## Wolfgang Pauli Institute (WPI) Vienna

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## Upcoming talks

 Tournus Magali (École Centrale de Marseille) Oskar-Morgenstern-Platz 1, Hörsaal 2, ground floor. Thu, 23. Nov 17, 14:15 Scalar conservation laws with heterogeneous flux in the BV framework We consider a scalar conservation law with a flux containing spatial heterogeneities of bounded variation, where the number of discontinuities may be infinite. We address the question of existence of an adapted entropy solution in the BV framework. A sufficient key condition guaranteeing existence is identified and new BV estimates are given. This provides the most general BV theory available. Moreover, we show with a counter-example that if this hypothesis is violated, the problem may be ill-posed in the BV framework. Thematic program: Models in Biology and Medicine (2016/2017)

## Talks of the past month

 Blakie Blair WPI, OMP 1, Seminar Room 08.135 Fri, 23. Jun 17, 11:00 Self-bound droplets of a dipolar Bose-Einstein condensate Recent experiments with Bose-Einstein condensates of dysprosium [1] and erbium [2] atoms have observed the formation of droplets that can preserve their form, even in the absence of any external confinement [3]. These droplets occur when the long-ranged dipole-dipole interaction between the atoms dominates over the short-ranged contact interaction. In this regime meanfield theory predicts that the condensate is unstable to collapse, however the Lee-Huang-Yang corrections to the meanfield energy [3] can stabilize the system as one or many finite sized droplets. I will discuss our current understanding of these droplets, and introduce a new type of nonlinear Schrodinger equation used to describe their equilibrium and dynamical properties. Note:   Click here for further information Thematic program: Classical and Quantum Transport (2016/2017)

 Yong Zhang WPI, OMP 1, Seminar Room 08.135 Thu, 22. Jun 17, 14:00 “Numerical methods/analysis for Schrödinger equations and micro-magnetism” We present some mathematical methods occurring in the modeling and simulation of Nonlinear Schrödinger equations and nonlocal potentials. We focus on Gross-Pitaevskii equations describing Bose Einstein Condensates and stray field calculations in micro-magnetism. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

 François Golse WPI, OMP 1, Seminar Room 08.135 Thu, 22. Jun 17, 10:00 A convergence rate estimate for the semiclassical limit with Lipschitz continuous force field We propose an explicit bound for the convergence rate in the semiclassical limit for the Schrödinger equation which holds for potentials with Lipschitz continuous gradient. This bound is based on an analogue of the Wasserstein metric used in optimal transportation, adapted to measuring the distance between a quantum and a classical density. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

 Olivier Pinaud (Colorado State University) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Jun 17, 14:00 Waves in random media and applications We will review some results concerning uncertainties in the derivation of kinetic equations from wave propagation in random media, that is modeled by a wave or a Schroedinger equation. Kinetic equations usually describe quadratic quantities in the wavefield such as the energy or wave-wave correlations, and can be used to solve some imaging problems in complex media. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

 Shi Jin (University of Wisconsin-Madison and Shanghai Jiao Tong University) WPI, OMP 1, Seminar Room 08.135 Wed, 21. Jun 17, 10:00 Semiclassical computational methods for oscillatory and uncertain quantum dynamics with band-crossings Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry connection, charge transfer, chemical reaction etc. In this talk, we will discuss some recent works in developing semiclassical methods for band-crossing in surface hopping. For such systems we will also introduce an nonlinear geometric optics method based "asymptotic-preserving" method that is accurate uniformly for all wave numbers, including the problem with random uncertain band gaps. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

 Mohammed Lemou WPI, OMP 1, Seminar Room 08.135 Tue, 20. Jun 17, 15:30 "Averaging techniques and application to numerical methods for highly oscillatory Vlasov and Klein-Gordon models" A brief description of averaging theory for highly-oscillatory problems will be first presented with an emphasis on the so-called classical and stroboscopic averaging methods. Then I will present two general strategies to construct efficient numerical schemes for a class of highly oscillatory PDEs: the so-obtained numerical schemes have a uniform accuracy with respect to the frequency. Two applications will be considered: the Vlasov kinetic equation with strong magnetic field and the Klein-Gordon equation in the non-relativistic regime. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

 Olof Runborg (Mathematik Institution, Stockholm) WPI, OMP 1, Seminar Room 08.135 Tue, 20. Jun 17, 10:00 Uncertainty Quantification for High Frequency Wave Propagation We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest (QoI) related to the solution $u^\varepsilon$ and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. In the talk we will discuss how the rate of convergence for the stochastic collocation and the complexity of evaluating the QoI depend on the short wavelength $\varepsilon$. We find in particular that QoIs based on local averages of $\vert u^\varepsilon\vert ^2$ can give fast convergence rates, despite the fact that $u^\varepsilon$ is highly oscillatory in both physical and stochastic space. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Quantum dynamics and uncertainty Quantification" (2017)

 Cuesta Carlota WPI, OMP 1, Seminar Room 08.135 Mon, 19. Jun 17, 15:00 Analysis of travelling waves in a nonlocal Korteweg-de Vries-Burgers equation arising in a two-layer shallow-water model We study travelling wave solutions of a Korteweg-de Vries-Burgers equation with a non-local diffusion term. This model equation arises in the analysis of a shallow water flow by performing formal asymptotic expansions associated to the triple-deck regularisation (which is an extension of classical boundary layer theory). The resulting non-local operator is of fractional differential type with order between 1 and 2. Travelling wave solutions are typically analysed in relation to shock formation in the full shallow water problem. We show rigorously the existence of these waves in the case of a quadratic nonlinearity. The travelling wave problem for the classical KdV-Burgers equation is usually analysed via a phase-plane analysis, which is not applicable here due to the presence of the non-local diffusion operator. Instead, we apply fractional calculus results available in the literature and a Lyapunov functional. In addition we discuss the monotonicity of the waves in terms of a control parameter and prove their dynamic stability in case they are monotone. We also discuss some partial results concerning the existence of travelling waves in the case of a cubic nonlinearity. This existence problem and the monotonicity of the waves in the quadratic case for a small dispersion term in relation with the diffusive one are still open problems, for this reason we have also developed numerical schemes in order to support our conjectures. We will discuss in a second part of the talk, a pseudo-spectral method that approximates the initial value problem. The basic idea is, using an algebraic map, to transform the whole real line into a bounded interval where we can apply a Fourier expansion. Special attention is given to the correct computation of the fractional derivative in this setting. Interestingly, there is a connection of the mapping method to fractional calculus, that we will also mention. Thematic program: Models in Biology and Medicine (2016/2017)

 Jinkai Li WPI, OMP 1, Seminar Room 08.135 Fri, 16. Jun 17, 11:00 Some mathematical analyses on two dynamical models for atmosphere with moisture (with Sabine Hittmeir, Rupert Klein, Edriss S. Titi) In this talk, we will present some recent mathematical results, mainly the global wellposedness and convergence of the relaxation limit, on two kinds of dynamical models for the atmosphere with moisture. In the rst part of this talk, which is a joint work with Edriss S. Titi [1], we will consider a tropical atmosphere model introduced by Frierson, Majda, and Pauluis (Commum. Math. Sci. 2004); for this model, we will present the global well-posedness of strong solutions and the strong convergence of the relaxation limit, as the relaxation time " tends to zero. It will be shown that, for both the nite-time and instantaneous-relaxation systems, the H1 regularities on the initial data are sucient for both the global existence and uniqueness of strong solutions, but slightly more regularities than H1 are required for both the continuous dependence and strong convergence of the relaxation limit. In the second part of this talk, which is a joint work with Sabine Hittmeir, Rupert Klein, and Edriss S. Titi [2], we will consider a moisture model for warm clouds used by Klein and Majda (Theor. Comput. Fluid Dyn. 2006), where the phase changes are allowed, and we will present the global well-posedness of this system. [1] Jinkai Li; Edriss S. Titi: A tropical atmosphere model with moisture: global well- posedness and relaxation limit, Nonlinearity, 29 (2016), 2674{2714. [2] Sabine Hittmeir; Rupert Klein; Jinkai Li; Edriss S. Titi: Global well-posedness for passively transported nonlinear moisture dynamics with phase changes, arXiv:1610.00060 Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Manuel Baumgartner WPI, OMP 1, Seminar Room 08.135 Fri, 16. Jun 17, 10:00 Diffusional Growth in Clouds (with Peter Spichtinger) Di usional growth is the most important growth mechanism for newly formed cloud droplets and ice crystals. Non-linear di usion equations control the transport of water vapor towards the cloud particles. Although the solution of these di usion equations is circumvented in numerical cloud models, it remains computationally expensive to include the details of di usional growth due to severe timestep restrictions. Moreover, as soon as ice crystals are present in a cloud consisting mostly of cloud droplets, the Wegener- Bergeron-Findeisen process becomes active and the ice crystals grow at the expense of the cloud droplets. In the rst part of the talk, we discuss the aspect of locality of the Wegener-Bergeron- Findeisen process, i.e. an ice crystal does only a ect its immediate vicinity. Its presence decouples the di usional growth behavior of nearby droplets from environmental conditions. We show some simulation results and a possible way to include locality in the context of bulk-microphysics. The second part considers the case of a liquid cloud. In the context of numerical models, the microphysical details of the di usional growth and the timestep restrictions are e ectively avoided through the technique of saturation adjustment. We will show some of these techniques and analyze an air parcel model containing activation of new droplets using asymptotics. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Matthias Hieber WPI, OMP 1, Seminar Room 08.135 Fri, 16. Jun 17, 9:00 Thermodynamical Consistent Modeling and Analysis of Heat-Conducting Fluids In this talk, we derive and discuss thermodynamically consistent models for heat-conduction fluids. Our approach is based on the entropy principle. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Annette Muller WPI, OMP 1, Seminar Room 08.135 Thu, 15. Jun 17, 15:30 The DSI as an indicator for diabatic processes across the scales In atmospheric ows, the Dynamic State Index (DSI) indicates local deviations from a steady wind solution. This steady wind solution is based on the primitive equations under adiabatic and inviscid conditions. Hence, from theoretical point of view, atmospheric dynamics is regarded relative to a solution derived from uid mechanic's rst principles. Thus, this parameter provides a tool to capture diabatic processes. The DSI can be designed for di erent uid mechanical models on distinguished scales, we will introduce a DSIQG for the quasi-geostrophic ow, a DSIRo for the Rossby model and DSImois that is based on the equations of motions including moisture processes. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Wojciech W. Grabowski WPI, OMP 1, Seminar Room 08.135 Thu, 15. Jun 17, 14:00 Modeling condensation in cloud-scale models Condensation of water vapor to form and grow cloud droplets is the most fundamental process of cloud and precipitation formation. It drives cloud dynamics through the release of latent heat and determines the strength of convective updrafts. Cloud-scale models simulate condensation by applying two drastically di erent methods. The rst one is the bulk condensation where condensation/evaporation is assumed to always maintain saturated conditions. The second approach involves prediction of the in-cloud super- or sub-saturation and can be used in models that predict not only condensate mass but also relevant features of the droplet size distribution (e.g., models with the 2-moment microphysics or with the bin microphysics). This presentation will address the question whether the di erence between the two approaches has a noticeable impact on convective dynamics. Model simulations with the bin microphysics for shallow non-precipitating convection and with the double-moment bulk microphysics for deep convection will be discussed to document the di erences in cloud eld simulations applying the two methodologies. For the shallow convection, the di erences in cloud eld simulated with bulk and bin schemes come not from small di erences in the condensation, but from more signi cant di erences in the evaporation of cloud water near cloud edges as a result of entrainment and mixing. For the deep convection, results show a signi cant dynamical impact of nite supersaturations and a strong microphysical e ect associated with upper-tropospheric anvils. Implications of these results for modeling convective dynamics will be discussed and a possible intermediate modeling methodology will be suggested. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Piotr Smolarkiewicz WPI, OMP 1, Seminar Room 08.135 Thu, 15. Jun 17, 11:00 Finite-volume integrators for cloud-resolving simulations of global atmospheric flows This work extends to moist-precipitating dynamics a recently documented high-performance nite-volume integrators for simulating global all-scale atmospheric ows (doi:10.1016/j.jcp. 2016.03.015). A key objective of the current development is a seamless coupling of the conservation laws for moist variables engendered by cloud physics with the semi-implicit, non-oscillatory forward-in-time integrators already proven for dry dynamics. The representation of the water substance and the associated processes in weather and climate models can vary widely in formulation details and complexity levels. The adopted representation assumes a canonical warm-rain" bulk microphysics parametrisation, recognised for its minimal physical intricacy while accounting for the essential mathematical complexity of cloud-resolving models. A key feature of the presented numerical approach is global conservation of the water substance to machine precision | implied by the local conservativeness and positivity preservation of the numerics | for all water species including water vapour, cloud water, and precipitation. The moist formulation assumes the compressible Euler equations as default, but includes reduced anelastic equations as an option. The theoretical considerations are illustrated with a benchmark simulation of a tornadic thunderstorm on a reduced size planet, supported with a series of numerical experiments addressing the accuracy of the associated water budget. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Rupert Klein WPI, OMP 1, Seminar Room 08.135 Thu, 15. Jun 17, 10:00 The role of multiscale convection in hurricane intensi cation Paeschke et al (2012) showed analytically how non-axisymmetric external diabatic forcing of a tilted vortex in dry air can amplify or attenuated the ow depending on the relative orientation of vortex tilt and the "heating dipole". Here we include a bulk moist microphysics closure and describe how boundary layer processes and multiscale deep moist convection can interact to produce this e ect self-consistently. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Tom Dörffel WPI, OMP 1, Seminar Room 08.135 Thu, 15. Jun 17, 9:00 Intensification of atmospheric vortices through asymmetric diabatic heating (with Ariane Papke, Rupert Klein) The dynamics of atmospheric vortices such as tropical storms, hurricanes and mid-latitude cyclones is driven by a variety of interacting scales. [1] developed an asymptotic theory for the dynamics of strongly tilted atmospheric vortices in the gradient-wind regime, embedded into a synoptic-scale geostrophic background eld. One central outcome of the theory is the evolution equation for the nearly axisymmetric primary circulation. It predicts that Fourier-mode 1 of asymmetric diabatic heating/ cooling patterns can spin up or spin down a vortex depending on the relative arrangement of the heating dipole relative to the vortex tilt. Based on this methodology further investigations led to the conclusion that this theory is generalizable to Rossby numbers of order 1 and higher, i.e. cyclostrophic balance. Accompaning the asymptotics numerical experiments are conducted to test the theory within an anelastic model [2]. In this talk we present the latest results showing consistency of numerical simulations and theoretical predictions. [1] E. Paschke, P. Marschalik, A. Z. Owinoh and R. Klein, Motion and structure of at- mospheric mesoscale baroclinic vortices: dry air and weak environmental shear, J. Fluid Mech. 701: 137{170, (2012) [2] J. M. Prusa, P. K. Smolarkiewicz and A. A. Wyszogrodzki, EULAG, a computational model for multiscale ows, Comput. Fluids 37: 1193{1207 (2008) Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Boualem Khouider WPI, OMP 1, Seminar Room 08.135 Wed, 14. Jun 17, 17:00 A zonally symmetric model for the monsoon-Hadley circulation with stochastic convective forcing Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the e ect of climate change on the earth system. Climate models are large computer codes based on the discretization of the uid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between small-scale processes due to atmospheric moist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the rst modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly dicult. We develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal second-order convergence under grid re nement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes. This is joint work with Michale De La Chevrotiare. Thematic program: Classical and Quantum Transport (2016/2017) Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Olivier Pauluis WPI, OMP 1, Seminar Room 08.135 Wed, 14. Jun 17, 16:00 Thermodynamic analysis of atmospheric motions In this talk, I will show how to extract thermodynamic cycles from high resolution simulations of atmospheric ows. On the one hand, thermodynamic processes are typically analyzed in terms of the behavior of individual parcel trajectories. On the other hand, most atmospheric ows are associated with in nitely many turbulent lagrangian trajectories. The Mean Air Flow As Lagrangian Dynamics Approximation (MAFALDA) has been recently developed to address this problem. It MAFALDA, the ow is rst averaged in isentropic coordinates, typically pressure and equivalent potential temperature, and the mean ow is then treated as a set of thermodynamic cycles. This o er a systematic procedure to analyze the thermodynamic transformation in atmospheric ows, which is applied here to compare the thermodynamics behavior of convection and hurricanes. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Sam Stechmann WPI, OMP 1, Seminar Room 08.135 Wed, 14. Jun 17, 15:00 Precipitating Quasi-Geostrophic Equations and Minimal Cloud Mi- crophysics Two simpli ed models are presented for precipitating atmospheric dynamics. First, a minimal version of cloud microphysics is presented. The time scales of all microphysical processes are assumed to be fast, and the resulting microphysics has only one parameter, the terminal velocity of falling rain drops. It is shown that, despite its simplicity, this minimal microphysics scheme can reproduce distinct canonical modes of convective organization (scattered convection and a squall line) under appropriate environmental conditions. This suggests that the essential physical processes underlying moist convection are simply phase changes and falling rain drops. Second, a precipitating version of the quasi-geostrophic (QG) equations is presented. The precipitating QG (PQG) equations include phase changes between water vapor and liquid water, which arise as Heaviside nonlinearities in the new PQG PDEs. Finally, we present an initial application of the PQG equations, in a linearized setting that can be solved analytically, to understanding meridional moisture transport by baroclinic eddies. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Didier Bresch WPI, OMP 1, Seminar Room 08.135 Tue, 13. Jun 17, 14:00 Mathematical analysis of relevant compressible geophysical models In this talk, we talk about mathematical results related to compressible uid systems with applications to geophysical flows. We focus on pressure laws, viscosity e ects, bi-fluid flows description. Some singular limits are also discussed. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Didier Bresch WPI, OMP 1, Seminar Room 08.135 Tue, 13. Jun 17, 11:00 Mathematical analysis of relevant compressible geophysical models In this talk, we talk about mathematical results related to compressible uid systems with applications to geophysical flows. We focus on pressure laws, viscosity e ects, bi-fluid flows description. Some singular limits are also discussed. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Olivier Pauluis WPI, OMP 1, Seminar Room 08.135 Tue, 13. Jun 17, 9:00 Tutorial 2: Thermodynamic cycles and heat engines The atmosphere can be describe as a heat engine that continuously generates kinetic energy by transporting energy from a warm source, i.e. the Earth surface, to a cold sink, i.e the colder troposphere. However, the ability of the atmosphere to generate kinetic energy is strongly reduced by the hydrological cycle. We will analyze how the impacts of moist processes can be a quanti ed in terms of a Gibbs penalty associated with the evaporation of water in unsaturated air and its removal as liquid water. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Rupert Klein (FU Berlin) Oskar-Morgenstern-Platz 1, Hörsaal 4, ground floor. Mon, 12. Jun 17, 17:00 How Mathematics helps structuring climate discussions Mathematics in climate research is often thought to be mainly a provider of techniques for solving the continuum mechanical equations for the ows of the atmosphere and oceans, for the motion and evolution of Earth's ice masses, and the like. Three examples will elucidate that there is a much wider range of opportunities. Climate modellers often employ reduced forms of "the continuum mechanical equations" to eciently address their research questions of interest. The rst example discusses how mathematical analysis can provide systematic guidelines for the regime of applicability of such reduced model equations. Meteorologists de ne "climate", in a narrow sense, as "the statistical description in terms of the mean and variability of relevant quantities over a period of time" (World Meteorological Society, http://www.wmo.int; see the website for a broader sense de nition). Now, climate researchers are most interested in changes of the climate over time, and yet there is no unique, well-de ned notion of "time dependent statistics". In fact, there are restrictive conditions which data from time series need to satisfy for classical statistical methods to be applicable. The second example describes recent developments of analysis techniques for time series with non-trivial temporal trends. Modern climate research has joined forces with economy and the social sciences to generate a scienti c basis for informed political decisions in the face of global climate change. One major type of problems hampering progress of the related interdisciplinary research consists of often subtle language barriers. The third example describes how mathematical formalization of the notion of "vulnerability" has helped structuring related interdisciplinary research e orts. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Didier Bresch WPI, OMP 1, Seminar Room 08.135 Mon, 12. Jun 17, 15:45 Mathematical analysis of relevant compressible geophysical models In this talk, we talk about mathematical results related to compressible uid systems with applications to geophysical flows. We focus on pressure laws, viscosity e ects, bi-fluid flows description. Some singular limits are also discussed. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Olivier Pauluis WPI, OMP 1, Seminar Room 08.135 Mon, 12. Jun 17, 14:05 Tutorial 1: Thermodynamic properties of cloudy air In this tutorial, I will review the thermodynamic properties cloudy air and how they are typically treated in numerical models. This will include the concepts of saturation, equation of state for moist air, moist entropy and potential temperature of many kinds. We will then discuss the implications for buoyancy and convective processes. Event: Workshop on "Mathematics of Moist Atmospheric Dynamics: Modeling, Analysis and Computations" (2017)

 Human Rezaei (Inra Jouy-en-Josas, France) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 15:20 Prion quasi-species and molecular basis of auto-perpetuation of Prion structural information. Davy Martin1, Joan Torrent i Mas1, Stéphanie Prigent1, Mathieu Mezache2, Marie Doumic-Jauffret2, Vincent Béringue1 and Human Rezaei1* 1. National Institute for Agricultural Research (INRA), Pathological Macro-assemblies and Prion Pathology group (MAP2), UR892, Virologie Immunologie Moléculaires, Jouy-en-Josas, 78350-F, France 2. Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598, Paris, France The prion phenomenon is based on autonomous structural information propagation towards single or multiple protein conformational changes. Since this last decade the prion concept referring to the transmission of structural information has been extended to several regulation systems and pathologies including Alzheimer and Parkinson’s diseases. The unified theory in Prion replication implies structural information transference (SIT) from the prion to a non-prion conformer through a mechanism also called improperly, with regards to biophysical considerations “seeding” phenomenon. Therefore considering prion replication as a structural information transduction from a donor (i.e. template) to an acceptor (i.e. substrate) through a transduction interface a new questioning arises: what are molecular mechanisms of the auto-perpetuation of the Prion structural information and its faithfulness? Considering the Prion propagation as more or less faithful perpetuation of structural information, in the present work, we explored the concept of prion quasi-species (i.e. existence of prion heterogeneous assemblies) and highlighted the existence of prion network, which has an autopoietic behaviour (autoreplicative). Our observations strongly suggest that specific criteria in term of: protein structure, delayprocess and thermo-kinetics should be collated before a system become dissipative and autopoietic. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Sara Merino-Aceituno (Imperial College, London, United Kingdom) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 14:30 A new flocking model through body attitude coordination We present a new model for multi-agent dynamics where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate around it adopting different configurations. Agents try to coordinate their body attitudes with the ones of their neighbours. This model is inspired by the Vicsek model. The goal of this talk will be to present this new flocking model, its relevance and the derivation of the macroscopic equations from the particle dynamics. In collaboration with Pierre Degond (Imperial College London) and Amic Frouvelle (Université Paris Dauphine). Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Alexander K. Buell (Institute of Physical Biology, University of Düsseldorf) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 13:50 Kinetic and thermodynamic analysis of peptide self-assembly In this talk I will discuss various aspects of the kinetics and thermodynamics of the self assembly of peptides into amyloid fibrils and crystals. I will present a theoretical framework that allows to determine free energy barriers and entropies from kinetic data of amyloid fibril growth [1,2]. I will contrast the kinetic behaviour of longer, amyloid forming sequences with that of aromatic dipeptides that form crystals, rather than amyloid fibrils [3,4]. Furthermore, I will present the phenomenon of autocatalytic secondary nucleation, whereby new amyloid fibrils nucleate on the surface of existing ones [5,6]. In particular, I will show how this phenomenon manifests itself in kinetic measurements of protein aggregation, and how biosensing can be used to explore its molecular origin [6,7]. [1] A. K. Buell, J. R. Blundell, C. M. Dobson, M. E. Welland, E. M. Terentjev, and T. P. Knowles, Phys. Rev. Lett. 104, 228101 (2010). [2] A. K. Buell, A. Dhulesia, D. A. White, T. P. J. Knowles, C. M. Dobson, and M. E. Welland, Angew. Chem. Int. Ed Engl. 51, 5247 (2012). [3] T. O. Mason, T. C. T. Michaels, A. Levin, E. Gazit, C. M. Dobson, A. K. Buell, and T. P. J. Knowles, J. Am. Chem. Soc. 138, 9589 (2016). [4] T. O. Mason, A. Levin, C. M. Dobson, E. Gazit, T. P.J. Knowles and A. K. Buell, JACS under revision, (n.d.). [5] A. K. Buell, C. Galvagnion, R. Gaspar, E. Sparr, M. Vendruscolo, T. P. J. Knowles, S. Linse, and C. M. Dobson, Proc. Natl. Acad. Sci. 111, 7671 (2014). [6] R. Gaspar, G. Meisl, A. K. Buell, L. Young, C. F. Kaminski, T. P. J. Knowles, E. Sparr, and S. Linse, Q. Rev. Biophys. 50, (2017). [7] A. Šariæ, A. K. Buell, G. Meisl, T. C. T. Michaels, C. M. Dobson, S. Linse, T. P. J. Knowles, and D. Frenkel, Nat. Phys. 12, 874 (2016). Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Yi Yin (Inria Paris and Univ. Pierre et Marie Curie, France) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 12:00 Automated quantification of amyloid fibrils morphological features based on image analysis of transmission electron microscopies Yi Yin*, 1, Stéphanie Prigent1, Joan Torrent, Dirk Drasdo1, Human Rezaei, and Marie Doumic1 1. INRIA Paris, and Sorbonne Universités UPMC Univ. Paris 6, Laboratoire Jacques-Louis Lions, Paris, France, * yi.yin@inria.fr Protein aggregation into fibrils is a key process in amyloid diseases and also in other biological processes. The quantification of fibrils’ morphology and molecular structures is urgently needed in understanding of the key mechanisms and properties of fibrils. In this study, we propose an automated image analysis procedure to extract and quantify fibril morphological features from transmission electron microscopy (TEM) images. Fibrils are segmented by a ‘maximum entropy’ thresholding method and then the ‘fast marching’ skeletonization is applied to detect the fibril centerlines. The individual information of each fibril is gathered based on the fibril segmentation and extracted centerline, including the length (following the curvature of the fibrils, which are rarely straight lines), the varying width along the length, the curvature, as well as the number, position and length of branches. The intricate overlapping and branching structures are identified based on the angles between fibril segments. The proposed method was tested on experiments on the prion protein (PrP), which also allows us to explain in detail the parameters needed for the image analysis. Our method has high estimation accuracy (e.g. width estimation as shown in the figure). The results from different mutants of the PrP protein fibrils showed the potential of the method in fibrils classification through a statistical analysis. Romain Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Frédéric Halgand (University Paris-Sud, France) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 11:20 Prion protein conformational landscape studied by mass spectrometry and ion mobility Guillaume van der Rest, Human, Rezaei, Frédéric Halgand, Université Paris Sud, Laboratoire de Chimie Physique Prion protein is involved in deadly neurodegenerative diseases. Its pathogenicity is linked to its structural conversion (a-helix to b-strand transition). However, recent studies suggest that prion protein can follow a plurality of conversion pathways which hints towards different conformers that might coexist in solution. We therefore decided to screen the ovine and human PrP monomers using ion mobility coupled to mass spectrometry following electrospray ionization. After a short presentation of ion mobility for studying ionized proteins in the gas phase, we will briefly discuss issues with the collision cross section calibration procedure that we have encountered when using travelling wave ion mobility. We will also discuss the development of an automated data extraction pipeline for which we developed a Python/Qt script base interface. Infusion of monomeric PrP solutions have shown that at least three PrP conformers are observed in the gas phase. PrP monomers are known to lead to the formation of oligomeric species in specific conditions (temperature, pH and buffer), which are not compatible with mass spectrometry. We have therefore developed a size-exclusion chromatography IMS-MS setup with the aim to study the oligomers produced in these conditions. The development of this SEC-IMS-MS methodology will be presented as well as its application for calibration with standard protein complexes. Although we did not achieve resolution of the large (O1 ~36-mer) oligomeric species, optimization of the experimental parameters led to the observation of the small (O3) oligomeric species. One key observation in this process was that the abundance of the gas phase monomeric conformers changed upon the oligomerization process. First results allow us to interpret this as an effect of monomer concentration on the ratio of conformers present in solution, which is observed only in specific buffer conditions. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Magali Tournus (University of Marseille, France) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 10:10 Estimating the division rate and kernel in the fragmentation equation. We consider the pure fragmentation fragmentation equation and address the question of estimating the fragmentation parameters (division rate and fragmentation kernel) from measurements of the size distribution at various times. Under the assumption of a polynomial division rate and a self-similar fragmentation kernel, we use the well-known asymptotic behaviour of the solution to guarantee the well-posedness of our inverse problem and provide a representation formula for the fragmentation kernel. The tools used are the Mellin transform and the Wiener-Hopf method. Motivations for studying this problem and applications to amyloid fibril breakage will be described in the talk of W.F. Xue. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Wei-Feng Xue (University of Kent at Canterbury, United Kingdom) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Thu, 8. Jun 17, 9:30 Nano-scale properties of amyloid fibril fragments A number of devastating human disorders, for example Alzheimer's disease (AD), Hungtington's diseases, type 2 diabetes and transmissible spongiform encephalopathies (TSEs), are associated with the abnormal folding and assembly of proteins. The net result of this misfolding is the formation of large insoluble protein deposits and small toxic and transmissible protein particles in a state called amyloid. What are the molecular mechanisms that govern the amyloid fibrils’ potential to seed the formation of new aggregates, to propagate the amyloid state as prion particles, and to damage cells in amyloid-associated diseases? We have developed AFM imaging approaches that are capable of resolving the fibril particle concentrations, their length distributions, as well as their toxic and infective potential to cells. With these approaches, we have shown that the disease-associated properties of amyloid can be linked to small nano-sized amyloid particles created through the breakage of amyloid fibrils. The approaches we have developed offer new opportunities to determine, quantify, and predict the course and the consequences in amyloid assembly of cytotoxic, infectious as well as functional amyloid systems. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Nicola Vettore, Institute of Physical Biology, University of Düsseldorf, Germany SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 17:15 Temperature dependence of amyloid fibril stability studied through equilibrium denaturation Nicola Vettore and Alexander K. Buell, Institute of Physical Biology, University of Düsseldorf Amyloid fibrils are thermodynamically very stable [1], but the origin of their enhanced stability with respect to the native state has not yet been elucidated in molecular detail. The high stabilities of amyloid fibrils render the study of their equilibrium behaviour challenging. One way to approach this issue, in direct analogy to the study of protein folding equilibria is denaturation with commonly used denaturants, such as GdmCl or Urea. A theoretical framework to extract from such measurements the free energy difference between the fibril state and the soluble state, based on Oosawa's linear polymerisation model, was proposed in [2]. Here we present experimental results of amyloid fibril equilibrium denaturation measured via capillary fluorescence over a wide range of temperatures. The data highlight how the influence of temperature seems of primary importance not only for the kinetics of fibril formation, but also for the thermodynamic stability of the fibrillar structures. We will also present our attempts to describe the temperature-dependence of fibril stability within a general thermodynamic framework. [1] A. J. Baldwin, T. P. J. Knowles, G. G. Tartaglia, A. W. Fitzpatrick, G. L. Devlin, S. L. Shammas, C. A. Waudby, M. F. Mossuto, S. Meehan, S. L. Gras, J. Christodoulou, S. J. Anthony-Cahill, P. D. Barker, M. Vendruscolo, and C. M. Dobson, J. Am. Chem. Soc. 133, 14160 (2011). [2] T. Narimoto, K. Sakurai, A. Okamoto, E. Chatani, M. Hoshino, K. Hasegawa, H. Naiki, and Y. Goto, FEBS Lett. 576, 313 (2004). Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Mathieu Mézache, Inria Paris and Univ. Pierre et Marie C, France SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 17:15 An oscillatory kinetic model for the Prion aggregation process. From Belousov-Zhabotinsky reaction to a Prion polymerisation/depolymerisation chemical system. We investigate the oscillatory behaviour of the PrP protein during the polymerization/depolymerization process. In order to modelize this oscillatory process, we study a simplified Belousov-Zhabotinsky reaction from a kinetic point of view. This simplified oscillatory system of chemical reactions allows us to introduce a modified Becker-Döring system where the trajectories oscillate. A key to have a closed oscillatory polymerization/depolymerization system is to consider different specices of polymers and monomers. We finally present several system where the numerical simulations show a more or less sustained oscillatory behaviour. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Angélique Igel-Egalon, INRA Jouy-en-Josas, France SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 17:15 Depolymerization instead of fragmentation spreads the replication unit of prion assemblies Reine1, Charles-Adrien Richard1, Tina Knäpple1 Vincent Béringue1* and Human Rezaei1* 1: INRA, UR892, Virologie Immunologie Moléculaires, Jouy-en-Josas 78350, France *: Corresponding authors The prion phenomenon is based on autonomous structural information propagation towards single or multiple protein conformation changes. During this last decade the prion concept referring the transmission of structural information has been extended to several regulation systems and pathologies including Alzheimer and Parkinson’s diseases. Despite intensive investigation, the molecular basis of structural information transmission remains obscure. Templating (i.e. secondary nucleation as vector of structural information) has been proposed as origin of autocatalytic structural information perpetuation. However, the templating process does not consider the spreading process which consists in an exponential amplification of structural information. Active fibril fragmentation (AFF) constitutes a solution for exponential spreading and amplification of the structural information as strongly suggested in fungi prions (Shorter and Lindquist, Mol Cell, 2006). In the present work, we demonstrate that mammalian Prion assemblies (PrPSc) are constituted from an oligomeric elementary brick called suPrP. We show that in physiological conditions Prion assemblies are in equilibrium with suPrP. The existence of such equilibrium as simple depolymerization/condensation process is sufficient to spread the replicative unit through the release of suPrP, followed by its Brownian diffusion and condensation into PrPSc and discards the requirement of fragmentation for prion spreading. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Marie Doumic (Inria Paris & Wolfgang Pauli Institute, France & Austria) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 16:15 Modelling protein polymerisation: results and open questions Mathematical modelling of protein polymerisation is a challenging topic, with wide applications, from actin filaments in myocytes (muscle tissues) to the so-called amyloid diseases (e.g. Alzheimer's, Parkinson's or Creuzfeldt-Jakob's diseases). In this talk, we will give an overview of recent results for both deterministic - where statistical mechanical fluctuations arising from intrinsic noise are negligible - and stochastic approaches, envisaged as giving complementary insights on the still largely mysterious intrinsic mechanisms of polymerisation. A data assimilation approach is developed in parallel of more specific methods for fragmentation estimation. The results we will present are partly joint work with A. Armiento, J. Calvo, S. Eugène, M. Escobedo, P. Moireau, B. Perthame, H. Rezaei, P. Robert, M. Tournus and W.F. Xue. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Christian Schmeiser (University of Vienna and Wolfgang Pauli Institute, Austria) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 14:10 Homeostatic regulation of actin density at the leading edge of lamellipodia Some recent contributions to the modeling of the polymerization and depolymerization of actin filaments will be reviewed. Some results of the embedding of these models into the Filament Based Lamellipodium Model will be presented. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Sascha Martens (Max F. Perutz Laboratories (MFPL), University of Vienna, Austria) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 11:20 Mechanism of p62-mediated protein aggregation in selective autophagy Autophagosomes are double membrane-bound organelles that are formed de novo during a process called autophagy. Autophagosomes mediate the bulk degradation of cytoplasmic material such as aggregated proteins, dysfunctional or surplus mitochondria and intracellular pathogens. Autophagy is conserved from yeast to human and has been shown to protect the organism from conditions such as starvation, neurodegeneration and infectious diseases. During autophagosome formation initially small membrane structures termed isolation membranes are formed. These isolation membranes expand and thereby gradually enclose cytoplasmic cargo. Finally, isolation membranes close to give rise to mature autophagosomes. After their formation autophagosomes fuse with lysosomes within which their inner membranes and the contents are degraded. Autophagy has the ability to selectively capture and subsequently degrade aggregated and ubiquitinated proteins. This is mediated by the p62 cargo receptor, which is required for the aggregation of these proteins into larger structures. These structures then serve as templates for autophagosome formation. I will present our results from a fully reconstituted system, which enabled us to dissect the interplay between p62 and ubiquitin positive proteins during protein aggregation in selective autophagy. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Laurent Pujo-Menjouet (University of Lyon, France) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 10:10 Modelling prion dynamics: a fruitful collaboration between mathematicians and biologists In a previous work by Alvarez-Martinez et al. (2011), the authors pointed out some fallacies in the mainstream interpretation of the prion amyloid formation. It appeared necessary then to propose an original hypothesis able to reconcile the in vitro data with the predictions of a mathematical model describing the problem. The model presented here, has been developed accordingly with the hypothesis that an intermediate on-pathway leads to the conformation of the prion protein into an amyloid competent isoform thanks to a structure, called micelles, formed from hydrodynamic interaction. Experimental data have been compared to the prediction of our model leading to a new hypothesis for the formation of infectious prion amyloids. In the last part, we will introduce a new model describing another dangerous liaison: the interaction between prion proteins and Abeta peptides that may lead to Alzheimer’s disease. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Cassandra Terry, MRC Prion, UCL Institute of Technology, London, United Kingdom SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Wed, 7. Jun 17, 9:30 Structural characterisation of ex vivo mammalian prions. Cassandra Terrya Adam Wenborna Nathalie Grosa Jessica Sellsa Susan Joinera Laszlo L.P. Hosszua M. Howard Tattuma Silvia Panicob Daniel K. Clareb, John Collingea, Helen R. Saibilb and Jonathan D.F. Wadswortha* a, MRC Prion Unit and Department of Neurodegenerative Disease, UCL Institute of Neurology, Queen Square, London WC1N 3BG, UK b, Institute of Structural and Molecular Biology, Department of Biological Sciences, Birkbeck College, University of London, Malet Street, London WC1E 7HX, UK Prions cause lethal neurodegenerative diseases in mammals, including scrapie in sheep and goats, bovine spongiform encephalopathy (BSE) in cattle and Creutzfeldt–Jakob disease (CJD) in humans. Mammalian prions are hypothesised to be fibrillar or amyloid forms of prion protein (PrP) which self-propagate by means of seeded protein polymerisation but structures observed had not been definitively correlated with infectivity and the three-dimensional structure of prions remained unknown. We developed new methods to obtain pure preparations of intact prions from mouse brain1 and showed that pathogenic PrP is assembled into rod-like assemblies (PrP rods) that faithfully transmit prion strain-specific phenotypes when inoculated into mice. We have utilised the precision of cell culture prion infectivity assays to define the physical relationship between PrP rods and prion infectivity and used electron tomography to define their architecture. Our 3D analysis2 demonstrates that ex vivo infectious PrP rods from different strains observed have a common hierarchical assembly comprising twisted pairs of short fibres with repeating substructure which are markedly different to non-infectious PrP fibrils generated in vitro. References 1. A. Wenborn, C. Terry, N. Gros, S. Joiner, L. D’Castro, S. Panico, J. Sells, S. Cronier, J. Linehan, S. Brandner, H.R. Saibil, J. Collinge, J.D.F Wadsworth, Sci. Rep. A novel and rapid method for obtaining high titre intact prion strains from mammalian brain, 2015, 5, 10062. C. Terry, A. Wenborn, N. Gros, J. Sells, S. Joiner, L.L.P Hosszu, M.H. Tattum, S. Panico, D.K. Clare, J. Collinge, H.R. Saibil, J.D.F Wadsworth. Open Biology. Ex vivo mammalian prions are formed of paired double helical prion protein fibrils, 2016, 6, 160035. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Romain Yvinec, INRA Tours, France SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Tue, 6. Jun 17, 16:50 Time scales in a coagulation-fragmentation model} This work is motivated by protein aggregation phenomena in neurodegenerative diseases. A key observation of in-vitro spontaneous polymerization experiments of prion protein is the large variability of the so-called 'nucleation time', which is experimentally defined as the lag time before the polymerization of proteins truly starts (typically several hours in a 10-20 hours experiment). In this context, we study a stochastic version of a well-known nucleation model in physics, namely the Becker-Döring model [1]. In this model, aggregates may increase or decrease their size one-by-one, by capturing or shedding a single monomer particle. We will present numerical and analytical investigation of the nucleation time defined as a first passage time problem [2, 3]. Finally, we will present limit theorem techniques to study the link from the discrete size Becker-Döring model to a continuous size version (the Lifshitz-Slyozov model), which may be of importance to study large size aggregates formation. For general coefficients and initial data, we introduce a scaling parameter and show that the empirical measure associated to the Becker-Döring system converges in some sense to the Lifshitz-Slyozov equation when the scaling parameter goes to 0. When the aggregation is favorable, we derive a mean-field transport PDE limit together with an entrant boundary condition, leading to an effective reduced dynamical model [4]. When the aggregation is initially unfavorable, we shed light on metastable behavior and phase transition phenomena. [1] E. Hingant, R. Y., arXiv:1609.00697 (2016). [2] R. Y., M. R. D'Orsogna, and T. Chou. J. Chem. Phys., 137:244107, (2012). [3] R. Y., S. Bernard, E. Hingant, L. Pujo-Menjouet, J. Chem. Phys., 144(3):034106, (2016). [4] Julien Deschamps, Erwan Hingant, R.Y., arXiv:1605.08984 (2016). Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Vincent Béringue (Inra Jouy-en-Josas, France) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Tue, 6. Jun 17, 16:10 Small prion assemblies are involved in prion replication Angélique Igel-Egalon1¶, Mohammed Moudjou1¶, Florent Laferrière1¶, Tina Knäpple1, Laetitia Herzog1, Fabienne Reine1, Hubert Laude1, Human Rezaei1*, Vincent Béringue1* 1VIM, INRA, Université Paris-Saclay, 78350 Jouy-en-Josas, France ¶Equal contributors, *Senior authorship Mammalian prions are proteinaceous pathogens responsible for fatal, neurodegenerative disorders in human and animals. They are formed of misfolded assemblies (PrPSc) of the host-encoded cellular prion protein (PrPC). In the infected species, prions replicate by seeding the conversion and polymerization of host PrPC. Distinct prion strains are recognized within the same host-species, exhibiting defined PrPSc biochemical properties and stereotyped biological traits. While strain information is encoded within the conformation of PrPSc assemblies, the storage of the structural information and the molecular requirements for self-perpetuation remain uncertain. In particular, the polymerization steps and its dynamic nature remains mostly hypothetical. It is widely believed that monomeric PrPC is constantly recruited within the forming aggregates allowing PrPSc fibril growth. Fibril fragmentation is supposed to provide further converting seeds, favouring prion exponential replication. Whether this proposed mechanism is versatile or strain-dependent remains to be determined, as is the real contribution of fragmentation. We have investigated this issue by analysing the dynamic of PrPSc assembling during cell-free prion amplification by protein misfolding cyclic amplification (PMCA). We show that: i) prion amplification occurs through preferential amplification of small oligomeric forms of PrPSc that can further assemble into larger aggregates; ii) disassembling rather than fragmentation sustains the self-perpetuation of the process, iii) different prion strains exhibit similar amplification dynamic. Thus, prion replication may proceed through an assembly/disassembly process. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 Klemens Fellner (University of Graz, Austria) SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Tue, 6. Jun 17, 15:00 Equilibration and Quasi-Steady-State Asymptotics of a Volume-Surface Reaction-Diffusion Model for Asymmetric Protein Localisation The protein Lgl (Lethal giant larvae) is part of a conserved protein complex, which is responsible for the asymmetric localisation of cell-fate determinants, for instance, in Drosophila SOP precursor cells. We formulate continuum models, which consider the phosphorylated and the unphosphorylated conformations of Lgl within the cell cytoplasm and on the cell cortex. After presenting illustrative numerical simulations, we prove first the equilibration of the underlying complex-balance volumesurface reaction-diffusion system and perform further a rigorous quasi-steady-state-approximation in a fast-reaction limit. Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)

 John H Viles, Queen Mary, University of London, United Kingdom SkyLounge, 12th floor of Oskar-Morgenstern-Platz 1, 1090 Vienna Tue, 6. Jun 17, 14:20 Co-fibrillisation of truncated isoforms of Amyloid-â and ion-channel formation in Alzheimer’s Disease Amyloid-â peptide (Aâ) isoforms of different lengths and aggregation propensities coexist in vivo. These different isoforms are able to nucleate or frustrate the assembly of each other. Nterminal truncated Aâ(11-40) and Aâ(11-42) make up one fifth of plaque load yet nothing is known about their interaction with full-length Aâ(1-40/42). Here we show that in contrast to C-terminal truncated isoforms which do not co-fibrillise, deletions of ten residues from the N-terminus of Aâ have little impact on its ability to co-fibrillise with the full-length counterpart. As a consequence N-terminal truncated Aâ will accelerate fibre formation and co-assemble into short rod-shaped fibres with its full-length Aâ counterpart. Furthermore we show Cu2+ forms a very tight tetragonal complex with truncated Aâ(11-40) with a femtomolar affinity. These observations have implications for the assembly kinetics, morphology and toxicity of all Aâ isoforms. The process by which amyloid-â (Aâ) disrupts synaptic activity, and causes neuronal cell death in Alzheimer’s disease remains poorly understood. A potential mechanism of toxicity is in the ability of Aâ to form, membrane-spanning ion channels. However, there has been a mismatch between the channel forming properties of Aâ isoforms, 40 and 42 amino acids long, and their known relative pathogenicity. We observe ion channel formation by oligomeric Aâ42, but also show Aâ40 does not form ion channels in cellular membranes. This makes a strong link between ion channel formation and the pathology of Aâ isoforms. Molecules that block these ion channels may represent therapeutic targets. [1] Ion Channel Formation by Amyloid-â42 Oligomers but not Amyloid-â40 in Cellular Membranes DC Bode, MD Baker, JH Viles* (2017) J of Biol Chem 292, 1404-1413 [2] Truncated Amyloid-â (11-40/42) from Alzheimer's Disease Binds Copper2+ with a Femtomolar Affinity and Influences Fibre Assembly J D Barritt, J H. Viles* (2015) J of Biol Chem, 290, 27791-27802 [3] The Rapid Exchange of Zinc2+ Enables Trace Levels to Profoundly Influence Amyloid-â Misfolding and Dominates Assembly Outcomes in Cu2+/Zn2+ Mixtures C J Matheou, N D Younan, J H Viles* (2016) J Mol Biol 428, 2832-2846 Thematic program: Models in Biology and Medicine (2016/2017) Event: Workshop on "Protein Aggregation: Biophysics and Mathematics" (2017)