Sub-group contributed talks (9:30-11:00am)

CDEV: The interplay of intracellular pattern formation, geometry, polarisation and mechanics (9:30-11:00am)

Erwin Frey Ludwig-Maximilians University Munich
"Self-organization principles of intracellular pattern formation"

Dynamic patterning of specific proteins is essential for the spatiotemporal regulation of many important intracellular processes in procaryotes, eucaryotes, and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. We will discuss quantitative models for intracellular Min protein patterns in E. coli, Cdc42 polarization in S. cerevisiae, and the bipolar PAR protein patterns found in C. elegans. By analyzing the molecular processes driving these systems we will show how to derive a theoretical perspective on general principles underlying self-organized pattern formation of proteins in cells.

Veronica Grieneisen Cardiff University
"Self-organization through the mesoscale, lessons from plant patterning and adaptive responses"

This core ability of a cell to polarize in isolation from others then leads to the collective emergence of tissue polarity, which will be dependent on the mode of cell-cell interaction. In plants, such tissue polarity will allow for information flow over large distances, be it to guide development or to interface the environment, such as in plant-nutrient uptake. We will show how for such organism-level coordination of signals, sub-cellular components turn out to be extremely important. Also, we will discuss temporal-spatial dynamical constraints operating on such polarized tissues which are likely to have a evolutionary-developmental role in the systems we encounter in nature.

Stan Maree Cardiff University
"Intracellular patterning coupled to cell shape can lead to sensitization of signal detection"

A lot of animal and plant cell polarity can be understood by simple biochemical processes. Exploring their dynamics shows that simple circuits are able to generate a plethora of diverse cellular patterns. Firstly, I will discuss how we can explore the potential for break-of-symmetry within cells. I will then explore, how through modelling we can better understand the feedbacks between these patterns and biophysical triggers that cause cell shape changes. Finally, I will show how polarity formation can also be used as an integrator for sensing external cues, and discuss how alterations of this could cause tissue-level disruption. To extend these insights directly to experimental data, I will then show how our modelling framework can also be used for segmentation of imaging data, showing examples that range from complex epithelia to organoids.

Padmini Rangamani University of California at San Diego
"Stability analysis of a bulk-surface model for membrane-protein clustering"

Protein aggregation on the plasma membrane (PM) is of critical importance on 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 uniquely through protein-protein interaction and diffusion is an important step towards a more 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. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. We also obtain the distribution of the size of the protein aggregates and their spatial locations depending on both initial conditions and kinetic parameters using computational methods. Our results suggest that spatial heterogeneity emerges only when the cluster diffusion rates decay as a function of cluster size.

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

Shilian Xu Monash University
"Saturation of influenza virus neutralization and antibody consumption can both lead to bistable growth kinetics"

Influenza virus is a major human health threat. Neutralizing antibodies elicited through prior infection or vaccination play an irreplaceable role in protection from subsequent infection. The efficacy of antibody-dependent vaccines relies on both virus replication and neutralisation, but their quantitative relationship was unknown. Here we use mathematical models to quantitatively investigate viral survivability determined by antibody concentration and inocula size. We performed focus reduction assays for 49 seasonal influenza A/H3N2 viruses circulating during 2017–2019 against influenza antisera raised in ferrets, and find that the antibody consumption rates of individual reactions were either small or large, and this was strongly positively correlated with virus saturation. Regardless of antibody consumption rate, virus-antibody interactions always lead to antibody-induced bistable viral kinetics. As a result, at a specific interval of antibody concentration, small viral inocula are eliminated but not large virus inocula, which is triggered by saturated virus neutralization or antibody consumption. Our finding highlights virus-antibody interaction with different antigenic properties, thereby explaining commonly observed influenza re-infection and enhancing vaccine efficiency.

Jacob Summers University of Tennessee
"Mathematical modeling of Mycobacterium tuberculosis dynamics in macaques"

Mycobacterium tuberculosis (Mtb) is the causative agent of tuberculosis (TB), infecting a large proportion (~30%) of the world’s population. Only a small proportion of infected individuals develop clinical disease, and factors determining why some individuals remain asymptomatic and some become sick remain unknown. Unfortunately, understanding disease progression in humans remains challenging because most people do not know they are infected. Instead, several different animal species such as mice and monkeys can be infected with Mtb, thus, providing potential explanations for progression of humans to TB. Several recent studies provided interesting insights into early Mtb dynamics in monkeys. In particular, it was found that infection of monkeys with a set of individually barcoded Mtb strains resulted in most local foci of infection (called granulomas) to contain a single barcode. This suggested that individual granulomas were started by a single bacterium. We used stochastic mathematical models to understand whether this observation is also consistent with the hypothesis that multiple strains cause granuloma formation but most die during early dynamics. Our model included the simplest possible way to describe early stochastic dynamics (linear birth-death model); interestingly, we could not find one set of model parameters that allowed us to accurately describe both mean number of bacteria per granuloma and distribution of founder strains in different granulomas. This suggests early Mtb dynamics in monkeys are unlikely to be described by a simple birth-death model, and other biological aspects must be included in the model, in particular, impact of the immune response on rates of Mtb replication and death.

Suneet Singh Jhutty Frankfurt Institue for Advanced Studies (FIAS); Goethe University Frankfurt, Germany
"Mapping Influenza from blood data using deep learning"

Seasonal and pandemic influenza causes enormous economic loss and leads to health complications and death. A better understanding of the role of different blood constituents during infection is necessary. Mathematical analysis of data can help us to better understand the link between blood properties and the influenza virus. Furthermore, the measurement of influenza viral load in a person is laborious and time-consuming. Therefore, it is crucial to have a reliable and fast method to determine the viral load in a patient. Here, we analyze blood data from mice and explore the different correlations between the key players during an infection. We test successfully a novel approach to use deep learning to infer viral load from this blood data. Hence, the viral load is directly inferred from a blood test. Using a simple multilayer perceptron, we train the algorithm with a comparatively small data set, to map blood data to the viral load. This shows the general possibility to use blood constituents measured in every routine blood count (like lymphocytes and erythrocytes) to infer the viral load in the body. Even with high variability in the data, the model prediction is reasonably accurate. Our results may lead the way to allow the measurement of the viral load from already collected blood data in the future. Hence, it would not only reduce the workload but be probably also faster. Lastly, our results suggest that platelets and granulocytes play an essential role during influenza infection.

Yuhuang Wu University of New South Wales, Sydney
"Impact of fluctuation in frequency of HIV reactivation during antiretroviral therapy interruption"

Antiretroviral Therapy (ART) provides effective control of human immunodeficiency virus (HIV) replication and maintains the viral loads of HIV at undetectable levels. Interruption of ART causes recrudescence of HIV plasma viremia due to the reactivation of latently HIV-infected cells, generally within weeks of discontinuation of ART. Here we characterize the timing of both the initial and subsequent successful viral reactivations following ART interruption in macaques infected with simian immunodeficiency virus (SIV). We compare these to previous results from human patients infected with HIV. We find that on average the time until the first successful viral reactivation event is longer than the time between subsequent successful reactivations. Based on this result, we hypothesise that the reactivation frequency of both HIV and SIV may fluctuate over time and that this may have implications for treatment of HIV. We develop a stochastic model to simulate the behaviour of viral reactivation following ART interruption that incorporates fluctuations in the frequency of reactivation. Our model is able to explain the difference in timing between the initial and subsequent successful reactivation events. Furthermore, we show that one of the impacts of a fluctuating reactivation frequency would be to significantly reduce the efficacy of “anti-latency” interventions for HIV that aim to reduce the frequency of reactivation. It is therefore essential to consider the possibility of a fluctuating reactivation frequency when assessing the impact of such intervention strategies.

Vitaly Ganusov University of Tennessee
"Structure-imposed constrains make Brownian walkers efficient searchers"

Pathogen-specific CD8 T cells face the problem of finding rare cells that present their cognate antigen either in the lymph node or infected tissue. To optimize the search for rare targets it has been proposed that T cells might perform a random walk with long displacements called Levy walks enabling superdiffusive behavior and shorter search times. Many agents ranging from molecules to large animals have been found to perform Levy walks suggesting that Levy walk-based search may be evolutionary selected. However, whether random walk patterns are driven by agent-intrinsic programs or being shaped by environmental factors remains largely unknown. We examined the behavior of activated CD8 T cells in the liver where both the movement of the cells and the underlying structural constrains can be clearly defined. We show that Plasmodium-specific liver-localized CD8 T cells perform Brownian, short displacement walks and yet display superdiffusive overall displacement, the cardinal feature of efficient Levy walks. Because liver-localized CD8 T cells are mainly associated with liver sinusoids, we show that linear structure of the sinusoids is sufficient to cause T cells to superdiffuse even when movement lengths are Brownian. Simulations of Brownian or Levy walkers in structures derived from the liver sinusoids illustrate that structure alone can enforce superdiffusive movement. Moreover, Brownian walkers require less time and thus are more efficient than Levy walkers at finding a rare target when T cells search for the infection in physiologically-derived liver structures. Importantly, analysis of fibroblastic reticular cell networks on which CD8 T cells move in lymph nodes also allows for superdiffusion in simulations which is not observed experimentally suggesting that structure is not the only factor determining movement patterns of T cells. Our results strongly suggest that observed patterns of movement of CD8 T cells are likely to result as a combination of a cell-intrinsic movement program, physical constrains imposed by the environmental structures, and other environmental cues. Future work needs to focus on quantifying relative contributions of these factors to the overall observed movement patterns of agents.

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

Samson Ogunlade James Cook University
"Modeling the potential of wAu-Wolbachia strain invasion in mosquitoes to control Aedes-borne arboviral infections"

Arboviral infections such as dengue, Zika and chikungunya are fast spreading diseases that pose significant health problems globally. In order to control these infections, an intracellular bacterium called Wolbachia has been introduced into wild-type mosquito populations in the hopes of replacing the vector transmitting agent, Aedes aegypti with one that is incapable of transmission. In this study, we developed a Wolbachia transmission model for the novel wAu strain which possesses several favourable traits (e.g., enhanced viral blockage and maintenance at higher temperature) but not cyctoplasmic incompatibility (CI) - when a Wolbachia-infected male mosquito mates with an uninfected female mosquito, producing no viable offspring. This model describes the competitive dynamics between wAu-Wolbachia-infected and uninfected mosquitoes and the role of imperfect maternal transmission. By analysing the system via computing the basic reproduction number(s) and stability properties, the potential of the wAu strain as a viable strategy to control arboviral infections is established. The results of this work show that enhanced maintenance of Wolbachia infection at higher temperatures can overcome the lack of CI induction to support wAu-Wolbachia infected mosquito invasion. This study will support future arboviral control programs, that rely on the introduction of new Wolbachia variants.

Maryam Aliee University of Warwick
"Estimating the distribution of extinction times of infectious diseases in deterministic models"

For many infectious diseases the eventual aim of control measures is eradication - completely removing the pathogen from host populations and the environment. Theoretical models can be used to predict the time to extinction under specific interventions. In general, this question requires the use of stochastic models which recognise the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when considering parameter uncertainty. On the other side, deterministic models are practical and tractable, however, the endpoint of an infection is by definition ambiguous in these models since the populations are represented by continuous variables that never reach zero. We study the extinction problem in deterministic models with the help of an effective ``birth-death'' description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth-death framework. We compare these predictions with the solutions of the corresponding forward Kolmogorov equations. We then extend this framework to estimate the extinction time of more complex and realistic infection dynamics, African sleeping sickness, gHAT, which is a vector-borne disease transmitted to humans by tsetse. This method will enable us to improve predictions of the timing of elimination of transmission for gHAT using our existing deterministic framework.

Sung-mok Jung Hokkaido University
"Reconstruction and analysis of the transmission network of African swine fever in People’s Republic of China, August 2018–September 2019"

Introduction of African swine fever (ASF) to China in mid-2018 and subsequent transboundary spread across Asia devastated regional swine production, affecting live pig and pork product-related markets worldwide. In order to explore the spatiotemporal spread of ASF in China, we reconstructed possible ASF transmission networks using nearest neighbour, exponential function, equal probability, and spatiotemporal case-distribution algorithms. From these networks we estimated the reproduction numbers, serial intervals, and transmission distances of the outbreak. The mean serial interval between paired units was around days for all algorithms, while the mean transmission distance ranged from 332–456 kilometers. The reproduction numbers for each algorithm peaked during the first two weeks and steadily declined through the end of 2018 before hovering around the epidemic threshold value of one with sporadic increases during 2019. These results suggest that: 1) swine husbandry practices and production systems that lend themselves to long-range transmission drove ASF spread, and 2) outbreaks went undetected by the surveillance system. China and other affected countries have stepped up efforts to control ASF within their jurisdictions, and continued support for strict implementation of biosecurity standards and improvements to ASF surveillance are essential for halting transmission in China and further spread across Asia.

Usman Sanusi Technical University of Munich
"Influence of quiescence on host-parasite coevolutionary dynamics"

Mathematical Modelling is widely being used as a tool to predict and understand the spread of infectious disease such as HIV, tuberculosis, Measles, Malaria, corona virus,. . . . However, most diseases have an intra-host quiescent stage defined sometimes as covert infection (malaria for example), while other parasites have dormant stages in the environment. The influence of these two life-history traits seems to be neglected by mathematicians when developing their models [1]. In this research, we develop a coevolutionary model similar to [2,3] to predict and understand the spread of disease considering the effect of intra-host quiescence. Analytical results are obtained for the stability of the system. We especially derived a stability conditions for a five by five system with quiescent stage. Numerical simulations were also performed and we show that the period of oscillations and the time to damping off is almost double under the quiescence compared to the classic epidemiological model. We finally extended the model to include the effect of stochasticity on disease transmission and study analytically the outcome using a Markov-Chain model. The model dynamics with stochasticity follow the deterministic one.

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

Fiona Macfarlane University of St. Andrews, Scotland, frm3@st-andrews.ac.uk
"Bridging the gap between individual-based and continuum models of growing cell populations"

Stochastic individual-based modelling approaches allow for the description of single cells in a biological system. These models generally include rules that each cell follows independently of other cells in the population. Various mechanisms and biological phenomena can be described using these simplistic mathematical models. However, these models cannot be analysed mathematically. Therefore, it can be beneficial to derive the corresponding deterministic model from the underlying random walk of the stochastic model. The resulting deterministic models, usually partial differential equations (PDEs), can then be analysed to provide further information about the biological systems studied. We have developed a range of simple IB models that describe biological systems with various properties of interest, such as, volume-filling and chemotaxis and pressure-dependent growth and proliferation. For each model, we were able to derive PDEs from the underlying random walk. We carried out comparisons between the stochastic and deterministic model highlighting situations where there is agreement in the models, and situations where they do not agree. Ultimately, the results illustrate how the simple rules governing the dynamics of single cells in our individual-based model can lead to the emergence of complex spatial patterns of population growth observed in continuum models. These models can be applied to a variety of biological situations such as tumour growth, tumour invasion and wound healing.

Alexey Penenko ICM&MG SB RAS, Russian Federation, a.penenko@yandex.ru
"Inverse Modeling of Biological Processes with Adjoint Ensemble Methods"

In order to study complicated natural processes through mathematical modeling, it is necessary to take into account both mathematical models of the processes and the available measurement data collected about these processes. We refer to this modeling approach as inverse modeling. In biological studies, the models can change very rapidly, so the unified algorithms that do not take much effort to apply them to different models are preferable. The general inverse modeling framework based on the ensembles of the adjoint equation solutions is considered in the context of biomedical applications with the advection-diffusion-reaction models. The sensitivity relations and adjoin equations allow constructing the approximation of the inverse modeling problem stated a system of ordinary or partial differential equations in the form of a parametric family of quasi-linear operator equations with the sensitivity operators. This approximation allows both solving, analyzing, and comparing a wide range of biomedical inverse problems in a unified fashion.

Karina Islas Rios Monash University Australia karina.islasrios@monash.edu
"NetScan: a computational tool for discovering and visualizing biochemical networks with defined topological structures."

Our quantitative understanding of biochemical networks empowered by computational modelling have shown that the topology (or structure) of a network often have determining roles in shaping the network’s dynamic and steady state behaviours. For examples, negative feedback can give rise to oscillation while positive feedback can bring about bistability to the host network. Thus, being able to systematically identify sub-networks with defined topological structures within the human protein interactome is critical for the discovery of biochemical networks with desired behavioural properties. However, this is a non-trivial task given the enormous complexity of the human protein-protein interaction network. Structural principles of biochemical networks can be discovered by focusing on small sub-networks. Finding those sub-networks in the assembly of complex biochemical networks can be achieved by implementing graph theory-based algorithms. Here, we develop NetScan, an open source web-based application capable of ‘scanning’ the large and complex human signalling interactome within the Signor 2.0 and STRING databases to identify all sub-networks with given structural topologies, e.g. those with a specific negative feedback, positive feedback or feed-forward loop wiring. NetScan allows users to specify the specific input topologies and the interactome network within which it will explore, and return all the smallest sub-networks with the desired topologies. The resulting sub-networks are displayed in two forms: a detailed version which includes all interaction links, and a simplified version presenting the net effects between the nodes. In summary, NetScan is a web application that provides unprecedented ability to systematically identify and visualise sub-networks within the human protein-protein interaction network with specific topological wiring.

Hyukpyo Hong Korea Advanced Institute of Science and Technology, Republic of Korea, hphong@kaist.ac.kr
"Derivation of stationary distributions of biochemical reaction networks via structure transformation"

Long-term behaviors of biochemical reaction networks are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method for deriving stationary distributions from deterministic steady states by transforming a network to have a special dynamic property. Specifically, we merge nodes and edges of a network to make the steady states complex balanced, i.e., the in- and out- flows of each node are equal. By applying our approach to networks that model autophosphorylation of EGFR, PAK1, and Aurora B kinase and a multi-timescale toggle switch, we identify robustness, sensitivity, and multi-modality of their stationary distributions. Our method provides an effective tool to understand long-term behaviors of stochastic biochemical systems.

Linard Hoessly University of Copenhagen, Denmark, hoessly@math.ku.dk
"Stationary distributions of stochastic reaction networks via decomposition"

Stochastic reaction networks (CRNs) are often used to describe systems with small molecular counts, which applies to many processes in living systems. They are usually modelled through continuous-time Markov processes. Studying dynamics of stochastic CRNs is in general hard, both analytically and by simulation. In particular stationary distributions of stochastic reaction networks are only known in some cases like, e.g., complex balanced or autocatalytic CRNs. I will review some results on form of stationary distribution and convergence to stationary distribution. Then, I am going to analyse CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs, which allows recursive application. To illustrate the theory I present examples of stochastic reaction networks of interest in order to highlight the decomposition.

NEUR: Rhythms, Sleep, Reward, Vision (9:30-11:00am)

Kevin Hannay University of Michigan
"Circadian State Estimation using Wearable Data"

Almost every living thing exhibits daily cycles in behavior and physiology known as circadian rhythms. In humans, disrupted circadian rhythms have been implicated in a spectrum of both mental and physical health maladies including cancer, diabetes, addiction, depression and sleep disorders. Therefore, it is a matter of vital importance to understand and predict human circadian rhythms. In previous work we have derived and fit a low dimensional dynamical model for human circadian rhythms. However, the heterogeneity of circadian behaviors (early birds/night owls) in the human population must be accounted for in the model. In this work we investigate how data collected by wearable devices (apple watch, fitbit, etc) can be used to personalize the circadian parameters and improve forecasting accuracy.

Maia Angelova Deakin University
"Data driven model for detecting insomnia from multi-night actigraphy time series data"

Sleep is an important part of human existence as we spend 1/3 of our lives sleeping. It is a complex multi-dimensional cycle that reflects developmental changes in mental and physical health, along with the day-to-day state fluctuations. Insomnia is characterised by the inability to fall asleep or stay asleep and/or waking too early and being unable to fall back asleep. Insomnia is a sleep disorder that remains under-diagnosed. We propose a new data driven model for classification of nocturnal awakenings in acute and chronic insomnia and normal sleep from nocturnal actigraphy collected from pre-medicated individuals with insomnia and normal sleep controls. Our model does not require sleep diaries or any other subjective information from the individuals. We derive dynamical and statistical features from the actigraphy time series data. These features are then combined in machine learning model to classify individuals with insomnia from healthy sleepers. The model includes a classifier followed by optimization algorithm that incorporates the predicted quality of each night of sleep for an individual to classify into acute/chronic insomnia or healthy group. The developed model provides a signature of acute/chronic insomnia obtained from actigraphy only and is very promising as a pre-screening tool to detect the condition in home environment. M Angelova, C Karmakar, Y Zhu, SP Drummond, J Ellis. (2020). Automated Method for Detecting Acute Insomnia Using Multi-Night Actigraphy Data. IEEE Access, 8, 74413-74422.

Davide Maestrini UCLA
"A mathematical model of 'wanting', 'liking, and brain reward circuitry in drug addiction"

We propose a mathematical model combining the so-called opponent process theory and the reward prediction error (RPE) in the context of drug addiction. Using this model, we investigate the different dynamics towards addiction and provide a possible description of the process of detoxification. The opponent processes are modeled by introducing a response kernel that integrates dopamine-induced neuronal activity to form a sense of reward. The shape of the kernel, which might be associated with physical and biological characteristics of neurocircuits of the brain reward system, plays a key role in determining the overall experience of consumption of addictive substances and the mismatch between the expected reward and the actual eward, the reward prediction error (RPE). With time and repeated exposures to drugs of abuse, the response kernel will change based on the value of the RPE and on the process of neuroadaptation. The dynamics of this change represents the evolution towards addiction and is mathematically described as a trajectory in a three-dimensional parameter space representing the RPE. In our framework, the surface representing the RPE is divided in two regions representing positive and negative values of value of the RPE, respectively. We show that the dynamics associated with naïve drug users is represented by a trajectory lying in the first, positive-RPE region but, with time and repeated exposure to drugs of abuse, the trajectory will enter into the second, negative-RPE region. After transition to addiction, the subsequent dynamics is largely confined within the negative-RPE region. We finally propose models for exiting the negative-RPE parameter regions and connect it to a description of a detoxification protocols, such as the use of methadone to address heroin addiction.

Paul Roberts University of Sussex
"Using mathematics to investigate the mechanisms behind vision loss"

The retina is a tissue layer at the back of the eye that uses photoreceptor cells to detect light. Photoreceptors can be characterised as either rods or cones. Rods provide achromatic vision under low light conditions, while cones provide high-acuity colour vision under well-lit conditions. The term Retinitis Pigmentosa (RP) refers to a range of genetically mediated retinal diseases that cause the loss of photoreceptors and hence visual function. RP leads to a patchy degeneration of photoreceptors and typically directly affects either rods or cones, but not both. During the course of the disease, degenerate patches spread and the photoreceptor type unaffected by the mutation also begins to degenerate. The cause underlying these phenomena is currently unknown; however, several key mechanisms have been hypothesised: oxygen toxicity, trophic factor depletion and the release of toxic substances by dying cells. Here we present mathematical models, formulated as systems of PDEs, to investigate the trophic factor hypothesis. Using a combination of numerical simulations and mathematical analysis, we determine the geographic variation in retinal susceptibility to degeneration, evaluate the degree to which in vivo spatio-temporal patterns of degeneration can be replicated by our models and predict the effects of various clinically-relevant treatment strategies.

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

Ryan John Murphy Queensland University of Technology, Australia
"Mechanical cell competition in heterogeneous epithelial tissues"

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. To study this phenomenon, we propose a one-dimensional mechanical model of cell migration in heterogeneous epithelial tissues that includes cell-length-dependent proliferation and death mechanisms. Proliferation and death are modelled in the discrete model stochastically and arise as source/sink terms in the corresponding continuum model that we derive. Applications we discuss include the evolution of homogeneous tissues experiencing proliferation and death, and cancer invasion with a cancerous tissue competing for space with an adjacent normal tissue. This framework allows us to postulate new mecha- nisms that explain the ability of cancer cells to outcompete healthy cells through mechanical differences rather than by having some intrinsic proliferative advantage.

Aleksandra Ardaseva University of Oxford, Oxford, UK
"Modelling evolutionary adaptation of cancer cells to fluctuating oxygen levels"

A major challenge in malignant tumours is cell heterogeneity, which has been proposed to arise due to temporal variations in nutrient supply caused by highly irregular vasculature. Such variability requires cells to adapt to potentially lethal variations in environmental conditions. Risk spreading (“bet-hedging”) through spontaneous phenotypic variations is an evolutionary strategy that allows species to survive in temporally varying environments. Individuals within a species diversify their phenotypes ensuring that at least some of them can survive in the face of sudden environmental change. We aim to investigate whether cancer cells may adopt this strategy when dealing with rapidly changing levels of nutrient due to temporally-varying blood flow. Here, we present a system of nonlocal partial differential equations modelling the evolutionary dynamics of phenotype-structured cancer cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continuous variable that provides a simple representation of its metabolic phenotype, ranging from fully oxidative to fully glycolytic. The cells are grouped into two competing populations that undergo heritable, spontaneous, phenotypic variations at different rates. A combination of analysis and numerical simulations indicates that under certain conditions the cell-oxygen dynamics can lead to regions of chronic hypoxia (low oxygen level) and cycling hypoxia. Moreover, the model shows that under chronic-hypoxic conditions lower rates of phenotypic variation lead to a competitive advantage, whereas higher rates of phenotypic variation can confer a competitive advantage under cycling-hypoxic conditions. In the latter case, bet-hedging evolutionary strategies, whereby cells switch between oxidative and glycolytic phenotypes, can spontaneously emerge. These results shed light on the evolutionary processes that may underpin the emergence of phenotypic heterogeneity in vascularised tumours, and suggest potential therapeutic strategies.

Phillip J. Brown The University of Adelaide, Australia
"Modelling colon cancer: Investigating serrated crypts using a new model for deformable membranes"

Serrated sessile polyps (SSPs) are a type of lesion found in the colon that are known to lead to colorectal cancer. They develop when there are disruptions in the processes controlling the function of colonic crypts - the test-tube shaped structures that make up the lining of colon. It is currently not clear what will cause a healthy crypt to become serrated. The crypt has been extensively modelled, owing to its relatively simple composition. However, little modelling work has focused on the formation of serrated crypts, perhaps because of the relatively difficult task of modelling the epithelial monolayer on a deformable supporting structure. In this talk, we will introduce new a modelling approach that allows us to build a deformable membrane, sidestepping the issues that made the predominant off lattice models less suitable. We will then present some preliminary findings on the potential causes behind the characteristic appearance of serrated crypts elucidated by this model.

Lisa C. Tucker-Kellog Singapore
"During multi-drug combination therapy, the speed of evolving drug-resistance is affected by the uniformity of pairwise synergism, additivity, or antagonism between the drugs"

Introduction: The search for combination therapies against cancer has focused on studying synergistic combinations (drug combinations with greater-than-additive efficacy) because they exhibit enhanced therapeutic efficacy at lower doses. Although synergistic combinations are intuitively attractive, therapeutic success often depends on whether drug resistance develops. In computational modeling of drug-resistance evolution, our recent work (Saputra et. al, Cancer Res, 2018) delineated conditions under which synergistic pairs of drugs would have worse long-term performance than non-synergistic pairs of drugs, due to faster evolution of drug-resistance. In this work, we extend our modeling to three-drug combinations. In a multi-drug cocktail, some pairs of drugs may be synergistic while other pairs of drugs in the same cocktail may be additive or antagonistic (quantified using the combination index). Does this matter for evolution of drug-resistance? We develop theoretical generalizations about relative performance, for winning the race between cancer-killing efficacy versus drug-resistance evolution, using multi-drug cocktails with equal efficacy but different distributions of combination index (CI). Methods: We performed mathematical modeling of tumor cells evolving under selective pressure from synergistic, additive, and antagonistic three-drug combinations. Starting with small populations of drug-sensitive cells, we allowed rare mutational events to change a cell’s phenotype toward any single drug, which over time created potential for the presence or absence of drug-resistance against any or all drugs in the multi-drug therapy. Meanwhile, proliferation and death were simulated according to the combined cocktail efficacy toward each phenotype of cell. Results and Discussion: Longer duration of cancer control was achieved by multi-drug combinations having higher uniformity of pairwise CI (i.e., all pairs of drugs within the cocktail having similar levels of synergism, or all pairs having similar levels of antagonism), compared with multi-drug cocktails having equal initial efficacy and equal overall CI, but greater differences in the pairwise CI’s. In other words, treatment was more likely to fail sooner if the three drugs had non-uniform amounts of pairwise synergism, compared with cocktails that had more uniform CI between the drug-pairs within the cocktail. The difference in outcomes was due to partially resistant phenotypes that achieved greater competitive advantage (meaning greater clonal expansion and greater sabotage of therapy) by resisting the most synergistic aspects of the cocktail. This is because resisting one part of a synergistic group destroys not on

Yangjin Kim Konkuk University, Republic of Korea
"How the surgery-induced transition of reactive astrocytes to stem cell-like phenotypes leads to recurrence of GBM by Cxcl5: hybrid multi-scale approaches"

Glioblastoma multiforme (GBM) is the most aggressive form of brain cancer with a short median survival time. GBM is characterized by the hallmarks of aggressive proliferation and cellular infiltration of normal brain tissue. Tumor cells also interact with many cells including astrocytes and immune cells, and extracellular matrix (ECM) in a tumor microenvironment (TME) via exchanging molecular signals in order to increase survival rates in response to biochemical and biomechanical challenges. miRNAs and their downstream molecules are known to play a pivotal role in regulation of the balance of proliferation and aggressive invasion in response to metabolic stress in the tumour microenvironment (TME). Surgery-induced transition in reactive astrocyte populations can dramatically change the growth and invasion dynamics of GBM cells. In this work, we develop a multi-scale mathematical model of the tumor astrocytes dynamics in response to surgical resection of the primary tumor in TME. The hybrid model takes into account miR-451-LKB1-AMPK-OCT1-mTOR pathway signalling (ODEs), individual cell dynamics of the tumour, reactive astrocytes, stem cell-like astrocytes (lattice-free individual model), and signal transport by diffusible molecules (PDEs). We show how the effects of fluctuating glucose on tumour cell dynamics need to be reprogrammed by taking into account the recent history of glucose variations and an LKB1/OCT1 reciprocal feedback loop, which then determines tumor cell proliferation and migration. The model shows that surgery-induced changes in TME are the important factors for inducing the critical transition from reactive astrocytes to stem cell-like phenotypes. The model illustrates how variations in glucose availability significantly affect the activity of signalling molecules and, in turn, lead to critical cell migration. The model also predicts that (i) microsurgery of a primary tumour induces phenotypical changes in reactive astrocytes and stem cell-like astrocytes promoting tumour cell proliferation and migration by Cxcl5, (ii) this critical transition essentially increases the recurrence potential of GBM and leads to the low survival rate of patients. Finally, we investigated a new anti-tumour strategy by Cxcl5-targeting drugs in order to prevent this critical recurrence of the tumor.

OTHE: Other Contributed Talks (9:30-11:00am)

Josephine Solowiej-Wedderburn Surrey
"Sensing some resistance: A mathematical model for the contractile mechanosensory mechanism within cells"

It is becoming increasingly clear that physical force and the mechanical properties of their microenvironment play a crucial role in determining cellular behaviour and coordination. Un- derstanding these differences has significant implications for tissue engineering applications and to determine how the mechanical microenvironment may affect, for example, cancer growth and invasion. We use a continuum elasticity-based model with an active contractile component to describe the mechanosensory mechanism of a cell or cell layer adhered to a substrate. The model context focuses on the most common biophysical experimental set-ups investigating cel- lular contractility, which infer the cell-generated force from observed deformations of substrates with experimentally known mechanical properties. The mathematical model is analysed and solved using both analytical approaches (exploiting approximations and symmetry arguments) and Finite Element Methods. We use the model to explain observed cellular adaptations to changes in the mechanical properties of the underlying gel. In particular, we consider the dis- tribution of adhesion throughout a cell. For experimentally realistic distributions of adhesion points, the model is capable of recreating cell shapes and deformations that are consistent with those experimentally observed. Furthermore, energy considerations are shown to have significant implications for the optimisation of cell adhesion. Thus, we demonstrate the neces- sity of considering the whole cell-substrate system, including the patterning of adhesion, when investigating cell stiffness sensing.

Ashlee N. Ford Versypt Oklahoma State
"Investigation of Short Chain Fatty Acids on the Gut-Bone Axis: From Mechanism to a Computational Systems Approach"

Short chain fatty acids produced by the microbial community in the gut play a role in regulating the immune system. Butyrate is a specific short chain fatty acid that can be modulated through diet. In this collaborative project, we seek to formulate a series of ordinary differential equations to provide a mechanistic description of the dynamic effects of butyrate on cells of the immune system locally in the intestine and on bone health through systemic consequences. The team involves three mathematical biologists with chemical engineering backgrounds and an experimental collaborator with expertise in the physiological interactions between the digestive, immune, and musculoskeletal systems.

Shaza Alsibaai McGill University
"Mathematical Modeling of Human Erythropoiesis"

As red blood cells (RBCs), also called erythrocytes, are known for their vital function of transporting oxygen to tissues, their production rate unsurprisingly depends on the tissues need for oxygen (hypoxia). The hormone erythropoietin (Epo) is the main factor regulating erythropoiesis, the process by which erythrocytes are produced. In adult humans, Epo is produced principally in the kidney and released in response to hypoxia in order to stimulate the production of more erythrocytes. Patients suffering from severe kidney impairment therefore under-produce RBCs and subsequently suffer from severe anemia. Exogenous administration of synthetic Epo is required, but what is the optimal dose, and how frequently should it be given? To even begin to address such questions, and to understand the underlying process requires a mathematical model. We develop a model consisting of two delay differential equations that reflects the effect of Epo on increasing the production rate of erythrocytes by preventing the apoptosis of its precursor cells. The explicit modelling of the Epo concentration will allow for later use of the model in the case of exogenous dosing of Epo. We analyse our proposed model, and as expected, are able to prove the non-negativity of solutions and the existence of a unique steady-state solution for the system which represents the normal number of mature erythrocytes and the concentration of Epo for a healthy human. We find a simple condition on the other parameters under which the steady state is locally asymptotically stable for arbitrary large delays. When this parameter condition is violated we show that the steady state is stable for small delays and loses its stability through a Hopf bifurcation.

Torbjörn Lundh Gothenburg
"Möbius invariances in biology"

We will discuss several examples where using the extension of our rigid transformations to the class of Möbius mappings will gain insights into both the morphogenesis and dynamic use of anatomical features in fungi, mammals and especially primates. The examples will range from 'Growth and Form' to data augmentation in AI.

Jessica Crawshaw U. Melbourne
"Examining the mechanical forces driving vascular regression using a fluid-structure-growth model"

Vascular regression is a critical process concluding the maturation of developing capillary networks, in which redundant blood vessels are removed. Recent research suggests that forces from the local blood flow (haemodynamic forces) trigger polarized endothelial cell migration against the flow, resulting in capillary collapse and regression. However, vascular regression is also driven by several additional pathways including local adhesion forces and cellular signalling factors. Due to the delicate nature of these microvessels, it is difficult to experimentally untangle the roles of each pathway during vascular development. As such, the development of computational models to analyse the relationship between the local haemodynamic forces and the surrounding vasculature during regression are invaluable. In this talk, we will present a novel computational framework to mathematically study and isolate the role of haemodynamic and adhesive forces in vessel deformation and endothelial cell migration during vascular regression. To model regression, we describe the capillary wall as a discretised hyperelastic membrane, hosting a multicellular model of endothelial cells. The capillary wall and the endothelial cells interact with and respond to the local blood flow in an iterative manner, creating a coupled fluid-structure growth simulation. This discrete approach provides a natural framework to consider the relationship between the capillary wall and the local blood flow, and allows for the easy inclusion of structural heterogeneities across the capillary wall. Using this model we are able to examine the relative roles of the haemodynamic forces and the local adhesion forces in vascular regression, and the network level ramifications of local regression.

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

Sharon Bewick Clemson University
"Nested Metapopulations"

Metapopulation theory has a long history in ecology, where it is used to describe the dynamics of organisms that frequent patchy and ephemeral habitats. Recently, metapopulation theory has been used to model host-associated microbiomes, with hosts acting as patches, and microbes as dispersing organisms. Extending this framework to scenarios where the hosts themselves exist as metapopulations gives what we term 'nested metapopulations'. Although similar models have been studied in epidemiology, the focus is typically the effect of limited dispersal among patches on disease spread. What is not considered, however, is the other key premise of ecological metapopulations - frequent extinction events at the patch scale. We explore models of nested metapopulations, focusing on how host-scale metapopulation structure and microbe-scale metapopulation structure interact to govern the distribution of microbes across both hosts and the habitat patches in which they live.

Lihong Zhao University of Idaho
"Eco-evolutionary Dynamics of Microbial Communities"

Microbes form complex communities which have profound effects on host health status. Understanding the evolutionary dynamics of microbial communities is a key step towards the goal of manipulating microbiomes to promote beneficial states. While interactions within a microbial community and between microbes and their environment collectively determine the community composition and population dynamics, we are often concerned with traits or functions of a microbiome that link more directly to host health. To study how traits of a microbiome are impacted by eco-evolutionary dynamics, we recast a classic resource-mediated population dynamic model into a population genetic framework which incorporates traits. Using simple communities as example, we illustrate how natural selection, mutation, and shifts in the environment work together to produce changes in trait values over time.

Erida Gjini Instituto Gulbenkian de Ciência
"A critical transition in N-strain co-colonization dynamics"

Interacting systems with multiple strains generate epidemiological, ecological and evolutionary dynam- ics. These dynamics are typically hard to analyze, especially for high number of strains and population structure. Diversity in interaction traits enables the strains to create dynamically their niches for growth and persistence, ‘engineer’ and respond to their common environment. How such a network of interactions with others mediates collective coexistence remains hard to understand, and integrate with intervention effects such as drugs and vaccines. Furthermore, the gradients shaping stability and complexity in such systems remain poorly understood. In a mathematical study, we present a new analytic framework for an N-strain SIS epidemiological system with altered susceptibilities to co-colonization/co-infection between strains. We map the multi- strain SIS dynamics to a replicator equation for N frequencies using separation of timescales. This framework enables explicit examination of the key drivers of competition and coexistence regimes in such a system. We find the ratio of single to co-colonization μ critically determines the type of equilibrium and number of coexisting strains. This key quantity in the model encodes a trade-off between overall transmission intensity R0 and mean interaction coefficient in strain space k, and links our model with the stress-gradient hypothesis (SGH) in ecology. I will show how this co-colonization model provides fresh insights for understanding critical transitions in community dynamics potentiated by mean-field and environmental gradients.

Christel Kamp Paul-Ehrlich-Institut
"Kinetic fingerprint of bacterial depletion indicates phage synergy"

Phages are viruses that infect bacteria which leads to complex dynamics depending on their specific, potentially changing life styles: Lysogenic phages integrate into bacterial genomes and propagate through bacterial replication. Lytic phages replicate within their host cells and destroy them during phage release making them highly specific anti-microbial agents. Bacterial and phage population dynamics do not only depend on life styles but also on the details of the infection process of a specific bacterium and corresponding phage: Some phages can enter a bacterium at multiple sites whereas others are restricted to a single or few entry points. Bacteria further defend against phage induced lysis by various mechanisms including adaptive CRISPR-Cas immunity. Generally, the interaction between lytic phages with their corresponding susceptible bacteria is followed by rapid emergence of bacterial resistance against these phages. The time scales for the emergence (and sustainment) of resistance as well as the specific temporal evolution of bacterial and phage population sizes depend on the characteristics both of the specific phage and corresponding bacterial strain. This pattern can be seen as a kinetic fingerprint which gives insights into the underlying dynamics including binding kinetics and mechanisms of bacterial resistance and phage evasion. In studying the interaction between Klebsiella pneumoniae and its corresponding phage we see enhanced inter-phage synergy leading to faster depletion of bacterial populations than expected from simple mass action kinetics. Within our modelling framework we discuss potential underlying mechanisms of phage binding and synergy as well as the relevance of the kinetic fingerprint in characterizing the interaction between bacteria and phages.

David Versluis Leiden University
"Multiscale Modelling of the Colonic Microbiota in Infants"

Nearly immediately after birth, a complex and dynamic ecosystem forms in the human gastrointestinal tract. The characteristics of this system influence the infants health in both the short- and long-term. It differs in striking ways from that found in adults,both in composition and in dynamics. The first few days generally feature an initial dominance of facultative anaerobic species such as Enterobacteriaceae, most often followed by a dominance of anaerobic species, particularly Bifidobacteriaceae. While the influence of oxygen in this succession is often hypothesised, there is no clear view of the impact or mechanism of this influence. We use a multi-scale spatiotemporal model of the infant colon to simulate the effects of variations in initial oxygen concentration on the composition and metabolic activity of the microbiota from birth to three weeks of age. Using flux balance analysis with molecular crowding on a consortium of genome-scale metabolic models from the AGORA project, we calculate species-specific bacterial fluxes for different locations and time points at a high resolution. The resulting fluxes are integrated together into a model of the ecosystem that feeds back into the flux calculations [3]. The model takes into account the nutrition and development of the infant, and can so give insight and produce predictions for the composition and metabolite formation of the infant microbiota over time and under different conditions. We find that the initial presence of oxygen can explain the specific early dominance of Enterobacteriaceae and the succession by Bifidobacteriaceae out of a broad consortium of infant microbiota species. This is derived solely from the genome-derived differences in oxygen metabolism between species, without having to take into account oxygen toxicity. We also show a complex network of spatial separation and metabolic interactions emerging within the infant gut. Our general aim is to reach a deeper understanding of the major metabolic influences, such as prebiotics and nutrition as a whole, on the development of the infant microbiota. This in turn is the first step towards a more comprehensive understanding of the formation of a steady state adult GI-tract microbiota. This research was financially supported by Friesland Campina.

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

Subgroup Keynote

11:15am

David Ho,
Columbia University

Immunobiology & Infection Subgroup

Potent Neutralizing Monoclonal Antibodies Directed to Multiple Epitopes on the SARS-CoV-2 Spike

The SARS-CoV-2 pandemic rages on with devasting consequences on human lives and the global economy. The discovery and development of virus-neutralizing monoclonal antibodies could be one approach to treat or prevent infection by this novel coronavirus. Here we report the isolation of 61 SARS-CoV-2-neutralizing monoclonal antibodies from 5 infected patients hospitalized with severe disease. Among these are 19 antibodies that potently neutralized the authentic SARS-CoV-2 in vitro, 9 of which exhibited exquisite potency, with 50% virus-inhibitory concentrations of 0.7 to 9 ng/mL. Epitope mapping showed this collection of 19 antibodies to be about equally divided between those directed to the receptor-binding domain (RBD) and those to the N-terminal domain (NTD), indicating that both of these regions at the top of the viral spike are quite immunogenic. In addition, two other powerful neutralizing antibodies recognized quaternary epitopes that are overlapping with the domains at the top of the spike. Cyro-electron microscopy structures of one antibody targeting RBD, a second targeting NTD, and a third bridging two RBDs revealed recognition of the closed, “all RBD-down” conformation of the spike. Several of these monoclonal antibodies are promising candidates for clinical development as potential therapeutic and/or prophylactic agents against SARS-CoV-2.

Subgroup Keynote

12:15pm

Adam Martin,
Massachusetts Institute of Technology, @martinlabmit

Cell & Developmental Biology Subgroup

Folding tissues across length scales: Cell-based origami

Throughout the lifespan of an organism, tissues are remodeled to shape organs and organisms and to maintain tissue integrity and homeostasis. Apical constriction is a ubiquitous cell shape change of epithelial tissues that promotes epithelia folding and cell/tissue invagination in a variety of contexts. Apical constriction promotes tissue bending by changing the shape of constituent cells from a columnar-shape to a wedge-shape. Drosophila gastrulation is one of the classic examples of apical constriction, where cells constrict to fold the primitive epithelial sheet and internalize cells that will give rise to internal organs. We have used a combination of imaging, experimental perturbation, and modeling, to determine how actomyosin organization promotes tissue folding. The actin cytoskeleton is organized in both time and space to facilitate apical constriction. We found that actomyosin contraction is pulsatile and requires dynamic regulation of upstream signaling processes. In addition, we found that actomyosin becomes organized into oriented fibers, which generates anisotropic tension that is critical for tissue shape. Furthermore, connectivity within the network of actomyosin fibers is highly redundant, promoting the robustness of folding.

Career Fair

Sub-group contributed talks (1:30-3:30pm)

CDEV: Integrating cell mechanics and cell mechanosensing (1:30-3:30pm)

Ulrich Schwarz University of Heidelberg
"Emergence of elasticity in cell mechanics"

Biological cells adapt shape and behavior to their mechanical environment through an intricate system of mechanotransduction processes. While in highly dynamic situations like development, cell migration or wound healing, cells need to be soft and viscous, in homeostatic situations like maintenance of connective or epithelial tissues, they have to keep stresses and strains for long times, like an elastic material. Because the actomyosin cytoskeleton determining cell mechanics is in a state of constant turnover, achieving effectively elastic behavior is a real challenge for cells. In this talk, I will first discuss the experimental evidence for the elastic behavior of cells, including the invaginated shapes of single cells in connective tissue and the elastic nature of epithelial monolayers as revealed by traction force and monolayer stress microscopy. I then will discuss different mechanisms which allow this elastic behavior to emerge on cellular scales, including the generation of stress fibers, the exchange dynamics of fast and slow myosin motors in myosin minifilaments and their regulation through the Rho-pathway, which can be controlled e.g. by optogenetics. In each case, I will address the fundamental question how multi-scale modeling and homogenization techniques can be used to mathematically connect the microscopic and macroscopic scales.

Fabian Spill University of Birmingham
"Role of physical and geometrical drivers of tumour metastasis"

Cancer mostly kills through metastasis - the process where cancer cells leave the primary tumour and colonialize distant organs. Such movement of cells naturally requires forces. How cells generate forces through molecular pathways is thus an intense field of study. Moreover, it is becoming increasingly appreciated that forces, and other physical properties, not only arise from intracellular pathways, but can also reprogram pathways, for instance, through molecular mechanosensors. I will present recent results obtained from mathematical modelling and experimental work aimed at investigating the interplay of physical, geometrical and molecular drivers of tumour progression. At the example of an endothelial cell monolayer, I will show how forces alter the chemical binding rates of cell-cell adhesions, which consequently can lead to gaps in the monolayer. Experiments show that these gaps can be exploited by cancer cells when transmigrating through the endothelial monolayer - a crucial process during metastasis. I will then present some work on modelling mechano-chemical pathways in cells. Pathways including the YAP/TAZ and Rho signalling pathways are sensitive e.g. to extrinsic factors such as extracellular stiffness, or intrinsic factors such as cellular geometry. The complex interplay of such factors can lead to reprogramming of cells. Consequently, a physically altered tumour microenvironment can activate intracellular pathways and, independent or complementary to genetic changes, alter tumour cells towards more aggressive behaviour.

Carina Dunlop University of Surrey
"Cytoskeletal contractility in mechanosensing"

Cells have been demonstrated to be extremely sensitive to the physical properties of their external environments, changing behaviours as diverse as proliferation, differentiation and migration in response. The mechanism by which this mechanosensing is achieved is broadly understood. Molecular motors em- bedded within the cellular cytoskeletal network bring the network into tension - this contraction is resisted by the cellular adhesion to the external environment with the degree of resistance thus broadly signalling information about the local external stiffness. Great strides have been made in understanding the molec- ular signalling mechanisms mechanisms with research focusing on the focal adhesions, supramolecular adhesive patches, and on pathways such as YAP/TAZ. However, there is emerging evidence of signalling away from focal adhesions including at the nuclear envelope (nuclear mechanotransduction). This necessitates a spatially resolved model of cell stiffness sensing that incorporates intracellular mechani- cal interactions. Here I will present a continuum elasticity model of cellular contractility and stiffness sensing that accounts for the experimentally observed variations in contractile activity within cells. This model demonstrates how on stiff substrates non-uniform contraction will lead to localised regions of internal cell stretch well away from focal adhesions. Additionally where the cell shape is elongated (as is often observed on stiff substrates) this effect is enhanced with increased internal stretch as compared with isotropic cells. These internal strains offer a potential physical mechanism linking physical exter- nal substrate stiffness to stretch activated molecular signalling within the cell and at the nuclear envelope.

Benedikt Sabass Forschungszentrum Juelich
"Substrate durokinesis of the bacterium P. aeruginosa"

Bacteria can generate mechanical forces that are important for the colonization of surfaces, forma- tion of biofilms, and infection of host cells. In Gram-negative bacterial pathogens, such as Pseudomonas aeruginosa, forces result from ATP-hydrolysis-driven extension-retraction cycles of extracellular filaments called type-IV pili. How bacteria adapt their pilus-based behavior to the mechanical environment is not known. Here, we show that the early stage of surface colonization by P. aeruginosa is modulated by substrate-dependent pilus activity. Our experimental data reveals a complex response of the bacterial migration machinery to substrate properties, including adaptation of the dynamics of pili, their spatial arrangement, and their number. The combination of the experimental data with mathematical modeling allows us to construct a comprehensive picture of the stochastic dynamics of pilus-based motion of P. aeruginosa on different substrates. Overall, our findings reveal how mechanoregulation is involved in essential aspects of the migratory behavior of a paradigmatic bacterial pathogen.

IMMU: Subgroup Contributed Talks (1:30-3:30pm)

Sahak Makaryan University of Southern California
"In Silico Control and Optimization of Granzyme B and Perforin-1 Secretion in Natural Killer Cells"

Natural killer (NK) cells are immune effector cells that can detect and lyse cancer cells. NK cell exhaustion, a phenotype characterized by reduced effector functionality, can limit the NK cell’s capacity for cell lysis. The processes mediating NK cell exhaustion are many, unfortunately, rendering a single preventative approach unlikely to be optimal in all cases. In lieu of prevention, we investigated in silico whether the effects of exhaustion can be nullified by strategies that maximize the continuous secretion of effector molecules. Here, we constructed a system of nonlinear ordinary differential equations (ODEs) that describes the dynamics of the cytolytic molecules granzyme B (GZMB) and perforin-1 (PRF1). The model predictions were calibrated to published, experimental data where the model parameters were estimated via the Metropolis-Hastings algorithm. Furthermore, the model was interrogated using an information-theoretic global sensitivity analysis, to determine which model parameters (i.e., inputs) shared a significant degree of mutual information with the secreted amount of effector molecules (i.e., outputs). Interestingly, we found the inhibition of phosphatase activity maximizes the secretion of GZMB and PRF1. We appended the baseline model with a system of ODEs describing a synthetic Notch (synNotch) signaling circuit as a method for controlling the production and secretion of the cytolytic molecules. Briefly, the synNotch receptor is chimeric molecule consisting of a target-ligand specific single-chain variable fragment (scFv) in its extracellular domain, a string of cleavable amino acid sequences in its transmembrane domain and a transcription factor in its intracellular domain. Once bound to a target ligand, the synNotch receptor is cleaved by membrane proteases. This unchains the transcription factor from the cell membrane, and thereby freeing the molecule to initiate gene expression by binding to a plasmid. We included two separate plasmids in the model: (1) a multi-cistronic plasmid coding for the effector molecules and (2) a plasmid coding for a long-noncoding RNA (lncRNA) molecule that binds and sequesters the phosphatase from inhibiting signal transduction. The synNotch model was optimized by determining the optimal quantity of plasmids and synNotch receptor to maximize the secretion of the effector molecules while using the minimum amount of material. We found the optimal synNotch system depends on the frequency of NK cell stimulation: for fewer rounds of stimulation, both plasmids should be given at maximal dose; for many rounds of stimulation, the model predicts only the cytolytic molecule-coding plasmid should be given and at maximal value. This suggests that inhibition of phosphatase activity, while beneficial in the short-term, is not optimal for multiple rounds of stimulation. In total, we developed a theoretical framework that provides actionable insight into engineering robust NK cells for clinical applications.

Naveen Vaidya San Diego State University
"HIV Infection and Antiretroviral Therapy: the Brain as a Reservoir"

It is not fully understood whether the brain acts as an HIV reservoir causing obstacle to cure through treatment. In this talk, I will present a novel mathematical model describing virus dynamics under antiretroviral therapy to study the role of the brain in virus persistence. Using experimental data from SIV infected macaques, we identify key parameters related to the brain infection, including virus-transfer across blood-brain barrier. Our model predicts that the brain can be an important reservoir causing long-term virus persistence in the brain, despite successful control of viral load in the plasma by antiretroviral drugs.

Cristina Leon RUDN University, Russia
"Reaction-diffusion model of viruses coexistence in the space of genotypes"

We propose a mathematical model describing the competition of two viruses, in the host organism, taking into account virus mutation, reproduction, and genotype dependent mortality, either natural or determined by an antiviral treatment. The model describes the virus density distribution u(x; t) for the first virus and v(y; t) for the second one as functions of genotypes x and y considered as continuous variables and of time t. The model consists of a system of reaction-diffusion equations with integral terms characterizing virus competition for host cells. The analysis of the model shows the conditions of virus coexistence or elimination in the host organism. This study continues the cycle of works devoted to reaction-diffusion models of virus mutation and evolution.

Mohammad Aminul Islam Oklahoma State University
"Computational modeling of the gut-bone axis and implications of butyrate treatment on osteoimmunology"

The interplay between gut microbiota and the immune system has a pivotal role in the maintenance of bone health. Recently, short-chain fatty acids (SCFAs) produced by gut microbiota have emerged as key regulatory participants in shaping the immune system. Butyrate, the most versatile among SCFAs, has been observed to have local and systemic effects including inducing the differentiation of peripheral regulatory T cells (Tregs) in the intestine, blood, and bone marrow [1]. Tregs are the central actors of the negative feedback component of the immune system. The interaction between Tregs and cytotoxic CD8+ T cells suppress the inflammatory status and promote the production of Wnt10b to increase bone anabolism [2]. Studies in the mouse models show that the ablation of butyrate in the intestine alters the bone marrow density. However, the therapeutic benefit of butyrate in bone anabolism remains poorly understood. We developed a multi-compartment physiologically based pharmacokinetic model to track and quantify the effects of butyrate on Tregs in the gut, blood, and bone marrow. The model consists of five species butyrate, naive CD4+ T cells, Tregs, TGF-β, and Wnt10b distributed across three compartments intestine, blood, and bone. We consider an open system with the processes of formation, excretion, differentiation, cell death, and migration to another compartment. The variation of butyrate concentration from homeostasis value changes the percentage of Tregs, and the production of TGF-β, and Wnt10b. Using the model, we analyze experimental data reported in [2] to evaluate the expansion of Tregs, TGF-β, and Wnt10b in the bone marrow. The probiotic LGG increases butyrate concentration in the intestine and serum blood by 0.18 μM and 0.29 μM respectively. Our simulation result shows 5% increase of Tregs, 3.4-fold increase of TGF-β, and 3-fold increase of Wnt10b in the bone marrow consistent with the net change information due to stimulus of a probiotic microbiota in the gut. The computational approach described here gives insight into the pharmacokinetics of butyrate, biodistribution of Tregs in the gut-bone axis, fold changes of Wnt10b in bone marrow, and their contributions to modulating bone formation. Research reported in this abstract was supported by NIH NIGMS R35GM133763.

Georges Ferdinand Randriafanomezantsoa Radohery Kirby Institute, University of New South Wales, Sydney
"Incorporating parasite viability data into PK/PD modelling of artemisinin treatment of human malaria"

Malaria is a global health threat killing one child every two minutes. The rise of artemisinin resistance, which is the main component of most recommended anti-malarial regimens, has prompted the need to develop better alternative antimalarial treatments. Modelling plays an important role in the development of these new antimalarial drugs. Pharmacokinetic/Pharmacodynamic (PK/PD) models of antimalarial treatment, which relate drug concentration to parasite killing, are central in assessing and optimizing drug therapy effectiveness. A common assumption in these models is that the parasites that remain in circulation after treatment are all viable. Recently a method was developed to estimate the concentration of viable parasites after artesunate treatment, rather than simply total parasite numbers. Here, we aimed to include this additional parasite viability information into an adapted PK/PD model to more accurately estimate the drug killing rate in sensitive and resistant infections. We use data from volunteers infected with artemisinin-sensitive or resistant P. falciparum blood-stage parasites and treated with a single dose of oral artesunate monotherapy during a volunteer infection study. Parasite qPCR counts before and after treatment, the proportion of viable parasites after treatment and dihydroartemisinin plasma concentration were obtained and modelled using age-structured P. falciparum parasite population growth and a PK/PD model. We use these models for separately measuring parasite killing rate and parasite clearance rate. The addition of viability data into PK/PD model of artesunate monotherapy provided a good fit of the data. The model estimated an in vivo DHA’s EC50 of 1.42 μg/L (95% CI: 0.07, 2.78). In artemisinin-sensitive infections, the parasites mean killing half-life is 0.20 h (95% CI: 0.16 h,0.26 h) and the mean removal half-life of dead parasites was 2.77 h (95% CI: 2.4 h, 3.4 h). Further, we showed that the reduced killing observed in resistant infections were consistent with a 9-fold reduction in the sensitivity of parasites in the first 12 h of the lifecycle, and drug-killed resistant parasites were estimated to be removed slower than drug-killed sensitive parasites. Incorporating parasite viability data into PK/PD models allows refining the estimation of parasite killing rates and provides information on the stage-specific activity of antimalarial drugs in vivo. Killing half-life is faster than previously thought. These differences are likely to have important implications for optimal dosing strategies and predicting overall drug efficacy.

MEPI: Subgroup Contributed Talks (1:30-3:30pm)

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Folashade Agusto University of Kansas
"To isolate or not to isolate: The impact of changing behavior on COVID-19 transmission"

In this talk I will present a model developed for COVID-19 using a system of ordinary differential equation following the natural history of the infection. Using appropriate payoff functions relating to the perception of risk measured using disease incidence and severity of infection the model is coupled to a series of human behaviors including ignoring social distancing, and breaking out of isolation and quarantine. Analysis and simulations of the model show the possibility of multiple waves of infection. Discouraging the population from disease magnifying behavior such as escaping from isolation and quarantine eliminates the multiple waves of infection and greatly flattens the curves.

Alexander Beams University of Utah
"Mask, or JASC? What are the conditions under which SARS-CoV-2 becomes Just Another Seasonal Coronavirus?"

Background: Will SARS-CoV-2 become Just Another Seasonal Coronavirus? It bears some important resemblances with its more benign cold-causing relatives, after all. For example, Coronavirus NL63 uses the same ACE2 receptor to gain entry into cells, and circumstantial evidence suggests Coronavirus OC43 may have caused a pandemic in the late 1800's. Both are now just 'common colds'. Is it possible that SARS-CoV-2 will take the same path? Hypotheses: We are writing models to address how three factors might push SARS-CoV-2 towards JASC. First, evidence suggests asymptomatic cases tend to shed less virus. If viral dose affects disease severity, and vice versa, selection might act to alleviate virulence. Second, we know that kids are far less likely to experience more severe forms of COVID-19, and different disease outcomes in kids vs adults will influence the epidemiology in important ways. Third, the JASC hypothesis might be sensitive to the duration of immunity to SARS-CoV-2. Eventually we hope to consider cross-immunity or interaction with other viruses, including seasonal coronaviruses, with a view to understand the COVID-19 pandemic in the context of the pre-existing respiratory virome. Results: Our models show that JASC is possible if viral dose correlates with disease severity and if immunity is sufficiently strong and long-lasting. We will present analyses of how our three factors influence the long-term outcomes of the pandemic. Conclusions: Although it is too early to say for certain, it is possible that SARS-CoV-2 could persist in humans as another cold-causing virus.

Juan Gutierrez University of Texas at San Antonio
"Modeling COVID-19 Under Lockdown Conditions"

Coronavirus disease 2019 (COVID-19) is a novel human respiratory disease caused by the SARS-CoV-2 virus. Asymptomatic carriers of the virus display no clinical symptoms but are known to be contagious. Recent evidence reveals that this sub-population, as well as persons with mild symptoms, are major contributors in the propagation of COVID-19, a first for a respiratory virus. In another first, COVID-19 caused generalized restrictions to human movement and interactions. In this talk, we will discuss a traditional compartmentalized mathematical model taking into account asymptomatic carriers and lock-down conditions. The theoretical model is used to calibrate a model for the City of San Antonio, Texas.

Diego Volpatto Laboratorio Nacional de Computacao Cientifica
"A Bayesian approach to assess the spread of COVID-19 using an extended SEIRD model with implicit quarantine mechanism: applications in Brazilian locations"

In this work, we develop a generalized SEIRD model that implicitly takes into account the quarantine mechanism to describe the spread of COVID-19 with applications in Brazil. We assume uncertain scenarios with limited testing capacity, lack of reliable data, under-reporting of cases, and restricted testing policy. To deal with data and model uncertainties, we developed a Bayesian framework for the identification of model parameters. A global sensitivity analysis is performed beforehand to identify the most significant parameters on either the cumulative numbers of confirmed and death cases, or the effective reproduction number. Less important parameter values are set according to the current knowledge on the disease in order to overcome the bottleneck of parameter identifiability. We show that the model parameter related to social distancing measures is one of the most influential along all stages of the disease spread and the most influential after the infection peak. Different relaxation strategies of social distancing measures are then investigated in order to determine which strategies are viable and less hazardous to the population. The results highlight the need of keeping social distancing policies to control the disease spread. Specifically, the considered scenario of abrupt social distancing relaxation implemented after the occurrence of the peak of positively diagnosed cases can prolong the epidemic, with a significant increase of the projected numbers of confirmed and death cases. An even worse scenario could occur if the quarantine relaxation policy is implemented before evidence of the epidemiological control, indicating the importance of the proper choice of when to start relaxing social distancing measures. The employed approach and subsequent analysis applied over the Brazilian scenarios may be used to other locations.

Julie Spencer Los Alamos National Lab
"Prioritizing Mitigation Strategies for COVID-19 in New Mexico"

As of July 12, 2020, the novel zoonotic virus SARS-CoV-2 caused 15,028 confirmed infections and 545 deaths in the State of New Mexico. New Mexico ranks as the third highest state in the United States for per capita testing, and the time from identification of a traced contact to quarantine is two days; however, during the past seven days, cases have been increasing by 1.8% per day, leaving open the question of how best to intervene in the epidemic, given limited resources. Recent modeling studies have addressed mitigation strategies for COVID-19; however, there is a need for an age-structured mitigation model that provides pre-symptomatic, asymptomatic, symptomatic, testing, and quarantine compartments. We developed a deterministic, Susceptible-Exposed-Infected-Recovered (SEIR) model to assess the merits of a range of non-pharmaceutical intervention measures. We simulated all combinations of three social distancing levels, six testing levels, three testing turnaround speeds, and four testing accuracy levels, in order to evaluate 216 mitigation scenarios. We found that social distancing and testing are both necessary for decreasing total infections and for delaying the peak of the epidemic. We additionally found that increasing the turnaround speed of test results and decreasing the proportion of false negative tests has the potential to result in 27% fewer infections and 33% fewer deaths over the course of a two-year simulated epidemic. The epidemic outcomes are mitigated more effectively when school-aged individuals have less contact, as when schools are closed or operating virtually, than when working-aged individuals have less contact, as when businesses are closed or operating virtually. These are difficult but important prioritizations. UNCLASSIFIED LA-UR-20-25199

MFBM: Subgroup Contributed Talks (1:30-3:30pm)

David Hardman University of Edinburgh, Scotland, david.hardman@ed.ac.uk
"Optimising muscle cell co-culturing protocol through a combined in vitro-agent based modelling approach"

The Myochip project is a prospective organ-on-a-chip platform co-culturing neurons, muscle cells and endothelial cells to create functional skeletal muscle. Cell culturing involves a wide range of variables and optimal protocols are currently undefined when co-culturing different cell types in vitro. A ‘trial and error’ based experimental approach to optimisation is inefficient and costly and relies on animal-derived in vitro models. We propose a combined and iterative in silico} / in vitro approach to optimising experimental cell culturing protocols using a small number of experiments to validate parametric mathematical models which can in turn be used to predict optimum conditions. Here, we focus on the trade-off between the cell differentiation media required to allow co-culturing of muscle fibres with neurons and optimal muscle cell growth. During myogenesis, myoblast cells fuse together to create multinucleated myotubes which elongate and mature into muscle fibres. Fixed and time-lapse images of muscle cells were acquired throughout the differentiation and early myotube formation phases for cells cultured in muscle differentiation medium, neuron differentiation medium and a 1:1 mixture of both media. Metrics of myoblast migration speed, migration direction and rate of fusion were quantified from time-lapse imaging and used to inform a mathematical agent-based model (ABM) of myoblast motion and fusion. Metrics of myotube growth and alignment over time were quantified and used to validate the ABM output. The validated ABM can then be used to conduct virtual trials in different media conditions in order to ascertain the optimum balance between muscle growth and specialisation of differentiation medium.

Doris Schittenhelm Friedrich-Alexander-Universität Erlangen-Nürnberg Germany doris.ds.schittenhelm@fau.de
"A Bayesian framework for parameter estimation from fluorescence data"

Measurements of fluorescence intensity are a good way of monitoring time-dependent cellular processes, and can be used for estimating parameter of such models. In addition to uncertainty from modelling, experimental set-up and measurement, there is another source of error that needs to be factored in: Crosstalk denotes the interaction of neighboured samples during measurement and cannot be ignored in fluorescence intensity measurement scenarios. In order to quantify the indispensability of crosstalk, we formulate two models for the measurement process: one without crosstalk and one with crosstalk. These models contain a high number of unknowns due to properties of the measurement instrument and of the experimental set-up. Our goal is to identify the most plausible model from given data and assumed measurement uncertainties and use it for parameter estimation afterwards. For this we employ a Bayesian model selection approach where we compute the evidence for either model with the nested sampling algorithm, which is suited for high-dimensional problems. This allows us to simultaneously pick the most favourable model and obtain parameter samples from the posterior.

Endre T Somogyi Indiana University Bloomington, United States, andy.somogyi@gmail.com
"Real-Time Interactive, Scriptable 3D Simulation of Cell / Virus-Like-Particle Endocytosis With Tellurium / Mechanica"

Endocytosis / Exocytosis is one of the more common mechanisms a biological cell uses to transport materials through the cell membrane. Understanding biological responses to cell-membrane / virus-like-particles is a key to developing potential therapeutics and vaccines to viruses. Endocytosis is a cellular mechanism where a cell internalizes substances from the external environment. In endocytosis, external objects such as nanoparticles, virus-like particles (VLP), or chemicals adhere to the cell surface. The cell then envelopes these adsorbed particles typically by wrapping a portion of its own cell membrane around these particles. The adsorbed material then becomes trapped inside the vesicle, effectively becoming a ‘cargo’ or ‘payload’, and the cell transports this vesicle into the cell. In endocytosis, external objects can either adhere directly to the cell membrane with a certain affinity, or they can bind to explicit membrane receptors. There are many unanswered scientific questions when we are trying to better understand the endocytosis process. The realism, the amount of physical detail required in a ‘useful’ model, can differ widely and very much depends on what kinds of questions we ask. For example, do we need to include individual lipids?, explicit individual atoms? Or is it sufficient to have a more coarse-grained model that treats individual VLPs as discrete particles? We are developing tools that will give users the flexibility they need to create multi-scale biophysics models that include different (and therefore more appropriate) levels of physical detail and realism. We present a new particle-based simulation environment, Mechanica, that enables users to interactively create, manipulate and simulate models of biological cells and tissues using physics-motivated python API. Using Mechanica, researchers can explore the kinds of information and ask the questions required to model accurately, say, at a level that sits between coarse-grained molecular dynamics and cell-center models. We present a composite particle based simulation approach where we augment the traditional cell-center-model type cells with explicit surface receptor binding sites, and model explicit external VLP particles, where we have explicit surface receptors that can diffuse about the cell surface, and explicitly bind to external VLPs. We allow VLPs to explicitly bind to surface receptors, and we demonstrate our event model, where users can bind cellular responses such as particle adsorption to events. Our user model description API is based on physical and chemical abstractions which enables a great deal of freedom for our users in the kinds of semantic meaning they ascribe to physical objects. For example, a user could choose to allow one of our ‘particles’ to represent a molecule, nano-particle, cellular organelle, or even a complete cell.

Patrick S. Eastham Florida State University, United States, peastham@math.fsu.edu
"A framework for simulating precipitate reactions in microfluidic devices"

Chemical processes within flows are ubiquitous. There exists an important class of reactions that result in a phase change from liquid to solid: precipitation reactions. Inspired by recent microfluidic experiments, this talk describes a novel mathematical framework for handling such reactions occurring within a slow-moving fluid flow. A key challenge for precipitate reactions is that, in general, the location of the developed solid is unknown a priori. To model this situation, we use a multiphase framework with fluid and solid phases; the aqueous chemicals exist as scalar fields that react within the fluid to induce phase change. To demonstrate the functionality of this framework, we conduct full-scale simulations in a realistic microfluidic geometry. The framework can be applied to precipitate reactions where the precipitate greatly affects the surrounding flow, a situation appearing in many laboratory and geophysical contexts including the hydrothermal vent theory for the origin of life. More generally, this model can be used to address low Reynolds number fluid–structure interaction problems that feature the dynamic generation of solids.

Anastasios Siokis Helmholtz Centre for Infection Research, Germany, anastasiossio@gmail.com
"An agent-based simulation platform studying the immunological synapse dynamics"

During immunological synapse (IS) formation, T cell receptor (TCR) signaling complexes, integrins, as well as costimulatory and inhibitory molecules exhibit characteristic spatial localization. The IS is built around a TCR-peptide-major histocompatibility complex (pMHC) core, and is surrounded by an integrin ring (Monks, et al., 1998). Small immunoglobulin superfamily (sIGSF) adhesion complexes form a corolla of microdomains outside the integrin ring, which is shown to recruit and retain the major costimulatory and checkpoint complexes that regulate the responses to TCR engagement (Demetriou, et al., 2019). The positioning of these molecules drives T cell signaling and fate decision, making forces that govern IS formation of particular interest. To gain insights into the mechanisms underlying molecular reorganization and characteristic pattern formation during IS formation, we developed a general agent-based simulation platform able to test different hypotheses. The simulations suggest the following: 1. A radial gradient of integrin complexes (LFA-1-ICAM-1) in the peripheral supramolecular activation cluster (pSMAC) toward the central SMAC (cSMAC) emerged as a combined consequence of actin binding and diffusion and modified the positioning of other molecules (Siokis, et al., 2018). 2. The costimulatory complexes CD28-CD80 passively follow the TCR-pMHC microcluster centripetal movement, however their characteristic localization in a ring-like pattern around the cSMAC only emerges with a particular CD28-actin coupling strength that induces a centripetal motion (Yokosuka, et al., 2008; Siokis, et al., 2018). 3. sIGSF complexes are passively excluded to the distal aspect of the IS provided their interactions with the ramified F-actin transport network are sufficiently weak (Siokis, et al., 2018; Siokis, et al., 2020). 4. Attractive forces between sIGSF adhesion (such as CD2-CD58) and costimulatory complexes (such as CD28-CD80) relocate the latter from the IS-centre to the corolla (Siokis, et al., 2020). 5. Size-based sorting interactions with large glycocalyx components, such as CD45, explain the sIGSF adhesion corolla `petals' (Siokis, et al., 2020). 6. A short-range self-attraction between sIGSF complexes explain the corolla `petals' (Siokis, et al., 2020). This establishes a general simulation framework that can recapitulate complex pattern formation processes observed in cell-bilayer and cell-cell interfaces. The presented results have implications for the understanding of T cell activation and fate decision.

ONCO: Subgroup Contributed Talks (1:30-3:30pm)

Noemi Andor Moffitt Cancer Center
"Invasion of homogeneous and polyploid populations in nutrient-limiting environments?"

Breast cancer progresses in a multistep process from primary tumor growth and stroma invasion to metastasis. Progression is accompanied by a switch to an invasive cell phenotype. Nutrient-limiting environments promote chemotaxis with aggressive morphologies characteristic of invasion. It is unknown how co-existing cells differ in their response to nutrient limitations and how this impacts invasion of the metapopulation as a whole. We integrate mathematical modeling with microenvironmental perturbation-data to investigate invasion in nutrient-limiting environments inhabited by one or two cancer cell subpopulations. Hereby, subpopulations are defined by their energy efficiency and chemotactic ability. We estimate the invasion-distance traveled by a homogeneous population. For heterogeneous populations, our results suggest that an imbalance between nutrient efficacy and chemotactic superiority accelerates invasion. Such imbalance will spatially segregate the two populations and only one type will dominate at the invasion front. Only if these two phenotypes are balanced do the two subpopulations compete for the same space, which decelerates invasion. We investigate ploidy as a candidate biomarker of this phenotypic heterogeneity to discern circumstances when inhibiting chemotaxis amplifies internal competition and decelerates tumor progression, from circumstances that render clinical consequences of chemotactic inhibition unfavorable.

Parthasakha Das IIEST, SHIBPUR, India
"Optimal treatment strategies with multiple therapeutic approach in Cancer remission: A model based study"

In this talk, a delayed tumor-immune model is proposed and analyzed in the presence of a multi-therapeutic drug. Local dynamics of drug-free steady states are studied and Hopf-bifurcation is observed with delay bifurcation parameter. By formulating a quadratic control based functional, an optimal control problem is constructed with treatments as control variables. The formulation of the functional is aimed at minimizing the proliferation rate of tumor cells and the detrimental effects of injected drugs. Additionally, maximizing the effector cells and maintaining an attributed level of normal cells are also a priority. By applying Pontryagin’s maximum principle, the sufficient and necessary conditions of optimality system are established. The sensitivity analysis of cost functional is performed with different combinations of control variables. The cost-effectiveness analysis is carried out to determine the most cost-effective strategy. The numerical results verify analytical findings and demonstrate that a multi-therapeutic treatment protocol can alleviate tumor burden within a few months of drug administration.

Anna K. Miller H. Lee Moffitt Cancer Center, Tampa USA
"Modeling the spatiotemporal dynamics of the vicious cycle in multiple myeloma"

Multiple myeloma is a cancer characterized by the expansion of plasma cells in the bone marrow and causes bone pain in over 80% of patients. Bone pain occurs as a result of the interaction between myeloma cells and the trabecular bone microenvironment. Bone is a highly dynamic tissue that is maintained in homeostasis through a balance between bone resorption and bone formation. Multiple myeloma tips the balance in favor of bone resorption, creating a “vicious cycle” in which growth factors released by bone resorption leads to increased survival of multiple myeloma cells, which in turn results in more bone destruction. Multiple myeloma is treatable but largely incurable due to the failure of treatment to completely eradicate the disease. Because the interactions between multiple myeloma and the bone microenvironment contribute to the progression of the disease, it is essential to understand the spatiotemporal dynamics of the vicious cycle to improve treatment response. To explore these dynamics, we developed a hybrid agent-based model that is integrated with published data and data generated by the Lynch lab. We simulate the progression of myeloma growth and bone disease, starting from normal bone remodeling dynamics. To test the assumptions of the normal bone model, we perturb model parameters and show that the model is consistent with data from similar in-vivo experiments. We discuss which model assumptions and parameters are necessary to drive the vicious cycle and capture the data from an in-vivo model of multiple myeloma. This computational model provides a foundation to explore how spatiotemporal dynamics between multiple myeloma and bone microenvironment contribute to drug resistance and tumor growth which ultimately has the potential to help improve treatment strategies.

Fabio A. Milner Arizona State University
"A model for acute myeloid leukemia (AML)"

Idasanutlin (RG7388) is a selective MDM2 antagonist showing promising responses in phase 1 studies of relapsed AML. The drug is presently undergoing Phase I and II clinical trials. RG7388 was generally well tolerated, with GI toxicity being the most commonly reported adverse event. In laboratory cultures of MOLM-13 wild type cells it was observed that using increasing dosages of RG7388 led, within 3 months, to a complete replacement of wild type (drug-sensitive) cells by mutant (drug-resistant) cells. We propose a model for the growth of the two strains of cells in such cultures that is designed to elucidate whether the replacement is due to the RG7388 selecting for mutant type cells or rather generating the mutants the TP53 mutant clones.

Inmaculada C. Sorribes Duke University
"Detailed quantitative framework of in silico xenografts implanted with high-grade gliomas reveals novel dosage schedule of several chemotherapeutic agents"

Glioblastoma multiforme (GBM) is one of the most lethal cancers, with a 5-year survival rate below 25%. GBM-associated death rates remain high, in part because the last few decades have produced only modest advances in treatment. Consequently, the standard therapy for GBM remains palliative, rather than curative, and patients ultimately die from this disease. Chemotherapy has proven to be effective against cancers in general; however, in the case of brain tumors, it has failed to produce sustained remission. Developed in collaboration with experimentalists we present a quantitative framework that captures the specific pharmacokinetics and pharmacodynamics of three different chemotherapeutic agents: temozolomide, Avastin, and vincristine. The effect of these drugs is incorporated into a simple tumor growth model and parametrized using clinical data. The resulting models are used to virtually simulate novel dosage schedules for these drugs and predict their potential in improving survival times.

Sara Hamis School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland
"Bridging in vitro and in vivo research via an agent-based modelling approach"

Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and we here propose using an agent-based model to bridge the gap between in vitro and in vivo research. In order to capture the multi-scale nature of cancer, when simulating cancer growth and treatment re- sponses, we use a multi-scale, agent-based model that links individual cell behaviour with the macroscopic behaviour of cell organisation and the microenvironment. We highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development and in finding optimal treatment schedules. In pursuit of hindering the onset of drug resistance in melanoma, we investigate various targeted drug dosing regimens in silico.

OTHE: Other Contributed Talks (1:30-3:30pm)

Eleanor Doman UCL, London
"Investigating the mechanical properties of peripheral nerve tissue using new biomechanical models"

It is estimated that 2.8% of trauma patients suffer damage to the peripheral nerve system leading to potentially permanent disability. The current gold standard treatment for peripheral nerve injury, the nerve autograph, is estimated to have a success rate of 40 to 50% depending on the scale of the injury. New nerve repair options are currently being developed including the use of tissue engineered implants to replace the injured nerve. However for this to be an effective treatment, the implant must match the mechanical properties of the native tissue to prevent additional damage due to the build-up of localised stress. Peripheral nerves are complex structures with mechanical properties that vary with nerve type and along the length of each nerve. Past experimental work has inferred a link between the mechanical properties of nerve and the nano-structural make-up of the nerve. Data on the mechanical properties of living tissue is difficult to obtain, however, the data on structure of the nerve can be obtained from cadavers. Our work therefore focuses on constructing new biomechanical models that predict the mechanical properties of a nerve given structural data. To do this we use asymptotic homogenisation - an analytical technique that exploits differences in spatial scales to solve PDE systems on spatially complex domains. We will discuss our work on constructing general biomechanical models and their specific application to peripheral nerves.

Julia Arciero IUPUI
"Modeling blood flow regulation and tissue oxygenation in the retina"

Glaucoma is a serious ocular disease characterized by damage to retinal ganglion cells that results in irreversible vision loss. Impaired tissue perfusion has been identified as a significant contributing factor to glaucoma. Theoretical modeling provides a useful tool for predicting the effect of several hemodynamic factors on retinal oxygenation. In this study, a heterogeneous model of the retinal arteriolar vascular network is used to show the impact of flow regulation on tissue oxygenation as oxygen demand is varied. The metabolic signal (Si) is implemented as a wall-derived signal that reflects the oxygen deficit along the network, and three cases of conduction are considered: no conduction, a constant signal, and a flow-weighted signal. The model shows that the increases in average tissue PO2 due to a flow-weighted signal are often more significant than if the entire level of signal is increased. This indicates that the heterogeneity of the downstream conducted responses serves to regulate flow better than a constant conducted response. A hybrid model is also presented that combines a heterogeneous arteriolar network with a compartmental vascular network model for the capillaries and veins. This hybrid model combines a wall-derived conducted metabolic response with spatial data from the retinal arterial network to yield improved predictions of retinal tissue oxygenation.

Peter Mortensen Glasgow
"Action potential propagation in a myocyte-fibroblast model of cardiac tissue"

Coupling electrophysiological models of myocytes and fibroblasts is key to understanding the electrical response of fibrotic regions and associated arrhythmias. There has been extensive work on the analysis of these cell-level models which have been upscaled to organ level. However, there is a lack of understanding of the effects of fibroblast coupling has on the spatial propagation of the action potentials. We identify two properties of the degree of fibrosis. Firstly, the number of fibroblasts in relation to the number of myocytes and secondly the geometry of the fibrotic region. Using direct numerical simulations of a monodomain model of fibrous cardiac tissue, we demonstrate that action potentials (APs) slow down as the severity of fibrosis is increased until eventually excitation is fully blocked. We also identify two cases of non-uniform fibroblast distribution. Here direct numerical simulations show that successful AP propagation is dependent on the geometry of the fibrous region and the number of fibroblasts per myocyte.

Katarzyna Rejniak Moffitt Cancer Center
"In silico tools for deconvolution of complex tumor microenvironments: Organoid3D and silicoDCIS"

Malignant tumors are highly heterogeneous in terms of their cellular composition, varying levels of oxygenation, acidity, and nutrients, as well as local changes in the extracellular matrix. Furthermore, tumor tissue and tumor microenvironment properties can dynamically evolve not only during tumor growth but also when anticancer treatments are administered. We developed a suite of computational models to recapitulate the complexity of cancers, especially their physical and chemical microenvironments. These simulation tools were used to: derive hypotheses about the development of ductal microinvasions; formulate hypotheses on relative importance of microenvironmental factors and chemotherapeutic treatments on the growth of organoids derived from a non-tumorigenic breast cell line and its mutants; examine the interactions of tumor cell and stromal cells in co-cultures. The developed in silico tools are versatile enough to be adjusted to other organoid cultures, other tumor tissues and other components of the tumor microenvironment to generate testable hypotheses about tumor progression and response to treatments.

Ruben Perez-Carrasco Imperial
"Effects of cell cycle variability on stochastic gene expression"

Many models of stochastic gene expression do not incorporate a cell cycle description. I will show how this can be tackled mathematically studying how mRNA fluctuations are influenced by DNA replication and cell cycle duration stochasticity. Results show that omitting cell cycle details can introduce significant errors in the predicted mean and variance of gene expression for prokaryotic and eukaryotic organisms, reaching 25% error in the variance for mouse fibroblasts. Furthermore, we derive a negative binomial approximation to the mRNA distribution, indicating that cell cycle stochasticity introduces similar fluctuations to bursty transcription. Finally, I will show how disregarding cell cycle stochasticity can introduce inference errors in transcription rates bigger than 10%.

POPD: Subgroup Contributed Talks (1:30-3:30pm)

Eva Kisdi University of Helsinki
"The evolution of habitat choice facilitates niche expansion"

Matching habitat choice and local adaptation are two key factors that control the distribution and diversification of species. We study their joint evolution in a structured metapopulation model with a continuous distribution of habitats. Habitat choice follows as the outcome of dispersal with non-random immigration, a process always acknowledged yet rarely incorporated into theoretical models. For fixed local adaptation, we find the evolutionarily stable habitat choice as a function linking the probability of settlement to the local environment. When the local adaptation trait co-evolves, the metapopulation can become polymorphic. Our main result shows that coexisting strains with only slightly different local adaptation traits evolve substantially different habitat choice. In turn, different habitat use selects for divergent local adaptations. We thus propose that the joint evolution of habitat choice and local adaptation can facilitate niche expansion via diversification under wide conditions, also when the local adaptation trait evolving alone would attain an ESS restricted to a narrower niche.

Enpei Zhang University of Helsinki
"Evolution of maturation time in a stage structure prey-predator model"

We study the evolution of predator's maturation time. Longer maturation time resulting in stronger adult predator allows the predator to improve predation ability, reduce handling time and increase survival probability. To understand whether two predators can attain a stable coexistence via evolutionary branching of maturation time, we apply the method of critical function analysis to construct three different types of trade-off functions between maturation time with predator's capture rate, handling time and death rate, respectively. A new method to calculate the invasion fitness is applied in non-equilibrium dynamics. Evolutionary branching of maturation time is possible in the cases of capture rate and handling time. The coexistence of two predators induced by branching is evolutionarily stable. In the case of death rate, the monomorphic predator population can evolve to an evolutionarily stable strategy.

Daniel Cooney Princeton University
"PDE Models of Multilevel Selection: The Evolution of Cooperation and the Shadow of Individual Selection"

Here we consider a game theoretic model of multilevel selection in which individuals compete based on their payoff and groups also compete based on the average payoff of group members. Our focus is on the Prisoners’ Dilemma: a game in which individuals are best off cheating, while groups of individuals do best when composed of many cooperators. We analyze the dynamics of the two-level replicator dynamics, a nonlocal hyperbolic PDE describing deterministic birth-death dynamics for both individuals and groups. Comparison principles and an invariant property of the tail of the population distribution are used to characterize the threshold level of between-group selection dividing a regime in which the population converges to a delta function at the equilibrium of the within-group dynamics from a regime in which between-group competition facilitates the existence of steady-state densities supporting greater levels of cooperation. In particular, we see that the threshold selection strength and average payoff at steady state depend on a tug-of-war between the individual-level incentive to be a defector in a many-cooperator group and the group-level incentive to have many cooperators over many defectors. We also find that lower-level selection casts a long shadow: if groups are best off with a mix of cooperators and defectors, then there will always be fewer cooperators than optimal at steady state, even in the limit of infinitely strong competition between groups.

Cecilia Berardo University of Helsinki
"Evolution of density-dependent handling times in a predator-prey model."

The competitive exclusion principle states that in a constant population two species competing for the same limited resource cannot coexist. This cannot be generalised to non-constant populations. In particular, it has been shown that two predator species competing for the same niche can coexist if the population exhibits non-equilibrium dynamics such as limit cycles. In addition to the ecological question, there emerges the problem whether the coexistence of different predator types competing for a single prey is evolutionarily robust and attainable. Geritz et al. [1] used the theory of adaptive dynamics to study the evolution of the handling time in a model with Holling type II functional response. They found that under certain conditions the handling time undergoes evolutionary branching and leads to the establishment of the evolutionarily robust coexistence of two predator types. Essential is the assumption of a trade-off between the handling time and the conversion factor connecting the predator's birth rate to its capture rate. It was found that the predator type with the short handling time dominates in the part of the population cycle where the prey is abundant, while the other type prevails when the prey is rare. Ecologically this makes sense: when the prey density is low, prospects of capturing new prey are diminished and it becomes worthwhile to cling to the prey one has already got despite of its gradually decreasing returns. When the prey is common, however, it is easy to replace the partially spent prey by a new one. In this presentation we derive a Holling type II functional response with handling time that depends on the prey density. The ecological setting raises some considerations on the importance of the mechanistic approach when we look at the functions which model the population dynamics as well as leads to new interesting evolutionary questions. Using the theory of adaptive dynamics, we investigate if at least some level of density dependence is favoured whether or not the population is cycling. A further question is if the density dependence can eliminate the possibility of coexistence of different predator types. This makes sense when a single predator with density dependent handling time dynamically shifts its niche between low and high prey densities depending on the phase of the population cycle in a way that a predator with a fixed handling time cannot.

Maksim Mazuryn Technical University of Denmark
"Diel Vertical Migration as a Mean Field Game"

The phenomenon of diel vertical migration is one of the largest daily movements of marine species where animals remain in deep, dark water during daylight hours to avoid visual predation and migrate to upper levels at dusk to feed. The migration of each organism can be rationalized as a trade-off between growth and survival with strategies as spatial distributions of the populations. The dynamics driving vertical migration have broad implications for fluxes through the food-web predator-pray interactions [2, 4]; for vertical transport of carbon from upper to deeper layers (i.e. the so-called 'biological carbon pump') with implications for global climate. Here, we present progress of ongoing work on a framework for expressing diel vertical migration as a 'vertical game' in terms of partial differential equations. In the model setup we consider a population of animals distributed in the water column. It is assumed that each animal in this game moves optimally, seeking regions with high growth rate and small mortality, avoiding regions with high population density. The Nash equilibrium for this mean field game is characterized by a system of partial differential equations, which governs the population distribution and migration velocities of animals. The derived system of PDEs has similarities to equations that appear in the fluid dynamics, specifically the Euler equations for compressible inviscid fluids. For the established framework we derive a discretized system of equations to solve the PDEs governing this game theoretical model and present results of numerical simulations. The discretization process is based on the spectral collocation method which has exponential convergence rate for smooth enough functions compared to finite difference schemes. This allows us to reduce computational complexity of the discrete version of PDEs. Recent results either doesn't take into account cost of movement [4] or doesn't resolve time continuously [2]. We formulate the equations in continuous time, incorporate costs on excessive movements in our model and illustrate the theory with numerical examples.

Closing Plenary

3:30pm

Carl Bergstrom,
University of Washington, @CT_Bergstrom

Misinfodemic 2020: How quantitative misinformation misleads the public about COVID-19, and what mathematical biologists can do about it.

Most people think they have pretty good bullshit detectors, at least when it comes to advertising hyperbole, weasel words, and politicians’ promises. Quantitative claims are harder: Numbers have the sense of objectivity and precision, and people feel less confident in challenging them. Yet with COVID-19, quantitative epidemiology is on the front page of every newspaper on every day of the week. Shortly before the pandemic broke out, I finished a book on how to spot and refute quantitative misinformation. Every lesson in the book has proven useful during the current pandemic. In this talk, I will present a tour of how misleading numbers, statistics, mathematics, and data graphics have muddied the social and traditional media streams that we all rely upon during COVID. I will give examples of deliberate disinformation, and examples of unintended misinformation around the pandemic. And I will explore how as citizens and as educators we all can promote data reasoning and quantitative literacy.

Schedule for Thursday, August 20

Coffee with friends & colleagues

8:00am

Subgroup Keynote

8:30am

Sub-group contributed talks (9:30-11:00am)

CDEV: The interplay of intracellular pattern formation, geometry, polarisation and mechanics (9:30-11:00am)

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

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

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

NEUR: Rhythms, Sleep, Reward, Vision (9:30-11:00am)

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

OTHE: Other Contributed Talks (9:30-11:00am)

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

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

Subgroup Keynote

11:15am

Subgroup Keynote

12:15pm

Career Fair

Sub-group contributed talks (1:30-3:30pm)

CDEV: Integrating cell mechanics and cell mechanosensing (1:30-3:30pm)

IMMU: Subgroup Contributed Talks (1:30-3:30pm)

MEPI: Subgroup Contributed Talks (1:30-3:30pm)

MFBM: Subgroup Contributed Talks (1:30-3:30pm)

ONCO: Subgroup Contributed Talks (1:30-3:30pm)

OTHE: Other Contributed Talks (1:30-3:30pm)

POPD: Subgroup Contributed Talks (1:30-3:30pm)

Closing Plenary

3:30pm