactions in transcriptional error correction and translation-transcription coupling"
  • Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process. We model the backtracking mechanism of RNA polymerase which usually happens when the polymerase tries to incorporate a mismatched nucleotide. Previous models have made simplifying assumptions such neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a discrete stochastic model that includes interacting (exclusionary) RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. Moments of conditional first passage times to error correction or error incorporation are also computed. We also develop a very similar model for describing translation-transcriptional coupling during which a ribosome simultaneously elongates (and produces a polypeptide) while interacting with the leading RNAP.
  • Claudia Neuhauser (University of Houston, United States of America)
    "Fighting Cancer with Viruses--Mathematical Models to Guide Therapy"
  • Virotherapy of cancer relies on engineered viruses that selectively attack and kill cancer cells but leave healthy cells unaffected. The success of this therapy relies on the successful establishment of an infection that results in the death of cancer cells. To gain a better understanding of the dynamics, we developed spatially explicit, stochastic models of multi-species interactions to map out under what conditions the symbiont (virus) effectively eliminates the host (cancer cells). I will present rigorous results and conjectures based on simulations. I will report on an experimental system (in vitro and in vivo) that was developed by Dr. David Dingli (Mayo Clinic) and uses this mathematical framework to predict the effectiveness of virotherapy in cancer.
  • James Glazier (Indiana University, United States of America)
    "Multicellular modeling of viral infection and immune response in epithelial tissues and response to drug therapy"
  • Simulations of tissue-specific effects of viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding, and parallel development by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage. We studied the effects on progression of treatment potency and time of first treatment for an antiviral. We also show an extended version of the simulation with additional immune cell types calibrated to match extensive existing data on the progression of murine influenza infection. Simulations suggest that the microenvironment in which a virus spreads plays a dominant role in disease onset and progression, and that spatially-resolved models may be important to better understand and more reliably predict future health states based on susceptibility of potential lesion sites using spatially resolved patient data on the state of an infection.
  • Joanna Wares (University of Richmond, United States of America)
    "Developing a computational modeling course in the time of COVID-19"
  • What happens when you decide, in January, that you will teach Computational Modeling in Public Health in the coming fall (2020), and then COVID-19 breaks out? You turn your class into a COVID-19 modeling class! Here, I describe efforts to teach upper-level undergraduate mathematics students how to create and analyze their own mathematical models, both differential-equations and agent-based types. I will explain my first attempt at the course design, and how I utilized the wealth of papers and examples provided by the scientific community in 2020 to answer questions about COVID-19. I will also describe some of the research my students developed in the course and then continued in the following semester. In their research, one focus was on understanding the underlying socio-economic inequities in COVID-19 outcomes.

Understanding lung function and disease through mathematical modeling and experiment

Organized by: Uduak George (San Diego State University, United States), Mona Eskandari (University of California Riverside, United Staes)
Note: this minisymposia has multiple sessions. The second session is MS15-CBBS.

  • Hannah Pybus (School of Mathematical Sciences, University of Nottingham, United Kingdom)
    "Airway constriction in asthma - is it the chicken or the egg?"
  • Despite its prevalence in the population, the causes of asthma remain poorly understood. Airway hyperresponsiveness causes airway constriction at low doses of agonist which is thought to activate cytokines, such as Transforming Growth Factor β (TGF-β). TGF-β is thought to play a key role in promoting airway remodelling, which in turn could exaggerate hyperresponsiveness in a positive feedback loop; however, it is not clear what comes first. To begin to elucidate this, our research combines mathematical models of contracting airways with ex vivo precision-cut lung-slice (PCLS) stretching experiments to study stress-driven TGF-β activation in asthmatic airways. In this talk, we describe our mathematical model that couples subcellular mechanotransductive signalling pathways to nonlinear hyperelastic models of airway mechanics to predict the levels of TGF-β activation in different experimental conditions. We account for TGF-β-mediated contraction of the airway smooth muscle and the subsequent change in effective mechanical properties of the PCLS as TGF-β activation progresses. In agreement with the experimental results, we find that TGF-β activation increases as the airway deforms with imposed stretch. Our work shows that airway contraction, induced by active TGF-β signalling, in conjunction with airway wall stiffening generates stress differences across the airway wall and consequently initiates a positive feedback loop of TGF-β activation. Our work gives access to the highly complex stress distribution within the airway wall and surrounding parenchyma that can be used to investigate the effects of contractile heterogeneity and examine airway wall structure. This integrated study provides information that is of vital importance in interpreting PCLS experiments that seek to clarify the mechanochemical mechanisms underpinning TGF-β activation, a key aspect of the disease, that has only recently received attention.
  • Ashley Schwartz (Computational Science Research Center, San Diego State University, United States)
    "New metrics for quantifying the spatial inhomogeneity of abnormal fluid in MR images of cystic fibrosis lungs"
  • Cystic fibrosis (CF) is a genetic disease that can produce thick mucus accumulation in the lung, limiting a person’s ability to breathe. Treatment plans for CF are often determined from disease severity as determined by the spirometry metric percent predicted forced expiratory volume in 1 second (ppFEV1). Spirometry does not yield information about mucus accumulation behavior and location that imaging may provide. Magnetic resonance (MR) imaging is an imaging technique with no radiation effects that yields information about fluid density, or water content, within the lung from blood, lung tissues, and lung abnormalities such as excess mucus. In this talk, we will present an automated image processing algorithm that makes use of three-dimensional MR images to locate, segment, and describe the lung abnormalities in CF versus control lungs. The spatial location and behavior of lung abnormalities is categorized into three different spatial behaviors: (i) generalized, (ii) localized diffuse, and (iii) localized. Lungs with generalized behavior have little but sparse abnormal lung fluid. Localized lungs have a focality or concentration of abnormal lung fluid in a particular region of the lung and sparsity elsewhere, while localized diffuse lungs have a high concentration of abnormal lung fluid in multiple regions. Control patients mostly presented as generalized. CF patient’s abnormal fluid behavior did not directly correlate with severity level as determined by ppFEV1. This suggests CF disease is heterogeneous within severity levels and ppFEV1 may be missing additional information about disease behavior. The algorithm developed provides unique information about abnormal lung fluid behavior that may be used to distinguish differences in CF disease missed by traditional spirometry metrics.
  • Nourridine Siewe (Rochester Institute of Technology, United States)
    "A Mathematical Model of the Role of MIF in Severe Malarial Anemia: What Happens in TB"
  • Tuberculosis (TB) is the leading cause of death by infectious disease worldwide. The pathogen responsible for this infection is Mycobacterium tuberculosis (MtB). Due to the large number of people affected by TB daily, it remains a public health concern because of lack of treatment options, causing scarcity of resources, and the abundance of drug-resistant TB strains. To assist in the fight against this disease, we propose building a mathematical model of the interactions between the human immune system and MtB. This model will be described by a system of ordinary differential equations to capture the complex interactions between the variety of cells and proteins involved in this biological system. The model will include the effect of commonly used drugs to treat TB, namely isoniazid and rifampin, whose pathways contribute in decreasing the number of MtB in the host. This model will allow for the quick and easy analysis of experimental TB treatments, expediting the process of developing new treatment protocols.
  • Blessing Emerenini (Rochester Institute of Technology, United States)
    "Trends in the mathematical modeling of Bacteria-Phage combat in lung treatment"
  • Presence of pathogenic microorganisms in our environment entail enormous problems for humans and livestock. The problem of pathogenic microrganisms is even grievous when they reside in host vital organs such as the lung. Bacteria is one of such pathogenic microorganisms and they prefer to live in communities called Biofilms. Existence of Biofilm in any system is a huge problem because by its nature it is usually difficult to get rid of it by mere antibiotics. There are currently many ongoing studies that focus on how to do away with such pathogens from our systems. One of the medical approaches to treating inhost bacteria infection is by introducing bacteriophages (a.k.a phage therapy). In order to understand the different strategies of pathogenic infections and phage-bacteria interactions, pathogen-host infection dynamics helps us to derive better treatments to extenuate infectious diseases or develop vaccinations, thus preventing the occurrence of infections altogether. In this study we present a general review of methods and characterizations to facilitate right decision for understanding interdisciplinary modeling approaches.

Understanding lung function and disease through mathematical modeling and experiment

Organized by: Uduak George (San Diego State University, United States), Mona Eskandari (University of California Riverside, United Staes)
Note: this minisymposia has multiple sessions. The second session is MS14-CBBS.

  • Ariel Nikas (Emory University, School of Medicine, United States)
    "Using morphoelasticity to model early lung branching"
  • Morphoelasticity, an emerging area of continuum mechanics, can describe the large strains of organogenesis. We apply this framework modeling lung branching. Many previous models of lung branching morphogenesis were focused on the complex morphogen signaling systems and either omit explicit modeling of shape change, or model shape change by moving a surface normal to itself without explicit mechanics equations. Previous models have shown that morphogen flux distribution corresponds to the location of branching, and that this distribution is reliant on local geometry. We explicitly modeled both the morphogen signaling and the resulting growth dependent on the calculated morphogen flux distribution, in a novel application of morphoelastic shell modeling for lung growth. We concluded that local geometry affects the resulting shape change. Specifically, we observed tubule lengthening for all local geometries and shouldering for epithelium of elliptical cross-section. We also observed that the thickness of the epithelium affects the resulting shape change. This modeling approach of shell mechanics combined with morphoelasticity allowed us to test complex hypotheses on growth and can be generalized for many other organ systems.
  • Mona Eskandari (University of California at Riverside, United States)
    "Characterizing pulmonary mechanics using an experimental-computational framework"
  • COVID-19 has driven respiratory biomechanics to the forefront. Classified now as an endemic, investigative pulmonary research using computational biomechanical models is central to gaining predictive insights regarding fundamental lung physiology. The complex and hierarchical structure of the lung challenges advancements, given the bulk mechanical behavior representation is disconnected from its local tissue response. We address this knowledge gap by introducing the first structural inverse finite element model of the breathing lung using a reduced order surface representation. Using a custom-designed apparatus to imitate inflation and deflation in the ex-vivo lung, we interface the system with large deformation digital image correlation capabilities to ultimately link local strains to inflation volumes and pressures, compounding the role of the intricate bronchial network, parenchymal tissue, and visceral pleura behavior. An optimized heterogenous and hyperelastic continuum model employing adjoint methods accurately captures the experimentally observed topological lung surface strain distributions for varying pressure levels. This novel multiscale framework can facilitate in-silico explorations to improve ventilation strategies and examine how chronic disease endurance modifies the lung's load-bearing biomechanics.
  • Ramana Pidaparti (University Of Georgia Athens, United States)
    "Computational Models and Informatics for Lung Inflammation and Aging"
  • At Design Informatics and Computational Engineering (DICE) laboratory in the College of Engineering at UGA, quantitative analysis through airway lung models and informatics, computations and imaging data that correlates to inflammation, disease and aging is being conducted. A multi-scale model for cellular inflammation was developed for compliant lung geometry under mechanical ventilation by investigating respiratory mechanics at the organ, tissue and cellular levels. The cluster analysis of lung simulation data revealed that the clusters of airway strain data are correlated to airflow characteristics. The results from the inflammation model indicated that for the strain conditions considered, the model is capable of predicting the innate healing capacity of the tissue. Overall, the airway mechanical characteristics as well as lung function are compromised (about 40%-50%) due to aging. This talk provides an overview of the research at DICE lab in the College of Engineering at the University of Georgia.
  • Uduak George (San Diego State University, United States)
    "Mathematical modeling of fibroblast growth factor expression in developing lungs"
  • Fibroblast growth factor 10 (Fgf10) is a key regulator of lung development. Fgf10 is expressed at the sub-mesothelium, distal to the branching epithelial structures. Despite enormous progress in understanding the mechanisms that control lung development, the factors that determine the spatio-temporal expressions of Fgf10 are not well understood. In this study, we implemented a novel method to study Fgf10 expression at the lung mesothelium by using a system of surface reaction-diffusion equations. Numerical approximation of the equations was carried out by using the surface finite element method. Simulations of Fgf10 expression were done on murine lungs segmented from three-dimensional confocal microscopy images. Our simulation results reproduced some of the reported Fgf10 expression patterns from wet lab experiments available in the literature. The model identified the rate of reaction of Fgf10 and Fgf10 inhibitors as a possible key parameter in the regulation of Fgf10 expression. It also identified the size of the lung mesothelium, as a possible regulator of Fgf10 expression during murine lung morphogenesis.

Recent advances in random and deterministic modeling in biology/health sciences

Organized by: Maria C.A. Leite, (University of South Florida St.Petersburg), Juan Carlos Cortés López (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain), Rafael J. Villanueva Micó (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain)
Note: this minisymposia has multiple sessions. The second session is MS11-CBBS.

  • Francisco Rodríguez (Dept. of Applied Mathematics and Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Spain)
    "Ecohydrological feedbacks, delay responses and random perturbations in mean field dryland vegetation models"
  • Positive feedbacks between increased connectivity and loss of resources are recognized as potential landscape-scale factors driving degradation and desertification in semiarid regions. Common dryland vegetation models exhibit bistability as the result of different mechanisms yielding local positive feedbacks that reinforce the persistence and growth of vegetation patches, with an unstable equilibrium for vegetation separating the stable equilibria of vegetated and desert states. The existence of bistability allows for abrupt transitions between the alternative stable states, the so called catastrophic shifts, either as the result of gradual worsening of the environmental conditions or due to single or randomly distributed perturbations. Using a spatially explicit cellular automata (CA) dryland model, it has been shown that feedbacks between vegetation pattern and resource loss, measured through an index of spatial bare soil connectivity (Flowlength, FL), dramatically decrease ecosystem resilience and restoration potential. In this work, we considered mean field approximations to this CA model and other common dryland models, and showed that positive global ecohydrological feedbacks mediated by bare-soil connectivity, as captured by the expected value of the FL index, effectively decrease resilience and suffice to induce bistability in absence of additional local feedbacks. We also explored how the presence of delayed responses could affect recovery after random perturbations.
  • Sandra Delgadillo (Universidad Autónoma de Aguascalientes, México)
    "Full probabilistic analysis of random first-order linear differential equations with Dirac delta impulses (Pre-recorded)"
  • In this talk, we address, from a probabilistic standpoint, a first-order linear differential equation with an infinite train of Dirac delta impulses. We consider that all its initial condition and coefficients are absolutely continuous random variables with a joint probability density function. We take extensive advantage of the Random Variable Transformation method to determine, first, an explicit expression for the probability density of the solution stochastic process. Secondly, of the random sequences for the maxima and minima for the case, the impulses application times are evenly spaced, with period $T$. From these sequences, we determine the probability of stability of the solution stochastic process. All the theoretical results are illustrated by means of several numerical examples. Finally, we briefly discuss the results of a sensitivity analysis performed, via Sobol indexes, for a fixed and random period T.
  • Carlos A. Braumann (Department of Mathematics & CIMA, Universidade de Évora, Portugal)
    "Harvesting optimization in a randomly varying environment"
  • We can describe the dynamics of a harvested population in a randomly varying environment by stochastic differential equations models. Previously [N.M. Brites and C.A. Braumann (2017), Fisheries Res. 195: 238-246; N.M. Brites and C.A. Braumann (2019), Fisheries Res. 216: 196-203], we have compared the profit performance of two harvesting policies, the optimal policy (with variable harvesting effort) and the optimal sustainable policy (with constant harvesting effort). The former is inapplicable in practice due to the fast and abrupt variations of the harvesting effort associated with the frequent environmentally induced variations in population size. Furthermore, it requires the knowledge of the population size at each instant - an inaccurate, lengthy, and expensive task. The optimal sustainable policy considers the application of a constant harvesting effort and, under suitable conditions, leads [see, in a more general setting, C.A. Braumann (1999), Mathem. Biosc. 156: 1-19], to population sustainability and the existence of a stationary probability density. This policy has the advantage of being easily applicable and there is no need to estimate the population size. The performance of the two policies was compared in terms of profit over a finite time horizon. Using data based on real harvested populations and the usual logistic and Gompertz growth models, we show that there is only a slight reduction in profit by using the optimal sustainable policy (based on constant effort) instead of the inapplicable optimal policy (based on variable effort). We also present here stepwise effort policies [introduced in N.M. Brites and C.A. Braumann (2019), Stat. Optim. Inform. Comp. 7(3): 533-544], which are applicable, and compare them with the previous policies. Extensions to Alee effects models can be seen in N.M. Brites and C.A. Braumann (2020), Appl. Stoch. Models Bus. Ind. 36: 825–835. Acknowledgements: Carlos A. Braumann belongs to the research center CIMA - Centro de Investigação em Matemática e Aplicações, Universidade de Évora, supported by FCT (Fundação para a Ciência e a Tecnologia, Portugal), project UID/04674/2020. Nuno M. Brites was partially supported by the Project CEMAPRE/REM - UIDB/05069/2020 - financed by FCT/MCTES through national funds.
  • Roberto Ku-Carrillo (Universidad Autónoma de Aguascalientes, Mexico)
    "On a linear random differential equation with periodic harvesting and migration"
  • process. Given the abundance of evidence that evolution is not strictly

Stochastic methods for biochemical reaction networks

Organized by: Wasiur KhudaBukhsh (The Ohio State University, United States), Hye-Won Kang (University of Maryland at Baltimore County, United States)
Note: this minisymposia has multiple sessions. The second session is MS19-CBBS.

  • Ankit Gupta (ETH Zurich, Switzerland)
    "A deep learning approach for solving chemical master equations"
  • Stochastic reaction network models are a popular tool for studying the effects of dynamical randomness in biological systems. Such models are typically analysed by estimating the solution of the chemical master equation (CME) that describes the evolution of the probability distribution of the random state-vector representing molecular counts of the reacting species. The size of the CME system is typically very large or even infinite, and due to this high-dimensional nature accurate numerical solutions of the CME are very difficult to obtain. In this talk we will present a novel deep learning approach for estimating CME solutions and illustrate it with a number of examples. The proposed method only requires a handful of stochastic simulations and it yields not just the CME solution but also its sensitivities to all the model parameters.
  • Grzegorz Rempala (The Ohio State University, United States)
    "Approximating bio-chemical dynamics using survival models"
  • In a stochastic chemical network one can often use the notion of a reaction hazard in order to provide a simple statistical model for the system evolution. This approach is especially helpful if we want to consistently follow the fate of a single molecule of some special species through its different transformations, as is the case, for instance, for a single individual in the classical model of an SIR epidemic network. I will provide some general results on the usage of the method and its mathematical properties with particular attention given to stochastic epidemic models. This is joint work with Daniele Cappelletti from Politecnico di Torino.
  • Jinsu Kim (University of California Irvine, USA)
    "Mixing times for stochastically modeled biochemical reaction systems"
  • Mixing times of Markov chains play a significant role in studying stochastic systems as they indicate how fast the system will be stabilized. In this talk, I will introduce analytic approaches such as Lyapunov-Foster criteria and Spectral gap theory that can be used to find a class of reaction networks whose associated Markov process admits exponential ergodicity, which means the associated probability density function converges to its stationary distribution exponentially fast. Beyond the theoretical aspects, I will also talk about how exponential ergodicity can be applied in computational system biology.
  • Wasiur KhudaBukhsh (The Ohio State University, United States)
    "Chemical reaction networks with covariates"
  • In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. We consider relaxing this assumption by incorporating age-dependent random time delays into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of Partial Differential Equations (PDEs) in the large-volume limit, as opposed to Ordinary Differential Equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms.

Stochastic methods for biochemical reaction networks

Organized by: Wasiur KhudaBukhsh (The Ohio State University, United States), Hye-Won Kang (University of Maryland at Baltimore County, United States)
Note: this minisymposia has multiple sessions. The second session is MS18-CBBS.

  • David Anderson (University of Wisconsin Madison, USA)
    "Time-dependent product-form Poisson distributions for reaction networks"
  • It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this talk, I will discuss the following related question: under what conditions will the time-dependent distribution of a reaction network be a product of Poissons for all time? I will provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical “complex-balancing” for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). This is joint work with Chaojie Yuan (Indiana) and David Schnoerr (Imperial College London).
  • Lea Popovic (Concordia University, Canada)
    "Stochastic reduction of spatially heterogeneous biochemical reaction networks"
  • We start from a measure valued process which models the full particle behaviour of chemical reaction networks in spatially heterogeneous systems. Scaling of such a process with a high abundance of some species types and large reaction rates of some reactions leads to a reaction-diffusion pde deterministic limit, or to a mixture of discrete-Markov-and-continuous-deterministic limit process. In this talk we consider a reduced stochastic description of the original measure-valued process by approximating its fluctuations around the limiting process.
  • Hye-Won Kang (University of Maryland at Baltimore County, United States)
    "Stochastic modeling of metabolic enzyme complexes"
  • Enzymes in purine biosynthesis and glucose metabolism have been shown to spatially organize into different types of multienzyme complexes. These multienzyme complexes regulate metabolic flux in living human cells. Metabolic pathways for purine biosynthesis and glucose metabolism are associated with each other, but their metabolic enzyme complexes are spatially independent in human cells. We hypothesize that these metabolic enzyme complexes communicate with each other when they are in close location. This talk will introduce a stochastic model for metabolic enzyme complexes using the Langevin dynamics to investigate their spatial communication.
  • Felipe Campos (University of California, San Diego, USA)
    "Error bounds for the one-dimensional constrained Langevin approximation for density-dependent Markov chains"
  • The Constrained Langevin Approximation (CLA) is a reflected diffusion approximation for stochastic chemical reaction networks proposed by Leite & Williams. In this work, we extend this approximation to (nearly) density dependent Markov chains, when the diffusion state space is one-dimensional. Then, we provide a bound for the error of the CLA in a strong approximation. Finally, we discuss some applications for chemical reaction networks and epidemic models, illustrating these with numerical examples. Joint work with Ruth Williams.

WiMB: Mathematical modeling and its application

Organized by: Qimin Huang (Case Western Reserve University, USA), Katie Storey (University of Michigan, USA)

  • Atanaska Dobreva (Arizona State University, USA)
    "Investigating pathological mechanisms in cone photoreceptor vitality and the timing of rescue strategies via bifurcation analysis and time-varying sensitivity analysis"
  • Photoreceptors are the sensory cells of the eye, which perform the most essential role in vision. There are two types of photoreceptors: rods for night and peripheral vision and cones for color vision. Glucose is the main fuel for photoreceptors, and they break it down to form lactate, lipids and other metabolites needed to create energy and to renew the light-absorbing outer segments, which are periodically shed. Thus, properly functioning metabolic processes ensure the structural integrity and vitality of photoreceptors. The progression of degenerative retinal diseases such as age-related macular degeneration (AMD) and retinitis pigmentosa (RP) has been linked to nutrient deprivation. We analyzed a mathematical model for the metabolic dynamics of a cone photoreceptor via bifurcation analysis and time-varying global sensitivity analysis (GSA) in order to identify factors that increase the risk of cone degeneration in AMD and RP when glucose supply to photoreceptors is low. Our results indicate that the factors of greatest importance include glucose availability and transport, utilization of lipids for photoreceptor outer segment renewal and -oxidation of fatty acids to provide auxiliary metabolites for energy production. In addition, the GSA helped to uncover insights into timing of intervention strategies to rescue the cone cell.
  • Katie Storey (University of Michigan, USA)
    "A Framework for Performing Data-Driven Modeling of Tumor Growth with Radiotherapy Treatment"
  • Recent technological advances make it possible to collect detailed information about tumors, and yet clinical assessments about treatment responses are typically based on sparse datasets. In this work, we propose a workflow for choosing an appropriate model, verifying parameter identifiability, and assessing the amount of data necessary to accurately calibrate model parameters. We compare tumor growth models of varying complexity in an effort to determine the level of complexity needed to accurately predict tumor growth dynamics and response to radiotherapy. We consider a simple, one-compartment ordinary differential equation model which tracks tumor volume and a two-compartment model that accounts for tumor volume and the fraction of necrotic cells within the tumor. We investigate the structural and practical identifiability of these models, and the impact of noise on identifiability. We also generate synthetic data from a complex, spatially- resolved, cellular automaton model (CA), investigating the fit of the ODE models to tumor volume data generated by the CA, using sequential model calibration. Our results suggest that if tumor volume data alone is provided then a tumor with a large necrotic volume is the most challenging case to fit. However, supplementing data on total tumor volume with additional necrotic information enables the two-compartment ODE model to perform significantly better than the one-compartment model, in terms of parameter convergence and predictive power.
  • Qimin Huang (Case Western Reserve University, USA)
    "Investigating the impact of combination phage and antibiotic therapy: A modeling study"
  • Antimicrobial resistance (AMR) is a serious threat to global health today. The spread of AMR, along with the lack of new drug classes in the antibiotic pipeline, has resulted in a renewed interest in phage therapy, which is the use of bacteriophages to treat pathogenic bacterial infections. This therapy, which was successfully used to treat a variety of infections in the early twentieth century, had been largely dismissed due to the discovery of easy-to-use antibiotics. However, the continuing emergence of antibiotic resistance has motivated new interest in the use of phage therapy to treat bacterial infections. We have modeled an ODE system to investigate the effect of immune system on combination treatment of the phage and antibiotic. Our result shows the frequency and concentration of dose as well as the timing of phage administration are important factors of the combination phage therapy.
  • Hwayeon Ryu (Elon University, USA)
    "Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization"
  • We analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage pathways are equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by laboratory experiments to deepen our understanding of macrophage polarization.

Sub-group contributed talks

CBBS Subgroup Contributed Talks

  • Jolene Britton University of California, Riverside
    "A Metabolism-Based Multiscale Model of Fungal Development and Growth"
  • Bacterial-fungal interactions play a fundamental role in many processes including crop biofuel development and biosystem design. In this work, we focus on the interactions between the fungi Laccaria bicolor and the bacterium Psuedomonas fluorescens and their integral role in the fitness of the roots of the Populus tree. L. bicolor synthesizes trehalose which stimulates growth and chemotaxis of P. flourescens. Furthermore, P. flourescens provides L. bicolor with thiamine thereby increasing fungal mass. We developed a multiscale computational model to investigate these interdependent interactions. The growth and branching of the fungal mycelia are modeled using an off-lattice spatial discrete submodel which is dependent on both diffusive and active translocation of internal nutrients and uptake of external nutrients. The fungal growth model is coupled with a thermodynamic-kinetic maximum entropy ODE model for metabolism, containing over 200 reactions including protein and nucleic acid synthesis, from which the costs of growth and maintenance can be calculated. Trehalose secretion, especially at the tips of the hyphae, acts as a source of diffusive chemoattractant for P. fluorescens colony. Numerical simulations of these coupled models under various conditions aid in characterizing the energetic costs of growth and maintenance of L. bicolor in the presence of P. fluorescens.
  • Brenda Lyn A. Gavina University of the Philippines
    "Optimization of dosing strategy for anovulation"
  • A female's reproductive life from the average age of 12.5 until 51 is governed by the menstrual cycle. During this cycle, pituitary and ovarian hormones fluctuate. Abnormal concentrations of these hormones often cause cycle irregularities. However, there are cases where an abnormal cycle, in particular anovulation, is desired. For instance, in contraception and in managing premenstrual symptoms. Exogenous hormones such as synthetic progesterone and synthetic estrogen have been used to attain anovulatory state by controlling hormone levels in the body. Nonetheless, large doses are associated with adverse effects such as increased risk for thrombosis and myocardial infarction. This talk focuses on the application of optimal control to a simple modification of the model in (Margolskee et al., 2011) in order to determine the minimum dosages of exogenous estrogen and progesterone that result to anovulation. Exogenous hormone profile and timing of administration are obtained. These results may give clinicians insights to improve dosing strategies in ovulation suppression.
  • Daniel Plaugher University of Kentucky
    "Modeling the Pancreatic Cancer Microenvironment in Search of Control Targets"
  • Pancreatic Ductal Adenocarcinoma is among the leading causes of cancer related deaths globally due to its extreme difficulty to detect and treat. Recently, research focus has shifted to analyzing the microenvironment of pancreatic cancer to better understand its key molecular mechanisms. This microenvironment can be represented with a multi-scale model consisting of pancreatic cancer cells, pancreatic stellate cells, as well as cytokines and growth factors which are responsible for intercellular communication between the PCCs and PSCs. We have built a stochastic Boolean model, validated by literature and clinical data, in which we probed for intervention strategies that force this gene regulatory network from a diseased state to a healthy state. We implemented methods from phenotype control theory to determine a procedure for regulating specific genes within the microenvironment. After applying well studied control methods such as stable motifs, feedback vertex set and computational algebra, we discovered that each produces a different set of control targets that are not necessarily minimal nor unique. Each control set contains cytokines, KRas, and HER2/neu which suggests they are key players in the system's dynamics. Many of these model predictions are supported by literature and have potential to be new targets.
  • Furkan Kurtoglu Indiana University
    "Integration of Intracellular Kinetic Models to Multiscale Agent-Based Models"
  • Multiscale Agent-Based Models (ABM) provide a framework to model across different scales while intracellular kinetic models capture dynamic trends at the molecular level. In this work, we integrated intracellular kinetic models to a 3-D physics-based multiscale ABM tool (PhysiCell). Cells are represented as intelligent agents which behave according to rules and parameters. As a result, dynamic molecular models which are represented as ordinary differential equations (ODEs) in Systems Biology Markup Language (SBML) format were solved in PhysiCell using libRoadrunner, a fast, SBML solver package. To achieve this goal, cells uptake/secrete chemicals to/from the microenvironment. Custom data associated with PhysiCell agents is used as an interface between ABM and ODEs, updating the SBML in pre-defined time intervals. Kinetic ODEs are simulated at this point and results are updated to the custom data which can be used to control phenotypic parameters. Therefore, phenotypic changes in intelligent agents are determined by molecular level events. Moreover, having cell-specific custom data provides the heterogeneity through tissue or domain. This advancement makes PhysiCell models easier to produce since modelers can use SBML to write their dynamic phenotypes without writing complex functions in C++.

CBBS Subgroup Contributed Talks

  • Anushaya Mohapatra BITS, Pilani, Goa Campus, India
    "The ideal free distribution and the evolution of partial migration"
  • In this talk, we will discuss how the ideal free distribution (IFD) arises in the context of a partially migrating population using a stage-structured matrix model. Partial migration is a unique form of phenotypic diversity wherein migrant and non-migrant individuals coexist together. We show that the ideal free distribution is evolutionary stable in a global sense, assuming that both migrants and non-migrants experience density dependent competition with each other during reproduction. We also establish that the partially migrating species satisfies a dichotomy: Either both morphs have the same fitness, a scenario that corresponds to an IFD. Or, one morph has a higher fitness than the other. Evolutionary process however, will drive the population to the IFD.
  • Debasmita Mukherjee Sunandan Divatia School of Science, SVKM's NMIMS Deemed to be University, Mumbai, India
    "Atherosclerosis: A Mathematical Model for Early Prognosis"
  • Atherosclerosis, an arterial disease that causes malfunction of the cardiovascular system, occurs due to the accumulation of plaque in the intima, the innermost layer of artery. A suitable mathematical model is presented here in terms of a nonlinear autonomous system of ten Ordinary differential equations that incorporate various cellular components such as low-density lipoproteins (LDL) high-density lipoproteins (HDL), free radicals, oxidized LDL, chemoattractant, monocytes, macrophages, T-cells, smooth muscle cells (SMCs) and necrotic core (or plaque cells) as dependent variables. The present model is found to be globally stable theoretically and numerically under certain conditions. Since the model system is large in size, the concept of global stability can be physically visualized through appropriate projections of specific subsystems into three- and two-dimensional subspaces. Since the present model is globally stable, it can resist to some extent any wider arbitrary range of assumed parameter values not found in the literature. The aim of the model under study is to provide a computational framework that allows searching for important parameters that are likely to aid in clinical investigations of this malignant disease.
  • Michael Getz Indiana University, Bloomington
    "Continuum to Discrete event modeling within PhysiCell"
  • Agent based modeling frameworks such as PhysiCell contain many discrete and continuum components such as the cells and tissue microenvironment. These components events require use of uncoupled solvers to evaluate the problem across simulation time. At the interface between solvers special cases must be defined as low concentrations can become a source of error where fractions of objects are consumed by many discrete cells- similarly when a discrete (Cell) object is translated to a continuum framework (ODE) attention must be also payed to reduce error in the event. Better reduction of error allows for larger simulations for a cheaper cost, such as if an epithelium model (spatially simulated) is coupled to the lymph node (ODE). Examples with an infection model of COVID are shown including lymph node recruitment of immune cells.
  • Raneem Aizouk City, university of London
    "Modelling conflicting individual preferences: target sequence and graph realization"
  • we will consider a group of individuals, who each have a target number of contacts they would like to have with other group members. We are interested in how close this can some to being realized, and consider the long term outcome for the group under a reasonable dynamics on the number of contacts. The individuals will be represented as vertices, and the number of contacts as the vertex degree. It is well known that not all degree sequences can be realized as undirected graphs and the Havel-Hakimi algorithm characterizes those that can. Our main concern is to reach graphs that minimize the total deviation between what is desired and what is possible. The set of all such graphs and the set of all such associated sequences are termed the minimal sets. This problem has previously been considered by Broom and Cannings, and it is a hard problem to tackle for general target sequences. We consider the n-element arithmetic sequence for general n, including obtaining a formula which generates the size of the minimal set for a given arithmetic sequence. We also consider a strategic version of the model where the individuals are involved in a multiplayer game.

CBBS Subgroup Contributed Talks

  • David Lacoste Laboratory Gulliver, ESPCI, Paris
    "Emergence of homochirality in large molecular systems"
  • The selection of a single molecular handedness among the two possible configurations of a given molecule, or homochirality, is observed across all living matter and is a mystery in the origin of life. Here, we show that large chemical systems, are likely to undergo a spontaneous symmetry breaking toward a homochiral state as the number of chiral species increases [1]. Through an analysis of a large chemical database, we find that there is no need of very large molecules for chiral species to dominate over achiral ones; it already happens when molecules contain about 10 heavy atoms.Refs: G. Laurent, D. Lacoste, and P. Gaspard, PNAS (2021) 118 (3) e2012741118;
  • Martijn de Jong Leiden University
    "Cellular Potts model of convergent extension can explain shape variability of gastruloids"
  • Gastrulation is a crucial process during embryonic development. During this process, the embryo elongates and cells start rapidly differentiating. We have studied an in vitro model of this process and noticed that the shapes of the resulting tissues had a wide variation. Here we show that a Cellular Potts Model (CPM), based on modified filopodial-tension of convergent extension after Belmonte et al. (P Comput Biol 2016) mimics the variability of the shapes closely. The model periodically places hookian springs between cells, which model filopdia pulling cells close to each other. If cells extend filopida in random polarization directions and align polarizations to their neighbors, the resulting tissues form two or multiple lobes, closely resembling the shapes formed by gastruloids. We analyzed the shapes using lobe contribution elliptic Fourier analysis (LOCO-EFA), which supports the observed qualitative similarities between simulations and gastruloids.
  • Robert Planque Vrije Universiteit Amsterdam
    "Stability of a reaction pathway adaptively controlled to maximise flux"
  • Single celled organisms such as bacteria and yeasts are able to tune enzyme levels that catalyze the reaction pathways by which they eventually make new copies of themselves. Depending on nutrient conditions, more or less enzyme is invested in different parts of their reaction network, so that reaction rates are constantly high, and cellular growth rate is maximised. In this talk I will present an analysis of a reaction network coupled to a set of equations for synthesis and degradation of enzymes involved in this network. These enzyme equations are designed such that the steady state flux through the network is optimal when it is in steady state. The resulting dynamical system is an ODE system with two sets of algebraic equations attached. I will discuss the challenges to analyse this system, including quasi-steady state analysis, local stability, and if we have succeeded by the time of this conference, also global stability.
  • Bime Markdonal Ghakanyuy University of Buea, Cameroon
    "Investigating the Impact of Multiple Feeding Attempts on Mosquito Dynamics via Mathematical Models"
  • A deterministic nonlinear ordinary differential equation model for the dynamics of terrestrial forms of the Anopheles sp mosquito population is derived and studied. The model is designed to capture and assess the impact of multiple probing attempts by mosquitoes that quest for blood meals in human populations. There exists a threshold parameter, whose nature is affected by the manner in which we interpret the transitions involving the different classes on the gonotrophic cycle path. The trivial steady state of the system, which always exists, can be globally asymptomatically stable for positive values of the threshold parameter that are less than unity. The non-trivial steady state, when it exist, is stable for a range of values of the threshold parameter but can also be driven to instability via a Hopf bifurcation. Our analysis reveals that waiting class mosquitoes contribute positively in sustaining mosquito populations. A nonlinear analysis, based on the center manifold theorem, is used to derive expressions for the amplitude and phase of the oscillating solutions that arise through Hopf bifurcations. We conclude that to understand the human-mosquito interactions, it is informative to consider multiple feeding attempts that are known to occur when mosquitoes quest for blood meals within humans.

CBBS Subgroup Contributed Talks

  • Xueying Wang Washington State Univeristy
    "Impact of Varying Networks on Disease Invasion"
  • We consider the spread of an infectious disease in a heterogeneous environment, modelled as a network of patches. We focus on the invasibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, $mathcal{R}_0$, and study how changes in the network structure affect the value of $mathcal{R}_0$. We provide a detailed analysis for two model networks, a star and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in $mathcal{R}_0$. We develop both combinatorial and matrix analytic techniques, and illustrate our theoretical results by simulations with the exact $mathcal{R}_0$.
  • Shaza Alsibaai Department of Mathematics & Statistics, McGill University, Montréal, Canada.
    "The Necessity of Including a Sub-model for Iron Metabolism in Mathematical Modelling of Erythropoiesis"
  • Erythropoiesis is a tightly regulated process beginning from hematopoietic stem cells (HSCs) and ending with mature red blood cells (RBCs). Hemoglobin within RBCs is responsible for transporting oxygen to body tissues. During erythropoiesis, about 20 to 25 mg of iron are used each day for hemoglobin synthesis, and most of this comes from recycling senescent RBCs. Many mathematical models of erythropoiesis in the literature neglect iron metabolism during erythropoiesis. However, such models are not useful in scenarios where there is iron overload or iron deficiency. At the same time, to understand the underlying control mechanisms, we seek to minimize the number of variables in the model, to circumvent issues with parameter identifiability that arise in ODE many-compartment models. In this talk, I will discuss a mathematical model we propose to capture the main physiological features of erythropoiesis. The model consists of five coupled delay differential equations, three of which track the iron during erythropoiesis including the hemoglobin iron within RBCs, and the other two equations model the dynamics of the major regulating hormones. I will present the derivation of the model, the positivity property of the model's solutions and the stability of its homeostatic steady state, and its numerical implementation.
  • Gess Iraji Brandeis University
    "Mathematical Modeling of Clogging in Microfluidic Structures from Simple to Complex Geometries"
  • We develop a mean-field model to study clogging in microfluidic devices and microvascular networks. Clogging in microfluidic cell sorters, which sort cells based on deformability, leads to disruptions in their performance, lower predictability and reliability, and a shorter lifetime in some cases. Our mean-field approach predicts the time of failure of single-column devices with a constant pressure gradient, constant flow rate, or independent channels. In addition, it provides insight into the clogging time and behavior of multiple-column devices and more complex porous structures, such as microvascular networks. To confirm our results, we use a time-driven stochastic simulation, numerically solve systems of differential equations, and use tools from probability theory and reliability engineering. In the case of capillary beds, we consider how the graph Laplacian spectrum provides some insight into the progress of clogging in the network.

CBBS Subgroup Contributed Talks

  • Donggu Lee Konkuk University
    "Role of OCT1 in regulation of miR-451-LKB1-AMPK-OCT1-mTOR core signaling network and cell invasion in glioblastoma"
  • Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short central survival time. GBM is characterized by aggressive proliferation and critical cellular infiltration. miR-451 and its downstream molecules (LKB1, AMPK, OCT1, mTOR) are known to play a pivotal role in balancing proliferation and aggressive invasion in response to metabolic stress in a tumor microenvironment (TME). Recent studies have shown that OCT1 and LKB1 play an important role in regulation of the mutual inhibition between cell proliferation and migration. In this work, we develop a mathematical model of signaling pathway dynamics in GBM evolution which focuses specifically on the relative balance of proliferative capacity and invasion potential. In the work, we represent the miR-451/LKB1/AMPK/OCT1/mTOR pathway by a mathematical model and show how the effect of fluctuating glucose on tumor cells needs to be reprogrammed by taking into account the recent history of glucose variations and an LKB1-OCT1 mutual feedback loop. The simulations show how changes in glucose have a significant effect on the level of key signaling molecules, determining in promotion or inhibition of glioma cell migration (Kim, Lee, & Lawler, Phil Trans Roy Soc-B, 2020).
  • Yukitaka Ishimoto Akita Prefectural University
    "In-vivo cell flow visualisation using deep learning and other means"
  • In recent years, measurements of cellular movements and forces in living body have been paid much attention, chiefly for regenerative therapy and medical applications. It is because they are thought to give deeper insight on tissue mechanics and engineering. There are various ways of invasive and non-invasive measurements. Among them, cell deformations and flow play an pivotal role for elucidation of tissue/organ morphogenesis. However, conventional flow visualization techniques, such as PIV and PTV, often fail to capture the cell flow due to cellular morphological events. To adequately develop such measurements, it is critical to establish precise detection of positions/shapes and correspondence between individual cell shapes at different timepoints. In this work, we show our two distinct attempts of flow visualization of deforming epithelial sheet. One is for particle tracking velocimetry (PTV) of four-dimensional cell flow by using deep neural network model (DNN) onto deforming nucleus images. The other is to track cell shape changes of the sheet by extracting cell boundaries from live-imaging data and further fitting them to a vertex-edge configuration of the bubbly vertex model. Further extensions of both attempts will also be discussed.
  • Tara Hameed Imperial College London
    "A systematic workflow to assess the useability of data in model development"
  • Data sparsity is one of the bottlenecks we often encounter in model development, especially for disease modelling or in fields where interdisciplinary cross-collaboration is still being developed. When a model is fit to sparse data, it is hard to discern whether potential model misfit is caused by inherent model misspecification, which requires reformulation of the model, or by data sparsity, which requires further data collection. We proposed a systematic workflow to assess the degree to which the available data can inform mathematical models theoretically, by upcycling a known statistical workflow that uses simulation studies. The proposed workflow quantifies the useability of the experimental data in terms of expected quality of parameter estimation and model prediction. Application of the workflow to our mathematical model of early-stage invasive aspergillosis (pulmonary fungal infection), adapted from a previous model, allowed us to suggest future experiments that could provide more “useable” data to infer the model's nonlinear interaction parameters and to make better predictions. The presented workflow could be useful when models are developed with data sparsity as a limiting factor for model-based inference.
  • Anibal Thiago Bezerra Instituto de Ciências Exatas, Universidade Federal de Alfenas
    " Gastric Emptying and Orocaecal Transit Analyses of Diabetic and Control Individuals Through Deep Neural Networks"
  • Classical analysis of experimental data generally relies on statistical methods. These methods, however, can be contradictory depending on the methodology and the adopted metrics. In the quantification of gastric emptying (GE) and orocaecal transit (OCT), this is the case in the discrimination between rats who have dysfunctions or diseases like diabetes and the ones that do not. Metrics involved in this context are mean gastric emptying time (MGET), orocaecal transit time (OCTT), and mean caecum arrival time (MCAT). To overcome their limitations, here we present an artificial neural network (ANN) capable of discriminating between control and diabetic individuals rats through GE and OCT data analysis of alternate current biosusceptometry (ACB). For GE, the ANN classification reached an accuracy above 90% after a few epochs. The respective sensitivity was 88%, and the specificity was 83%. For OCT, the accuracy also achieved 90%, with a specificity of 75% and unitary sensitivity. These achieved results support that the proposed ANN can be an alternative methodology to the classical method employed over the years in the gastrointestinal transit area. This work is supported by funding from grant #2020/05556-0, São Paulo Research Foundation (FAPESP).

CBBS Subgroup Contributed Talks

  • Helen Zha University of Oxford
    "Lubrication model of a valve-controlled, gravity-driven bioreactor for platelet production"
  • We investigate the effect of valve dynamics, scaffold permeability, and bioreactor length on the scaffold shear stress, and fluxes in the bioreactor. The model is extremely computationally efficient, thus we can quickly simulate its operation under different valve configurations and geometric parameters, to optimise some function of shear stress and fluxes.
  • Sahar Jafari Nivlouei Department of Physics, University of Coimbra, Portugal
    "3D Multiscale Modeling of Tumor Vascular Growth: Evaluation of the effectiveness of chemotherapy"
  • Developing a multiscale model that includes relevant mechanical and biological properties of endothelial and tumor cells, it is possible to simulate tumor growth and angiogenesis, in a simplified but realistic way. The present model covers multiple time and spatial scales, including extracellular, cellular and intracellular scales. At the intracellular scale, a Boolean network model is used to implement signaling transduction that determines the cell phenotype. Using an agent-based cellular Potts model, it is possible to simulate the cells' biophysical and molecular interactions. A set of PDEs describes tumor-secreted VEGF, vessel-secreted nutrients and cytotoxic drug pharmacodynamics. Results show that the tumor growth rate increases considerably as new capillaries form around the tumor cells, and the malignant tumor progression leads to a high degree of vascularization. Moreover, a systematic study of chemotherapy allows to evaluate typical clinical protocols in what concern with therapy initiation and dose comparison. Accordingly, a delay in chemotherapy initiation does not have a significant effect in the long term, as the tumor volume continues to increase throughout therapy. However, it has been observed that although the therapeutic efficacy may be not enough to prevent tumor regrowth, there is a significant decrease in the tumor size after chemotherapy.
  • Richard Foster Virginia Commonwealth University
    "Modeling Breathing Asynchrony in the Preterm Infant"
  • Extremely preterm infants are at risk of developing chronic lung disease after birth due to factors such as weak intercostal muscles, surfactant deficiency, and a highly compliant (floppy) chest wall. These factors can cause asynchronous volume change between the rib cage and abdomen chest wall components, termed 'thoracoabdominal asynchrony' (TAA), which compromise breathing and could lead to lung volume loss. We constructed a respiratory model that simulates TAA under several clinical conditions by incorporating a chest wall partitioned into independent rib cage and abdominal components with respective intercostal and diaphragm muscle activation functions. Nonlinear compliance functions for the rib cage and abdomen were derived from experimental data. Simulation results indicate that TAA occurs when more than ~80% of driving pressure comes from the diaphragm and when a simulated endotracheal tube increases upper airway resistance ~5-fold. This is the first known explicit simulation of independent chest wall component volume changes with nonlinear compliances and resulting breathing asynchrony.
  • Alberto Coccarelli College of Engineering, Swansea University
    "Computer modelling for decrypting vascular function"
  • Ca2+ signalling plays a pivotal role in the generation of vascular tone, which in turn determines the level of blood perfusion within tissues. Despite its implication in the onset of several pathological conditions (such as hypertension, myocardial ischemia), vascular function is still poorly understood and therefore there is an urgent need to develop computer models for providing a mechanistic understanding of the underlying dynamics. Within this context, endothelial cells represent system's sensor able to monitor haemodynamic variables as well as the presence of endogenous agents. This information is then translated by endothelial cells into second messenger molecules (such as Ca2+, IP3) which ultimately may up- or down-regulate the level of contraction of the smooth muscle cells. Here we introduce a model for computing the Ca2+ dynamics in endothelial cells induced by agonist intervention. With respect to its predecessors, this model accounts for a new component describing the interaction between calcium stores and store-operated channels, which constitutes the main way for Ca2+ entry within the cell. Through numerical experiments, a link between this subcellular component and the experimentally recorded Ca2+ oscillations is established. Finally, the developed model is employed for quantifying the variability in Ca2+ response observed within the cell population.

CBBS Subgroup Contributed Talks

  • Anna Claudia Mello de Resende Laboratório Nacional de Computação Científica (LNCC)
    "Integrating Image-Driven Deformation with Tumor Growth Models"
  • As a solid tumor evolves, compressive stresses accumulate within the tumor due to growth. These stresses play important roles on tumor cells phenotype differentiation and tumor microenvironment conditions. Many mathematical models have been developed to represent tumor growth under deformation. From a continuum mechanics point of view, they are usually built by performing a kinematic decomposition, applying the momentum balance equation, and adding constitutive relations. This framework involves a series of assumptions that ultimately impact the prediction of the tumor deformation. A different framework can be pursued by using in vivo data to recover the tumor deformation. Here we investigate the use of a classical optical flow methodology known as the Lucas-Kanade technique to track tumor deformation in a synthetic experimental breast cancer setting. We also perform a model-free sensitivity analysis to study the impact of parameter uncertainties on the tumor evolution in the proposed modeling framework. We focus on the identification of the set of influential parameters with respect to the tumor area evolution, recognized as a meaningful quantity of interest. We show that optical flow techniques may capture deformations appearing in breast cancers, being a useful alternative to integrate in vivo deformation data to mathematical tumor models.
  • Dorsa Mohammadrezaei Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
    "In-vitro and In-silico Study on a 3D-Bioprinted Breast Cancer Tumor Model"
  • 3D culture methods, by incorporating significant properties of cellular habitat, such as heterogeneous microenvironment, complex interactions of cells with their neighbor cells as well as local extracellular matrix, and complicated diffusion processes of nutrients and oxygen, provide a closer prediction of the real system. One of the most recent 3D biofabrication methods is 3D bioprinting which has contributed dramatically to the development of three-dimensionality and heterogeneity of the tumor microenvironment adequately to replicate characteristics of cancer tumor in vivo. Although 3D bioprinting is rapidly progressing in cancer-related studies, there is still a need to gain a better insight into cell growth mechanism post printing. Computational tools, such as cellular Automata Modelling can be a good complement to the In-vitro experiments that assists to simulate the breast cancer cells activity and growth while cells are encapsulated within porous hydrogel-based construct fabricated using extrusion-based 3D bioprinting technique.
  • Noemi Andor Moffitt Cancer Center
    "Tipping cancer cells over the edge; the context-dependent cost of DNA content variation"
  • The tip-over hypothesis of DNA damage therapy sensitivity proposes that cytotoxic therapy is effective if it pushes a cancer cell's somatic copy number alteration (SCNA) load above a tipping point. We present evidence that the tipping point is accounted for not by elevated SCNA load alone, but by an inability of the tissue micro-environment (TME) to provide the necessary resources. The energetic costs of DNA content levels required for high SCNA loads do not, in the absence of cytotoxic therapy, justify the masking benefits they bring. We investigate Oxygen, Phosphate and Glucose as candidate rate-limiting substrates of dNTP synthesis of cancer cells with variable DNA contents. Hereby we focus on stomach and brain tumors as two representative cancer types whose TME can “afford” different amounts of DNA. Our results point to the potential of tumor cell DNA content and dNTP substrate availability to predict a tumor's vulnerability to increasing SCNA rate.
  • Anna Miller Department of Integrated Mathematical Oncology, Moffitt Cancer Center
    "An integrated computational model of multiple myeloma-bone dynamics under treatment"
  • Multiple myeloma is a largely incurable cancer characterized by the expansion of plasma cells in the bone marrow. Osteolytic lesions occur as a result of a “vicious cycle” between myeloma cells and trabecular bone that tips the balance of normal bone remodeling in favor of bone resorption. Standard of care treatments include bisphosphonates to slow down bone loss, and bortezomib, an anticancer therapy. Understanding how the composition of the bone microenvironment impacts the success of treatments using in vitro and in vivo methods alone remains a challenge. However, integration of biology and computational modeling allows a unique insight into the spatiotemporal aspects of myeloma progression and how treatments impact the disease.To explore these dynamics, we developed a hybrid agent-based model that incorporates key cell types that drive normal bone remodeling, including osteoclasts and osteoblasts, and use published data as well as our own to calibrate parameters such as the dose-dependent responses of treatments on myeloma and bone cells. We simulate the progression of myeloma growth and bone disease, starting from bone homeostasis, and explore how the “vicious cycle” is modified in the presence of treatments. This computational model has the potential to provide insight into better treatment strategies.

CBBS Subgroup Contributed Talks

  • Prasenjit Ghosh PhD Candidate, Indian Institute of Science, Bengaluru, India
    "Discrete particulate modeling of cell nuclei"
  • The nucleus of a cell plays a pivotal role in regulating cellular function and providing mechanical integrity. We present a three-dimensional discrete particle model of the nucleus that incorporates the nuclear lamina and chromatin-containing nucleoplasm. The exterior, including the lamina, is modeled by a shell of bonded particles that can exhibit elastic, geometrically nonlinear, and buckling characteristics. The interior, comprising the viscous fluid-like nucleoplasm and the elastic chromatin meshwork, is modeled with particles that undergo viscoelastic interactions. Such a particle framework allows for a realistic representation of the discreteness in nuclear structure and heterogeneity in nuclear properties. In addition, contact dynamics between particles is naturally handled within this framework. This is advantageous when considering the dynamic linkages between intranuclear components (chromatin and the lamina) or between the nucleus and the cytoskeleton. The efficacy of this particle model is compared with different experimental assays, and relevant insights are provided.
  • Benjamin Wölfl University of Vienna, Vienna Graduate School of Population Genetics
    " On branch length distributions in the coalescent and its application in the i-ton density score"
  • Efficient backward-time and forward-time simulation of simple to complex evolutionary scenarios are combined in order to describe the branch length distributions of branches with i underlying leaves in the extant sample in the correlated coalescent trees across linked loci in the genetic basis of a single independent trait. This takes into account the effect of genetic linkage on the decay of coalescent tree correlation across neighboring loci. Specifically, also the distributional shape under polygenic adaptation is investigated. Generally, there is no analytical expression for these branch length distributions which raises the importance of a computational insight. Ultimately, this distribution is used in order to construct a hypothesis test of selection versus no selection which does not only make use of singletons as in the singleton density score (SDS), but generally the density of i-tons via the newly introduced i-ton density score (IDS) test statistic. In this way, attention is placed on the characteristics of this distribution under different evolutionary scenarios, in particular when we are not only facing a simple recent hard selective sweep. Among other organisms, this method may then for instance be applied to human genetic data sets.
  • Diego Samuel Rodrigues FT-UNICAMP
    "A Bayesian Framework for Mathematical Modeling of In Vivo Pharmacokinetic Profiles of Magnetic Particles"
  • This contribution is about a Bayesian framework devoted to parameter estimation of an ordinary differential equation (ODE) model describing pharmacokinetic (PK) profiles of magnetic nanoparticles. Data comes from in vivo experiments in which one injected the nanoparticles into the bloodstream and measured them by alternate current biosusceptometry both in the heart and liver. The non-linear ODE model comprises three compartments, one for the heart and the other two for the liver, from which the nanoparticles partially return to the bloodstream. Reported simulations and calibration of curves and parameters were performed in R language using FME Package and others. As for results, it includes uncertainty analysis, credibility regions, and an identifiability discussion. As a perspective, we intend to use the described methodology for investigating possible changes in PK profiles originated by liver cancers. This work is supported by funding from grant #2020/05556-0, São Paulo Research Foundation (FAPESP).
  • Jackie Taylor University of Minnesota, Twin Cities
    " An advection-diffusion-aggregation model for the colony formation and vertical motility of Microcystis aeruginosa"
  • The cyanobacterium Microcystis aeruginosa is one of the most common algal species capable of forming harmful algal blooms. There are two key traits related to the ubiquity of M. aeruginosa: colony formation under stressful environmental conditions and vertical motility via buoyancy regulation. While the importance and mechanisms of these traits have been thoroughly investigated, there is currently no model of M. aeruginosa transport and population dynamics that couples colony formation and motility. This talk will introduce such a model, consisting of a system of partial differential equations describing (i) the vertical diffusion of M. aeruginosa colonies in a stratified lake environment, (ii) the vertical advection of M. aeruginosa colonies as a function of water temperature and colony size, and (iii) a Smoluchowski term for the aggregation of colonies due to Brownian motion, shear, and differential settling. Model results will be compared to field trends, and the promises and perils of the method will be discussed.