Thursday, June 17 at 02:15am (PDT)
Thursday, June 17 at 10:15am (BST)
Thursday, June 17 06:15pm (KST)


Recent advances in random and deterministic modeling in biology/health sciences

Organized by: Maria C.A. Leite, (University of South Florida St.Petersburg), Juan Carlos Cortés López (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain), Rafael J. Villanueva Micó (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain)
Note: this minisymposia has multiple sessions. The second session is MS11-CBBS.

  • Francisco Rodríguez (Dept. of Applied Mathematics and Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Spain)
    "Ecohydrological feedbacks, delay responses and random perturbations in mean field dryland vegetation models"
  • Positive feedbacks between increased connectivity and loss of resources are recognized as potential landscape-scale factors driving degradation and desertification in semiarid regions. Common dryland vegetation models exhibit bistability as the result of different mechanisms yielding local positive feedbacks that reinforce the persistence and growth of vegetation patches, with an unstable equilibrium for vegetation separating the stable equilibria of vegetated and desert states. The existence of bistability allows for abrupt transitions between the alternative stable states, the so called catastrophic shifts, either as the result of gradual worsening of the environmental conditions or due to single or randomly distributed perturbations. Using a spatially explicit cellular automata (CA) dryland model, it has been shown that feedbacks between vegetation pattern and resource loss, measured through an index of spatial bare soil connectivity (Flowlength, FL), dramatically decrease ecosystem resilience and restoration potential. In this work, we considered mean field approximations to this CA model and other common dryland models, and showed that positive global ecohydrological feedbacks mediated by bare-soil connectivity, as captured by the expected value of the FL index, effectively decrease resilience and suffice to induce bistability in absence of additional local feedbacks. We also explored how the presence of delayed responses could affect recovery after random perturbations.
  • Sandra Delgadillo (Universidad Autónoma de Aguascalientes, México)
    "Full probabilistic analysis of random first-order linear differential equations with Dirac delta impulses (Pre-recorded)"
  • In this talk, we address, from a probabilistic standpoint, a first-order linear differential equation with an infinite train of Dirac delta impulses. We consider that all its initial condition and coefficients are absolutely continuous random variables with a joint probability density function. We take extensive advantage of the Random Variable Transformation method to determine, first, an explicit expression for the probability density of the solution stochastic process. Secondly, of the random sequences for the maxima and minima for the case, the impulses application times are evenly spaced, with period $T$. From these sequences, we determine the probability of stability of the solution stochastic process. All the theoretical results are illustrated by means of several numerical examples. Finally, we briefly discuss the results of a sensitivity analysis performed, via Sobol indexes, for a fixed and random period T.
  • Carlos A. Braumann (Department of Mathematics & CIMA, Universidade de Évora, Portugal)
    "Harvesting optimization in a randomly varying environment"
  • We can describe the dynamics of a harvested population in a randomly varying environment by stochastic differential equations models. Previously [N.M. Brites and C.A. Braumann (2017), Fisheries Res. 195: 238-246; N.M. Brites and C.A. Braumann (2019), Fisheries Res. 216: 196-203], we have compared the profit performance of two harvesting policies, the optimal policy (with variable harvesting effort) and the optimal sustainable policy (with constant harvesting effort). The former is inapplicable in practice due to the fast and abrupt variations of the harvesting effort associated with the frequent environmentally induced variations in population size. Furthermore, it requires the knowledge of the population size at each instant - an inaccurate, lengthy, and expensive task. The optimal sustainable policy considers the application of a constant harvesting effort and, under suitable conditions, leads [see, in a more general setting, C.A. Braumann (1999), Mathem. Biosc. 156: 1-19], to population sustainability and the existence of a stationary probability density. This policy has the advantage of being easily applicable and there is no need to estimate the population size. The performance of the two policies was compared in terms of profit over a finite time horizon. Using data based on real harvested populations and the usual logistic and Gompertz growth models, we show that there is only a slight reduction in profit by using the optimal sustainable policy (based on constant effort) instead of the inapplicable optimal policy (based on variable effort). We also present here stepwise effort policies [introduced in N.M. Brites and C.A. Braumann (2019), Stat. Optim. Inform. Comp. 7(3): 533-544], which are applicable, and compare them with the previous policies. Extensions to Alee effects models can be seen in N.M. Brites and C.A. Braumann (2020), Appl. Stoch. Models Bus. Ind. 36: 825–835. Acknowledgements: Carlos A. Braumann belongs to the research center CIMA - Centro de Investigação em Matemática e Aplicações, Universidade de Évora, supported by FCT (Fundação para a Ciência e a Tecnologia, Portugal), project UID/04674/2020. Nuno M. Brites was partially supported by the Project CEMAPRE/REM - UIDB/05069/2020 - financed by FCT/MCTES through national funds.
  • Roberto Ku-Carrillo (Universidad Autónoma de Aguascalientes, Mexico)
    "On a linear random differential equation with periodic harvesting and migration"
  • process. Given the abundance of evidence that evolution is not strictly

Mathematical approaches to vascular biology

Organized by: Jessica Crawshaw (The University of Melbourne, Australia), James Osborne (The University of Melbourne, Australia), Lowell Edgar (The University of Edinburgh, Scotland)
Note: this minisymposia has multiple sessions. The second session is MS18-CDEV.

  • Alys Clark (The University of Auckland, New Zealand)
    "What drives vascular remodelling in the uterus in pregnancy? Vascular adaptions to elevated blood flow."
  • During pregnancy, the placenta transfers nutrients between the mother and the developing fetus. To do this it must establish a supply of nutrients from the mother’s circulation in the uterus, and so it adapts the maternal blood vessels of the uterus to carry increasing volumes of blood to its surface. If this process does not occur as it should, it can lead to pregnancy complications such as fetal growth restriction. Uterine vascular adaption occurs due to changes in mechanical forces acting on the blood vessel walls (with increases in blood flow), changes in the structure of the vascular walls (termed outward remodelling) and changes in the hormonal environment of the uterus. This occurs in a multi-scale manner, with adaption at each level in the circulatory network potentially impacting up and downstream function. Here we present data-driven mathematical models of uterine vascular adaption that aim to tease apart the impact of individual contributors to function in a healthy pregnancy. We show that small radial arteries that are potential rate limiters for the volume of blood that can be delivered through the uterus in pregnancy, adapt to be more compliant in rodent pregnancies, and that arteries from rodent pregnancies are more robust to increases in flow without vasoconstriction than outside of pregnancy. Finally, we demonstrate how quantitative descriptions of vascular anatomy and numerical simulations can help to translate data from rodent models to human pregnancies at the organ scale.
  • Richard Clarke (The University of Auckland, New Zealand)
    "Understanding the mechanical impact of the endothelial glycocalyx’s microstructure"
  • The Endothelial Glycocalyx Layer (EGL) is a thin, brush-like layer that coats the inside of blood vessels. It is believed to serve as a protective barrier against excessive fluid shear, as well as perform a number of other biological functions, such as mechanotransduction. The fragile nature of the EGL, however, makes it very difficult to examine experimentally, and so theoretical models can provide interesting and useful insights. In the past the EGL has been modelled as an isotropic, homogeneous porous layer. However, there is an increasing volume of evidence to suggest that the EGL has a microstructural organisation that brings in to question this assumption. In this talk I will explain some of our recent work using Homogenisation Theory to explore the connections between the EGL’s microstructure, and its bulk macroscopic properties.
  • Michael Watson (The University of Sydney, Australia)
    "A Multiphase Model of Cap Formation in the Atherosclerotic Plaque"
  • Atherosclerosis is characterised by the growth of fat-filled plaques in the artery wall. In advanced disease, vascular smooth muscle cells (SMCs) enter the plaque and deposit a cap of fibrous tissue over the fatty plaque core. The fibrous cap isolates the thrombogenic plaque material from the bloodstream and prevents the formation of blood clots that cause heart attacks or strokes. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance remain poorly understood. In this talk, I will discuss recent work on modelling the dynamics of cap formation. We use multiphase PDEs with non-standard boundary conditions to simulate plaque SMC migration and tissue remodelling in response to endothelium-derived growth factors. The model results reproduce several observations from experiments in atherosclerosis-prone mice and provide novel insight into the relationship between fibrous cap stability and cap region SMC numbers.
  • Fabian Spill (The University of Birmingham, England)
    "Organisation and dynamics of the microvasculature"
  • The microvasculature is a highly dynamic organ. Naturally, during its formation, blood vessel cells move, divide and form networks. Interestingly, the cells maintain dynamic features after the formation of stable networks, where they move around, exert forces on neighbouring cells and extracellular matrix, and form gaps in between the cells. These gaps are critical for the passage of fluid or transmigrating cells. The latter is a critical feature for the immune system, where immune cells need to cross the vasculature into surrounding tissues to reach sites of infection. It is also a deadly process, where cancer cells cross the vasculature during metastasis. I will discuss some ongoing work on characterising 3D microvascular networks through image analysis and extracting relevant features such as transport capabilities. The analysis shows how network formation depends on conditions such as extracellular matrix. Next, I will discuss a model of blood vessel cell dynamics that can predict how gaps in between the cells form, in dependence on forces and adhesion properties. Experiments validated the model predictions and indicate that these gaps can be exploited by metastasising cancer cells that cross the vasculature to invade surrounding tissues.

Image Analysis and Machine Learning for Bio-Medical Applications

Organized by: Amit Roy-Chowdhury (University of California, Riverside), G. Venugopala Reddy (University of California, Riverside)
Note: this minisymposia has multiple sessions. The second session is MS16-DDMB.

  • Henrik Jonsson (Cambridge Sainsbury Laboratories, UK)
    "Integration of live imaging and spatial modelling in plant development"
  • The shoot apical meristem is a stem cell niche providing cells to the continuous development of new flower organs. By using live imaging we can track individual cells over several days of the meristem and flower development and by combining molecular markers into a single organ, we can address questions of regulatory aspects of patterning and morphogenesis. I will present how we use this to evaluate existing hypotheses for the regulation of gene expression and growth and how we can evaluate novel hypotheses in parallel at a large scale.
  • Anuradha Kar (ENS-Lyon, CNRS, France)
    "Deep learning for cellular segmentation in 3D confocal images"
  • Confocal microscopy is a prominent mode of imaging plant tissue surfaces and deeper cellular layers. Confocal images of plant organs are used to create three-dimensional digital models of the tissues with cellular resolution using image analysis algorithms. These digital models are the foundations for quantitative analysis of plant morphogenesis, lineage construction and understanding gene functions and expression patterns. The first step towards creating a 3D representation of a tissue from confocal images is the task of cellular segmentation in which each cell within an image is to be identified as an independent 3D object . Several computational methods for 3D cell segmentation have been developed over the years, a prominent one being the watershed technique. However, this method requires manual tuning of its parameters and its accuracy is frequently affected by poor signal and noise levels in the image. In recent times, cell segmentation pipelines using advanced computational algorithms known as deep learning have emerged which have demonstrated high accuracy and automatic segmentation capabilities even in poor quality images. In this presentation , we will look into the concept of several such deep learning based segmentation pipelines and see how they can be trained to perform 3D segmentation of confocal images of floral meristems. We will discuss their pros and cons and present our tools and libraries which may be used for quantitative and visual comparison of the performances of such emerging deep learning based segmentation techniques.
  • Richard Smith (Univ of Koln, Germany and John Innes Center, Norwich, UK)
    "Quantifying life on surfaces with MorphoGraphX"
  • How an organism achieves its shape is a fundamental question in developmental biology. Form emerges from the interaction of genetic and mechanical processes that drive changes in the geometry of cells and tissues. Ideally it would be great to quantify the evolution of cell shape, proliferation and gene expression in full 3D, however this is often technically challenging. 2D planar projections are sometimes an option, however they do not work on highly curved organs. Our lab has developed MorphoGraphX ( a software that bridges this gap by enabling image processing directly on curved surfaces, what we informally refer to as 2.5D images. Many developmental processes happen on surfaces, such as in the epidermal layer of cells in plants or on epithelial layers in animals. Once cells are segmented, they require annotation, it is not just enough to know the positions and shapes of 100s or 1000s of cells, we need to also know where they are in the organism or organ, in order to decipher how they are responding to developmental signals. Organs are thought to be patterned genetically by gradients of morphogens and that determine growth rates and cell and tissue polarity. Not unlike genomic sequence data, which is of little use without annotation, knowledge of the cells' position and polarity within the organ they are developing is key to make sense of the data. Here I will present an array of tools we have developed in MorphoGraphX to annotate cells with positional information, both for 2.5 and full 3D images.
  • Albert Do (University of California, Riverside)
    "Multiscale modeling of the Arabidopsis shoot meristem signaling network"
  • Growth in plants is coordinated by collections of undifferentiated cell clusters known as meristems. These meristems in turn are coordinated by highly complex regulatory networks. The WUSCHEL (WUS) transcription factor is a key regulator in the shoot apical meristem governing above ground growth. One of WUS‚Äôs most important targets is the CLAVATA3 (CLV3) signaling peptide. WUS and CLV3 have a complex bidirectional relationship both upregulating and repressing each other that does not easily fit within standard regulatory paradigms. To model this relationship, a hybrid system of meristem signaling consisting of deterministic ODE based and stochastic based dynamics was constructed. The ODE portion models protein/RNA dynamics while the stochastic portion models the binding of WUS to the CLV3 gene regulatory region/cis regulatory module (CRM). This deterministic/stochastic model is able to accurately replicate expression patterns seen in experimental data, generate data that fits what is known about the biology in scenarios that have not yet undergone rigorous wetlab analysis, and provides a way to directly observe the dynamics of WUS binding patterns on the CRM.

Translational effects of trait changes in aquatic ecosystems

Organized by: Hanna Schenk (German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig; Leipzig University, Germany), Michael Raatz (Max Planck Institute for Evolutionary Biology, Germany)

  • Ken H. Andersen (Center for Ocean Life, Natl. Inst. of Aquatic Resources, Technical University of Denmark, Denmark)
    "Using size-spectrum models to address global food security"
  • Our assessments of the biomass, production, and future trajectory of fish communities on a global scale relies on process-based models calibrated to observations. The scarcity of observations in the vast oceanic regions places a large burden on the quality of the process descriptions that underpins model predictions. Here I review a novel class of trait-based “size spectrum” models that simulate fish communities and their response to fishing. Size spectrum models are based around predator-prey interactions between smaller prey and larger predators. The models resolve the growth of individuals from eggs, with a size of around 1 mg, to the size of adults. All physiological processes are parameterized with respect to the size of individuals. Differences between species are represented by the maximum size, which varies from 1 g for small meso-pelagic fish to 100’s of kg for large pelagic predators like tuna. The models are in the form of coupled partial differential-integro equations that can be solved efficiently with standard techniques. I will show examples of how size spectrum models simulates regional fish communities or the global biogeography of fish biomass, and how they are used for strategic fisheries management and climate change projections.
  • Andrea Campos Candela (The Leibniz-Institute of Freshwater Ecology and Inland Fisheries (IGB), Germany)
    "Towards a mechanistic understanding of phenotypic trait changes, adaptive behaviour and life history based on dynamic energy budgets"
  • Understanding phenotypic trait changes in spatial and temporal environmental gradients needs understanding the fitness consequences of phenotypic trait variation. This challenge requires connecting behavioural and physiological traits that mediate survivorship and reproductive success with the environmental context. Mechanistic frameworks such as the Dynamic Energy Budget (DEB) theory linking individual internal state dynamics with immediate changes in environmental conditions offer a new perspective to improve such understanding. Drawing on first bioenergetics principles informed by DEB theory, I present a dynamic state-dependent behavioural and life history model to explore the optimal strategies that maximize fitness in ecological contexts varying in food availability and predation risk. Novel contributions of this framework are manifold: 1) I encourage the use of DEB theory in the adaptive context to meet mortality payoff functions integrating ecological extrinsic risks as predation; and, specifically 2) explore the behavioural processes of energy acquisition and the bioenergetics processes of energy mobilization and energy allocation, that 3) together link emerging optimal phenotypic traits with individual internal and external states. Finally, 4) by assuming state-dependent dynamic trade-offs, DEB primary parameters can be dynamic during ontogeny, which breaks down the fixed rules within DEB while opening an interesting research line for future model developments. Results within the exploratory simulated scenarios support that processes related with energy mobilization and allocation can absorb more of the selective pressure driven by the extrinsic risk of mortality, while the process related with energy acquisition strongly correlates with food. I would like to motivate debate about feasible ways of extending this framework, with a physiological and mechanistic-based perspective, to more complex and meaningful scenarios.
  • Maite Erauskin-Extramiana (AZTI BRTA, Spain)
    "The influence of climate change and fishing pressure in global top predator abundance and body size in the future"
  • Tunas and billfishes are the main large pelagic commercial fished species. Tunas comprised around 5.5 million tonnes and USD 40 billion in 2018, being an economically important contribution to many nations. Tuna stocks are well covered by management assessments which estimate that 13% of the stocks are still overfished and 22% are at intermediate levels. Climate change studies and projections forecast that current global fish catches might decrease by the end of the century. However, there are sparse studies and projection for the higher trophic levels where tunas and billfishes belong. A combined Size-Spectrum and Dynamic Bioclimatic Envelope Model (SS-DBEM) was used to project the effects of climate change and fishing for 19 globally distributed large pelagic fishes under climate change (RCP 2.6 and 8.5) and fishing scenarios (0.8 to 1.2 times Maximum Sustainable Yield, MSY). The results suggest that high trophic level species will be more impacted by climate change than by fishing pressure if kept close to the Maximum Sustainable Yield. Projected impacts trends were more driven by species sizes than by the group they belong to. There are mixed responses of main commercial tuna stocks biomass by RFMOs with projections of decreases up to 43% and increases up to 68% by 2050, whereas some stocks can have higher increases up to 168% by 2100. Furthermore, their size is expected to decrease 15% on average by 2050 and 10% by 2100 except for the yellowfin East Pacific stock. Price and demand are often driven by body size, therefore this can reduce the revenue by the fishing industry due to climate change even in stocks that benefit from an increase of biomass. Industry can adopt adaptation strategies such as increase value of their products through added value processing to increase revenue with the same catches, or reduce fuel consumption and time at sea with higher digitalization and the use of decision support systems to reduce searching time and optimize routes considering environmental conditions, or through certified sustainability actions. Reducing fuel reduction would be also a mitigation measure to climate change since it reduces vessels emissions, i.e. a win-win for industry and the environment.
  • Hanna Schenk (German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig; Leipzig University, Germany)
    "Optimal harvest of evolving fish"
  • A side effect of targeting large fish is a strong selection pressure on a smaller size at maturation. This has resulted in fisheries-induced evolution of earlier maturation in several fish species. Due to life-history trade-offs fish that mature at a younger age also grow more slowly. The fisheries-induced evolution thus reduces the economic benefits for fisheries, especially as large fish are proportionally more valuable than small fish. We include these processes in an economic-ecological-evolutionary demographic fishery model to study economic implications of fisheries-induced evolution and to derive optimised fishing management strategies. Economic benefits of fishing depend on the size structure of catches, as prices depend on the size of the fish caught. Economic costs of fishing depend on the size of the fish population and the gear. We apply the model to the North Sea cod fishery and find that the optimal fishing strategy is sensitive to discounting. Whereas for a low discount rate the optimal strategy is to rebuild a population structure with late maturation and strong growth the optimal strategy for a high discount rate would not attempt to reverse the fisheries-induced evolution and rather continue to fish on the evolved population.

Recent developments in phylogenetic network reconstruction and beyond

Organized by: Guillaume Scholz (University of Leipzig, Germany), Katharina Huber (University of East Anglia, United Kingdom)
Note: this minisymposia has multiple sessions. The second session is MS11-EVOP.

  • Steven Kelk (Maastricht University, The Netherlands)
    "Quantifying the dissimilarity of trees using phylogenetic networks and data reduction"
  • Purely topological methods for constructing rooted phylogenetic networks often operate by puzzling multiple incongruent trees together in a parsimonious fashion. Early results in this area established a link between the construction of networks and distance measures on pairs, or sets, of trees. In some cases 'pre-network' distance measures turned out to have an unexpected relevance when applied to network construction. Interestingly, it is not only the case that distance measures can help in constructing networks. In this talk I give a brief summary of recent work in which networks are used 'backwards' to establish improved results for the computation of computationally intractable distance measures. I will focus in particular on using networks to develop aggressive kernelization (i.e. data reduction / pre-processing) rules for computation of the NP-hard TBR (Tree Bisection and Reconnect) distance, and present some empirical results demonstrating the impact of these aggressive rules in practice. This is based on ongoing joint work with several authors.
  • Mike Steel (University of Canterbury, New Zealand)
    "Ranked tree-child networks"
  • Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics. Although these networks have a number of attractive mathematical properties, many combinatorial questions concerning them remain intractable. However, endowing these networks with a biologically-relevant ranking structure yields mathematically tractable objects, which we term ranked tree-child networks (RTCNs). We explain how to derive exact and explicit combinatorial results concerning the enumeration and generation of these networks. We also explore probabilistic questions concerning the properties of RTCNs when they are sampled uniformly at random. These questions include the lengths of random walks between the root and leaves (both from the root to the leaves and from a leaf to the root); the distribution of the number of cherries in the network; and sampling RTCNs conditional on displaying a given tree.
  • Marc Hellmuth (Stockholm University, Sweden)
    "From modular decomposition trees to rooted median graphs"
  • The modular decomposition of a symmetric map $deltacolon Xtimes X to Upsilon$ (or, equivalently, a set of symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features of $delta$ in labeled trees. A map $delta$ is explained by a vertex-labeled rooted tree $(T,t)$ if the label $delta(x,y)$ coincides with the label of the last common ancestor of $x$ and $y$ in $T$, i.e., if $delta(x,y)=t(lca(x,y))$. Only maps whose modular decomposition does not contain prime nodes, i.e., the symbolic ultrametrics, can be explained in this manner. Here we consider rooted median graphs as a generalization to (modular decomposition) trees to explain symmetric maps. We first show that every symmetric map can be explained by ``extended'' hypercubes and half-grids. We then derive a a linear-time algorithm that stepwisely resolves prime vertices in the modular decomposition tree to obtain a rooted and labeled median graph that explains a given symmetric map $delta$. We argue that the resulting ``tree-like'' median graphs may be of use in phylogenetics as a model of evolutionary relationships.
  • Barbara Holland (University of Tasmania, Australia)
    "Modelling convergence and divergence of species in phylogenetic networks"
  • In a 2018 paper we gave a non-technical introduction to convergence–divergence models, a new modelling approach for phylogenetic data that allows for the usual divergence of lineages after lineage-splitting but also allows for taxa to converge, i.e. become more similar over time. We show that these models are sufficiently flexible that they have some interesting identifiability issues. Specifically, we show many 3-taxon data sets can be equally well explained by supposing violation of the molecular clock due to change in the rate of evolution along different edges, or by keeping the assumption of a constant rate of evolution but instead assuming that evolution is not a purely divergent process. Given the abundance of evidence that evolution is not strictly tree-like, this is an illustration that as phylogeneticists we need to think clearly about the structural form of the models we use. For cases with four taxa, we show that there will be far greater ability to distinguish models with convergence from non-clock-like tree models. This talk will describe the convergence-divergence model and discuss some potential applications.

Intravital imaging in immunology: experimental and computational approaches

Organized by: Barun Majumder (University of Tennessee, USA), Soumen Bera (University of Tennessee, USA)
Note: this minisymposia has multiple sessions. The second session is MS18-IMMU.

  • Joost Beltman (Division of Drug Discovery and Safety, Leiden Academic Centre for Drug Research, Leiden University, The Netherlands, The Netherlands)
    "Quantifying the role of T cells in tumor control through computational modeling"
  • Immunotherapies are an emerging strategy for treatment of solid tumors, for example by means of adoptive T cell therapies and stimulation of T cell functionality by specific antibodies. Improved understanding of the mechanisms employed by cytotoxic T lymphocytes (CTL) to control tumors will aid in the development of immunotherapies. CTLs can directly kill tumor cells in a contact- dependent manner or may exert indirect effects on tumor cells via secretion of cytokines. Here, we aim to quantify the importance of these mechanisms in various settings by application of computational models to experimental data acquired in mice. We developed ordinary differential equation models and agent- based models (ABMs) of tumor regression following adoptive transfer of a population of CTLs. Models were parameterized based on in vivo measurements of CTL infiltration over time, tumor volume measurements, and on image-based quantification of rates of tumor cell proliferation and apoptosis. We find that in two different settings direct, contact-dependent killing was insufficient to cause tumor regression and that antiproliferative effects by T-cell-produced cytokines have a large role in tumor control. Thus, our work highlights the potential importance of cytokine-induced antiproliferative effects in T-cell–mediated tumor control.
  • Sachie Kanatani (Johns Hopkins Bloomberg School of Public Health, USA)
    "Comparative intravital imaging of human and rodent malaria sporozoites"
  • Malaria infection starts with the injection of Plasmodium sporozoites into the host's skin. Sporozoites are motile and move in the skin to find and enter blood vessels to be carried to the liver. We present the first characterization of P. falciparum sporozoites in vivo, analyzing their motility in mouse skin and human skin xenografts and comparing their motility to two rodent malaria species. These data suggest that in contrast to the liver and blood stages, the skin is not a species-specific barrier for Plasmodium. Indeed, P. falciparum sporozoites enter blood vessels in mouse skin at similar rates to the rodent malaria parasites. Furthermore, we demonstrate that antibodies targeting sporozoites significantly impact the motility of P. falciparum sporozoites in mouse skin. Though the sporozoite stage is a validated vaccine target, vaccine trials have been hampered by the lack of good animal models for human malaria parasites. Pre-clinical screening of next-generation vaccines would be significantly aided by the in vivo platform we describe here, expediting down-selection of candidates prior to human vaccine trials.
  • Irina Grigorova (University of Michigan Medical School, USA)
    "Studying the role of CCL3 in the interactions between Germinal Center B cells and follicular regulatory T cells"
  • Follicular regulatory T cells (Tfrs) play multiple roles in the control of B cells response. From one side, they repress autoreactive and foreign antigen-specific germinal center (GC) B cells at the peak of GC response. From the other side, they promote GC B cell cycling in IL-10 dependent fashion and ensure optimal affinity maturation. However, which factors direct GC B cell interactions with Tfr cells has been unclear. Based on the single cell and bulk qPCR analysis we found that CCL3 is upregulated in about 10% of CCs that express Myc and are undergoing positive selection. Both ex vivo chemotaxis analysis and multiphoton intravital imaging suggests that CCL3 produced by GC centrocytes (CCs) promotes their direct contacts with Tfr cells. qPCR and transwell analysis revealed expression and synergistic involvement of CCR5 and CCR1 chemokine receptors on Tfr cells in their chemotaxis to CCL3. Both an adoptive transfer and mixed bone marrow chimeras models suggest that at the peak of GC response CCL3 promotes moderate repression of GC response. However, after the peak of GC response B cell-intrinsic production of CCL3 promotes prolonged participation of B cells in GCs, affinity maturation, as well as better memory and plasmablast response. To summarize, our studies suggest the existence of the local chemotactic cues between B cells and Tfr cells within GCs that direct interactions between the cells and are important for optimal regulation of GC response.
  • Barun Majumder (Department of Microbiology, University of Tennessee Knoxville, USA)
    "Correlation between speed and turning naturally arises for sparsely sampled cell movements"
  • Mechanisms regulating cell movement are not fully understood. One feature of cell movement that determines how far cells displace from an initial position is persistence, the ability to perform movements in a direction similar to the previous movement direction. Persistence is thus determined by turning angles between two sequential displacements. Recent studies found that a cell's average speed and turning are negatively correlated, suggesting a fundamental cell- intrinsic program whereby cells with a lower turning ability (i.e., larger persistence) are intrinsically faster. Using simulations, we show that a negative correlation between the measured average cell speed and turning angle naturally arises for cells undergoing a correlated random walk due to sub- sampling, i.e., when the frequency of sampling is lower than frequency at which cells make movements. Assuming heterogeneity in persistence and intrinsic speeds of individual cells results in a negative correlation between average speed and turning angle that resembles experimentally observed correlations. Changing the frequency of imaging or calculating displacement of cohorts of cells with different speeds resulted in similar results whether or not there is a cell- intrinsic correlation between cell speed and persistence, and we could find many different parameter sets that allow to approximately match experimental data binned into cell cohorts. Interestingly, re-analysis of data of T cells in zebrafish showed that the observed correlation between persistence and speed is highly sensitive to sampling frequency, disappearing for coarsely sampled data. Our results thus challenge an established paradigm that persistent cells have intrinsically faster speeds and emphasize the role of sampling frequency may have on inference of critical cellular mechanisms of cell motility.

Modelling the transmission of COVID-19 in indoor spaces

Organized by: Raquel González Fariña (Cardiff University, United Kingdom), Katerina Kaouri (Cardiff University, United Kingdom)

  • Christian Kähler (Universität der Bundeswehr München, Germany)
    "From droplets to pandemic – how to prevent SARS-CoV-2 infections via droplets and aerosols"
  • The SARS-CoV-2 pandemic is currently presenting humanity with major challenges. Containing the spread of the virus requires enormous financial, technical and social efforts, and it is impossible to predict how well humanity will cope with the problem. Since the infectious disease not only has an acute course, but can also cause long-lasting systemic damage to infected individuals, prevention of infection is most important. It is generally accepted that the transmission of viruses is largely via droplets and aerosol particles. Therefore, the question of how these aerosol particles are generated and released and how they spread through the room and cause infection is particularly important to answer. Next, there is the question of how to best protect against infection. The answer to this question depends on the areas for which protection is to be established, because different protective measures have to be taken in a pedestrian zone than in buses and trains or in offices, schools and restaurants. To address these two problems, the first part of the talk will present the formation of aerosol particles in the body, their ejection by breathing, speaking, singing and coughing, and their dispersion in space. In the second part, the effectiveness of different protective measures is analyzed experimentally using laser based measurement data. In particular, the effectiveness of different masks for individual protection, as well as the usefulness of room air cleaners and protective walls, is demonstrated quantitatively. A deeper understanding of the spread processes and the protection options is imperative to effectively limit the spread of the pandemic and thus the costs for the state, the economy and society. Whether society is finally ready to protect itself effectively depends on the insight of the population, but also on the way the measures are implemented politically. This will also be discussed during the lecture, because this pandemic can only be contained if science, technology, politics and the population pull together.
  • Chenfeng Li (Swansea University, United Kingdom)
    "CFD simulation of airborne virus transmission aided by a machine learning surrogate model"
  • In this study, the airborne virus transmission is investigated using computational fluid dynamics simulation. The study is carried in three steps. First, a standard boxroom scenario is considered, and different conditions in relation to the door, window and mechanical ventilation are investigated using OpenFOAM, a well-established CFD simulator. The resulting data are organized a series of relation curves to reveal the sensitivity of virus transmission with respect to the change of ventilation conditions. Next, a machine-learning based surrogate model is constructed from the simulation data obtained from the first step. The experiment shows at an acceptable level of accuracy, the surrogate model can quickly predict the flow field and the associated airborne virus transmission for the boxroom scenario at different environmental and ventilation conditions. In the last step, the study focuses on the impact of having people in the room. To achieve this, a coupled CFD-DEM approach is adopted, where the air flow is captured by the CFD solver, and the moving objects are captured by the DEM (discrete element method) solver. The two solvers are fully coupled, representing accurately the influence of people on the air flow, thereby the airborne virus transmission. In all these studies, we assume the virus particles are sufficiently small, such that they do not have a significant impact on the air flow and merely get transported by the air. The information obtained this investigation quantify the relative risks of virus transmission with respect to changing environmental and ventilation conditions, as well as the impact from human activities.
  • Simon Parker (Defence Science and Technology Laboratory, United Kingdom)
    "Transmission of virus in carriages - development of a multiroute viral exposure model for public transport"
  • Understanding the potential exposure of passengers during the use of public transport is of particular interest for transport planning. The Transmission of Virus on Carriages model has been developed to address this need. This stochastic model estimates passenger exposure to SARS-CoV-2 on an underground train carriage via three routes: close range droplet, small aerosol and surface contact. Passenger input data reflects realistic ridership at different stations on the journey. In addition to the effect of ventilation details, the effect of airborne and surface viral decay and surface deposition are accounted for. Touching of high-touch surfaces within the carriage is included and is used to study the transfer of fomite contamination between surfaces and passengers. Variation in passenger density throughout a journey contributes to different close range exposures. Stochastic representation of infectious passenger boarding and other events allow the model to be used to explore key parameters such as disease prevalence in the travelling population, carriage loading and adherence to mask wearing rules. The results from the model clearly show the relative importance of different routes of exposure and the value of different mitigation measures. Future work is focused on improving the representation of multiple respiratory activities and on extending the model to other types of public transport.
  • Raquel González Fariña (Cardiff University, United Kingdom)
    "Predicting the spatiotemporal risk of airborne infection in indoor spaces using an advection-diffusion-reaction equation"
  • Probabilistic models for indoors airborne transmission of viruses, such as the Wells-Riley model (Riley et al., 1978) and its extensions applied to COVID-19, for example (Buonanno et al., 2020), assume that the concentration of infectious particles in the room is uniform in space. We have developed a spatially dependent generalisation to such models to determine the infection risk in indoor spaces. We model the concentration of airborne infectious particles using an advection-diffusion-reaction equation where the particles are emitted by an infected person, advected by airflow, diffused due to turbulence, and removed due to the room ventilation, biological inactivation of the virus and gravitational settling. The model is quasi-three-dimensional and incorporates a recirculating flow due to air-conditioning. We are able to obtain a semi-analytic solution which allows for very fast simulations. An important aspect of our work is that we include realistic particle size distributions. We consider that the particle emission rate and the gravitational settling rate depend on the size of the particles. Most airborne transmission models only account for a single particle size and, thus, assume a constant settling rate. We find that this simplifying assumption may significantly alter the predicted infection risk in a room. We also quantify the effect of several ventilation settings and different activities such as breathing, talking and coughing, on the particle concentration and the infection risk. Finally, we determine the time to probable infection (TTPI), at any location in a room, paving the way for formulating recommendations. Good agreement with CFD models and existing data is obtained.

Aggregation - Growth - Fragmentation Phenomena arising in biology

Organized by: Magali Tournus (Ecole Centrale Marseille, France), Marie Doumic (INRIA Paris, France), Miguel Escobedo (Universidad del País Vasco, Spain)

  • Thomas C T Michaels (Department of Physics and Astronomy, University College London, UK)
    "Spatiotemporal control of filamentous protein aggregation"
  • Liquid cellular compartments form in the cyto- or nucleoplasm and can regulate aberrant filamentous protein aggregation. Yet, the mechanisms by which these compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that even for weak interactions aggregates strongly partition into the liquid compartment. Aggregate partitioning is caused by a positive feedback mechanism of aggregate nucleation and growth driven by a flux maintaining the phase equilibrium between the compartment and its surrounding. Our model establishes a link between specific aggregating systems and the physical conditions maximizing aggregate partitioning into the compartment. The underlying mechanism of aggregate partitioning could be used to confine cytotoxic protein aggregates inside droplet-like compartments but may also represent a common mechanism to spatially control irreversible chemical reactions in general.
  • Alex Watson (University College London, UK)
    "Growth-fragmentation and quasi-stationary methods"
  • A growth-fragmentation is a stochastic process representing cells with continuously growing mass and sudden fragmentation. Growth-fragmentations are used to model cell division and protein polymerisation in biophysics. A topic of wide interest is whether or not these models settle into an equilibrium, in which the number of cells is growing exponentially and the distribution of cell sizes approaches some fixed asymptotic profile. In this work, we present a new spine-based approach to this question, in which a cell lineage is singled out according to a suitable selection of offspring at each generation, with death of the spine occurring at size-dependent rate. The quasi-stationary behaviour of this spine process translates to the equilibrium behaviour, on average, of the growth-fragmentation. We present some Foster-Lyapunov-type conditions for this to hold.
  • Wei-Feng Xue (School of Biosciences, University of Kent, UK)
    "The division of amyloid fibrils – Experimental analysis and future challenges"
  • The division of amyloid protein fibrils is required for the propagation of the amyloid state, and is an important contributor to their stability, pathogenicity and normal function. Here, I will present our experimental work on resolving amyloid division and biological impact of their size distributions. By applying new theoretical results emerging from collaboration with mathematicians, these experiments to profile the dynamical stability towards breakage for different amyloid types using AFM imaging reveal particular differences in the division properties of disease- and non-disease related amyloid. Here, the disease associated amyloid formed from alpha-synuclein show lowered intrinsic stability towards breakage and increased likelihood of shedding smaller particles compared with non-disease related amyloid models. Our results enable the comparison of protein filaments’ intrinsic dynamic stabilities, and suggest mapping stability differences of polymorphic amyloid structures as an important challenge to resolve in unravelling their toxic and infectious potentials.
  • Magali Tournus (Ecole Centrale Marseille, France)
    " Recovering the parameters of the fragmentation equation"
  • We consider a suspension of particles that undergo fragmentation. We address the question of estimating the fragmentation parameters – i.e. the division rate B(x) and the fragmentation kernel k(y,x) – from measurements of the size particles distribution at various times. This is a natural question for any application where the sizes of the particles are measured experimentally whereas the fragmentation rates are unknown. The application that drives our work is the study of mechanical properties of amyloid fibrils that undergo fragmentation (are the mechanical properties related to toxicity?). In this talk, I will present the biological questions that motivate our work and the new experiments performed by Wei-Feng Xue team at Canterbury, then I will explain why the inverse problem is well posed under reasonable assumptions, and I will focus on how we can recover the fragmentation rate and kernel in practice.

Recent advances in mathematical neuroscience: cortically inspired models for vision and synaptic plasticity

Organized by: Luca Calatroni (Laboratoire I3S, CNRS, UCA & Inria Sophia Antipolis Méditerranée, France), Mathieu Desroches (MathNeuro Project-Team, Inria Sophia Antipolis Méditerranée & Université Côté d’Azur, France), Valentina Franceschi (Dipartimento di Matematica, Università degli Studidi Padova, Italy), Dario Prandi (Université Paris-Saclay, CNRS, CentraleSupélec, L2S, France)
Note: this minisymposia has multiple sessions. The second session is MS05-NEUR.

  • Marcelo Bertalmío (Spanish National Research Council (CSIC), Spain)
    "Evidence for the intrinsically nonlinear nature of receptive fields in vision"
  • The responses of visual neurons, as well as visual perception phenomena in general, are highly nonlinear functions of the visual input, while most vision models are grounded on the notion of a linear receptive field (RF). The linear RF has a number of inherent problems: it changes with the input, it presupposes a set of basis functions for the visual system, and it conflicts with recent studies on dendritic computations. Here we propose to model the RF in a nonlinear manner, introducing the intrinsically nonlinear receptive field (INRF). Apart from being more physiologically plausible and embodying the efficient representation principle, the INRF has a key property of wide-ranging implications: for several vision science phenomena where a linear RF must vary with the input in order to predict responses, the INRF can remain constant under different stimuli. We also prove that Artificial Neural Networks with INRF modules instead of linear filters have a remarkably improved performance and better emulate basic human perception.
  • Emre Baspinar (CNRS/NeuroPSI, France)
    "A biologically-inspired model for Poggendorff type illusions"
  • In this talk, we will see a new biologically-inspired sub-Riemannian model employing Wilson-Cowan type mean field equations described in the model geometry proposed in [1], and in a similar fashion as in [2]. The model is applied to reproducing orientation-dependent Poggendorff- type illusions. The novelty of the model is that it embeds sub-Riemannian diffusion into the neuronal interaction term appearing in the mean field equations. This tunes the neuronal interactions in agreement with the functional architecture of the visual cortex. [1] G. Citti and A. Sarti, “A cortical based model of perceptual completion in the roto-translation space,” Journal of Mathematical Imaging and Vision, vol. 24, no. 3, pp. 307–326, 2006. [2] M. Bertalmío, L. Calatroni, V. Franceschi, B. Franceschiello, and D. Prandi, “Cortical-inspired Wilson–Cowan type equations for orientation-dependent contrast perception modelling,” Journal of Mathematical Imaging and Vi- sion, pp. 1–19, 2020.
  • Rasa Gulbinaite (Netherlands Institute for Neuroscience, The Netherlands)
    "Resonance frequencies in the visual cortex and illusory perception"
  • Sensory cortices stimulated by rhythmic sounds, lights, or touch will respond in a rhythmic manner at frequencies identical or harmonically related to the stimulus. These responses are maximal when a certain cortical circuit is driven at or close to the frequencies it generates naturally. The resonance frequencies are also tightly linked to the system's response to a single impulse (impulse response function). Using examples from human EEG studies and widefield glutamate imaging in mice, I will demonstrate that resonance phenomena are preserved across species and across spatial scales of neural activity; and illustrate how stimulation at resonance frequencies can create illusory percepts.
  • Ludovic Sacchelli (LAGEPP, Université Claude Bernard Lyon 1 (UCBL), France)
    "Cortical-inspired sound processing: hearing with the visual cortex"
  • We propose a mathematical model of sound reconstruction based on a functional architecture of the auditory cortex (A1). The model is inspired by the geometrical modeling of vision, where variational information in the perceived image plays a major role. Sound processing in A1 occurs in the time frequency domain, where sound signals can be understood as images where times plays a fundamental role. In order to respect these symmetries, the inclusion of variational information in sounds translates to a lift from the time frequency domain to the Heisenberg group. In that space, sound signals undergo reconstruction via adapted Wilson-Cowan integro-differential equations that we illustrate with preliminary numerical experiments.