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

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

Galane J. Luo University of Birmingham
"A fluid mechanical model of the plant cell wall reveals underlying mechanism for helical organ morphology"

Plant morphology emerges from cellular growth. The turgor-driven diffuse growth of a cell can be highly anisotropic: significant in the longitudinal direction and negligible in the radial direction. Such anisotropy is ensured by cellulose microfibrils (CMF) reinforcing the cell wall in the hoop direction. To maintain the cell's integrity during growth, new wall material including CMF must be continually deposited. In this talk, I will present a mathematical model which describes the cell as a cylindrical pressure vessel and the cell wall as a fibre-reinforced viscous sheet, explicitly including the mechano-sensitive angle of CMF deposition. The model incorporates interactions between turgor, external forces, CMF reorientation during wall extension, and matrix stiffening. I will explain the general formulation of the model from a fluid mechanics perspective, and summarise the technical steps required in order to obtain evolution equations for growth variables such as cell length and twist. I will discuss how the handedness of helical cell growth depends on external torque and intrinsic wall properties, and interpret numerical simulation results in light of recent experimental findings. Overall, the model provides a meaningful step towards a unified mechanical framework for understanding left- and right-handed growth as seen in many plants. Such a framework can help us harness the potential of plants in our effort to address society's sustainable development needs.

Euan Smithers University of Birmingham
"How do plant leaf pavement cells form puzzle piece like shapes? Using a multi-model approach to simulate chemical and visco-elastic mechanical processes and experimental methods to discover their secrets."

Pavement cells in the plant leaf epidermis form interesting and intriguing interlocking puzzle like shapes with undulations of lobes and indents. However, no one has been able to fully explain how these shapes form. There are two possible pathways of pavement cell development, one involving a combination of plant Rho like GTPases signalling proteins and cytoskeleton components, specifically microtubules which could provide a feedback loop and the second being possible mechanical effects from the tissue. As a result, we have developed three models, one to model microtubule behaviour, the second to model the protein signalling dynamics and the third to model the mechanics of the cells, using a stochastic network, reaction diffusion equations solved via the finite element method and a visco-elastic vertex element model. I shall also outline some of the experimental procedures we have carried out to test how pavement cells develop. We can demonstrate that the signalling pathways provide a feedback loop to sustain pavement cell shape, but don’t initiate the shape, while the mechanical effects from the tissue can initiate pavement cell lobes.

Ulyana Zubairova Russian Academy of Science
"Leaf epidermal pattern development in the cereals: lessons from LSM-image analysis and computer simulations"

The leaf epidermis of a monocotyledonous plant gives a unique model system for studying morphogenesis due to diverse cell types and constant growth direction. For such leaves, a unidirectional growth occurring for a long time enables us to observe a series of successive morphogenetic stages at one snapshot. In this work, we propose the concept of using a growing wheat leaf to study dynamical changes in morphogenesis, including stress-induced changes. Linear leaf of wheat, during its formation for a long time, maintains a phase of steady growth. Therefore, it is possible to observe a series of successive events of morphogenesis fixed in the cellular architecture of a mature leaf. High-resolution 3D LSM-images allow extracting quantitative characteristics describing the cellular structure of leaf epidermis. However, to obtain a large number of statistical data methods of high throughput, computer-based image segmentation should be used. We developed a workflow for the detection of structural properties of leaf epidermis from 3D images obtained from confocal LSM-images (Zubairova, U. S., Verman, P. Y., Oshchepkova, P. A., Elsukova, A. S., & Doroshkov, A. V. (2019). LSM-W 2: laser scanning microscopy worker for wheat leaf surface morphology. BMC systems biology, 13(1), 22.). The workflow includes the protocol of sample preparation, image processing ImageJ-plugin, and data extraction algorithms. The data on the cellular architecture further acts as a basis for the elaboration and verification of spatial models accounting for structural features of leaves. For the leaf epidermis of cereals, a brickwork-like pattern combined with unidirectional growth allows to reduce the dimension and use a quasi-one-dimensional representation of the cellular ensemble in the model. This idea was realized in the model (Zubairova, U., Nikolaev, S., Penenko, A., Podkolodnyy, N., Golushko, S., Afonnikov, D., & Kolchanov, N. (2016). Mechanical behavior of cells within a cell-based model of wheat leaf growth. Frontiers in plant science, 7, 1878.) growth of a linear leaf blade. The model allows for fitting of the visible cell length using the experimental cell length distribution along the longitudinal axis of leaf epidermis. In this work, we assume a unidirectional growing cell ensemble starting from a meristem-like layer of generative cells and then generating parallel cell rows from every cell of the initial layer. We considered the growth zone of the leaf includes division and elongation zones; also, the division zone consists of a region of asymmetric divisions forming specialized cells (trichomes and stomata). The model was verified on qualitative and quantitative data on stress-induced disturbances of morphogenesis in the epidermis of a wheat leaf. The study was carried out with a grant from the Russian Science Foundation (project No. 19-74-10037).

Tamsin Spelman University of Cambridge
"Nucleus shape in plant root hair cells"

A plant root hair is a single long thin cell, which in Arabidopsis is ≈ 10 μm in diameter and reaches ≈ 1 mm in length, growing rapidly at speeds of ≈ 1 μm/min. The nucleus tracks the growing tip remaining ≈ 75 μm back from the growing front [1]. While the nucleus motion has been studied, less work has considered the nucleus shape during growth and how this impacts cell growth. Using a numerical model, we analyse the forces imposed on the nucleus by the cytoskeleton (the internal fibre network of the cell), for a range of nucleus shape, size and position enclosed within a cuboidal domain. We compare our results with experimental data from root hairs grown within microchannels. We segment the experimental images to reconstruct the 3D nuclei shapes, from which we can also estimate the spacial distribution of forces being imposed.

David Holloway BCIT
"Polar auxin transport dynamics of primary and secondary vein patterning in dicot leaves"

The growth regulator auxin plays a central role in development across plants. Auxin spatial patterning is critical in the phyllotactic arrangement of leaves along a stem, the shapes of the leaves themselves, and venation within leaves. These patterns depend on polar auxin transport (PAT) at the cellular level, particularly the preferential allocation of PIN efflux proteins to certain areas of the plasma membrane. Two general mechanisms have been studied: an up-the-gradient (UTG) allocation dependent on neighbouring-cell auxin concentrations, and a with-the-flux (WTF) allocation dependent on the flow of auxin across walls. Auxin appears to flow both towards auxin maxima (associated with UTG) and away from auxin maxima (associated with WTF), depending on the developmental phenomena. Both types of flow are implicated in vein patterning in leaves. We have developed a UTG+WTF model to quantify these combined dynamics. The model simulates intracellular and membrane kinetics and intercellular transport, and is solved for a 2D leaf of several hundred cells. Building upon earlier models for primary vein (mid-vein) formation, we developed a model for the formation of the secondary vein pattern. These arise from the margin of the leaf, in a distal to proximal sequence, and connect with the mid-vein to form the main vascular network of the leaf. These networks can be characteristic of species, and associated with species-specific leaf morphologies. The model responds to decreasing PAT, as in experiments increasing the PAT inhibitor NPA, with: a switch from several distinct vein initiation sites to many less-distinct sites; a delay in vein canalization; inhibited connection of new veins to old; and finally loss of patterning in the margin, loss of vein extension, and confinement of auxin to the margin. We have removed assumptions of long range attraction factors from earlier work. Simulations of vein patterning and leaf growth indicate that growth itself may help bridge the scale from the cell-cell resolution of the PIN-auxin dynamics to vein patterns on the whole-leaf scale.

EDUC: Education Minisymposium II (9:30-11:00am)

Dmitry Kondrashov University of Chicago
"Quantitative modeling remotely"

I teach the course Introduction to Quantitative Modeling for Biology, which is integrated into the biological sciences curriculum at University of Chicago and serves around two hundred students every year. I will discuss the adaptation of this course to online learning, present student assessments results from spring 2020, and share materials that can be incorporated into other courses.

Glenn Ledder University of Nebraska-Lincoln
"Teaching Mathematical Epidemiology at Different Mathematical Levels Using a Multiple Representation Theory of Mathematical Modeling"

The COVID-19 pandemic has made mathematical epidemiology a topic of critical importance, providing mathematics educators with an unparalled opportunity. This opportunity is accompanied by a challenge: how do mathematics educators, some of whom have little personal experience with mathematical modeling, teach mathematical epidemiology to their students in courses ranging from precalculus to differential equations, and do so in a way that builds understanding of epidemic disease dynamics as well as mathematical methods? We address this issue by presenting a framework based on a multiple representation theory of mathematical modeling and using that framework to offer examples of building blocks that include a physical simulation activity, model development, parameterization, various methods for analysis and visualization of results, and guidelines for how to get students to use writing to facilitate their understanding.

Heiko Enderling Moffitt Cancer Center
"High school internship program in integrated mathematical oncology"

Modern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well-versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education traditionally occurs in disciplinary silos, which creates a steep learning curve at the graduate and postdoctoral levels that increasingly bridge multiple disciplines. Numerous colleges have begun to embrace interdisciplinary curricula, but students who double-major in mathematics (or other quantitative sciences) and biology (or medicine) remain scarce. We identified the need to educate junior and senior high school students about integrating mathematical and biological skills, through the lens of mathematical oncology, to better prepare students for future careers at the interdisciplinary interface. The High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center has so far trained 59 students between 2015 and 2019. We report here on the program structure, training deliverables, curriculum, and outcomes. We hope to promote interdisciplinary educational activities early in a student's career.

Brian Winkel SIMIODE
"SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations: Biological SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations: Biological Efforts"

SIMIODE is an NSF funded Community of Practice based at www.simiode.org which supports faculty and students in efforts to motivate and teach differential equations in context through modeling. While differential equations is a widely applicable branch of mathematics we share a number of efforts in biological applications which are featured in SIMIODE: population growth, death, and immigration; ant tunnel building; LSD and problem solving; malaria and Ebola; acorns, rodents, and snakes; crop harvesting; intraocular gas bubbles; tumor growth; drug administration; inner ear drug delivery; epidemics; and dialysis. We discuss examples of modeling in the life sciences using data and the full modeling cycle, while introducing mathematical content and supporting students in learning the underlying mathematics. Further, we share news of SCUDEM - SIMIODE Challenge Using Differential Equations Modeling, now in its fifth year is an annual international team challenge, in which students engage in model building using differential equations and share their results for faculty judging and commentary and peer review.

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

Lubna Pinky University of Tennessee Health Science Center
"Quantifying the Effects of Dose, Strain and Tissue Tropism on Parainfluenza Virus Infection Kinetics"

Human parainfluenza viruses (HPIVs) are a leading cause of acute respiratory infection hospitalization in children yet little is known about the growth and clearance kinetics. In mice, longitudinal measurements are possible by using reporter sendai viruses that express luciferase, where the insertion location yields wild-type (rSeV-luc(M-F)) or attenuated (rSeV-luc(P-M)) phenotypes. Bioluminescence from individual animals suggests that there is a rapid increase in expression within the first 1-2 days followed by a peak, biphasic clearance, and resolution. However, these kinetics vary with dose, strain, individuals, and the upper and lower respiratory tracts. To quantify the differences, we first translated the bioluminescence measurements taken from nasopharynx, trachea, and lungs into viral loads. We then fit a mathematical model to the estimated viral load data for each scenario using nonlinear mixed effects modeling. The results confirmed a higher rate of virus production with the rSeV-luc(M-F) virus compared to its attenuated counterpart, and suggested that the infected cell clearance was expedited when infected with rSeV-luc(M-F) in lungs with high dose. Our analysis suggested that the number of infected cells scales with dose, and that distinct infected cell clearance rates are associated with each dose, strain, individual and respiratory tract compartment. This analysis provides important insight into parainfluenza infection kinetics and the dynamical differences based on dose, viral attenuation, individual heterogeneity, and tissue tropism.

Maria Rodriguez Martinez IBM Research Europe, Zurich (Switzerland)
"Multiscale clonal model of Germinal Center B cell differentiation"

Germinal Centers (GCs) are B cell follicles in the secondary lymphoid organs where B cells proliferate, mature their B cell receptors (BCRs) following exposure to antigen and interaction with other GCs cells, and eventually differentiate as plasma cells or memory B cells. We have recently developed a stochastic hybrid model of the GC reaction that combines: i) an intra-cellular gene circuit that captures the regulatory interplay of a few key master regulators of the differentiation process; and ii) an extra-cellular component that accounts for the stochastic events that take place in the GC, such as antigen acquisition and competition for T cell help (https://www.mdpi.com/2073-4409/9/6/1448). Mimicking the evolutionary processes undergone by B cells, in our model new B cells constantly emerge exhibiting mutated BCRs that present different affinity to the existing pool of antigens, which in turn probabilistically bias their evolution to certain fates. We faithfully recapitulate the process of BCR maturation by explicitly modelling the hypermutation process that takes place in the BCR genes. We compare the model predictions to experimental data of matched single-cell transcriptional high-resolution maps and BCR repertoire sequencing of GC B cells. Our explicit modeling of B cell maturation enables us to characterise the evolutionary processes and competition at the heart of the GC dynamics, and explains the emergence of clonal dominance as a result of initially small stochastic advantages in the affinity to antigen. Interestingly, a subset of the GC undergoes massive expansion of higher-affinity B cell variants (clonal bursts), leading to a loss of clonal diversity at a significantly faster rate than in GCs that do not exhibit clonal dominance. Our work contributes towards an in silico vaccine design, and has implications for the better understanding of the mechanisms underlying autoimmune disease and GC-derived lymphomas.

Gustavo Hernandez Mejia Frankfurt Institue for Advanced Studies (FIAS); Goethe University Frankfurt, Germany
"Antibodies cross-reaction in influenza A infections: a modeling approach"

Disclosing key phenomena of how antibodies (Abs) induced by one influenza strain are effective against another, the so-called cross-reaction, is central for the design of universal flu vaccines. Here, using data of mice infected with influenza, we develop a stochastic mathematical modeling scheme to explore the impact of consecutive influenza A infection in the cross-reactome. The model successfully recapitulates the antibody cross-reactive data from mice infected with different H3N2 influenza strains. Of note, without framework modifications, the model can also represent the Abs response in mice to diverse H1N1 strains. Furthermore, we found that while the antigen differences, time of infection, and the B-cells population shape between infections directly influence the Abs outcome, the naive B-cells repertoire has minor effects on Abs behavior. Importantly, we found that affinity changes in immunity between infections satisfy necessary conditions for a successful Abs cross-reaction. We envisage this work will add to the forces among public makers, virologists, biologists, and theoreticians, bringing clarity of mind when experimental and clinical evidence is fragmented.

Paul Macklin Indiana University
"Community-driven multiscale modeling of SARS-CoV-2"

The 2019 novel coronavirus (SARS-CoV-2) is a pathogen of critical significance to international public health. Knowledge of the interplay between molecular-, cellular-, and multicellular-scale processes that drive disease dynamics is limited. Multiscale simulation models can shed light on these dynamics, identify actionable 'choke points' for intervention, screen potential therapies, and identify potential biomarkers that differentiate patient outcomes. In this talk, we present progress by a multi-institution, multi-disciplinary coalition of over 40 mathematical biologists, immunologists, virologists, pharmacologists, and others to build a comprehensive multiscale model of SARS-CoV-2 infection dynamics and immune response in lung tissue. We will demonstrate and explore the current spatio-temporal agent-based model prototype, which includes intracellular virus and chemokine transport, virus-ACE2 receptor binding, receptor trafficking, viral replication dynamics (and subsequent viral release), infected cell phenotypic responses, cell-cell communication, immune cell recruitment, chemotactic exploration, T cell attacks on infected cells, and phagocytosis. This coalition-based approach is developing submodels in parallel and coordination, allowing us to rapidly advance towards a framework that can drive many independent investigations on COVID-19. Moreover, the novel mix of domain experts is fueling creative advances and new technical capabilities in multiscale tissue modeling. We anticipate that this progress will drive advances in immunology, inflammation, CAR T cell therapy, and virus-driven carcinogenesis for years to come. Interested members of the audience can try this open source framework live in a web browser at https://nanohub.org/tools/pc4covid19.

MEPI: Models of Infectious Diseases and Control (9:30-11:00am)

Hyojung Lee National Institute for Mathematical Sciences, Korea
"Transmission dynamics of Coronavirus disease (COVID19) in Korea"

The novel coronavirus outbreak has rapidly spread out from Wuhan, Hubei Province, China to other countries since December, 2019. More than 2,000 cases have confirmed since the first case was reported on 20 January, 2020 in South Korea. . The aim of this research is to analyze the transmission dynamics of COVID-19 in South Korea during the early phase of the outbreak. To do so, first, using the 30 confirmed cases, we estimated the basic epidemiological parameters from the data of the symptom onset dates by employing maximum likelihood estimation. Second, super-spreading events were occurred in Daegu, Korea from 31 January, 2020. Accounting for the heterogeneous transmission dynamics, we construct the mathematical model to estimate the geographic reproduction number. Finally, we assess the effect of the control interventions by simulating the various control scenarios to suggest the most effective intervention to halt the transmission

Robert Smith? University of Ottawa
"Assessing potential COVID-19 outcomes for a university campus with and without physical distancing"

By early March of 2020, it became apparent that COVID-19 was going to have a significant impact on institutions throughout society. On March 12, the University of Ottawa commissioned an informal modeling study to aid in their decision-making process. Here we present the results from that study: a differential-equation model was created in order to describe the states of susceptibility, exposure, infection, asymptomatic individuals, recovery and death. Our results shows that, in the worst-case scenario, the epidemic would peak at 7000 cases on campus with 63 dead, starting 115 days after the first case. Reducing contacts by 50% could lower the number of cases and fatalities, but it would expand the timeframe by several years. One day after this modeling study was completed, the University of Ottawa closed campus entirely. It follows that modeling and simulation in the midst of a fast-moving pandemic can be valuable tools for decision-makers.

Aurelio A de los Reyes Institute of Mathematics, University of the Philippines Diliman
"Intervention strategies to mitigate HIV/AIDS transmission in the Philippines"

Human Immunodeficiency Virus (HIV) impairs a person’s immune system leading to Acquired Immunodeficiency Syndrome (AIDS) – a condition characterized by severe illnesses. The number of HIV infections has more than doubled in the Philippines within the last decade, prompting the need to develop a model of disease transmission in the country. In this study, disease-free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Available data is utilized to identify model parameters giving insights on the trend of the disease in the country. Furthermore, effectiveness of control measures including precaution, HIV screening, Anti-Retroviral Treatment, and Pre-Exposure Prophylaxis (PrEP) are investigated in the framework of optimal control theory. These various control efforts are compared with regard to cost efficiency and effectivity in minimizing the number of infected individuals. Given limited available control measures, PrEP-only scenario is shown to be most cost effective.

Jonggul Lee National Institute of Mathematical Sciences, South Korea
"Spatial heterogeneity and control measures during avian influenza epidemic 2014-2015 in Korea"

During the winter of 2014-2015, an epidemic of highly pathogenic avian influenza (HPAI) led to high mortality in poultry and put a serious burden on the poultry industry of the Republic of Korea. Effective control measures considering spatial heterogeneity to mitigate the HPAI epidemic is still a challenging issue. Here we develop a farm-based HPAI model to analyze the spatiotemporal evolution of the epidemic and assess the impact of control strategies. The epidemiological and geographical data of the domestic poultry farms in South Korea are used to find the best-fitted parameters of the model. We investigate potential for two control measures against HPAI: preemptive culling and farm rest. The best culling radius to maximize the final size of the susceptible farms and minimize the total number of culled farms is calculated from the model. The reproductive number of a farm is calculated as an indicator of virus transmission in a given area. Simulation results indicate that this parameter is strongly influenced not only by epidemiological factors such as transmissibility and/or susceptibility of poultry species but also by geographical and demographical factors such as the distribution of poultry farms (or density) and connectivity (or distance) between farms. Based on this result, we suggest the optimal culling radius and number of resting farms with respect to the reproductive number in a targeted area.

MFBM: Stochastic methods for epidemiology and biochemical reaction networks (9:30-11:00am)

Eben Kenah The Ohio State University, United States, kenah.1@osu.edu
"Pairwise survival analysis for measuring and controlling risk in epidemics"

When a disease is transmitted from person to person, infections in different individuals are not independent. These “dependent happenings” cause fundamental problems for standard principles of epidemiologic study design and data analysis in infectious disease epidemiology. Pairwise survival analysis is an extension of standard survival analysis to the transmission of infectious diseases through households, hospitals, or other situations where there is a clearly-defined population at risk of infection. We show how this framework can be used to assess and control for confounding and selection bias. We then show how these methods can be used to extend traditional derivations of case-control and case-cohort designs to obtain novel study designs for outbreak investigations and public health intervention trials for emerging infections. Finally, we consider the possibilities for incorporating pathogen genetic sequences.

Jessica Stockdale Simon Fraser University, Canada, jessica stockdale@sfu.ca
"How long does it take to detect a change in COVID-19 control measures?"

Countries around the world have implemented population-wide interventions in efforts to control COVID-19, with varying extent and success. Many jurisdictions are moving to relax measures, while others are re-intensifying them to curb growing spread. But uncertainty remains around the length of time between a population-level change in control measures and its observable impact on detected cases. I will describe our recent work in estimating the time frame for a substantial difference between the cases that occur following a change in control and those that would have occurred under continued strategy, under a compartmental model for disease transmission incorporating physical distancing. Using a likelihood-based approach and data from British Columbia, Canada, we examine how long it takes to detect such a difference given delays and noise in reported cases. We find that these time frames are long: longer than the mean incubation period and the often-used 14 days.

Forrest Crawford Yale University, United States, forrest.crawford@yale.edu
"Causal evaluation of infectious disease interventions using stochastic transmission models"

Deterministic and stochastic models of infectious disease transmission are widely used to understand the dynamics of epidemics, and project the impact of control measures, in human populations. However, most clinical evaluations of vaccines and other interventions designed to prevent infection do not use these models. Instead, clinical infectious disease epidemiologists use randomized trials and statistical regression models to evaluate interventions. Recent work has shown that these approaches may deliver erroneous estimates of the susceptibility effect of the vaccine, even when treatment is randomized or all baseline confounders are measured. In this presentation, we develop approaches to causal evaluation of interventions in networked populations in randomized and observational trials using a flexible semi-parametric class of stochastic transmission models. We show analytically and by simulation that causal susceptibility and infectiousness effects are identified, and that researchers do not need to specify the functional form of some model components in order to make useful inferences. The approach illustrated in an application to evaluation of risk factors for tuberculosis in a large-scale cluster cohort study.

Boseung Choi Korea University, South Korea, cbskust@korea.ac.kr
"Statistical inference for epidemic models using the Survival dynamical system based on the Bayesian approach"

I introduce new methods for Bayesian Markov Chain Monte Carlo-based in references in certain of a stochastic model for epidemic data. SIR (Susceptible-Infected-Removed) model is the classical method for modeling infectious disease spread. In this research, we applied solutions of ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models to individual-level SIR model by introducing survival or cumulative hazard functions derived from population-level equations. We call the method as survival dynamical system (SDS). In this research, we also construct an additional estimation step for initial number of susceptible by utilizing a hierarchical Bayesian approach for inference of the number of trials in the Binomial distribution. we applied the SDS approach to data from a 2009 influenza A(H1N1) outbreak at Washington State University.

NEUR: Dynamics and Noise in Neural Networks (9:30-11:00am)

Cheng Ly Virginia Commonwealth
"The Circuit Mechanisms that alter Spiking Statistics in Mammalian Olfactory Bulb Cells"

The olfactory bulb is one of the primary stages of odor processing, possessing a unique architecture hallmarked by fast dendro-dendritic synapses between all inhibitory cells (perioglomerular cells (PGC) and granule cells (GC)) connected to excitatory cells (mitral/tufted cells (MC)). Although there has been ample theoretical and experimental studies of the olfactory bulb (OB), dissecting the circuit mechanisms of modulation of the first and second order (MC) spiking statistics of populations is lacking. In particular, we analyze data from our (Shew) lab in spontaneous and odor-evoked states n vivo, with multi-electrode arrays that enable studying second order spiking statistics with simultaneous recordings. Based on a multicompartment large-scale biophysical model, we develop a reduced firing rate model that enables us to efficiently and accurately capture our data. We show that granule cell inhibition in particular helps decorrelate in the spontaneous state but is unlocked so that there is stimulus-induced correlation in the evoked state; this is in contrast to many cortical sensory systems where there is often stimulus-induced decorrelation. We also consider pharmacological drug applications to manipulate inhibitory synaptic strengths (both PGC and GC) that alter the spiking statistics. Our model qualitatively captures the statistically significant changes.

Kelsey Gasior Florida State
"Mathematically Modeling Neuron Biophysics in Response to Ramped Input Current"

In the nervous system, olfactory bulb dopamine-secreting neurons (OBDA neurons) process different odors by inhibiting other downstream neurons. Recently, novel experiments were performed wherein current applied to individual neurons was continuously ramped to mimic biologically realistic neuronal input (at Florida State University, the Trombley lab performed) in comparison to previous standard protocols where current is applied in steps. However, this new stimulus protocol raises the questions of what is the proper way to interpret these data and how can mathematical analysis help? In this project, we have developed an integrated experimental-mathematical methodology to study transient dynamics in the electrical activity of single neurons while maintaining a close interdisciplinary collaboration with the biologists who carry out these electrophysiological experiments. One of the aims of our work is to create a positive feedback loop wherein experimental data informs the mathematical model, and in turn, the model directs future experiments. In particular, we are using bifurcation analysis to characterize the onset and offset of tonic spiking as well as the frequency of spiking in a neuron stimulated with both slow and fast applied current ramps. This work allows us to understand how different ion channels shape the transient response dynamics in OBDA neurons. Importantly, we have also developed mathematical tools that can be used to explore the behavior of other cell types as it is our belief that the ramping technique could be extended to study the single-neuron dynamics of all neuron types. The use of fast-slow analysis helps us to understand how the ramped applied current and the slow M-type Potassium channel influence tonic spiking behavior and frequency. Ultimately, this work helps close the gap between mathematical modeling and biological data in computational neuroscience.

Jan Kirchner Max Planck Institute for Brain Research
"Local and global organization of synaptic inputs on cortical dendrites"

Synaptic inputs on cortical dendrites are organized with remarkable subcellular precision at the micron level. This organization emerges during early postnatal development through patterned spontaneous activity and manifests both locally where nearby synapses tend to share functional properties, and globally with distance to the soma. Recent experimental studies reveal species-specific differences in this organization between mouse, ferret and macaque visual cortex: While in the mouse, synapses are retinotopically organized along the proximal-distal axis of the dendrite, no such organization is present in the ferret or macaque. Instead, here synapses are organized into local clusters according to orientation preference. We propose a computational framework that combines activity derived from retinal waves with functional and structural plasticity to generate these different types of organization across species, as well as across scales by including attenuating backpropagating action potentials. Within this framework, a single anatomical factor -- the size of the visual cortex and the resulting magnification of visual space -- can explain the observed differences. This allows us to make predictions about the organization of synapses also in other species and indicates that the proximal-distal axis of a dendrite might be central in endowing a neuron with its powerful computational capacities.

Fereshteh Lagzi University of Chicago
"Cell-type specific inhibitory plasticity can speed up assembly formation and slow down assembly degradation"

It is popular to ascribe distinct network functions to the different inhibitory neuron subtypes that makeup cortical circuits. Carving out functionally determined, cell-type specific circuit wiring is an essential component of this hypothesis. However, the plasticity rules for different interneuron subtypes, and how their interactions shape network dynamics are largely unexplored. We use in vitro patch clamp techniques paired with cell-specific optogenetic stimulation to measure the spike timing dependent plasticity (STDP) rules of the inhibitory inputs onto excitatory (E) pyramidal neurons from both Parvalbumin (PV) and Somatostatin (SOM) interneurons in mouse orbital frontal cortex (OFC). Consistent with past studies, PV inhibition shows a symmetric STDP that is often associated with the homeostatic control of excitatory firing rates. By contrast, SOM inhibition shows an asymmetric Hebbian STDP rule, so that recurrent SOM inhibition onto driving E neurons will ultimately depress. To understand the role of these different plasticity mechanisms in network dynamics we exploit large-scale network simulations of networks of spiking neuron model with plastic synapses, along with associated mean field theories of synaptic dynamics. We show that the asymmetric SOM plasticity rule promotes cross-inhibition between distinct E neuron assemblies, effectively providing a mechanism for competition between functionally grouped principle neurons. This competition will enhance computations where input comparisons must be made, as is often the case in decision task where the OFC is known to be essential. However, strong cross inhibition could lead to extreme (and unstable) winner-take-all assembly dynamics. Fortunately, the symmetric PV plasticity rule provides stability for the circuit, ensuring rich network dynamics. Finally, the increased correlations due to the asymmetric Hebbian learning for SOM connections to pyramidal cells can speed up assembly formation during training and slow assembly degradation post training.

ONCO: Differentiation and stemmness, in cell migration, cancer invasion, and development (9:30-11:00am)

Luke Tweedy Beaton Institute of Cancer Research, Glasgow
"Seeing around corners: Cell migration is determined by the complex interaction of environmental topology and attractant degradation"

Cell migration is often guided by gradients of attractants. Many cells are known to degrade the molecules that attract them, creating dynamic gradients that evolve and change as the cells migrate up them. In unrestricted environments, this enables more robust directed migration over much greater distances than can be explained by chemotaxis to an externally imposed gradient. However, its effects in a complex topology remain unclear. This is important to understand, because the in-vivo topologies in which cells migrate are almost invariably complex. We therefore modelled the behaviour of cells solving a variety of mazes, varying dead end lengths and complexities. We then tested each design experimentally. We found specific rules governing the collective decisions of cells connecting cell speed, attractant diffusivity and dead-end length and complexity. We even found topologies in which a majority of cells would favour a dead end over a path to a large attractant reservoir. This self-generated view of chemotaxis in complex environments will help us better understand immune responses and the patterns of metastasis for some cancers.

Niklas Kolbe Faculty of Mathematics and Physics, Kanazawa University, Japan
"Stochastic modelling of TGF-β signalling in single cells"

The cytokine TGFb plays an important role in cancer progression as it can both prevent uncontrolled tissue growth and trigger epithelial-to-mesenchymal transition. To better understand the intracellular responses of the cells to the cytokine we have developed a stochastic model that we present in this talk. This model explains heterogeneous signaling dynamics between the cells found in experimental data where time-resolved measurements at the single-cell level were taken. We elaborate on our parameter estimation technique considering the distribution of features in the time paths and demonstrate the accordance of model simulation and measurement data. Joint work with Lukas-Malte Bammert (JGU Mainz), Stefan Legewie (IMB Mainz), Maria Lukacova (JGU Mainz), Lorenz Ripka (IMB Mainz)

Cicely Macnamara School of Mathematics and Statistics, University of St. Andrews, UK
"Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue"

The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individual-based model which allows one to simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary blood-vessel network or along the striations of fibrous tissue.

Filip Klawe Institute of Applied Mathematics, Heidelberg University, Germany
"Mathematical model of stem cell specification in a growing domain"

We will study a mathematical framework for analysis and simulation of development of stem cell based, growing organs with cell self-renewal and differentiation regulated by signalling factors. Considered model consists of PDEs which describe concentrations of signals in moving domain Ω(t) and ODEs. One of the ODEs describes evolution of domain Ω(t) The main novelty of our work is a coupling between of PDEs solutions and deformation of the domain. There is no general approach which allow us to obtain mathematical results for such phenomena. However, assuming that Ω(t) is a circle and it is changing uniformly in all directions we are able to prove existence and uniqueness of solution. The considered model may be used to describe the signal concentration (and domain evolution) of shoot apical meristem of arabidopsis thaliana. We present numerical simulations which show that model fits to its biological origin.

OTHE: Flow and Transport in Complex Tissues, Part I (9:30-11:00am)

Alys Clark Auckland
"Emerging organ-scale function via large-scale network models of blood flow and exchange"

For healthy development and aging we must acquire sufficient oxygen from our environment to supply our metabolic demands. Before we are born we get oxygen from our mother’s blood through the pla- centa, and after birth the lungs take over the placenta’s role exchanging oxygen from the air. These two exchange organs have complex vascular branching structures with multiple generations of asymmetrically branching blood vessels which provide a large capillary surface area for exchange. Disruptions to this vascular branching and heterogeneity in blood delivery (perfusion) have been implicated in a number of diseases. Often, micro-vascular dysfunction contributes to an organ scale pathology, which can be difficult to detect in clinical imaging. We present organ-scale computational models vascular networks in lung and placenta, which take as inputs vascular anatomy derived from imaging, and simulate both haemodynamic and exchange function. This allows functional prediction of how anatomical perturbations in vascular structures contribute to organ function in health and disease, and provides steps toward determining what constitutes normal and abnormal levels of vascular heterogeneity in representative populations.

Igor Chernyavsky Manchester
"Structural and physical determinants of transport in complex microvascular networks"

Across mammalian species, solute transport takes place in complex microvascular networks. How- ever, despite recent advances in three-dimensional (3D) imaging, there has been poor understanding of geometric and physical factors that determine solute exchange and link the structure and function. Here, we use an example of the human placenta, a fetal life-support system, where the primary exchange units, terminal villi, contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. We show how the irregular internal structure of a terminal villus determines its exchange capacity for a wide range of solutes, integrating 3D image-based properties into new non-dimensional parameters. We characterise the structure-function relationship of terminal villi via a simple and robust algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. The developed theory accommodates for nonlinear blood rheology and tissue metabolism and offers an efficient method for multi-scale modelling [2]. Our results show how physical estimates of trans- port, based on scaling arguments and carefully defined geometric statistics, provide a useful tool for understanding solute exchange in placental and other complex microvascular systems.

Felix Meigel Max Planck Institue
"Robust increase in supply by local vessel dilation in globally coupled microvasculature"

Vascular networks pervade all organs of animals and are the paradigm of adaptive transport net- works. In the brain, neural activity induces changes in blood flow by locally dilating vessels in the brain microvasculature. How can the local dilation of a single vessel increase flow-based metabolite supply, given that flows are globally coupled within the microvasculature? Here, we build a theoretical model for flow-based transport and absorption of nutrients and determine how capillary geometry and network topology affect the control by active adaptation. On the level of an individual capillary, we derive ana- lytically how vessel parameters affect the change in supply due to dilation. Solving the supply dynamics for a rat brain microvasculature, we find one parameter regime to dominate physiologically. This regime allows for robust increase in supply independent of the position in the network, which we explain ana- lytically. We show that local coupling of vessels promotes spatially correlated increased supply by dilation.

Edwina Yeo Oxford
"Magnetically-driven Cell Aggregation in Blood"

In regenerative medicine magnetic cell targeting aims to deliver stem cells precisely to an injury site. For a safe and effective therapy, the stem cells must be delivered in large numbers under physiological flow conditions, but critically, the aggregation of cells at the target site must be controlled. Mathematical modelling offers insight into the dynamics of the system and allows efficient examination of physiological and therapeutic parameters. We adapt existing continuum models for the delivery of magnetic nanoparticles [2] to magnetic cell delivery. Cells are captured on the vessel wall closest to the magnet, this leads to the growth of a solid cell aggregate which obstructs the flow. We determine how the interplay between aggregate growth af- fects stem cell capture and identify parameter regimes in which potentially dangerous vessel blockage is predicted.

POPD: Emergence and Stability of Population Structure and Biological Aggregates Across Scales (9:30-11:00am)

Olivia Chu Princeton University
"An Adaptive Voter Model in Heterogeneous Environments"

In human social systems, it is natural to assume that individuals’ opinions influence and are influenced by their interactions. Mathematically, it is common to represent such systems as networks, where nodes are individuals and edges denote connections. Adaptive network models explore the dynamic relationship between node properties and network topology. For opinion dynamics, adaptive voter models provide two mechanisms through which changes can occur within the network. First, through homophily, an edge forms between two individuals who already agree; second, through social learning, an individual adopts one of their neighbor’s opinions. Central to these models is assortative mixing: individuals more frequently attach to those who are similar to them, which facilitates the formation of sub-communities of like-minded individuals. However, it is not always the case that individuals want to cluster into homogeneous groups. Instead, they might attempt to surround themselves with individuals who both agree and disagree with them, in an effort to attain a balance of inclusion and distinctiveness in their social environments. In this work, we explore the effects that such preferences for heterogeneous environments have on the dynamics of the adaptive voter model.

Feng Fu Dartmouth College
"How phenotypic similarity begets cooperation"

Tag-based cooperation, or cooperation based on phenotypic similarity, has long been seen as a potent mechanism of cooperation. The evolutionary origin and variability of tag-based cooperation has yet to be fully answered. Here we show analytically and by means of simulations that tag-based cooperation can always evolve by natural selection in the presence of sufficient tag diversity. Our work provides fundamental insights into understanding the widespread of tag-based cooperation in the real world from microbial populations to complex human societies.

Yuriy Pichugin Max Planck Institute for Evolutionary Biology
"Evolution of clonal life cycles: recipes for multicellularity, equal split, and single-cell bottleneck"

There is a huge variety in reproduction modes observed even among the simplest organisms. Many species are unicellular but some form simple colonies. Some of the colonies reproduce by splitting into equal parts others produce unicellular propagules. What is the driving force, which shapes the evolution of life cycles? What are the conditions promoting uni- or multi-cellular life cycles? We developed the stage-structured matrix population model of the growth and reproduction of unstructured multicellular organisms. Using this model, we investigated the conditions favoring the evolution of diverse life cycles: unicellular, with an equal split of a colony, and with the reproduction via single-cell bottleneck. We identified the set of profiles of size-dependent growth and death rates promoting each of these life cycles. We found that the conditions promoting a single-cell bottleneck are the steady improvement in the performance of the colony with its size. At the same time, the equal splits require the sudden rise in growth rate (drop in the death rate) at the size of the newborn offspring. Altogether, our findings demonstrate the patterns behind the evolution of multicellular life cycles.

Pawel Romanczuk Hombolt University of Berlin
"Flocking in complex environments – attention trade-offs in collective information processing"

The ability of biological and artificial collectives to outperform solitary individuals in a wide variety of tasks depends crucially on the efficient processing of social and environmental information at the level of the collective. Here, we model collective behavior in complex environments with many potentially distracting cues. Counter-intuitively, large-scale coordination in such environments can be maximized by strongly limiting the cognitive capacity of individuals, where due to self-organized dynamics the collective self-isolates from disrupting information. We observe a fundamental trade-off between coordination and collective responsiveness to environmental cues. Our results offer important insights into possible evo- lutionary trade-offs in collective behavior in biology and suggests novel principles for design of artificial swarms exploiting attentional bottlenecks.

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

Sub-group minisymposia (11:15am)

CDEV: Understanding development through theory and experiment (11:15am-12:45pm)

Shane Hutson Vanderbilt University
"Something's wrong in the (cellular) neighborhood: Mechanisms of wound detection in epithelia"

When a sheet of epithelial cells is wounded, cells around the wound are recruited from their near quiescent state to reactivate motility and proliferation behaviors similar to early development. As the first stage of that recruitment, surrounding epithelial cells undergo a dramatic increase in cytosolic calcium. This increase occurs quickly: calcium floods into damaged cells within 0.1 s, moves into adjacent cells over ~20 s, and appears in a much larger set of surrounding cells via a delayed second expansion over 40-300 s. Nonetheless, increased calcium is a reporter; cells must detect wounds even earlier. Using the calcium response as a proxy for wound detection, we identify an upstream G-protein-coupled-receptor (GPCR) signaling pathway, including the receptor and its chemokine ligand. We present experimental and computational evidence that the pathway involves the chemokine acting as a protease bait. Its pro-peptide form is already present extracellularly and is converted to an active form by multiple proteases released during cell lysis/wounding. We will discuss the experimental evidence and corresponding computational models developed to test the plausibility of these hypothesized mechanisms.

Stanislav Y Shvartsman Princeton University
"From data to knowledge in studies of developmental patterning"

I will present our ongoing work on model-based data integration in studies of pattern formation in the early Drosophila embryo, an experimental system that offers unrivaled opportunities for combining cutting edge molecular genetics, live imaging, and omics-based techniques.

Celeste Nelson Princeton University
"How to fold a tube into a lung"

'Our real teacher has been and still is the embryo, who is, incidentally, the only teacher who is always right.' – Viktor Hamburger Evolution has generated an enormous diversity of biological form. Given this diversity, it is highly likely that every tissue structure that one can imagine has been built by the embryo of one species or another. We are interested in uncovering the physical (mechanical) mechanisms by which epithelial sheets fold themselves into branching tubes in the embryo, and using those mechanisms to engineer tissues in culture. Over the past half century, developmental biologists have identified several biochemical signaling pathways and genetic control mechanisms necessary for tissue morphogenesis. In parallel, biological systems must obey Newton’s laws of motion, and physical forces need to be generated in order to sculpt simple populations of cells into complex tissue forms. Inspired by the evolutionary diversity of embryonic forms, we have created microfabrication- and lithographic tissue engineering-based approaches to investigate the mechanical forces and downstream signaling pathways that are responsible for generating the airways of the lung. I will discuss how we combine these experimental techniques with computational models to uncover the physical forces that drive morphogenesis. I will also describe efforts to uncover and actuate the different physical mechanisms used to build the airways in lungs from birds, mammals, and reptiles.

Roeland Merks Leiden University
"Mathematical Modeling of Cell-Extracellular Matrix Interactions to Explain Collective Cell Behavior and Cell Migration"

During embryonic development, the behavior of individual cells must be coordinated to create the large scale patterns and tissue movements that shape the whole embryo. Apart from chemical signals exchanged between cells, a prominent role is played by the extracellular matrix (ECM); these are the hard or jelly materials (e.g. collagens, fibronectin) that form the micro-environment of many cells in tissues. To get a better grip on the role of the extracellular matrix in determining the behavior of cells, we are developing mathematical and computational approaches to analyse the interactions of the mechanics of cells and the extracellular matrix (ECM). The cell models are usually based on the Cellular Potts model, whereas the ECM is model is based on a variety of approaches, including the finite-element model and molecular dynamics. I will discuss how these mathematical approaches help to elucidate the regulation of cell migration, collective cell behavior during angiogenesis and other mechanisms, including epithelial branching and the evolution of multicellularity.

EDUC: Education Minisymposium II (11:15am-12:45pm)

Chonilo S. Saldon Zamboanga del Norte National High School
"High School Students' Interest in Applied Mathematics"

With the the implementation of the Enhanced Basic Education Curriculum in the Philippines doubled with the students'access to college scholarship,more students are considering Mathematics and Science-related courses. Using a mixed-method approach, this study looks into the beliefs, interest and motivation in pursuing applied mathematics in college. Implications shall be discussed in terms of career advising on secondary level.

Widodo Samyono Jarvis Christian College
"Jarvis Summer Undergraduate Research Experience 2020"

Jarvis Christian College is a small liberal arts HBCU at Hawkins, Texas. With the NSF Funding through Targeting Infusion Project (TIP) Historically Black Colleges and Universities Undergraduate Programs (HBCU-UP) we were able to have a summer undergraduate research in computational and mathematical biology. In this presentation we would like to share our challenges and opportunities for doing undergraduate research in computational and mathematical biology with underrepresented minority students in STEM. We will explain how we prepare ourselves and our students and how we change the challenges to opportunities.

Winfried Just Ohio University
"COVID-19 modeling for quantitative literacy courses"

There is a deluge of information about the COVID-19 pandemic. Many of our students are struggling with making sense of it all, especially the science and math behind the various models. This talk will present a collection of materials that can be used in quantitative literacy courses to sort out some of the confusion and demonstrate how the math that is usually taught in such courses helps in understanding the real world and making good decisions. In these materials, the models are explained by Alice, a student of epidemiology, to three of her peers from other disciplines. The protagonists bring a variety of attitudes and concerns to the discussions. Together, they sort things out and gain remarkable insights with using very simple mathematics.

IMMU: Increasingly biologically accurate models of influenza A virus infection spread in vivo & in vitro (11:15am-12:45pm)

Christian Quirouette Ryerson University
"A mathematical model describing the localization and spread of influenza A virus infection within the human respiratory tract"

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But it also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell’s beating cilia, the PCF and its virus contents are also pushed along, upwards towards the nose and mouth. Many mathematical models (MMs) describe the course of influenza virus infections in vivo, but none consider the impact of both diffusion and advection on the infection’s kinetics and localization. Our MM represents the HRT as a one-dimensional track extending from the nose down to the lower HRT, wherein stationary cells interact with virus which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away virus, preventing infection from disseminating below the depth of deposition. Higher virus production rates (10-fold) are required at higher advection speeds (40 micron/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT located downstream of the advection flow see more virus than lower parts, and so infection grows, peaks, and resolves later in the lower HRT. Clinically, the infection would appear to progress from the upper towards the lower HRT, as reported in mice, even when the lower HRT infection precedes, and indeed causes, that in the upper HRT. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It can also captures the kinetics of both seasonal and avian strain infections via parameter changes consistent with reported differences between these strains. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viruses (flu, RSV, COVID-19) within the HRT during an infection.

Amber Smith University of Tennessee Health Science Center
"Modeling Influenza–Mediated Acute Lung Injury"

Influenza viruses infect millions of individuals each year and cause a significant amount of morbidity and mortality. Understanding how the virus spreads within the lung, how efficacious host immune control is, and how each influences acute lung injury and disease severity is critical to combat the infection. Thus, we used an integrative model-experiment exchange to establish the dynamical connections between infection, lung injury, and disease kinetics. Examining these connections during neuraminidase inhibitor (NAI) therapy further validated the model and analysis, and suggested that profound effects on lung injury are possible with minimal changes to host-pathogen kinetics. This work provides important biological and mathematical insight and enhances our ability to effectively forecast the disease and antiviral efficacy.

Daniel Rüdiger Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
"Multiscale model of DIP replication and its effects on influenza A virus infection in animal cell culture"

Defective interfering particles (DIPs) that lack part of the viral genome are considered for use as antivirals against flu, because they can strongly impede wild type influenza A virus (IAV) replication. Multiple mathematical modeling approaches have been applied to examine the mechanisms of DIP inter- ference. However, these models focused on either the intra- or the extracellular level of virus replication. In this work, we extend a recently published multiscale model to describe DIP propagation in animal cell cultures infected by IAV. This new model covers fundamental steps during the intracellular replica- tion and the spread of DIPs on the population level. Particularly, the model incorporates the infection conditions, i.e. the multiplicity of infection (MOI), which may change drastically during an infection and represent a crucial factor for IAV replication and DIP interference. To elucidate DIP infection dynamics we conducted a set of cultivations observing the effects of DIPs on wild type virus replication using various IAV and DIP seed virus concentrations. Based on these experimental data, we calibrated our multiscale model to enable the prediction of DIP-induced infection dynamics for a wide range of MOI conditions. Furthermore, we used the model to elucidate options for antiviral therapy, i.e. the DIP to IAV ratio required to inhibit the progression of an influenza infection in animals or humans. In summary, we established a mathematical model that provides a comprehensive description of DIP replication on the intra- and extracellular level to facilitate the development of antiviral therapies, and to describe DIP production in animal cell culture for therapeutic use.

João Rodrigues Correia Ramos Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
"A dynamic model for cell growth, metabolism and virus production of MDCK suspension cells"

Cell culture-based influenza virus production is well established and different virus replication stages have been studied experimentally in detail. In addition, quantitative mathematical models have been derived that describe dynamics of viral replication at the intracellular and the cell population level. However, to better understand the complex interplay between the virus and its host cell, metabolism during virus replication should be considered in more detail. In this context, MDCK suspension cells were cultivated in shaker flasks and concentrations of external and internal metabolites monitored during cell growth and influenza A virus infection. To characterize the impact of virus infection on host cell metabolism, we have formulated a dynamic mathematical model combining a segregated cell growth model with a structured model of intracellular metabolism in a similar manner as models established for other cell lines. Overall, it considers the dynamics of cell growth, virus production, substrates, metabolic by-products and concentration of key intracellular metabolites from glycolysis, citric acid cycle (TCA), glutaminolysis and pentose phosphate pathway. Model parameters were fitted using mock-infections, and simulations describe well the time courses of the viable cell concentration, mean cell diameter, external substrates, metabolic by-products, and key intracellular metabolites. After virus infection, using the same set of parameters, the model also describes well the dynamics of the viable cell concentration, mean cell diameter changes, substrates, and the virus titer. Only minor differences were found for infected versus mock cultures in the glycolytic pathway. Nev- ertheless, differences between experimental data and model simulations regarding metabolites of TCA and metabolic by-products suggest changes in metabolism, which might be virus-induced. As virus in- fection also affects apoptosis and cell lysis, the interpretation of such differences is not straightforward and experimental findings as well as parameters fitted need to be evaluated in more detail to confirm a virus-related impact on the TCA. Overall, this work will contribute to a better understanding of the complex interplay between cell growth, changes in cell size, virus production and metabolism and support the identification of parameters rele- vant for increasing specific viral productivity of MDCK suspension cells.

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

Edward Hill University of Warwick
"Predictions of COVID-19 dynamics in the UK: short-term forecasting, analysis of potential exit strategies and impact of reopening schools"

Efforts to suppress transmission of SARS-CoV-2 in the UK saw non-pharmaceutical interventions being invoked throughout March 2020, culminating in the application of lockdown measures. From mid-April, COVID-19 cases were declining and there was good evidence to suggest that the effective reproduction number had dropped below 1. A multi-phase relaxation plan to emerge from lockdown was put in place, including primary schools being scheduled to partially reopen in England on 1st June. Regarding the future course of the COVID-19 outbreak in the UK, mathematical models have provided, and continue to provide, short and long term forecasts to support evidence-based policymaking. We present a deterministic, age-structured transmission model for SARS-CoV-2 that uses real-time data on confirmed cases requiring hospital care and mortality to provide predictions on epidemic spread in ten regions of the UK. The model captures a range of age-dependent heterogeneities, reduced transmission from asymptomatic infections and produces a good fit to the key epidemic features over time. We illustrate how the model has been used to generate short-term predictions, assess potential lockdown exit strategies, and the impact of children returning to school. We found that significant relaxation of social distancing measures from 7th May could lead to a rapid resurgence of COVID-19 disease and the health system being quickly overwhelmed by a second epidemic wave. On reopening schools, whilst children returning to educational establishments results in more mixing between children and an increase in transmission of the disease, the magnitude of that increase can be low dependent upon the age-groups that return to school and the behaviour of the remaining population. Our work confirmed the effectiveness of stringent non-pharmaceutical measures in March 2020 to suppress the epidemic. It also provided support for the need for a cautious, measured approach to relaxation of lockdown measures, to support the health service through subduing demand on hospital beds. Finally, it indicated that any reopening of schools would result in increased mixing and infection amongst children and the wider population, although the opening of schools alone at that time was unlikely to push the value of R above one.

Ruian Ke Los Alamos National Lab
"Estimating the epidemic growth rate and the reproductive number R0 of SARS-CoV-2 and implications for vaccination"

SARS-CoV-2 is a novel pathogen causes the COVID-19 pandemic. Some of the basic epidemiological parameters, such as the exponential epidemic growth rate and R0 are debated. We collected and analyzed data from China, eight European countries and the US using a variety of inference approaches. In all countries, the early epidemic grew exponentially at rates between 0.19-0.29/day (epidemic doubling times between 2.4-3.7 days). I will discuss the appropriate serial intervals to estimate the basic reproductive number R0 and argue that existing evidence suggests a highly infectious virus with an R0 likely between 4.0 and 7.1. Further, we found that similar levels of intervention efforts are needed, no matter the goal is mitigation or containment. We further show that regular repeated vaccinations will be required to maintain herd immunity if the duration of protective immunity is consistent with other known coronaviruses and that individual-level heterogeneity in protective immunity can significantly affect vaccination policy.

Thi Mui Pham UMCUtretcht
"Impact of self-imposed prevention measures and short-term government intervention on mitigating and delaying a COVID-19 epidemic"

Background: With new cases of COVID-19 surging around the world, many countries have to prepare for moving beyond the containment phase. Prediction of the effectiveness of non-case-based interventions for mitigating, delaying or preventing the epidemic is urgent, especially for countries affected by the ongoing seasonal influenza activity. Methods: We developed a deterministic transmission model to evaluate the impact of self-imposed pre- vention measures (handwashing, mask-wearing, and social distancing) due to the spread of COVID-19 awareness and of short-term government-imposed social distancing on the peak number of diagnoses, attack rate and time until the peak number of diagnoses. Findings: For fast awareness spread in the population, self-imposed measures can significantly reduce the attack rate, diminish and postpone the peak number of diagnoses. A large epidemic can be prevented if the efficacy of these measures exceeds 50%. For slow awareness spread, self-imposed measures reduce the peak number of diagnoses and attack rate but do not affect the timing of the peak. Short-term government policies on social distancing (e.g. community-wide quarantine) that are initiated early can only postpone the epidemic peak whereas later implementation can lead to a reduction of the attack rate and a flatter peak. Interpretation: Handwashing, mask-wearing and social distancing as a reaction to information dissem- ination about COVID-19 can be effective strategies to mitigate and delay the epidemic. We stress the importance of rapidly spreading awareness on the use of these self-imposed prevention measures in the population. Early-initiated short-term government-imposed social distancing can buy time for healthcare systems to prepare for an increasing COVID-19 burden.

Jasmina Panovska-Griffiths University College London
"Determining the optimal strategy for reopening schools, workplaces and society in the UK: modelling patterns of reopening, the impact of test and trace strategies and risk of occurrence of a secondary COVID-19 pandemic wave"

Background: As evidence is emerging that the UK lockdown has slowed the spread of the pandemic, it is important to assess the impact of any changes in strategy, including school reopening and broader relaxation of physical distancing measures moving forward. This work uses an individual-based model to predict the impact of two possible strategies for reopening schools to all students (full-time versus part-time rotas) in the UK from September 2020, in combination with different assumptions about the scale-up of testing. Methods: We use Covasim, a stochastic agent-based model for transmission of COVID-19, calibrated to the UK epidemic. The model describes individuals’ contact networks stratified into household, school, workplace and community layers, and uses demographic and epidemiological data from the UK. We simulate six different scenarios, representing the combination of two school reopening strategies and three testing scenarios, and estimate the number of new infections, cases and deaths, as well as the effective reproduction number (R) under different strategies. To account for uncertainties within the stochastic simulation, we also simulated different levels of infectiousness of children and young adults under 20 years old compared to older ages. Findings: We found that with increased levels of testing (between 59% and 87% of symptomatic people tested at some point during an active COVID-19 infection, depending on the scenario), and effective contact tracing and isolation, an epidemic rebound may be prevented. Assuming 68% of contacts could be traced, we estimate that 75% of those with symptomatic infection would need to be diagnosed and isolated if schools return full-time in September, or 65% if a part-time rota system were used. If only 40% of contacts could be traced, these figures would increase to 87% and 75%, respectively.However, without such measures, reopening of schools together with gradual relaxing of the lockdown measures are likely to induce a secondary wave that would peak in December 2020 if schools open full-time in September, and in February 2021 if a part-time rota system were adopted. In either case, the secondary wave would result in R rising above 1 and a resulting secondary wave of infections 2-2.3 times the size of the original COVID-19 wave. When infectiousness of <20 year olds was varied from 100% to 50% of that of older ages, we still find that comprehensive and effective TTI would be required to avoid a secondary COVID-19 wave. Interpretation: To prevent a secondary COVID-19 wave, relaxation of physical distancing including reopening schools in the UK must be accompanied by large-scale testing of symptomatic individuals and effective tracing of their contacts, followed by isolation of diagnosed individuals.

MFBM: Stochastic methods for epidemiology and biochemical reaction networks (11:15am-12:45pm)

Ankit Gupta ETH Zurich, Switzerland, ankit.gupta@bsse.ethz.ch
"The probability distribution of the reconstructed phylogenetic tree with occurrence data"

Stochastic birth-death processes are extensively used in epidemiology to model the underlying population dynamics of infected individuals. In such models the infection history of extant population naturally gives rise to a phylogenetic tree which can be used to study the evolution of the epidemiological process in the past. In this talk we study the problem of computing the probability distribution of such phylogenetic trees arising from partially sampled birth death processes. We consider observations from three distinct sampling schemes. First, individuals can be sampled and removed, through time, and included in the tree. Second, they can be occurrences which are sampled and removed through time and not included in the tree. Third, extant individuals can be sampled and included in the tree. The outcome of the process is thus composed of the reconstructed phylogenetic tree spanning all individuals sampled and included in the tree, and a timeline of occurrence events which are not placed along the tree. We derive a formula for computing the joint probability density of this outcome, which can readily be used to perform maximum likelihood or Bayesian estimation of the parameters of the birth-death model. In the context of epidemiology, our probability density enables the estimation of transmission rates through a joint analysis of epidemiological case count data and phylogenetic trees reconstructed from pathogen sequences.

Grzegorz Rempala The Ohio State University, United States, rempala.3@osu.edu
"Mathematical Model of a Pandemic: 2019-20 Coronavirus Analysis"

The modeling of a pandemic may be typically divided into three time phases: the early stochastic one, the mid-course deterministic one and the final, also stochastic. I will show on the example of Corona virus pandemic of 2019 how such model may be effectively used for predictions about disease dynamics applying both multiscale approximation and the idea of survival dynamical system obtained from the aggregate network model.

Hye-Won Kang University of Maryland at Baltimore County, United States hwkang@umbc.edu
"A stochastic model for enzyme clustering in glucose metabolism"

A sequence of metabolic enzymes tightly regulates glycolysis and gluconeogenesis. It has been hypothesized that these enzymes form multienzyme complexes and regulate glucose flux. In the previous work, it was identified that several rate-limiting enzymes form multienzyme complexes and control the direction of glucose flux between energy metabolism and building block biosynthesis. A recent study introduced a mathematical model to support this finding, in which the association of the rate-limiting enzymes into multienzyme complexes in included. However, this model did not fully account for dynamic and random movement of the enzyme clusters, as observed in the experiment. In this talk, I will introduce a stochastic model for enzyme clustering in glucose metabolism. The model will describe both the enzyme kinetics and the spatial organization of metabolic enzyme complexes. Then, I will discuss underlying model assumptions and approximation methods

Wasiur KhudaBukhsh The Ohio State University, United States, khudabukhsh.2@osu.edu
"Incorporating delays and non-Markovian dynamics into biochemical reaction networks"

Markov models for many biophysical systems are often found to be unrealistic because of the assumption that the interactions occur instantaneously or that the inter-reaction times follow an exponential distribution. In this talk, we consider relaxing those assumptions by incorporating delays into the system’s dynamics. We show that this modification leads to approximations by means of Partial Differential Equation (PDE) limits instead of the classical Ordinary Differential Equation (ODE) ones. Describing the dynamics by means of measure-valued processes is at the heart of such approximations. While the theory is developed for a general class of chemical reaction networks, we will also discuss some concrete examples.

NEUR: Stochastic and Mean-Field Analysis in Neuroscience (11:15am-12:45pm)

James MacLaurin NJIT
"Coarse-Graining of the Primary Visual Cortex"

Experimental evidence indicates that the dynamic response of the primary visual cortex to stimulii continues over relatively slow timescales of O(100ms). Typically, the initial 'bump' of activity, that is centered at a particular orientation, slowly softens and dissipates after the stimulus is removed. To explain this phenomenon, we develop a realistic microscopic neural field model, and perform a coarse-graining to obtain a macroscopic neural field equation. The microscopic model contains slow synaptic dynamics, and stochasticity resulting from synaptic transmission failure. At the macroscopic level, after a coarse-graining procedure, this stochasticity results in a neural field equation with an integral convolution (as is standard in neural field equations) but also a spatial Laplacian, and with the diffusion coefficient proportional to the population activity. Our macroscopic equation can be thought of as a spatially-extended population density equation: it combines the strengths of neural-field equations and population density equations into a single formalism. It allows a deeper understanding of how changes in the average synchronization of neurons affects the macroscopic dynamics. It partly parallels the efforts of Coombes et al in recent years to derive such 'next-generation neural field equations'. We next perform a Large Deviations analysis to study the typical stochastic fluctuations about the limiting equation. This allows us to determine the most likely abnormal behavior that could be induced in the system by finite size effects. This work is based on a preprint (joint with Bart Krekelberg) entitled 'Coarse-Graining of Neural Networks with Stochastic Dynamic Connections.'

Youngmin Park Brandies U
"Dynamics of Vesicles Driven into Closed Constrictions by Molecular Motors"

We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We explore the effects of noise on the reduced lubrication model proposed in (Fai et al, Active elastohydrodynamics of vesicles in narrow, blind constrictions. Phys. Rev. Fluids, 2 (2017), 113601). The Fokker-Planck approximation fails to capture mean first passage times of velocity switching (tug-of-war effect), and the agent-based model is computationally expensive. For relatively efficient computations, we turn to the master equation and find that it requires an additional calculation to account for non-equilibrium dynamics in the underlying myosin motor population. We discuss remaining questions and future directions in this ongoing work.

Victor Matveev NJIT
"Mass-Action vs Stochastic Modeling of First Passage Time to Ca2+-Triggered Vesicle Release"

Like most physiological cell mechanisms, synaptic neurotransmitter vesicle release (exocytosis) is characterized by a high degree of variability in all steps of the process, from Ca2+ channel gating to the final triggering of membrane fusion by the SNARE machinery. The associated fluctuations can be quite large since only a small number of Ca2+ ions enter the cell through a single channel during an action potential, and further increased by the stochasticity in the Ca2+ binding to Ca2+ buffers and sensors. This leads to a widely-held assumption that solving mass-action reaction-diffusion equations for buffered Ca2+ diffusion does not provide sufficient insight into the underlying Ca2+-dependent cell processes. However, several comparative studies showed a surprisingly close agreement between deterministic and trial-averaged stochastic simulations of Ca2+ diffusion, buffering and binding, as long as Ca2+ channel gating is not Ca2+ dependent. We present further comparison of stochastic and mass-action simulations, focusing on Ca2+ dynamics downstream of Ca2+ channel gating and considering spatially-resolved reaction-diffusion modeling in 3D. Namely, we compare the distributions of first-passage-times (FPT) to full binding of the model Ca2+ sensor for vesicle fusion obtained using stochastic and deterministic approaches. We note that in the deterministic formulation, FPT density is equivalent to the time-dependent rate of the final irreversible transition to the fusion-ready sensor state. We show that the discrepancy between deterministic and stochastic approaches in simulating the FPT density can be surprisingly small even when only as few as 40 ions enter the cell per single channel-vesicle complex, despite the fluctuations caused by the Ca2+ binding and unbinding. Further, we demonstrate this close agreement between stochastic and deterministic FPT computation using a highly simplified two-compartment model, whereby the FPT density can be computed exactly using either of the two approaches. The reason for the close agreement between the two methods is that in the absence of Ca2+-induced Ca2+-release, the non-linearities in the exocytosis process involve only bi-molecular reactions. Therefore, the discrepancy between the two approaches is primarily determined by the size of correlations between reactant molecule number fluctuations rather than the fluctuation amplitudes. The small size of reactant correlations is in turn determined by the relationship between the rate of diffusion relative the rate of Ca2+ buffering and binding, as suggested in prior studies. In most common parameter regimes, FPT density is not very sensitive to the fluctuations in the rates of Markovian transitions between distinct sensor states arising from the Ca2+ fluctuations, which in turn leads to small discrepancies between the two approaches. This work is supported by NSF grant DMS-1517085.

ONCO: Applications and challenges of using quantitative imaging data for biologically-based mathematical oncology (11:15am-12:45pm)

David A. Hormuth, II The University of Texas at Austin, Austin, Texas USA
"Translating image driven models of response to radiation therapy from the pre-clinical to clinical setting"

Magnetic resonance imaging (MRI) is able to provide quantitative, non-invasive measurements of tissue and tumor properties related to perfusion, vascularity, proliferation, and cellularity that can be used to observe tumor growth throughout the course of therapy. We and others have leveraged this type of quantitative data to initialize and calibrate biologically-based models of tumor growth and response. Here, we investigate the use of diffusion weighted (DW-) MRI and dynamic contrast-enhanced (DCE-) MRI to non-invasively estimate tumor cellularity and vascularity, respectively, in high grade gliomas at the pre-clinical and clinical levels. At the pre-clinical level, we have developed a 3D, two-species reaction diffusion-based model describing the spatial-temporal evolution of tumor and blood volume fractions [1] during the course of fractionated radiation therapy. Images collected during therapy are used to calibrate tumor-specific growth and response parameters. These calibrated parameters are then used in a forward evaluation of the model to predict response following therapy. We observed less than 12.3% error in tumor volume predictions. At the voxel-level, we observed 6.6% and 14.1% in voxel-wise estimates of tumor and blood volume fraction, respectively. At the clinical level, we have developed a 3D reaction diffusion-based model describing the spatial-temporal evolution of tumor cellularity during and following chemoradiation. Using images collected at pre-treatment and at the 1-month post-chemoradiation visit, we calibrate for patient-specific model parameters. The calibrated parameters are then used to provide individualized predictions of tumor growth and treatment response. In a preliminary study with four patients, we observed less than 11.1% error in tumor volume predictions and 9.5% error at the voxel- level. These two studies demonstrate the utility of quantitative imaging data to initialize and calibrate mathematical models of tumor growth and response that can accurately predict both changes in tumor volume and intratumoral heterogeneity.

Sarah Brüningk Institute of Molecular Systems Biology, ETH Zurich, Zurich Switzerland
"Intermittent radiotherapy as alternative treatment for recurrent high grade gliomas: A modelling study based on longitudinal tumour measurements"

Recurrent high grade glioma patients are faced with a poor prognosis for which there cur- rently exists no curative treatment option. In contrast to prescribing high dose hypofrac- tionated stereotactic radiosurgery (HFRS, 5x ≥ 6 Gy in daily intervals) with curative intent, we suggest a personalized, palliative treatment strategy aiming for tumour volume management by delivering intermittent high dose treatment every six weeks (iRT, ≥ 6 Gy per fraction). We performed a simulation analysis to compare HFRS, iRT and iRT plus boost (3x ≥ 6 Gy on consecutive days, delivered at time of progression) based on a simple mathematical model of tumour growth, radiation response and patient specific resistance to additional treatments (PD-L1 inhibitor and vascular disruptive agents). Our model uses only two patient specific parameters describing the surviving fraction fol- lowing each HFRS treatment fraction, and the rate of resistance evolution. Tumour growth rate and the efficacy of non-HFSR treatments were estimated for the patient population as a whole. Model parameters were fit from clinical tumour growth response curves of 16 patients of the Phase 1/2 clinical trial NCT02313272 that combined HFSR with beva- cizumab (10 mg/kg, every 2 weeks) and pembrolizumab (100 or 200 mg, every 3 weeks). Tumour volume was assessed by T1-weighted contrast enhanced magnetic resonance imag- ing at four to ten (median six) time points per patient. The obtained parameters were used to estimate the growth response of alternative iRT and iRT+boost treatments for up to 5-10 treatment fractions. Treatment efficacy was scored based on time to regrowth to the last recorded tumour volume per patient. The median coefficient of determination of the model fits was 0.93(0.67,0.99). The model predictions indicated that iRT may delay time to progression only for a subset of eleven patients, whereas iRT+boost treatment was equal or superior to HFSR in 15 out of 16 cases. For up to ten intermittently delivered fractions, iRT+boost was predicted to be marginally significantly better (p = 0.048) than HFRS. This simulation did not include other aspects of iRT, such as synergistic action with im- munotherapy through repeated antigen sampling, or the flexibility to treat both distal and primary lesions. Despite choosing this worst case estimate, our results suggest that iRT+boost may be a promising treatment alternative for recurrent high grade glioma patients.

Andrea Hawkins-Daarud Precision Neurotherapeutics Innovation Program, Mayo Clinic, USA
"Assessing clinical utility of a model based patient-specific response metric for glioblastoma incorporating uncertainty quantification from image acquisition and segmentation"

Glioblastomas are lethal primary brain tumors known for their heterogeneity and invasiveness. A growing literature has been developed demonstrating the clinical relevance of a biomathematical model, the Proliferation- Invasion (PI) model, of glioblastoma growth. Of interest here is the development of a treatment response metric, Days Gained (DG). This metric is based on individual tumor kinetics of cellular diffusion and proliferation estimated through segmented volumes of hyperintense regions on T1-weighted gadolinium enhanced (T1Gd) and T2-weighted magnetic resonance images (MRIs). This metric was shown to be prognostic of time to progression and to be more prognostic of outcome than standard response metrics. While promising, the original paper did not account for uncertainty in the calculation of the DG metric leaving the robustness and the ultimate utility of this response metric in question. Using the Bayesian framework, we consider the impact of two sources of uncertainty: 1) image acquisition and 2) interobserver error in image segmentation. We first utilize synthetic data to characterize what non-error variants are influencing the final uncertainty in the DG metric. We then consider the original patient cohort along with additional cohorts from the recurrent setting to investigate clinical patterns of uncertainty and to determine how robust this metric is for predicting time to progression and overall survival in multiple scenarios. Our results indicate that the key clinical variants are the time between pre-treatment images and the underlying tumor growth kinetics, matching our observations in the clinical cohort. In the original cohort, we demonstrated that for this cohort there was a continuous range of cutoffs between 94 and 105 for which the prediction of the time to progression and was over 80% reliable [3]. While further validation must be done, this work represents a key step in ascertaining the clinical utility of this metric.

Victor M. Perez-Garcia Universidad de Castilla – La Mancha, Spain
"If you have mathematical models then you have imaging biomarkers: Applications to gliomas, lung cancer, breast cancer and head & neck cancer"

The ultimate goal of mathematical models fed with imaging and molecular/clinical data is to provide prediction machines allowing to get precise estimates for patient survival, time to relapse, and to set up personalized therapeutic schedules. However, this is a very complex task due to our limited knowledge of the many biological processes involved and the scarce amount of information available today for patients. A more accessible goal is to use mathematical models to obtain qualitative information allowing to classify patients in classes according to features found to be relevant in the modelling. When those features can be obtained from medical images, we speak of imaging biomarkers. In this talk I will present different types of mathematical models and discuss how each modelling approach leads to the finding of imaging biomarkers that turn out to be true when tested on real patients imaging data. Specifically I will present: MRI-based biomarkers in glioblastoma based on either partial differential equations or discrete mesoscopic simulators [1-3], prognostic PET-based biomarkers based on the peak activity validated for lung and breast cancer [4] and PET-based prognosis biomarkers based on scaling laws for lung cancer, breast cancer, gliomas, and head & neck cancer [5]. These imaging biomarkers are all easy to implement in clinical practice since they do not require model simulations but just measurement of meaningful quantities on the images.

OTHE: Flow and Transport in Bacterial Biofilms, Part II (11:15am-12:45pm)

Mohit Dalwadi Oxford
"Using homogenization to determine the effective nutrient uptake in a biofilm from microscale bacterial properties"

In biofilm models that include nutrient delivery to bacteria, it can be computationally expensive to include many small bacterial regions acting as volumetric nutrient sinks. To combat this problem, such models often impose an effective uptake instead. However, it is not immediately clear how to relate properties on the bacterial scale with this effective result. For example, one may intuitively expect the effective uptake to scale with bacterial volume for weak uptake, and with bacterial surface area for strong uptake. I will present a general model for bacterial nutrient uptake, and upscale the system using homogenization theory to determine how the effective uptake depends on the microscale bacterial properties [1, 2]. This will show us when the intuitive volume and surface area scalings are each valid, as well as the correct form of the effective uptake when neither of these scalings is appropriate.

Alexandre Persat EFPL
"Cellular advective-diffusion drives the emergence of bacterial surface colonization patterns"

In the wild, bacteria predominantly live as multicellular aggregates called biofilms. In contrast to lab- oratory settings, natural biofilms commonly comprise multiple strains or species that interact with each other. The nature of such interactions depends on the relative proximity of different strains and thus on the spatial organization of the biofilm. However, little is known about how environmental factors affect this organization. Here, we demonstrate that biofilms of the freshwater bacterium /emphCaulobacter crescentus form distinct patterns of surface colonization depending on local hydrodynamic conditions. By imaging C. crescentus biofilms grown in microfluidic chambers under controlled flow, we observed that surface colonization rate decreases with increasing flow velocity. We also probed the effect of flow intensity on spatial lineage structure using two C. crescentus clones. Surprisingly, segregation increased with flow velocity, in contrary to the assumption that flow induces lineage mixing. To understand how these colonization patterns arise, we developed a theoretical model based on the balance between ad- vection and diffusion: planktonic cells released from the biofilm effectively diffuse as they swim with random trajectories, while they are transported unidirectionally by flow. As flow intensity increases, the residence time of planktonic cells in the channel decreases, reducing their spreading across the channel and decreasing encounters with the surface. To sum up, our work demonstrates that hydrodynamic forces impact biofilm architecture and lineage distribution in multi-strain biofilms. This indicates that social interactions within biofilms are not only dictated by biological factors, but also by mechanical conditions imposed onto the community.

Sara Jabbari Birmingham
"Targeting bacterial adhesion as a novel therapeutic for Pseudomonas aeruginosa infections"

The rise in antibiotic resistance, combined with the shortage in discovery of new classes of these drugs, has led to the pursuit of creative ways to tackle bacterial infections that do not necessarily kill bacteria in conventional ways. Many of these approaches, however, are only partially successful when tested in infection models. We focus here on an approach that targets the ability of bacteria to bind to host cells – the first stage in infection and of biofilm formation. Through differential equation modelling and com- parison against experimental data, we investigate why the treatment is not fully effective. Furthermore, we use the model to predict how to improve the treatment in a variety of scenarios, including through changes in drug design and/or combination with alternative therapies. We illustrate when the therapy could replace or reduce antibiotic use, ultimately suggesting experimental pathways that should aid in accelerating the development of this novel therapy.

Philip Pearce Harvard
"The biofilm life cycle in high flow environments"

Bacterial biofilms represent a major form of microbial life on Earth. In their natural environments, ranging from human organs to industrial pipelines, biofilms have evolved to grow robustly under signifi- cant fluid shear. Despite intense practical and theoretical interest, it is unclear how strong fluid flow alters aspects of the biofilm life cycle including their formation, growth, and dispersal. In this talk, I will discuss how external flow affects biofilms across multiple scales at each of these stages of their life cycle, through transport of quorum sensing molecules, realignment of growing cells, and biofilm deformation and erosion.

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

Annalisa Iuorio University of Vienna
"Modelling competitive interactions and plant-soil feedback in vegetation dynamics"

Plant-soil feedback has been proved to play an important role in the formation of vegetation patterns for a single species. In real-life, however, plants rarely grow in monoculture; hence multi-species scenarios are more realistic. In these cases, additional effects between different species - such as competition and interaction - must be considered. Moreover, plant-soil feedback is recognised as a causal mechanism for plant-species coexistence. Using a mathematical model consisting of four PDEs, we investigate mechanisms of inter- and intra-specific plant-soil feedback on the coexistence of two competing plant species. In particular, the model takes into account both negative and positive feedback influencing the growth of the same and the other plant species. Both the coexistence of the plant species and the dominance of a particular plant species are examined with respect to all model parameters. Analytical and numerical results reveal the emergence of spatio-temporal patterns.

Lukas Eigentler University of Dundee
"Spatial self-organisation enables species coexistence in a model for dryland vegetation patterns"

Vegetation patterns are a ubiquitous feature of drylands across the globe. Despite the competition for water, species coexistence of herbaceous and woody species is commonly observed. Thus, tree-grass coexistence in drylands provides an apparent contradiction to the principle of competitive exclusion. In this talk, I propose that a pattern-inducing spatial self-organisation principle, caused by a positive feedback between local vegetation growth and water redistribution towards dense biomass patches, can also act as a coexistence mechanism for plant species in water-limited ecosystems. To this end, I present a bifurcation analysis of an ecohydrological PDE model for two plant species interacting with a sole limiting resource, based on the Klausmeier reaction-advection-diffusion system for vegetation patterns. Patterned solutions occur as periodic travelling waves and thus theory on limit cycles in dynamical systems can be utilised in the analysis. Firstly, a stability analysis of the system's single-species patterns, performed through a calculation of their essential spectra, provides an insight into the onset of coexistence states. I show that coexistence solution branches bifurcate off single-species solution branches as the single-species states lose their stability to the introduction of a second species. Secondly, I present a comprehensive existence and stability analysis to establish key conditions, including a balance between the species' local competitive abilities and their colonisation abilities, for species coexistence in the model. Finally, I show that the inclusion of intraspecific competition dynamics has a significant impact on the coexistence mechanism that significantly differs from results on classical, nonspatial competition models. (Joint work with Jonathan A. Sherratt)

Gabriel Maciel ICTP - SAIFR & IFT - UNESP
"Spatial self-organization promotes coexistence between two species in nonlocal competition models"

Nonlocal interactions are a remarkable feature of several ecological systems ranging from microorganisms and coral reefs to plants and animals. The potential of spatially extended interactions to generate patterns of space distribution in single populations has been extensively explored in the past few decades. In systems of two competing species, nonlocal interactions and the self-organization of populations can have critical dynamical effects but our understanding in these situations is still very limited. In this talk, I will present a kernel-based model for the dynamics of two species competition with nonlocal interactions. Inspired by different biological examples I will show that we can have two distinct scenarios that differ in how intra and interspecific interaction ranges are determined based on each species competition characteristics. In both scenarios we will see that pattern formation offers a coexistence mechanism where the inferior competitor takes advantage of low density locations in the superior competitor spatial distribution.

Nikunj Goel University of Texas at Austin
"Dispersal increases the resilience of tropical savanna and forest distribution"

Global change may induce changes in savanna and forest distributions, but the dynamics of these changes remain unclear. Classical biome theory suggests that climate is predictive of biome distributions, such that shifts will be continuous and reversible. This view, however, cannot explain the overlap in the climatic ranges of tropical biomes, which some argue may result from fire-vegetation feedbacks, maintaining savanna and forest as bistable states. Under this view, biome shifts are argued to be discontinuous and irreversible. Mean-field bistable models, however, are also limited, as they cannot reproduce the spatial aggregation of biomes. Here we suggest that both models ignore spatial processes, such as dispersal, which may be important when savanna and forest abut. Using a combination of spatial mathematical models and remote sensing data, we examine the contributions of dispersal to determining biome distributions. We find that including dispersal in biome dynamics resolves both the limitations mentioned above of biome models. First, local dispersive spatial interactions, with an underlying precipitation gradient, can reproduce the spatial aggregation of biomes with a stable savanna-forest boundary. Second, the boundary is determined not only by the amount of precipitation but also by the geometrical shape of the precipitation contours. These geometrical effects arise from continental-scale source-sink dynamics, which reproduce the mismatch between biome and climate. Dynamically, the spatial model predicts that dispersal may increase the resilience of tropical biome in response to global change: the boundary continuously tracks climate, recovering following disturbances, unless the remnant biome patches are too small.

SMB Business Meeting

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

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

Adriana Dawes Ohio State University
"Dynein dynamics in the first cell cycle of the C. elegans embryo"

Asymmetric cell division, where daughter cells inherit unequal amounts of specific factors, is critical for development and cell fate specification. In polarized cells, where specific factors are segregated to opposite ends of the cell, asymmetric cell division occurs as a result of positioning the centrosomes along the polarity axis. In many systems, this positioning involves both translocation as well as rotation of the nucleus and its associated centrosomes. Using an individual-based stochastic model of centrosome-associated microtubule dynamics and experiments in early embryos of the nematode worm C. elegans, we explore the role of the motor protein dynein under both wild type and knockdown conditions. We show that dynein activity but not localization is implicated in specific centrosome movement defects in the first cell cycle.

Tracy Stepien University of Florida
"Spreading Mechanics and Differentiation of Astrocytes During Retinal Development"

In embryonic development, formation of the retinal vasculature is critically dependent on prior establishment of a mesh of astrocytes. Astrocytes emerge from the optic nerve head and then migrate over the retinal surface in a radially symmetric manner and mature through differentiation. We develop a PDE model describing the migration and differentiation of astrocytes, and numerical simulations are compared to experimental data to assist in elucidating the mechanisms responsible for the distribution of astrocytes.

Renske Vroomans Origins Center
"Conservative evolution of epithelial morphogenesis"

Morphogenesis is a complex process involving multiple levels of organisation. Cell differentiation within tissues is governed by extensive gene expression regulation within cells and communication via chemical signals between cells. Based on their gene expression, cells may divide and change their physical properties, leading to cell- and tissue-level physical forces which can in turn feed back on gene expression between cells. This developmental process may change over time due to Darwinian evolution, but development itself influences the course of evolution by determining the effect that mutations have on the final phenotype. Currently, it is not well-understood how the complex interactions involved in morphogenesis impact the kind of evolutionary changes that can occur. Here, we investigate the evolution of developmental mechanisms that govern morphogenesis with Embryomaker, an in silico model of 3d epithelium development. We look at short-term evolutionary changes that occur under conservative selection, meaning that the final shape of the tissue is conserved while all else -- gene expression pattern, growth pattern, developmental trajectory -- is allowed to change. We find that substantial change can occur at all levels of organisation, from the structure of the gene regulatory network to gene expression pattern, the duration of the developmental process and the course of morphogenesis. In some cases we observe an increase in the reliability of the developmental process despite not explicitly selecting for it, and show how it is caused by a non-trivial combination of mutations which on their own do not improve -- or even diminish -- fitness. Finally, we show how the coupling of gene expression regulation to morphogenesis influences which mutations are accepted, and thereby the ancestry of genes in the genome.

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

Matthew Jones Dartmouth College
"Spatial Games of Fake News"

When it becomes so quick and easy to freely 'share' another's understanding (via retweets/reposts), rather than researching and formulating one's own, social media platforms seem to facilitate the spread of fake news. A recent study used an online crowdsourcing fact-checking approach as one possible intervention to reduce misinformation. However, it remains largely unclear under what conditions crowdsourcing fact-checking efforts can actually deter the spread of misinformation. To address this issue, we model such distributed fact-checking efforts as 'peer policing' that will reduce the perceived payoff to share or disseminate false information (fake news) and also reward the spread of trustworthy information (real news). We use the diffusion approximation method and agent-based simulations to quantify the degree of penalty vs reward needed to make sharing fake news unfavorable in social networks. In the limit of weak selection, we obtain closed-form analytical conditions, which can be expressed as an inequality of these payoff values, with coefficients summarizing the effect of fact-checkers' presence. In reality, fact-checking is subject to human errors. Some fake news occasionally goes unnoticed and endorsed, and some real news is temporally labelled to be fake by fact-checkers. We also quantify the precision threshold required for fact-checkers to ensure fair and transparent policing of wrongdoers while in favor of real news spreaders. Our work has practical guide for developing model-based mitigation strategies for controlling the spread of misinformation that interferes with the political discourse.

Emma Southall Emma Southall
"Identifying indicators of critical transitions in epidemiological data"

A challenging problem in infectious disease modelling is assessing when a disease has been eliminated. Control campaigns have substantial economic consequences; as such there are high demands to reduce costs and reallocate resources. However, if campaigns are stopped prematurely it can result in disease resurgence and subsequently put control efforts back by decades. Early-warning signals offer a computationally inexpensive technique to monitor the progress towards elimination, using statistical indicators calculated on time series data. Early-warning signals are widely used in many fields to anticipate a critical threshold prior to reaching it. A system undergoes the phenomenon known as critical slowing down as it crosses through a threshold. Theory predicts that fluctuations away from the mean will recover more slowly as the system approaches a critical transition (Scheffer et al., 2009). This is key in infectious disease modelling to assess when the basic reproduction number is reduced below the threshold of one. Recent theoretical advances have shown indicators of critical transitions in epidemiology such as measuring the variance in synthetic disease data. Our work highlights several challenges when applying this theory in practice. One potential problem is known as 'detrending' the data, which can be difficult to achieve in a single time series (Dessavre & Southall et al., 2019). Accurately detrending the signal removes the mean to obtain the fluctuations, whilst preserving any statistical properties. We present a novel approach using a metapopulation framework to successfully detrend data using the mean of different geographical subpopulations. A second limitation is that often only incidence-level data is available publicly. However, current theoretical analyses of statistical indicators concentrate on prevalence data, instead of new cases. We demonstrate that indicators calculated on simulated incidence time series data exhibit vastly different behaviours to those previously studied on prevalence data (Southall et al., 2020). Inconsistencies in time series traits between different diseases systems and a variety of disease data types could lead to misleading results when applied to collected data. In this talk we present methods for dealing with the typical data collected and our results show promising methods for calculating early-warning signals of elimination on real-world noisy data.

Scott Greenhalgh Siena College
"A generalized differential equation compartmental model of infectious disease transmission"

For decades, mathematical models of disease transmission have provided researchers and public health officials with critical insights into the progression, control, and prevention of disease spread. Of these models, one of most fundamental is the SIR differential equation model. However, this ubiquitous model has one significant and rarely acknowledged shortcoming: it is unable to account for a disease’s true infectious period distribution. As the misspecification of such a biological characteristic is known to significantly affect model behavior, there is a need to develop new modeling approaches that capture such information. In this talk, we illustrate an innovative take on compartmental models, derived from their general formulation as systems of nonlinear Volterra integral equations, to capture a broader range of infectious period distributions, yet maintain the desirable formulation as systems of differential equations. Our results include a compartmental model that captures any Erlang distributed duration of infection with only 3 differential equations, instead of the typical inflated model sizes required by differential equation compartmental models, and a compartmental model that captures any mean, standard deviation, skewness, and kurtosis of an infectious period distribution with 4 differential equations. The significance of our work is that it opens up a new class of easy-to-use compartmental models to predict disease outbreaks that does not require a complete overhaul of existing theory, and thus provides a starting point for multiple research avenues of investigation under the contexts of mathematics, public health, and evolutionary biology.

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

Archana Hari UMBC, United States, archh1@umbc.edu
"A novel methodology and web application for computing, visualizing and analyzing genome-scale metabolic flux networks"

Genome-scale metabolic models not only represent the biochemical circuits within cells but can also be used to simulate and analyze cellular phenotypes. However, there is a lack of methodologies and user-friendly tools to visualize the complex reaction graphs within these genome-scale metabolic models and simulate their flux behaviors. For this, we have developed a novel methodology and implemented it in a freely-available web application called Fluxer ( https://fluxer.umbc.edu ) that streamlines the simulation and visualization of genome-scale metabolic flux networks with an easy-to-use interface. The application can take as input any metabolic model encoded with the Systems Biology Markup Language format, automatically perform Flux Balance Analysis using linear programming and apply different methods to compute flux graphs. The flux networks can be visualized as spanning trees and complete graphs with different layouts. The interactive graphs can be used to study major pathways contributing to any metabolic reaction or biosynthesis of any metabolite as well as to simulate reaction knockouts. In addition, Fluxer can compute the k-shortest paths between two reaction or metabolites within the model. Nodes can display detailed metabolic and reaction information, including molecular weights, reaction fluxes, and molecular structures. Over 80 whole-genome metabolic reconstructions are readily available for visualization and analysis. The proposed methodology enables efficient analysis and visualization of genome-scale metabolic models towards the discovery of key metabolic pathways.

Peter Stechlinski University of Maine, United States, peter.stechlinski@maine.edu
"Sensitivity analysis of nonsmooth biological models"

Nonsmooth dynamical systems are an appropriate modeling framework for a variety of problems in mathematical biology, ranging from glucose-insulin kinetics to rioting activity. The presence of nonsmoothness in these models arises from switching phenomena, such as a biochemical threshold signaling sudden insulin release, or a bandwagon effect in rioting behavior corresponding to an outburst of social activity. Nonsmooth modeling frameworks now possess a sensitivity theory that is relevant for nonsmooth ODEs, nonsmooth differential-algebraic equations, optimization-constrained ODEs, and complementarity systems, among others. In this talk, the nonsmooth sensitivity theory is presented, including the generalized derivatives theory upon which it is built. The theory yields an auxiliary, nonsmooth system whose unique solution characterizes (local) sensitivity information. The theory is highlighted using examples from mathematical biology, with numerical implementations that give nonsmooth sensitivity indices. The results can be used to help inform policy decisions (e.g., in rioting) or for design purposes (e.g., in the intravenous glucose tolerance test for type 2 diabetes) by uncovering the mechanisms driving the dynamics.

Ivo Siekmann Liverpool John Moores University, United Kingdom, i.siekmann@ljmu.ac.uk
"Data-driven modelling of ion channels incorporating uncertainty using hierarchical Markov models"

Ion channels are proteins that regulate the flow of ions across the cell membrane. Patch clamp recordings enable us to watch a single ion channel in action by detecting the electrical current flowing through the channel over time. At first glance we only see that the channel opens and closes stochastically but often a closer look reveals that it also alternates between two or more levels of activity – highly active modes where the channel opens and closes frequently, nearly inactive modes in which the channel is mostly closed, as well as intermediate levels of activity. The striking differences in the dynamics the channel exhibits in the different modes suggest that each mode is associated with a distinct three-dimensional configuration (conformation) of the channel protein. Applying statistical change point analysis to a large single channel data set collected from the inositol-triphosphate receptor (IP3R) highlights the importance of this observation: We find that the dynamics of the IP3R is entirely regulated by switching between two modes. In order to build a mathematical model that takes this into account we develop a novel model, the hierarchical Markov model, which enables us to separate modelling the slower dynamics of mode switching from the faster dynamics of opening and closing characteristic of each mode. We will illustrate this approach by fitting a hierarchical Markov model to type 1 and type 2 IP3R data for a wide range of concentrations of IP3R, Ca2+ and ATP. In contrast to most other ion channel models currently available we account for uncertainty by calculating probability distributions for the parameters of our model following a Bayesian Markov chain Monte Carlo (MCMC) approach.

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

Lucas Stolerman UCSD
"Stability Analysis of a Bulk–Surface Reaction Model for Membrane Protein Clustering"

Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood. Therefore, understanding the spatial patterns that can emerge on the PM solely through protein–protein interaction, lateral diffusion, and feedback is an important step toward a complete description of the mechanisms behind protein clustering on the cell surface. In this work, we investigate the pattern formation of a reaction–diffusion model that describes the dynamics of a system of ligand–receptor complexes. The purely diffusive ligand in the cytosol can bind receptors in the PM and the resultant ligand–receptor complexes not only diffuse laterally but can also form clusters resulting in different oligomers. Finally, the largest oligomers recruit ligands from the cytosol using positive feedback. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. Our main result is a threshold phenomenon, in which a sufficiently high recruitment of ligands promotes the input of new monomeric components and consequently drives the formation of a single-patch spatially heterogeneous steady state.

Hammed Fatoyinbo Massey U Palmerston North
"Spatiotemporal dynamics in spontaneous excitable cells"

Pacemaker dynamics is the spontaneous excitation-contraction coupling in muscle cells. It may arise as a result of interaction between ion fluxes through the voltage-gated ion channels. In this work, we consider a model of electrically coupled pacemaker smooth muscle cells to investigate the formation of spatiotemporal patterns. We analyse the behaviour of an isolated smooth muscle cell using numerical bifurcation analysis. By modulating model parameters, the result reveals transitions between Type I and II excitabilities in the parameter space. Numerical simulations of our model show that the pattern can bifurcate from been stable to spatiotemporal chaos.

Chitaranjan Mahapatra UCSF
"Evaluation of a mathematical model for estradiol effect on membrane excitability of detrusor smooth muscle cell"

The urinary bladder is composed of detrusor smooth muscle (DSM) cell to perform contraction, triggered by the intracellular calcium concentration after the generation of the action potential (AP). The DSM cells display enhanced spontaneous APs during the overactive bladder state. Estradiol, which is a natural sex hormone, has been suggested to be beneficial in the treatment of overactive bladder. This study aims in investigating the quantitative analysis of estradiol on membrane excitability of DSM cells. To simulate the estradiol effect, conductances of calcium- and voltage-dependent potassium channels (BK channels) were increased by 40% of its control value in a published DSM model cell. We found that the resting membrane potential (RMP) was more negative (─ 53 mV) than the control (─ 50 mV) value. The peak amplitude of the AP due to estradiol treatment was also significantly decreased. Similar to in the control condition, we have implemented the voltage clamp protocol to investigate the whole cell outward current. Under the effect of the estradiol, the amplitude of outward current was greatly increased due to BK channel. These findings are consistent with the experiment in guinea pig and rat DSM cells. The future investigation would provide some insight towards the modulating role of voltage-gated Ca2+ current in DSM cells due to estradiol treatment.

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

Renee Brady-Nicholls Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center Tampa, USA
"Forecasting Individual Responses to Intermittent Androgen Deprivation Therapy Using PSA Dynamics"

Prostate cancer (PCa) is the second most common cancer in men and the fifth leading cause of death worldwide. Intermittent androgen deprivation therapy (IADT), whereby treatment is cycled on and off, is an attractive therapy option that can reduce cumulative dose and limit toxicities, when compared to continuous therapy. We simulate prostate-specific antigen (PSA) dynamics, with enrichment of PCa stem-like cell (PCaSC) during treatment as a plausible mechanism of resistance evolution. Simulated PCaSC proliferation patterns correlate with longitudinal serum PSA measurements in 70 biochemically recurrent PCa patients. Learning dynamics from each treatment cycle in a leave-one-out study, model simulations predict patient-specific evolution of resistance with an overall accuracy of 89% (sensitivity=73%, specificity=91%). Previous studies have shown a benefit of concurrent therapies with ADT in both low- and high-volume metastatic hormone-sensitive PCa. Model simulations based on response dynamics from the first IADT cycle identify patients who may benefit from concurrent docetaxel, demonstrating the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics.

Balázs G. Madas Centre for Energy Research, Hungary
"Low dose hyper-radiosensitivity as a consequence of bystander signalling aiming to reduce the mutation load of the cell population"

Radiation therapy is frequently applied in cancer treatment. The fraction of surviving cells is a crucial quantity predicting both tumour control and normal tissue toxicity. The gold standard in vitro measurement for cell survival is the colony forming assay (CFA), which is based on the ability of a single cell to grow into a colony. The relationship between surviving fraction (SF) and absorbed dose (D) can be described by a linear-quadratic function: SF=exp(-aD-bD^2), where a and b depend on radiation type other cell properties. However, many cell lines show hyper-radiosensitivity (HRS) resulting in a local minimum in the surviving curve below 1 Gy. It is an interesting phenomenon and it may also have clinical implications related to the potential benefits of hyperfractionation. It is generally thought that HRS is a mechanism that protects against carcinogenesis following low dose ionizing radiation. Recently, it has been shown that minimizing the mutation load at the cell population level may result in local minimum in survival-dose relationships if both spontaneous and radiation induced mutations are considered. The model proposed, however, does not account for how cells receive the information required to reduce the mutation load. The aim of the present study was to test whether bystander signalling through the medium provides enough information for the cells to reduce the mutation load of the population with their individual survival or death decision. For this purpose, a mathematical model of bystander signalling was elaborated. Cells are located randomly in a disc shaped dish. Extracellular signals are produced by cells with mutagenic damages. The signal production is proportional to the number of mutagenic damages, while the signal strength decreases by the distance from the signal producing cell. A cell goes into apoptosis if the difference between the number of its mutagenic damages and the number of spontanenous mutations per cell division is high compared to the signal strength at its location. The threshold signal strength for this decision equals to the mean signal strength if all cells have one mutagenic damage. The number of mutagenic damages follows Poisson distribution, and its mean is proportional to absorbed dose. Simulations were performed to reproduce the deviation from the linear quadratic survival curve in case of 45 experimental datasets. During this fitting process, the spontaneous mutation rate and the mutagenic damage induction rate were varied. The model describes most experimental data very well, while the spontanenous mutation rate is close to the reasonable number of 1 mutation per cell division, and the mutagenic damage induction rate is in the order of magnitude of 1 per Gy. These results confirm that low dose hyper-radiosensitivity can be a consequence of bystander signalling aiming to reduce the mutation load of the cell population.

Guillermo Lorenzo The University of Texas at Austin, USA
"Image-based mechanistic modeling of prostate cancer for personalized forecasting of tumor growth"

The current clinical management of prostate cancer (PCa) enables its detection at early organ-confined stages by combining regular screening and patient classification in risk groups. Although these newly diagnosed tumors do not usually pose a threat to the patient, most PCa cases are prescribed a radical treatment immediately after diagnosis (e.g., surgery or radiotherapy). However, the limited individualization of the clinical management beyond risk-group definition has led to significant overtreatment and undertreatment rates, which might adversely impact the patients' lives and life expectancy, respectively. Thus, PCa is a paradigmatic disease in which an individualized predictive technology could make a crucial difference in clinical practice, thereby separating less aggressive tumors that could be safely monitored from lethal tumors that require immediate treatment. To address this critical need, we propose to use routine clinical and imaging data to construct and parametrize personalized mathematical models of PCa growth including the key mechanisms involved in this pathology. We can then run computer simulations with these models to forecast the growth of a patient's tumor, which may assist physicians in clinical-decision making. Our models have been able to qualitatively reproduce tumor growth over the local anatomy of a patient's prostate extracted from imaging data. We have also been able to capture the dynamics of the Prostate Specific Antigen (PSA), which is a ubiquitous biomarker in PCa clinical management. We have also studied the inhibitive effect of growth-induced mechanical stress on PCa and how the compression exerted by concomitant benign prostatic hyperplasia dramatically impedes tumor growth. Our ongoing efforts aim at leveraging longitudinal clinically-available quantitative magnetic resonance data to initialize and parameterize our PCa growth models. We believe that our imaging-based models could constitute a promising computational technology to assist physicians to provide a personalized clinical management of PCa.

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

Rosemary Dyson Birmingham
"Vesicle transport and cytoplasmic streaming in the pollen tube tip"

The rapid elongation of the pollen tube in seed plants cannot occur without the transport of sufficient cell wall and membrane material to the growing apex. The movement of this material, delivered via exocytic secretory vesicles, can be categorised under two regimes: 'long distance' movement in the shank (via active transport along actin ﬁlaments), and 'short distance' movement in the apex (where vesicles diffuse and advect freely). Many current models of vesicle transport focus on diffusion in the apical region alone, neglecting advective eﬀects as well as the resulting distribution proﬁle in the pollen tube shank. Using the method of regularised Stokeslets with an adjustment made for axisymmetry, we produce a complete advective velocity proﬁle for cytosolic ﬂow in the tube based on the drag induced by the active transport of vesicles along actin. We use this to calculate exocytic and endocytic vesicle motion in the tube, incorporating vesicle uptake and deposition at the wall, and generating insight into pollen tube growth dynamics.

Omer Karin Weizmann Inst.
"A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks"

Stress activates a complex network of hormones known as the Hypothalamic-Pituitary-Adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a new mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by the HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia and postpartum. Dysregulation occurs for a wide range of parameters, and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Preeti Dubey Loyola
"Modeling early hepatitis D virus kinetics in transgenic-hNTCP mice"

The hepatitis delta virus (HDV) is a dependent virus of hepatitis B virus that uses hepatitis B surface antigen to create its envelope and achieve secretion. HDV infection is the most severe form of chronic viral hepatitis. Currently, no therapies have been approved that can cure delta hepatitis. Understanding of early HDV-host dynamics post infection is lacking. I will present early serum HDV kinetics in transgenic mice expressing human NTCP (tg-hNTCP), the receptor for hepatitis B virus and HDV, and non-tg control mice after inoculation and provide insights into HDV-host interplay using mathematical modeling.

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

Wolfram Moebius University of Exeter
"Two layers of chance associated with spatially expanding populations: How demographic noise and environmental heterogeneity shape the evolutionary path of a population"

In nature, populations expand into new habitat at different spatial and temporal scales. The expansion process can thereby affect the evolutionary path of the growing population, a topic that has gathered much interest recently. The effects of environmental heterogeneity on the evolutionary dynamics of such range expansions remains poorly understood so far - not least due to the large variety of environmental heterogeneity found in nature. We investigate these effects in two different scenarios: neutral evolution of an expanding population and emergence of a new genotype that can spread exclusively in parts of the environment. Specifically, we first consider the effects of isolated obstacles and hotspots as well as bumps in an otherwise flat habitat. The former two are regions which hinder and accelerate the invasion, respectively. We find that those structures have characteristic consequences for neutral genetic diversity. We observe an additional layer of ‘survival of the luckiest’ – complementary to, yet qualitatively different from, founder effects occurring in the presence of 'spatial bottlenecks'. Second, we investigate the establishment of a new genotype that we allow to spread exclusively in some parts of the environment but constrain to have a selective disadvantage elsewhere. We describe the role that environmental structure has in shaping the fate of this new genotype.

Philipp Altrock H. Lee Moffitt Cancer Center
"Time scales and wave formation in non-linear spatial public goods games"

Evolutionary public good (PG) games capture the essence of production of growth-beneficial factors that are vulnerable to exploitation by free-riders who do not carry the cost of production. PGs emerge in cellular populations, for example in growing bacteria and cancer cells. We study the eco-evolutionary dynamics of a PG in populations that grow in space. In our model, PG-producer cells and free-rider cells can grow according to their own birth and death rates. Co-evolution occurs due to public good-driven surplus in the intrinsic growth rates at a cost to producers. A net growth rate-benefit to free-riders leads to the well-known tragedy of the commons in which producers go extinct. What is often omitted from discussions is the time scale on which this extinction can occur, especially in spatial populations. Here, we derive analytical estimates of the ε-extinction time in differ- ent spatial settings. As we do not consider a stochastic process, the ε-extinction time captures the time needed to approach an extinction state. We identify spatial scenarios in which extinction takes long enough such that the tragedy of the commons never occurs within a meaningful lifetime of the system. Using numerical simulations we analyze the deviations from our analytical predictions.

Debora Princepe University of Campinas
"Modeling Mito-nuclear Compatibility and Its Role in Species Identification"

Mitochondria play a key role in population genetics and evolutionary biology. Praised as a reliable genetic marker, the utility of mtDNA derives from its particular molecular properties, including high evolutionary rate, uniparental inheritance, and small size. Such properties make the mtDNA a powerful substrate for inferring geographic structure of populations and phylogenetic relationships. An important application is the use of a standardized segment of the mtDNA for species identification in animals, called the DNA barcode. The high rate of success to distinguish both phylogenetically close and distant species of vertebrates motivates a fundamental question: why does the barcode work and how does it relate to the nuclear DNA (nDNA) divergences during speciation? Nuclear and mitochondrial DNA’s interact during the respiration process, which depends on the coordination of genes from both sources. Recent observations of coevolution between these genomes suggest that this genetic interaction affects organism fitness; thus, mtDNA may play a fundamental role in speciation. Here we study how mito-nuclear interactions affect the speciation process and whether the accuracy of species identification by mtDNA is a consequence of the mito-nuclear coevolution. We investigate the validity of mtDNA-based barcoding in an evolving population, comparing the classification provided by mtDNA with the classification based on nuclear genetic content. Starting from an individual-based model for spatially distributed populations, we simulate the evolution of a population of individuals who carry a recombining nuclear genome and a mitochondrial genome inherited maternally. We compare a null model fitness landscape that lacks any mito-nuclear interaction against a scenario in which interactions influence fitness. Fitness is assigned to individuals according to their mito-nuclear compatibility, which drives the coevolution of the nuclear and mitochondrial genomes. Depending on the model parameters, the population breaks into distinct species and the model output then allows us to analyze the accuracy of mtDNA barcode for species identification depending on the selection strength over the mito-nuclear compatibility. We also register the signatures left in the genetic content and spatial distribution of the populations due to selection imposed on mito-nuclear compatibility. These analyses allow us to evaluate the effects of mito-nuclear interaction on the diversification process and examine to what extent mito-nuclear coevolution assists speciation.

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

Click to view posters for each subgroup

Sub-group Keynote

3:30pm

Robert Insall,
University of Galsgow, @robinsall

Methods for Biological Modeling Subgroup

Cells, cancer and mazes: Understanding what steers cells, using cycles of mathematics, modelling and experiments.

Chemotaxis is important to many of the things cells do in vivo, particularly during development and disease. It is also a favourite topic for mathematical biologists. However, despite decades of studies of how cells can interpret chemotactic gradients, there has been very little attention to how gradients form, and where the information comes from. We have studied a particularly interesting aspect of this problem - self-generated gradients, in which cells form their own gradients at the same time as interpreting them and migrating up them. Self-generated gradients are fascinating, and ideal for mathematical biologists - they are so dynamic that they are nearly impossible to measure, and they incorporate multiple levels of feedback. I will describe how we use modelling, mathematics and experiments on Dictyostelium and cancer cells to understand different self-generated gradients. In particular I will show how cells can solve arbitrarily complex mazes, escape from tumours, and use the information in a gradient to move down-gradient as well as up-gradient.

Happy hour with friends and colleagues (4:30)

Schedule for Wednesday, August 19

Coffee with friends & colleagues

8:00am

Subgroup Keynote

8:30am