Invited Speakers - Abstracts
MATHEMATICAL APPROACHES TO MODELLING AND REMODELLING BIOLOGICAL TISSUES
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
Abstract: As the eld of mathematical biology has matured, closer collaboration with experimentalists and clinicians has become more wide common, these changes bringing multiple bene ts to both communities. For example, the mathematical models can increase our understanding of biological systems while the biological questions can stimulate new theoretical challenges. This symbiotic relationship can be exemplified by studies of biological tissues.
Biological tissues are complex, evolving structures, characterised by multiple interactions that act across diverse space and time scales. In this talk I aim to illustrate how theoretical studies of biological tissues can provide new mechanistic insight into their behaviours while also acting as a source of mathematically challenging problems. I will take my inspiration from recent studies of cancer, wound heal ing, tissue engineering and retinitis pigmentosa, a degenerative disease that causes blindness.
Keywords: Mathematical Modelling, Wound healing, Tissue engineering, Cancer.
BIOLOGICAL AND BIO-INSPIRED MOTILITY AT MICROSCOPIC SCALES: LOCOMOTION BY SHAPE CONTROL
MathLab@SISSA-International School for Advanced Studies, Italy
Abstract: Cell motility is key to many biological functions, and it is accomplished by coordinated shape changes. Locomotion strategies employed by unicellular organisms are particularly interesting because they are invisible to the naked eye, and offer surprising new solutions to the question of how shape can be programmed. In recent years, we have studied locomotion by shape control using a variety of methods: modeling, theory, and numerical simulation, observations at the microscope, manufacturing of prototypes. A concrete case study is provided by our results on Euglena gracilis, a unicellular protist that is able to move both by agellar propulsion and by highly coordinated changes of the shape of the whole cell body [1, 2]. We will survey the most recent ndings within this stream of research, and point out to current directions and challenges for the future.
Keywords: Cell motility, Shape control, Mechano-biology, Active matter.
Acknowledgements: This work has been supported by the ERC Advanced Grant 340685-MicroMotility.
References:
[1] M. Rossi, G. Cicconofri, A. Beran, G. Noselli, A. DeSimone (2017). Kinematics of agellar swimming in Euglena gracilis: Helical trajectories and agellar shapes, Proc Nat Acad Sci USA 114,13085{13090
[2] G. Noselli, A. Beran, M. Arroyo, A. DeSimone (2018). Experimental and theoretical study of metaboly in Euglena gracilis. Preprint.
ADAPTIVE DYNAMICS AND THE EVOLUTION OF DIVERSITY
Department of Mathematics and Statistics, University of Helsinki, Finland
Abstract: Natural selection is usually paraphrased as the survival of the fittest - or the demise of all others. How can natural selection explain the enormous diversity of variants living together in Nature? Adaptive dynamics nds the answer in deriving fitness explicitly from models of population dynamics. This leads to an ever-changing fitness landscape, which facilitates not only the coexistence of multiple species but also the formation of new lineages through a process called evolutionary branching. After a brief introduction to the mathematical framework of adaptive dynamics, I consider three questions relating to diversity. First, is there an upper bound to the number of species, and if so, how does a "saturated" community evolve? Second, can natural selection lead to extinction? Third, when diversity evolves, it may be just variation but not speciation. Will natural selection lead to the origin of new species?
Keywords: Adaptive dynamics, Evolutionary branching, Evolutionary suicide, Speciation.
BIG DATA, GOOGLE AND DISEASE DETECTION: A STATISTICAL ADVENTURE
Department of Statistics, Harvard University, USA
Abstract: Big data collected from the Internet have generated signi cant interest in not only the academic community but also industry and government agencies. They bring great potential in tracking and predicting massive social activities. We focus on tracking disease epidemics in this talk. We will discuss the applications, in particular, Google Flu Trends, some of the fallacy and the statistical implications. We will propose a new model that utilizes publicly available online data to estimate disease
epidemics. Our model outperforms all previous real-time tracking models for influenza epidemics at the national level of the US. An extended version of the model gives accurate tracking of Dengue fever in Asian and South American countries. We will also draw some lessons for big data applications.
Keywords: Influenza, Dengue fever, Internet search, Forecasting.
MODELLING THE WANING AND BOOSTING OF IMMUNITY
Julius Center for Health Sciences and Primary Care, University Medical Center, Utrecht, The Netherlands
Joint work with Odo Diekmann (Utrecht University), Wilfred de Graaf (Utrecht University) and Peter Teunis (RIVM).
Abstract: The immune status of an individual host is determined by the increase of immunity during infection, waning of immunity after clearing the infection, and boosting by renewed exposure to the pathogen. The process of boosting, the rate at which immunity wanes, and the level of protection it confers, all influence the transmission dynamics of the pathogen. Information about the immune status of a population is often available from serological studies, but it may be unclear what this means for the level of protection against infection or symptomatic disease. We would like to understand how an intervention changes a population's immune status and the incidence of symptomatic infection for an infectious disease with waning immunity. In this talk I will introduce a mathematical model for the waning and boosting of immunity. The model is defined on two levels. On the within-host level we defined a model that distinguishes between episodes of infection and time periods of waning of immunity (De Graaf et al. 2014). During infection, a simple 2-dimensional system of ODE's describes the time evolution of pathogens and immunity within the host. Between infection episodes immunity wanes until a new exposure triggers the next infection episode. We then lift the model to the population level by studying the distribution of immune states in a population under the assumption of a constant force of infection. The events of exposure and infection are described by a time-homogeneous Poisson process, between exposures immune status wanes deterministically. This model can be formulated in terms of a renewal equation, for which a stable stationary distribution can be derived. The modelling framework will be illustrated with applications to pertussis epidemiology. For pertussis, longitudinal and cross-sectional serological data are available, which can be used to parameterize the model. We were interested in obtaining estimates for the incidence of symptomatic infections, the ratio of symptomatic to asymptomatic infections, and the immune level at which protection from symptomatic infection occurs. We found remarkable correspondence between predictions of the within-host model with observations reported in the literature concerning the serological correlate of protection. The modelling framework has strong links with a statistical model used for estimating incidence from serological data.
Keywords: Mathematical model, Waning immunity.
References:
[1] de Graaf WF, Kretzschmar ME, Teunis PF, Diekmann O. (2014). A two-phase within-host model for immune response and its application to serological profiles of pertussis, Epidemics 9:1-7.
MODELING INTERACTING NETWORKS OF NEURONS AS PROCESSES WITH VARIABLE LENGTH
Laboratoire AGM UMR CNRS 8088 Université de Cergy-Pontoise, France
Abstract: A class of recently introduced models to describe networks of neurons as stochastic processes with memory of variable length will be presented. These are non-Markovian processes in high or infinite dimension in which the past dependence of transition probabilities or intensities has a range that is finite but depends on the particular history. Starting from existence results, we study related mean-field models in continuous time and their large population limits, and discuss the relation with associated Piecewise Deterministic Markov Processes (PDMP's) and state results concerning their longtime behavior. Finally, two important problems of statistical inference in such models will be considered: estimation of the spiking rate function and estimation of the neuronal interaction graph. The talk is based on joint work with Susanne Ditlevsen, Aline Duarte, Antonio Galves and Guilherme Ost.
Keywords: Multivariate nonlinear Hawkes processes, Mean-field approximations, Piecewise deterministic Markov processes, Multi-class systems, Oscillations.
EPIDEMIC MODELS STRUCTURED BY PARASITE LOAD AND IMMUNE LEVEL
Department of Mathematics, University of Trento, Italy
Abstract: A growing number of researchers are developing models that link within-host infection dynamics to population-level epidemic dynamics [2]. Multiscale immunoepidemiological are relevant, for instance, in evolutionary epidemiology [4] where they also naturally allow for host heterogeneity [5], or for describing the dynamics of infections with temporary immunity [1] more accurately than SIRS models. Another area of likely interest are infections, such as varicella/zoster [3] where severe disease depends on immunological status. The development of useful multiscale immunoepidemiological models poses strong mathematical and numerical challenges. Within this broad area, I will present some simple models whose analysis have led to interesting biological insights, and discuss some instances where a feedback arises from epidemic to within-host processes resulting into new dynamical features.
Keywords: Immunoepidemiology, Evolutionary epidemiology, Immunity boosting and waning.
References:
[1] W.F. de Graaf, M.E.E. Kretzschmar, P.F.M. Teunis, P. F. M., O. Diekmann. A two-phase within-host model for immune response and its application to serological pro les of pertussis. Epidemics 9, 1-7.
[2] J. R. Gog et al. (2015). Seven challenges in modeling pathogen dynamics within-host and across scales, Epidemics 10, 45-48.
[3] G. Guzzetta et al. (2013). Hope-Simpson's progressive immunity hypothesis as a possible explanation for Herpes Zoster incidence data. Am. J. Epidemiol. 177, 1134-1142.
[4] N. Mideo, S. Alizon, S., T. Day. (2008). Linking within- and between-host dynamics in the evolutionary epidemiology of infectious diseases. TREE 23, 511-517.
[5] A. Pugliese (2011). The role of host population heterogeneity in the evolution of virulence. J. Biol. Dyn. 5, 104-119.
MODELS OF LEARNING AND EVOLUTION: WHAT DO THEY HAVE IN COMMON?
Evolutionary Systems Research Group, MTA Ecologogical Research Center, Tihany, Hungary, and Parmenides Centerfor the Conceptual Foundations of Science, Pullach, Germany
Abstract: In the past several scholars have noted some relationship between learning and evolution and various levels of abstraction. William James was wondering about the possible role of a process analogous to evolution of natural selection in the brain, whereby adaptive answers to complex problems might arise. Changeux and Edelman were considering selectionist approaches to brain dynamics during its development: while their approach has been experimentally validated, replicator dynamics has not been entertained by them. The first question is then whether true evolutionary dynamics can unfold in the brain (evolution in learning). On the flip side of the coin Richard Watson has raised the idea whether associative, reinforcement and deep learning dynamics could play a role in the evolution of ecosystems, developmental genetic regulatory networks and evolutionary transitions in individuality (learning in evolution). A third, potentially unifying theme is the analogy between Bayesian inference and the discrete-time replicator equation: here the question is whether similar algorithms could realize either of them in some natural systems. I shall review the relevant concepts and mathematical formulations behind these ideas. Open questions will be raised that, if answered positively, could entail that there will ultimately be only one uni ed theory including evolution and learning as subcases.
Keywords: replicator equation, Bayesian models, Hebb synapse, reinforcement, adaptation.
Acknowledgements: This project is supported by the Templeton World Charity Foundation (Learning in evolution, evolution in learning) and by funded by National Research, Development, and Innovation Office Grants NKFI-K119347 and GINOP-2.3.2-15-2016-00057.
ANALYSIS OF COLLECTIVE CELL BEHAVIOURS UNDERLYING PRIMITIVE STREAK FORMATION IN THE CHICK EMBRYO
School of Life Sciences, University of Dundee, Dundee, DD1 5EH, UK
Joint work with Silke Henkes (CSMB, University of Aberdeen, Aberdeen, UK), Rastko Sknepnek (School of Science and Engineering, University of Dundee, Dundee, UK) and Ping Lin (School of Science and Engineering, University of Dundee, Dundee, UK)
Abstract: How dynamic cell behaviours such as differentiation, division, cell shape change and movement are integrated at the tissue, organ and organism level is a key question in biology. This is particularly important during gastrulation, a key process during the early embryonic development of all higher organisms involving large scale tissue deformations and cell movements. During gastrulation the three germlayers, the ectoderm, mesoderm and endoderm take up their correct topological positions in the embryo. In amniotes including humans the mesendoderm precursors are formed from a single layered epithelial sheet of cells, the epiblast. During gastrulation these mesoderm and endoderm precursors ingress through a structure known as the primitive streak to form the inner layers of the embryo [1]. The mesendoderm precursor cells in the epiblast move in two large scale vortex flows towards and along the midline of the embryo to form the primitive streak [2]. We investigate the cellular mechanisms that drive these large scale tissue flows in the chick embryo, as well as the mechanisms that integrate these cell behaviours during streak formation on an embryo wide scale. Using a dedicated lightsheet microscope we are able to follow detailed cell behaviours such as cell division, ingression, cell-shape change and cell-cell intercalations of over 200.000 cells in the chick embryo epiblast. Our experiment have shown that the large scale epiblast tissue cortex flows resulting in the formation the primitive streak are driven by localised anisotropic pulling forces generated by mesendoderm cells. These forces appear to be generated by two main cellular mechanisms: directional cell-cell intercalation and apical contraction followed by ingression of mesendoderm cells [3]. We currently investigate the interplay between mechanical and chemical cell-cell signalling mechanisms that integrate these key behaviours at the tissue scale, using a combination of experimentation and cell based and continuous modelling approaches [4]. Specifically we test the hypothesis that junctional Myosin II accumulation resulting in apical contraction and cell-cell intercalation is a tension sensitive process and that this mechanosensitive process is a key part of the mechanism of tissue wide integration of cell behaviours during primitive streak formation.
Keywords: Gastrulation, Collective Cell behaviours, Cell-based modelling
References:
[1] Stern, C.D., Gastrulation, from cells to embryo's, ed. C.D. Stern. 2004, New York: Cold Spring Harbor Laboratory Press.
[2] Chuai, M., D. Hughes, and C.J. Weijer, Collective epithelial and mesenchymal cell migration during gastrulation. Curr Genomics, 2012. 13(4): p. 267-77.
[3] Rozbicki, E., et al., Myosin-II-mediated cell shape changes and cell intercalation contribute to primitive streak formation. Nat Cell Biol, 2015. 17(4): p. 397-408.
[4] Barton, D.L., et al., Active Vertex Model for cell-resolution description of epithelial tissue mechanics. PLOS Computational Biology, 2017. 13(6): p. e1005569.
Reinhart Heinrich Award
QUANTITATIVE APPROACHES TO INVESTIGATING EPITHELIAL MORPHOGENESIS
Faculty of Biology, Medicine and Health, University of Manchester, Michael Smith Building, Oxford Road, M13 9PT, Manchester, UK
Joint work with Ruth E. Baker (University of Oxford) and Alexander G. Fletcher (University of Sheffield)
Abstract: Morphogenesis - the generation of biological shape and form - is fascinating, and its study promises to shed light on a wide range of developmental defects and inform strategies for the arti cial growth of organs. Recently, the experimental study of morphogenesis has thrived due to a rise in quantitative methods. The resulting avalanche of quantitative data requires us to rethink the scientific method. We need to design quantitative hypotheses through mathematical models, make quantitative experimental predictions, devise methods for quantitative data analysis, and design methods for quantitative inference using models and data. Our work aims to enable this transition for the integrative analysis of morphogenesis in epiithelia, one of the major tissue types in animals. We conduct the rst systematic numerical analysis of a widely used cell-based model of epithelia, the vertex model, and estimate to what extent quantitative model predictions may be influenced by parameter values and implementation details. We then apply this model to a key question in developmental biology by constructing a quantitative theory for tissue size control in the embryonic epidermis of the fruit y Drosophila, using the model to predict the outcomes of future experiments. We further devise a method for estimating mechanical parameters of vertex models from imaging data and quantify the uncertainty associated with such estimates. Finally, we propose a novel algorithm for robust cell tracking in live-imaging microscopy videos of epithelial tissues that illustrates how graph theoretic concepts may be used to overcome challenges in quantitative data analysis. Together, these contributions will enable the quantitative study of epithelia for a wide range of applications.
Keywords: replicator equation, Bayesian models, Hebb synapse, reinforcement, adaptation.
Acknowledgements: JK acknowledges funding from the Engineering and Physical Sciences Research Council through a studentship.
References:
[1] J. Kursawe, R. E. Baker, A. G. Fletcher. (2017). Impact of implementation choices on quantitative predictions of cell-based computational models J. Comp. Phys. 345, 752-767
[2] J. Kursawe, P. A. Brodskiy, J. J. Zartman, R. E. Baker, A. G. Fletcher (2015). Capabilities and Limitations of Tissue Size Control through Passive Mechanical Forces. PLoS Comput. Biol. 11, e1004679
[3] J. Kursawe, R. E. Baker, A. G. Fletcher. (2018). Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues J. Theor. Biol. 443, 66-81
[4] J. Kursawe, R. Bardenet, J. J. Zartman, R. E. Baker, A. G. Fletcher. (2016). Robust cell tracking in epithelial tissues through identi cation of maximum common subgraphs J. R. Soc. Interface 13, 20160725