Sub-group minisymposia (9:30-11:00am)

CDEV: Subgroup Contributed Talks (9:30-11:00am)

Leonie van Steijn Leiden University
"Regulation of persistent cell migration by the extracellular matrix"

Amoeboid cell motility is an important process in many eukaryotic cell types such as immune cells. Adequate immune cell motility is necessary to clear infections. The motility of cells is affected by interaction with the extracellular matrix (ECM) as well as by chemoattractants and other molecular signals. To study cell-ECM interactions, we consider two situations that we study using a combination of experiments and mathematical modeling. These two environmental cues are also present for in vivo immune cells as they move through tissue filled with other cells and ECM. First is topotaxis where cell motion is guided by the topography of the environment. As a model of amoeboid cell motility through pores in the ECM, we study the motility of Dictyostelium discoideum cells on a substrate covered with microscopic pillars. The pillars are spaced widely enough to let the cells through and there is a gradient from densely packed pillars to more widely spaced pillars. Here the cells perform a random walk with a slight drift to the more widely spaced area. Using a Cellular Potts model, we study how cell persistence mode affect topotaxis using the actin-derived persistence of the Act-model and an active Brownian particle-based persistence. We find that both modes result in topotactic drift comparable to the experimentally found drift, but the actin-based persistent cells show a more efficient drift. Next we study how ECMs of more dense structure affect the motility of B-lymphocytes. B-lymphocytes show different motitility modes on different matrices: a slow but persistent random walk on collagen IV with low cell-ECM contact area and a faster Brownian walk on fibronectin with high cell-ECM contact area. Expanding the Act-model with cell-ECM bonds that can form, grow and shrink, and rupture, we can obtain different cell motion with by using different rupture energies and new bond formation. Simulated cells mostly show a persistent random walk, with low persistence and low diffusivity for poorly attached cells, and high persistence and high diffusivity for dynamically attached cells. Cells with sustained attachement show pivoting behaviour which was persistent in short time-scales, but subdiffusive on long time scales. We conclude that cell-ECM interactions can affect cell motility in multiple ways. ECM pores can steer cells from denser to looser ECM areas through topotaxis, whereas attachment to the ECM can alter the motility type of cells. Combined, these cues could lead to a range of different possible motility types. How in vivo cells integrate these cues together with other cues such as chemokine signalling is subject for further studies.

Emine Atici Endes Heriot-Watt University
"Modelling Scratch Wound Healing Assay using an Improved Non-local Equation"

Wound healing assays, in the other words scratch assays, are based on observing cells migrate into a wound or open space created an artificial scratch on a monolayer of cells. The assays are commonly used to quantify the rate of gap closure, which is a measure of the speed of the collective motion of cells and they are able to evaluate cell migration usefully in vitro wound healing. Obviously, the actual wound is more complex than the wound is done by making a scratch on a cell monolayer, however; the scratch wound assay is a technically simple, inexpensive, and fast method for analysis of cell migration and does allow modeling and testing of cell migration under well-defined conditions. We introduce a novel continuum model that extended the derived continuous model of a single population of cells. To derive our continuum model, we consider an integro-advection-diffusion-reaction equation for the adhesion of the single-cell motility in one dimension. And in this specific study, we analyse the applicability of our model to scratch-wound healing assay based on some experimented cases.

Bradford Peercy University of Maryland, Baltimore County
"A Minimal Model for STAT regulation in Initiation of Clustered Border Cell Migration"

Cell migration is pivotal in development as well as homeostasis, immune function, and pathology. It is important to understand the molecular activity that allows some cells to assume the migratory cell fate. The critical interaction we consider, in Drosophila melanogaster, is between the well-conserved Signal Transducer and Activator of Transcription (STAT) and downstream transcription factors Apontic (APT) and Slow Border Cells (SLBO). We derive a detailed mechanistic mathematical model and then reduce it to the three main transcription factors. The reduction maintains the steady state behavior including a bistable switch between stationary and migratory states. However, the basins of attraction vary, and the manifolds separating the basins can be associated with delays in cell fate decisions. Experiments with miRNA disruption of cell migration compare well with the equivalent model manipulation.

Ulrich Dobramysl University of Cambridge
"Sensing and triangulation of chemical gradients"

In many biological processes, in particular embryonic and brain development, cells need to follow chemical gradients to arrive at a precise location. They need to determine the direction and position of sources releasing diffusing molecular guidance cues from information gathered by receptors located on the cell membrane. Using matched asymptotics, we developed a model that relates the chemical fluxes to receptors to the gradient source position. We learned that simple direction sensing using comparison of fluxes is strongly limited. In contrast, full recovery of the gradient source position from receptor fluxes is possible even over relatively large distances. We quantify the uncertainty associated with location triangulation and show how the accuracy depends on the number and distribution of receptors.

Dimitris Goussis Khalifa University, UAE
"Endogenous and exogenous IgG competing for FcRn receptors: multi-scale analysis"

In many cases of IgG subclass deficiencies or FcRn malfunction, it is desired to elevate the levels of IgG, in order to strengthen the immune system. Conversely, in cases in which pathogenic or excess IgG antibodies are the aetiological agents, it is desirable to lower the IgG levels, in order to alleviate the symptoms; as in autoimmune diseases. One of the most efficient approaches to decrease the pathogenic IgG levels is to enhance its catabolism by administering recombinant IgG, which competes with the endogenous for the binding to the FcRn receptor. It was shown experimentally that the administration of exogenous IgG with high affinity, delivers better results in enhancing the degradation of the endogenous pathogenic IgG, than the classical intravenous immunoglobulin (IVIG) treatment, which is only effective in high doses. In this study, the competing interactions of the exogenous IgG and endogenous (pathogenic) IgG, when binding with the FcRn receptor are analyzed, on the basis of the model proposed in. A multi- scale analysis is carried out by employing the Computational Singular Perturbation (CSP) algorithmic methodology. With this algorithm, the constraints that develop progressively, form the start of the process to the fixed point, are identified, along with the reduced model that governs the evolution of the system within these constraints. CSP provides the tools for system-level understanding, by identifying the physical processes that (i) contribute to the emergence of the constraints (equilibria), (ii) drive the slow evolution of the system within these constraints and (iii) are responsible for the development of the fast and slow timescales in the dynamics of the model. The objective of this manuscript is to provide meaningful insights regarding the dynamical properties of the competitive binding of the endogenous and exogenous IgG with the FcRn receptor. Given that the modulation of the IgG-FcRn interaction allows for the control of the IgG half- life, the analysis provides a guideline to engineer effective recombinant IgG antibodies, in order to reduce the endogenous IgG levels.

IMMU: Immunobiology and Infection Minisymposium (9:30-11:00am)

Rob de Boer Universiteit Utrecht, Utrecht, The Netherlands
"Why do some populations of cells accumulate deuterium faster than lose it?"

Deuterium labelling experiments are often used to infer the kinetic properties (i.e., turnover rates, maintenance mechanisms) of various cell populations in vivo. For a homogeneous population that is at steady state, it is natural to expect that the population gains and loses labelled cells at the same rate. However, if the measured population is kinetically heterogeneous, it is natural to expect that the rate at which the labeling curve increases (i.e., the up-slope) is slower than the rate at which it decreases (i.e., the down-slope). Surprisingly, recent data from multiple deuterium-labelling experiments have the opposite property, and predict a gain of label that is faster than the rate of loss. Using various mathematical models, we search for mechanisms that can account for such unexpected labelling data. We show that the short-term labeling data can be explained when the deuterium remains available for a longer duration than it was administered. For the long-term labeling data we study models where (a) the population was considered to behave like a stem-cell population, or (b) the phases of the cell cycle were modeled with delay equations (i.e., with the Smith-Martin model). Both provide scenarios where the gain of label can be faster than its loss. However, the effect is small and these two models fail to give a good description of the experimental data. When we finally drop the assumption that the population remains at steady state, we readily explain the experimental data with a simple source, division and death model. This mechanism however requires that these populations are largely expanding by a source from a precursor compartment, and not by cell division (i.e., self-renewal).

Katia Koelle Emory University, Atlanta, GA, USA
"Considering the consequences of cellular coinfection in within-host viral dynamics and modeling"

Within-host viral dynamic models often times categorize cells as infected or uninfected, similar to epidemiological microparasite models. However, in vitro and in vivo studies indicate that cellular coin- fection occurs frequently in influenza, HIV, and coronaviruses, among other viral pathogens. Here, I first discuss work from my group that develops simple models that allow for cellular coinfection in a scalable manner, with cellular multiplicity of infection affecting the phenotypes of infected cells, such as their death rate, viral production rate, and interferon induction rate. I then present work focusing on quantitatively characterizing the evolutionary consequences of cellular coinfection for newly arising mutations (both beneficial and deleterious). Our findings indicate that cellular coinfection decreases the ability of selection to act on individual mutations and results in genetic drift playing a larger role in modulating allele frequencies in a within-host viral population.

Carmen Molina Paris University of Leeds, Leeds, UK
"A stochastic Model of Infection: Francisella T ularensis"

With a mouse infection model, agent-based computation and mathematical analysis, we study the pathogenesis of Francisella tularensis infection. A small initial number of bacteria enter host cells and proliferate inside them, eventually destroying the host cell and releasing numerous copies that infect other cells. Our analysis of disease progression is based on a stochastic model of a population of infectious agents inside one host cell, extending the birth-and-death process by the occurrence of catastrophes: cell rupture events that affect all bacteria in a cell simultaneously. Closed expressions are obtained for the survival function of an infected macrophage, the number of bacteria released as a function of time after infection, and total bacterial load. We compare our analysis with the results of agent-based computation and, via Approximate Bayesian Computation, with experimental measurements carried out after of murine aerosol infection with the virulent SCHU S4 strain of the bacterium. The posterior distribution is consistent with the estimate that the time between rounds of bacterial division is less than 6 hours in vivo.

Catherine Weathered Purdue University, West Lafayette
"Mycobacterium Avium infection in the lungs: effects of bacterial phenotype and biofilm"

Mycobacterium avium complex (MAC), a type of nontuberculous mycobacteria, are environmental mi- crobes, capable of colonizing and infecting humans following inhalation of the bacteria. MAC-pulmonary disease is difficult to treat and prone to recurrence, and both incidence and prevalence are increasing. MAC form biofilms and diverse colonies in the environment. These biofilms can aid in epithelial cell invasion, cause premature apoptosis in macrophages, and inhibit antibiotic efficacy [4]. We hypothesize a balance of bacterial factors (phenotypic diversity and biofilm formation) and host immune factors (speed and magnitude of response) is key to establishing and prolonging infections in the lung. To test these hypotheses, we developed a 3D agent-based model (ABM) that incorporates known interactions between bacteria, biofilm and immune cells in virtual lung tissue. We implement our model in Repast Simphony. The simulation grid represents a length of lung airway with a layer of mucus. Bacterial agents are classified as either sessile or planktonic phenotypes that determine their behavior: biofilm formation, macrophage phagocytosis and replication rate. All bacterial agents and infected macrophages release a generic chemoattractant representing pathogen associated molecular patterns and chemokines respectively. These chemoattractants diffuse through the grid and are treated as continuous variables. Macrophages probabilistically follow the chemoattractant gradient, phagocytose bacteria, and accumulate apoptotic signals (representing hyperstimulation in the TNF-α pathway) through exposure to biofilm and internal bacteria. Model results show an early relationship between the initial number of macrophages or distance that chemoattractants diffuse, and the ratio of planktonic to sessile bacteria. Larger initial macrophage numbers result in a stronger and more sustained reduction in planktonic bacteria early after infection. However, as the infection progresses, the bacterial population is sustained by the sessile bacteria that are protected in biofilms or inside infected macrophages, allowing the planktonic population to recover. This effect is offset with further chemoattract diffusion, as the macrophages can clear the infection early or recruit more macrophages. Thus, the model predicts that both bacterial phenotypes and a suppressed immune responses affect the bacterial ability to survive, propagate, and eventually establish infection. Future directions of this work include exploring the continued role of phenotypes later in infection and treatment, and adding drug pharmacokinetics and cell-level pharmacodynamics to better understand the role of biofilm in treatment efficacy.

MEPI: Modeling COVID-19 to inform control efforts, Part II (9:30-11:00am)

Annelies Wilder-Smith Umea University
"COVID-19 Outbreak on the Diamond Princess Cruise Ship: Estimating the Epidemic Potential and Effectiveness of Public Health Countermeasures"

Background: Cruise ships carry a large number of people in confined spaces with relative homogeneous mixing. On 3 February, 2020, an outbreak of COVID-19 on cruise ship Diamond Princess was reported with 10 initial cases, following an index case on board around 21-25th January. By 4th February, public health measures such as removal and isolation of ill passengers and quarantine of non-ill passengers were implemented. By 20th February, 619 of 3700 passengers and crew (17%) were tested positive. Methods: We estimated the basic reproduction number from the initial period of the outbreak using SEIR models. We calibrated the models with transient functions of countermeasures to incidence data. We additionally estimated a counterfactual scenario in absence of countermeasures, and established a model stratified by crew and guests to study the impact of differential contact rates among the groups. We also compared scenarios of an earlier versus later evacuation of the ship. Results: The basic reproduction rate was initially 4 times higher on-board compared to the R0 in the epicentre in Wuhan, but the countermeasures lowered it substantially. Based on the modeled initial R0 of 14.8, we estimated that without any interventions within the time period of 21 January to 19 February, 2920 out of the 3700 (79%) would have been infected. Isolation and quarantine therefore prevented 2307 cases, and lowered the ${R}_0$ to 1.78. We showed that an early evacuation of all passengers on 3 February would have been associated with 76 infected persons in their incubation time. Conclusions: The cruise ship conditions clearly amplified an already highly transmissible disease. The public health measures prevented more than 2000 additional cases compared to no interventions. However, evacuating all passengers and crew early on in the outbreak would have prevented many more passengers and crew from infection.

Samuel Clifford LSHTM
"Can traveller interventions delay a local outbreak?"

Interventions aimed at travellers, such as syndromic screening, sensitisation to symptoms, and contact tracing on onset of symptoms may help delay the establishment of a SARS-CoV-2 outbreak in a previously unaffected country. Here we consider how the probability of detecting an infected traveller varies with the sensitivity of screening and duration of travel relative to the incubation period. We also show how a combination of these traveller interventions may be effective at delaying the establishment early on in a global outbreak but become less effective as the rate at which infected travellers arrive increases.

Jonathan Dushoff McMaster University
"Time distributions and coronavirus control"

Early investigations of coronavirus epidemiology have highlighted a number of practical (and interesting) questions about time distributions, including generation and serial intervals; and latent, incubation, and infectious periods. I will discussing different ways of measuring (and defining) these distributions, and implications for disease prediction and control.

Caroline Colijn Simon Fraser University
"Modelling and estimation for COVID19: classic estimates of key parameters and the role of genomic data"

The novel coronavirus that was identified in Wuhan, China in December 2019 spread widely following reports of initial cases who were likely exposed at the Huanan seafood market in the city of Wuhan. The subsequent spread, rapid control measures, and reported international cases caused global public health concern. The scientific community responded rapidly, sharing data for modelling and estimation, and sharing viral sequences. These strongly suggested that there was a single introduction event from an animal reservoir to humans in approximately November 2019. However, key epidemiological parameters remained uncertain even in late February, as reporting fractions and social distancing measures varied between places, and because the time at which an individual is infected is of course unknown. We present early estimates of the incubation period and serial interval for several reported clusters, using contact tracing data. We describe the differences in model predictions based on these estimates and early models based on SARS parameters. We then discuss how early viral sequences and classic epidemiological estimates of key parameters can be integrated to refine estimates and inform transmission models.

MFBM: Topological and network analyses for data (9:30-11:00am)

Maria-Veronica Ciocanel Duke University, United States, ciocanel@math.duke.edu
"Ring Channel Dynamics using Topological Data Analysis"

Contractile rings are structures made of actin filaments that are important in development, wound healing, and cell division. In many model organisms, ring channels allow nutrient exchange to developing egg cells and are regulated by forces exerted by myosin motor proteins. I will present an agent-based modeling and data analysis framework for the interactions between filaments and motor proteins inside cells. This approach may provide key insights for the mechanistic differences between two motors that are believed to maintain the rings at a constant diameter. In particular, we develop methods leveraging topological data analysis techniques to investigate time-series data of filament interactions. Our proposed methods clearly reveal the impact of kinetic parameters on significant topological hole formation, thus giving insight into ring channel formation and maintenance. I will also discuss methods available for distinguishing between noise and signal in these topological summaries of the filament organization through time.

John Lagergren NC State, United States, jhlagerg@ncsu.edu
"Biologically-informed neural networks guide mechanistic modeling from sparse experimental data"

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks, are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities.

John Nardini NC State, United States, jtnardin@ncsu.edu
"Analyzing Collective Motion with Machine Learning and Topology"

We use topological data analysis and machine learning to study a seminal model of collective motion in biology. This model describes agents interacting nonlinearly via attractive-repulsive social forces and gives rise to collective behaviors such as flocking and milling. To classify the emergent collective motion in a large library of numerical simulations and to recover model parameters from the simulation data, we apply machine learning techniques to two different types of input. First, we input time series of order parameters traditionally used in studies of collective motion. Second, we input measures based on topology that summarize the time-varying persistent homology of simulation data over multiple scales. This topological approach does not require prior knowledge of the expected patterns. For supervised machine learning methods for classification of mechanistic model parameters, the topological approach outperforms the one that is based on traditional order parameters.

Adelie Garin EPFL, Switzerland, adelie.garin@epfl.ch
"Topological Data Analysis for (biological) image analysis"

Topological data analysis (TDA) methods extract features representing the number of connected components, loops and cavities of shapes at different scales through an iterative process called a filtration. In this talk, we describe several TDA tools to improve image processing (classification, comparison and reconstruction). These methods provide a global view of images, which takes into account intrinsic geometric and topological properties of the images and complement standard methods very well. They can be used for several purposes in image analysis: classification (of leaves, cells, neuron shapes,…), comparison (to differentiate a healthy tissue from a tumour for instance) or to help optimisation algorithms to reconstruct deteriorated images (for example to reconstruct 3D neuron images from scanned sliced brains).

ONCO: Multiscale models of cancer heterogeneity, with applications in drug development and precision medicine (9:30-11:00am)

Matthias Reuss Stuttgart Research Center Systems Biology, University of Stuttgart
"Spatial-temporal multiscale modelling and simulation of vascular tumour growth - development of new multicellular simulators based on structural consistency between model and computer architecture"

Multiscale modelling and simulation in systems medicine is an emerging methodology and discipline to tackle the challenges posed by complex disease, including cancer. We will present applications of a 3D multiscale hybrid discrete-continuum model to simulate angiogenesis and vascular tumour growth. The model uses a cellular automaton approach and couples intracellular dynamics, active cell movement, cell- cell interaction, extracellular diffusion, and a dynamically evolving vascular network. The model accounts for the interplay between subcellular events and the macroscopic properties of the tumour. Simulation of larger tumours taking into account the structure of the tissue and blood supply consisting of millions of interacting cells, and the architectures of real tissues, e.g. liver lobules, or validation of theoretical findings with aid of imaging and simulations of therapies for larger patient communities, are both compu- tationally challenging. Therefore, we will introduce new hardware and software developments applicable to multiscale modeling based on structural consistency between the multiscale model and the architecture of the computer hardware. These efficiently solve the problems of interactions between subcellular and tissue levels. I will summarize multicellular simulators based on hybrid structures of parallelised graphic and central processors. I will present applications of these hybrid parallelised computer systems to integrate simulation of 3D-growth of larger vascularized tumours, dynamic models of intracellular metabolism of hepatocytes, and the the 3D architecture of liver lobules. The coupled modeling of blood perfusion between intravascular and interstitial spaces in the microvasculature permits the simulation of the perfusion CT to create model-based images which can be compared with clinical observations from radiology.

Holger Perfahl Stuttgart Research Center Systems Biology, University of Stuttgart
"Hybrid Modelling of Transarterial Chemoembolisation Therapies (TACE) for Hepatocellular Carcinoma (HCC)"

We will present an agent-based multiscale model of vascular tumour growth and angiogenesis to describe transarterial chemoembolisation (TACE) therapies. The model describes tumour and normal cells nested in a vascular system that changes structure in response to tumour-related growth factors and also interacts with oxygen that influences cell viability. Within the extended model TACE is included as a two-step process. First, the purely mechanical influence of the embolisation therapy is modelled by a local occlusion of the tumour vasculature. We distinguish between partial and complete responders, where parts of the vascular system are occluded for the former and the whole tumour vasculature is destroyed for the latter. In the second part of the model, drug eluting beads release the chemotherapeutic drug doxorubicin at destroyed vascular locations. Simulation results are parameterised to qualitatively reproduce clinical observations. Our simulations reveal that directly after a TACE treatment an unstable tumour state can be observed, where regrowth and total tumour death are equally likely. This short time-window is favorable for another therapeutic intervention with a less radical therapy. This procedure produces a more favorable outcome. Simulation results with an oxygen therapy within the unstable time- window demonstrate a potentially positive manipulated outcome. Finally, we conclude that our TACE model motivates new therapeutic strategies and can help clinicians to understand intertwined relations and crosstalk in tumours.

Samuel Handelman Internal Medicine, University of Michigan
"Incorporation of morphological features to inverse problems in high-content screening of anti-cancer therapies"

Cell-based assays are a mainstay of drug development, including especially for anti-cancer drugs and anti-cancer drug combinations. However, these assays generally use cell-death as an endpoint, which is more suited to simple cytotoxicity than to anti-cancer efficacy. This is especially a challenge in the context of combination therapies, where the correct linkage function in a statistical model of two co-administered cytotoxic compounds is not obvious. Therefore, we propose imaging-based and molecular markers of cancer cell phenotype, as an alternative efficacy endpoint in cancer drug screening. We will combine and compare results in combination therapy screens with different efficacy measures and a range of linkage functions corresponding to different assumptions on the nature of cancer drug synergy. These approaches have the added benefit of better addressing inter-cellular heterogeneity, which is evident even in clonal cell lines. Finally. we will review relevant biological background helpful to a quantitative audience in contextualizing the other talks in this session.

Harsh Jain Mathematics, Florida state University
"A Standing Variation Model of Prostate Cancer Response to Live Cell Vaccination"

Making quantitative predictions with data-driven models, the core approach of applied mathematical biology, requires parameter estimation from imperfect measurements. Therefore, parameter identifiability and estimability become a major concern. In this talk, I will present a model of immunotherapy in the treatment of prostate cancer. I introduce our novel approach, standing variation modeling, which exploits practical unidentifiability in model parameters to capture individual heterogeneity. In particular, we use experimental data to infer distributions on parameters that are critical to tumor growth and to the resultant immune response of the body. Sampling model parameters from these distributions allows us to simulate heterogeneity, both, at the level of the tumor cells, and the individual being treated. Model simulations offer an explanation for the very limited success of this prostate cancer immunotherapy that has been observed in practice.

OTHE: Eco-evolutionary dynamics across scales of organisation (9:30-11:00am)

Paula Vasconcelos Uppsala
"How does joint evolution of consumer traits affect resource specialization?"

The origin and maintenance of diversity in nature are central themes in evolutionary biology and ecology. Recently, the framework of adaptive dynamics has been applied to try and shed light onto these questions, with interesting results. The phenomenon of disruptive selection when extreme phenotypes have a fitness advantage over more intermediate phenotypes is particularly interesting because, under this regime, selection favors the evolution of adaptive phenotypic diversity. More specifically, it can drive speciation as well as the evolution and maintenance of polymorphism within a species. The conditions that result in this specific selective regime are well understood at the theoretical level, but with one fun- damental restriction: the majority of research is based on the assumption of a single evolving quantitative trait. However, biological organisms are complex and initial results from the few models that incorporate multidimensional trait evolution indicate that increasing the number of co-evolving traits facilitates the emergence of disruptive selection. To systematically extend the existing theory, we study the conditions for the emergence of disruptive selection based on models with several co-evolving traits. These models are (i) characterized by a set of evolving traits that determines the fitness of individuals in a population due to interactions with a complex environment (prey, predators, pathogens), and (ii) mechanistic in the sense that each trait has an interpretation at the level of the organism. This approach thus allows us to better understand when and under what circumstances multiple coevolving traits facilitate or hinder the emergence of biological diversity. In this work, we analyze the evolutionary dynamics of consumer traits in a consumer-resource model. Consumer growth depends on search efficiency, handling time and conversion efficiency for two resources. Feeding on these alternative resources is subject to trade-offs such that, for instance, increasing search efficiency for one resource can only be achieved by decreasing search efficiency for the other. We investigate the evolution of these traits in isolation and various combinations. Our results show how moving from one to two, and then three coevolving traits affects the conditions un- der which resource polymorphism arises through evolutionary branching. We also show that the critical trade-off curvatures that lead to the different evolutionary outcomes that is, whether evolution leads to one generalist, one specialist or two specialists depend decisively on the specific combination of coevolv- ing traits. Finally, we show that, with multidimensional trait spaces, the parameter range can be split into one region in which evolutionary branching is independent of the mutational variance-covariance matrix, and another in which branching depends on it.

Lynn Govaert Eawag
"Towards an integrated theory of eco-evolutionary communities"

The increasing amount of studies showing evidence of rapid evolution occurring on similar timescales as ecological processes, have demonstrated the importance of including eco-evolutionary dynamics to further our understanding on population, community and ecosystem processes. Most empirical studies still focus on the ecological consequences of evolutionary change within a single species. However, in natural systems species co-occur together, comprising a community. Hence, all member species may display an evolutionary response. Thus focusing on evolution of a single species may lead to an over- or underestimation of evolution on ecological processes. To understand the role of eco-evolutionary dynamics within communities of multiple coexisting species, there is a need for a formal theory of eco-evolutionary communities integrating processes of evolutionary biology and community ecology operating at different temporal and spatial scales. Based on previous frameworks of evolutionary biology and community ecology, I here present an integrated framework for eco-evolutionary communities, bringing together theoretical, conceptual and technical approaches of these two fields. Integrating fundamental processes of evolutionary biology and community ecology improves our understanding of eco-evolutionary dynamics within multi-species communities and allows the design of new experimental approaches and testing for new hypotheses.

Charles Mullon Lausanne
"Eco-evolutionary dynamics under non-random interactions"

Organisms continuously modify their living conditions, transforming their environment, microbiome, and sometimes culture. Where these modifications influence the fitness of conspecifics, a feedback emerges between the evolution of traits and the environment in which they are expressed. To investigate such feedback, it is typically assumed that individuals interact at random. In this case, one can study the invasion of a rare mutant trait in an environment set by a common resident ignoring mutant-mutant interactions. However, non-random interactions are common in nature. In this talk, I will report some of my results on the effect of non-random interactions on eco-evolutionary dynamics, focusing on two mechanisms that lead to such non-random interactions: spatial structure and biased behaviours between parents and their offspring. In both cases, selection depends on complex feedbacks between individuals of the same mutant lineage. By disentangling and quantifying these feedbacks, this research can help understand the nature of adaptation via non-genetic modifications, with implications for how organisms evolve to transform their environments, microbiome, or culture.

Josep Sardanyés CRM Barcelona
"Dynamics of cooperation: from origins of life to ecosystems"

In this talk we will introduce the hypercycle model, originally conceived by Manfred Eigen and Peter Schuster to study the dynamics of prebiotic replicators. Hypercycles are dynamical systems formed by replicators with catalytic activity, thus they have been also employed to investigate cooperation in complex ecosystems at different levels. Following this mathematical model, we will show the dynamics and bifurcations tied to cooperation, from origins of life to models of facilitation in metapopulations and dynamics of semiarid ecosystems. We will emphasise on the evidences we have of such dynamics in real biological systems (both at the experimental or field levels), thus showing that dynamical systems theory offers us a unique framework to understand the basic mechanims behind the dynamics and the transitions in systems with strong nonlinearities.

POPD: Mathematical models of evolutionary rescue (9:30-11:00am)

Stephan Peischl University of Berne
"The effect of gene flow on evolutionary rescue"

It seems certain that a substantial fraction of our planet’s current biodiversity will be lost to extinction as species’ habitats change at an accelerating rate. Some species, however, may be able to escape that fate by adapting, shifting their geographical ranges, or both. This leads to the questions of when, where and how might adaptation allow species to survive, leading to ‘evolutionary rescue’. Some basic answers to those questions come from theory. Experimental and theoretical studies have highlighted the impact of gene flow on the probability of evolutionary rescue. Mathematical modelling and simulations of evolutionary rescue in spatially or otherwise structured populations showed that intermediate migration rates can often maximise the probability of rescue in gradually or abruptly deteriorating habitats. In this talk, I present several mathematical approaches to studying evolutionary rescue in spatial or otherwise structured populations with gene flow between sub-populations, using discrete or continuous space models. I present simple conditions for when gene flow facilitates evolutionary rescue as compared to isolated populations, investigate the role of long-distance dispersal, as well as the role of phenotypic variation in dispersal traits.

Robert Noble ETH Zurich
"The logic of containing tumours"

Challenging the paradigm of maximum tolerated dose, evolutionary theory suggests that the emer- gence of resistance to cancer therapy may be prevented or delayed by exploiting competitive ecological interactions between drug-sensitive and resistant tumour sub-clones. Recent studies have shown that a treatment strategy aiming for containment, not elimination, can control tumour burden more effectively than more aggressive approaches in vitro, in mouse models, and in the clinic, but theoretical understand- ing of these outcomes is underdeveloped. I will present a new, mathematically rigorous framework for understanding tumour containment that unifies and generalizes previous formulations. Results obtained within this framework provide timely guidance for empirical research including the design of clinical trials.

Mario Santer Max Planck Institute for Evolutionary Biology
"Evolutionary Rescue and Drug Resistance on Multicopy Plasmids"

Bacteria often carry 'extra DNA' in form of plasmids in addition to their chromosome. Many plasmids have a copy number greater than one such that the genes encoded on these plasmids are present in multiple copies per cell. This has evolutionary consequences by increasing the mutational target size, by prompting the (transitory) co-occurrence of mutant and wild-type alleles within the same cell, and by allowing for gene dosage effects. We present a mathematical model for bacterial adaptation to harsh environmental change if adaptation is driven by beneficial alleles on multicopy plasmids. Successful adaptation depends on the availability of advantageous alleles and on their establishment probability. The establishment process involves the segregation of mutant and wild-type plasmids to the two daughter cells, allowing for the emergence of mutant homozygous cells over the course of several generations. To model this process, we use the theory of multi-type branching processes, where a type is defined by the genetic composition of the cell. Both factors – the availability of advantageous alleles and their establishment probability – depend on the plasmid copy number, and they often do so antagonistically. We find that in the interplay of various effects, a lower or higher copy number may maximize the probability of evolutionary rescue. The decisive factor is the dominance relationship between mutant and wild-type plasmids and potential gene dosage effects. Results from a simple model of antibiotic degradation indicate that the optimal plasmid copy number may depend on the specific environment encountered by the population.

Jacek Miękisz University of Warsaw
"Evolution of populations with strategy- dependent time delays"

We address the issue of the stability of coexistence of two strategies with respect to time delays in evolving populations. It is well known that time delays may cause oscillations. Here we report a novel behavior. We show that a microscopic model of evolutionary games with a unique mixed evolutionarily stable strategy (a globally asymptotically stable interior stationary state in the standard replicator dynamics) and with strategy-dependent time delays leads to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, stationary states of such dynamics depend on time delays. Moreover, at certain time delays, an interior stationary state may disappear or there may appear another interior stationary state. This shows that effects of time delays are much more complex then it was previously thought.

15 minute break (11:00-11:15am)

Sub-group minisymposia (11:15am)

CDEV: Shapes, patterns, and forces in development biology (11:15am-12:45pm)

Steffen Rulands Max Planck Institute
"Setting up the epigenome: a collective phenomenon"

Methods from single-cell multi-omics allow measuring several layers of regulation along the one- dimensional sequence of the DNA. The biological function of these processes relies, however, on emergent processes in the three-dimensional space of the nucleus, such as droplet formation through phase sepa- ration. How can measurements along the sequence of the DNA be translated into an understanding of emergent dynamics in nuclear space? Here, we combine single-cell NMT-sequencing experiments with a theoretical and computational approach to rigorously map measurements along the DNA sequence to a description of the emergent spatial dynamics in the nucleus. Drawing on scNMT-seq experiments in vitro and in vivo we demonstrate our approach in the context of early development. We show how epigenetic modifications of the DNA, DNA methylation, are established through the interplay between chemical and topological modifications of the DNA, leading to the formation of condensates of methylated DNA in the nucleus. Using this theoretical framework, we finally identify epigenetic processes that precede lineage decisions in the early embryo. Our work sheds new light on epigenetic mechanisms involved in cellular decision making. It also provides a general framework of how mechanistic insights into the spatio-temporal processes governing cell-fate decisions can be gained by the combination of methods from single-cell multi-genomics, computational biology and theoretical physics.

Alessandra Bonfanti University of Cambridge
"Characterising the rheology of soft tissues using Fractional Viscoelastic models"

When subjected to external mechanical loading, many biological materials, such as ligaments, lung tissue, endothelial cells, or collagen fibrils, exhibit a viscoelastic power-law behaviour. Using standard viscoelastic models involving combinations of spring and dashpot elements to capture this behaviour oversimplifies the response; this limits our ability to adequately quantify the characteristics of these materials. Alternatively, empirical expressions designed to fit the power-law behaviour may provide effective means to describe experimental measurements, but the use of such ad-hoc models without a proper constitutive relationship limits the scope of the measurements and restricts their predictive capability. Fractional calculus provides a convenient framework to accurately capture power-law behaviours. Various empirical expressions introduced to fit experimental data can be derived or approximated with simple fractional models, often using fewer parameters. Furthermore, this approach seems to be well suited to extract material properties. As we demonstrated in the context of single cells and simple tissues, fitting a model on one set of experiments, can be used to predict the response of the same material to a broad range of external stimuli. Furthermore, using consistent models accross various experimental measurement methods enables us to compare material parameters that could not be easily compared otherwise. This allows us to shed new light on behaviour previously reported in the literature. Fractional calculus is a niche area of mathematics that has been available for a long time in the literature. It has to date attracted limited attention in the biological field, or any other area due to the mathematical complexity. To promote the use of such generalised fractional viscoelastic models, we provide an open source library RHEOS for numerical analysis of experimental data. The occurrence of such power-law behaviour also in non-living tissues, e.g. gels, casein, plants; implies that fractional viscoelastic models can have a great impact on.

Mathias Sonja Uppsala University
"Impact of force function formulations on the numerical simulation of center-based models"

Center-based models are a framework for the computational study of multicellular systems with widespread use in cancer modeling and computational developmental biology. At the core of these models are the numerical scheme used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter there are multiple choices that could potentially affect both the biological behavior captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of center-based models rely on different force functions for their default behavior and it is not straightforward for a modeler to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between the different force functions results in good agreement of the population radius of a growing monolayer. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level. We illustrate that the different force functions show varying sensitivity to this issue.

Clinton Durney UBC
"Quantifying cellular contributions to salivary gland tubulogenesis"

Epithelial cells organize themselves into tubes for the necessary functions of gas and nutrient transport, and the production and secretion of hormones and enzymes. The tubes of the Drosophila salivary gland result from the organization and collective motion of a flat sheet of polarized epithelial cells through a budding process. Through orchestrated cell movements and cell rearrangements, the nascent tube begins to form. In this talk, we develop a novel 3D-vertex model that allows for the investigation and quantification of the role that cellular mechanics and cellular rearrangements play during this vital morphogenetic process. The novel 3D model is able to quantify cell mechanical behavior and analyze the effect of different forces during invagination. Using this biophysical model, we investigate how patterning of forces on the apical surface cause cell shape changes that lead to invagination. Specifically, we investigate the roles of apicomedial induced cellular constriction, junctional actomyosin, a supracellular actomyosin cable and cellular intercalations have during gland morphogenesis.

IMMU: Immunobiology and Infection Minisymposium (11:15am-12:45pm)

Cristian van Dorp Los Alamos National Laboratory, Los Alamos, NM, USA
"Stochastic viral dynamics modeling of time series from HIV-1 cure experiments in macaque and mouse models"

Conventional wisdom has it that the only way to control HIV-1 infection is lifelong antiretroviral drug therapy (ART). However recent observations indicate that functional cure, i.e., control of HIV infection in absence of ART, is possible. Treatment strategies to achieve functional cure have therefore become a very active area of research. The efforts to develop a functional cure for HIV-1 must overcome the persistence of the latent reservoir of infected CD4+ T cells. These cells contain integrated HIV-1 DNA and are both long-lived and can re-active producing new viral particles that re-establish infection after ART interruption. All progress towards a HIV-1 cure must contend with this problem. Proposed strategies for curing HIV-1 include methods to reduce the size of the reservoir, or induce immune responses that can prevent viral rebound after ART interruption. Such novel treatments are typically tested in the macaque model or in humanized mice. We analyze data from two such studies: a macaque model to assess the effect of early ART initiation, which may limit latent reservoir size, and a CD4+ T-cell xenograft mouse model to assess the effect of immuno-therapies targeted at HIV-specific CD8+ T cells (HSTs). Stochasticity plays a major role in both these experiments. The formation of the latent reservoir and reactivation from this reservoir leading to viral rebound are both thought to be highly stochastic processes. In the mouse model, the virus escapes from the CD8+ T-cell immune response in a largely unpredictable manner, despite the fact that biological variation between repeated experiments is reduced to a minimum. We are therefore motivated to develop stochastic viral dynamics models to describe the data, rather than the standard deterministic viral dynamics model, and further, we estimate parameters using Sequential Monte Carlo methods for panel data. This allows us to integrate data from repeated experiments in our inference. In our investigation of early SIV infection with macaque data, we compare different models of reservoir formation. We show that a model in which reservoir establishment saturates at high viral loads, can reconcile early establishment with the observed distribution of rebound times. In our investigation of immuno-therapies with mouse data, we succeed in disentangling viral rebound due to escape from the HST response, from rebound due to typical expansion and contraction dynamics of the HSTs.

Stanca Ciupe Virginia Tech, Department of Mathematics, Blacksburg, VA, USA
"Understanding the antiviral effects of RNAi-based therapy on chronic hepatitis B infection"

Reaching functional cure following chronic hepatitis B virus infections is hindered difficult by the presence of large numbers of HBsAg in the blood of infected patients. Therapies with the RNA interfer- ence drug ARC-520, which silence viral translation, together with daily administration of the nucleoside analogue drug entecavir have showed reduction in the overall levels of serum HBsAg in HBeAg-positive, treatment naive patients. Understanding the relative effects of ARC-520 alone, and in combination with entecavir, is particularly important in informing the development of new generation antiHBsAg drugs. A mathematical model describing the mechanistic interactions between HBV DNA, HBsAg, and HBeAg in the presence of ARC-520 and entecavir has been developed. We fitted the model to patient data and investigated the long term dynamics of the virus and viral protein titers under entecavir alone and under combination therapy. We run in silico boosting experiments and used them to determine the tradeoff between viral protein decay and drug induced toxicity. Such results can inform policy.

Ruy Ribeiro Faculdade de Medicina da Universidade de Lisboa, Lisbon, Portugal
"How do CD8+ T cells control HIV infection?"

Human immunodeficiency virus (HIV) infection is still one of the most important causes of morbidity and mortality in the world, with a disproportionate human and economic burden especially in poorer countries. Despite many years of intense research, an aspect that still is not well understood is what immune mechanisms control the viral load during the prolonged asymptomatic stage of infection. Because CD8+ T cells have been implicated in this control by multiple lines of evidence, there has been a focus on understanding the potential mechanisms of action of this immune effector population. One type of experiment used to this end has been depleting these cells with monoclonal antibodies in the SIV-macaque model and then studying the effect of that depletion on the viral dynamics. These experiments generated controversial results, with dynamical models developed to help interpret these data leading to conflicting conclusions. We propose a new explanation for these results and provide both new experimental data and modeling evidence that helps to reconcile previous observations. In this hypothesis the main effect of CD8+ T cells occurs before viral integration.

Eva Stadler University of New South Wales, Sydney
"Heterogeneity in the risk of latent malaria parasite reactivation explains the timing and pattern of infection recurrences in (Plasmodium vivax) malaria endemic settings"

The parasite Plasmodium vivax causes both blood-stage malaria infection and the formation of latent liver-stage parasites called hypnozoites. These recurrence of infection through hypnozoite activation is a major contributor to the total new infections in Plasmodium vivax endemic regions. After being treated for a single infection it is well known that some individuals will experience a second recurrence very rapidly while others will not experience a recurrence for some time. The mechanisms governing the ‘schedule’ of reactivation are not completely understood. A variety of conceptual models have been proposed, including a ‘biological clock’ mechanism, induction by external factors such as fever, or simply random reactivation of hypnozoites. In addition to these models, we propose an alternative explanation that there is heterogeneity in the risk of malaria relapse within the population. To explore the mechanisms governing P. vivax recurrence, we constructed differential equation models of each of the above conceptual models of hypnozoite reactivation. The models were compared, through fitting and simulation, to previously published time-to-infection data from a malaria endemic region following 1299 people for about one year. The data used in our study provided a powerful opportunity to study the mechanisms underlying P. vivax relapse because rather than including only a single infection event for each individual, multiple occurrences were recorded in many individuals over a one-year follow-up. However, the multiple measurements within each individual added complexity to fitting our custom time-to-infection model and required us to build these models within a mixed-effects type model framework. Our results show that the models with population heterogeneity in the reactivation rate provided the simplest and best explanation of the data and unlike the other conceptual models, heterogeneity could explain the observed patterns of P. vivax recurrences between individuals.

MEPI: COVID-19 Contributed Talks II (11:15am-12:45pm)

Nicholas Steyn University of Auckland
"The effect of border controls on the risk of COVID-19 re-incursion in New Zealand"

As of mid-July, New Zealand appears to have eliminated community transmission of COVID-19, allowing for almost no domestic restrictions on activity. The risk of re-incursion is mitigated by strict quarantine requirements at the border. These measures include a mandatory 14-day stay in a government managed facility, multiple RT-PCR tests, and regular symptom checkups. We use a simple individual based model to investigate the risk that international arrivals pose. Arriving individuals are randomly assigned an infection status and, if relevant, an exposure date. False negative testing rates and infectiousness vary over time; while the asymptomatic status, symptom onset date, and daily contacts are assigned according to estimated distributions. Results suggest that minimising mixing in the facilities should be the primary focus of risk reduction efforts. We also propose a measure that can be used to estimate the level of transmission occurring within the facilities: the ratio of cases detected in their second week of stay to cases detected in their first week.

Lin Wang University of Cambridge
"Serial interval of SARS-CoV-2 was substantially shortened over time by non-pharmaceutical interventions"

Studies of novel coronavirus disease (COVID-19) have reported varying estimates of epidemiological parameters including serial interval distributions, i.e. the time between illness onset in successive cases in a transmission chain, and reproduction numbers. By compiling a line-list database of transmission pairs in mainland China, we show that mean serial intervals of COVID-19 have shortened substantially from 7.8 days to 2.6 days within a month (January 9 to February 13, 2020). This change is driven by enhanced non-pharmaceutical interventions, in particular case isolation. We also show that using real-time estimation of serial intervals allowing for variation over time, provides more accurate estimates of reproduction numbers than using conventionally fixed serial interval distributions. These findings would improve assessment of transmission dynamics, forecasting future incidence, and estimating the impact of control measures.

Louise Dyson University of Warwick
"The impact of contact networks upon SARS-CoV-2 transmission in workplaces and universities"

Following the first cases of COVID-19 being reported in the UK in late January 2020, by early March it was evident that sustained community transmission was occurring. As part of social distancing measures enforced to tackle the epidemic, non-key workers were not allowed into the workplace and universities moved to online teaching and examination for the remainder of the 2019/2020 academic year. As steps are taken to relax social distancing measures, questions surround the ramifications on community disease spread of workers returning to the workplace and students returning to university. To study these aspects, we present a network model to capture the transmission of SARS-CoV-2 over four overlapping sets of networks: (i) fixed workplace contacts; (ii) social contacts; (iii) contacts at home; and (iv) dynamic workplace contacts (for workers who see people from multiple places, such as in the service sector). Additionally, we showcase the flexibility offered by the framework by describing its use in a university setting. We assess the impact of contact tracing adherence upon the spread of infection and the total number of individuals in isolation. We also consider the impact of backwards tracing, whereby resources are focused upon identifying the source of any reported infected cases, and larger scale isolation of portions of the population if case level alerts are triggered. Our results suggest that high adherence with contact tracing can result in a significant reduction in the number of infected individuals and the total number of people who would be required to isolate over the duration of the epidemic. We observe only a weak effect of backwards contact tracing - there is a slight reduction in epidemic size as the probability of successfully tracing the source of infection increases. Finally, we observe that, in order for reactive closures to be effective, such a policy needs to be enacted when only a small proportion of those that interact with that setting have recently begun to display symptomatic infection. We conclude that ensuring high adherence to contact tracing should be prioritised in order to reduce future infection levels.

Robin Thompson University of Oxford
"Mathematical modelling in the earliest stages of the COVID-19 pandemic"

In the early stages of the COVID-19 pandemic, when cases had only been reported in China, it was important to assess the risk that cases exported elsewhere would lead on to local epidemics. In this talk, I will show how the epidemic risk was assessed in countries worldwide. I will also present a simple approach for extending this analysis for models in which additional epidemiological complexity is included (e.g. presymptomatic transmission, age-structure, time-varying infection rates). This shows how epidemic risk estimates can be generated, informed using outbreak data, and then adjusted in real-time as more information becomes available about any newly invading pathogen.

MFBM: Topological and network analyses for data (11:15am-12:45pm)

Samuel Heroy University of Oxford, United Kingdom, samuel.heroy@maths.ox.ac.uk
"Rigidity percolation in random rod networks"

In certain classes of both biological (e.g. actin) and material-based (e.g. nanocomposites) networks, the underlying system undergoes a transition in the mechanical strength at a critical system density. For instance, in a composite material composed of rigid interacting monodisperse particles randomly dispersed in a soft polymer matrix, the system experiences a phase transition at a critical particle density, whereas this transition may depend for instance on the mean number of filaments per contact in an actin network. This experimental phenomenon, termed rheological percolation, has been shown to occur in many systems at a density that is beyond the contact percolation threshold, demonstrating that a more complex mechanism is responsible for the observed mechanical gains. In this study, we construct a network model in which sphereocylinders are randomly dispersed in a medium and contact at intersection points (supposing penetrability). Idealizing these sphereocylinders (rods) as attractive particles that stay fixed at but can rotate about their points of contact (hinge-like connections), we posit that the rheological transition occurs when the rods form a spanning component that is not only connected, but connected in such a way as to remove all nontrivial degrees of freedom in the component (rigidity percolation). We build on results from two dimensions (see the paper https://epubs.siam.org/doi/abs/10.1137/17M1157271) to develop an approximate algorithm that identiﬁes such spanning components through hierarchically identifying and compressing provably rigid motifs—contact patterns by which rigid components interact to form larger rigid components. We apply this algorithm to networks we generate at various density/system size, using a ﬁnite size scaling approach to rigorously estimate a rigidity percolation transition point bound, which we show agrees fairly well with a simple mean ﬁeld estimation. We also estimate the transition point (and critical exponents) for networks with different rod aspect ratios, and find that the transition point scales with the square of the aspect ratio. In this study, we construct a network model in which sphereocylinders are randomly dispersed in a medium and contact at intersection points (supposing penetrability). Idealizing these sphereocylinders (rods) as attractive particles that stay fixed at but can rotate about their points of contact (hinge-like connections), we posit that the rheological transition occurs when the rods form a spanning component that is not only connected, but connected in such a way as to remove all nontrivial degrees of freedom in the component (rigidity percolation). We build on results from two dimensions (see the paper https://epubs.siam.org/doi/abs/10.1137/17M1157271) to develop an approximate algorithm that identiﬁes such spanning components through hierarchically identifying and compressing provably rigid motifs—contact patterns by which rigid components interact to form larger rigid components. We apply this algorithm to networks we generate at various density/system size, using a ﬁnite size scaling approach to rigorously estimate a rigidity percolation transition point bound, which we show agrees fairly well with a simple mean ﬁeld estimation. We also estimate the transition point (and critical exponents) for networks with different rod aspect ratios, and find that the transition point scales with the square of the aspect ratio.

Yu-Min Chung UNC Greensboro, United States, y_chung2@uncg.edu
"On the morphology of mitochondria via a multi-parameter persistent homology approach"

Mutations in autophagy-gene Optineurin (OPTN) are associated with Primary Open Angle Glaucoma (POAG) and amyotrophic lateral sclerosis, but the pathophysiological mechanism is unclear. The E50K OPTN mutation is associated with glaucoma. Recent studies have shown that OPTN may play an important role in regulating mitochondrial networks and interacting with parkin as part of the mitophagy pathway. We hypothesized that loss of normal OPTN function disrupts mitochondrial morphology. To investigate and quantify the phenomena, we use multi-parameter persistent homology on confocal images of cells from transgenic mice with the E50K mutation and genetic knockout of optineurin. In particular, we combine methods in mathematical morphology to form a multi-parameter filtration. We will show that such filtration contains both topological and geometric information about the mitochondria, and will demonstrate ways to extract meaningful features from it. Preliminary results support the hypothesis. This is a joint work with Chuan-Shen Hu at National Taiwan Normal University, Emily Sun, and Dr. Henry C. Tseng at Duke Eye Center.

Alexandria Volkenning Northwestern University, United States, alexandria.volkening@northwestern.edu
"Topological data analysis of zebrafish skin patterns"

Wild-type zebrafish feature black and yellow stripes across their body and fins, but mutants display a range of altered patterns, including spots and labyrinth curves. All these patterns form due to the interactions of pigment cells, which sort out through movement, birth, and competition during development. Using an agent-based approach, we have coupled deterministic cell migration by ODEs with stochastic rules for updating population size to reproduce stripe pattern development and predict cell interactions that may be altered in mutant patterns. Within a single zebrafish mutant, however, there is a lot of variability, and this makes it challenging to first identify the features of a pattern that we are trying to reproduce and then judge model success. Moreover, agent-based models have many parameters, and empirical descriptions of zebrafish patterns are largely qualitative. To help address these challenges, we draw on topological data analysis to develop a set of methods for automatically quantifying pattern features in a fully interpretable, cell-based way. We apply our techniques to both simulated data and real fish images, and we show how to quantitatively distinguish between and characterize different patterns.

Ashish Raj UCSF, United States, ashish.raj@ucsf.edu
"Inference on models of network spread and protein aggregation in Alzheimer’s and dementia"

Alzheimer’s disease, Parkinson’s and other related dementias involve widespread, stereotyped and progressive deposition of misfolded proteins. There is mounting evidence for “prion-like” trans-neuronal transmission, whereby proteins misfold, trigger misfolding of adjacent same-species proteins, and there- upon cascade along neuronal pathways, giving rise to networked spread along white matter projections. The question of how protein aggregation and subsequent spread lead to stereotyped progression in the brain remains unresolved. We present here mathematically precise parsimonious modeling of these patho- physiological processes, extrapolated to the whole brain. We model monomer seeding and production at specific seed regions, aggregation using Smoluchowski equations; and networked spread using our prior Network-Diffusion model, whereby anatomic connections govern the rate at which two distant but con- nected brain regions can transfer pathologic proteins. These models involve several unknown parameters, some or all of which might be individual-specific. Hence parameter inference is a challenging problem, without which downstream applications of such models in disease diagnosis, prognosis and therapy will not be possible. We present several inference strategies we have explored in our lab, including nonlinear cost function minimization, variational Bayesian inference, and purely machine learning methods like support vectors and neural nets. Unlike most previous theoretical studies of protein aggregation, using these techniques our theoretical models are able to be fitted to and validated by experimental in vivo imaging and fluid protein measurements from large datasets.

ONCO: Data-based modeling in cancer research with focus on clinical applications (11:15am-12:45pm)

David Cheek Program for Evolutionary Dynamics, Harvard University
"DNA sequence evolution in the Yule process"

We study a fundamental model of DNA evolution in a growing population of cells: cell divisions follow the Yule process, and each cell contains a sequence of nucleotides which can mutate at cell division. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive fraction of the population. The model is free from the popular but disputed infinite sites assumption. Violations of the infinite sites assumption are widespread while their impact on mutation frequencies is negligible at the scale of population fractions. Some results are generalised to allow for cell death, selection, and site- specific mutation rates. To illustrate our results we estimate mutation rates in a lung adenocarcinoma.

Christoph Engel Institute for Medical Informatics, Statistics and Epidemiology (IMISE), University of Leipzig
"Utility of specialized clinical registries for knowledge-generating care in oncology: Results from two large German consortia on hereditary cancer predisposition syndromes"

Colon and breast cancer are among the most common cancers. An estimated 5% of these cancers are due to a hereditary cancer disposition caused by germline mutations in DNA repair genes. Mutation carriers have a greatly increased risk of developing cancer and therefore require intensified early detection measures. In order to precisely quantify the underlying cancer risks, to identify risk factors and to evaluate the benefit of early detection measures, two multi-centre interdisciplinary clinical registry studies have been established in Germany, which collect and analyse quality-controlled care data in a standardised manner. I will present selected results from the “German Consortium for Familial Intestinal Cancer” and the “German Consortium for Hereditary Breast and Ovarian Cancer” which had a direct impact on future patient care. Example 1: Individuals with Lynch syndrome (LS) are at highly increased risk for colorectal cancer (CRC). Regular colonoscopic surveillance is recommended, but there is no international consensus on the appropriate interval. Comparing prospective data from three countries with different surveillance policies (annually, 1–2-yearly, 2–3-yearly), we found that a policy of strict annual colonoscopies was not associated with lower CRC incidence or stage. However, we could identify several factors suitable for risk stratification. This study led us to change our recommendations for colonoscopic surveillance of LS patients in Germany. Example 2: Individuals with high breast cancer risk are recommended to participate in an intensified multimodal breast imaging program. Using cohort data from 10 years of prospective surveillance we could confirm the importance of MRI in high-risk screening, compared with mammography and ultrasound. However, the efficacy of the program was limited with regard to high-risk patients without a predisposing germline mutation. Moreover, both from retrospective and prospective registry data we determined age-dependent breast cancer risks in different risk groups. As in example 1, these results also led to modifications of future clinical decision strategies. In conclusion, these examples demonstrate that specialized clinical- epidemiological registries provide an important means to generate evidence for the further development of risk-adapted early cancer de- tection strategies. The registries are also a valuable basis for planning and conducting controlled clinical trials.

Saskia Haupt Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University
"Modeling multiple pathways in hereditary colorectal cancer development"

Lynch syndrome is the most common inherited colorectal cancer syndrome and accounts for 5–10% of the overall colorectal cancer burden. Like many other tumors, Lynch syndrome cancers develop through multiple pathways incorporating different driver mutations. However, a comprehensive understanding of LS tumor evolution which allows for tailored clinical interventions for treatment and even prevention is still lacking. We suggest a system of coupled ordinary differential equations modeling the evolution of the different pathways in order to address some of the most relevant unanswered questions in LS management. It is based on existing data on Lynch syndrome cancer incidence as well as mutational and molecular data for the individual pathways. The ansatz strikes a balance between being expressible on the one hand and not being too complex on the other hand. This yields an explainable and predictive behavior and makes the model amenable to a thorough mathematical analysis. It can be extended in a straightforward manner to include more mutated genes or to take new and improved measurements of mutation probabilities into account.

Matthias Kloor Department of Applied Tumor Biology, Heidelberg University Hospital
"From disease models to clinical applications — lessons from Lynch syndrome colorectal cancer"

Lynch syndrome is caused by heterozygous germ line mutations of the DNA mismatch repair (MMR) genes. During life, somatic mutation events (second hits) lead to loss of MMR function in multiple crypts within the colonic mucosa. From thousands of such MMR-deficient crypt foci, however, only a very small part develops into clinically manifest cancers. These cancers are mostly diploid, but characterized by the microsatellite instability (MSI) phenotype, i.e. the accumulation of numerous insertion/deletion muta- tions at repetitive microsatellite sequences. Mutations affecting microsatellites in genes coding for tumor suppressor genes promote MSI tumor development in Lynch syndrome. Using a bioinformatics-based model, we have predicted a set of coding microsatellite mutations with likely driver function in Lynch syndrome. These mutations also lead to shifts of the translational reading frame and to the generation of MMR deficiency-related frameshift peptides (FSPs). The well-defined pattern of MMR deficiency- induced mutations and neoantigens has wide-ranging implications on the clinical course of the disease: as exactly the same mutations recurrently occur in exactly the same tumor suppressor genes, Lynch syndrome cancers share a small and predictable set of highly immunogenic FSP neoantigens. Immune responses against these FSP neoantigens can already be detected in tumor-free Lynch syndrome mutation carriers, suggesting that there is a lifelong interaction between the immune system and emerging precan- cerous cell clones. This is also reflected by the fact that immune-mediated elimination of immunogenic tumor cells leaves traces in manifest MSI cancers, a process termed immunoediting. We will discuss how bioinformatics approaches and mathematical modeling can help unraveling fundamental processes of cancer evolution, and how this information can be used to design novel, innovative approaches for cancer therapy and even prevention.

POPD: Subgroup Contributed Talks (11:15am-12:45pm)

Joany Mariño Memorial University
"Symbiosis increases population size and mitigates environmental fluctuations in a physiologically-structured model parameterized for bivalves"

As a nutritional strategy, symbiosis increases the metabolic capabilities of the host. In thyasirid clams, it has been shown that trophic symbiosis can alter the energy allocation pattern of a host. However, the possible role of symbiosis as a life history strategy that can shape population dynamics remains unknown. Here, we show how nutritional symbiosis and the abundance of and dependence on symbionts can modulate the host's population dynamics and buffer resource limitation. We used Dynamic Energy Budget (DEB) theory to build a physiologically-structured population model that explicitly includes energy acquisition and allocation at different stages of an organisms' life cycle. We formulated the model deriving the demographic rates from a DEB model and assuming equal mortality rates in both populations. We parameterized the model for two cohabiting clam species: asymbiotic (specialists that feed on free-living bacteria) and symbiotic thyasirids (generalists that gain nutrients from both free-living and symbiotic bacteria). We demonstrate that, without seasonal fluctuations, symbiotic thyasirids have higher abundances than asymbiotic thyasirids since the symbiotic bacteria act as an energy reserve allowing for higher energy allocation to reproduction. In a seasonal environment, when temperatures are low and resource is limiting, symbiotic and asymbiotic thyasirids have similar population sizes; nonetheless, the symbiotic population is less prone to extinction. Our findings suggest different adaptations to resource fluctuation: asymbiotic thyasirids depend on a larger energy reserve, while symbiotic thyasirids rely on symbiont assimilation. Our results highlight the relevance of linking individual energetics and life-history traits to population dynamics and are the first step towards a general understanding of the role of symbioses in populations' resilience.

Catherine Wangen Utah State University
"Modeling phenological consequences of warming climate for a southern population of mountain pine beetle"

The mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) attacks living Pinus trees, and reproduces in the phloem. Adults must attack a host simultaneously to overwhelm host defenses and successfully colonize. Temperatures directly but non-linearly affect MPB progress through life stages and the phenology of adult emergence. MPB are successful in a thermal niche where they are univoltine and synchronize emergence. Changing temperatures have broadened that niche geographically, leading to tree mortality of over 5.2 Mha in the western US. Successful bivoltine MPB have not been observed in the field, although a phenology model parameterized for northern US MPB populations suggests bivoltinism is possible in the southern MPB range under future warming scenarios. Bivoltinism could have devastating impacts on pine forests. However, northern and southern MPB are genetically different in response to temperature, requiring geographic-specific model parameters. Using rate curves parameterized with developmental observations from MPB in Arizona we have constructed a predictive cohort model for a southern MPB population. Initiating the model with field attack data and using temperature data recorded under the bark of attacked hosts, we simulated warming scenarios by adding to the yearly mean to test thermal regimes that would result in a bivoltine MPB population. We successfully constructed a predictive cohort model for a southern MPB population. A key result is a new method for projecting observed variability in oviposition, through multiple larval instars, into emergence distributions. Comparison of the cohort model with field emergence data allows us to infer developmental rates for unwitnessed pre-ovipositional adults and also validate model predictions. Model responses to simulated temperatures highlight thermal regimes that promote bivoltinism for the southern MPB population.

Maria Martignoni University of British Columbia Okanagan
"Mathematical insights into mechanisms leading to coexistence and competitive exclusion among mutualist guilds"

Microbial inoculants have been used as organic fertilizers worldwide. One of the most widely used commercial products are arbuscular mycorrhizal (AM) fungi, as these fungi can associate with a vast variety of crops. Despite the potential benefits for soil quality and crop yield associated with the use of AM fungi, experiments assessing the effective establishment of the fungi in the field have given inconsistent results, where some observations show field establishment and improved crop yield, while other studies show poor establishment of the inoculated species. Additionally, it is not yet clear whether the introduction of commercial inoculants could lead to a biodiversity loss in the native fungal community, and ultimately have a negative impact on plant growth. Here we develop a series of ordinary and partial differential equation models to study the spatio-temporal dynamics of a guild of mutualists (the fungal species) sharing a resource provided by the same partner (the host plant), constituing a shared resource for all fungi. Our results allow to assess the risks and benefit of inoculation, by identifying under which conditions inoculation can effectively boost productivity, when it has no significant effect on plant growth and on the native fungal community, and when it represents an invasion risk. More generally, our models provide important ecological insights into the mechanisms responsible for coexistence and competitive exclusion among mutualist guilds, and constitute a framework to predict the consequences of species manipulation in mutualist communities. Indeed, the models are simple enough to apply to a broad range of mutualisms found in nature, such as pollination or seed dispersal.

Subgroup Business Meeting

Sub-group contributed talks (1:30-2:30pm)

CDEV: Subgroup Contributed Talks (1:30-2:30pm)

Jonathan Harrison University of Warwick
"Hierarchical Bayesian modelling of chromosome segregation allows characterisation of a distinct dynamic signature of errors in cell division"

Cells divide via a self-organising process known as mitosis where a crucial step is the high fidelity separation of duplicated chromosomes to daughter cells. Errors in segregating chromosomes during cell division are a hallmark of cancer and are associated with developmental syndromes. How cell division achieves high fidelity remains an outstanding question, in particular how errors are detected and corrected. Through automated tracking of chromosomes at fine spatio-temporal resolution over long timescales, we can produce detailed quantification of the behaviour of human cells during mitosis. We propose a force-based stochastic differential equation model, dependent on hidden states governed by a Markov process, to describe the oscillations and segregation of chromosomes in mitosis. By fitting this dynamic model to experimental data in a Bayesian framework, we can infer the timing of the metaphase-anaphase transition (chromosome separation) for each duplicated chromosome pair. By extending this to a hierarchical Bayesian framework, we are able to capture rare reversal events during anaphase in the model. Model comparison provides evidence that the hierarchical model with reversals is preferred over a model without reversals. Application of this computational modelling pipeline to experimental data allows characterisation of a distinct signature of model parameters related to lagging chromosomes, and subsequent correction of these errors by the cell.

Marcin Zagorski Jagiellonian University
"How is information decoded in developmental systems?"

The development of multicellular organisms is a dynamic process in which cells divide, rearrange, and interpret molecular signals to adopt specific cell fates. Despite the intrinsic stochasticity of cellular events, the cells identify their position within the tissue with striking precision of one cell diameter in fruit fly or three cell diameters in vertebrate spinal cord. How do cells acquire this positional information? How is this information encoded and how do cells decode it to achieve the observed level of cell fate reproducibility? These are fundamental questions in biology that are still poorly understood. In this talk, I will combine both information theory methods and mechanistic models to address these questions in the context of spinal cord development. I will consider the two opposing morphogen signals that are integrated to specify the arrayed pattern of neural progenitor domains that later on give raise to different type of neurons. Based on the maximum likelihood estimation rule I will define decoding map that provides predictions for shifts in the target gene domains in mutants. The predictions will be validated using experimental data obtained from naïve chick neural plate explants and from embryos with altered ventral morphogen signaling. I will present a simple model of a gene regulatory network that integrates the two morphogen signals and is sufficient to recapitulate the observed shifts in the target domains. I will investigate to what extent the level of noise in the input signals affects precision of the resulting gene expression pattern. Interestingly, the observed precision of gene expression pattern is close to the theoretical limit of precision of decoding of noisy signals.

Tim Liebisch Frankfurt Inst. of Advanced Study
"Cell Fate Clusters in ICM Organoids Arise from Cell Fate Heredity & Division – a Modelling Approach"

Background: During the mammalian preimplantation phase, cells undergo two subsequent cell fate decisions. During the first cell fate decision, cells become either part of an outer trophectoderm or part of the inner cell mass. Subsequently, the inner cell mass (ICM) segregates into the epiblast and the primitive endoderm, giving rise to the embryo and the placenta respectively. Recently, ICM organoids have been published as an in vitro model system towards preimplantational development. ICM organoids mimic the second cell fate decision taking place in the in vivo mouse embryos. In a previous study, the spatial pattern of the different cell lineage types was investigated. The study revealed that cells of the same fate tend to cluster stronger than expected for the currently hypothesised purely random cell fate distribution. Three major processes are hypothesised to contribute to the final cell fate arrangements at the mid and late blastocysts or 24 h old and 48 h old ICM organoids, respectively: 1) intra- and intercellular chemical signalling; 2) a cell sorting process; 3) cell proliferation. Methods & Results: In order to quantify the influence of cell proliferation on the emergence of the observed cell lineage type clustering behaviour, an agent-based model was developed. The model accounts for mechanical cell-cell interactions, cell growth and cell division and was applied to compare several current assumptions of how ICM neighbourhood structures are generated. The model supports the hypothesis that initial cell fate acquisition is a stochastically driven process, taking place in the early development of inner cell mass organoids. The model further shows that the observed neighbourhood structures can emerge due to cell fate heredity during cell division and allows the inference of a time point for the cell fate decision. Discussion: Simulations based on the model show that cell divisions involving cell fate heredity seem sufficient to lead to the local clustering observed in 24 h old ICM organoids, and that the initial cell differentiation process takes place only during a small time window, during or prior to ICM organoid composition. Our results leave little room for extracellular signaling believed to be important in cell fate decision, therefore we are discussing an alternative role of chemical signaling in this process.

IMMU: Subgroup Contributed Talks (1:30-2:30pm)

Esteban Abelardo Hernandez Vargas Universidad Autonoma de Mexico (UNAM)
"In-host Mathematical Modelling of COVID-19 in Humans"

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. In this talk, mathematical models will be introduced to represent SARS-CoV-2 dynamics in infected patients. Considering different starting times of infection, parameters sets that represent infectivity of SARS-CoV-2 are computed for the target cell limited model and compared with other viral infections that can also cause pandemics. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post onset of symptoms. The model with eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, both, the target cell limited model and the model including immune responses, predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and it could be below detection levels during the first 4 days post infection. These models can serve for future evaluation of control theoretical approaches to tailor new potential drugs against COVID-19.

(CANCELLED) Christopher Rowlatt University of St Andrews
"(CANCELLED) Modelling the within-host spread of SARS-CoV-2 infection, and subsequent immune response, using a hybrid multi-scale individual-based model"

The coronavirus 2019 (COVID-19) pandemic, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has affected millions of people worldwide. A dysfunctional immune response, and the interaction with secreted cytokines (cytokine storm), has been observed to correlate with disease severity. However, the precise mechanisms which lead to disease severity remain unclear. In this talk, we employ a hybrid multi-scale individual-based model to study the spread of SARS-CoV-2 on an epithelial monolayer, its interaction with the host immune response and the immune cell cross-talk, as well as the interaction with secreted cytokines.

Rajat Desikan Indian Institute of Science Bangalore
"Targeting TMPRSS2 and Cathepsin B/L together may be synergistic against SARS-CoV-2 infection"

The entry of SARS-CoV-2 into target cells requires the activation of its surface spike protein, S, by host proteases. The host serine protease TMPRSS2 and cysteine proteases Cathepsin B/L can activate S, making two independent entry pathways accessible to SARS-CoV-2. Blocking the proteases prevents SARS-CoV-2 entry in vitro. This blockade may be achieved in vivo through ‘repurposing’ drugs, a potential treatment option for COVID-19 that is now in clinical trials. Here, we found, surprisingly, that drugs targeting the two pathways, although independent, could display strong synergy in blocking virus entry. We predicted this synergy first using a mathematical model of SARS-CoV-2 entry and dynamics in vitro. The model considered the two pathways explicitly, let the entry efficiency through a pathway depend on the corresponding protease expression level, which varied across cells, and let inhibitors compromise the efficiency in a dose-dependent manner. The synergy predicted was novel and arose from effects of the drugs at both the single cell and the cell population levels. Validating our predictions, available in vitro data on SARS-CoV-2 and SARS-CoV entry displayed this synergy. Further, analysing the data using our model, we estimated the relative usage of the two pathways and found it to vary widely across cell lines, suggesting that targeting both pathways in vivo may be important and synergistic given the broad tissue tropism of SARS-CoV-2. Our findings provide insights into SARS-CoV-2 entry into target cells and may help improve the deployability of drug combinations targeting host proteases required for the entry.

MEPI: Subgroup Contributed Talks (1:30-2:30pm)

Laura Strube Virginia Tech
"The role of repeat infection in the dynamics of a simple model of waning and boosting immunity"

Some infectious diseases produce lifelong immunity while others only produce temporary immunity. In the case of short-lived immunity, the level of protection wanes over time and may be boosted upon re-exposure, via infection or vaccination. Previous work developed a simple model capturing waning and boosting immunity, known as the Susceptible-Infectious-Recovered-Waned-Susceptible (SIRWS) model, which exhibits rich dynamical behavior including supercritical and subcritical Hopf bifurcations among other structures. Here, we extend the bifurcation analyses of the SIRWS model to examine the influence of all parameters on these bifurcation structures. We show that the bistable region, involving both a stable fixed point and a stable limit cycle, exists only for a small region of biologically realistic parameter space. Furthermore, we contrast the SIRWS model with a modified version, where immune boosting depends on the occurrence of a secondary infection. Analysis of this extended model shows that oscillations and bistability, as found in the SIRWS model, depend on strong assumptions about infectivity and recovery rate of secondary infection. Understanding the dynamics of models of waning and boosting immunity is important for accurately assessing epidemiological data.

Miranda Teboh-Ewungkem Lehigh University
"Mathematical assessment of the impact of human-antibodies on sporogony during the within-mosquito dynamics of Plasmodium falciparum parasites"

We develop and analyze a deterministic ordinary differential equation mathematical model for the within-mosquito dynamics of the Plasmodium falciparum malaria parasite. Our model takes into account the action and effect of blood resident human-antibodies, ingested by the mosquito during a blood meal from humans, in inhibiting gamete fertilization. The model also captures subsequent developmental processes that lead to the different forms of the parasite within the mosquito. Continuous functions that model the switching transition from oocyst to sporozoites as well as human antibody density variations within the mosquito gut are proposed and used. In sum, our model integrates the developmental stages of the parasite within the mosquito such as gametogenesis, fertilization and sporogenesis culminating in the formation of sporozoites. Quantitative and qualitative analyses including a sensitivity analysis for influential parameters are performed. We quantify the average sporozoite load produced at the end of the within-mosquito malaria parasite's developmental stages. Our analysis shows that an increase in the efficiency of the ingested human antibodies in inhibiting fertilization within the mosquito's gut results in lowering the density of oocysts and hence sporozoites that are eventually produced by each mosquito vector. So, it is possible to control and limit oocysts development and hence sporozoites development within the mosquito by boosting the efficiency of antibodies as a pathway to the development of transmission-blocking vaccines.

Maia Martcheva University of Florida
"Coinfection Dynamics of Heroin Transmission and HIV Infection in a Single Population"

We propose a model of a joint spread of heroin use and HIV infection. The unique disease-free equilibrium always exists and it is stable if the basic reproduction numbers of heroin use and HIV infection are both less than 1. The semi-trivial equilibrium of HIV infection (heroin use) exists if the basic reproduction number of HIV infection (heroin use) is larger than 1 and it is locally stable if and only if the invasion number of heroin use (HIV infection) is less than 1. When both semi-trivial equilibria lose their stability, a coexistence equilibrium occurs, which may not be unique. We compare the model to US data on heroin use and HIV transmission. We conclude that the two diseases in the US are in a coexistence regime. Elasticities of the invasion numbers suggest two foci for control measures: targeting the drug abuse epidemic and reducing HIV risk in drug-users.

MFBM: Subgroup contributed talks (1:30-2:30pm)

Rui Borges Vetmeduni Vienna, Austria, ruiborges23@gmail.com
"Consistency and identifiability of the polymorphism-aware phylogenetic models"

Polymorphism-aware phylogenetic models (PoMo) constitute an alternative approach for species tree estimation from genome-wide data. PoMo builds on the standard substitution models of DNA evolution but expands the classic alphabet of the four nucleotide bases to include polymorphic states. By doing so, PoMo accounts for ancestral and current intra-population variation, while also accommodating population-level processes ruling the substitution process (e.g. genetic drift, mutations, allelic selection). PoMo has shown to be a valuable tool in several phylogenetic applications but a proof of statistical consistency (and identifiability, a necessary condition for consistency) is lacking. Here, we prove that PoMo is identifiable and, using this result, we further show that the maximum a posteriori (MAP) tree estimator of PoMo is a consistent estimator of the species tree. We complement our theoretical results with a simulated data set mimicking the diversity observed in natural populations exhibiting incomplete lineage sorting. We implemented PoMo in a Bayesian framework and show that the MAP tree easily recovers the true tree for typical numbers of sites that are sampled in genome-wide analyses.

Zoe Lange Frankfurt Institute for Advanced Studie, Germany, zlange@fias.uni-frankfurt.de
"Force Inference – Estimating the dynamics of mechanical forces in epithelial tissues from time-lapse images"

Embryonic development, wound repair and cancer growth are complex results of collective cell migration. Collective cell migration is based on the biochemical and mechanical interactions between cells with individual cells regulating their mechanical state and exerting forces on the surrounding tissue. To gain further insights into the multi-scale effects of force propagation from cells to tissues and the shaping properties on whole organisms, it is of great interest to study spatial and temporal dynamics of forces. Force inference is a computational approach to estimate tissue stress from images using a biomechanical model and a mathematical inverse method. It is a good supplement to experimental force measurement techniques like laser ablation. As a non-invasive observation technique, it requires no mechanical probing of the tissue and yields results for the whole system at once. The force inference method proposed by Ishihara and Sugimura (2012) applies a Bayesian framework to handle the indefiniteness of a system of linear force-balance equations. In this study, we use cell-vertex simulation generated data to validate our implementation of Bayesian force inference and apply it to investigate force dynamics in a classical wound healing assay. We discuss our workflow including image segmentation, graph construction and calibration based on force geometry relation, as well as robustness for segmentation errors and theoretical limits of force inference. We find that the method is challenged by ragged boundaries produced with a scratching technique. We show that pressure gradients flatten with closing of the wound.

Anastasios Matzavinos Brown University, United States, tasos@brown.edu
"Bayesian uncertainty quantification for particle-based simulation of lipid bilayer membranes"

A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to Bayesian uncertainty quantification using transitional Markov chain Monte Carlo (TMCMC) is extremely parallelizable and has opened the door to a variety of applications which were previously too computationally intensive to be practical. In this talk, we first explore the machinery required to understand and implement Bayesian uncertainty quantification using TMCMC. We then describe dissipative particle dynamics, a computational particle simulation method which is suitable for modeling biological structures on the subcellular level, and develop an example simulation of a lipid membrane in fluid. Finally, we apply the algorithm to a basic model of uncertainty in our lipid simulation, effectively recovering a target set of parameters (along with distributions corresponding to the uncertainty) and demonstrating the practicality of Bayesian uncertainty quantification for complex particle simulations. This work was partially supported by the NSF through grant no. DMS-1552903.

ONCO: Subgroup Contributed Talks (1:30-2:30pm)

Pirmin Schlicke Chair for Mathematical Modeling at the Center of Mathematics, Technical University of Munich, Germany
"How Mathematical Modeling Could Contribute to the Quantification of Metastatic Tumor Burden Under Therapy"

Cancer is one of the leading death causes globally with about 8.2 million deaths per year with rising numbers in recent years. About 90% of cancer deaths do not occur due to primary tumors but to metastases, of which most are not clinically identifiable due to their relatively small size at primary diagnosis and limited technical possibilities. However, as therapeutic decisions are formed depending on the existence of metastases and their properties - non-identified metastases might have huge influence in the treatment outcome. It is therefore of clinical interest to give an estimation of the metastatic burden to assist in planning optimal treatments accordingly for individual cancer patients. A mathematical model addressing this problem has been developed based on a transport equation introduced by (Iwata et. al.) and extended by currently available systemic treatment options such as chemo- and immunotherapy. The model is defined in a continuous setting which allows it to also model the transition of a single primary tumor towards a metastatic disease, therefore indicating the metastatic cascade necessary to develop multiple metastatic tumors. Numerical implementation of the model framework allows for parameter estimation from clinical data, in our case we gathered parameter values from systemically treated lung cancer patients. We successfully quantified the total metastatic burden retrospectively for those patients over time given systemic treatment. In silico experiments allow for insights in differing therapeutic schedules, different medications and the further development of the metastatic burden. A sensitivity analysis on the model framework gave valuable insights in the behavior of model parameters and the clinical outcome.

Maximilian Strobl Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center Tampa, USA
"Personalising adaptive cancer therapy in theory and in practice: the role of resistance costs and cellular competition"

Control and conquer - this is the philosophy behind adaptive therapy, which seeks to exploit intra- tumoral competition to avoid, or at least, delay the emergence of therapy resistance in cancer. Motivated by promising results from theoretical, experimental and, most recently, clinical studies, there is an in- creasing interest in extending this approach to other cancers. As such, it is urgent to understand the characteristics of a cancer which determine whether it will respond well to adaptive therapy, or not. One plausible such candidate is the “cost of resistance” in which acquisition of the resistance mechanism decreases a cell’s fitness in the absence of drug. To investigate the role of fitness costs, we initially study a simple 2-population ODE model in which we assume tumour cells are either drug-sensitive or resistant and compete in a Lotka-Volterra fashion. We identify the initial fraction of resistance, the proximity of the tumour to carrying capacity, resistance costs and turnover as important determinants of the benefit of adaptive therapy over standard-of-care continuous therapy. Moreover, we show that a resistance cost is neither a necessary nor a sufficient criterion for the success of adaptive therapy, but that the effect of a cost is dependent on the tumour’s proximity to carrying capacity and the rate of cellular turnover. Subsequently, we test whether our conclusions extend into space by considering a 2-D on-lattice cellular automaton model. While all the aforementioned factors remain important, we show that they interact in a non-linear fashion with the spatial architecture of the tumour. To conclude, we will show applications of our insights to the development of an adaptive therapy trial for the treatment of ovarian cancer with PARP inhibitors. This illustrates some of our theoretical predictions and raises new questions about when to adapt therapy and when not to. Overall, our work helps to clarify under which circumstances adaptive therapy may be beneficial and suggests that turnover may play an unexpectedly important role.

Johannes Reiter Stanford University School of Medicine, Stanford, USA
"A mathematical model of ctDNA shedding predicts tumor detection size"

Early cancer detection aims to find tumors before they progress to an uncurable stage. Prospective studies with tens of thousands of healthy participants are ongoing to determine whether asymptomatic cancers can be accurately detected by analyzing circulating tumor DNA (ctDNA) from blood samples. We developed a stochastic mathematical model of tumor evolution and ctDNA shedding to investigate the potential and the limitations of ctDNA-based cancer early detection tests. We inferred ctDNA shedding rates of early stage lung cancers and calculated that a 15 mL blood sample contains on average only 1.5 genome equivalents of ctDNA for lung tumors with 1 billion cells (size of 1 cm3). We considered two clinically different scenarios: cancer screening and cancer relapse detection. For monthly relapse testing with a sequencing panel covering 20tumor-specific mutations, we found a median detection size of 0.24 cm3 corresponding to a lead time of 160 days compared to imaging-based relapse detection. For annual screening, we found a median detection size of 2.8-4.8 cm3 depending on the sequencing panel size and on the mutation frequency. The expected detection sizes correspond to lead times of 390-520 days compared to current median lung tumor sizes at diagnosis. This quantitative framework provides a mechanistic interpretation of ctDNA-based cancer detection approaches and helps to optimize cancer early detection strategies.

OTHE: Other Contributed Talks (1:30-2:30pm)

Anne Talkington Chapel Hill
"A PBPK model for clearance of PEGylated nanomedicines"

Physiologically based pharmacokinetic (PBPK) models are a means of conducting virtual experiments on a large scale as an alternative to extensive trials that would be prohibitively time-consuming, unethical, or otherwise costly. PBPK can be used to compute and test optimal dosing strategies, among other features, of proposed treatments using known or learned kinetics of the system mimicking complex human physiology. In turn, PBPK modeling can enable more efficient design and optimization of in vivo experiments, and consequently accelerate pre-clinical screening and development. I will discuss the application of PBPK modeling to an important problem in the medical community – the accelerated clearance of PEGylated drugs in the presence of anti-PEG antibodies (APA). While this phenomenon renders an entire class of drugs (i.e., PEGylated drugs) ineffective in many patients, the medical community is largely unaware of how drastically this can alter prognosis or how to mitigate this effect. I will describe a multi-compartment PBPK model to accurately capture and ultimately predict clearance behavior, with the goal of validating results against drug biodistribution data obtained via PET/CT technology. Specifically, I will focus on the initial transient dynamics as nanomedicines are cleared from the circulation in patients with high APA titers. I will then discuss further applications for this model in the context of targeted therapeutics.

Tatiana Marquez-Lago UAB
"Mathematical methods for microbiome research"

The complex community of the human microbiota and its specific role in health maintenance and disease has become an intense topic of study –and debate- over the last years. We do know that microorganisms colonizing human bodies exceed the total number of human cells, and that the number of microbial genes inside our bodies is roughly 100 times higher than the number of genes contained in the human genome, impacting human biology in various ways. For instance, the human immune system is in great part composed of and trained by resident microorganisms, and different microbiome compositions associate with the onset and progression of a large variety of human diseases, including diseases typically considered as non-communicable. Functional, causal links remain largely unexplored in many cases, however, in great part due to sampling limitations, data volume and integration complexity. Due to this gap and the importance of studying microbiome interactions, we have developed methods and tools toward multi-scale analysis and predictive (mechanistic) modeling, as well as integration of multi ‘omics’ data. On the one hand, feature selection and machine learning allows identification of patterns and relationships in large data collections, such as those in human microbiota studies. On the other, mathematical modeling and simulations provide a comprehensive framework to identify connections and key (onset) mechanisms in disease models. Both approaches are essential for analysis and forward engineering personalized therapeutics. In this talk, I will discuss available tools and mathematical methods in this area of research, and what is still needed toward integrative models of host-microbiota dynamics.

Camile Kunz Goethe U.
"Chemotaxis impact on pattern formationChemotaxis impact on pattern formation"

During embryo development there is a rapid growth in cell numbers that forms complex structures. Skin pattern formation is an early process during the embryogenesis and happens before the cells fully differentiate. In the present project we consider skin patterning in mouse embryos, where cell aggregates form based on a hierarchical process, involving interactions between the epidermal cell populations. The reaction-diffusion pre-pattern is driven by fibroblast growth factor (FGF20), bone morphogenic protein (BMP) and WNT. Considering mathematical models, there are two main processes involved in the pattern formation: Turing reaction-diffusion systems and chemotaxis. The Turing system models the concentration of two interacting chemicals, and the patterns arises from an instability driven by a difference between their diffusion coefficients. Some previous studies show that this behavior is essential for self-organization in the mouse hair follicle and chicken feather pre-pattern formation. Another key mechanism is chemotaxis, where the cells move in the direction of a chemical attractant, where patterns can also be observed. Experimental data indicates a hierarchical system, where cell chemotaxis is guided by a Turing system. We aim at developing mathematical models to describe the underlying biological processes leading to skin patterning, especially the interaction of chemotaxis with reaction-diffusion (Turing) systems. A mathematical model using partial differential equations is solved numerically, and some results are presented and compared to the experimental data. We study the parameter-dependence of the model and different model structures, and their impact on the pattern forming process. According to the experimental data the Turing system and the chemotaxis seems to be intrinsically related on the mouse skin patterning. Using a numerical approach for the PDE system, we develop a framework to study quantitatively how chemotaxis and Turing systems are related and their impact on the patterning process.During embryo development there is a rapid growth in cell numbers that forms complex structures. Skin pattern formation is an early process during the embryogenesis and happens before the cells fully differentiate. In the present project we consider skin patterning in mouse embryos, where cell aggregates form based on a hierarchical process, involving interactions between the epidermal cell populations. The reaction-diffusion pre-pattern is driven by fibroblast growth factor (FGF20), bone morphogenic protein (BMP) and WNT. Considering mathematical models, there are two main processes involved in the pattern formation: Turing reaction-diffusion systems and chemotaxis. The Turing system models the concentration of two interacting chemicals, and the patterns arises from an instability driven by a difference between their diffusion coefficients. Some previous studies show that this behavior is essential for self-organization in the mouse hair follicle and chicken feather pre-pattern formation. Another key mechanism is chemotaxis, where the cells move in the direction of a chemical attractant, where patterns can also be observed. Experimental data indicates a hierarchical system, where cell chemotaxis is guided by a Turing system. We aim at developing mathematical models to describe the underlying biological processes leading to skin patterning, especially the interaction of chemotaxis with reaction-diffusion (Turing) systems. A mathematical model using partial differential equations is solved numerically, and some results are presented and compared to the experimental data. We study the parameter-dependence of the model and different model structures, and their impact on the pattern forming process. According to the experimental data the Turing system and the chemotaxis seems to be intrinsically related on the mouse skin patterning. Using a numerical approach for the PDE system, we develop a framework to study quantitatively how chemotaxis and Turing systems are related and their impact on the patterning process.

POPD: Subgroup Contributed Talks (1:30-2:30pm)

Peter Jagers Chalmers & University of Gothenburg
"Galton and Watson were (almost) right: virtually all populations are eventually extinct"

145 years have passed since the publication of Galton’s and Watson’s famous paper where they claimed that “all surnames (and by analogy all populations) tend to extinction”. Strangely, their theorem was largely accepted for more than half a century, until Haldane and Steffensen established the true dichotomy between subcritical populations always dying out and supercritical, which either die out or else grow exponentially. But this is under stable conditions. For population-size-dependent reproduction, we show the following very general extinction theorem: Consider a process giving the size of a population in discrete time. Asume that reproductive events occur one-by-one so that at each step the population either decreases by one (an individual dies) or increases by a random number (the number of children born at the event). Note that theses changes are neither assumed independent nor identically distributed. On the contrary, there is a carrying capacity K, such that the process constitutes a supermartingale when larger than K and a submartingale otherwise. Further, zero is assumed to be the only absorbing state. Then the process dies out almost surely.

Max Souza Universidade Federal Fluminense
"Fitness potentials and qualitative properties of the Wright-Fisher dynamics"

We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the 1-D Kimura Equation (2 type and no mutation). In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis — similar to the one used in classical mechanics — providing the basic tool for a simple heuristic that describes both the short and long term dynamics. Using this toolkit, we propose a definition of an evolutionary stable state in finite population that includes the case of mixed populations. We also discuss extensions to more than two types and weak mutation. This is joint work with Fabio A. C. C. Chalub.

Matthew Nitschke University of Adelaide
"The effect of bottleneck size on evolution in nested darwinian populations"

Recent theories about the transition from unicellular life have introduced the idea of ecological scaffolding as a potential explanation for how early groups of cells would have gained the properties necessary to participate in evolution by natural selection. This is the idea that particular ecologies and environments can scaffold Darwinian properties onto groups of cells. The scaffolding allows cells to directly participate in the process of evolution by natural selection as if they were members of multicellular collectives, with groups participating in a birth-death process. The ingredients for this process to operate are only patchily distributed resources and a regularly occurring dispersal process that also creates a bottleneck. In this talk, I will discuss the effect of bottleneck size on this process and how this alters the evolutionary dynamics at both levels of the system.

Poster Session (2:30-3:30pm)

Click to view posters for each subgroup

Sub-group Keynote

3:30pm

Andrea Bild,
City of Hope, @AndreaBildLab

Mathematical Oncology Subgroup

Competitive and cooperative interactions between resistant and sensitive breast cancer cells during therapy

Our research focuses on estrogen receptor positive breast (ER+) cancer, the most commonly diagnosed and metastatic subtype. In a tumor, neighboring subclonal cancer cell populations interact both through competition for resources and through cooperation, by the production of growth promoting signals. Promoting competition can maintain drug sensitivity when resistant cells get outcompeted. Cooperation can promote cell survival under selective pressure, as well as potentially protect cellular populations that may otherwise be susceptible to treatment. Our research program integrates three key components to quantify cancer cell interactions: serial patient tumor samples molecularly profiled at the single cell level, a parallel in vitro model system where mechanisms can be tested through experimental manipulation and measured over time, and integrative dynamic mathematical models of the growth and interaction of subclonal cancer populations. By embedding the time course data and differential equation models into a Bayesian inference framework, we can estimate the strength of positive and negative interactions between subclonal populations during treatment and identify key mechanisms driving cell communication. Our analyses of patient derived samples further indicates that heterogeneous multi-clonal ER+ breast cell populations evolve to acquire alternative signaling states that drive cell cycle progression independent of estrogen availability, and that cells can cooperate to survive during therapy through the increased production and local sharing of growth promoting factors.

Happy hour with friends and colleagues (4:30)

Schedule for Tuesday, August 18

Coffee with friends & colleagues

8:00am

Subgroup Keynote

8:30am