Thursday, June 17 at 04:15am (PDT)
Thursday, June 17 at 12:15pm (BST)
Thursday, June 17 08:15pm (KST)


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.

Mathematical approaches to vascular biology

Organized by: Jessica Crawshaw (The University of Melbourne, Australia), James Osborne (The University of Melbourne, Australia), Lowell Edgar (The University of Edinburgh, Scotland)
Note: this minisymposia has multiple sessions. The second session is MS17-CDEV.

  • Jessica Crawshaw (The University of Melbourne, Australia)
    "To collapse or not to collapse: how do mechanical forces drive vascular regression?"
  • Vascular regression is a critical process concluding the maturation of developing capillary networks, in which redundant blood vessels are removed. Recent research suggests that forces from the local blood flow (haemodynamic forces) trigger polarized endothelial cell migration against the flow, resulting in capillary collapse and regression. However, vascular regression is also driven by several additional pathways including local adhesion forces and cellular signalling factors. Due to the delicate nature of these microvessels, it is difficult to experimentally untangle the roles of each pathway during vascular development. As such, the development of computational models to analyse the relationship between the local haemodynamic forces and the surrounding vasculature during regression are invaluable. In this talk, we will present a novel computational framework to mathematically study and isolate the role of haemodynamic in vessel deformation and collapse during vascular regression. To model regression, we describe the capillary wall as a discretised hyperelastic membrane, coupled with a lattice-Boltzmann model of blood flow in an iterative manner. This discrete approach provides a natural framework to consider the relationship between the capillary wall and the local blood flow, and allows for the easy inclusion of structural heterogeneities across the capillary wall. Using this model we are able to examine the role of the haemodynamic forces during vascular regression, as well as the network level ramifications of local regression.
  • Daria Stepanova (CRM Centre for Mathematical Research, Spain)
    "Multiscale approach to understanding cell rearrangements in early angiogenesis"
  • Angiogenesis is the process whereby endothelial cells (ECs) migrate from a pre-existing vascular bed guided by local environmental cues and interacting with each other to eventually create a new vascular network. We introduce a multiscale model of migration-driven angiogenic sprouting which accounts for the individual phenotype selection of ECs, cell-cell and cell-extracellular matrix interactions. The model, calibrated and validated against various experimental data, captures the characteristic behavior of ECs: branching, cell mixing and, chemotactic sensitivity. These properties, rather than being hard-wired into the model, emerge naturally due to accounting for heterogeneous behavior of ECs depending on their gene expression pattern. This allows us to use the model to investigate the role of cell rearrangements during angiogenic sprouting on the vascular network structure. In particular, we show how cells with impaired gene expression of a specific receptor are characterised by reduced levels of cell rearrangement which influences the branching pattern of vascular networks. Overall, our results support the hypothesis that cell rearrangements play a central role in angiogenesis.
  • Katie Bentley (The Crick Institute, England)
    "Filopodia speed up Notch selection of endothelial tip cells: in silico predictions confirmed in vivo"
  • I will describe our recent proof of concept in silica/in vivo study demonstrating that filopodia (actin-rich, dynamic, finger-like cell membrane protrusions) play an unexpected role in speeding up collective endothelial decisions during the time-constrained process of 'tip cell' selection during blood vessel formation (angiogenesis). We first validate simulation predictions in vivo with live imaging of zebrafish intersegmental vessel growth. Further simulation studies then indicate the effect is due to the coupled positive feedback between movement and sensing on filopodia conferring a bistable switch-like property to Notch lateral inhibition, ensuring tip selection is a rapid and robust process. We then employ measures from computational neuroscience to assess whether filopodia function as a primitive (basal) form of active perception due to the sensorimotor coordination apparent in filopodia and find evidence in support. By viewing cell behaviour through the 'basal cognitive lens' we acquire a fresh perspective on the tip cell selection process, revealing a hidden, yet vital time-keeping role for filopodia. Finally, I’ll discuss a myriad of new and exciting research directions stemming from our conceptual approach to interpreting cell behaviour.
  • Lowell Edgar (The University of Edinburgh, U.K)
    "Force transmission between migrating endothelial agents regulates functional shunting during angiogenic remodelling"
  • During angiogenic remodelling endothelial cells (ECs) composing blood vessels polarise and migrate against the direction of flow. The cellular mechanisms which prevent functional shunting during this process remain poorly understood despite being relevant to arteriovenous malformations and dysfunctional microcirculation and local hypoxia in cancer. We hypothesise that force transmission between migrating ECs plays a crucial role in shunt formation and have designed a model based on force-transmitting agents to investigate. EC agents consisted of nested ellipses polarised against flow. Force transmission between neighbouring agents, based on overlap, consists of extrusive (pushing) forces which maintain spacing and cohesive (pulling) forces which maintain the collective. We simulated migration within an idealised capillary plexus in which agents either split apart or combined at bifurcations based on the convergence/divergence of flow. Extrusion forces stabilise the vasculature and allow cells to intercalate to reduce stress. Excessive amounts of cohesion disrupted this intercalation, creating tension and prolonged flow reversals. Flow reversals switch convergence/divergence at bifurcations, which aggregates cells and leads to shunting and perfusion loss. Our results implicate dysfunctional junctional remodelling and/or force transmission as a possible mechanism vascular malformation and implicate new targets for investigation in future experimental studies.

Mathematical Modeling of Exposure and Target Interaction in Pharmaceutical Development of Therapeutic Proteins

Organized by: Jeroen Elassaiss-Schaap (PD-value BV, Netherlands), Johannes Schropp (University of Konstanz, Germany)

  • Leonid Gibiansky (QuantPharm LLC, North Potomac, MD, USA)
    "Target-mediated drug disposition in the pharmacokinetics of monoclonal antibodies and its quasi-steady state solutions"
  • The term TMDD refers to the biological processes and models where drug-target binding significantly influences both pharmacodynamics (PD) and pharmacokinetics (PK). These are typical for the biologic drugs with high specificity to the intended target. The TMDD model describes the processes on the widely different time scales: fast drug-target binding and relatively slow drug distribution and elimination. Given the typical clinically relevant sampling, this model is rarely identifiable thus requiring use of approximations. Various TMDD approximations have been developed. Investigation of the TMDD equations identified distinct phases in the concentration time profiles. The initial fast phase reflects drug-target binding processes. This phase is followed by a slow phase where the drug, target, and drug-target complex are in a slowly changing equilibrium. Several approximations that differ by the underlying assumptions have been developed. The quasi-steady state (QSS) approximation describes the TMDD system where the elimination of the drug-target complex is much slower than the elimination of the free target. In this case, the drug-target complex contributes significantly to the drug kinetics. The QSS approximation was successful in describing PK and PD of monoclonal antibodies that target soluble receptors. When the drug-target complex is eliminated faster than the free target, the QSS equations can be simplified to result in the Michaelis-Menten (MM) approximation. The MM approximation was shown to describe PK of many monoclonal antibodies that target membrane receptors. For drugs that bind to both soluble and membrane receptors, the QSS approximation of the two-target TMDD equations can be used. TMDD modeling framework can be adapted to many different systems, e.g. drugs that bind to targets with two binding sites, drugs with two identical binding sites, antibody-drug conjugates, etc.
  • Wojciech Krzyzanski (University at Buffalo, USA)
    "Application of Quasi-equilibrium Approximation to Reduction of Complex Physiologically Based Pharmacokinetic Models of Monoclonal Antibodies"
  • Physiologically based pharmacokinetic (PBPK) models are commonly used to describe the time courses of plasma concentrations of monoclonal antibodies. These models use ordinary differential equations to quantify monoclonal antibodies disposition in compartments such as the plasma, lymph node, as well as major peripheral organs. In addition, each organ consists of vascular, interstitial, and endosomal sub-compartments. The drug molecules are distributed to all compartments, taken up by the organs, internalized to the cell cytoplasm, and degraded in the endosomes or recycled to the interstitial space. In result, a PBPK model becomes a high dimensional nonlinear system with many parameters. We present a model reduction technique that is based on the quasi-equilibrium assumptions about the rates of processes of the dynamical system that simplifies the PBPK model to a three-compartment linear model. The technique is applied to a previously published PBPK model for monoclonal antibodies.
  • Johannes Schropp (University of Konstanz, Germany)
    "Bispecific-Antibodies: Properties, Approximation and Optimal Dosing Strategy"
  • Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown, i.e., promise as immune-oncology drugs. We present a general target-mediated drug disposition model for these BsAbs, which bind to two different targets on different cell membranes. In addition, a quasi-equilibrium approximation with less binding parameters and, if necessary, reduced internalization parameters is presented. The model is used to investigate the kinetics of BsAb and TC. The analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, an optimal dosing strategy of BsAbs, which immediately create and maintain maximal possible TC concentration, is presented.
  • Weirong Wang (Janssen, USA)
    "Target-mediated drug disposition of immuno-oncology drugs: mathematical models for exposure and pharmacodynamics, and its translation between animal and man"
  • The therapeutic effect of all biotherapeutics is driven by its interaction with the therapeutic target. These interactions are often called target engagement (TE) when the target is a soluble protein and receptor occupancy (RO) when the target is a cell surface receptor. TE and RO assessments play a central role in translational pharmacology. Although TE or RO itself does not guarantee efficacy, it reflects the dynamics of drug engagement and corresponding target modulation and provides a mechanism to extrapolate drug effects between preclinical species and humans, as well as between healthy and disease populations. Together with mechanism and physiologically based PK/PD modeling, TE and RO are commonly used to facilitate rational dose selection and clinical study design.

Collective Behavior and Social Evolution

Organized by: Daniel Cooney (University of Pennsylvania, USA) & Olivia Chu (Princeton University, USA)
Note: this minisymposia has multiple sessions. The second session is MS16-EVOP.

  • Ricardo Martinez-Garcia (ICTP South American Institute for Fundamental Research)
    "The exploitative segregation of plant roots: a game-theory approach to below-ground plant growth"
  • Plant roots determine carbon uptake, survivorship, and agricultural yield and represent a large proportion of the world’s vegetation carbon pool. The study of below-ground competition, unlike above-ground shoot competition, is hampered by our inability to observe roots. We have few observations of intact root systems in soil and lack a comprehensive theory for root system responses to their environment and the presence of other individuals. In this presentation, I will first review previous efforts to explain plant below-ground interactions and discuss how they lead to seemingly contradictory predictions. Then, I will introduce our recent work and show how it resolves existing controversy and provides a unifying framework to study below-ground plant interactions. I will conclude by discussing future research lines that depart from our results and how they can be addressed with extensions of our original model.
  • Max Souza (Fluminense Federal University)
    "Stochastic evolution of finite populations: the fingerprints of fixation"
  • On the one hand, once we are given a finite population stochastic finite population model without mutations and a (possibly frequency dependent) fitness function, the computation of the corresponding fixation probability is straightforward. On the other hand, one might ask what the fixation probability can tell us about the underlying process. Starting from classical Moran and Wright-Fisher processes, we will discuss some qualitative properties of the corresponding fixation probability. We also address when the fixation probability uniquely characterises knowing the fixation characterises these processes. In particular, we will see that for each fixation probability vector that is strictly increasing, there is exactly one Moran process that realises it. For the Wright-Fisher process, however, the situation is more involved and almost any fixation pattern is attainable — though not necessarily in a unique way. If time allows, we will also address the corresponding inverse problem and some asymptotic results for large populations.
  • Nina Fefferman (University of Tennessee)
    "How infectious diseases may have shaped the evolution of social organization"
  • Sociality itself represents a tradeoff between pooled benefits and shared risks. Looking at societal organization in social species may reveal the footprints of selective pressures to find balance between two major constraints: mitigation of the transmission of infection and population-level efficiency of division of labor. In this talk, we'll discuss a simple model that abstracts the organization of collaborative roles from different social insect taxa and contrasts their performance under disease-free and outbreak scenarios. We'll explore how infectious diseases may have selected for organizational strategies that maintain cohort stability and show why this trait would be unlikely to have been maintained in the absence of outbreak risks.
  • Joseph Johnson (University of Michigan)
    "A Dynamical Model for the Origin of Anisogamy"
  • The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike some prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population’s mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

Intravital imaging in immunology: experimental and computational approaches

Organized by: Barun Majumder (University of Tennessee, USA), Soumen Bera (University of Tennessee, USA)
Note: this minisymposia has multiple sessions. The second session is MS17-IMMU.

  • Paulus Mrass (Department of Molecular Genetics and Microbiology, University of New Mexico, USA)
    "Quantitative imaging identifies CXCR4 as a molecular switch that balances confinement and ballisitic migration of cytotoxic T cells within flu- infected lungs"
  • Cytotoxic T cells play an important role in protective immune responses against the flu, but the molecular mechanisms that regulate this function remain incompletely understood. In the present study we established a live imaging model that enables quantification of T cell motility within intact flu-infected lung tissue. This setup revealed that cytotoxic T cells show heterogenous migration patterns, characterized by intermittent periods of confinement and ballistic relocation. A special feature of our imaging model was the capacity to separately measure T cells that are in close proximity to flu-infected regions and those that are distant. Comparison of these two groups revealed that T cells that reside in flu-positive regions are signficantly more confined than T cells in flu-negative regions. This finding indicated that exposure to cognate peptides is one mechanism that contributes to the heterogeneous migration patterns of cytotoxic T cells within flu-infected lungs. To dissect the molecular mechanisms that regulate interstitial migration of T cells further, we analyzed T cell motility after treatment of lungs with pharmacological inhibitors. This approach revealed that AMD3100, a specific inhibitor of the chemokine recetpor CXCR4, caused a signficant suppression of interstitial migration within flu-negative regions. Unexpectely, we also found that inhibition of CXCR4 had an oppositive effect of T cells within flu-positive regions, i.e. the T cells became less confined. From these findings, we conclude that CXCR4 functions as a molecular switch that boosts interaction with target cells by two distinct mechanisms: (1) by enhancing motility towards flu-positive regions; and (2) by limiting motility within flu- positive regions, which likely facilitates the initiation of cognate interactions with target cells. Indeed, when we inhibited CXCR4 in flu-infected mice with AMD3100, this led to a reduction of degranulation of cytotoxic T cells infiltrating flu-infected lungs. Together, quantitative imaging has revealed that CXCR4 controls the functionality of lung-infiltrating cytotoxic T cells by regulation of intra-tissue motility.
  • Arja Ray (Department of Pathology, University of California San Francisco, USA)
    "Visualizing T cell behavior in solid tumors to define barriers to immunotherapy"
  • Cancer immunotherapy relies on the effective function of cytotoxic CD8 T cells in the tumor microenvironment (TME). Other immune cells such as tumor- associated macrophages (TAMs) and the tumor stroma are critical components of the TME that inform CD8 T cell function. In tumors with abundant T cell infiltration, immunotherapy using bi-specific T cell engagers (BiTE) mediates physical interactions between T cells and tumor cells, thereby forcing tumor recognition and cytotoxic killing. However, this immunotherapy has had limited success in solid tumors, leading to questions regarding the barriers posed by the TME in this context. Using intravital imaging, we discovered vast heterogeneity in the movement of BiTEs out of perfused blood vessels in intact live tumors, from unhindered diffusion in some regions to being entirely contained within blood vessels in others. Indeed, the sufficiency of tumor-resident T cells to mediate tumor rejection was a function of dosage, thereby indicating that the bioavailability of such functional molecules in the TME is a key factor restricting their efficacy in solid tumors. Many solid tumors, on the other hand, are characterized by a lack of T cell (and other immune cell) infiltration, commonly referred to as an “immune desert” tumor. It has been postulated that TAMs play a key role in trapping T cells at the tumor margins, thereby leading to a T cell sparse tumor nest. Using a novel mouse model to specifically mark TAMs, we performed live imaging of TAM:T cell localization and interactions in the TME. Indeed, in an immune desert tumor model, T cells tend to be trapped near the tumor margins, co-localized with TAMs on a bed of robust deposition of fibrous collagen. Using spatial transcriptomics, we identify a unique TAM population at the tumor margin that are putatively involved in fibrosis in communication with CAFs. We hypothesize that this TAM subset is a key component of the immune- stromal cross-talk that leads to excessive fibrosis and exclusion of T cells from the TME in immune desert tumors. Overall, visualizing and defining the microenvironment around T cells in immune rich and immune desert tumors reveals distinct barriers to effective T cell function and points to the necessity of tailored approaches to improve cancer immunotherapy for different solid tumors.
  • Judy Cannon (University of New Mexico School of Medicine, USA)
    "Effect of tissue environment on T cell movement"
  • T cells are a key effector cell type in the immune response, migrating through tissues in order to clear infection such as influenza infection in the lung. T cells must move through many different types of tissues to mount an effective response: naïve T cells migrate in and out of lymph nodes searching for antigen on dendritic cells, while activated T cells migrate to peripheral tissue such as lung to clear influenza infection. We investigate how different tissues such as lymph node and lung environments affect T cell motion using two photon microscopy to visualize effector T cells moving in different tissue settings. We perform quantitative analysis of in situ T cell movement and find that T cell speeds vary independent of the tissue environment or type of T cells. Naïve T cells in the lymph nodes move with similar average speed as effector T cells in the flu-infected lung, but effector T cells in an acute lung injury model move much more slowly. Interestingly, despite similar speeds, T cells in the lung do not show a coupling of speed and persistence that many other cell types have been seen to demonstrate, suggesting that the lung environment may exert effects on T cell movement to drive specific types of motion. T cells in the lung also show greater persistent motion than T cells in lymph nodes. The combination of in situ imaging and quantitative analysis of cell movement can uncover how specific tissue environments impact T cell movement and search for infection within different tissue contexts.
  • Soumen Bera (Department of Microbiology, University of Tennessee Knoxville, USA)
    "Mathematical modeling of CD8 T cell-mediated elimination of malaria liver stages using intravital imaging experiments"
  • CD8+ T cells are one of the most critical immune defenses against intracellular pathogens capable of finding and eliminating the infected cells and preventing blood-stage diseases. Intravital imaging technic helps demonstrate the killing of liver stages Malaria parasites by memory induced or activated CD8+ T cells. Using these technics and mathematical modeling, we have recently shown the formation of large clusters consisting of variable number of effectors CD8+ T cells around the parasite-infected hepatocytes is rapid, indicating the high efficiency of CD8+ T cells for finding their target within complex organs like the liver. However, it has not been clear how many activated CD8+ T cells are required to eliminate the malaria parasites within a short period of time. Using a combination of intravital experimental data and mathematical modeling, we have provided detailed insights about the CD8+ T cells dynamic against the parasite phenotypes. The parasite's death corresponding to a high number of CD8+ T cells indicates a prolonged interaction between them; however, the death of parasites with a smaller number of T cells due to multiple factors. Using alternative mechanistic models, increasing the number of CD8+ T cells response better predict the parasite phenotypic dynamics compare to others, indicating increasing CD8+ T cells prompt the killing process. However, alternative mathematical models showed the fixed killing efficiency per T cell per parasite that means a higher number of T cells has higher killing efficiency. Finally, dose-response analysis indicates a smaller number of T cells is required to kill the parasites after a couple of hours of CD8+ T cells transfer, but with increasing time, a high number of T cells is required to eliminate the parasite. With different alternative methods, our analysis indicates novel insights about quantifying CD8+ T cells dynamic in the process of parasite elimination. 

Women in Mathematical Epidemiology

Organized by: Katharine Gurski (Howard University, United States), Kathleen Hoffman (University of Maryland, Baltimore County, United States)
Note: this minisymposia has multiple sessions. The second session is MS19-MEPI.

  • Zhilan Feng (Purdue University, United States)
    "Applications of mathematical models in epidemiology"
  • Mathematical modeling of infectious diseases has affected disease control policy throughout the developed world. Policy goals vary with disease and setting, but preventing outbreaks is common. In this talk, I will present several examples to demonstrate how various models can be used to answer questions related to disease control and prevention for specific diseases in real populations. These models are systems of integral and/or differential equations. The mathematical results are motivated to address specific biological questions.
  • Marissa Renardy (Applied BioMath, United States)
    "Structural identifiability analysis of PDEs: A case study in continuous age-structured epidemic models"
  • Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.
  • Olivia Prosper (University of Tennessee Knoxville, United States)
    "Within-mosquito parasite heterogeneity and its impact on population-level malaria transmission"
  • The malaria parasite Plasmodium falciparum requires a vertebrate host and a female Anopheles mosquito to complete a full life cycle, with sexual reproduction occurring in the mosquito. This sexual stage of the parasite life cycle allows for the production of genetically novel parasites. In the meantime, a mosquito’s biology creates bottlenecks in the infecting parasites’ development. In earlier work, we developed a stochastic model of within-mosquito parasite dynamics and the generation of parasite diversity within a mosquito. We demonstrated the importance of heterogeneity in parasite dynamics across a population of mosquitoes on estimates of parasite diversity. Here, we investigate the implications of this heterogeneity on population-level transmission dynamics of malaria.
  • Miranda Teboh-Ewungkem (Lehigh University, Lehigh University)
    "Using Continuous-time Systems of Non-Linear Ordinary Differential Equations to study Removal of Mosquito-Breeding Site Density Under Community Action and Temperature Effects"
  • : A system of two first order nonlinear ordinary differential equations is used to model and theoretically investigate the dynamics of the formation of mosquito breeding sites in a uniform environment. The model captures the dynamic interplay between community action, climatic factors, and the availability of mosquito breeding sites. The developed model is analysed using standard methods in nonlinear dynamical systems' theory. Model results show that it is possible to attempt the problem of the dynamics of formation of breeding sites by considering the level of human consciousness as measured through human response to community action. Different feedback response functions are used to excite the breeding site removal and community action. For the case where the response functionals are both constants, we identify an indicator function whose size can indicate whether in the long run, community action can lead to the removal and elimination of breeding sites near human habitats. Using a predictor-corrector procedure that fits real climatic data to a continuous periodic function, we demonstrate how climatic variables can be included in the model and how models for the time variation of temperature and precipitation in a given area can be constructed just by appropriately choosing the parameters of a sinusoidal function and then correcting the output using nonlinear least squares analysis. Numerical simulation results are used to complement our analytical results.

Mechanical Models of Complex Diseases

Organized by: Fabian Spill (University of Birmingham, USA)

  • Vijay Rajagopal (University of Melbourne, Australia)
    "Surface area-to-volume ratio, not cellular viscoelasticity is the major determinant of red blood cell traversal through small channels."
  • The remarkable deformability of red blood cells (RBCs) depends on the viscoelasticity of the plasma membrane and cell contents and the surface area to volume (SA:V) ratio; however, it remains unclear which of these factors is the key determinant for passage through small capillaries. We used a microfluidic device to examine the traversal of normal, stiffened, swollen, parasitised and immature RBCs. We show that dramatic stiffening of RBCs had no measurable effect on their ability to traverse small channels. By contrast, a moderate decrease in the SA:V ratio had a marked effect on the equivalent cylinder diameter that is traversable by RBCs of similar cellular viscoelasticity. We developed a finite element model that provides a coherent rationale for the experimental observations, based on the nonlinear mechanical behaviour of the RBC membrane skeleton. We conclude that the SA:V ratio should be given more prominence in studies of RBC pathologies.
  • Bindi Brook (University of Nottingham, UK)
    "Inflammation driven mechanical model of asthmatic airway remodelling"
  • Inflammation, airway hyper-responsiveness and airway remodelling are well-established hallmarks of asthma, but their inter-relationships remain elusive. In order to obtain a better understanding of their inter-dependence, we have developed a mechanochemical morphoelastic model of the airway wall accounting for local volume changes in airway smooth muscle (ASM) and extracellular matrix in response to transient inflammatory or contractile agonist challenges. We use constrained mixture theory, together with a multiplicative decomposition of growth from the elastic deformation, to model the airway wall as a nonlinear fibre-reinforced elastic cylinder. Local contractile agonist drives ASM cell contraction, generating mechanical stresses in the tissue that drive further release of mitogenic mediators and contractile agonists via underlying mechanotransductive signalling pathways. In this talk I will discuss our model predictions and in particular how they: (i) reveal novel mechanotransductive feedback by which hyper-responsive airways exhibit increased remodelling, for example, via stress-induced release of pro-mitogenic and pro- contractile cytokines; (ii) emergence of a persistent contractile tone observed in asthmatics; (iii) enable identification of various parameter combinations that may contribute to the existence of different asthma phenotypes, and combination of factors which may predispose severe asthmatics to fatal bronchospasms. Finally I will discuss how we plan to use this model to investigate how perturbations from a homoeostatic state might drive asthma pathogenesis.
  • Herbert Levine (Northeastern University, USA)
    "The role of extracellular matrix in motility and metastasis"
  • In order for cells to migrate from a primary tumor to the circulation as part of the metastatic cascade, it needs to traverse region of fibrous extracellular matrix (ECM). This material has interesting mechanical properties such as strain-stiffening and plasticity, and interesting effects on cells moving through it, such as contact guidance . And, cells themselves can secrete enzymes that modify the ECM, thereby engaging in 'reciprocal' communication with their microenvironment. Here we use simple computational models to try to better understand this set of phenomena.
  • Stephanie Fraley (University of California San Diego, USA)
    "A spatial model of YAP/TAZ mechanotransduction reveals new insights into how cells sense ECM dimensionality"
  • YAP/TAZ is a master regulator of mechanotransduction; cytoplasmic-to-nuclear translocation of YAP/TAZ responds to different physical cues, including substrate stiffness, substrate dimensionality, and cell shape, and is critical for cellular function and tissue homeostasis. However, the relative contributions and synergies of these biophysical signals to YAP/TAZ translocation remains unclear. For example, in 2D culture, YAP/TAZ nuclear localization correlates strongly with substrate stiffness while in 3D, YAP/TAZ translocation can increase with stiffness, decrease with stiffness, or remain unchanged. Here, we use spatial modeling of YAP/TAZ translocation in response to substrate stiffness to quantitatively analyze the relationships between substrate stiffness, cytosolic stiffness, nuclear mechanics, cell shape, and substrate dimensionality. Our model predicts that increasing substrate activation area through changes in culture dimensionality, while conserving cell volume, forces distinct shape changes that result in nonlinear effect on YAP/TAZ nuclear localization. Moreover, differences in substrate activation area versus total membrane area can account for counterintuitive trends in YAP/TAZ nuclear localization in 3D. Based on this multiscale investigation of the different system features of YAP/TAZ nuclear translocation, we predict that how a cell reads its environment is a complex information transfer function of multiple mechanical and biochemical factors. These predictions reveal design principles of cellular and tissue engineering for YAP/TAZ mechanotransduction.

Mathematics of Microswimming

Organized by: Qixuan Wang (UC Riverside, United States), Bhargav Rallabandi (UC Riverside, United States), Mykhailo Potomkin (UC Riverside, United States)
Note: this minisymposia has multiple sessions. The second session is MS19-MMPB.

  • Chaouqi Misbah (CNRS and Univ. Grenoble, France)
    "Swimming of Cells and Artificial Particles Driven by Shape Changes and Chemical Activity"
  • Locomotion is essential for living cells. It enables bacteria and algae to explore space for food, cancer to spread, and immune system to fight infections. Amoeboid swimming will be first discussed exhibiting variety of behaviors (like navigation, asymmetric motion in a channel, etc.). Then we discuss generic trajectories obtained for active particles driven by a chemical activity. These types of particles display trajectories of intriguing complexity, from regular (e.g. circular, helical, and so on) to irregular motions (run-tumble), the origin of which has remained elusive for over a century. This dynamics versatility is conventionally attributed to the shape asymmetry of the motile entity, to the suspending media, and/or to stochastic regulation. A universal approach highlighting that these movements are generic, occurring for a large class of cells and artificial microswimmers, without the need of invoking shape asymmetry nor stochasticity, but are encoded in their inherent nonlinear evolution. We show, in particular, that for a circular and spherical particle moving in a simple fluid, circular, helical and chaotic motions (akin to a persistent random walk) emerge naturally in different regions of parameter space. This establishes the operating principles for complex trajectories manifestation of motile systems, and offers a new vision with minimal ingredients.
  • Kirsty Wan (University of Exeter, United Kingdom)
    "Locomotor patterning in quadriflagellate microswimmers: lessons from quadrupeds and robots"
  • When animals first evolved from underwater to terrestrial living, they first had to overcome the formidable challenge of coordinating and controlling their limbs to generate effective legged locomotion involving gaits such as crawling, walking galloping. Surprisingly, it was recently discovered that many species of single-celled algae exhibit similar gaits for swimming, despite being only tens of micrometers across and lacking in a nervous system. Among these, species that have four flagella (whip-like appendages that can bend and deform actively in a fluid) are particularly abundant in nature. Species that appear morphologically similar may nonetheless be associated with distinct gaits and swimming speeds. In this talk i will discuss our recent efforts to integrate fluid dynamical modelling, live-cell experiments, and robophysical models to understand the swimming gaits of quadriflagellate algae. Continuing research into these microscopic swimmers may provide key insights into the evolutionary origins of decentralized locomotor control in living systems.
  • Hermes Gadêlha (Department of Engineering Mathematics and Bristol Robotics Laboratory, University of Bristol, United Kingdom)
    "Coarse-graining formulations for sperm swimming and other flagellates"
  • The inertialess fluid-structure interactions of active and passive inextensible filaments and slender-rods are ubiquitous in nature. The coupling between the geometry of deformation and the physical interaction governing the fluid dynamics is complex. Governing equations negotiate multi-scale interactions with non-holonomic constraints. Such systems are structurally convoluted, prone to numerical errors, often requiring penalization methods and high-order spatio-temporal propagators. In this talk we will discuss how the coarse-graining formulation greatly simplifies the several biophysical interactions and overcomes numerical instability. The dynamical system is straightforward and intuitive to implement, and allows for a fast and efficient computation. Only basic knowledge of systems of linear equations is required, and implementation achieved with any solver of choice. Generalizations for complex interaction of multiple rods, Brownian polymer dynamics, active filaments and non local hydrodynamics are also straightforward.
  • Ye Chen (New Jersey Institute of Technology, United States)
    "Helical locomotion in a porous medium"
  • Microorganisms and artificial microswimmers often need to swim through environments that are more complex than purely viscous liquids in their natural habitats or operational environments, such as gel-like mucus, wet soil and aquifer. The question of how properties of these complex environments affect locomotion has attracted considerable recent attention. In this work, we focus on helical locomotion for its ubiquity as a propulsion mechanism adopted by many swimming bacteria. We present a theoretical model to examine how the additional resistance due to the network of stationary obstacles in a porous medium affects helical locomotion. Compared with previous theoretical and experimental results, we will elucidate the effects of the resistance on various types of helical locomotion. We also remark on the limitations as well as potential connections of our results with experimental measurements of bacterial swimming speeds in polymeric solutions.

Mathematical Models for Decision-Making

Organized by: Nicholas Barendregt (University of Colorado Boulder, United States), Jonathan Rubin (University of Pittsburgh, United States)

  • Nicholas Barendregt (University of Colorado Boulder, United States)
    "Normative and dynamic decision urgency in unpredictable environments"
  • Decision-making in uncertain environments often requires adaptive forms of evidence accumulation, but less is known about the decision rules needed to achieve optimal performance. While recent studies of decision models in stochastic and dynamic environments have resulted in several phenomenological models, such as the monotonically collapsing decision threshold of the “urgency-gating model” (UGM), we lack a general, normative description of decision rules and their relation to human decision-making. In this talk, we will develop a normative, Bayes-optimal framework for decision tasks in uncertain and dynamic environments. Using the classic “tokens task” paradigm, we apply Bayesian model fitting and model comparison methods to the normative model, the UGM, and several other heuristic models. Our work demonstrates that the humans using the normative strategy exhibit non-monotonic urgency and identifies regions of parameter space where different types of urgency are optimal. Extending these methods to tasks where the reward for a correct response varies in time, we again find that normative decision rules exhibit rich non-monotonic behavior, providing testable hypotheses for experimentalists to probe in future psychophysics tasks.
  • Timothy Verstynen (Carnegie Mellon University, United States)
    "Rethinking the computational architecture of cortico-basal ganglia-thalamic pathways"
  • Humans and other mammals exhibit a high degree of control when selecting actions in noisy contexts, quickly adapting to unexpected outcomes in order to better exploit opportunities arising in the future. This flexible decision-making is mediated, in part, by cortico-basal-ganglia-thalamic (CBGT) circuits that both control action selection and use feedback signals to modify future decisions. In this talk we will highlight how new insights into the circuit-level architecture of CBGT pathways are informing our understanding of the algorithms of decision-making and learning. Specifically we will show how components of the CBGT circuit map to modifiable parameters that balance the speed-accuracy tradeoff during adaptive decision making.
  • Alex Roxin (Centre de Recerca Matemàtica, Spain)
    "Bump attractor dynamics underlying stimulus integration in perceptual estimation tasks"
  • Perceptual decision and continuous stimulus estimation tasks involve making judgments based on accumulated sensory evidence. Network models of evidence integration usually rely on competition between neural populations each encoding a discrete categorical choice. By design, these models do not maintain information of the integrated stimulus (e.g. the average stimulus direction in degrees) that is necessary for a continuous perceptual judgement. Here, we show that the continuous ring attractor network can integrate a stimulus feature such as orientation and track the stimulus average in the phase of its activity bump. We reduced the network dynamics of the ring model to a two-dimensional equation for the amplitude and the phase of the bump. Interestingly, these reduced equations are nearly identical to an optimal integration process for computing the running average of the stimulus orientation. They differ only in the intrinsic dynamics of the amplitude, which affects the temporal weighting of the sensory evidence. Whether the network shows early (primacy), uniform or late (recency) weighting depends on the relative strength of sensory stimuli compared to the amplitude of the bump and on the initial state of the network. The specific relation between the internal network dynamics and the sensory inputs can be modulated by changing a single parameter of the model, the global excitatory drive. We show that this can account for the heterogeneity of temporal weighting profiles observed in humans integrating a stream of oriented stimulus frames. Our findings point to continuous attractor dynamics as a plausible mechanism underlying stimulus integration in perceptual estimation tasks.
  • Wiktor Mlynarski (Institute of Science and Technology Austria, Austria)
    "Attention as efficient and adaptive inference in dynamic environments"
  • Top-down attention is thought to reflect allocation of limited processing resources to task-relevant computations and representations. According to this hypothesis, attentional processing could be characterized by two fundamental theoretical frameworks: probabilistic inference and efficient coding. Probabilistic inference specifies optimal strategies for learning about relevant properties of the environment from local and ambiguous sensory signals. Efficient coding provides a normative approach to study encoding of natural stimuli in resource-constrained sensory systems. By emphasizing different aspects of information processing they provide complementary approaches to study sensory computations. Here we attempt to bring them together by developing general principles that underlie the tradeoff between energetic cost of sensory coding and accuracy of perceptual inferences. We then apply these general principles to optimize a model of population coding in the visual cortex. The model dynamically adapts a representation of natural images to support maximally accurate perceptual inference at minimal activity cost. The resulting optimality predictions reproduce measured properties of attentional modulation in the visual system and generate novel hypotheses about the functional role of top-down feedback, response variability, and noise correlations. Our results suggest that a range of seemingly disparate attentional phenomena can be derived from a general theory combining probabilistic inference with efficient coding in a dynamic environment.

Measuring and modeling the cell-state transitions in cancer progression and treatment

Organized by: Mohit Kumar Jolly ( Assistant Professor, Center for Biosystems Science and Engineering, Indian Institute of Sceince Bengaluru, India), Kishore Hari (PhD Student, Center for Biosystems Science and Engineering, Indian Institute of Sceince Bengaluru, India)
Note: this minisymposia has multiple sessions. The second session is MS19-ONCO.

  • Caterina AM La Porta (Professor of General Pathology Department of Environmental Science and Policy, University of Milan; CEO ComplexData SRL, Italy)
    "Explaining the dynamics of melanoma aggressiveness: at the crossroads between biology and artificial intelligence"
  • Melanoma is one of the most aggressive and highly resistant tumor. Cell plasticity in melanoma is one the main reason behind its metastatic capacity. I will discuss the recent results obtained by our group on cellular plasticity and CSCs in melanoma. The detailed molecular mechanisms controlling melanoma plasticity are still not completely understood. We combine mathematical models of phenotypic switching with experiments on IgR39 human melanoma cell line to identify possible key targets to impair phenotypic switching. Our results shed new light on melanoma plasticity providing a potential target and guidance for therapeutic studies
  • Shensi Shen (West China Hospital, Sichuan University, Chengdu, China; Gustave Roussy Cancer Campus, Villejuif, France, China)
    "Persistent cancer cells : blazing the trail with metastatic melanoma"
  • The probability to achieve an objective response with anti-BRAF+MEK therapy in patients with BRAFV600E/K mutant melanoma is around 70% . However, after one year, half of the patients who initially responded to this combined therapy develops secondary resistance. Among these patients, some also resist to anti-PD1 immunotherapy as single agent or in combination with anti-CTLA4. For these patients, the medical needs are huge since there is presently no effective alternative treatment. Resistance to targeted agents can be due to the presence of pre-existing rare resistant clones in heterogeneous tumor cell population or the stochastic acquisitions of drug resistance through genetic mutations under therapeutic selective pressures. The latter case is the most frequent, wherein some cells of an isogenic tumor cell-population survive in spite of the presence of anticancer drug(s). Such cells are defined as 'persistent cancer cells' and their survival capability is dependent on the presence of anticancer agents. I will discuss how persistent melanoma cells adaptively tolerate the treatment from the aspect of reversible mRNA translational reprogramming and accompanying metabolic rewiring, eventually how these aspects can be modelled in an agent-based stochastic modeling.
  • Michael P H Stumpf (Professor of Systems Biology, School of BioSciences, University of Melbourne, Australia)
    " Stochastic Dynamics and Cell Fate Decision Dynamics in Development and Cancer"
  • The metaphor of the Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process, in both health and disease. Recent accessibility of single-cell transcriptomic data has provided new opportunities for quantifying this originally conceptual tool that could offer insight into the gene regulatory networks underlying cellular development. Here, we highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems, and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape.
  • Kishore Hari (PhD Student, Center for Biosystems Sceince and Engineering, Indian Institute of Science Bengaluru, India)
    "Mechanisms of phenotypic plasticity in Metastasis, a network topology perspective"
  • Metastasis, the process of cancerous cells invading multiple organs of the body, causes more than 90% of cancer-related deaths. No unique mutations could be associated with metastasis, and no cancer treatment so far can target metastasis. Recent studies suggest that metastasis is driven mainly by multiple interdependent axes of phenotypic plasticity, such as metabolic plasticity, drug resistance, dormancy, stemness, and Epithelial-mesenchymal plasticity (EMP). In particular, EMP – a developmental axis of phenotypic plasticity – is believed to be crucial for metastasis as it imparts the adherence and migratory characteristics to cancerous cells. Despite extensive physicochemical investigations, the mechanisms of the emergence of such phenotypic plasticity are still not understood. To understand these mechanisms, we take a two-pronged approach. On the one hand, we study the regulatory network topologies underlying EMP to identify characteristics that can give rise to plasticity. On the other hand, we construct models based on population dynamics data to understand the dynamics of switching and infer phenotypic plasticity mechanisms other than network topology, such as stochasticity, ecological interactions between various EMP phenotypes, and epigenetics. Our results suggest that the EMP networks have a high fraction of positive feedback loops, which can give rise to phenotypic plasticity. Furthermore, small perturbations that reduce the number of positive feedback loops and increase the number of negative feedback loops can reduce phenotypic plasticity over a large parameter space.